[Elsevier Oceanography Series 14] N.G. Jerlov (Eds.) - Marine Optics (1976, Elsevier Science)

Elsevier Oceanography Series, 14
MARINE OPTICS
N.G. JERLOV
Professor of Physical Oceanography
University of Copenhagen
Copenhagen
Second revised and enlarged edition of Optical Oceanography
(Elsevier Oceanography Series, 5 )
ELSEVIER SCIENTIFIC PUBLISHING COMPANY
Amsterdam -- Oxford --New York 1976
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Copyright @ 1976 by Elsevier Scientific Publishing Company, Amsterdam
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Printed in The Netherlands
PREFACE TO THE SECOND EDITION
As in all branches of oceanography progress in ocean optics is being made
at a rapid rate. New techniques have made possible improved accuracy in the
observations, and extension of measurements t o greater depths in the sea.
Today optical methods including remote sensing are utilized more frequently
and to greater advantage for characterizing water masses, tracing pollutants,
studying primary production, etc.
This second completely revised edition of the monograph is intended to
incorporate recent advances in the field while retaining the character and the
basic format of a text book. As in the first edition no attempt has been made
to deal specifically with imaging systems of different kinds. The author
hopes that the book will be useful as a reference book, and that it can answer
questions which confront the student or the specialist.
I wish to express my sincere thanks to Dr. Murray Brown, Mrs. E. Hallden,
Drs. N. Hdjerslev, G. Kullenberg, to Mr. B. Lundgren, K. Nygkd, and Mrs. R.
Pelt at the Institute of Physical Oceanography, Copenhagen, for their most
generous cooperation.
NILS JERLOV
To Elvi
CHAPTER 1
INTRODUCTION
NATURE OF THE SUBJECT
Optical oceanography considers the sea from an optical standpoint and is
generally considered as a special branch of oceanography. The subject is
chiefly physical, and aspires t o employ strict definitions of the quantities
measured. Underwater optics have wide applications in oceanography and
related fields, and attract growing attention t o the possibility of characterizing water masses by means of their optical properties.
The various dissolved and particulate substances present in sea water
largely determine its optical properties. It is a primary task of optical oceanography t o find out which ingredients are optically active and t o study their
optical behaviour. This presupposes an intimate knowledge of the properties
of the water itself as a pure liquid.
An exchange of ideas and techniques between oceanography and meteorology is important. Both fields have an interest in the physical processes
occurring at the sea surface which determine the interchange of energy
between the atmosphere and the sea. On the other hand, the propagation of
light in the atmosphere and in the sea is dominated by different physical processes. The atmosphere is primarily a scattering medium whereas in the
ocean absorption as well as scattering plays an essential role. It has long been
known that the total radiant energy from sun and sky loses half of its value
in the first half metre of water, owing chiefly to strong absorption in the
infra-red.
HISTORICAL NOTE
Though a detailed historical perspective lies outside the purview of this
introduction, some highlights in the pre-war development of underwater
optics may be mentioned. The progress of research has been intimately connected with the evolution of instrumental technique. For the earliest
measurements, only photographic methods were available. The initial study
of 'radiant energy dates back t o 1885 when Fol and Sarasin exposed photographic plates in the Mediterranean off the Cote d'Azur. It merits attention
that Knudsen (1922), by using a submerged spectrograph together with a
photographic recording method, was successful in measuring spectral
radiance at different levels in the sea.
2
The introduction of photoelectric cells for marine observations (Shelford
and Gail, 1922) revolutionized optical technique. In the 1930’s much pioneer work was done on the design and use of radiance and irradiance meters
(Atkins and Poole, 1933; Clarke, 1933; Utterback and Boyle, 1933;
Pettersson and Landberg, 1934; Jerlov and Liljequist, 1938; Takenouti,
1940; and Whitney, 1941). Pettersson (1934) also devised the first examples
of in situ beam transmittance and scattering meters. The study of particle
distribution in the deep sea by means of scattering measurements is based on
Kalle’s (1939a) original method.
In a series of papers Shuleikin (1923, 1933) presented for the first time a
correct explanation for the colour of the sea and made a quantitative analysis of the structure of the light field in turbid media. Important results on
the significance of soluble yellow matter for the transmission of light and for
the colour of the sea were obtained by Kalle (1938). Gershun (1936, 1939)
propounded a general theory for light fields and introduced new photometric
concepts, e.g., scalar irradiance, which are indispensable in modern theory.
Finally there is the paper by Le Grand (1939), which presents an analysis of
methods employed in underwater optics together with deductions of fundamental laws.
Research spanning three decades has yielded surprisingly few results on
the penetration of light in offshore waters. This is partially due t o the difficulties involved in measuring with broad filters. Since 1955, however, the
situation has completely changed, due t o the introduction of photomultiplier tubes and interference filters. This technique, which enables us t o study
all optical parameters with a high accuracy, paved the way for a rapid development. Another strong impetus is provided by the invention of the laser,
which is now a profitable tool in oceanographic optics. The advent of these
tools has started a new epoque in the domain. Furthermore, remote optical
sensing has furnished the oceanographer with the ability t o view synopticly
vast regions of the ocean.
TERMINOLOGY
It was recognized by the Committee on Radiant Energy in the Sea (of the
International Association of Physical Oceanography, IAPO) that a firm basis
of definitions is imperative in optical oceanography. The definitions recommended by the Committee follow t o some extent those published by the
Commission Internationale d’Eclairage (Anonymous, 1957) and the International Dictionary of Physics and Electronics (New York, 1956); in
addition, adequate definitions are introduced for the great number of terms
specific for optics of the sea. The Committee has considered it beyond its
scope t o find a purely logical approach t o the difficult definitions of such
fundamental concepts as transmission, scattering and reflection. Those who
3
want t o dig deeper into the problems of definition are referred t o an interpretation by Preisendorfer (1960).
General principles
Some basic principles in the standard terminology are as follows. When
dealing with radiant energy from sun and sky, the terms radiance and irradiance are considered t o be fundamental; the concept of radiant intensity,
which refers t o point sources, has less application. Attenuation is preferred to
extinction for representing the combined process of absorption and scattering. Meters are named after the quantity measured, e.g., radiance meter,
irradiance meter, scatterance meter and beam transmittance meter (formerly
transparency meter). The terms transparency and turbidity are not given
strict definition; they are still used as rough indicators of the optical properties of water.
The list of terms and symbols for fundamental quantities, properties of
the sea and instruments is presented below. The sketches in Fig. 1 are a
complement t o the definitions, and also bring out the essential features of
the instrumental design.
I E d
BEAM TRANSMITTANCE
InFt/Fo= InTz-cr
fEu
U
DOWNWARD
IRRADIANCE
UPWARD
IRRADIANCE
-::::”VOLUME SCATTERING FUNCTION
dI@)
p ( e ) : d I ( B ) / Edv
RADIANCE
Fig. 1. Sketches complementing t h e definitions of quantities a n d properties.
Definitions
Fundamental quantities
Wuuelength. The distance between t w o successive points of a periodic wave in the direction of propagation, for which t h e oscillation has t h e same phase.
4
N o t e : The wavelength of monochromatic radiant energy depends o n t h e refractive
index of t h e medium. Unless otherwise stated, values of wavelengths are those in air.
Symbol: h
Unit:
m
I n m = 1 0 - 3 p m = 1 0 -rn~
S u n zenith distance. The angle between t h e zenith and t h e sun's disc.
Symbol : i
Quantity of radiant energy. Quantity o f energy transferred by radiation
Symbol: Q
Unit:
joule, J ; erg 1 erg = 1 0 - 7 J
Radiant flux. The time rate o f flow of radiant energy.
Symbol: F
Unit:
watt, W
Relation : F = Q / t
Radiant intensity ( o f a source in a given direction). The radiant flux emitted by a source,
o r by a n element of a source, in a n infinitesimal c o n e containing the given direction,
divided by the solid angle of t h a t cone.
N o t e : F o r a source which is n o t a point source: The quotient of t h e radiant flux
received a t a n elementary surface and t h e solid angle which this surface subtends a t any
point of the source, when this quotient is taken to t h e limit as t h e distance between the
surface and t h e source is increased.
Symbol: I
Unit:
watt per steradian, W/sr
Relation : I = d F / d w
Radiance. Radiant flux per unit solid angle per unit projected area of a surface.
Symbol: L
Unit:
w a t t per square metre and per steradian, W/m2sr
Relation : L = d 2 F / d A cos E d w
Irradiance ( a t a p o i n t of a surface). The radiant fIux incident o n a n infinitesimal element
of a surface containing t h e point under consideration, divided by t h e area of t h a t element.
Symbol: E
watt per square metre, W/m2
Unit:
Relation : E = d F / d A
Downward irradiance. The radiant flux o n an infinitesimal element of the upper face
(0 --180°) o f a horizontal surface containing t h e point being considered, divided by t h e
area of t h a t element.
Symbol: E d
Unit:
w a t t per square metre, W/m2
Relation : E d = d F / d A
Upward irradiance. The radiant flux incident o n a n infinitesimal element of t h e lower
face (180 -360O) of a horizontal surface containing t h e point being considered, divided
by t h e area of t h e element.
Symbol: E ,
Unit:
w a t t per square metre, W/m2
Relation : E , = d F / d A
Irradiance on a vertical plane. The radiant flux o n a n infinitesimal element of a vertical
surface (90') containing t h e point under consideration, divided by t h e area of t h a t
element.
Symbol: E ,
Unit:
w a t t per square metre, W/m2
Relation :E , = d F / d A
.
5
Radiant excitance (at a p o i n t o f a surface). The radiant flux emitted by an infinitesimal
element of a surface containing the point under consideration, divided by the area of that
element.
Symbol: M
watt per square metre, W/mZ
Unit:
Relation : M = d F / d A
Spectral distribution curve o f a radiometric quantity such as radiant flux, radiance, etc.
Curve representing the spectral concentration of the quantity as a function of wavelength
(or frequency).
Scalar irradiance. The integral of a radiance distribution at a point over all directions about
the point.
Symbol: Eo
Unit:
watt per square metre, W/m2
Relation: Eo = J L d w
4n
Spherical irradiance. Limit of the ratio of radiant flux onto a spherical surface to the area
of the surface, as the radius of the sphere tends toward zero with its cer.tre fixed.
Symbol: E,
Unit:
watt per square metre, W/mZ
Relation : E, = F,/4nrz
where F , is the radiant flux onto the sphere of radius r.
E, = $ * Eo (eq. 8 )
Properties of the sea
Reflectance. The ratio of the reflected radiant flux to the incident radiant flux.
Symbol: p
Relation: p = F,/Fo
Irradiance ratio (reflectance). The ratio of the upward to the downward irradiance at a
depth in the sea.
Symbol: R
Relation: R = E,/Ed
Transmittance. The ratio of the transmitted radiant flux to the incident radiant flux (in
either irradiance or radiance form).
Symbol: T
Relation : T = F J F 0
Beam transmittance. See: Attenuance.
Absorptance. The ratio of the radiant flux lost from a beam by means of absorption, to
the incident flux.
Symbol: A
Relation: A = F,/Fo
Scafterance. The ratio of the radiant flux scattered from a beam, to the incident flux.
Symbol: B
Relation: B = F b / F o
Forward scatterance. The ratio of the radiant flux scattered through angles 0--90° from a
beam, t o the incident flux.
Symbol : B f
'
Backward scatterance. The ratio of the radiant flux scattered through angles 90-180°
from a beam, to the incident flux.
Symbol : B ,
6
Attenuance. The ratio of t h e radiant flux lost from a beam of infinitesimal width by
means of absorption and scattering, to the incident flux.
Symbol: C
Relation : C = F , /PO
1 - C = (I - A ) ( 1 - B ) = T (beam transmittance)
AOsorption coefficient. The internal absorptance of an infinitesimally thin layer of the
medium normal t o t h e beam, divided by the thickness ( A r ) of the layer.
Symbol: a
Unit:
m-l
Relation: a = -- A A l A r = - A F / F A r
For homogeneous medium : ar = - In( 1 - A )
Volume scattering function. The radiant intensity (from a volume element in a given
direction) per unit of irradiance o n the volume and per unit volume.
Symbol: pC0)
Unit:
m-l sr-l
Relation: P ( 6 ) = dI(b')/E du
(Total) scattering coefficient. The internal scatterance of an infinitesimally thin layer of
t h e medium normal t o t h e beam, divided by the thickness ( A r )of t h e layer.
Symbol : b
Unit:
m-l
Relation: b = - A B / A r = - A F I F A r
0
471
For homogeneous medium: br = - ln(1 - B )
Forward scattering coefficient. The coefficient which relates to forward scatterance.
Symbol : b f
Unit:
m-l
t.
Relation: b f = 2nJ p ( 0 ) sin 0 db'
0
For homogeneous medium: b f r = - l n ( 1 - B f )
Backward scattering coefficient. The coefficient which relates t o backward scatterance.
Symbol : 6,
Unit:
m-l
Relation: bb = 2n
s p ( 0 ) sin b' db'
71
f71
For homogeneous medium : bbr = - In( 1 - Bb )
(Total) attenuafzon coefficient. The internal attenuance of an infinitesimally thin layer of
the medium normal t o the beam, divided by the thickness ( n r )of t h e layer.
Symbol. c
Unit:
m-'
Relation : c = - A C I A r = A FIF Ar
~
c=a+b
For homogeneous medium : cr = - In( 1 - C ) = - In T
(Vertical) attenuation coefficient of a quantity (for instance L or E). The vertical gradient
of the logarithm of the quantity.
Symbol: K
7
Refractive index. The phase velocity of radiant energy in free space divided by the phase
velocity of the same energy in a specified medium.
It is equal t o t h e ratio of t h e sine of t h e angle of incidence (in vacuo) t o the sine of the
angle of refraction.
Symbol: n
Relation : n = sin i/sinj
Optical length. The geometrical length of a path multiplied with the total attenuation
coefficient associated with t h e path.
Symbol: T
Relation : T = cr
Degree o f polarization. If a polarized radiance meter with retardation plate removed is
directed t o accept t h e beam, the polarizer rotated 180° and maximum and minimum radiances recorded, then t h e degree of polarization is the ratio of the difference between
maximum and minimum radiances t o t h e sum of them, i.e., t h e ratio of the polarized
fraction t o t h e total energy.
Symbol: p
Relation : p = (L-L d n ) / ( L m
L ~ n )
+
A s y m p t o t i c radiance distribution. The radiance distribution which is the limit of the distribution in t h e hydrosphere as t h e depth increases infinitely. It is symmetrical around
t h e vertical and independent of sun zenith distance.
Ins trum en ts
Diffuser. A device used t o alter t h e angular distribution of t h e radiant flux from a source
and depending essentially o n the phenomenon of scattering.
Collector. A device required to fulfil t h e definition of the quantity being measured, for
instance, a Gershun tube in radiance measurements or a cosine collector in irradiance
measurements.
Cosine collector. A collector which accepts radiant flux in accordance with the cosine
law.
Optical filter. A device which changes, by absorption or interference, the magnitude or
t h e spectral distribution of t h e radiant energy passing through it.
Neutral filter. An optical filter which reduces the magnitude of the radiant energy witho u t changing its relative spectral distribution.
Selective or coloured filter. An optical filter which changes, by absorption, t h e spectral
distribution of t h e energy passing through it.
Interference filter. An optical filter which transmits, a t normal incidence, only a narrow
band of wavelengths, o t h e r wavelengths being suppressed b y t h e destructive interference
of waves transmitted directly through t h e filter and those reflected 2n times, where n is
an integer (from back and front faces of t h e filter).
Photoconductive cell. A photocell whose electrical conductance changes under irradiation.
A voltage supply is required in t h e cell circuit.
Photovoltaic cell. A photocell which sets u p a potential difference between its terminals
when exposed t o radiant energy. It is a selfcontained current and voltage generator.
Photoemissive cell. A photocell whose working depends u p o n the photoemissive effect,
i.e., t h e capacity of certain surfaces t o release electrons under the influence of radiant
energy.
8
Photo-multiplier cell. A t u b e (valve) in which secondary emission multiplication is used to
increase the o u t p u t for a given incident radiant energy.
Zrradiance meter. A radiant flux meter with plane (usually circular) cosine collecting surface (usually a n opal glass) of effective area A . If F is t h e radiant flux recorded by the
meter then the associated irradiance is by definition E = F / A .
Spherical irradiance meter. A radiant flux meter with spherical collecting surface of effective area A , every elemental area of which is a cosine collector. If F is t h e radiant flux
recorded by t h e meter, then t h e associated spherical irradiance is E , = F / A .
Radiance meter. An irradiance meter which collects radiant energy from a set of direcmagnitude
tions and which has its field of view limited to a circular solid angle of
(defined, f o r example, by a cylindrical tube) whose axis is fixed normal to t h e plane o f
t h e collecting are6 of t h e meter. If E is t h e reading of t h e meter, t h e associated radiance is
a
L =E/R.
(Beam) attenuance meter or (beam) transmittance meter. A radiance meter which measures the beam transmittance, T , of a fixed path. The beam attenuance C = 1 -- T .
Scalterance meter. An assembly of a light source and a radiance meter which directly
measures the scatterance values of a n optical medium. Scatterance meters fall i n t o three
main classes : Free-angle, fixed-angle and integrating scatterance meters. The first t y p e is
designed to determine in principle all values of t h e volume scattering function a t a given
point, t h e second is designed t o determine t h e function for a fixed angle, and t h e third
type is designed t o integrate directly t h e function over all angles so as t o record t h e total
scattering coefficient.
S o m e relations
Preisendorfer (1961) has pointed out the desirability of a division of
optical properties of the sea into two mutually exclusive classes, consisting
of inherent properties and apparent properties. An inherent property is one
that is independent of changes of the radiance distribution; an apparent
property is one for which this is not the case. The inherent optical properties
are the coefficients of attenuation, absorption and scattering, as well as the
volume scattering function; apparent properties are, for instance, the coefficients of radiance attenuation and irradiance attenuation. Subsequent chapters will demonstrate the utility of the apparent properties in experimental
studies of the underwater field, and will also formulate relationships among
the various properties.
Some features in the relationship between radiance and irradiance will
now be discussed. We begin by observing that the definition of radiance does
not bring out its dual nature. This may be interpreted as follows (Gershun,
1939).
Consider a surface element ds, at 0 which emits energy in the direction
0 , (Fig. 2) and another element ds, at P which receives the emitted energy
from the direction 0 2 . The two surface elements are assumed to be small
compared with the distance r between them. The intensity d l in the direction 0 , is defined by:
9
Fig. 2. Diagram accompanying t h e definition of radiance. (After Gershun, 1939.)
Since the solid angle dw, is given by:
dw
1
= ds2 cos O 2
r2
the irradiance d E at P must be:
This formula embodies the well-known inverse-square law and the cosine law
of irradiance.
The radiance L for the outgoing field is by definition:
L = -.Ap--2F
ds, cos O,dw,
-
dl
____
ds, cos 8 ,
or :
L = -
d2Fr2
dslds2 cos O 1 cos O 2
The same expression is found for the incoming field. The symmetry of the
equation:
d2F =
Lds,ds2 cos 8 , cos O 2
r2
requires that the radiance for the outgoing field be equivalent to that for the
incoming field. From eqs. 1 and 2 the irradiance at P may be written in the
form :
10
dE =
d2F
= Lcos8,dw2
--
dS2
[31
A case of special interest is the irradiance on a plane surface receiving
energy from a hemisphere of constant radiance. Considering that:
dw, = 2 ~ s i n 8 ~ d 8 ,
[41
we obtain from eq.3:
d E = L cos %,
and :
E = 27rL
E
= nL
- 27r sin e2d8,
;-V
sin%2cos8Zd82
[51
i)
Therefore a cosine diffuser, i.e., a Lambert diffuser, emits in all directions
the same radiance:
[GI
Next, consider rays contained within dw directed towards a small sphere
with radius r (Gershun, 1939). The flux received by the sphere is proportional to its projected area:
d F = 7rr2Ldw
and the entire flux from all directions:
F = 7rr2
/
Ldw = 7rr2E,
4n
Hence the spherical irradiance is:
[71
CHAPTER 2
SCATTERING
THE SCATTERING PROBLEM
Scattering, together with absorption, is the fundamental process which
determines the propagation of light in sea water. One may visualize scattering simply as the deviation of light from rectilinear propagation. The scattering process leads to a change in the distribution of light which has farreaching consequences. The significant factor in scattering studies is the
volume scattering function, which represents scatterance as a function of the
scattering angle.
The theoretical and experimental investigation of the scattering problem
associated with a marine environment presents considerable difficulties. One
reason is that scattering in sea water has two entirely different components,
namely the scattering produced by the water itself and that produced by
suspended particles. The scattering by pure water shows relatively small
variations, effected only by changes in temperature and pressure, whereas
the particle scattering is dependent on the highly variable concentration of
particulate matter. Sea water should be looked upon as a polydisperse
assembly of randomly oriented irregular particles which are capable of
absorption. The complete treatment of particle scattering cannot avoid
the complexity of taking particle absorption into account.
SCATTERANCE METERS
Different types of meters
The scattering quantities have exact mathematical definitions which dictate the design of the meters t o be used. In principle, measurements of scatterance involve irradiation of a sample volume by a beam of light and recording of the light scattered by the volume through various angles. Thus the
basic parts of the scatterance meter are a light source, gving a beam with a
low divergence, and a detector, generally a photomultiplier tube and associated optical system to produce a well-defined beam of detectivity, also of
low divergence. The scattering volume is defined by the intersection of the
light beam with the detectivity beam.
Several types of scatterance meters have been developed. In routine work
14
a fixed angle is useful; this is most often chosen at 45" (Kalle, 1939a; Jerlov,
1953a; Beardsley Jr. et al., 1970), at go", where polarization effects are of
special interest (Ivanoff, 1959), or at any angle between 40 and 150"
(Karabashev and Yakubovich, 1971). Free-angle instruments yield values of
the volume scattering function, p ; the geometry of these meters generally
imposes limitations on their angular range. Finally, integrating meters have
been designed which directly record the total scattering coefficient, b.
Another ground of subdivision is to distinguish laboratory meters and in
situ meters.
Laboratory meters
There are on the market laboratory scatterance meters with high resolving
power which apparently admit of rapid measurements of the volume scattering function. However, the meters require adaptation to the special study of
ocean water. Because the latter has a low scatterance, produced by a relatively small number of particles, the beam should be chosen fairly wide; this,
on the other hand, makes small angles inaccessible. A more satisfactory way
is t o smooth the signal from the detector. Since stray light is a crucial factor,
it is also expedient t o place the scattering cell in water or benzene in order t o
reduce the disturbing reflexions at its exterior walls.
The question arises whether water samples drawn from a water bottle and
transferred to a scattering cell are representative of the condition in the
water region. Firstly, great precautions are necessary t o avoid contamination
of the sample (Jerlov, 1953a). The water bottle should be coated with
ceresin or teflon. It is obligatory t o agitate the sample in the water bottle
and in the scattering cell in order t o secure a homogeneous sample and prevent settling of large or heavy particles. By turning the (round) cell (Jerlov,
1953a) or by using a teflon-covered stirring bar (Spielhaus, 1965) , sufficient
agitation is obtained. Ivanoff (1960a) collects the samples in special glass
water bottles which are placed directly in the meter and turned by means of
a motor.
Considering the rapid disintegration of living cells in a sample, an immediate processing is desirable. On the other hand, heating of the sample may
occur during the tests; this often leads t o formation of oxygen bubbles,
which multiplies the scattering of the sample. When using a pumping system
instead of collection with water bottles, several of the mentioned disadvantages are avoided but a major difficulty arises due t o the formation of
bubbles. To avoid this effect it is necessary t o work with positive pressure.
Spielhaus (1965) has discussed the errors in the in vitro method. Inexplicably large standard errors indicate that it is impossible to assess the effect of
withdrawing the sample from its environment. Ivanoff et al. (1961) have
stated that the laboratory method, if employed with the utmost care, yields
consistent results but that the in situ method is highly preferable.
15
Fig. 3. In situ scatterance meter ( 10-170°) described by Petzold ( 1 9 7 2 ) .
In situ meters
In accordance with this preference, two in situ free-angle meters are
selected t o represent the family of scatterance instruments. Petzold's (1972)
meter (Fig. 3) has been made short and handy by deflecting the irradiating
beam and the beam of detectivity 90" by means of prisms. The projector
rotates about the sample volume in the measuring interval 10-170". At 0"
the direct beam is measured and a t 180" the receiver entrance is blocked and
the dark signal is recorded.
Another in situ meter (10-165") is designed with a view t o reducing the
disturbing effect of natural light (Fig. 4). When released, the lamp unit falls
slowly down - checked by a paddlewheel revolying in the water - and
rotates around the centre of the scattering volume element. The rotation
brings twelve successive stops in front of the photomultiplier tube. The
width of these stops is proportional t o sin 8, so that the measured scattering
emanates from a constant volume.
16
Fig. 4.In situ scatterance meter (10-165')
n
..--
Water
-
used by Jerlov (1961).
Air
1-/-&Zgw-.-.-Screen
c
Fig. 5. Three types of in situ scatterance meter for small angles. A. For 0.5' angle
(Duntley, 1963). B. F o r angles betwee; 1.5 and 14' (Bauer and Ivanoff, 1965). C . For
several defined angles between 1.5 and 5 (G. Kullenberg, 1968).
17
Great interest is focussed on scatterance a t small angles, which makes up a
considerable part of the total scatterance. These measurements are technically the most intricate and require a meter with high resolution. A unique
meter has been devised by Duntley (1963) (Fig. 5). His instrument employs
a highly collimated beam in connection with an external central stop, so that
a thin-walled hollow cylinder of light is formed (cross-hatched in Fig. 5).
Only light scattered by the water in this cylinder is collected through an
evaluated angle of 0.47" k 0.15'.
By means of a laser and a system of mirrors, G. Kullenberg (1968) has
contrived t o isolate scattering through a small angular interval defined by the
half-angle of the cone of the entrance mirror (Fig. 5). Several such mirrors
can be used t o cover angles between 1.5 and 5'.
A third alternative for measuring small-angle scatterance is t o use an
optical system whose basic form is illustrated in Fig. 5B. Flux which is scattered in the direction 8 converges in the focal plane of the lens at a distance
x = f * t g O from the optical axis. It is readily seen that the scattered irradiance at x is proportional t o P ( 0 ) .
Several instruments have been built based on this geometry. Bauer and
Ivanoff (1965) screened off the central beam, placed a photographic plate
in the focal plane and were able t o evaluate P ( 0 ) in the range 1.5-14" densitometrically. A firm theoretical and experimental basis for the calibration
of this meter was presented by Bauer and Morel (1967). Other workers have
chosen a photomultiplier as detector: Sokolov et al. (1971), who used a laser
as light source, mounted a rotating screen with several spirally placed holes
in the focal plane and were able t o cover the range 0.57-8.6". Petzold
(1972) employed several annular diaphragms which could be stepped into
position. In the described version he measured the irradiance of the central
beam P ( 8 ) at evaluated mean angles as small as 0.085', 0.169' and 0.338'.
McCluney (1974) has used a fixed and a rotating mask. The set of masks
constitute a modulator imposing a different modulation frequency to each
angular interval. This meter requires a rather complicated electronic system.
Softley and Dilley (1972) have measured directly the radial distribution of
flux in a plane normal t o a pulsed laser beam using an image dissector tube.
Integrating meter
The best adaptation t o routine observation in the sea is dispkyed by the
integrating meter designed after the principle introduced by Beutell and
Brewer (1949), Jerlov (1961) and Tyler and Howerton (1962). A small
light source S, consisting of a lamp and an opal glass of surface area A ,
is assumed t o be a cosine emitter of radiance Lo (Fig. 6). A radiance detector
is placed at 0 with its axis parallel t o the surface of S and facing a light trap
T . With due regard t o the attenuation by the water, the irradiance E R on
the volume element dv at R is found from eq. 2 t o be:
18
Fig. 6. Integrating scatterance meter according t o the principle of Beutell and Brewer
(1949).
E K = L o A sin36 e-chcosecO
h2
The intensity dl, scattered by the volume element in the direction R O is
given by :
dl,
= ERP(8)du = E R p ( 8 ) x 2 d w d x
Hence the radiance L of du recorded at 0 will be:
Considering that x = r - h cot 6, we obtain:
The geometry of the meter is adapted so as t o minimize the distance
h ( h < r ) . For forward scattering (6' = 0 t o i n ) , the term f = ch(cosec 8 cot 8 ) of the attenuation exponent may then be neglected in comparison
with cr. For 8 = n the term f = 03; furthermore, the function p ( 8 ) is very
small for back-scattering (8 =
t o n). Therefore, with accuracy sufficient
for all practical purposes, the radiance is found with the term f of the exponent omitted:
.3
L = -
e-cr j p ( 8 ) sin 8d8
h
0
Introducing the total scattering coefficient:
1
b = 271 p ( 0 ) sin8 d0
we obtain:
The performance of in situ scatterance meters may be affected by ambient
natural light in the upper strata of the ocean. It is difficult t o combine effec-
19
tive screening from natural light with free water circulation through the scattering centre. A simple and effective means of diminishing the disturbing
effect of natural light is t o place a red filter in front of the detector. A
chopped or modulated light source together with a suitable electronic system
eliminates the disturbance, provided that the detector operates always in its
linear range. An original record of the total scattering coefficient for red
light as a function of depth is given in Fig. 7.
Fig. 7 . Original record of the total scattering coefficient f o r red light as a function of
d e p t h in the Sargasso Sea.
It is requisite for the whole body of optical problems t o know the scattering coefficients in absolute units. A great deal of effort has been expended in
calibrating procedures. Tyler (1963a) has discussed the theoretical basis for
the scatterance meter and extended the theoretical analogies by Pritchard
and Elliot (1960) for application t o scattering by ocean water. This cannot
be discussed in detail here.
SCATTERING BY WATER
Rayleigh theory
Scattering by pure water is often considered as a problem of molecular
scattering. An introduction into this domain is provided by the Rayleigh
equation (Rayleigh, 1871). A homogeneous electrical field E induces in a
particle a dipole, the strength, p , of which is given by:
p = aE
where a is the polarizability of the particle.
20
The oscillating dipole radiates in all directions. For the case of N particles
which are small relative t o the wavelength, isotropic and distributed a t random, the radiant intensity in the direction 8 is given by:
1 =
87r4Na2E2
h4
(1+ cos2 e )
-
which brings out the well-known fourth-power law of the wavelength. It
should be noted that in a strict sense only spherical t o p molecules have a
scalar p olarizabili ty .
Fluctuation theory
An approach which is better adapted t o scattering by liquids is that of
fluctuation theory (Smoluchowski, 1908; Einstein, 1910). This attributes
the scattering t o fluctuations in density or concentration which occur in
small-volume elements of the fluid independent of fluctuations in neighbouring volume elements.
With a beam of unpolarized light, the volume scattering function o O ( O )
is found from:
n2 QkT
Po(8) = --(n2-l)2(n2+2)2(1+cos2~)
18 X4
where Q = thermal compressibility, k = Boltzmann’s constant, n = refractive
index and T = absolute temperature. The equation also establishes the
dependence of scattering on temperature and pressure.
This formula is valid for isotropic scattering centres. If the existing anisotropy which gives rise t o depolarization of the scattered light (see p. 44) is
taken into account, the complete equation becomes:
IT^ q k T
+
po(S) = - __ ( n Z- 1)2(n2 2)’
18 h4
(1
+
[91
It is experimentally evidenced that this formula does n o t very well conform with the properties of a dense medium as water. In the theoretical
deduction it is preferable to introduce directly observed values of the change
of the refractive index with pressure, anlap; the resulting equation takes the
form (Morel, 1974):
from which follows:
87r
b , = -&(90)
3
2+6
1+6
__
21
TABLE I
Theoretical scattering function for pure water
(After Morel, 1974)
Szattering angle 0
0
Scattering function P O ( 0 ) (475 n m )
(
m-l)
0 and 180
10 and 170
20 and 160
30 and 150
45 and 135
60 and 120
75 and 105
90
3.15
3.11
2.98
2.78
2.43
2.09
1.85
1.73
TABLE I1
Volume scattering function a t 90° and total scattering coefficient f o r pure water
and sea water as a function of the wavelength
(After Morel, 1974)
350
375
400
425
450
475
500
525
550
575
600
6.47
4.80
3.63
2.80
2.18
1.73
1.38
1.12
0.93
0.78
0.68
103.5
76.8
58.1
44.7
34.9
27.6
22.2
17.9
14.9
12.5
10.9
8.41
6.24
4.72
3.63
2.84
2.25
1.80
1.46
1.21
1.01
0.88
134.5
99.8
75.5
58.1
45.4
35.9
28.8
23.3
19.3
16.2
14.1
~
The scattering function (475 nm) for pure water computed from eq. 10 is
given in Table I. The dispersions of pO(9O) and bo for pure water are represented by data established by Morel (1974) (Table 11).
Measurements
Many workers - Raman (1922) being the first - testify t o the difficulty
of preparing optically pure water. Small traces of particulate contamination
augment the scatterance drastically, especially at small angles. The possibility
of obtaining accurate results is dictated chiefly by one's success in preparing
pure water.
22
From the results of Dawson and Hulburt (1937) i t is clear that the scattering by pure water roughly obeys the
law. Taking the dispersion of n and
an/aP into account, Morel (1974) has been able t o fix the exponent at the
precise value of - 4.32. Morel has given an account of all phases of purewater scattering. His careful measurements of the scattering function on
water distilled three times in vacuum without boiling indicate that experimental and theoretical values accord well (Table 11).
The scattering due t o the various solutes present in pure sea water is difficult t o observe, since sea water can be purified only by filtering.It has been
generally held that the scattering produced by the ions in sea water would be
minute. New findings show that the ions are responsible for m appreciable
increase in scattering. This increase is due t o concentration fluctuations and
therefore proportional t o the salinity of the water. Morel (1974) has
achieved results which indicate that pure ocean water ( S = 35--39°/00)
scatters 30% more than pure water (Table 11).
REFRACTIVE INDEX AND DISPERSION O F SEA WATER
The refractive index enters the formulas for scattering by sea water. The
question arises as t o what degree the index is influenced by changes in temperature and salinity of the water. Sager (1974) has treated this problem
exhaustively (Table 111). It is evident that the dependence of the index on
salinity is more marked than the dependence on temperature; neither effect
is of great consequence, however.
The dispersion of refraction is more important. Lauscher (1955) has
selected accurate refractive-index data as a function of the wavelength (Table
IV). Although the dispersion amounts t o only 4% over the actual spectral
range, it must be accounted for in the scattering computations, e.g., by
means of eq. 10.
It may be gathered, however, that for all practical purposes the mentioned
effects can be neglected and a value for the refractive index of n = 4 adopted,
which corresponds t o a light velocity of 2.25 * 10' m/s.
PARTICULATE MATTER IN THE SEA
Concentration and nature
A basic examination of the particulate matter in the sea distinguishes two
main classes: organic and inorganic matter. Large quantities of inorganic
materid are brought t o the ocean by land drainage and by winds. The organic
substances are present in variable proportions generally less in deep water
than in the upper layers (Table V). The organic fraction can be estimated
23
TABLE I11
The refraction difference ( n - 1.30000) * l o 6 as a function of temperature
and salinity for = 589.3 nm
(After Sager, 1974)
Salinity
Temperature (OC)
(O/OO)
0
10
20
30
0
5
10
15
20
25
30
35
40
3400
3498
3597
3695
3793
3892
3990
4088
4186
3369
3463
3557
3652
3746
3840
3934
4028
4123
3298
3390
3482
3573
3665
3757
3849
3940
4032
3194
3284
3374
3464
3554
3644
3734
3824
3914
TABLE IV
Dispersion of refraction for pure water ( t = 20°C)
(After Lauscher, 1955)
Wavelength
(nm)
Refractive index
Wavelength
(nm)
Refractive index
250
308
359
400
434
1.3773
1.3569
1.3480
1.3433
1.3403
486
589
768
1000
1250
1.3371
1.3330
1.3289
1.3247
1.3210
at 20-60% for the oceans (Lisitsyn, 1962; D.C. Gordon Jr., 1970b; C .
Copin-Montegut and G. Copin-Montegut, 1972). Parsons (1963) gives the
following rough relative figures t o illustrate the role of the living component:
soluble organic 100 ; particulate detritus 10; phytoplankton 2; zooplankton
0.2; fish 0.002. The organic detritus is t o a large extent composed of remnants of disintegrated phytoplankton cells and of exoskeletons of zooplankton. Quartz is an important constituent in the inorganic material. Soluble
decay products and weakly soluble components such as CaC03 and Si02
participate in the general chain of biological transport. It has also been
observed that a formation of organic detritus from soluble or colloidal
matter takes place in the sea by flocculation (Jerlov, 1955a; Chapter 3) and
by adsorption processes (Sutcliffe et al., 1963).
Refractive index
As regards the refractive index of marine particles relative t o that of sea
water we face the problem that the two main categories, organic and
24
TABLE V
Amount of particulate matter in the ocean
Area
Depth
Concentration
(mg/l)
References
1 . Total
Oceans
deep water
0.05
Jacobs and Ewing (1969)
North Atlantic
surface water
0.04-0.15
Folger and Heezen (1967)
Northeastern
Atlantic
surface water
deep water
0.06-0.13
0.02-0.05
C. Copin-Montegut and
G. Copin-Montegut (1972)
2. Organic fraction
Atlantic
0.04-0.17
Riley et al. (1965)
North Atlantic
0.0 5-0.2 0
D.C. Gordon Jr. (1970b)
Central Pacific
deep water
surface water
deep water
0 .o 1-0.0 2
0.02
0.01
Northeastern
Atlantic
surface water
deep water
0.03
0.01
D.C. Gordon Jr, (1971),
C. Copin-Montegut and
G . Copin-Montegut (1972)
inorganic matter have quite different indices. The behaviour of some marine
organisms has been studied by Jerlov (195513) who concludes that particles
composed of calcium carbonate or silica show high refraction whereas minimum is obtained for green algae, the chief constituent of which is cellulose.
For a culture of the unicellular phytoplankter Isochrysis galbana Carder et
al. (1972) have found an index of 1.03. An interpretation made by Zaneveld
et al. (1974) makes probable that an index of 1.05 may be representative
for the whole class of particulate organic matter. They also point out that if
an organism has a hard shell with index 1.15 and soft watery protoplasm
with index 1.04 such a particle appears t o scatter light more like two particles
with these separate indices. Investigators of inorganic matter concur in
adopting a relative refractive index in the range 1.15-1.20 for this component (Armstrong, 1965; Pavlov and Grechushnikov, 1966).
Shape and size distribution
The work of establishing particle sizes in the ocean has been accompIished
t o some extent by direct visual or by photographic studies. These indicate
the presence of many large scatterers, mostly above 1mm (Fig. 8; Nishizawa
e t al., 1954; Costin, 1970). Direct observation reveals that fairly large
detrital aggregates are formed in the sea, t o which living cells are added.
These aggregates are mostly encountered in surface waters. Inoue et al.
(1955) stress that these delicate structures disintegrate during the process of
sampling. The research by Krey (1961) also gives evidence of relatively largesized detritus.
25
Fig. 8. Large scatterers ( t w o specimens of Sagittu) seen a t 1 0 m depth from the
“Kuroshio” diving chamber. ( P h o t o from N. Inoue and M. Kajihara.)
There is every reason t o believe that particle-size distributions in coastal
waters are not consistent. Pickard and Giovando (1960) found geometric
mean diameters of 6-17pm. Computations by Hanaoka e t al. (1960) indicate diameters of 2--5pm in baywater of Japan. From scattering measurements on water samples collected off the Po river, in conjunction with a
particle-settling procedure, Jerlov (1958) derived a size-distribution curve
peaked at 3.5 pm.
Microscopic examination furnishes accurate information not only about
the size distribution but also on the shape and area of particles. Some results,
not extended below l p m , are presented in Table VI. They argue in favour
TABLE VI
Normalized cross-sectional areas for particle distribution in the sea
(Microscopic examinations)
Fraction
(Pm)
Area Reference
<2
4-10
10-20
20-40
40-100
100-200
1
11
25
38
50
6
Jerlov (1955b)
1-2.5
2.5-5
5-10
10--25
25-50
50
1
0.5
1.1
10
12
8
Ochakovsky
(1966b)
>
Fraction
Area
(pm)
surface deep*
>
b = 0.10 m-l
Reference
<1
1
1-5
0.3
5-10
1.0
10-50 126
50-100
100
40
1
0.3
1.7
28
14
22
Lisitsyn (1961)
7
14
21
28
42
56
1
1.5
3.7
4.4
2.0
0.7
D.C. Gordon Jr.,
(19704
1
0.9
0.9
1.1
0.6
1.1
* 100 m for Lisitsyn (1961); not specified for D.C. Gordon J r . (1970a).
26
of dominant cross-section, which is the significant factor for scattering, being
above 2 p m in diameter and demonstrate the necessity of paying regard t o
the large particles.
On the other hand, the Coulter Counter (CC) technique used by several
workers shows a tendency of overestimating the number of small particles.
The inconsistent results of microscopic and CC investigations have been
explained by D.C. Gordon Jr. (1970a): “The Coulter Counter measures
particle volume, and to convert these units to both size and frequency one
assumes all particles are spheres which may not be realistic in light of the
variety of particle shape”. In this connection i t should be mentioned that
the particle distribution in a few restricted areas may be atypical for the
ocean as a whole. This concerns the Bahamas Banks where aragonite drewite
precipitates from the warm highly saline waters and therefore small particles
are abundant.
A hyperbolic distribution (Bader, 1970) has been suggested for describing
the family of marine particles:
N = const. D-?
[I21
where N is the number of particles larger than size D and the exponent y is a
characteristic constant.
Fig. 9 illustrates the usefulness of eq. 1 2 which obviously should be considered as a fairly crude approximation. For the different groups of plots in
the diagram the exponent y fluctuates between 0.7 and 6 with the highest
values for CC plots; an average value may be estimated at 2.5. It is obvious
especially from the world-wide observations of Sheldon et al. (1972) that in
highly productive areas certain sizes show some dominance in the distribution. G. Kullenberg (197413) mentions that the hyperbolic distribution does
not hola tme for the strong-scattering largest particles nor for the smallest
which are removed by processes of dissolution, adsorption and flocculation.
PARTICLE SCATTERING
Geometric optics
The scattering process may be treated on a purely theoretical basis as a
forward solution of Maxwell’s equations. However, a short discussion within
the framework of classical large-particle optics will facilitate our understanding of the concept of scattering. Scattering may be looked upon as the
result of three physical phenomena:
(1)Through the action of the particle, light is deviated from rectilinear
propagation (diffraction).
(2) Light penetrates the particle and emerges with or without one or more
internal reflections (refraction).
( 3 ) Light is reflected externally.
27
Fig. 9. Examples of cumulative size distributions (prepared by K. NygOard). 1 = Theoretical, Pacific deep water over red clay, 1.9
y
3.5, B. Kullenberg (1953); 2 = microscopic, Swedish fjord, 1.1 y 2.1, Jerlov (1955b); 3 = microscopic, Mediterranean,
0.7
y 2.0, Ochakovsky (1966b);4 = microscopic, mean North Atlantic, 1.3 y 2.0,
D.C. Gordon Jr. (1970a); 5 = Coulter Counter, western North Atlantic, 2.0
y 3.6,
Sheldon et al. (1973); 6 = Coulter Counter, Mediterranean, 2.4
4.3, Brun-Cottan
(1971); 7 = Coulter Counter, subtropical West Pacific, 3.1 y 6, Matsumoto and
Nakamoto (1973).
< <
< <
< <
< <
< <
< <
< <
28
It is a matter of some significance that diffraction is independent of the
composition of the particle, whereas refraction and reflection are determined
by the refractive index of the particle.
Particle size is the major parameter in scattering. The influence of shape
from the point of view of geometric optics has been discussed in a conclusive
way by Hodkinson (1963). In the case of irregular, nonabsorbing, randomly
oriented particles, the diffraction pattern should be similar t o that produced
by spherical particles with the same projected area. There will also be little
change in the external reflections, since the probability of reflection for all
angles of incidence will be equal. The first refraction by irregular particles
will also be similar t o that for spheres, whereas the second refraction may
show appreciable angular deviations. It follows that opaque irregular
particles, for which refraction is negligible, behave in the same way as
opaque spheres.
Mie theory
In 1890 Lorenz published a paper on light propagation inside and outside
a transparent sphere and thus anticipated later computations by Mie, Debye
and others.
Mie (1908) has employed electromagnetic theory t o derive a rigorous
expression for the perturbation of a plane monochromatic wave by spherical
nonabsorbing particles. The Mie theory is difficult t o comprehend in simple
terms. The basic equations are introduced here in order t o give an idea of the
general reasoning which is utilized.
The treatment of a monodisperse system of particles of given refractive
index is based on the assumption that the scattered light has the same wavelength as the incident light and that the particles are independent in the
sense defined by Van de Hulst (1957). Independence requires that the distance between the spheres is a t least three times their radii and has the consequence that the intensities scattered by the individual particles can be added.
Another limitation is that the particles are assumed t o be irradiated only by
the original beam, i.e., no multiple scattering occurs. Hence total scatterance
is proportional t o the number of particles.
The quantity i, is defined as the intensity scattered in the direction 6 by
a single isotropic sphere from an incident polarized beam of unit intensity
whose electric vector is perpendicular t o the plane of observation (i.e., the
plane containing the direction of propagation of the incident wave and the
direction of observation). Similarly, the quantity i 2 refers to the electric
vector in the plane of observation. The Mie theory furnishes these quantities:
29
with x = - cos 8, and P,(x) = Legendre polynomial of order n.
The functions A , and Bn involve the Riccati--Bessel and Riccati-Hankel
functions, and are related to the Bessel functions of half-integral order. The
only physical parameters which enter into these functions are.:
a = 7rD/h
= ma
where D = diameter of the particle, h = wavelength of the incident wave in
the surrounding medium, and m = refractive index of the particle relative to
the surrounding medium.
The quantity scattered in the direction 8 from a randomly polarized beam
of unit intensity will be:
h2
i(0) = __ (il + i2)
87T2
On integrating i(8) with respect to 8, we obtain the total scattered radiation:
1 = 27r
6”
J’ +
i(6)sin 8d8 = - (il
x2
47r 0
i 2 ) sin 8 d 8
~ 5 1
If this integral is divided by the cross-sectional area 7rD2/4of the particle,
a dimensionless quantity K is obtained:
Eqs. 13 and 16 yield the following result:
The quantity K is called the efficiency factor, or the effective area coefficient. It follows from the definition of the scattering coefficient b that with
N particles per unit volume we have:
b = KN7rD2/4
[I81
For the case of a polydispersed system, the scattering coefficient is given
by:
30
The results of the Mie theory are obtained as a series which converges
rather slowly for particles as large as several wavelengths in diameter. However, this does not present any serious problem for modern electronic computers.
Enlargmg the treatment t o encompass absorbing particles requires the
introduction of a complex refractive index:
m = n-in'
POI
where n' = ah/47r, a being, as usual, the absorption coefficient. The steps of
computation in this case are described by Van de Hulst (1957).
Application of the Mie theory to sea water
The current interest for computations by means of the Mie theory is
motivated in the main by the desideratum of determining the refractive
index of particles and possibly their absorption. Sea water is a dilute suspension of independent particles of various sizes, shapes and composition.
Multiple scattering may be disregarded for the usually small volumes which
are studied in scatterance meters. Due t o the observation technique with a
small scattering volume the rare large particles are not included in the
measurement; there is no doubt that in situ measurements also underestimate the large scatterers.
The particulate matter scatters by and large as a collection of spherical
particles (Beardsley Jr., 1968a); considerable deviations occur, however, in
the back-scatter field (Holland and Gagne, 1970) which according t o the
observations shows an irregular behaviour. The theory for large scattering
angles remains incomplete so far, even though approaches t o the problem
have been made (Fukuda, 1964).
Calculations for monodisperse systems have been important steps in the
progress of the theoretical research (Gumprecht and Sliepcevich, 1953;
Ashley and Cobb, 1958; Pangonis and Heller, 1960; Sasaki et al., 1960,
1962a; Jerlov, 1961; Spielhaus, 1965; Ochakovsky, 1966b; Mankovsky,
1972). By matching size and refractive index for particles a fair agreement
can be obtained between theory and observation. The curves of the scattering function exhibit the oscillatory trend which is typical for monodisperse
suspension. If particles of a wide range of sizes are present, the fluctuating
features would be virtually obliterated.
It is a conspicuous trend in such curves that with increasing particle size
the forward scattering is intensified and that a slight minimum is formed at
90°, indicating that scatterance through this angle is less than back-scatter at
180".
Burt (1956) has presented a useful scattering diagram (Fig. 1 0 ) which
shows the effective area coefficient K as a function of size, wavelength and
relative refractive index. His computations are based on Rayleigh's law and
31
E f f e c t i v e Area Coefficient
K
W
14 0
1.30
x
u
..
-0
c
u
;.u 120
?
K
-:uo
.-0
L
K
Y
I00
nm
800
s, 1 0 0
5 600
2
500
3 400
v o et
Fig. 10. Particle scattering diagram computed on t h e basis of Rayleigh’s equation and the
Mie theory for nonabsorbing spheres. (After Burt, 1956.)
the Mie theory for nonabsorbing spheres. The diagram covers a radius range
0.01-5 pm and an index range 1.02-1.40, including indices for particulate
material present in natural waters. With increasing particle radius the coefficient increases rapidly at small radii, then it passes a maximum for sizes of
the same order as the wavelength ( K > 3.0) and tends - after some fluctuations - towards a constant value of 2.0 for large sizes irrespective of the
wavelength. It may seem anomalous that a large particle scatters twice the
amount of light it can intercept by its geometric cross-section. This is, however, a well-known diffractive phenomenon. A circular opaque disc observed
a t a great distance also diffracts around its edges, and into a narrow solid
angle, a quantity of light which is exactly the same as that intercepted by the
disc (Babinet principle).
Some experimental data of the effective area coefficient are contained in
the following references. Hodkinson (1963) studied size-graded fractions of
quartz, flint and diamond dust in water and demonstrated the approach of
the K factor t o a numerical value of 2. Jerlov and B. Kullenberg (1953)
measured scatterance on uniform minerogenic suspensions. Their results
(Table VII) provide evidence that the scattering coefficient is proportional
t o the concentration of particles, and that large-particle scattering with K =
2 occurs for sizes above l p m . This is consistent with coefficients computed
by Burt (1954b).
The most realistic approach is t o apply the Mie theory on polydisperse
systems (Spielhaus, 1965). A laudable initiative was taken by Beardsley Jr.
32
TABLE VII
Efficiency factor for various suspensions
Suspension
Pn
K
Minerogenic
1
3
7
9
12
1.4
2.2
2.4
2.2
2.3
Calcareous
10
30
2.7
3.2
et al. (1970) who considered the particle-size interval 2 --11pm using a
Coulter Counter. In order t o secure convergence in the calculations it is obligatory t o place a lower and an upper limit t o the size distribution; in this
case the latter was (for technical reasons) chosen too low.
A critical review of recent papers on Mie calculations for polydisperse
systems has been given by G. Kullenberg (197413) who points out that
assumptions of the size distribution are often unrealistic. O.B. Brown and
H.R. Gordon (1972) have contributed useful tables of the scattering function for four wavelengths, refractive index between 1.01 and 1.15 and size
ranges from 1.017 to 20 pm. Very comprehensive computations of the function and its polarization components have been accomplished by Morel
(1973a) covering different indices and exponents for hyperbolic size distributions. Two groups of functions presented in Fig. 11 demonstrate good
agreement between computed and measured results. Assuming particle size
without limits and with an index of 1.05 and wavelength of 419nm he
arrives at valuable information about the parts played by different sizes in
the total scattering. Thus with an exponent of 2.5, 10% are due t o sizes
above 100pm, 10% are due t o sizes below l . l p m while 50% are at 5pm.
This argues in favour of the small sizes contributing little t o the total
scattering consistent with data in Table VI.
G. Kullenberg and Berg Olsen (1972) have tried a somewhat different
approach by choosing relatively low values of the hyperbolic exponent.
For the computations they have employed Deirmendjian’s scheme (1969).
The example with the Sargasso Sea in Fig. 12 shows a theoretical curve with
an index of 1.20 and an exponent of 2 which is a good fit t o the observed
plots. From his comparative studies of theoretical and experimental scattering functions G. Kullenberg (1968, 1974b) concludes that scattering in the
Sargasso Sea and also in the Mediterranean is chiefly produced by inorganic
particles larger than 1-2pm. This view is amply supported by a series of
calculations (O.B. Brown and H.R. Gordon, 1973; Zaneveld et al., 1974).
The mentioned investigation by Zaneveld et al. (1974) has provided some
interesting results. Their assumption was that a water sample consists of a
33
102-
Index
Exponent
1.050
3.0
Index
Exponent
1.100
2.3
Fig. 11. Computed polarization components of the scattering functions; h = 419 nm,
0.02 d
20 Rrn compared with measured values (dashed lines). (After Morel, 1973a.)
< <
linear superposition of 40 components each having a specific size distribution and refractive index. By Mie computations applied t o a scattering function measured in the Sargasso Sea it is shown that the resultant index was
bimodal with conspicuous maxima at 1.05 and 1.20.
THE VOLUME SCATTERING FUNCTION
0bservations
A body of experimental data on the volume scattering function p is given
in Table VIII, supplemented by Figs. 13 and 14. These results comprise
observations in different oceanic waters, and are obtained by means of the
various types of instruments described. We distinguish between the laboratory (in vitro) method and the in situ method with a view to laying more
emphasis on the latter values.
Shape of the scattering function
The j?-curves exhibit the distinctive properties of a polydispersed system,
being smoothed in contrast t o the oscillatory curve for a monodisperse
system. The most striking feature in the curve shape is the pronounced forward scattering. The behaviour of the function at small angles is amply
illustrated in Fig. 13.
34
e x p o n e n t 2.0
10'
Fig. 12. Computed scattering function and observations for the Sargasso Sea: exponent =
2, index = 1.20, h = 632.8 nm, 4 d
39 pm. (After G. Kullenberg, 1968.)
< <
A remarkable point in Table VIII is the similarity between the forward
0-functions for most surface waters. For waters poor in particles, however,
the scattering by the water itself plays a greater part in the total scattering,
and the 0-function tends to approach the symmetrical function valid for
pure water. Convincing proof of this statement is furnished by Sasaki et al.
(1962a; Table VIII, column 6 ) and by G. Kullenberg (1968; column 12). A
group of functions derived from systematic measurements (in vitro) by
Ivanoff and Morel (1964) and Morel (1966) exhibit the change of the function from surface water to clear deep water in the western Mediterranean
(Fig. 14). The back-scattered field forms a regular pattern in this diagram.
It follows from these results that the scatterance (546 nm) by the water itself
at go", /3,,(90), makes up 13% of the total scatterance at go", /3(90), in the
surface water and no less than 70% in the deepest water. But there is in the
latter case still a large span between /3 and Po at small angles.
35
3--._
'.._
Mankovsky et aI. 119701
Morrison 119701
Nyffeler 119701
P c t z o l d 119721
5 K o p o l c v i c h and Burenkov (19721
1
2
3
L
10-31
I
0.5
0.2
2
5
10
Scattering angle 8
20
45
90
Fig. 1 3 . Comparison between different scattering functions (normalized a t 15').
10
5
1
0.5
30.
I
I
I
I
-45'
60'
75'
90"
105'
Scattering a n g l e
120'
135'
150'
Fig. 14. Family of scattering functions (30 150') for water samples of t h e western
Mediterranean ( 1 - 4 ) compared with t h e theoretical function for pure water (5). (After
Morel, 1966.)
TABLE VIII
Observations of t h e volume scattering function normalized a t 90' ;surface water except column 6
Angle 0
(O
1
1
1.5
3
5
7
10
20
30
45
60
75
90
105
120
135
150
165
180
Laboratory measurements
(1)
Hulburt (1945)
Chesapeake Bay
(2 1
(3)
Atkins and
Kozlyaninov
Poole (1952)
(1957)
English Channel East China Sea
(4)
Spielhaus (1965)
Sargasso Sea
(5 )
Ochakovsky (1966b)
Mediterranean
(6)
Sasaki e t al. (1962a)
off Japan
(white light)
(blue light)
(546 n m )
(546 n m )
600m
(576 n m )
3000m
(576 n m )
39
22
5.5
2.9
1.2
1.0
0.8
0.7
1.0
1.2
30
14
3.8
1.8
1.8
1.0
1.1
1.o
1.4
1.8
247
61
22
8.5
3.0
1.4
1.o
1.o
1.2
1.5
2.2
3.1
232
62
18
6 .O
2.5
1.5
1.o
0.82
0.67
0.90
(blue light)
7,200
10,000
1,100
830
312
62
22
6.9
3.1
1.8
1.o
0.49
0.44
0.50
22
6 .O
2.7
1.6
1.o
1.o
0.9
1.o
230
57
12
7.7
4.6
2.3
1.o
0.9
0.8
0.8
0.9
TABLE VIII ( c ontinue d)
Angle 6'
(O
1
1
1.5
3
5
7
10
20
30
45
60
75
90
105
120
135
150
165
180
In situ measurements
(7)
Jerlov (1961)
east North
Atlantic
(81
Tyler (1961a)
Californian
coast
(9 )
Duntley (1963)
Lake Winnipesakee
(10)
Bauer and
Ivanoff (1965)
off Monaco
(11)
Bauer and
Morel (1966)
The Channel
Mediterranean
(12)
G. Kullenberg (1968)
(465 n m )
(522 n m )
(522 n m )
(546 n m )
(546 n m )
465 n m
640 nm
loo*
29
9
3.5
1.2
26,100
8,500
2,990
1,300
500
118
29
8.2
4.4
2.09
1.24
1.00
0.97
1.14
1.37
1.72
1.82
4,000
2,500
1,500
900
380
69
22
8.7
3.05
1.57
1.00
0.89
0.93
1.12
1.38
1.67
14,000
1,300
292
74
23
7.5
2.96
1.72
1.oo
0.95
1.05
1.30
1.55
1.90
67
20
6.7
2.7
1.51
1.00
0.91
0.94
1.05
1.18
1.38
1.49
319
63
21
6.7
2.81
1.49
1.00
0.81
0.76
0.78
0.82
0.86
Sargasso Sea
* Normalized.
w
4
38
I
I
1
I
I
1 I I I I I
1
I
10
20
Scattering angle eo
5
1
1
40
I
I
I
60
I
I
90'
Fig. 15. Particle scattering functions obtained by deducting t h e theoretical function from
the measured function.
1 = Baltic surface, G. Kullenberg (1969); 2 = Mediterranean, Bauer and Morel ( 1 9 6 7 ) ;
3 = Atlantic surface, Jerlov ( 1 9 6 1 ) ; Gibraltar, 1 0 m depth, G. Kullenberg and Berg Olsen
( 1 9 7 2 ) ; 4 = Sargasso Sea, 10 -75 m d e p t h , G. Kullenberg (1968); western Mediterranean,
100 m depth, G. Kullenberg and Berg Olsen (1972).
Particle scattering
In this context we shall deal with the observed difference between total
scatterance and pure-water scatterance. Fig. 15 is a condensation of results
of different investigators, and indicates that the shapes of the function for
different water masses are fairly congruent. It would seem that the significant characteristics of particles do not show radical variation in the ocean.
Atkins and Poole (1952) suggest that the scattering within the region
20-155" is due chiefly to refraction through large transparent mineral particles, whereas refraction through organic matter due to its low refractive
may be responsible for the scattering through smaller angles. The
39
preponderance of forward scattering is also ascribed by Duntley (1963) to
refraction of rays by relatively large particles of biological material that have
a low relative index of refraction.
It is necessary, however, not t o overlook the effect of diffraction.
Through theoretical and experimental studies of size-graded fractions of
inter alia, quartz and coal dust suspended in water, Hodkinson (1963) has
demonstrated that the forward scattering is diffraction-dominated. Diffraction is of the same magnitude as refraction reflection at 15" even for
quartz, and at 30" for coal. The forward scattering is thus determined chiefly
by the size of particles, very little by their shape and fairly little by their
composition.
+
Brillouin scattering
When the spectral fine-structure of Rayleigh-scattered light from a liquid is
examined, it is found t o consist of three lines. One of these is at the frequency of the incident irradiance, the others are a symmetrical pair, the
Brillouin doublet (see: Cummins and Gammon, 1966). If F, is the scattered
flux in the central line, and 2 F b is the total flux in the Brillouin doublet it
was shown by Landau and Placzek (1934) that:
For pure water and pure sea water c p / c , = 1.01 and the central line is very
weak. Light scattered by suspended particles contributes only t o the central
line. Measurement of the Landau--Placzek ratio therefore gives a direct
measure of particle scatterance. The method has been tested on sea-water
samples by Stone and Pochapsky (1969): it is not suitable for routine work.
Scattering in coastal waters
Coastal waters are influenced by land drainage and are often supplied with
large quantities of terrigenous material. In consequence, they are likely t o
show less regular features than do offshore waters. It suffices t o state that
measurements in coastal regions (Jerlov and Fukuda, 1960; Pickard and
Giovando, 1960; Tyler, 1961a; Hinzpeter, 1962; Spielhaus, 1965;
G. Kullenberg, 1969; Morrison, 1970; Petzold, 1972) most often show more
pronounced forward scattering than does the general oceanic function.
TOTAL SCATTERING COEFFICIENT
When evaluating the total scattering coefficient by the integral:
f
b = 27~
0
p ( 0 ) sin 8 d8
[211
40
TABLE IX
Percentage of the scattering coefficient for different angular intervals
Surface ocean waters
Angle 8
Percentage
1
2
3
4
5
10
Angle 8
Percentage
(" )
(O)
22
38
47
54
59
73
15
20
30
45
90
180
79
84
90
92
98
100
the scatterance at small angles becomes crucial. It is demonstrated in Table
IX that half of the scatterance is contained within a cone of half-angle 3.5".
Considering the detailed procedure in determining small-angle scatterance, a
more feasible way t o arrive at absolute values of the total scattering coefficient would be t o use an integrating meter. Some values of b obtained in
this way are discussed later (see Table XV).
The regular behaviour of the angular dependence of scatterance suggests
that the total scattering coefficient b could be represented by scatterance
through a certain angle. Jerlov (1953a) studied the particle content in different oceans with the aid of scattering measurements through 45", and proved
by computation from available values of the scattering function that a linear
correlation exists between p(45) and the total scattering coefficient, b . The
apparent constancy of the ratio P(45)lb has been corroborated by Tyler
(1961b) for prepared stable suspensions and by Beardsley Jr. et al. (1970)
for Pacific waters. The ratio has been quite useful on account of the relative
ease by which p(45) can be measured. Some difficulties are involved in evaluating b for which the small-angle scattering plays such a leading role. Judging
from the data summarized in Table X the oceanic average of 3.2 is identical
with the ratio of 3.2 found for a suspension of quartz particles (Hodkinson,
1963). As the nature and size distribution of particles in coastal waters are
often specific, the ratio usually deviates largely from the oceanic value
(Morrison, 1970; Petzold, 1972). The search for small angles representative
of the whole scattering shouId obviously be rewarding because of the strong
forward scattering. Kopelevich and Burenkov (1971), and Mankovsky (1971)
recommend an angle of 4" which is supported from a theoretical viewpoint
by Morel (1973a).
DISPERSION OF SCATTERING
Wavelength selectivity of scattering by sea water arises from the following
three agencies:
41
TABLE X
Ratio of scatterance through 45' t o total scattering coefficient, p( 4 5 ) / b
Upper layer of the ocean
~~
Area
Wavelength
(nm)
Ratio
Sargasso Sea
Atlantic
Mediterranean
4 6 0 ; 650
4 6 5 ; 625
545
633
East China Sea
Black Sea
Baltic Sea
450
3.5
3.4
3.5
2.9
2.3
3.3
3.4
2.1
460 ;650
(x l o 2 )
Reference
G . Kullenberg ( 1 9 6 8 )
Jerlov ( 1 9 6 1 )
Ochakovsky (1966b)
G. Kullenberg and Berg Olsen ( 1 9 7 2 )
Mankovsky ( 1 9 7 1 )
Kozlyaninov ( 1 9 5 7 )
Mankovsky (1971)
G. Kullenberg ( 1 9 6 9 )
(1)Scattering by the water itself ( P o ) .
(2) Scattering by small-sized particles.
(3) Absorption by particles.
The highly selective (A-*) water scattering accounts for selectivity, according t o the value assigned Po in the total scatterance /3 at a given angle. This
influence is important in the back-scattered field for clear waters, but practically disappears at small angles for all natural waters.
The constellation between particle scatterance, size and wavelength in
Burt's diagram (Fig. 10) states that spectral selectivity occurs for sizes below
l p m . It is shown in the preceding text that the cross-section of small particles is believed to be of minor magnitude. This would imply that selectivity
due t o size is relatively small.
One may well be apprehensive about attributing selectivity solely t o size.
Due regard should be paid to the fact that scattering is associated with
absorption in the particles. This brings up the theme of coloured particles in
the sea, manifest, for instance, in discolourations due to abundance of organisms with specific colour (Chapter 13, p. 172). It is often found that the scatterance shows an irregular trend over the spectrum as illustrated in Table XI.
Evidence of higher scatterance in the red than in the blue is given by Jerlov
(1953a) (Table XII). These scattering objects which looked red also by visual
observation were encountered between 500 and 1,500m in the central
Pacific as a peculiar phenomenon at two stations only. For the rest it was
found that p(45) for particles is nearly the same at 465 nm and at 625nm.
Zaneveld and Pak (1973) have measured a t 45" an appreciable selectivity of
/3(436nm)@(546nm) = 1.10-1.45 (cf. Table XI). Similarly results were
obtained by Morel (1973a) who determined this ratio at 1.3. Observations
with different instruments in the Baltic also indicate that scatterance
(p(45) and b ) is dominant in the green (G. Kullenberg, 1969; H$jerslev,
1974a). Finally it may be added that for high angles wavelength dependence
of scattering appears in most cases.
42
TABLE XI
Dispersion of the scattering function in surface water off Plymouth
(After Atkins a n d Poole, 1954)
ppo) ( 1 0 - ~ ~ - ' )
p(45) ( 1 0 - ~ m - : )
blue
green
red
blue
green
red
81
I0
71
48
76
54
19
16
16
10
11
10
TABLE XI1
Scattering coefficient for the red and the blue: Pacific station (00'02'N 152'07'W)
(After Jerlov, 1953a)
Depth
(m)
0
25
49
74
98
147
197
295
Scattering coefficient
m-l)
blue
red
54
51
45
51
44
25
31
47
51
50
41
46
35
22
30
43
Depth
(m)
Scattering coefficient
(1o - ~
blue
394
492
590
787
984
1431
1918
2385
24
24
21
* 28
27
21
19
13
red
24
21
23
28
30
30
19
11
MULTIPLE SCATTERING
Multiple scattering involves the irradiation of every volume element of the
water not only by the original beam but also by light scattered from all other
elements, so that the light is scattered several times. The effect of multiple
scattering increases with the particle concentration and with the size of the
irradiated volume. Hartel's (1940) theoretical model based on the Mie theory
considers successive angular distributions for each successive order of scattering. Experimental facts match the predictions of the theory for spherical
particles in high concentrations. A comprehensive review of multiple scattering is presented by Woodward (1964).
Owing t o the small volumes and the low particle concentrations studied in
scatterance meters, multiple scattering is minute and can in most cases be
neglected. Nevertheless, studies on turbid media may help elucidate the scattering mechanism and thereby contribute t o understanding of scattering of
natural radiant energy in the sea. Timofeeva (1951b, 1957,1974) has contributed extensive laboratory investigations on concentrated suspensions, and
43
has demonstrated the change towards isotropic scattering when absorption
becomes small compared to scattering. Similar model experiments have been
conducted by Blouin and Lenoble (1962), who in particular applied the
radiate transfer approach to their results.
POLARIZATION OF SCATTERED LIGHT
Polarization, in addition to absorption and scattering, is a manifestation of
the interaction of light with matter. Properly speaking, we have to deal only
with unpolarized light and elliptically polarized light. In the unpolarized
state there is no preferred direction in the plane of oscillation of the electric
(and the magnetic) vector. Elliptical polarization implies that the terminus of
the electric vector describes an ellipse in this plane. Circular and linear polarization are special cases in which the ellipse degenerates into a circle and a
line, respectively. The partially polarized light which is usually encountered
in nature, is a mixture of unpolarized and polarized light.
Theory
Since polarization occurs in reflection and refraction processes at interfaces, it is not surprising to find polarization arising from the more complicated processes of scattering. The following simple reasoning may give some
insight into the nature of polarization for small particles (small with respect
to the wavelength) or scattering centres which produce isotropic scattering.
If Ill
and I L are the intensities of light scattered parallel and perpendicular to
a plane through the incident and scattered beams, the total intensity of light
scattered through angle 8 will be:
+
I = Ill I,!
By definition, the degree of polarization p is given by:
Simple geometric considerations show that:
IL = A 2
Il
=lA’ cos28,
[221
and thus that:
This formula was derived by Rayleigh and can also be deduced from the
Mie formula (eq. 13). It provides for a symmetrical p-curve and for complete
polarization at 8 =
The electric vector oscillates in a plane perpendicular
to the plane of vision. From the above equation it also follows that:
.4
44
I = 1(4n)(i
+ cos2e)
v41
which is valid for isotropic scattering centres.
Eqs. 23 and 24 are not strictly applicable t o water. It is a well-known fact
(Raman, 1922) that pure water permits only partial polarization at 8 =
The anisotropy of the scattering centres may be accounted for by adding to
eq. 22 an unpolarized intensity 2B2 scattered uniformly over all directions
(Dawson and Hulburt, 1941). We then have:
.4
I , = A' + B2
Ill
= A2 cos28
+ B2
It is now convenient t o introduce a polarization defect term 6 defined by:
This may be reexpressed as:
6 =
B2
-A~ B~
+
from which it follows that:
p(3n) =
1-6
1+6
~
The corresponding expression for the intensity may thus be written:
which is valid for pure water. Reliable measurements have determined 6 t o
be 0.090 which yieldsp(4.) = 83.5% (Morel, 1968).
The Mie computations which have been discussed at some length give the
and I L . Illustrative examples of these
scattering function as the sum of Ill
separate components are adduced in Fig. 11.
Mie's formal solution for spheres predicts that the scattered light is generally elliptically polarized, even if the incident beam has linear polarization.
For particles having linear dimensions about equal to the wavelength, the
polarization curve p ( 8 ) is not symmetrical; with increasing size it develops a
disordered series of maxima and minima which have no simple interpretation. The dispersion of polarization behaves in a similar irregular way. The
degree of polarization for a suspension will depend on several particle characteristics of observation besides the angle, namely: (1)composition, or rather
refractive index; (2) shape; and (3) size; generally the degree of polarization
is less for large particles than for small.
However, more significant information about the nature of scattering
objects is contained in the Muller or scattering matrix. The state of a light
beam is completely specified by the four Stoke parameters which may be
45
combined into a vector. Scattering is described as a matrix multiplication
(Chandrasekhar, 1950) :
(Z,Q,u,V) = const. F ( I o ,Qo ,uo ,Vo)
The matrix F has sixteen independent elements and is only dependent on
the properties of the scattering medium:
a1
bl
b,
b,
c1
a2
b4
b6
c3
c4
a3
b2
c5
c6
‘2
a4
The scalar scattering function is given by :
P ( 0 ) = +(a1 + bl + c1 + a21
1291
and the polarization produced by the scattering of an unpolarized beam:
P ( 0 ) = (a1 + bl - c 1 -a2)l(a, + bl + C l + a21
~301
For a medium which is isotropic and free of optical activity the matrix
reduces t o the simple form with six independent coefficients only (Perrin,
1942):
a,
b,
0
0
b,
a2
0
0
0
0
0
0
a3
6,
-62
a4
11311
The role of the scattering matrix has been discussed and interpreted by
several workers; we shall revert t o this subject in the next section.
Measurements
Polarization of scattered light is studied principally by meaw of a scatterance meter provided with a polarizing prism between the scattering volume
and the detector (Fig. 16). Ivanoff (1959) in particular has explored the
possibility of employing the scatterance p(90) and the degree of polarization
p ( 90) as independent parameters for characterizing water masses. A diagram
shown in Fig. 17 (Ivanoff, 1961) summarizes data collected in waters off
Monaco. The two limiting straight lines converge t o a point characterized by
p = 8876, which value thus represents pure water. If mean values are taken, a
linear relationship between /3 and p is obtained.
Timofeeva (1961, 1974) has made extensive studies of the polarization of
turbid suspensions. The angular distribution of the degree of polarization
46
1.5 I
I
I
I
I
1
I
-.
PHOTOMULTIPLIER
-0.5 1
LO
I
50
I
60
I
I
70
80
p%
I
90
Fig. 16. Principal design of laboratory polarimeter. (After Ivanoff, 1959.)
Fig. 17. Relation between scatterance p(90) and degree of polarization p ( 9 0 ) for waters
off Monaco. (After Ivanoff, 1961.)
does not conform to eq. 23 in this case. Polarization observations in the sea,
on the other hand, prove that maximum polarization occurs near 90" regardless of wavelength (Chapter ll),and that the angular distribution is best
described by the symmetrical eq.23. This is supposed by laboratory
measurements carried out by Hinzpeter (1962) and Sugihara and Kawana
(1973). Pavlov and Grechushnikov (1966), who have considered several
aspects of the underwater polarization problem, believe that the observed
symmetry arises from dominance of polarization produced by the water
itself.
All quantities in the scattering matrix are directly measurable in a polarimeter as in Fig.16 modified by mounting on the light source a polarizer capable of producing four different polarizations. Test results of the method
have been assessed especially by Pritchard and Elliott (1960) and by
Rozenberg et al. (1970). Beardsley Jr. (1968a) has measured all sixteen
elements on sea-water samples and concludes that those corresponding to the
diagonal terms a , , a 2 , a3 and u4 are significantly larger than the other
elements over almost all values of 6. A study of the matrix for polydisperse
systems of irregular, randomly oriented particles by Holland and Gagne
(1970) shows that the scatterance of such systems is quite consistent with
that theoretically derived for spherical particles except in the back-scatter
region where - as mentioned - considerable deviations occur. The matrix
has the symmetric character (eq.31) typical for an isotropic medium. Experimental analysis of the matrix for ocean water made by Kadyshevich et al.
(1971) and Kadyshevich and Lyubovtseva (1973) indicate, on the other
hand, that all elements in the matrix except c3 and c6 differ from zero. For
one thing they point out that the polarization parameter p(25-35) shows
large variations whereas p (90) is quite stable.
CHAPTER 3
BEAM ATTENUATION
THE ATTENUATION PROCESS
So far we have treated scattering as a separate phenomenon. The next step
is t o consider the attenuation resulting from the combined action of
scattering and absorption. A study which considers the fundamental features
in the attenuation process has been reported by Duntley (1963). The experiment deals with the angular distribution of radiance at different distances
from a uniform, spherica1,underwater lamp. The distribution curves in Fig. 18
show the existence of direct image-forming light; images are formed by
photons transmitted without being scattered between the lamp and the
receiver. The non-scattered or monopath irradiance E , at normal incidence at
a distance r from a lamp of intensity I is attenuated according t o Allard's law:
E, = Ie-''/r2
The distribution of scattered light appearing in Fig. 18 brings out the
pronounced forward scattering, common t o natural waters. This is seen as a
glow of light surrounding the lamp. The total light is the sum of the nonscattered (mono-path) and the scattered (multi-path) irradiance. Obviously,
the latter component becomes dominant at large lamp distances.
Further aspects of the characteristic transmission process are given by
Oo)oOO
r-----
n
1 L15' 12'
Fig. 18. Angular distribution of apparent radiance for different distances from a uniform
spherical lamp. (After Duntley, 1963.)
48
Replogle Jr. and Steiner (1965), who conclude that the scattered and unscattered components of light are separable. The unscattered light produces
images with angular resolution at least as small as 1'.
BEAM TRANSMITTANCE METERS
Principal function
The simple principle of the beam transmittance or attenuance meter is to
produce a parallel beam of light which, after passing a water path of fixed
length, impinges on a detector, usually a photocell. The performance of the
meter is improved by high collimation of the beam. With an optical system
of the type shown in Fig. 5, the divergence is minimized so as to become
negligible (Duntley, 1963).Obviously, a laser beam provides a perfect solution
to this problem.
WINDOW
I
LAMP
+ I
LENS/+WATER
FILTER
CELL
' 4
4
PATH-PILENS
DIAPHRAGM
Fig. 19. Typical design of in situ beam transmittance meter. (After Joseph, 1949a.)
The beam transmittance meter is designed for the purpose of measuring
attenuation coefficient, defined as absorption coefficient plus total scattering
coefficient. Therefore, the meter must be highly efficient in excluding the
scattered light. No meter could conform to this ideal requirement, because
the detector must have a reception cone of finite magnitude. This may be
critical on account of the strong scattering through small angles. The errors
due to this shortcoming of the meter have been discussed by Gumprecht and
Sliepcevich (1953), Williams (1955), Jones and Wills (1956), Jerlov (1957),
Preisendorfer (1958), and Duntley (1963). In particular, Gumprecht and
Sliepcevich have closely investigated the dependence of the meter's geometry
on the transmittance measurements. With a lens and a diaphragm in front of
the detector, the acceptance angle 20 is defined by (Fig. 19):
tgO = r / f
where r = radius of the aperture of the diaphragm and f = focal distance of
the lens.
In order to assess the effect of forward scattering, we tentatively put
r = 0.9 mm and f = 50 mm. The half-angle of acceptance 0 is then about 1".
For ocean water, about 7% of the total scattering occurs in the interval
0-1". This entails a systematic error of 4% in the attenuation coefficient for
49
blue light. It is obvious that the error can be reduced by simple means t o a
level which does not affect the accuracy of the results.
Laboratory meters
The precautions which should be taken with the water samples were
discussed on p. 14. A severe complication in most laboratory measurements
arises from total reflection from the walls of the sample tubes (Cooper, 1961).
The reflected light generates scattered light which enters the aperture of the
detector. If the tube is long compared with its width, even direct reflected
light may be recorded.
The remedy for this shortcoming would be t o use baffled tubes or t o place
the tubes in water, in which case the scattered light virtually disappears and
total reflection does not interfere.
For the measurement of low attenuance by ocean water, a long geometric
light path is desirable. Attempts have been made t o adapt spectrophotometers
t o meet this requirement. Lenoble and Saint-Guilly (1955) have studied the
attenuance of distilled water in the ultra-violet region by means of a spectrophotometer which can be provided with tubes of alternatively 1m and 4 m
length. Burt (1958) has modified a Beckmann DU Quartz Prism Spectrophotometer for work at sea using a 50-cm cell assembly.
lnitial experiments with laser light of different wavelengths have been
conducted by Knestrick et al. (1965). They utilized an optical path of no less
than 36 m in a model basin containing filtered Potomac river water. Careful
tests proved that scattered light did not contribute t o the measured signals.
In situ meters
N o further arguments seem t o be necessary for giving preference t o in situ
measurements which involve properties of the natural environment. The in
situ transmittance meter has for a long time been an effective means of
studying the optical properties especially of coastal waters. If furnished with
an adequate depth-sensing unit, the instrument yields records of transmittance as a function of depth even in rough weather.
The meter depicted in Fig. 19 (Joseph, 1949a) has served as a prototype
for several later models. Various designs which differ in technical details
have been described by Nishizawa and Inoue (1958), Fukuda (1958), Sasaki
et al. (1958b), Tyler e t al. (1959), Ochakovsky (1960), and Ball and LaFond
(1964). As a rule, the entrance window of the photocell unit is made smaller
than the width of the beam. Baffles mounted along the light path are used t o
reduce the disturbing effect of daylight. Following the original idea of
Pettersson (1934), some workers have utilized reflection against one or
several plane mirrors in order t o secure a long light path without employing
an instrument of unmanageable length (Wattenberg, 1938; Timofeeva, 1960).
50
It is advantageous t o use a prism in order t o separate the incident and the
reflected beam (Nikolayev and Zhil'tsov, 1968). Improvement of sensitivity
is achieved by introducing concave mirrors. Paramonov (1964) uses one
concave mirror in connection with close baffling of the incident as well as
the reflected beam. An optical path of 1 0 m , suitable for observations in
ocean water, can be attained by multiple reflections between three concave
mirrors of equal curvature (Jerlov, 1957).
It is expedient t o employ the signal obtained with the meter in air as a
check. The ratio of the signal for water t o that for air is, within wide limits,
independent of the emission of the lamp. It should be observed that by
submerging the meter the reflection losses at the windows are appreciably
diminished. Another effect which may increase the signal is that any existing
divergence of the beam in air will be reduced in water because of a predictable
change of the refraction a t the window of the lamp unit. This effect does not
appear if the total beam flux is received by the detector in water as well as in
air. Nor does it exist for meters which employ a highly collimated beam,
e.g., Sorensen and Honey (1968), a laser (G. Kullenberg et al., 1970) or a
cylindrically limited beam as shown in Fig. 3 (Petzold and Austin, 1968).
The latest technical developments have chiefly been directed toward the
improvement and perfection of lamp units, electronic equipment and signal
transmission systems (see e.g., Kroebel and Diehl, 1973). Not until recently
have efficient solutions of the problem of measuring the whole c-spectrum in
situ been presented. The instrument described by Matlack (1974), and used
by him down to great depths in the ocean, utilizes a grating monochromator
t o scan in the range 385-565nm. A folded water path, 7.5m in length, is
obtained by eight traversals of a three concave mirror White optical system.
In Lundgren's (1975) meter the length of the water path can be chosen at
0.5, 1.0 or 1.5 m. Employing two circular wedge interference filters it scans
in the interval 340-400 or 400-730 nm. The beam divergence is minimized
t o 0.4" and the receiver acceptance angle t o 0.5", both in water.
In general, the performance of transmittance meters is reliable. Here
attention is called only t o a treacherous error which may appear when the
meter is lowered through a sharp discontinuity layer: if the beam is not quite
horizontal due t o drift of the meter, it is deviated by refraction, and a false
maximum in c is recorded (Fig. 20).
Precise, absolute calibration of transmittance meters is a difficult problem
because of the difficulties in obtaining and maintaining water with accurately
known optical properties. With a suitable optical system the changes in
reflection losses at the windows due t o submersion can be calculated, and an
air reading used as a calibration (Petzold and Austin, 1968). For a doublebeam instrument with equal geometry in each beam most calibration problems are avoided. Such meters with different details of design have been
suggested by Joseph (1950), Nishizawa and Inoue (1964) and Matthaus
(1965).
51
15
20
1
Fig. 20. Comparison between t h e depth profile of t h e scattering coefficient b and t h a t of
the attenuation coefficient c (red light) in t h e Great Belt. Note t h e false maximum in c
a t 10 m .
Finally, we should point out the usefulness of towed meters (Joseph,
1955; Dera, 1963), which allow data t o be taken while the ship is under way.
Absorption meter
We have discussed at some length the observable parameters b and c. In
order t o check the fundamental equation c = a b it is equally necessary t o
find accurate values of a. Simple instruments which directly measure an in
situ absorption coefficient have been devised and described by Gilbert et al.
(1969) and by Bauer et al. (1971). The meter consists of a point source of
light and an irradiance meter placed at an optimal distance from the source
with its cosine collector perpendicular t o the light beam. The principle of the
meter is based on measurements by Duntley (1963) (see Fig. 18) and may be
simply expressed as follows: when the acceptance angle of the irradiance
meter is close t o 0" (collimated beam), c is recorded; when it is close t o 180",
all forward scattered light is received by the collector and an a-value sufficiently accurate for practical purposes is recorded.
It is a matter of course that the absorption coefficient also displays close
relationships with the apparent optical properties and in consequence can be
derived from these parameters (Chapter 7).
+
ATTENUANCE OF SEA WATER
Attenuance of pure water
A basic effect is due t o the water itself. Progress in the investigation of
this factor has been relatively slow, since the measurements - in common
52
with scattering measurements - are handicapped by the manifest difficulty
of preparing pure water.
James and Birge (1938), Hale and Querry (1973), Ivanoff (1974) and
Morel (1974) have given surveys of measurements in this field. In spite of
recurring instrumental defects, the results of these observations give evidence
of the principal mechanism of attenuation. The blue is most penetrant
whereas the red is strongly attenuated; there is a salient fall in transmittance
from 580 to 600nm.
TABLE XI11
Observed transmittance and attenuation coefficient, and theoretical scattering coefficient
for pure water
Wavelength
(nm)
375
400
425
450
475
500
525
550
575
600
625
650
675
7 00
725
750
775
800
Transmittance
(% m-')
Attenuation coefficient
Scattering coefficient
m-')
1
1
3
95.6
95.8
96.8
98.1
98.2
96.5
96.0
93.3
91.3
83.3
79.6
75.0
69.3
60.7
29
9
9
18
2
89.7 (580 n m )
75.2
73.7
70.4
64.5
52.3
17
7
7
rn-'
45
43
33
19
18
36
41
69
91
186
228
288
367
500
1,240
2,400
2,400
2,050
2
109 (580 nm)
272
305
351
438
648
1,750
2,680
2,630
7.68
5.81
4.41
3.49
2.76
2.22
1.79
1.49
1.25
1.09
1 = Clarke and James (1939); 2 = Sullivan (1963); 3 = Morel (1974).
It is generally thought that Clarke and James (1939) have been successful
in preparing pure water. The accuracy of their measurements is supported by
the fact that the values (Table XIII) agree fairly well with the apparent
optical properties of clear sea water. A comparison between attenuance and
scatterance proves that the attenuance is primarily an absorption effect. On
account of selective absorption, water acts essentially as a monochroinator
of blue light; an absorption maximum occurs at 750-760 nni.The possibility
of narrow-band fluctuations of the attenuance is investigated by Drummeter
Jr. and Knestrick (1967). They found three discernible but very shallow
53
absorption bands a t about 470, 515, and 550nm. The one a t 5 1 5 n m is
indicated in Clarke and James' observations. It is also obvious from in situ
spectral measurements (386-555 nm) carried out by Matlack (1974) that a
weak absorption band exists around 520 nm (see further Chapter 10).
The c-measurements on pure water are most ciritical in the range of the
large gradient dc/dh. Comparison between spectral curves obtained by Clarke
and James (1939) and by Sullivan (1963), respectively, reveals that they
agree at 580 nm but deviate considerably at 600 nm (Table XIII). Hulburt's
(1945) c-values, which are often used, are intermediate between the curves in
this range but they are decidedly too high in the shortwave part of the spectrum. It seems urgent t o reinvestigate the attenuation of pure water in the
red by means of an instrument with high resolution.
Fig. 21. Absorption curve of pure water for the infra-red.
In the infra-red range scattering can be disregarded compared t o absorption, and the determination of attenuance reduced t o an absorption measurement. In the distant infra-red difficulties arise in defining precisely the thin
layers of water required for the absorption measurements. The infra-red
attenuance is represented in Fig. 2 1 by observations of the absorption
coefficient in the region 0.7-2.5 pm published by Curcio and Petty (1951).
The general increase of absorptance towards longer wavelengths is associated
with the occurrence of several absorption bands due t o fundamental vibrational states of the water molecule or t o combinations of these.
The determination of ultra-violet attenuance encounters difficulties and
necessitates great precautions on account of the strong scattering and absorption arising even from traces of contaminations. The coefficients for the
interval 220-400 nm obtained by Lenoble and Saint-Guilly (1955) d o not
54
agree well with the values in TableXIII but are definitely greater. The
significant results that arise from their study are the high transparency in the
distant ultra-violet, which is consistent with radiance and irradiance measurements, and the absence of any absorption bands.
Little evidence is as yet forthcoming about the influence of temperature
on the attenuation of radiant energy by pure water, at least for temperatures
occurring in the sea. According t o Collins (1925), there are no clear indications that the absorptance in the region 700-820nm changes when the
temperature is raised from 0.5 t o 26°C. Increasing the temperature t o 95°C
brings out a clear temperature dependence in the infra-red inasmuch as the
intensities of the absorption bands are enhanced and the positions of their
maxima are slightly shifted toward shorter wavelengths. New and more
complete studies on light attenuation by pure water are needed t o ascertain
the magnitude of the effect of sea-water temperatures.
Attenuance of pure sea wafer
The question arises whether addition of sea salts to pure water causes a
change in attenuance. Judging from data in Table I1 a small salt effect would
appear at short wavelengths. After Berkefeld-filtering of clear ocean water,
Clarke and James (1939) found no palpable differences between the
attenuance of distilled water and that of the ocean water. Corroboratory
results are presented by Sullivan (1963), who compared the absorption of
distilled water with that of artificial sea water in the interval 580-790nm.
The substantive conclusion is that sea salts exert little influence on light
attenuation. Nor d o they act as absorbing media in the infra-red, as is shown
by the careful investigation of Visser (1967). The role of the salts in the
ultra-violet has been studied by Lenoble (1956a). They seem t o cause a weak
absorption which slowly increases toward shorter wavelengths without
revealing the presence of absorption bands. These findings are supported by
the observations of Armstrong and Boalch (1961). Below 2 3 0 n m a heavy
absorption by the bromide ion sets in (Ogura and Hanya, 1967).
Attenuance of particles
While pure sea water of given temperature displays an invariant light
attenuation, other optically active components contribute a variable part t o
the attenuation of ordinary sea water. Attention is first drawn t o the particulate matter which is found in highly variable concentration in the sea.
There is reason to believe that the attenuance caused by a mixture of
particles of different composition would iiicrease toward shorter wavelengths.
Experimental evidence is furnished in particular by Burt (1958), who made
measurements at thirteen wavelengths on samples drawn from the surface
down t o 1,170 m in the eastern tropical part of the Pacific Ocean. He was
55
also successful in securing uncontaminated filtered samples of ocean water,
for which the absorption coefficient due t o dissolved substances was determined. By deducting this coefficient from the total attenuation coefficient
we arrive at values of the attenuation coefficient due t o scattering and
absorption of particulate matter. The essential feature in the wavelengthselective attenuation by particles is brought out by the curve in Fig. 22
which is derived from Burt’s observations in fairly turbid water. Even if
scattering shows some dependence on wavelength (p. 42), the major part
of the selective effect is due t o absorption. Similar absorption curves for the
French Atlantic coast exhibit a steadily increasing coefficient from 0.5 at
700nm t o 1.0 at 3 5 0 n m (Morel, 1970). When phytoplankton is abundant,
the spectral changes imposed by chlorophyll may be decisive for the
absorption curve.
Fig. 22. Light attenuance caused by particulate matter. (After Burt, 1958.)
A bsorptance of dissolved organic substances
The optical action of the numerous organic substances dissolved in sea
water is gradually becoming known. In a classical investigation, Kalle (1938)
proved the significant role of soluble humus-like products which are yellow
and some of which fluoresce in the blue when excited by ultra-violet radiation. The present state of research on this complex mixture of compounds,
known under the collective name of “yellow substance”, is summarized by
Kalle (1962, 1966). Yellow substance is formed from carbohydrates by a
“Maillard” reaction. The formation is favoured by heat, alkalic reaction and
the presence of amino-acids, and leads t o end products of yellow or brown
melanoidines. Kalle concludes that in the sea, where carbohydrates and
amino-acids are present, chiefly melanoidines with fluorescent matter as a
by-product are likely t o be formed, whereas non-fluorescent pheno-humic
56
acid products of a browner colour seem t o be mostly of continental origin
(cf. Shapiro, 1957).
Large quantities of humus compounds are brought t o the sea by rivers,
especially in northern areas. Flocculation and precipitation of the fine
particulate or colloidal portion of humic matter as well as of clay and
organic detritus take place a t the conjunction of rivers with the sea
(Liineburg, 1953; Jerlov, 1953b; see Fig. 118). M. Brown (1957) has shown
that in the first place, high molecular-weight humic matter flocculates
rapidly. Jerlov (1955a) has estimated that yellow substance during its
passage and storing in the central Baltic Sea loses about 10--15% of its total
concentration. Because of its high dilution yellow substance may be treated
as a semi-conservative property in the marine environment (Duursma, 1965;
Skopintsev, 1 97 1).
Fig. 23. Absorption curve for yellow substance.
The production of yellow substance in the sea is a fact well supported by
experiments. The established presence of yellow substance in the upwelling
region west of South America proves its immediate marine origin, as this area
is practically devoid of fresh-water supply from drainage and precipitation.
An absorption curve for a high concentration of yellow substance is
adduced as a typical example of its wavelength-selective effect (Fig. 23). It
follows that yellow substance should preferably be studied in the ultra-violet.
The extension of experiments t o the far ultra-violet has proved fruitful,
57
leading t o important conclusions. Fogg and Boalch (1958) have shown that
ultra-violet absorbent substances are produced in filtrates of mass cultures of
marine algae. The occurrence of a formative process is further supported by
the finding of Yentsch and Reichert (1962) that the production of yellow
substance is inversely proportional t o the decomposition of the chloroplastic
pigments. Certain components in the yellow substance display a distinct
absorption peakat 250-265 nm (Chanu, 1959; Yentsch and Reichert, 1962).
But the absorption curve in the range 220-400nm for filtered Atlantic
water shows a trend of steady increase towards shorter wavelengths as is
evidenced by Armstrong and Boalch (1961). These workers have also drawn
attention t o the ultra-violet absorption due t o volatile organic matter,
probably of algal origin and t o some degree due t o nitrate, at least in deep
water; a slight effect of dissolved oxygen is distinguished below 230 nm
(G. Copin-Montegut et al., 1971).
I n situ determination of yellow substance
The in situ meter provided with colour filters enables us to arrive at values
of the total selective absorption due t o water, particles and yellow substance.
Joseph (1949a) has pointed out that sufficient means t o study the selective
absorption are provided by recording in two spectral ranges in the red and in
the ultra-violet. An abbreviated procedure makes a separation possible of the
selective effect caused by particles and yellow substance respectively (Jerlov,
1955a). The method implies that the absorption coefficient of yellow substance at 380 nm, a y , is expressed by the linear relation:
( c - cw )380nm - K ( c - cw 1655 nrn
-
- ay
where c, pertains t o attenuance by the water itself.
This approach assumes that the selective absorptance by particles is proportional t o the particle attenuance in the red; it is taken for granted that
the absorption of yellow substance vanishes in the red. The factor K is
dependent on the average particle characteristics and is found to be constant
for a given water mass. The usefulness of the method for the study of
Bermuda waters has been demonstrated by Ivanoff et al. (1961) and for the
Baltic sea by Hq5jerslev (1974a).
Synopsis of attenuance components
Table XIV has been prepared t o show the factors which play a part in the
attenuation by sea water and their dependence on the wavelength. It claims
only t o give general, qualitative information about the parameters involved.
Regional comparison of inherent properties
Table X V summarizes data which may serve t o illustrate the web of
relationships between the coefficients of inherent properties. These values
58
TABLE XIV
Summary of absorption and scattering characteristics (wavelength = h )
Absorption
character
Scattering
h-dependence
character
strong
invariant, small
compared t o absorption
Sea salts
negligible in the
(inorganic) visible, weak in
t h e ultraviolet
some increase
towards short h
appreciable
Yellow
substance
increase towards
short h
Water
invariant at
constant temp.
and pressure
variable
Particulate variable
matter
increase towards
short h
variable
h-dependence
variable
derive from measurements of total attenuance in conjunction with determinations of the absorption coefficient for yellow substance, a,, or the
scattering coefficient for particles, b,, or of both factors. Since coefficients
for the different components are additive, other parameters tabulated are
obtained from the relation :
c = c,
+ 6, + a, + a,
using the notations of Table XV.
In regard t o the uncertainty in the absolute values of the coefficients,
especially in b,, the data obtained by different workers may be deemed
reasonably consistent. Careful comparison is somewhat hampered by the fact
that the selectivity is assigned t o different wavelength intervals.
Some interest is focussed on the close connection between (c - c , ) ~
and~ ~
b,, or ultimately between a, and b, (Jerlov, 1974b). Understandably, these
two parameters must be intimately related for given particle characteristics,
as is also evidenced by measurements of Ivanoff et al. (1961) in Bermuda
waters. The low value of a, encountered in clear ocean water is in accordance
with the theoretical findings that small and relatively transparent particles
produce much more scattering than absorption (see Middleton, 1952, p. 36).
Regarding wavelength selectivity of attenuation, it has been established by
several investigations in different areas that a linear relationship exists
between the two parameters (c - c,)380m and ( c - c , ) ~(Fig.~ 24;~ ~
Jerlov, 1974b). This suggests that the line:
( c - CW)380
= 1.8(c - CW1655
is a good approximation for describing the wavelength selectivity of particles
~
TABLE XV
Comparison of inherent properties (m-' ) *
Region
+ b,
a, + ay
4 a p + ay)
Wavelength
c -cw
observed
b,
observed
Sargasso
Sea
Carribean
Sea
Equator
Central
Pacific
Romanche
Deep
Galapagos
440
0.05
0.04
655
440
0.06
0.09
0.06
0.06
440
0.09
0.05
0.04
440
0.12
0.07
0.05
655
440
0.11
0.24
0.07
0.08
Off Peru
(64 miles)
Galapagos
Northwestern
Galapagos
700
400
700
400
700
400
0.39
0.73
0.16
0.25
0.07
0.11
0.39
0.64
0.16
0.21
0.07
0.0s
0
0.09
0
0.04
0
0.03
Continental
slope
668
365
0.05
0.10
0.08
0
0.02
Clarke and
0.02 James (1939)
Bermuda
655
380
0.10
0.20
0.10
0.17
0
0.03
Ivanoff e t al.
0.03 (1961)
(-1
Continued on p p . 6-61,
ap
ap
Aa,
ay
observed
Aa,
Reference
0.01
0.06
0.11
0
0.04
0.00
0.03
0.04
0.16
Jerlov (1951)
0.03
0.12
0.09
0.04
Burt (1958)
0.03
m
TABLE XV (Continued)
0
Region
Wavelength
(nm)
c -cw
b,
a,+
Kattegat
655
380
655
380
655
380
0.23
0.54
0.27
1.15
0.38
1.72
0.15
0.16
0.20
0.21
0.28
0.31
0.23
0.44
0.27
0.49
0.38
0.64
South
Baltic Sea
Bot hnian
Gulf
Skagerrak
655
380
North
Atlantic
North
Sea
Baltic Sea
665
420
665
420
665
420
Sargasso Sea
633
484
440
375
0.03
0.03
0.05
0.02
655
375
0.08
0.06
0.04
0.04
Western
Mediterranean
area
b,
a,,
0.08
0.27
0.07
0.28
0.10
0.33
Aa,
0.19
0.21
0.23
ap+a,
0.08
0.38
0.07
0.96
0.10
1.41
0.3
A(ap +a,)
0.30
0.89
1.31
ay
0
0.11
0
0.68
0
1.08
0.4
0.01
0.01
0.01
0.01
0.02
0.01
0.08
0.04
0.04
0.02
0.04
0.02
0.11
0.68
Reference
Jerlov (1955a)
1.08
0.1
0
0.03
0.01
0.10
0.02
0.33
0.03
Aa,
0.03
0.09
Malmberg (1964)
Kalle (1961)
0.31
G. Kullenberg
et al. (1970)
0
Hdjerslev
(1973)
TABLE XV (Continued)
Region
Villefranche
offshore
50 m
1000 m
Coastal
Baltic Sea
Wavelength
(nm)
250
655
375
c-c,
1.98
0.65
3.42
b,
a,+
b,
a,
Au,
up f a y
0.44
A(ap+ay)
ay
0.98
0.2
1.65
0.15
0.20
0.15
0.80
0.6
Au,
Reference
G. Copin-Montegut
e t al. (1971)
HQjerslev
(1974a)
*c = total attenuation coefficient; c, = attenuation coefficient for water; b , = scattering coefficient for particles; up = absorption
coefficient for particles; uy = absorption coefficient for yellow substance; A = wavelength selectivity; c = c, f b, f up f a,.
62
-
04
~
I
E
-2 0 3
-
(D
3
The S o u n d
Ao2-
1
01
02
03
04
05
07
06
~ C - C , ) ~m-l
~ ~
08
0.9
Fig. 24. Relationship between attenuation coefficients (c - c,)
380 nm. Open circles refer to direct measurements of (c - c,).
t
I
LOO
500
600
nrn
10
'
11
12
for 655 nm and for
1
J
700
Fig. 25. Spectral distributions of the attenuation coefficient at different depths in the
Baltic Sea. (After Lundgren, 1975.)
and yellow substance in ocean waters, possibly with the exception of the
clearest waters. Three points in the diagram d o not fit in the scheme, namely
for the Kattegat, the Sound and the Baltic Sea which is attributed t o
abundance of yellow substance.
Since Clarke and James (1939) made their laboratory analysis of the
selective absorption of light by sea water, little material has been forthcoming
on the whole c-spectrum. Recent observations with an in situ c-meter in the
Baltic Sea show a group of spectral curves for the spectral range 400-700 nm
63
(Fig. 25; Lundgren, 1975); the change of shape of the curves with increasing
depth indicates that the content of yellow substance is lower at deep levels
than in the surface layer.
FLUORESCENCE
The initial research in the field of natural fluorescence of the sea was
made by Kalle (1949). For a given water mass, he found a close relationship
between fluorescence of filtered water samples and amount of yellow substance in accordance with the nature of fluorescent matter as a byproduct of
the formation of yellow substance. This is corroborated for Baltic water by
Karabashev and Zangalis (1972) and by M. Brown (1974) (Fig. 26). Fluorescence, as does yellow substance, has conservative properties. In mainland
water there is typically a higher proportion of yellow substance compared t o
fluorescent substance, and therefore the ratio of these two parameters is a
function of salinity (Chapter 14). The investigations by Duursma (1960)
further indicate that the relatively low quantities of fluorescent matter in
offshore waters are not of continental origin but are formed by breakdown
of organic material.
Fluorometers are essentially scattering meters provided with a UV lamp
(hydrogen o r mercury) together with a monochromator (or narrow-band
Fig. 26. Relationship between amount o f fluorescent matter and amount of yellow substance (absorption coefficient m-’ at 310 nm). Laboratory measurements o n water
samples from t h e Danish sounds. (After M. Brown, personal communication, 1975.)
64
I Bidirlillcd w a t e r
2 011 H a u r l l o n l o
j
3 Villelranche-rur-met
Fig. 27. Fluorescence emission spectra from various waters. Left diagram. (dfter Morel,
personal communication, 1972.) Right diagram also shows the corrected spectrum with
the Raman scatter eliminated. (After M. Brown, 1974.)
Fluorescence
0.2
T
,
2,000
3,000
L,OOO
Fig. 28. Example of the variation of fluorescence with depth in the northeastern Atlantic.
(After Ivanoff, 1973.)
filter) for defining the excitation wavelength A,, and with a monochromator
(or narrow-band filter) for measuring the fluorescent radiation at a wavelength X, (A2 > Al). Fluorescence is preferably recorded through an angular
interval around 90' where particle scattering is minimum. Fluorescence of
sea water can be determined in the laboratory with satisfactory accuracy
(see e.g., Traganza, 1969; Ivanoff and Morel, 1971). Different types of in
situ meters have been described by Duursma (1974). Like scattering meters
they suffer from interference by ambient daylight. This can be eliminated by
using a modulated light source (G. Kullenberg and Nyghd, 1971).
65
An examination of the spectral composition of the emitted light reveals
that the fluorescence of sea water comprises a rather broad and structureless
band (Fig. 27). As a main standard of fluorescence Kalle (1957) has used a
solution of 0.1 mg quinine bisulphate in 1 1 0.01 N H,S04. A promising
alternative of standard is afforded by the presence of a Raman scattering
band in the spectrum as in Fig. 27. Obviously it is advantageous t o choose
the exciting wavelength a t short wavelengths, say 310 nm, in order to avoid
too strong interference between the Raman band and t h e sea-water fluorescence band (Fig. 27; M. Brown, 1974). Similar diagrams have been
published by Traganza ( 1969). It is obligatory in fluorescence measurements
t o take necessary corrections and possible self-absorption into account
(Duursma and Rommets, 1961; Duursma, 1974).
TABLE XVI
Fluorescence (relative units)
Region
Central Baltic Sea
North Sea
Red Sea
Atlantic Ocean
The Channel-New York
Norwegian Sea
Iceland-Jan Mayen
Sargasso Sea
Tyrrhenian Sea
The Channel
North Sea
Sk agerrak
The Sound
Depth
(m)
Fluorescence
0
0
0
1.5-1.8
0.5-1.0
0.4
0
0.2-1.4
0
150
1,000
0
0
50
75
100--3,000
0
0
0
0
0.2
0.1
0.1
0.1
0.12
0.14
0.19
0.20-0.22
1-2.5
3
6.5
14
Reference
Kalle ( 1 9 4 9 )
Ivanoff ( 1 9 6 4 )
G. Kullenberg
(1967)
Some information about the regional distribution of fluorescent substance
is given in Table XVI and Fig. 28. Reference is further made to measurements
by Postma (1954); Duursma (1960);Otto (1967);Traganza(l969); Hq5jerslev
(1971); G. Kullenberg and Nygkd (1971); Yentsch (1971); Rommets and
Postma (1972) and Karabashev and Solov’yev (1973). A feature often found
in the depth profiles of fluorescence, below the well-mixed top layer of the
sea, is an increase towards greater depths. This is also the case for the Baltic
Sea (Karabashev et al., 1971; H@jerslev, 1971) and for the Black Sea
(Karabashev, 1970). But Kalle’s (1957) results from the Irminger Sea d o not
exhibit this characteristic.
66
Normally it is not necessary to pay attention t o fluorescence when
measuring the inherent properties a , b and c in ocean water. For highly
fluorescing waters it is advisable, however, to take steps t o eliminate this
effect by means of suitable blocking filters.
CHAPTER 4
GLOBAL RADIATION INCIDENT ON THE SEA SURFACE
SPECTRAL DISTRIBUTION
Before entering into a detailed study of the main theme of underwater
energy, proper consideration should be gwen to the primary energy source,
i.e., the global radiation (from sun and sky) incident on the surface of the
sea. The alteration of the sun’s radiation in the atmosphere is due chiefly to
scattering, which removes an appreciable part of the shortwave component
of sunlight. Thus two components of a different nature are formed; the sun’s
radiation is directed and covers a large spectral range from 290 to 3,000 nm,
whereas the skylight is more diffuse and is dominant in the shortwave part
of the spectrum. The spectral distribution of global radiation is only slightly
affected by air turbidity. It is little dependent on solar elevations above 15’;
at low sun heights the skylight becomes dominant which leads t o a relative
increase in the shortwave part of the spectrum (Table XVII; Fig. 29). On the
whole, clouds do not appreciably change the spectral composition in the
range 350 -800nm (Kondratyev, 1969). This is also evident from Fig. 30
showing average spectral distribution for some phases of daylight representing direct sunlight, sunlight skylight on a horizontal plane, overcast sky,
and zenith sky (Taylor and Kerr, 1941). The fine structure of the shortwave
radiation due t o Fraunhofer lines and absorption bands of water vapour and
oxygen is depicted in Fig. 31. Information about the whole spectrum
(300-2,500 nm) is presented in Fig. 74, which exhibits the most important
absorption bands caused by H,O and CO, .
The radiance distribution of a clear sky shows a marked maximum near
the sun, as is illustrated in Fig. 32. The presence of clouds is apt to change
the distribution of skylight drastically. The radiance from most overcast
skies can be represented by a cardioidal distribution according t o the empirical formula of Moon and Spencer (1942):
+
+
L ( i ) = L ( $ n ) ( l 2 cos i)
~321
In the treatment of problems of reflection, refraction and penetration of
radiant energy, it is good methodology to distinguish sunlight and skylight.
In consequence, the ratio of sky radiation t o the global radiation becomes a
significant factor. The major features in the trend of this ratio as a function
of wavelength and solar elevation are clearly brought out in Fig. 29, which
was derived by Sauberer and Ruttner (1941) on the basis of Kimball’s
70
TABLE XVII
Spectral distribution of irradiance from sun and sky in relative units
(After Kimball, 1924)
Wavelength
(nm)
Solar altitude ( )
11.3
350
375
400
4 25
450
475
500
525
550
575
600
625
650
675
700
725
750
65'
54
51
48
47
46
44
41
41
41
40
42
42
41
41
38
60'
Solar elevation
50'
40"
30'
20'
30
65
131
153
170
178
179
172
166
165
165
162
160
159
154
145
136
190
235
307
362
400
417
413
393
371
371
368
254
344
336
318
298
277
10'
50
I
LOO
,
,
I
I
500
,
I
,
I
I
600
,
1
nm
,
,'.
700
Fig. 29. Percentage of skylight in the global radiation (397--764 n m ) as a function of
solar elevation. (After Sauberer and Ruttner, 1941 .)
Fig. 30. Average spectral distribution for ( A ) zenith sky, (I?) sun C sky (horizontal plane),
( C ) overcast sky, ( D )direct sunlight. (After Taylor and Kerr, 1941.)
71
f
Fig. 31. Spectral distribution of direct solar radiation at sea level. A i r mass 1.0. Concentration of precipitable water 1 0 m m . Ozon 3.5 m m . Positions of t h e most intense
Fraunhofer lines and t h e major absorption bands are indicated.
Fig. 32. Radiance distribution for a clear sky (normalized a t zenith).
72
(1924) data. A noteworthy feature is the fact that the ultra-violet from the
sky matches that from the sun at low elevations.
POLARIZATION
The familiar facts are that the direct energy from the sun is unpolarized,
while the light from a clear sky is partly polarized. The degree of polarization is dependent on the part of the sky under observation, the solar
elevation and the air turbidity (Sekera, 1957). The polarization ranges from
M a x i r n u rn
Brewster point
Fig. 33. Neutral points in the atmosphere.
zero in the neutral points to maximum values of over 90% at about 90" from
the sun in the vertical plane through the observation point and the sun. The
position of the Arago neutral point is in the sun vertical on the antisolar side;
the Babinet point and the Brewster point are found above and below the sun
(Fig. 33). It may be added that clouds have a strong depolarizing effect.
CHAPTER 5
REFLECTION AT THE SEA SURFACE
THEORY
Reflectance for direct radiation
The reflectance for the electric vector of the radiation resolved into
components parallel and perpendicular to the plane of incidence, is given by
Fresnel's equations:
where i is the angle of incidence a n d j is the angle of refraction. The reflected
ray is in the plane of incidence and the angle of reflection is equal to i.
Since the solar radiation is unpolarized, its reflectance may be taken as a
mean value of the above quantities:
For normal incidence the distinction between parallel and perpendicular
components disappears, and the equation reduces to:
If i
+ j = 90" we have from eq.41:
tg i = n
(Brewster's law)
~361
and only light oscillating perpendicular to the plane of incidence is reflected.
This occurs at a water surface (n = 4) for i = 53.1" and in this case:
Values of the Fresnel reflectance according to the above equations are
tabulated as functions of the solar elevation (Table XVIII).
Linearly polarized light which is completely internally reflected suffers a
74
TABLE XVIII
Reflectance of radiation against a calm surface
Angle of
incidence i
( O
Reflectance (76)
1
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
PI1
PI
P S
2 .o
2 .o
1.9
1.8
1.7
1.4
1.2
0.9
0.6
0.3
0.1
0.2
0.4
1.7
4.7
11.0
24 .O
49.3
100
2.0
2.1
2.1
2.3
2.5
2.7
3.1
3.6
4.3
5.3
6.7
8.6
11.5
15.8
21.9
31.3
45.9
67.4
100
2.0
2.0
2.0
2.0
2.1
2.1
2.1
2.3
2.4
2.8
3.4
4.4
5.9
8.7
13.3
21.2
34.9
58.3
100
phase change between the parallel and perpendicular components giving rise
to elliptically polarized light. Waterman (1954) and Ivanoff and Waterman
(1958a) have proved that elliptically polarized light is detectable just below
the calm water surface in lines of sight beyond the critical angle (see Chapter
6).
Reflectance for diffuse radiation
The reflection of the diffuse component is more difficult to express quantitatively. A first approximation considers diffuse light of equal radiance
from all directions L of the sky. The reflectance p ( i ) for the angle of incidence i is taken from the Fresnel equations. It follows from the definition of
reflectance and from eq.5 that:
i p ( i)L sin i cos i d i
I
2n
)n
0
Pcl
=
p ( i ) sin 2 i d i
I
171
L sin i cos i d i
2n
0
0
[371
75
7 1
10'
0'
20'
30'
LO'
50'
60'
S o l a r c Lc v a t Io n
70'
80'
'0
Fig. 3 4 . Amount of reflected energy for different portions n of diffuse radiation in the
global radiation. (After Neumann and Hollman, 1961.)
Several workers have evaluated this integral for a smooth water surface
using Fresnel's reflectance. The consistent value is found t o be 6.6% (see
Burt, 1954a).
For the reflectance in the case of a cardional distribution of sky radiation
(eq.32), Preisendorfer (1957) has given an exact solution which yields 5.2%.
Reflectance for global radiation
W-hen dealing with the reflectance of global radiation we have to treat
separately the reflectance of direct energy or solar radiation, p s , and that of
sky radiation, pd .
The total reflectance is expressed as the sum:
Er
p = - = p,(l - n )
E
+ pdn
where E and E , are the incident and reflected irradiance respectively, and n
is the significant ratio of sky radiation to global radiation.
The result of computations of the reflected energy from eq.38 using p s values from eq.35 and p d = 0.066 and assuming the incoming radiation to
be a given function of the solar elevation, is illustrated, for example, by the
set of curves for several n-values in Fig. 34 (Neumann and Hollman, 1961).
The curve for solar radiation only ( n = 0) develops a prominent maximum at
76
t
j
-1.51
O0
30'
60'
V e r t i c a l angle i
go0
Solar zenith distance
Fig. 35. Reflected radiance L ( i ) divided by the sky radiance at zenith for calm weather
and for a Beaufort 4 wind. (After C. Cox and Munk, 1956.)
Fig. 36. Reflectance of solar radiation from a flat surface and from a surface roughened
by a Beaufort 4 wind. (After C. Cox and Munk, 1956.)
20" as well as a slight minimum at 50". The intersection point of the curves
at 29" represents the case of p s = pd = 0.066.
The assumption of uniform sky radiation is inadequate, and more realistic
approaches have been made. C. Cox and Munk (1956) have also employed a
semi-empirical model and considered a clear tropical sky on the basis of
observations at Bocaiuva, Brazil, for the sun at a zenith angle of 60". They
made the simple assumption that the reflectance is a function of the zenith
angle only, ignoring the increased radiance near the sun (Fig. 32). Their
results for clear and overcast sky conditions are presented in Fig. 35.
Effect of waves
The complete investigation of the interaction of light with the sea surface
confronts us with the additional problem of reflection from a windroughened surface. The following changes in reflection are immediately realized. With high solar elevations the angle of incidence will be increased on an
average, whereas it will be decreased for low elevations. The former effect is
not important, as the reflectance does not vary much with the solar elevation
if this is high. In contrast, the reflectance for a low sun is drastically reduced
by wave action. This principal feature was first formulated and investigated
by Y. Le Grand (1939). It appears that the reflectance is independent of the
presence of waves in some intermediate elevation interval. Burt (1954a),
employing a semi-theoretical model, actually found that such independence
occurs somewhere between solar elevations of 1 0 and 30".
77
TABLE XIX
Reflectance (%) of the sea for skylight
smooth
Uniform
Overcast
6.6
5.2
rough
Burt (1954a)
C. Cox and Munk ( 1 9 5 6 )
5.7
4.8
5 .O-5.5
4.3-4.7
The thorough interpretation of the wind effect given by C. Cox and Munk
(1956) also takes into account shadowing and multiple reflections for a low
sun. Their radiance curves in Fig. 36 demonstrate in essence that the wave
action becomes a factor for solar elevations below 20”. GriBEenko (1959)
and Hishida and Kishino (1965) have demonstratred similar wave effects at
low angles. As expected, the reflection of skylight is less affected by rough
sea (Table XIX). The computations for the atmosphere-ocean system by
Plass et al. (1975) prove that the downward flux just below the surface
always increases with wind speed, not only at small elevations but also to
some degree at high elevations. This is attributed t o the fact that with a
rough sea more radiance from the sky near the horizon can enter the water.
C. Cox and Munk point out that with an absolutely flat sea the horizon
would not be visible. Usually the sea contrasts with the sky and becomes
darker when the wind increases. The shadowing is also examined by
Lauscher (1955), who computed data which amply illustrate the irregular
reflection pattern from a wave of maximal steepness (Michell wave). The
effect of oil and natural slicks at the sea surface is to inhibit capillary and
very short gravity waves. According to C.S. Cox (1974) the presence of
monomolecular slicks affects the reflexion coefficient only slightly, but leads
to drastic change in the radiance distribution at the surface; slicked areas display low scattering and are characterized by sharp edges where capillary
waves reappear.
Glitter o f the sea
Glitter is a phenomenon bearing upon reflection of solar radiation. This
special aspect of reflection has given rise to much speculation. The glitter
pattern being open to everyone’s observation, it has in popular speech been
given poetic names such as “the road t o happiness” (Shuleikin, 1941) or
“the golden bridge” (Stelenau, 1961). The glitter arises when a flat surface is
roughened by wind and the image of the sun formed by specular reflection
explodes into glittering points. This is because water facets occur with an
orientation so as to reflect sunlight to the observer. Increasing roughness will
78
enlarge the width of the glittering band. The phenomenon is most spectacular at solar elevations of 30--35" (cf. Fig. 34). The pattern becomes narrower
when the sun sets.
The distribution of radiance of glitter has been the subject of theoretical
treatment with a view t o estimating the slopes of the sea surface. The interested reader may consult the original papers by Hulburt (1934), Duntley
(1952), C. Cox and Munk (1956), Schooley (1961), Mullamaa (1964b), and
Wu (1972). C.S. Cox (1974) reports about analyses made from a satellite
which is "moored" over the central Pacific.
Mullamaa has also considered the polarization of the reflected glitter,
which is shown t o be dependent both on solar elevation and on the direction
of reflection. The polarization at the maximum radiance is near zero at
i = 0" and increases with zenith distance to 100% at i = 35---45", subsequently decreasing t o 20% at i = 90".
CONCEPT OF ALBEDO
In order to scrutinize reflection events and secure adequate definitions,
the following symbols are pertinent:
E,, = downward irradiance in air.
E,, = upward irradiance in air.
E,, = downward irradiance in water.
E,, = upward irradiance in water.
Since reflection against the sea surface takes place from above as well as
from below, two kinds of reflectance are distinguished: (1)pa = reflectance
in air; and (2) p w = reflectance in water.
The albedo A of the sea is defined as the ratio of the energy leaving the
sea to that falling on it:
The above definitions yield the following identities
-Ewu
E,,
--Eau
E,,
Eau
= PaEad
+ E w u -pwEwu
From eq.39 the albedo may therefore be written:
A = p, + (1- p w ) --Ewu
Eaci
Some confusion in reflection studies has resulted from failure t o distinguish the reflection (at a surface) in a strict sense, namely p a , and the
albedo which is the sum of pa and the percentage of light back-scattered
79
from the sea. Furthermore, the factor p w must be accounted for. Because of
the relatively small variation of the scattering function in the back-scatter
field, we can assume in a first approximation that the upwelling light is completely diffuse and unpolarized. Because Fresnel reflection beneath the surface involves total reflection in the angle interval 48.6-go”, integration of
eq.37 yields pw = 48%. Hence it is not permissible t o neglect this factor as
most workers have done.
AUREOLE EFFECT
If an observer looks from a bridge at his shadow on the water surface, he
sees myriads of light and dark rays diverging from his head. Minnaert (1954)
explains this spectacular phenomenon as follows: “each unevenness in the
water’s surface casts a streak of light or shade behind it; all these streaks run
parallel to the line from the sun t o the eye, so that we can see them meet
perspectiveIy in the anti-solar point -- that is, in the shadow-image of our
head”.
EXPERIMENTAL VALUES O F REFLECTANCE
A selection among the multitude of reflection observations is called for.
The systematic studies of albedo as a function of various parameters made
by Anderson (1954) and For; (1954) will be our primary references. The
Lake Hefner results suggest that the albedo under clear skies is only weakly
dependent on wind speed and air-mass turbidity, including the effects of
clouds. We may infer that the albedo is primarily a function of solar altitude.
Even with a low stratus cloud cover, the dependence on the position of the
sun persists. This is consistent with the findings of Neiburger (1948), but
conflicts with earlier statements (Chapter 4).
Table XX shows the true reflectance for a flat level surface and clear sky.
These values have been drawn chiefly from Anderson’s results with due correction for the existing low shortwave back-scattering from the water of
Lake Hefner.
In rough weather it is difficult t o distinguish between the true reflectance
and the shortwave light back-scattered from the sea. White caps and air
bubbles in the surface layer contribute greatly to the albedo. Experiments
TABLE XX
Reflectance of unpolarized radiant energy (sun + s k y ) from a horizontal water surface
Solar altitude ( O )
Reflectance (5%)
90
3
60
3
50
3
40
30
4
6
20
12
10
27
5
42
have verified the reduction of reflectance at low solar elevations owing to
wave action. The present author found that a flat sea surface is a barrier to
the light from a distant lighthouse tower, whereas the reflection of this light
from a rough surface is remarkably low.
DISPERSION O F REFLECTION
It is established by observations that for solar elevation below 30' a
dependence of reflection of irradiance on wavelength is developed (Fig. 37).
Sauberer and Ruttner (1941) have given the right explanation of this effect
which - since the dispersion of light reflection is only 6% -- must be associated with the amount of diffuse light in the global light. This is 90% in the
violet and 22% in the red for a solar elevation of 10" (Fig. 29). The average
angle of incidence is thus much less for the violet than for the red, which
accounts for the stated difference in reflection.
:vi
20
10
30'
'
0
5
~
0
400
500
600
700 nrn
Fig. 37. Reflectance (%) of global radiation for different solar elevations as a function of
wavelength. Corrected for cosine error of the collector. (After Sauberer and Ruttner,
1941.)
CHAPTER 6
REFRACTION AT THE SEA SURFACE
REFRACTION LAW
The interface between air and sea is a boundary between two media of
different optical density. An electromagnetic wave falling on the surface
decomposes into two waves; one is refracted and proceeds into the sea, the
other is reflected and propagates back into the air (Fig. 38).
Fig. 38. Refraction and total internal reflection at t h e sea surface.
The law of refraction is:
sin
- -i - n
sin j
a relation known as Snell's law. The angles i and j are defined so as to describe
a refracted wave as being in the same plane as the incident wave. For definiteness we may take the refractive index n of sea water relative t o air to be
4 . From a geophysical point of view there is no need t o account for the
variation of the index with temperature, salinity and wavelength (Chapter 2,
p. 22).
For the case of grazing incidence (i = 90") a limiting angle of refraction
j = 48.5" is obtained. As seen from the sea, the sky dome is compressed into
a cone of half-angle 48.5". If they form an angle of more than 48.5" with the
vertical, upward travelling rays are totally reflected at the surface (Fig. 38).
Refraction is associated with polarization according t o Fresnel's formulae.
Direct sunlight penetrating into the water becomes partly polarized. Calculations by Mullamaa (1964a) testify that the degree of polarization increases
with the sun's zenith distance and reaches magnitudes as great as 27% during
sunset.
82
The linearity of skylight polarization remains unchanged by refraction
though there is a rotation of the plane of oscillation.
CHANGE O F RADIANCE AND IRRADIANCE AT THE SURFACE
It follows from simple geometrical considerations that the radiance L ,
below water of refractive index n is n 2 times the radiance La in air reduced
by reflection losses at the surface (Gershun, 1939):
L,
= n2(1--p)La
The downward irradiance in air and in water are respectively:
= La cos i d w ,
= La cos i sin i d @d i
d E , = L , cosjdw,
= L , c o s j s i n j d @d j
dE,
From eqs. 4 1 and 42 it follows that:
dE,
= (1- p ) d G ,
which verifies the obvious fact that the interface between air and water
changes irradiance on a plane parallel to the interface by reflection only.
EFFECT O F WAVES ON REFRACTION
Refraction according to Fig. 38 is described by Snell’s law only in the
ideal case of a flat surface. Waves cause fluctuations of the direction of
refracted rays which causes a smoothing of the edge of the Snell cone (Plass
et al., 1975). Deviations of the direction of maximum radiance can amount
to as much as i 15%according to theoretical deductions of Mullamaa (1964a).
Because of wave action, the image of the sun as seen from beneath the
surface disintegrates into a glitter pattern with features different from those
of the reflected glitter. The refracted glitter subtends a smaller angle and is
of the order of 1,000 times more intense than the reflected glitter. Due to
lens action of individual waves, the flashes can attain a level dangerously high
for the upwardly directed human eye. According t o C. Cox and Munk (1956)
the refracted glitter, in contrast to the reflected, expands and dims when the
sun approaches the horizon.
CHAPTER 7
THEORY O F RADIATIVE TRANSFER IN THE SEA
The penetration and distribution of underwater radiant energy is determined by absorption and scattering processes the natures of which have been
the subject of preceding chapters. From the change of the light field investigated by radiance measurements, complete information is derived about the
inherent properties of the water. It should be pointed out, however, that we
have so far dealt with relatively small transmittance distances and with small
scattering volumes. When light propagates t o great depths, selective absorption
will have a tremendous effect and the scattering volumes will be so large that
the full complexities of multiple scattering become important. Theoretical
studies which take account only of primary scattering must be regarded only
as a first approximation for turbid surface water. The various avenues of
approach t o the theoretical problems which have lead t o our present comprehension of underwater radiative transfer are outlined below with a view t o
presenting also deductions made under simplifying assumptions. Preisendorfer
(1965) has published a mathematical treatise O i l all phases of the radiative
transfer problem.
The theoretical study of radiative transfer in the sea was initiated by
Shuleikin (1933) who proved the significant fact that the radiance distribution tends to a stationary state with increasing depth in the sea. An original
approach t o the irradiance problem (Y. Le Grand, 1939) considers isotropic
scattering produced by sun rays only. The predicted irradiance as a function
of depth brings out the essential feature that the monochromatic irradiance
E is less attenuated in the upper layers than in deeper layers, so that the
logarithmic curve, i.e., In E plotted against z , shows acurvature. Similar simple
models employing Rayleigh scattering have been investigated in considerable
detail (Lauscher, 1947; Takenouti, 1949; Mukai, 1959). However, in the
light of facts proving the dominance of forward scattering, more realistic
assumptions about the scattering function are required.
SIMPLE INTEGRATION O F SCATTERED LIGHT
As an introduction, we shall investigate the general simple model without
making so far any assumptions about the scattering function. It is postulated
that in the near-surface layer the sunlight is the only source of scattering,
and that, multiple scattering may be disregarded. The radiance due t o
scattered light may then be found by simple integration.
84
Sun
Q
Fig. 39. Geometry for evaluating radiance of scattered light.
Let E be the irradiance just below the water surface (Fig. 39). The small
volume element du at P is irradiated by:
E
j e-cx seci
The volume element scatters intensity d 1 in the direction (8, $) which forms
an angle a t o the incident beam. If the azimuth is @($= 0” for the plane of
incidence), the angle 01 is obtained from the expression:
cos a = cos j cos 8
+ sin j sin 8 cos C$
The scattered intensity is by definition:
d I = E sec j e-cxsecj P ( a W
and the irradiance at Q on a plane normal to PQ is:
dEsc = E sec j e-cxsecJP(oc)dv *
where:
r2
e-cr
du = r’dwdr
Considering that at Q the radiance L , = dEsc/dw we obtain the radiance
L ( 0 ) in the direction 8 in the upper hemisphere (8 = 0 to 7r/2) and in the
vertical plane of the sun by integration with respect t o r from 0 t o z sec 8 :
L ( 8 ) = E sec j---p(8 - j )
c
sec 8
( e - c z s e c j - e-czsecO
)
sec 8 -sec j
[441
The radiance is zero at the surface and is maximum at a depth z, , independent of the scattering function. Maximization yields the value:
1 In sec 8 - In sec j
z, = F s e c O - s e c j
This formula was deduced by Lauscher who also points out that for 8 = j
it reduces t o :
85
z,
1
= ~cos j
C
For the lower hemisphere, integration is performed in the vertical plane of
the sun from the depth z t o infinite depths. This yields:
--j)
sec s
e-cz sec j
L ( 8 ) = E sec j -p(s
-c
sec 6 -sec j
~
1461
In this case the logarithmic curve is a straight line.
The downward irradiance of scattered light on a horizontal surface at Q
is gven by:
dEsc = E sec j e-cx secj?(a)sin 8 cos 6 e-cr d@d8dr
and, after integration with respect to r from 0 to z sec 8, by:
If skylight is neglected, the total irradiance Ed is the sum of the scattered
and the direct irradiances at the depth z , namely:
For a zenith sun ( j = 0 ) and for small optical depths (cz -+ 0) the equation
takes the simple form:
Because of the small percentage of back-scatter in the total function it is
permissible to write:
Ed = E e-Cz (1+ b z ) = E e-C2+bz = E e-'"
1481
which suggests that irradiance attenuation in the surface stratum is identified
as absorption only.
A general expression for upward irradiance which is entirely scattered
light is found by integrating t o infinite depths:
1
E, = E
j e-czsecj
-
p (a)sin 8
d@d6
sec 8 sec j
+
1491
86
DEPENDENCE O F SOLAR ELEVATION ON DOWNWARD IRRADIANCE
The influence of solar elevation on irradiance is indicated in eq. 47. It is
instructive to discuss a more simple form. The vertical irradiance attenuation
coefficient & is generally defined by:
~501
Ed = Ee-KdZ
Considering the directional character of the light field in the upper layers of
the sea it may be permissible, as a first approximation, t o describe the solar
elevation effect by the two equations (Kozlyaninov and Pelevin, 1966; Jerlov
and Nyghd, 1969a):
sin (90" - h,)
sin
__ i = 413
sin j
sin j
~511
Ed = E e - K d ( 9 0 ° ) Z / C O S j
where h, is the solar elevation and Kd(90") the coefficient for zenith sun.
The function c o s j depicted in Fig. 40 shows a decrease with decreasing
elevation of maximally 33%. For zenith sunlight in the surface layer eq. 51
reduces to 48. Skylight, whose distribution is dependent on elevation
(Fig. 29), is not included in the above calculation.
.
90'
9
cosj = (l---cos2hS)
112
16
80'
70'
60'
50'
40'
30'
20'
10'
0'
Solar e l e v a t i o n h s
-160'
120' 80" LO'
0'
LO'
80' 120'+160'
Fig. 40. Dependence of t h e function cos i and cos j (see Fig. 39) o n t h e solar elevation.
Fig. 41. Radiance of upward scattered light. zeflection takes place b e t y e e n + 9 0 and
-goo, and total reflection from 4-48.6 to f 9 0 and from -48.6 t o -90 . (After Jerlov
and Fukuda, 1960.)
SEMI-EMPIRICAL MODEL
A substantial improvement of the radiance model's consistency with
observations is gained by inserting measured values of the scattering function
into the equations (Jerlov and Fukuda, 1960). Crucial tests were made for
turbid water having the inherent properties c = 0.5 and b = 0.3. The
evaliiated maximum radiance for downward-scattered light is found at the
greatest depth, 1.9 m, for 8 = 0 and a t the surface for 8 = 90.
Upward-scattered light is distributed not only in the lower hemisphere but
also in the upper, since it is reflected at the sea surface (Fig. 41). Reflection
takes place between f 9 0 and -go", and total reflection in the intervals
+48.6" t o f 9 0 " and -48.6" t o -90" (horizontal surface). This leads t o
conspicuous peaks in the computed curves at t-90" and -go", as was first
recognized by Tyler (1958). A slight maximum at -150" is ascribed t o backscattering through 180" from the sun's position (+ 30").
The final step is to add underwater sunlight and skylight (Chapters 4 and
6) t o the field of radiance created by scattering. The structure of the total
light field thus built up exhibits, in spite of its complexity, a gratifying
agreement with the experimental findings (see Fig. 55).
SCALAR IRRADIANCE
It follows from the law of conservation of energy that the divergence of
the irradiance vector in an absorbing medium is related t o the absorption
coefficient in the following way (Gershun, 1936):
d i v E = -aE,
~521
For the sea, where horizontal variations of irradiance are small, eq. 52 takes
the form:
This allows determination of the absorption coefficient from observed
quantities, the scalar irradiance E , being obtained from the measured
spherical irradiance E , according to previous definitions.
Considering that E , is small compared with E d , eq. 53 reduces t o eq. 4 8
for zenith sun in the surface stratum.
With the downward vector of irradiance:
and :
E = Ed -Eu
88
we obtain from eq. 53:
a
KE
or :
-
E
-
EO
The irradiance ratio (reflectance) E,/Ed attains a maximum value of about
10% for blue light in the clearest water. Eq. 55 points out that a/KE comes
close t o the significant ratio of cosine collection t o equal collection ( E d / E o )
(see p. 102). The factor a/KE is a link between t h e inherent property a and
the apparent K E ; it is always less than 1.For the highly directed light in the
red (low value of b / c ) a maximum value of 0.93 occurs (TableXXI). A
theoretical analysis by Beadsley Jr. and Zaneveld (1969) leads to the
approximative result that :
a/Kd = Ed/Eo
0.8 (green light)
with an accuracy of better than 10%.This compares fairly well with the data
in Table XXI, but it is evident that a / K d can attain values as low as 0.60 for
high values of b / c (see p. 102).
TABLE XXI
Values of ,ii= a / K E derived from irradiance measurements between 1 0 and 40 m
a
,ii = a / K E
Reference
1
Wavelength
(nm)
52
535
0.09
0.75
Jerlov and
Liljequist (1938)
52
52
48
53
52
51
48
37 2
427
477
513
535
572
633
0.97
0.37
0.18
0.13
0.11
0.12
0.33
0.79
0.70
0.70
0.68
0.67
0.68
0.77
HQjerslev (197 4a)
Mediterranean
off Gibraltar
68
74
372
427
0.15
0.066
0.84
0.69
HQjerslev(1973)
South of
Sardinia
72
64
60
73
68
74
372
427
477
533
572
633
0.058
0.029
0.028
0.059
0.082
0.29
0.78
0.62
0.73
0.84
0.85
0.93
Region
Solar
elevation
(O
Baltic Sea
(m-')
89
Whitney (1938) has introduced the concept of mean path length, i.e., the
mean value of the path length that light quanta must travel t o descend 1m in
depth. The mean path length may be interpreted as the inverted value of an
average cosine, cos 8 , (Jerlov, 1951). In the strictly defined form:
the average cosine, p , is a useful parameter as already shown.
RADIATIVE TRANSFER EQUATION
A precise formulation of radiative transfer in an absorbing and scattering
medium such as the sea is given by the classical equation:
The first term on the right represents loss by attenuation, the second gain by
scattering. The latter quantity, called the path function, involves every
volume element in the sea as a source of scattering and is generalized in the
form :
1 1 P(8,@;8’,$‘)L(z,8’,~‘)sinO’dO’dq5’
2n
L*(z,8,$) =
n
r 581
@‘=0 O ’ = O
This integrodifferential equation lends itself t o diverse mathematical
treatments. Its potentialities for describing the underwater light field has
been explored at the Visibility Laboratory (San Diego) taking into account
multiple scattering of limited order. Duntley (1963) mentions that in this
case the equation is solved in practice by iterative procedures on the largest
electronic computers.
An investigation by Preisendorfer (1961) suggests definitions which lead
to a better understanding of the “inherent properties” involved in the
transfer. Eq. 57 may be written:
-.* - _1 . dL
= L
L
L
-
dr
It is possible by instrumental means t o minimize L , so that:
1 dL
c = --*L
dr
This applies t o the beam transmittance meter in which radiance attenuance
over a fixed distance is measured.
Another way t o minimize L , is t o direct underwater a radiance tube in
90
the apparent direction of the sun. Since z = r cos 8 :
c =
- - -L1 dd Lz cos 6
-
or:
c = KL cos8
E591
A special case may be specified by noting that radiance along a horizontal
path in the sea is generally constant. With dL/dr = 0, it is found that:
c = -L ,
L
The experimental arrangement which satisfies this equation would be t o take,
in the same horizontal direction, records of the actual radiance L and of the
radiance from a black target which yields L,. This measuring principle was
introduced by Y. Le Grand (1939) in his “l’ecran noir”.
The classical eq. 57 can also be used t o derive Gershun’s eq. 53. Considering that z = r cos 6 , i.e., that 6 is the angle between nadir and the
motion of flux, integrating eq. 57 over the sphere yields:
[GO1
where E , is the scalar irradiance.
RADIANCE MODEL OF T H E VISIBILITY LABORATORY
In a series of papers, Preisendorfer has brought t o completion the
theoretical model of radiance distribution in the sea. His work, stimulated by
Duntley’s (1948) original findings, is summarized in a comprehensive paper
of Preisendorfer (1964). The model considers a target point at depth zt and
at a distance r from the observation point at depth z . The path has the
direction (n- 6 , @ t n) where 0 is the angle between the nadir and the
direction of the flux. Hence we have z -zt = r cos 8. The field radiance is
measured by pointing a radiance meter a t depth z in the direction (8,$).
For an optically uniform medium an integration of eq. 57 along the path
( z t ,0 , @, r ) yields the following expression for the apparent radiance L , of the
target :
r
+ j”
L , ( ~ , o , @=
) ~ ~ ( z ~ , ~ , @ ) e -L*(z’,6,4)e-c(”-rf)
cr
dr’
0
[611
+
where L, is the inherent radiance of the target and z’ = zt r’ cos 6. The
apparent radiance L, may thus be written as the sum of a transmitted
91
inherent radiance and a path radiance which consists of flux scattered into
the direction ( n - 8, $ n ) at each point of the path (zt, 8, $, r ) and then
transmitted t o the observation point.
Preisendorfer has shown that an approximate form for L , ( z , d , $ ) can be
obtained from the two-flow Schuster equations for irradiance:
+
L , ( z , ~ , @=
) L,(o,d,$) e-K*a
where K , is independent of depth.
A combination of eqs. 61 and 6 2 results in the following relation:
[621
It is characteristic of this theory of radiative transfer that no mathematical
expression for the scattering function is introduced or tested but that the
whole path function is treated as a parameter with defined properties.
The validity of the formulas for the observed radiance distribution has
been investigated by Tyler (1960a) on the basis of his complete set of
accurate radiance data from Lake Pend Oreille. The key problem in such an
application is t o evaluate the path function L , . Tyler starts from eq. 63. For
a path of sight directed at the zenith ( 8 = 0", @ = O'), this reduces to:
where L , denotes the radiance of the zenith sky just below the surface
(zt = 0).
For the path of sight directed downward (8 = 180",$ = 0", L o = 0 for
r = -), we have the corresponding relation:
The attenuation of the diffuse light L , ( z )is described by the eq.:
t , ( z ) = ,?,,(0)e-K*Z.
It follows that:
The procedure involves determining L , ( z ) from experimental data from a
single depth employing eq. 6 4 and from L,(O) given by eq. 65. This allows
us t o evaluate L ( z ) for all depths by means of eq. 67. The net result of the
computations compares well with observations (see Fig. 58).
92
THEORY O F RADIATIVE TRANSFER
Chandrasekhar’s method
Lenoble (1958a, 1961a, 1963) has adopted the method developed by
Chandrasekhar (1950). The equation of transfer is expressed in the form:
o’=o
@‘=”
where Ei is the irradiance produced by the sunlight on a plane perpendicular
to its propagation in the water (Oo,@o). Here the angle 19 is measured from
the zenith to the direction of measurement.
The equation describes a mixed light field composed of direct sunlight and
diffuse light. By omitting the last term on the right-hand side one obtains a
first approximation for primary scattering only which is identical to that
obtained from the simple model discussed on p. 85.
The theory presumes a known law of scattering. For a scattering medium
of large particles, the scattering function can be developed into a series of
Legendre polynomials of the form:
The resulting N integro-differential equations are solved by the method of
discrete ordinates. An alternative is t o approximate the radiance by a
development in a series of spherical harmonics.
In practice, Lenoble has truncated the above series, retaining only three
terms ( N = 2), and expressing the scattering function by:
p ( e ) = 4Tb [i + 1.73 P , (cos s) + P, (cos s)]
--
(691
This approach is of course much better adapted t o the real shape of the function than are assumptions of isotropic and Rayleigh scattering. Confronted
with experiments, it has proved fruitful and has allowed the derivation of
inherent properties in the ultra-violet region (Table XXII). Schellenberger
(1963, 1965) has contributed a penetrating analysis of eq. 68, and has also
utilized a series of Legendre polynomials extended t o 22 terms which secures
a more realistic conformity t o the experimental function.
The availability of large electronic computers has made much more
elaborate numerical methods feasible. Raschke (1972) has treated a planeparallel atmospherewcean system separated by a plane ocean surface which
93
TABLE XXII
Absorption and scattering coefficients derived from radiance measurements
(After Lenoble, 1958a)
Region
Wavelength ( n m )
330
335
344
354
360
368
378
390
404
413
Off Monaco absorption
0.13 0.12 0.10 0.08 0.07 0.06 0.05 0.04 0.03 0.03
coefficient (m-')
scattering
0.10 0.09 0.09 0.07 0.08 0.08 0.08 0.08 0.07 0.07
coefficient (rn-')
Off Corse
absorption
0.17 0.16 0.14 0.11 0.10 0.09 0.07 0.06 0.05 0.05
coefficient (m-')
scattering
0.07 0.07 0.07 0.07 0.07 0.07 0.06 0.06 0.05 0.05
coefficient (rn-')
is assumed to have the reflection and transmission properties of a wind-ruffled
surface with a Gaussian distribution of slopes (C. Cox and Munk, 1956).
Enough terms (311) in the series of Legendre polynomials are retained t o
simulate the observed scattering function faithfully. Not only the radiance
but also the boundary conditions are expanded in Fourier series. The
upward- and downward-directed radiance are considered separately. One
therefore obtains for each medium N sets of two-couple integro-differential
equations. From the formal solution of these equations the radiation field in
a specified wavelength interval is calculated by an iterative procedure; each
additional interaction means that one more order of scattering is taken into
account. Details of the computational procedure are given by Korb and
Zdunkowski (1970).
Monte Carlo techniques
Monte Carlo methods applied t o radiation transfer problems consist
essentially in following a large number of photons through a large number of
collisions. Each photon is assigned a statistical weight that is adjusted at each
collision in order t o take account of the probability of absorption. The path
of each photon is followed until the statistical weight falls below a predetermined number (Plass and Kattawar, 1969). At each collision the new photon
direction is calculated by means of the probability distribution given by a
known or assumed scattering function. By this procedure multiple scattering
can be ten times as strong as primary scattering. At the interfaces, the laws
of reflection and refraction are applied t o calculate the probability of
reflection and transmission and the new photon direction.
Thus all known processes affecting a photon can in principle be taken into
account. Most prominant proponents of the Monte Carlo approach are
94
Kattawar and Plass, who have presented, in a series of papers, the results of
their calculations of upward and downward irradiance (Plass and Kattawar,
1972), and upward and downward radiance (Plass and Kattawar, 1969;
Kattawar and Plass, 1972) in the ocean and the atmosphere treated as a
system. Their powerful model considers both Rayleigh-scattering and absorption by the water itself as well as the scattering and absorption by suspended
particles.
It is evident that adequate mathematical methods are available for the
solution of radiative transfer problems. Still more effective matrix operator
methods are being developed (Kattawar, 1973; Kattawar and Plass, 1973;
Plass et al., 1973).
In general the results predicted by the above calculations agree well with
observations. A review of new developments of the theory of radiative
transfer in the oceans is given by Zaneveld (1974).
- Computed values
0 Measured
valuer
Fig. 42. Minimum in t h e upward irradiance over a highly reflecting sand bottom in the
Skagerrak. (After Joseph, 1950.)
RELATION BETWEEN UPWARD AND DOWNWARD IRRADIANCE
A great deal of emphasis has been placed on adequate derivations of the
irradiance ratio (reflectance) R = E,/E, from the classical two-flow model
(Whitney, 1938;Duntley, 1942;Poole, 1945; Lenoble, 1956b; Schellenberger,
1964; Pelevin, 1966; Kozlyaninov and Pelevin, 1966). For ocean water the
complication of accounting for multiple scattering is obligatory whereas for
turbid waters the assumption of primary scattering may be useful in some
95
cases. By assuming in the first approximation that the back-scattering
function, & , is constant (between 90" and 180") eqs. 47 and 49 yield:
R = 2 n ( & / c ) ( l -In 2) e-bz
1.2(pb/c)e-bz
for zenith sun in the surface layer. Joseph (1930) has also shown that a
simple two-flow system readily describes the change of upward irradiance
with depth over a light-reflecting bottom in conformity to observations
(Fig. 42).
H.R. Gordon et al. (1975) have used Monte Carlo simulations of the
transfer of radiant energy in the ocean. They have arrived a t an equation
which for all practical purpose can be expressed as:
where C varies from 0.32 t o 0.37 for zenith sun and overcast sky respectively.
In accordance with this Prieur and Morel (1975) found a theoretical C-value
of 0.33 for clear water.
Fig. 43. Computed upward and downward flux (460 n m ) a s a function of optical d e p t h
for clear ocean water for various values of the albedo A of t h e ocean floor. (After Plass
and Kattawar, 1972.)
The internal reflectance R is of particular interest near the bottom.
H.R. Gordon and O.B. Brown (1973, 1974) have shown by using a Monte
Carlo technique that the diffuse reflection at the bottom is often greatly
different from that which could be expected of a Lambert reflection. Plass
and Kattawar (1972) have also investigated this problem by means of their
realistic model of the atmosphere-ocean system (Fig. 43). The downward
flux is little affected by the bottom because reflected light must be scattered
downwards before it can contribute to the downward flux. The upward flux,
on the other hand, is greatly influenced by the albedo of the floor.
96
ASYMPTOTIC STATE
Radiance distribution
Some simple reasoning may help t o understand how the radiance distribution is modified with progressively increasing depth. It is obvious that the
complex structure predicted for the surface layer will disappear when details
in the distribution are smoothed out. On account of the strong forward
scattering, the distribution will be concentrated around the direction of
maximum radiance. Another associated phase of the process would be an
approach of the direction of maximum radiance towards zenith because
zenith radiance has the shortest path and is therefore least attenuated.
Consequently, the change would lead t o a distribution which is symmetrical
round the vertical.
Shuleikin (1933) and Whitney (1941) concluded from investigations of the
underwater light field that with increase of depth the radiance distribution
would eventually settle down to a fixed form. The mathematical formulation
of the final state has first been given by Poole (1945) and by Ambarzumian
(1946) for the case of isotropic scattering. It is:
C
where h is defined as the limit of the radiance attenuation coefficient K at
great depths:
K =
1 dL
--.L dz
lim K = h
z+-
r711
The factor h is independent of direction, and always less than the attenuation coefficient c. In this case the asymptotic polar surface is a prolate
ellipsoid with vertical axis and having eccentricity h / c . It is determined by
inherent properties only, and irrespective of atmospheric lighting conditions
and the state of the sea surface.
Rayleigh-scattering is another form which is mathematically tractable as
proved by Rozenberg (1959) and by Herman and Lenoble (1964). This
accounts for the role of molecular scattering in creating the asymptotic
light field.
A model making some allowance for the dominance of forward scattering
was employed by Lenoble (195610) who introduced the specified scattering
function (eq. 69) and accordingly obtained better agreement between the
predicted and observed values of the irradiance ratios E,IE, and E,IE,
( E , = irradiance on a vertical plane). Preisendorfer (1959) discusses the
asymptotic value, k , which is valid for deep waters when eq. 6 3 takes the
form:
97
It follows that the shape of all depth profiles of radiance will approach the
asymptotic value k , i.e., vertical radiance and irradiance attenuation is
the same for all directions. A mathematical proof of the existence of an
asymptotic distribution is furnished by Preisendorfer assuming that
1 dE0 - constant. This problem has also under various premises
-z)
been treated by Lundgren and Hq5jerslev (1971), Zaneveld and H. Pak (1972),
Hq5jerslev (1972). The final and general solution is given by Hq5jerslev and
Zaneveld (1976) who only stipulate stationary state and homogeneous water.
As established by eq. 72, the ratio of the radiance t o the path function is a
parameter which denotes the members of a family of ellipses. Tyler (196313)
has shown that the measurable quantity L ( O ) / L ( 9 8 )can be fitted empirically
t o an ellipse through the relation:
1
where c = k/c.Tyler tentatively putsa = 4,which fits with his near-asymptotic
radiance data from Lake Pend Oreille.
It is manifest that b / c and k / c are basic parameters for describing the
asymptotic state. Eq. 72 may be considered as a bridge between the domain
of inherent properties and that of apparent properties, and this bridge can be
passed in both directions. In short, L and k can be determined from and c,
as well as principally /3 and c from L and k .
The first problem has attracted a great deal of interest. Rozenberg (1958)
has examined the light conditions a t great depths and deduced the simple
relation k = ,& which is valid for a slightly absorbing, isotropic medium.
Herman and Lenoble (1968) and Zege (1971) have employed methods, the
chief idea of which is t o develop the scattering function and the radiance
into series of Legendre functions. Their results present asymptotic distributions associated with relationships between b / c and k / c . Schellenberger
(1970) also utilizes Legendre polynomials. By means of an elliptic fit as in
eq. 7 3 but with a = 8.7 he derives parameters of the near-asymptotic radiance
field from the scattering function. A numerical approximation t o the equation
of radiative transfer has been found by Beardsley Jr. and Zaneveld (1969).
This model which cannot here be discussed in detail also yields relations
between the actual coefficients. Prieur and Morel (1971) approach the problem from a different angle. They consider the scattering function as the sum
of a variable function for particles Pb and a constant function for the water
0, . The equation of radiative transfer is solved by a numerical iterative procedure. Conclusive results summarized in Fig. 44 go t o prove that the
relation between b / c and k / c is little influenced by Pm/pp, i.e., by the particle
I
"
'
"
'
'
-
Mediterranean
e
Vertical a n g l e
I
I
goo
I
I
Vertical angle
I
I
e
I
I
!
C
Fig. 44. Radiance distributions computed by Prieur and Morel ( 1 9 7 1 ) and compared with
observations (full circles) obtained with t i c = 0.5 - 0.6 (left) b y Lundgren ( 1 9 7 6 ) and
with k / c = 0.36 (right) by Jerlov a n d Nygard ( 1 9 6 8 ) .
content of the water; in fact the interval 0-0.10 in b,/b, represents all
ocean water. In accordance with other investigations the relation is, on the
other hand, strongly dependent on the shape of the scattering function.
In Fig. 45 theory is confronted with experiment. Two of the radiance
curves derived by Prieur and Morel are compared with the two available sets
of near-asymptotic radiance distributions, one representing clearest ocean
water (the Mediterranean) the other turbid water (the Baltic Sea). The
numerous results from laboratory measurements achieved by Timofeeva
(1974) have been expressed analytically by the curve in Fig. 45 which conforms well with observations from diverse lake waters. Obviously, the full
agreement within measured data concerning this particular problem of
( b / c , k / c ) dependence may be attributed t o the fact that the shape of the
scattering function does not show any drastic changes for natural waters.
It was postulated in the introduction t o this chapter that from the radiance
distribution and its variation with depth complete information can be derived
about the inherent properties. This is the second problem defined above also called the reverse problem. Zaneveld (1974) building on initial ideas by
Zaneveld and Pak (1972) has given a concise outline of the mathematical
method for arriving at a solution t o the inversion of the equation of radiative
99
k/c
I
I \
0.L
0.2
0.8
0.6
b/c
- M i l k y rnediurn(-d
0.2
0.L
0.6
0.8
b/c
Fig. 45. Relationships between k / c and b / c . Left: Computed curves for different values of
t h e ratio of the molecular scattering coefficient to the coefficient due t o particles (b,/b,).
(After Prieur and Morel, 1 9 7 1 . ) Right: Measured values for milky media and lake water.
(After Timofeeva, 1971b.)
transfer for any light field. By integration with respect to the azimuth the
distribution is transformed into an axially symmetric shape. This distribution
as well as the scattering functions are as usual described by a series of
Legendre functions:
m
L(0,z) =
n =O
[741
A,(z)P,(cosO)
Using the addition theorem for Legendre polynomials together with the
equation of radiative transfer the following equation is obtained :
1
?r
477
c -- 2n
__
+
Bn = - O
Pn (cos 8) cos 8 sin 8 d 8
J”
__
L(B,z)P, (cos 8) sin 8 d8
0
Considering that:
-[
c = lim
nl-
c---
2n4~
the attenuation coefficient and the scattering coefficient are found from
these equations.
100
The essence of this result is that the inherent coefficients b and c are completely described by the light field and its derivative with depth,
Polarization
Conclusions about polarization in the sea can be drawn from our discussion
of the polarization pattern generated by a beam of light (Chapter 2, p. 43).
On account of the symmetry of the asymptotic light field round the vertical,
the corresponding asymptotic polarization state will show maximum polarization in the horizontal direction. The polarization theory is not easily
employed even for the asymptotic state. Tyler (196313) made an estimate of
the degree of polarization for horizontal directions by assuming isotropic
scattering.
Polarization has been the object of several theoretical studies by Lenoble
(1958b, 1961b, c), who employs eq. 68 in its matrix form for diffuse radiant
energy. Computations of Rayleigh scattering suggest that the degree of
polarization in the asymptotic state is zero for zenith and for nadir radiance,
and is maximum in the horizontal direction. This finding should hold true
qualitatively for large particle scattering and is consistent with the observation
of maximum radiance in the direction of the zenith. Beardsley Jr. (1968b)
has devised a numerical method t o provide an approximation of the degree
of polarization. The scattering properties of the water are characterized by
a Muller matrix which is evaluated by observations (see Chapter 2, p. 45).
The most complete computations of polarization have been carried out by
Kattawar et al. (1973). Their results calculated by a Monte Carlo method
(see above) are presented in a series of diagrams showing the degree of
direction of polarization and the ellipticity as functions of wavelength, solar
elevation and turbidity of the water.
CHAPTER 8
TECHNIQUES O F UNDERWATER LIGHT MEASUREMENT
From a physical point of view the measurement of radiant energy does
not present any problems. The development of a simple and effective technique adapted for observation in the sea, however, has met with difficulties.
There is n o doubt that the work in this field has been hampered by technical
inadequacies. Unfortunately, the pitfalls associated with radiance and irradiance measurements have not been known t o all experimentalists, e.g., the
occurrence of non-linearity in the relation between light flux and photocurrent and the devastating effect of the band-width error which occurs with
broad colour filters. The advent of the photomultiplier tube has constituted
a major break-through by making narrow-band measurements t o great depths
possible. The technical means which form the basic units in the meters are
discussed below with a view t o pointing out the possibility of error in the
measurements.
COLLECTORS
Radiance collectors
A Gershun tube (Fig. 1)provides a simple means of limiting the angle of
acceptance so as t o measure radiance as we have defined it. In the meter
devised by Duntley et al. (1955) and extensively used by Tyler (1960b), an
internally baffled Gershun tube limits the angle t o 6.6". A lens-pinhole system (Fig. 4) is often preferred, as it considerably reduces the length of the
collector. By using such a system Lundgren (1976) has been able t o narrow
the angle t o 1.3" which gives unprecedented resolution of the radiance field.
A different type of collector is the "fisheye" lens with a 180" field of
view used together with a camera (Smith e t al., 1970). If 0 is the zenith angle
of an incident ray and (r,q5) are the coordinates of the image of this ray on
the plane of the camera film this lens has the property of projecting a hemisphere onto a plane such that:
r = f0
where f is the lens focal length.
102
Irrudiunce collectors
The conventional design employs flat plate collectors, usually opal glass or
opal plastic. These materials do not diffuse ideally and do not follow
Lambert's cosine law strictly; in addition they possess some wavelength
selectivity. The cosine error is not important when measuring downwelling
flux, which is concentrated within the refraction cone of semi-angle 48.5'.
Poole (1945) has pointed out that old measurements especially tend to
undervalue the upward irradiance on account of poor functioning of the
flat plate collector for relatively strong light with a large angle of incidence
(see also Pelevin, 1966). An improvement in the performance of the collector is obtained by elevating its surface above the instrument case so that
some light passes through the edge of the collector (see Smith, 1969).
In some cases we aim at securing the magnitude of the total light, regardless of angle, received at a given point. This would, for instance, be best for
assessing the energy available for photosynthesis. In this case a spherical ( 4 ~ )
collector which measures spherical irradiance and thus scalar irradiance is
ideal; it also has the advantage of being independent of the meter's orientation. In practice, however, a hemispherical collector seems t o provide sufficient means to arrive at a representative value of the spherical irradiance
since most light is within the refraction zone.
The measurement of scalar irradiance by means of a spherical collector
represents equal collection. The ratio of equal collection to cosine collection
for the upper hemisphere is defined by:
~vjpL(0,q5,z)
sin 0 cos 8 d0 d@
0
0
EL! - _
Eo
_
~
'71
271
0
0
L(I9,@p)sin I9 d8 d@
Jerlov and Liljequist (1938) investigated the factor E d / E , for coastal
waters and established its dependence on solar elevation, wavelength, turbidity and depth. For a low sun and very turbid water, E,/Eo can attain a
minimum value of 0.60. The highest value of 0.95 appears with zenith sun
and low values of b / c . Most frequently, one finds a factor of 0.75 --0.85. The
theory behind the spherical types of collectors is outlined by Gershun
(1936). A practical application is given by the instrument in Fig. 46 which is
provided with screened spherical collectors. It is readily found that the upper
collector measures an irradiance of & ( E o Ed - E,) whereas the lower collector measures analogously $ ( E o - Ed Eu).
For meters provided with a diffusing collector, it is obligatory to pay due
regard to the so-called immersion effect (Poole, 1936). This appears as a
reduction in meter sensitivity when the meter is lowered from the surface to
+
+
103
2
1 O p a l - f l a s h e d globe
2 B l a c k shield
3 F l a t opal-flashed
collector
L Diaphragms
5 P i n for s u s p e n s i o n
6 Colour f i l l e r s
7 P I N diode
8 Pressure gauge
Fig. 46. Meter for simultaneous measurement of scalar and vector irradiance. (After
HBjerslev, 1975.)
600
D r y Opal
Meter
reading loo
'
600
170
Wetted Opal
Thin w a t e r l a y e r
S u b m e r g e d Opal
D e e p w a t e r layer
100
78
Fig. 47. Reflection processes occurring for an opal glass used as cosine collector in irradiance meters. (After Westlake, 1965.)
104
a small depth of the same order as the radius of the collector. The immersion
effect is due largely t o changes in reflection at the upper surface of the collector when the meter is submerged. Fig. 47, prepared on the basis of calculations by Berger (1961) and Westlake (1965), gives a simplified illustration
of the phenomenon. According to Berger the immersion effect is less for silicate glasses than for plastics, which have a relatively low refractive index.
Since it may amount to 30% and is dependent on the optical 2eometrical
design of the meter, this effect should be determined experimentally for
each instrument.
In a thorough theoretical and experimental analysis of the surface effect
Aas (1969) has shown a wavelength dependence for most diffusing collectors
on account of selective absorption (see also Jerlov and Nygiird, 1969b and
Smith, 1969). Nowadays non-selective low-absorbing collectors are available
which greatly facilitate the devising of integrating (over the spectrum) meters
as quanta meters.
DETECTORS
As regards flux-receiving detectors, a number of visual, photographic and
photoelectric techniques are worth noting. Kozlyaninov (1961) has visually
compared the radiance in different directions and for different colours with
daylight by using a shipboard tube, the lower end of which is submerged in
the water.
Model experiments employing a spectrograph with photographic recording
- P h o t o m u l t i p l i e r , 511.
520
Se P h o t o v o l t a i c c e l l , q u a r t z w i n d o w .
Se P h o t o v o l t a i c c e l l , g l a s s w i n d o w .
_ _P_
h o t o.m u l t i p l i e r ,
-.-..
.....
0-000
-000-
Si P h o t o v o l t a i c c e l l , S c h o t t k y Barrier.
Si Photovoltaic cell, Schottky Barrier,
UV enhanced.
Si P h o t o v o l t a i c cell, P l a n a r
diffused P I N .
Fig. 48. Spectral sensitivity of various photoelectric cells.
105
were made already in 1922 by Knudsen. The spectrophotographic method,
though circumstantial, has the advantage of simultaneous measurements
throughout the spectrum. It has been perfected for radiance observations by
the French school (Y. Le Grand, 1939; Y. Le Grand et al., 1954; Lenoble,
1956c; and Ivanoff, 1956). Jerlov and Koczy (1951) were able to extend
monochromatic irradiance measurements down to 500m in the ocean by
means of a unique photographic method.
The choice of photoelectric detectors is generally limited to a few devices
only. In competition with other cells, the Se photovoltaic cell holds a central
position for routine measurements of fairly strong light (Fig. 48). A linear
relationship between light flux and photocurrent exists only if the cell is
exposed t o less than 1,000 lux, i.e., 1%of the brightest daylight, and only if
for the permissible upper light level. The
the load resistance is low (<50
temperature dependence of the Se cell is negligible for temperatures occurring in the sea.
The Si photodiodes offer a favourable alternative for measuring not only
in the red but in the whole spectrum. The Schottky barrier diode is
especially attractive because it can be obtained with large sensitive areas, and
because of its broad spectral response and large dynamic range (10-3-10-'0
W/cm2). As t o linearity and temperature stability it is comparable with the
Se-cell when operating with a low-impedance load. Optimized combinations
of photodiode and operational amplifier are commercially available.
Measurements with the sensitive photomultiplier tube were initiated by
Sasaki et al. (1955) and by Clarke and Wertheim (1956). The use of this tube
involves a far more complicated technique than does the photovoltaic cell. It
requires a very well stabilized high voltage. Gain shift with time can be
appreciable - 12% per day has been quoted - although in good tubes it can
be as low as 0.5 -1%per day. The tube is usable only in weak light because
of strong fatigue effects in the cathode, appreciable gain shift and temporary
increase of dark current following large input signals.
The full advantages of the tube appear in records of low light levels. We
should mention, however, the strong temperature dependence of the dark
current (30%/"C). A tube type with low inherent dark current should therefore be chosen, and i t is definitely of value t o incorporate a shutter in the
meter in order to check the zero.
In conclusion, photomultiplier tubes should only be used in applications
when their superior sensitivity is really needed. Strong light is measured
more accurately with the aid of photovoltaic cells.
a)
FILTERS
Neutral filters should be selected on the basis of their ability t o transmit
virtually independently of the wavelength. Such filters, consisting of thin
106
Fig. 4 9 . Shift of optical centre of various Schott filters when the meter is lowered. (After
Joseph, 1 9 4 9 . )
metal films vacuum-deposited on glass (microscope filters) are available with
different transmittance values.
Colour filters are inserted between the collector and the detector. Without
a collimator system, the light is partly transmitted obliquely through the
colour filter. As a consequence, the effective thickness of the colour filter is
greater than the geometric thickness. The notorious band-width error is due
to a change in the width of the transmitted band and its position in the spectrum due t o selective absorption by the water. Joseph (1949b) has presented
an exhaustive analysis of the shift with depth of the optical centre h, of
broad filters defined by:
h E ( A 7 ) * T(h)S(h)dh
h,(z) =
-
-
E ( X p ) T(h)S(h)dh
where S ( h ) is the sensitivity of the detector, T ( h )the transmittance of the
filter. It may be seen from his results in Fig. 49, representing several Schott
filters used in the clearest ocean water, that only with the ultra-violet filter
B12 U 1 and the blue filter B12 G5 are the shifts small enough t o
guarantee high accuracy. Joseph further demonstrates that the current concept of a surface loss in irradiance measurements, due to matters present just
below the surface has arisen from observation impaired by band-width
errors.
The problem of securing data for the red can be solved by forming a differential filter (Sauberer and Ruttner, 1941). If, for instance, the readings
with RG 630 are deducted from those with RG 610 the error is reduced t o a
permissible level. In turbid green waters the filter V G 9 ( 4 m m ) is suitable,
whereas the performance of the ultra-violet filter is inadequate. Generally
speaking symmetrical filters with a width of less than 50 nm can be used in
the upper layer of the ocean (0 -10 m) over the whole spectrum except near
the “slope” region at 600 nm where very sharp filters are required.
+
+
107
A difficulty not always appreciated is the disturbing effect of fluorescence
occurring with sharp cut-off glass filters. Thus the above-mentioned RG 610
fluoresces around 800 nm if excited in the green (Pfeiffer and Porter, 1964).
Therefore red-sensitive cells should only be used with this filter in combination with suitable blocking filters. Interference filters are often not free
from fluorescence since fluorescent glasses are commonly used as a substrate
or as protection for the dielectric layers (Turner, 1973).
The band-width error is insignificant for interference filters of narrow
band widths. Tyler (1959) has pointed out that light leakage may appear
outside the stated filter band even if secondary transmission peaks are eliminated. When measuring in the red, an infinitesimal leakage in the blue will
introduce an enormous error which becomes progressively larger as depth
increases. This treacherous error must be eliminated by employing suitable
blocking filters. The performance of interference filters requires low convergence of the incident beam. Lissberger and Wilcock (1959) have proved,
however, that the deterioration which appears as a displacement of the maximum wavelength towards shorter wavelengths and as an increase in the width
of the passband is small even at a convergence of semi-angle 10". Interference filters have also been successfully used in conjunction with a photovoltaic cell for irradiance measurements in the surface strata (Ivanoff et al.,
1961).
There are both strip and circular (wedge) graded spectrum filters recording
continuously over a large part of the spectrum. Great precautions must be
taken with these in order t o eliminate secondary transmission. The availability is appreciated of interference filters with sharp cut-off against long
wavelengths by which the longwave limit of a spectral region can be fixed.
ORIENTATION PROBLEM
The in situ orientation of irradiance meters presents no special difficulties.
It should be stressed, however, that an oblique (not vertical) cable often
entails angular deviation of a flat plate collector. This may be corrected by
mounting the meter on gimbals.
The setting of radiance meters at defined directions in the sea is a matter
of crucial importance. It may be assumed a priori that with a clear sun maximum radiance in all horizontal planes occurs in the azimuth of the sun,
which thus serves as reference direction. By rotating the meter around a
vertical axis, representative records for all azimuths can be obtained. The
securing of accurate vertical angles is more critical. Only in shallow depths
and with a heavy meter can one be assured that the vertical angle is unaffected by the drift of the ship or the drag of prevailing currents. For measurements at greater depths a reference direction is necessary. A simple solution
to this problem, which utilizes the gimbals principle, is afforded by the
108
Fig. 50. Radiance meter with t w o housings, o n e containing electronic equipment, t h e
other four measuring units. They can be turned round a horizontal axis by means of a
motor in t h e lowest housing. T h e whole assembly is turned round a vertical axis by means
of two propellers. (After Lundgren, 1976.)
arrangement shown in Fig. 50. The assembly is unaffected by the movements
of the meter provided that the units present equal torque section t o currents
above and below the pivots. In the fisheye lens instrument two tilt-sensing
transducers oriented at right angles t o each other are arranged in series with
the shutter switch in order t o prevent operation of the shutter until the
camera is level (Smith et al., 1970).
METERS
Radiance meters
The principal function of the radiance meter is clear from the preceding
discussion. Various technical solutions t o the problem of exploring the light
field have been given. The instrument of Duntley et al. (1955) scans
109
Fig. 51. Radiance meter stabilized with a large fin and with two measuring heads which,
by means of synchronous motors, scan in t h e horizontal plane and in different vertical
planes. (After Sasaki e t al., 196213.)
continuously in the vertical plane from zenith t o nadir; the azimuth position
is controlled by means of a servo-system in combination with a propeller t o
rotate the meter. The meter, designed by Sasaki et al. (1962b), is stabilized
with a large fin and has two measuring heads which, by means of synchronous motors, scan in the horizontal plane and in different vertical planes
respectively (Fig. 51). Timofeeva (1962) uses a spherical container in which
the receiving system is installed. It can be smoothly and reversibly turned
around a vertical axis and discontinuously every 10" (within certain limits)
around a horizontal axis. Among the meters mentioned before, Smith's
(1974) camera has the outstanding ability of taking momentary pictures.
On the spectrophotometric side we have t o note the designs given by the
French school (see Lenoble, 1958a). These meters are well adapted to underwater use and are especially suitable in the ultra-violet regon.
Irradiance meters
The proper use of the photovoltaic cell is demonstrated in a model of high
versatility devised by Holmes and Snodgrass (1961). A meter of advanced
technique has been designed by Boden et al. (1960). This is a telerecording
instrument with a photomultiplier tube which gives a logarithmic response
over seven decades of irradiance. The anode current is kept constant by varying automatically the high voltage which in turn is used as a measure of the
110
EM1 9 5 5 8 A
Fig. 52. Optical system of the Scripps spectroradiometer. (Tyler and Smith, 1966.)
light flux. Interference filters are automatically changed, and an electrically
operated shutter selects one of three positions, namely open, closed or pinhole.
A multicore cable is well suited for meters which record in the upper
strata, 0-200 m; a telemetering system is not needed in this case. It is worthwhile paying scrupulous attention t o the light-leakage problem in the meters.
A t deep levels the blue light is strongly dominant, and as little as two-fold
reflection of this light against the blackened interior of the meter may be
critical. Jerlov (1965) has built an irradiance meter which is provided with
an effective light screen for the multiplier tube in order t o eliminate the
effect of stray light. In all sixteen well-blocked double-interference filters
(band width 1 0 n m ) are used together with a multiplier tube t o determine
the absolute irradiance over the spectrum 375-700 nm.
The Scripps spectroradiometer (Fig. 52) carefully tested and calibrated by
Tyler and Smith (1966, 1970), is essentially a double-grating monochromator of the Ebert type. Great precautions have been taken t o reduce stray
light within the instrument. The wavelength setting can be changed in 5-nm
steps within the range 350-750 nm by remote control. For each wavelength
an integration time of 10 sec is normally used, which corresponds t o a
measuring time of 1 5 min for one depth if full resolution be utilized.
The dispersing system in the spectro-irradiance meter devised by Bauer and
Ivanoff (1970) is a Bausch and Lomb grating monochromator with a spectral
resolution of 5nm. The signal of the phototube is recorded on a roll of
photographic paper. The system sweeps over the range 400 --750nm in less
than 3 sec. Another phototube controls the high voltage of the recording
tube in such a way that a full-scale reading is maintained when the meter is
lowered in the water.
Simultaneous observations of the spherical, the downward and the upward
irradiance provide sets of data for employing the Gershun equation (60)
from which the absorption coefficient is derived. For this purpose Karelin
and Pelevin (1970), and Hq5jerslev (1973) have devised instruments which are
111
irtz
Nickel sulphate solu;ion
Picric acid solution
Aau'
UG5
Photocell
&@
U
Fig. 5 3 . Plan of t h e UVB photometer. (After Jerlov, 1951.)
essentially combinations of three different meters. A more elegant solution
utilizes the types of collectors mentioned (Fig. 46). By adding and subtracting respectively the two irradiance recorded, both the fundamental quantities E , and Ed - E , in the Gershun equation are directly determined. Calibration of this instrument is not needed.
The total irradiance comprising the whole global radiation is accessible for
observation by means of thermopiles. A modern type has been devised by
Bethoux and Ivanoff (1970).
The study of the biologically significant UVB (280-320nm) requires a
special technique: opal quartz glass cannot be used as collector because it
strongly scatters UVB. The meter shown in Fig. 53 (Jerlov, 1951) utilized
liquid filters contained between hemispherical quartz shells, together with a
Schott UG5 glass, t o isolate the relevant UVB which is 295-320nm
for daylight. The representative wavelength is 310 nm: the sensitivity is negligible above 320 nm. The meter measures practically downward irradiance.
It is desirable in biological productivity studies t o use integrating
recorders. Techniques for integrating irradiance over prolonged periods of
time have been described by Snodgrass (1961), Currie and Draper (1961)
and Dera et al. (1972).
Quanta meters
WG 15 (IAPSO, SCOR) has recommended that light measurements in
photosynthetic studies be made in terms of quanta within the range
350-700 nm.
112
,Collector.
Strip graded
spectrum filter.
Diaphragm.
G r a d e d a t t e n u a t o r , 75
Schott filter.
50[
Phot omultiplier.
A
a
Collector
Window
~
0 0 0
0
li!d
”/.
Collimator
25300
0
Filters
LOO
500
600
700nm
Photocell
B
Fig. 54. Quanta meters together with energy sensitivity curves.
A. French meter. (After Prieur, 1970.) B. Exploded view of t h e Danish meter. (After
Jerlov and Nyg8rd, 196913.)
A quantum is energetically defined by :
1quantum/sec = hc/X = 1987/h
-
W
-
where Plank’s constant h = 6.626 *
J sec, the speed of light c = 3 10’
mlsec and the wavelength X is in nm. Accordingly the spectral irradiance
E ( A) is produced by a total number of N ( A) quanta;
E(A) = N(A)hc/h
“791
Provided that a detector has a spectral-energy sensitivity proportional t o
wavelength :
S(X) = constant h
its reading related t o the number of quanta will be:
[go1
113
A*
Q = constant.hc1 N(h)dX
CSlI
A,
The properties of an ideal detector for measuring quanta are thus described
by eq.80, the prescribed sensitivity applied t o the interval 350 and 700 nm
and zero outside this range.
A great deal of work has been devoted t o designing suitable irradiance
meters for recording underwater quanta. Only the first two meters are mentioned here. Jerlov and Nyg%rd (196913) have succeeded in building a simple
and cheap instrument utilizing an ordinary Se-cell in combination with
Schott filters (Fig. 54). The collimator serves t o reduce irradiance and t o
adjust the flux transmitted through the different filter sectors t o the cell.
The meter can as well be employed with a spherical collector.
The French quanta meter (Prieur, 1970) is a rather sensitive instrument
recording by means of a photomultiplier tube in the region 370-700nm
(Fig. 54). The desired sensitivity distribution is chiefly achieved by a geometrical modification through a diaphragm of the spectrum obtained by a
strip-graded spectral filter.
Polarimeters
Like radiance meters, in situ polarimeters must be designed t o permit
measurements in different directions. As t o methods, one encounters the
usual display of visual, photographic and photoelectric techniques. The
initial observations by Waterman (1955) were made with a special polarization analyser, which, when traversed by convergent polarized light, forms
an interference pattern; this is then photographed and the figures are
contrast-evaluated. Visual methods may be employed for quantitative
observations down to depths accessible by divers. The extension t o greater
depths demands polarimeters with remote control. The meter designed by
Ivanoff (1957b) is composed of a revolving polaroid filter acting as ail
analyser and a photovoltaic cell in combination with a filter-changing device.
It allows scanning in a horizontal direction down t o a depth of 1 2 0 m .
Ample opportunities for studying polarization with a photoelectric as well as
with a photographic technique were afforded by dives with the underwater
chamber “Kuroshio” (Sasaki et al., 1959). The meter used by Timofeeva
(1962) is the radiance meter described, provided with a slowly revolving
polaroid analyser in front of the phototube. Lundgren’s (1976) radiance
meter acts as a polarimeter if the four measuring units are provided with
polaroid filters, the axis of which are turned O ” , 45”, 90” and 135” relative
to the instruments’s horizontal axis. Kaygorodov and Neuymin (1966) have
devised an instrument for measuring three-dimensional radiance and polarization in several spectral ranges down t o 2 0 0 m depth. It is equipped with a
small gyrocompass sensing upit and an inclinometer for measuring azimuth
and vertical angle.
114
CALIBRATION
The most obvious standardization method, elaborated by Jerlov and
Olssori (1944) employs the strong flux from the sun. For laboratory tests
and calibration of instruments artificial light sources are used. The spectral
distribution of radiant energy from the sun can be well simulated by a high
pressure Xe-lamp (Grum, 1968). For absolute calibration, standards of spectral irradiance are available. These are high power quartz-iodine lamps having
a coiled-coil tungsten filament (Stair et al., 1963; Schneider, 1970). Alternatively, a spectral calibration is performed by means of a strong light source
(Xe-lamp), a set of very narrow bandpass filters or a monochromator, and a
standard detector, usually an absolutely calibrated thermopile.
It is necessary to check the response of the detectors for linearity in the
actual range of measurements. Calibration of an irradiance meter is not complete unless the angular response of the collector and the immersion effect as
a function of wavelength have been determined.
MEASURING PROCEDURE
Field work will be briefly commented upon. Needless t o say, weather conditions place severe restrictions on underwater light observations, which
require fairly constant lighting conditions above the sea. Under clear skies
the meter should be freely exposed to the sun without being appreciably
affected by light reflected from the ship side. Owing t o pitching and rolling
motions of the ship, the meter cannot be lowered (from a beam) more than
5-7m outboard, and therefore shading due to the ship may influence the
results. Poole (1936) has considered the shading error and estimated its magnitude at about 10%in the uppermost 5 m for diffuse light; i t is of n o practical importance for bright sunlight. With the measuring arrangement used by
Aas (1969) the effect cannot be neglected, at least for diffuse light (Table
XXIII). This is an argument for the alternative of conducting experiments
from the stern; in this case the shading error is reduced t o a permissible level.
TABLE XXIII
Reduction (76) of downward irradiance because of shadow of t h e boat (length 5 2 m )
Observation made a t t h e sunny side of t h e ship from a 5 m bar (Aas, 1969)
Depth
(m1
5
10
20
34
40
50
Clear sky,
solar elevation 57'
Overcast,
solar elevation 40°
6
9
6
22
14
14
6
115
Readings should be taken in quick succession when the meter is lowered,
as this tends t o impede the development of cable obliquity. A depth-sensing
unit facilitates accurate depth determination. Deck photometers mounted on
gimbals and freely exposed serve to record fluctuations in the light over
water. It should be stressed that these are not always closely correlated t o
the variations of the light field at depth; a cloud shadow a t some distance
from the ship may effect the underwater unit whereas the deck photometer
receives full sunlight. Normalized values cannot accurately be compared with
those for a clear sun.
COLOUR METERS
In situ colour may be studied by direct visual observations employing
colour-measuring tubes the lower ends of which are placed just below the
surface (Kalle, 1938; Kozlyaninov, 1961). A direct method yielding objective data has been developed by Sugihara (1969). Using Schott filters in
combination with photomultiplier tubes with S-20 cathodes the CIE colourmixture data are simulated which makes possible a direct recordicg of the
tristimulus values X, Y and 2 (Chapter 13).
Due to the manifest interest in remote optical sensing, studies of ocean
colour have advanced to the frontline of the development in marine optics.
The idea of describing the spectral character of the upwelling light by a
ratio between the radiances of two selected wavelengths, instead of by a
conventionally derived numerical colour value has stimulated colour research.
According to this new model of colour representation a colour index is
defined (Jerlov, 1974b):
This index is readily measured with a simple meter containing two photovoltaic cells facing downward in order t o record nadir radiance. The cells are
provided with interference filters of 450 and 520 nm respectively. The index
is proved to be independent of solar elevation above 15" and little dependent
on cloudiness.
CHAPTER 9
RADIANCE
RADIANCE IN T H E UPPER LAYERS
Observed radiance distributions
It is clear from the preceding discussion that the radiance distribution
near the surface is rather complex due t o the effects of refraction and
reflexion at the air -water interface. Available observations also reveal the
fine details in the angular structure of radiance. Some typical examples are
shown in Fig. 55 for clear weather (Jerlov and Fukuda, 1960), hazy weather
(Sasaki et al., 1962b) and overcast sky (Tyler, 1958). The fact is established
that the angular dependence of radiance observed in turbid water for clear
skies agrees reasonably well with the trends predicted by the simple theory
(Chapter 7, p. 85)' which considers radiance as an integration of skylight and
of light generated by primary scattering. Discrepancies between the theoretical and the experimental picture may be attributed to the effect of wave
motion which is apt to smooth fine details in the theoretical pattern derived
for a flat surface. The weak maximum computed for 150" does not show up
in Fig. 55 because of lack of sufficiently dense observations in this region.
The distributions in Figs. 55-57 bear witness to the strong radiance maximum in the apparent direction of the sun. This es especially clear in Fig. 56
showing observations with a high resolution instrument (acceptance angle
1.3")below a flat sea surface; in this case an almost undisturbed image of the
refracted sun is recorded. Usually the angle subtended by the refracted glitter -- even for moderate winds - is larger than the acceptance angle of the
radiance meter, and therefore the glitter can not usually be comprehended
by a single radiance value.
Smith's (1974) observations with a fisheye lens (Fig. 57) reveal that minimum radiance is not at nadir but at the refracted anti-solar point since the
meter "sees" its own shadow (aureole effect, see Chapter 5). He points out
that this disturbance is an example of the unavoidable effect that instruments perturb the environment t o be studied.
The radiance curves for the upper layers clearly exhibit the conspicuous
fall of the curve at the edge of the refraction cone (f 48.5") as well as the
distinct peaks at 90" formed by light. from below which has been totally
reflected at the surface.
It is a primary trend of radiance measurements that with increasing depth
118
law0
lDOO
YI
z
u
2
.
l
-:
100
c
5
a
10
C
Fig. 55. Radiance distribution in the vertical plane of the sun for relatively turbid water.
A. Clear day, Gullmar Fjord, 535 nm. (After Jerlov and Fukuda, 1960.) B. Hazy weather,
off Japan, 520 nm. (After Sasaki e t al., 1962b.) C. Overcast sky, Lake Pend Oreille, 480
nm. (After Tyler, 1958.)
the distribution becomes less directed and more diffuse. It is clear from the
distributions of high resolution in Fig. 56 that the fine structure is gradually
extinguished and that the peaks at k 90" disappear rapidly towards greater
depth as predicted by the theory.
The spectacular phenomenon that radiance in some angular ranges of the
119
-1 80°
-goo
Fig. 56. Change with increase of depth of radiance in the vertical plane of the sun towards
the asymptotic state. Clear water of t h e Mediterranean. The angular resolution is 1 . 3 O .
Solar zenith angle is given together with depth. (After Lundgren, 1976.)
upper hemisphere in turbid water increases down to a certain depth was discovered by Timofeeva (1951a). Comparative results are presented in Fig. 58.
In this case the experimental and theoretical sides supplement each other
(Chapter 10). The theoretically predicted maxima in scattered light do
appear as real maxima only in angular ranges where at some depths L , > cL
(eq. 57). Depth profiles for zenith radiance obtained by Morel (1965) in the
Mediterranean exhibit some curvature but no maxima. In the direction of
the sun a maximum in the vertical radiance distribution is not possible.
120
Sun
t " " " ' i
>
:
o
l
-180O
-120'
'
'
-6OO
'
'
1 '
Oo
'
'
60°
'
'
'
120°
'
'
'
180'
Fig. 57. Radiance distribution in t h e vertical plane of the sun in t h e surface layer of the
Mediterranean. The angular resolution of radiance is 7.2O. (After Smith, 1974.)
Zenith and nadir radiance
A great deal of the experimental radiance material concerns studies of the
zenith radiance L o . It should be observed with regard to the above discussion
that the interpretation of the depth dependence of Lo is intimately connected with the scattering mechanism. Ivanoff (1956, 1957a) has evaluated Lo
spectra and shown that the spectral distribution (400--650 nm) is changed
with increase of depth in a way similar to that of irradiance (Fig. 59). Comparative studies of L o , L,, and L,,, have been made by Y . Le Grand and
Lenoble (1955), and by Lenoble (1956c, 1957b, 1958a). By numerous
observations in the region 318 -413 nm off the French Atlantic and Mediterranean coasts, Lenoble has laid a firm basis for our knowledge of the ultraviolet field. One example of spectral zenith radiance is adduced in Fig. 59.
Lenoble's theoretical analysis decomposes the radiance attenuation coeffiecient K into an absorption coefficient and a scattering coefficient and
represents these properties as spectral functions (Table XXII).
The behaviour of the radiance L180 with change of depth generally follows
the simple law of eq. 49. Its spectral composition is similar to that of upward
irradiance and will be treated in Chapter 10.
ASYMPTOTIC RADIANCE DISTRIBUTION
Approach to the asymptotic state
The broad outlines of the change of the light field with depth were
121
01
A
10-1
i
I
-90'
Radiance
10
1
-45.50
Relative Radiance
101
102
103
104
I
1
I
1
105
I
lo6
I
107
- 10
- 20
- 30
- 10
- 50
- 60
70
300
400
5w
6W nrn
L
Fig.58. Depth profiles of radiance for different zenith angles in the plane of the sun on a
clear day.
A. After Timofeeva (1951a). B. Lake Pend Oreille (after Tyler, 1960b). C. Gullmar Fjord
(after Jerlov and Fukuda, 1960).
Fig.59. Transmittance per meter of zenith radiance off Corsica for the ultraviolet region
(after Lenoble, 1958a) and for the visible region (after Ivanoff, 1957a).
explored in the first measurements (Jerlov and Liljequist, 1938; Whitney,
1941). The surface radiance curves, which are sharply peaked in the apparent
direction of the sun, are gradually transformed into distributions of less
directed character as the depth increases; the attenuation is maximum for
angles near the solar direction. The process by which the approach t o an
asymptotic distribution takes place through the combined effects of absorption and scattering is illustrated in the curves of Figs. 56 and 60 obtained
122
Fig. 60. Change with increase of depth of radiance in t h e vertical plane of the sun towards
the asymptotic state.
A. Baltic Sea, green light (continuous line, after Jerlov and Liljequist, 1 9 3 8 ; dashed line
after measurements by N. Jerlov and K. Nyg&d, 1 9 6 8 ) . B. Gullmar Fjord, blue light. C.
Lake Pend Oreille, green light (after Tyler, 1 9 6 0 b ) .
for different localities. Tyler’s (1960b) results for radiance through eighteen
vertical angles present data collected under favourable experimental conditions in the uniform water of Lake Pend Oreille. Actually, there is no reason
to believe that scattering in lake water would differ appreciably from that in
sea water.
123
150rn
4OOrn
Fig. 61. Polar diagram of near-asymptotic radiance distribution in the Sargasso Sea. Solar
elevation 60'.
Timofeeva (1951a) has demonstrated experimentally that the logarithmic
curves for different angles at increasingly greater depths tend to straight lines
parallel to each other, thereby providing powerful support for the theory. In
consequence the attenuation coefficient reaches an asymptotic value, valid
for all directions, which is the theoretical h-value (eq. 72).
It is mentioned in Chapter 7 that the change of the radiance distribution
with increasing depth is essentially a scattering effect. Simultaneously the
radiance is reduced by absorption. At near-asymptotic depths the low level
of radiance is hardly recordable by means of conventional meters with
photomultiplier tubes.
Duntley (1963) has pointed out that the shape of the radiance distribution in Tyler's family of curves has almost reached its asymptotic form at
41m depth whereas the peak of the curve is not at zenith but is rather, at
this depth, shifting at a maximum rate. This feature is corroborated by other
results in Fig. 60. By extrapolation, Duntley has found that the true asymptotic radiance (546 nm) distribution in Lake Pend Oreille is not reached until
100 m depth.
In the marine environment the transfer to an asymptotic state progresses
more slowly. The change of the light field is not yet completed at 100 m for
the residual green light in the Baltic (Fig. 60) at 275m and 400m for blue
light in the western Mediterranean (Fig. 56) and the Sargasso Sea (Fig. 61)
respectively .
The difference in shape of distribution between turbid and clear ocean
water is not important. The theory tells us that the asymptotic radiance distribution is determined by the scattering function p and the ratio h/c
(eq. 72). Under the plausible assumption that the scattering function does
not show large variations at great optical depths in the sea, Timofeeva
(1971a, 1974) has prepared Tables XXIV and XXV. The former yields ample
information about the ratio L(B)/L(O)as a function of the zenith angle B and
the parameter E = h / c , the latter about the dependence of average cosine F = ( E d - E,)/E, - o n E . The relevance of these functions is for sea water
limited to E-values > 0.3.
124
TABLE XXIV
The radiance distribution L(O)/L(O)as a function of t h e zenith angle 0 and t h e parameter E ( = k l c )
(After Timofeeva, 1971a)
klc
0"
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.98
0.93
0.85
0.74
0.64
0.54
0.46
0.38
0.30
0.24
0.20
0.18
0.16
0.15
0.14
0.13
0.13
0.12
0.97
0.87
0.72
0.55
0.39
0.29
0.21
0.14
0.10
0.07
0.06
0.05
0.04
0.03
0.03
0.02
0.02
0.02
1
0.96
0.81
0.63
0.45
0.30
0.19
0.13
0.08
0.05
0.04
0.03
0.02
0.02
0.01
0.01
0.01
0.01
0.01
1
0.94
0.78
0.58
0.38
0.24
0.14
0.07
0.05
0.03
0.01
0.01
0.01
0.01
0.01
1
0.94
0.76
0.54
0.33
0.19
0.10
0.05
0.03
0.02
0.01
0.01
1
0.94
0.75
0.51
0.29
0.15
0.07
0.03
0.02
0.01
0.01
1
0.94
0.74
0.50
0.27
0.13
0.06
0.02
0.01
0.01
1
0.93
0.74
0.49
0.26
0.11
0.05
0.02
0.01
1
0.93
0.74
0.49
0.25
0.10
0.04
0.01
0.01
1
1
0
TABLE XXV
Dependence of average cosine ( P ) o n E ( = k / c )
(After Timofeeva, 1974)
E = k/c
P
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0
0.19
0.34
0.46
0.54
0.61
0.66
0.70
0.74
0.77
0.80
-
E = k/c
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1
125
.-
I
9
,
.';
5m
.- 5.20m;Takenouti (1940)
%
.'.
(1911)
5m ( e x p . a n d theor.) Lenoble (1957a)
---535m;Whitney
11
-180"
f
I
f
-90'
1
I
I
I
0'
V e r t i c a l angle
I
I
90.
I
I
A
180.
Fig. 62. Symmetrical radiance distribution, independent of azimuthal angle for an overcast sky.
In the trivial case of zenith sun, strict symmetry around the vertical exists
for all levels and an analogous transformation t o a final shape takes place. An
overcast sky also presents a symmetrical distribution, and the asymptotic
state is evidently reached close to the surface as evidenced by Takenouti
(1940), Whitney (1941) and Lenoble (1957a) (Fig. 62).
Asymptotic distribution for different wavelengths
It is plainly brought out in the investigation of Jerlov and Liljequist
(1938) in the Baltic that the directionality in radiance is more marked for
the red and the blue than for the green, which shows minimum attenuance in
these waters. It is consistent with the general picture of radiance as outlined
by theory and experiments that the transformation to the final state of distribution is most slowly accomplished for the light which is least absorbed.
Thus it is noted in Fig. 61 that a considerable difference in asymptotic depth
occurs for the violet and the blue in the Sargasso Sea. The asymptotic distribution for 700nm prevails at less than 5 0 m depth in all natural waters.
CHAPTER 1 0
IRKADIANCE
There is still a paucity of experimental work on irradiance. Most data
result from sporadic observations with one to three colour filters having a
broad band width. Systematic and complete spectral measurements are
sparse even if the situation has improved during the last years. The explanation of this lack of relevant information for vast oceanic areas is t o be
found - besides in the technical difficulties - in the requirement of fairly
stable atmospheric lighting conditions and a sea state not too rough for the
measurements.
DOWNWARD IRRADIANCE I N THE UPPER LAYERS
Survey of observations in the visible
Firstly we shall go into particulars about measurements of downward
irradiance. In Fig. 6 3 spectral curves of irradiance Ed for different depths are
given which represent corrected data obtained with broad band filters and
data obtained with interference filters. The spectral distribution of irradiance
shows a maximum at 480-500 nm at the surface. With increasing depth, the
peak shifts slowly toward 465 nm in clear ocean water (east Mediterranean).
A salient asymmetry of the spectral curve develops as the violet becomes
stronger than the green. A slightly higher turbidity, such as occurs in the
Caribbean Sea, extinguishes the asymmetry and brings about a symmetrical
form of the distribution curve. Overall decreased irradiance transmittance
reduces the shortwave part of the spectrum more than the longwave part and
shifts the maximum of transmittance toward longer wavelengths because of
selective absorption by particles and yellow substance. This general principle
is confirmed by Neuymin et al. (1964) for north Atlantic waters. The Baltic
Sea, which is abundant in yellow substance, displays maximum shift of the
transmittance peak ( t o 550nm), while the ultra-violet of 3 7 5 n m is
extinguished even at 5 m.
Measurements of Ed with spectroradiometers have been made in a few
areas (Figs. 64 and 65). Especially material collected by Morel and Caloumenos
(1974) off West Africa, supplies needed information even if it lacks observations of irradiance below 400 nm. In all these curves minima appear due t o
Fraunhofer lines, chiefly at 395, 430 and 520nm, and in some cases t o
128
A
I
I
B
,
I
I
I
I
I
I
I
Baltic Sea
c
LOO
500
nrn
600
D
LOO
500
600
nrn
700
Fig. 63. Spectral distribution of downward irradiance for high solar elevations.
A. Eastern Mediterranean. B. Caribbean Sea (after Jerlov, 1951). C. Off Japan (after
Sasaki et al., 1958a). D. Baltic Sea (after Ahlquist, 1965).
350
I
400
A
I
450
.
I
500
.
I
550
l
I
600
.
I
650
.
I
.
750
nm
700
Fig. 64. Spectral distribution of downward irradiance. (After Tyler and Smith, 1970.)
129
0
1
- ~ a r g50
a s s oS e a
...... O f f S e n e g a l
.:'
I
350
LOO
L50
500
550
600
650 700
nrn
LOO
L50
500
550
600 6 5 0nrn700
Fig. 65. Spectral distribution of downward irradiance.
A . After Smith (1973). B. After Morel and Caloumenos (1974).
Percentage of surface irradionca
1
Percentage of surface irrodiance
2
5
10
20
50
100
m
10
20
30
LO
50
3
10
20
30
LO
A
550
525
500 L15 nrn
50
Fig. 66. Depth profilesof downward irradiance(cf. Fig. 6 3 ) in percent of surface irradiance
A. Caribhean Sea. B. East Mediterranean.
130
water-vapour bands (Fig. 31). A detail calls for attention: the 520 minimum
becomes more distinct with increasing depth especially for upwelling light
(see Fig. 77). The existence of a weak absorption band at 5 1 5 n m is also
indicated by measurements on pure water (Chapter 3 ) .
Another set of curves represents on a logarithmic scale the percentage of
irradiance compared to surface irradiance as a function of depth (Fig. 66).
The presence of a curvature, which is most obvious for the blue and the
violet, is a consequence of the change with depth of the radiance of scattered
light (Chapter 9) and is defined by integration of this distribution. The
strongest curvature is in clear water at 5 0 m for 475nm. With increase of
turbidity, it ascends and becomes less conspicuous.
Fig. 67. T h e attenuation coefficient K , of downward irradiance.
1 = the Sargasso Sea; 2 and 3 = t h e upwelling area off West Africa; 4 = close t o t h e
African coast. (After Morel and Prieur, 1975.)
It is of particular interest t o consider the optical properties of the limited
upwelling areas which contribute largely t o the primary production of the
sea. Morel and Prieur (1975) have measured the spectral irradiance attenuation coefficient K , off West Africa. In Fig. 67 the clearest natural water
(Sargasso Sea) is represented by curue 1 . In recently upwelled water chlorophyll imposes such a strong change on irradiance that the K , distribution is
like the absorption curve of chlorophyll a (curue 3 , chlor; a = 18.1mg/m3,
b = 2.0). Quite different distributions are encountered in the dark-green
131
water close t o land which contains a large variety of particles (curve 4 , chlor;
a = 1.5 mg/m3, b = 4.0).
Observations in the ultra-violet
There is every reason t o treat observations of the far ultra-violet in this
connection even if they are obtained by a somewhat different technique. In
1947 Jerlov found by means of his UVB meter (Fig. 53) that the transmittance of radiant energy of 310 nm in clear water exhibits maximum values of
86%/m, which is by far more than previously found. This kind of energy is
strongly influenced by absorption due t o particles and yellow substance. The
span of transmittance fluctuation is therefore large; in the tropical part of
the ocean it is from 50 t o 80%/m. In a coastal area such as the Skagerrak the
maximum value does not exceed 10%/m. The optical properties in the far
ultra-violet thus undergo a drastic change from oceanic t o coastal water
types.
OPTICAL CLASSIFICATION
Basis of classification
Attempts have been made t o bring about some systematic order in the
experimental material of irradiance. A scheme of optical classification of
ocean water was propounded by Jerlov (1951) in order to distinguish
different water types in terms of spectral transmittance of downward
irradiance at high solar altitudes. By synthesizing available observational data
from surface waters, three normal transmittance curves were obtained representing three different optical water types, I , II and III. Several factors combine t o permit a simple description of the attenuation process and its change
with turbidity. An essential basis for the classification is the observed fact
that the shape of the volume scattering function for surface water shows
only small variations from one occeanic area t o another. It has been demonstrated that particulate material and yellow substance are primary agencies
for selective absorption. A connection between these two parameters exists
in so far as yellow substance originates from decaying particles. The relationship between the irradiance attenuation coefficient (465 nm) and the
scattering coefficient 6, both given as mean values in the water column
0- -50 m, is more closely interpreted in Fig. 68. The limiting curve represents
the lowest attenuance for a given particle scattering. Some regions fall
significantly off this curve. Except for the Red Sea, which also contains a red
or yellow component, these are upwelling areas off the west coasts of
continents and regions of divergence. The deviations of these productive
areas are generally attributed t o selective absorption by yellow substance and
132
particles. They are also an effect of the larger particle size in nutrient-rich
water than in less fertile water, the larger size tending t o diminish the ratio
of scatterance t o absorptance.
0.100
'?
0
90
O D I V S 9" IND 0
OEQ P A C 0
EO I N D O
SEA
E MEDITERRANEAN
_I
Q
1-
2
GO10
20
30
LO
50
60
70
IHRADIANCE ATTENUATION COEFFICIENT
80
90
100 0110
0-531.t l L 6 5 n m l
Fig. 68. Comparison for oceanic stations of downward irradiance attenuation coefficient
(465 n m ) and scattering coefficient. (After Jerlov, 1951.)
It may be concluded that the distribution of particles and yellow
substance, and ultimately of irradiance attenuance, is controlled by those
dynamical processes in the sea which have an important bearing on productivity. The observed irradiances form a pattern which in broad outlines
corresponds to the general oceanic circulation, with minima in the upwelling
regions and maxima in the nutrient-poor areas of the eastern Mediterranean
and the Sargasso Sea.
Optical water types
The arranging of irradiance data in categories aims at a regional large-scale
classification distinguishing water masses in the upper layers, 0-10 m, which
are generally homogeneous in the ocean. It should be borne in mind that in
the surface region the irradiance attenuation coefficient Kd for high solar
elevation is close t o the absorption coefficient a. With highly stratified water
the top layer alone can be optically characterized with any certainty.
As a considerable number of oceanic spectral transmittances fall between
the two basic types I and 11, a subdivision was made by adding two intermediate types, IA and I B (Jerlov, 1964). An analysis of recent data has been
made in order t o broaden the basis of the classification published by Jerlov
(1968). The observations to be used should satisfy the following demands:
The experiments are conducted in offshore waters on a clear day at high
solar elevations and a smooth water surface; values normalized ( t o surface
irradiance) are not considered welldefined. Irradiance just below the surface
133
is either directly measured or accurately deduced from records above the
surface. The irradiance attenuation Kd must show small variations with
depth in the upper 10 m. Unfortunately a great deal of new data d o not fulfil
these requirements. Besides those observations mentioned the main sources
have been H@jersIev’s (1973, 1974b) measurements ( 3 7 5 - 6 3 3 nm) in the
Mediterranean and Morel and Caloumenos’ (1974) ( 4 2 5 - 6 0 0 nm) off West
Africa.
nm
700
Fig. 69. Transmittance per meter of downward irradiance in the surface layer for optical
water types. Oceanic types I, 11,111and coastal types 1 , 3 , 5 , 7, 9.
The outcome of the revision of the original water types 1-111 is exhibited
in Fig. 6 9 and Tables XXVI and XXVII. It is doubtful if a new water type of
higher turbidity could be created even if some material is available.
The spirit of the classification is that the irradiance attenuation coefficient
Kd for any wavelength can be expressed as a linear function of a reference
wavelength. For obvious reasons this is chosen at 475 nm (Fig. 70). Deviations
from the previous classification (Jerlov, 1968) occur at 600 nm where the
new Kd values are higher for types I , I A , IB and II. With reference t o the
discussion on pure water (Chapter 3) considering the larger scatter of K ,
values obtained by different workers for 6 0 0 n m it seems that the last word
is not said about the behaviour of the irradiance attenuation in the “slope”
region of 600nm. Furthermore type III shows lower Kd values at 550 and
575 and somewhat higher values around 4 2 5 n m which may be caused by
chlorophyll absorption. A special analysis of the wavelength 513nm for
ocean water clearly shows the presence of the weak absorption band
mentioned (transmittance = 96.2% for type 1 in Fig. 69).
Most irradiance data fit well on the set of transmittance curves in Fig. 69.
Some areas of the Sargasso Sea display the clearest water, slightly more
transparent than type I .
TABLE XXVI
Irradiance transmittance for surface water of different water types
Water
type
Wavelength ( n m )
310
350
375
400
425
450
475
500
525
550
575
600
625
650
675
700
I . Irradiance transmittance ( % / m )
I
86
94
96.3 97.2
IA
83
92.5 9 5
96.3
IB
80
90.5 94
95
I1
69
84
89
91
I11
52
73
80
83
1
17
30
45
60
3
9
19
32
46
5
3
10
21
33
7
5
12
21
9
2
5
9
97.8
96.9
95.9
92.2
85
70
58
46
31
15
98.1
97.4
96.5
93.5
87.5
78
68
57
41
21
98.2
97.5
96.8
94
89
84
75
65
49
29
97.3
96.9
95.9
93.2
89
87
80
70
56
37
95.8
95.3
94.7
92.7
89
88
82
73
61
46
93.9
93.5
93
91.5
88.5
88.5
83
74
63
53
91.5
91.0
90.5
89
86
86
81
72
63
56
79
78.5
78
77
74
74
72
67
62
55
74
73
72.5
71.5
69
69
67
62
58
52
70
69
68.5
67
64
64
63
58
53
47
66
65
64
63
60
60
57
52
46
40
57
56.5
56
54
52
52
49
45
40
33
80
73
66
44
20
2.7
0.5
83
77
70
51
26
8.2
2.1
0.4
83.5
78
72
54
31
18
5.5
1.4
76
73
66
50
32
25
11
2.7
0.3
65
62
58
47
31
27
13.5
4.5
0.7
53
51
49
41
30
30
15
5
1.0
0.2
41
39
37
32
23
22
12
3.7
1.0
0.3
9.5
9.1
8.6
7.4
5.2
5.0
3.7
1.8
0.8
0.3
4.7
4.5
4.3
3.5
2.4
2.5
1.8
0.8
0.5
0.2
2.7
2.5
2.4
1.8
1.2
1.1
1.0
0.4
0.2
1.5
1.4
1.3
0.9
0.5
0.6
0.4
0.2
0.4
0.3
0.3
0.2
0.1
0.2
2. Irradiance transmittance (%/I 0 m )
I
22
54
68
76
IA
16
46
60
68
IB
11
37
52
60
I1
2.5
17
30
38
ILI
0.2
4
11
16
1
0.6
3
5
7
9
TABLE XXVII
Downward irradiance attenuation coefficient K , * l o 2m-l(0--10 m)
Water
type
Wavelength ( n m )
310
350
375
400
425
450
I
IA
IB
I1
I11
15
18
22
37
65
6.2
7.8
10
17.5
32
3.8
5.2
6.6
12.2
22
2.8
3.8
5.1
9.6
18.5
2.2
3.1
4.2
8.1
16
1.9
2.6
3.6
6.8
13.5
1
3
5
7
9
180 120
240 170
350 230
300
390
80
110
160
210
300
51
78
110
160
240
36
54
78
120
190
25
39
56
89
160
475
500
525
550
575
600
625
650
675 700
1.8
2.5
3.3
6.2
11.6
2.7
3.2
4.2
7.0
11.5
4.3
4.8
5.4
7.6
11.6
6.3
6.7
7.2
8.9
12.0
8.9
9.4
9.9
11.5
14.8
23.5
24
24.5
26
29.5
30.5
31
31.5
33.5
37.5
36
37
37.5
40
44.5
42
43
43.5
46.5
52
56
57
58
61
66
17
29
43
71
123
14
22
36
58
99
13
20
31
49
78
12
19
30
46
63
15
21
33
46
58
30
33
40
48
60
37
40
48
54
65
45
46
54
63
76
51
56
65
78
92
65
71
80
92
110
136
0.68
KdlAl
64
60
56
52
48
44
40
36
32
28
24
20
I
16
12
8
4
Fig. 70. The downward irradiance attenuation coefficient K d ( h ) as a function of Kd
(475 nm) for different water masses.
PERCENTAGE OF SURFACE IRRADIANCE (465 nm)
0.5
1
2
5
10
20
50
100
Fig. 71. Depth profiles of downward irradiance in percent of surface irradiance for
defined optical water types. Oceanic types Z, ZA, IB,ZZ, IZZ and coastal types I , 5 , 9
(465 nm).
137
An extension of the classification t o greater depths - preferably to the
lower limit of the photic zone -greatly improves its usefulness. An argument
against this would be the optical nonuniformity of the water; stratification
leading to inhomogeneous water occurs for instance a t the eastern parts of
the Pacific and the Atlantic Ocean. So far, derived logarithmic curves for the
whole family of defined optical types are shown in Fig. 71 for blue light
(465 nm) only.
The coastal types 1-9 in Tables XXVI, XXVII and Fig. 69 are derived
from observations along the coast of Scandinavia and western North America.
These northern water masses are characterized by a relatively high amount of
yellow substance. Some recent material (Aas, 1967, 1969 and H@jerslev,
1974a) has substantially fortified the basis for this special classification. The
transmittance curve for the clearest coastal water, type I , coincides with that
for oceanic type III between 500 and 7 0 0 n m but tends toward much lower
penetration of shortwave light because of the high selective absorption which
marks these coastal waters.
The oceanic classification lends itself to a cartographic representation of
the trends in regional distribution of optical water types (Fig. 72). This
representation has also drawn on some recent measurements by Matsuike
(1967, 1973), Matsuike and Sasaki (1968), Matsuike and Kishino (1973),
Shimura and Ichimura (1973) and Carpenter (personal communication, 1972,
Antarctic waters), and in particular by Rutkovskaya and Khalemskiy (1974)
who have prepared a chart of optical types in the Pacific ocean using
published observations. Fig. 72 exhibits a dense observation net in a few
regions, e.g., such as has been established in the western North Atlantic,
whereas vast areas as the South Atlantic lack relevant data. The distribution
of optical water types strongly brings out upwelling areas at the west coasts
of the continents and even at the Equator. It is consistent with the general
circulation of the oceans with clear water around 20" latitude in the western
and central parts of the Atlantic and Pacific oceans. As mentioned, the
Sargasso Sea stands out as being slightly more transparent than type I . The
eastern Mediterranean exhibits a remarkably high clearness considering its
vicinity t o land. Very turbid water in the upwelling regions or near the shore
do not fit into the classi€ication.
QUANTA IRRADIANCE
Some of the initial broad-band measurements of quanta irradiance
(350-700nm) are exhibited in Fig. 73. The two groups of depth profiles
representative of different water masses are obtained with the Danish and
the French quanta meters, respectively. A consistent feature is the fast
decrease from the surface t o a few metres due t o absorption of the longwave
light. For the clearest water a curvature appears around 50 m identical with
138
60'
40
20
0
20
LO
60
80
100
120
1AO
I60
180
160
140
120
100
,
7 0"
60
40
IB
IA
<I
Y I A L 20
iD
IB
-0
I
I
I
Fig. 72. Regional distribution of optical water types.
IA
IB
20
40
~
~
60
70'
139
1
Percentage of s u r f a c e q u a n t a
2
5
10
20
50
0
rn
10
20
30
40
'
9'00'N.
g 0 2 0 ' N , 2O'LO'W
21'02'W
//
50
60
70
A
Sorgosso Sea
25OLI.N I I f 1 L' W
Fig. 73. Depth profiles of downward quanta irradiance.
that for blue light (Fig. 71). This gradually disappears when the water
becomes more turbid. The large space between the extreme curves demonstrates a considerable variation of the photic zone in the ocean.
A useful classification for quanta irradiance is possible on the basis of
direct observations or of computations from spectral-energy data (see
Chapter 15).
TOTAL DOWNWARD IRRADIANCE (300-2,500 nm)
The total irradiance comprising the whole energy spectrum from sun and
sky (300-2500 nm) is not accessible for accurate observation in the surface
layer because of strong absorption of the infra-red. The efficiency of water as
a monochromator is amply demonstrated in Fig. 74. The largest part by far
of the incident energy is converted into heat, which has considerable thermodynamic implications. For the ocean waters which have been classified
optically, Table XXVIII summarizes values of the total irradiance supplied t o
different levels.
DOWNWARD IRRADIANCE IN DEEP WATER
Below 100 m depth, the wavelength-selective attenuation mechanism has
isolated a narrow spectral range of mostly blue light (see Fig. 75). The change
140
t
E
L
I
200
Fig. 74. The complete spectrum of downward irradiance in the sea.
of the radiance distribution towards an asymptotic state is accompanied by
an approach t o nearly constant irradiance attenuation coefficient, which is
evidenced by the linearity of the logarithmic curves. It therefore suffices t o
present the average coefficient for actual depth intervals, as in the survey of
existing data in Table XXIX. Here, depths below 500 m have been deliberately omitted since a background of animal light might enhance the ambient
irradiance at these levels.
In connection with his studies on bioluminescence, Clarke (1933) has
contributed greatly t o the exploration of deep water by finding a minimum
value of 0.025 for the coefficient in the North Atlantic. For the rest, the
coefficient remains within the interval 0.030-0.040.
IRRADIANCE ON A VERTICAL PLANE
The irradiance on a vertical plane, i.e., the horizontal irradiance component
has attracted some attention because the ratio Eh/E, ( E d = the downward irradiance) is recognized as an indicator of the obliquity of the underwater light. By means of a cubical photometer, this ratio was accurately
measured by Atkins and Poole (1940, 1958). The information that may be
extracted from their observations indicates that the actual ratio E,/Ed varies
from 75 to 85% and that it attains a constant value with increasing depth.
&,
TABLE XXVIII
Percentage of total irradiance (300-2,500 nm) from sun and sky'
Depth
(m)
0
1
2
5
10
20
25
50
75
100
150
200
Oceanic water
Coastal water
I
IA
IB
11
111
1
3
5
7
9
100
44.5
38.5
30.2
22.2
100
44.1
37.9
29.0
20.8
100
42.9
36.0
25.8
16.9
100
42.0
34.7
23.4
14.2
100
39.4
30.3
16.8
7.6.
7.7
1.8
0.42
0.10
100
27.8
16.4
4.6
0.69
0.020
100
17.6
7.5
1.0
0.052
11.1
3.3
0.95
0.28
100
33.0
22.5
9.3
2.7
0.29
100
22.6
11.3
2.1
0.17
13.2
5.3
1.68
0.53
0.056
0.0062
100
36.9
27.1
14.2
5.9
1.3
4.2
0.70
0.124
0.0228
0.00080
F o r oceanic water t h e solar altitude is 90'; for coastal water 45'
0.97
0.041
0.0018
0.022
142
Fig. 75. Spectral distribution of downward irradiance in Golfe d u Lion. (After Kampa,
1961.)
Data obtained by Jerlov and Koczy (1951) suggest a value of 60% a t 400 m
in the Sargasso Sea. These findings are in general agreement with the
structure of the radiance distribution. This can be verified from Tyler and
Shaules’ (1964) integration of radiance, which yields irradiance on planes
of different vertical and azimuthal angles.
UPWARD IRRADIANCE
The upward irradiance E,, i.e., the irradiance falling on a horizontal
surface facing downwards, is a subject which has attracted great interest.
This component is readily observed, since it fluctuates much less because of
wave action than does the downward light.
Kalle (1939b) anticipated that the spectral distribution curve for E , in
clear water would be peaked at a wavelength smaller than the 4 6 5 n m
observed for E d . The shift is attributed t o highly wavelength-selective
molecular scattering which occurs t o some degree as multiple scattering. The
experimental proof was given by Jerlov (1951). Confirmatory spectral
distributions are furnished by Ivanoff et al. (1961) and Tyler and Smith
(1970). Thus upward irradiance in clear water exhibits distribution curves of
143
TABLE XXIX
Measurements of irradiance attenuation coefficients at deep levels i n clear weather
Area
Depth
range
(m)
Attenuation
coefficient
(m-l)
Reference
Off Tahiti
Sargasso Sea
100-400
100-400
4 00-5 0 0
0.034
0.040
0.038
Jerlov and Koczy (1951)
Florida Current
160-460
460-580
92-400
400-554
0.034
0.038
0.039
0.032
Clarke and Wertheim (1956)
Bay of Biscay
98-350
300-40 5
0 .O 38
0.033
Boden et al. (1960)
Off Californian coast
200-350
200-350
200-400
0.040'
0.0301
0.035'
Kampa (1961)
Off Madeira
200-400
400-530
0.032
0.035
Jerlov and Nyggrd (1961)
West Indian Ocean
200-8 0 0
0.02 2-0.0 33
Clarke and Kelly (1964)
North Atlantic
41'26'N 55'46'W
47'27'N 40'50'W
46'45'N 35'33'W
100-350
250-750
75-300
0.031
0.023
0.030
Clarke and Kelly (1965)
Slope water off
New York
Off Bermuda
Golfe d u Lion
Computed b y N.G. Jerlov.
quite different shape than does downward irradiance which is evident from
Figs. 76 and 77. It is logical t o assume that the maximum in the spectral
distribution of E , will, at great depths, occur at the wavelength of the
residual light. This shift toward longer wavelengths with increase of depth is
shown in Figs. 76 (left) and 79 (left). In turbid water, however, where
molecular scattering is strongly suppressed, the set of curves for Ed and E ,
are rather symmetrical round the wavelength of the most penetrating light
(Fig. 76, right).
A high value of R = E,/E, of 10% in the violet caused for the greater part
by molecular scattering is characteristic for the clearest water. With increasing
turbidity the R-value decreases and its maximum is shifted towards longer
wavelengths. Morel and Prieur (1975) have shown that for upwelling water
near West Africa this change may proceed until a distinct R-maximum of 1%
occurs at 5 6 0 n m (cf. Fig. 67). For the very high values of the scattering
coefficient (up t o 4 m - ' ) met with close to the coast the R-value again can
attain 10%varying little between 500 and 560 nm.
144
Fig. 76. Comparison between spectral distribution of downward and upward irradiance
for solar elevation of 55-60'.
Left: Sargasso Sea. (After Lundgren and Hdjerslev, 1971.) Right: Baltic Sea. (After
Ahlquist, 1965.)
B
S a r g a s s o Sea
North of H a i t i
LOO
450
500
550
600
nm
Fig. 77. Spectral distribution of upward irradiance. A. After Morel (1973b). B. After
Smith (1973).
SCALAR IRRADIANCE
Even in early research, attention was paid to the significance of scalar
irradiance which is the most representative parameter for the underwater
145
light field (Jerlov and Liljequist, 1938). Considering that scalar irradiance is
readily obtained from observation of spherical irradiance E , it seems
surprising that for a long time E , has not been incorporated into experimental investigations. The deficiency is largely remedied by Hg)jerslev (1973)
who systematically made comparative measurements of E d , E , and E , in
order to realize the application of Gershun's equation (60). The two families
of depth profiles in Fig. 78, one for clear the other for turbid water, show
the mutual dependence of E, and E ( = Ed - E,) which both enter the
equation. These observations constitute a proof of the parallelism of the
E,- and E-curves; the more directed the light is the closer the curves run.
.^
10
1
-1.
.^^
100
1
I
'
-1.
10
'
"""I
1
100
" " "
m
5
10
15
- 20
37 2
- 25
-
30
Fig. 78. Depth profiles of the irradiances Eo (scalar) and Ed - E, = E . (After Hdjerslev,
1973.)
DEPENDANCE O F IRRADIANCE ON SOLAR ELEVATION
Down ward irrad iance
The dependence of irradiance on solar elevation is a minor effect which
cannot always be distinguished from the experimental errors in the irradiance
observations. But it should certainly not be disregarded in accurate measurements. The existence of such an effect is evidenccsd from data given in
Tables XXX-XXXI. H4jerslev (197413) has made a thorough examination
of the problem by series of frequent records of "blue" irradiance as well as
of quanta irradiance (Fig. 79). The trend of these curves agrees with the
theoretical deduction that the effect occurs in the upper layers chiefly for
altitudes between 90 and about 40".
As we know, the effect does not exist in the asymptotic state. The
approach of the irradiance attenuation coefficient towards the asymptotic
value is fairly rapid and thus the solar-elevation effect will be limited t o
relatively small depths, which is brought out in Table XXXII.
146
TABLE XXX
Percentage of surface irradiance a t 50 m in t h e Indian Ocean and a t F n u a t i o n coefficients
80 )
(After Jerlov, 1951)
Kd between 0 and 50 m for t w o different solar altitudes (30"and
Wavelength
(nm)
550
525
500
475
450
425
400
375
Percentage of surface
irradiance a t 50 m
Attenuation coefficient
a t 0-50 m
altitude 30'
altitude 80'
altitude 30'
altitude 80'
3.3
5.6
12.4
15.8
16.2
13.8
12.3
8.5
3.5
6.9
15.8
22.7
22.7
20.2
17.0
11.2
0.068
0.056
0.041
0.037
0.036
0.039
0.041
0.048
0.067
0.052
0.037
0.029
0.029
0.031
0.035
0.043
TABLE XXXI
Downward irradiance attenuation coefficient f o r different solar elevations; optical d e p t h
T = 2.5
(After Kozlyaninov and Pelevin, 1966)
Solar
elevation
("1
Wavelength ( n m )
430
480
550
600
650
~
15
29
59
0.081
0.072
0.058
0.060
0.055
0.045
0.063
0.059
0.049
0.089
0.082
0.068
0.20
0.17
0.14
With the sun near the horizon the atmospheric light is mainly diffuse and
any elevation dependence is not t o be expected. Measurements by Clarke
and Kelly (1965) reproduced in Fig. 80 suggest that this is the case.
Additional information about the diurnal variations of irradiance can be
procured in Chapter 15.
In this connection Boden's (1961) observations of twilight should be mentioned (Fig. 81). They show that the shortwave light becomes progressively
stronger than the longwave light as time goes on. This effect is probably due
t o a change in the spectral composition of global radiation.
Upward irradiance
It was first observed by Sauberer and Ruttner (1941) that the irradiance
ratio E u/E d is dependent on the solar altitude, being higher for a low sun
147
.
..
20'
10'
Solar elevation
30'
LOo
m
.
4.-
1
50'
60'
-
70"
1
5 0 % of s u r f a c e q u a n t a i r r a d i a n c c ( 3 5 0 - 7 0 0 n m )
m
10
5 0 % of s u r f a c e i r r a d i a n c e l L 6 5 n m )
0
0
0 0
0"
-
u
.
=
O
20
30
.
LO
50
n
60
0
0
0
'
70
%
80
-
0
Fig. 79. Depths of 50%, 10% and 1%levels at different solar elevations for quanta irradiance (350-700 nm) and for blue irradiance (465 nm). Clear water off Sardinia. (After
H4jerslev, 1974b.)
TABLE XXXII
Downward irradiance attenuation coefficient K , for different solar elevations in the
Sargasso Sea
(After Lundgren and HQjerslev, 1971)
Depth
Solar altitude
Wavelength (nm)
(")
37 5
484
(4
12
25
50
0.047
0.043
0.032
0.023
37
25
56
0.041
0.040
0.031
0.022
62
25
56
0.051
0.045
0.033
0.029
87
25
56
0.055
0.051
0.034
0.034
125
25
56
0.054
0.055
0.035
0.036
148
f
10-'1
'
"
"
'
0635
0665
0655
0705
"
0715
'
'
0725
I
TIME
TIME (EST]
Fig. 80. Downward irradiance (photomultiplier t u b e without colour filter) during sunset
period in the western North Atlantic. (After Clarke and Kelly, 1965.)
Fig. 81. Spectral composition of downward irradiance a t 100 m for t h e period of a n hour
around sunrise. (After Boden, 1961.)
TABLE XXXIII
T h e ratio of upward to downward irradiance E,/Ed (%) in t h e Indian Ocean (After Jerlov,
(After Jerlov, 1951)
Solar
altitude
(" 1
Depth
(m)
Wavelength ( n m )
375
400
425
450
475
500
525
31
10
50
7.5
6.9
8.3
9.4
9.1
10.0
7 .O
8.3
6.0
7.1
4.0
3.7
1.6
80
2
10
25
50
5.5
5.8
6.1
4.1
5.8
5.9
5.5
4.4
5.8
6.1
6.5
5.2
5.2
5.2
5.4
4.6
4.1
4.4
4.5
4.1
2.6
2.9
2.9
3.2
1.3
1.4
1.4
149
25
450
5
6
7
8
9
10 11 1 2 13 i4 15 16 17 18 19
HOUR
~
Fig. 82. Diurnal change of t h e irradiance ratio E,/Ed (%). (After Agenorov, 1 9 6 4 . )
Fig. 8 3 . Fluctuations of downward irradiance as a function of “apparent optical d e p t h ”
(Kd 2). Westindian waters. (After Dera, 1970.)
than for a high one. This effect, amply illustrated in Table XXXIII and
Fig. 82 is a consequence of the shape of the scattering function. Thus with a
zenith sun in the water upward scattering from sun rays occurs at 90-180”,
and with a 45” sun at 45-135”.
INFLUENCE O F BOTTOM
The upward irradiance E , is normally affected by proximity t o the
bottom. In shallow waters, the accumulation of particles near the bottom
may cause strong back-scattering. In Bermuda waters Ivanoff et al. (1961)
found a logarithmic increase of the irradiance ratio E,/E, from 11%at the
surface to 29% at 10 m, 1m above the bottom. As shown by Joseph (1950),
a minimum in E , theoretically predicted develops at a certain depth above a
high-reflecting sand bottom (Fig. 42).
150
IRRADIANCE FLUCTUATIONS
The influence of waves on the radiative transfer through the sea surface t o
a point under water has a bearing on reflection and refraction at the surface
as well as on fluctuations in the length of the optical path. Everyone
measuring downward irradiance in the upper layers of the ocean even from a
stable platform has experienced the disturbing short-period fluctuations
occurring especially for longwave light. The dependence of the statistical
properties of irradiance on the state of the sea surface is a matter which is
theoretically and experimentally well investigated (J.I. Gordon, 1969;
Snyder and Dera, 1970; Dera, 1970; Nikolayev et al., 1972; Shevernev,
1973). Their analyses prove that irradiance fluctuations partly result from
variations in the length of the optical path, partly are due t o a lens effect of
the waves. Accordingly the spectral energy density curves of irradiance
fluctuations have two peaks, one associated with the principal peak of the
wave spectrum, the second peak of higher frequency due t o lens effects.
Dera (1970) has endeavoured t o make a synthesis of observations by
represeiiting the fluctuation factor dEd/E, as a function of the “apparent
optical depth”, Kd z (Fig. 83). The plots from different water masses and
for different wave heights are between the two limiting curves in the diagram
which show a pronounced maximum (>60%)a t about K , z = 0.2.
-
CHAPTER 11
POLARIZATION OF UNDERWATER RADIANT ENERGY
GENERAL POLARIZATION PATTERN
In order to form a true conception of the nature of polarization in the sea,
we shall recollect that the light passing the sea surface is partly polarized
(Chapter 4, p. 72). Skylight shows a polarization structure within its refraction cone, and refracted sunlight is polarized in a degree which increases with
its zenith angle. The polarization pattern of the penetrating light is radically
altered when the light is scattered by water and particles. It is evident from
radiance distributions that with increasing depth skylight becomes of
decreasing importance compared with scattered light emanating chiefly from
the direct sun rays. The general behaviour of the polarization of light scattered from a beam is out,lined in Chapter 2. It is interesting to check these
predictions against actual experimental findings. Such tests require that
regard be paid t o the dependence of polarization on the divergence of the
incident beam (Ivanoff, 1957a; Ivanoff and Lenoble, 1957). Reviews of the
polarization problems are given by Timofeeva and Neuymin (1968) and
recently by Ivanoff (1974) and Timofeeva (1974).
OBSERVATIONS
In his first investigation, Waterman (1955) ascertained that polarization is
dependent on the sun's position in the sky and persists down t o 200m
depth; the polarization effect is ascribed to scattering of directional light.
The effect of solar altitude has been carefully studied, mainly in horizontal
lines of sight, by Waterman and Westell (1956). Their results agree with the
theoretical prediction that maximum polarization occurs perpendicular to
the sun beam. In a horizontal plane, the degree of polarization varies periodically with the azimuth t o the solar bearing (Fig. 84). The maximal points
(peaks) at 5 90" are little affected by the solar altitude, whereas the minimal
points show a dependence on the altitude. The investigations of Waterman
and Westell also demonstrate that all changes in parameters which diminish
the directionality of underwater light, such as more diffuse atmospheric
light, increased turbidity and the presence of bottom reflections tend t o
reduce the polarization. Observations by Ivanoff (1957a) for several lines of
sight fit well with the theoretical pattern deduced by him on the basis of the
152
180”
Antisun
270”
0”
Sun
Bearing
90’
180’
Antisun
-
Fig. 8 4 . Degree of polarization in horizontal lines of sight as a function of solar bearing.
Solar elevation
55O. (After Waterman and Westell, 1 9 5 6 . )
Fig. 85. Degree of polarization (blue light) as a function of line of sight in the vertical
plane of the s u n ( n o t visible) a t 1 5 m depth in t h e Channel.(After Ivanoff, 1 9 5 7 a . )
radiance distribution. (Fig. 85). The systematic polarization experiments
conducted by Timofeeva (1962) have furnished a complete picture of the
polarization distribution in vertical planes of different solar azimuths (to the
solar bearing) (Fig. 86). It is demonstrated that non-symmetry relative t o the
direction of the sun and the vertical appears for all azimuths except 90” due
to the influence of the asymmetry of the sea’s irradiance. Strict symmetry
arises only for normal incidence of solar rays or with an overcast sky. A comparison between Figs. 8 5 and 88 verifies that increasing diffusivity of the
daylight tends to reduce the polarization.
Another instructive approach to the polarization problem is presented in
Fig.87, based on data obtained by Timofeeva (1969) in the Black Sea. The
group of curves in Fig.87 depicts the angle between the e-vector and the
horizontal line perpendicular t o the line of sight, $J,as a function of the
zenith angle 8 for different azimuthal planes. The neutral points N1-N4
( p = 0) appear in the diagram; they are, in analogy with atmospheric optics,
called after Brewster ( N I ) , Babinet (N2)and Arago ( N 3 ) ; ( N 4 unnamed).
The corresponding curve in Fig.87 showing the relation between the polarization and the zenith angle in the vertical plane of the sun suggests that
“negative” polarization occurs, which implies that the e-vector is in a vertical
plane. The two shaded lobes in the uppermost polar diagram of Fig. 86
represent negative polarization. From laboratory measurements on milky
media Timofeeva and Koveshnikova (1966) have been able to predict that
besides neutral points fields of “negative” polarization exist in the sea. This
is also indicated in Lundgren’s (1976) observations with a meter of high
resolution (1.3”; Fig. 88). On the other hand Ivanoff (1974) argues in his
comprehensive review of polarization measurements in the sea that negative
values of the degree of polarization have no sense as the e-vector may have
any orientation outside the vertical plane through the sun.
153
9 0"
6705
4 5"
2205
-180"
0"
-goo
-20
go"
e
O0
180'
-1
Fig. 86. Angular distribution of degree of polarization in vertical planes of different
azimuths from t h e sun. (After Timofeeva, 1974.)
Fig. 87. Above: Dependence of J/ (the angle between t h e e-vector and t h e horizontal line
perpendicular t o the line of sight) o n t h e vertical angle 0 .
Below: Degree of polarization as a function of 0 in t h e vertical plane through t h e sun. N1 ,
N 2 , N 3 and N 4 are t h e neutral points. (After Timofeeva, 1974.)
The correlation between degree of polarization and depth is consistent
with the origin of polarization by scattering. The degree of polarization as a
function of depth for vertical planes of different azimuths is exemplified in
Fig. 89 (Ivanoff and Waterman, 195813).The p-value diminishes rapidly from
0 to 4 0 m due to a change of the radiance distribution from a markedly
directed to a more diffuse character. The three curves depicted are likely to
converge with increasing depth into one line of constant p when the asymptotic radiance distribution is approached.
The angular distributions (Fig. 88) obtained by Lundgren (1976) with his
high-resolution polarimeter reveal a structural detail indicating a conspicuous
maximum of polarization at the Snell circle. At low solar elevation the polarization of the skylight becomes predominant as illustrated in Fig. 90. This
group of curves demonstrate the gradual reduction of the degree of polarization with increasing depth until - as predicted by the theory - a stationary state of polarization distribution is reached at asymptotic depths. As
directionality (from zenith) prevails in the asymptotic state the polarization
of underwater light persists to infinite depths.
154
Degree o f polarization
Vertical angle
Fig. 8 8 . Change of the angular distribution of degree of polarization with increasing
depth. Solar zenith distance is indicated a t t h e curves. Off Sardinia. (After Lundgren,
1976.)
Fig. 8 9 . Influence of depth o n degree of polarization (500 n m ) in vertical planes of different azimuths in clear water. Solar elevation 22-30'. (After Ivanoff and Waterman,
195813.)
The shape of the final polarization distribution is in analogy with the
asymptotic radiance distribution -- determined by the key parameter
E = h / c . Timofeeva (1974) has investigated the degree of polarization as a
function of E for various zenith angles in the deep regime of a milky medium.
This research gives evidence that the degree of polarization increases rather
rapidly with increasing value of E for vertical angles near 90" whereas it is
independent of E for small angles (<30") if E > 0.08. In this connection
Timofeeva emphasizes that results from laboratory measurements, e.g., on
milky media, may be applied t o advantage t o the marine environment and
facilitate the understanding of underwater light problem.
155
I
Fig. 90. Distribution of degree of polarization a t a solar elevation of 3--4". (After
Lundgren, 1976.)
Fig. 91. Effect of wavelength o n degree of polarization i n vertical planes of '
0 (solar
bearing) and 90°, 180' in clear water. Solar elevation 5 7 -61O. (After Ivanoff and
Waterman, 1958b.)
The dispersion of polarization is slight but definite. It accords with the
general principle that the least directed, Le., the least attenuated light (which
is blue in the ocean), displays the lowest degree of polarization (Fig. 91)
(Ivanoff, 195713; Ivanoff and Waterman, 195813;Timofeeva, 1962).
CHAPTER 1 2
VISIBILITY
CONTRAST
Recognizing an object in water always involves the perception of differences in radiance or colour between the object and its surroundings. For
visibility problems, therefore, we have t o deal with the concepts of contrast
and of contrast transmittance. If an object emits a radiance L , seen against a
uniformly radiant background of radiance L,, the contrast is defined by:
Thus the contrast varies from - 1 for an ideal black object t o 00 for a
radiant object observed against an ideal black background. In the latter case,
since the object is detected only by direct rays which are not scattered,
attenuation according t o Allard's law reduces the radiance with progressively
increased distance until it falls below the threshold of the eye.
In sea water a background always exists due t o scattering, primary or
multiple, of radiant energy emanating from the object. Prevailing daylight
produces background scattering and in addition scattering through the path
of sight t o the eye, which results in a veil of light reducing the contrast.
THEORETICAL
Though notable contributions t o the theory of underwater visibility have
been made by Sasaki et al. (1952), Ivanoff (1957c), and Sokolov (1963), the
achievements of the Visibility Laboratory have been predominant in this
domain since Duntley published his now classical work, The Visibility of
Submerged Objects (1952). The essential features of the' rigorous theory
given by Duntley and his collaborators (Duntley et al., 1957, 1963) are describ ed below.
The treatment requires a further development of the concept of contrast
pertaining t o radiance (the colour-contrast problem is not considered). If the
object and the background have radiances L o and L,, when observed at zero
distance, and L,. and Lbr when observed a t distance r, then we may introduce
inherent contrast C, and apparent contrast C, by the definitions:
158
We shall now consider an object or target at depth zt and at distance
r from an observer a t depth z ; the path of sight has zenith angle 19 and azimuth @, and z - zt = r cos 8.
The attenuat.ion of the radiance of daylight, or the field radiance in a uniform medium, is given by:
We recall that the attenuation coefficient K is constant for certain paths of
sight and that it becomes constant for all directions in the asymptotic
radiance distribution.
The transfer of field radiance is given by eq. 57:
and analogously for the apparent target radiance Lt :
Assuming a constant K , a combination of the last three equations, and
integration over the entire path of sight, results in the following expression :
KrcosO
Ltr(z,o,@) = Lto(zt,e,@)e-cr + L(zt,o,@)e-
.
- e-cr+KrcosO
)
[861
This completely describes the relation between the inherent radiance Lt and
the apparent target radiance Ltr. The first term on the right accounts for the
attenuation of image-forming light from the target, and the second indicates
gain by scattering of ambient light throughout the path of sight.
By replacing the subscript t by b in eq. 86, an analogous form representing
the background is obtained. By subtracting the apparent background
radiance from the apparent target radiance, the important relation :
LtJ-(Z,~,@)
- Lbr(Z,O,@) = [Lt,(zt,@,@)
- Lbo(zt,e,@)le
-cr
[871
is found. This proves that the radiance differences between target and background follow the attenuation law of a beam, since the factor e-cr = T,. is
the beam transmittance along the path of sight. By introducing the definition of contrast according t o eqs. 84 and 85, the ratio of apparent contrast
to inherent contrast may be written:
159
This equation represents the general case, and holds true for non-uniform
water and for different levels of ambient daylight.
Another expression for the significant contrast ratio is obtained by combining eqs. 86 and 87 with the definition of contrast so as t o eliminate the
apparent target and background radiances:
Some special cases are of interest. With an object in deep water, the inherent background radiance may be considered as identical with the field
radiance, i.e. L(zt,8,$) = &,O(Zt,d,@). This yields the simple form:
For horizontal paths of sight we have cos 8 = 0, and the equation reduces
to:
This single formula is a fully adequate expression for the reduction of
contrast for all kinds of targets.
MEASUREMENTS
Research on underwater visibility has been profitably stimulated by
developments in atmospheric vision. Sighting ranges in sea water are determined by the attenuation coefficient, and even in the clearest water they are
diminutive compared t o those in the atmosphere. In consequence, predictions of sighting ranges are needed for the important practical applications of
underwater visibility, e.g., underwater diving. Nomographic charts have been
prepared at the Visibility Laboratory on the basis of the above theory for
objects of arbitrary size - also Secchi disks - as a function of attenuation
coefficient, depth, solar elevation, target reflectance, bottom reflectance,
etc. The charts have been checked against field experiments, and their
validity proved. Simple rules of thumb are useful in practical work. Duntley
(1963) mentions that the underwater sighting range for most objects is 4 t o
5 times the distance:
i/(C -
q z )cos 8 )
160
and that along horizontal paths of sight large dark objects seen as silhouettes
against a water background can be sighted at the distance 4/c.
Little evidence is as yet available for deep water. An important contribution has been made by Cousteau et al. (1964) who, at different depths off
Corsica, measured the radiance at maximal distances of 3 6 0 m from a submerged lamp in horizontal directions. It was found that a lamp of 500 W
is visible t o the human eye at distances as great as 275 m.
VISIBILITY O F FIELD RADIANCE
Y. Le Grand (1954) has made computations which suggest that the darkadapted human eye can perceive light down to at least 8 0 0 m in the clear
ocean. Actual observations from the bathyscaphe indicate that the limit of
visibility lies between 600 and 700m. No systematic investigation has been
made in different water types regarding the depth levels at which field
radiance falls below the threshold of the eye.
MODULATION TRANSFER FUNCTION
Imaging systems
The imaging properties of light beams transmitted through water are of
considerable practical importance. Scattering of a medium such as water
exerts an influence on the resolution and range of all optical observation
systems. In particular, considerable interest is connected with the structure
of light fields produced by a narrow light beam propagating through water.
The theoretical aspect of this problem was thoroughly investigated by
Romanova (1969, 1970). The development of optimized imaging systems
has profited by the use of concepts from communication theory to express
the degradation of image quality imposed by the water. These problems have
been formulated and discussed among others by Wells (1969, 1973), Yura
(1971), Hodara (1973), Duntley (1974) and Zaneveld (1974).
Point spread function
It follows from the discussion on the performance of beam transmittance
meters that due t o primary and multiple scattering a collimated beam is not
focussed t o a point but t o a blur circle. The distribution of the blur is called
the point spread function f (8,R). This function carries significant information about the scattering properties of the medium. From a theoretical point
of view the effect of turbulence-induced variations of index of refraction is
another source of the blur. The optical turbulence which also causes loss of
161
resolution, has been investigated by Honey and Sorenson (1970), Yura
(1971) and Hodgson and Caldwell (1972). Normally this effect is not a limiting factor for practical optical systems (Duntley, 1974).
Transfer function
If the scattered light has circular symmetry round the unscattered ray,
and only small angles such that sin 192: 8 are considered the two-dimensional
Fourier transform of the point spread function takes the form of a onedimensional FourierBessel integral:
@,ax
F ( $ , R ) = 2n
1
J ~ ~ ~ ~ O , ~ C eI d) e~ ( B , R )
[92 1
0
m
[931
0
where $ is the angular spatial frequency (cycles/radian).
The transform F ( $ , R ) is called the modulation transfer function (MTF).
In a concrete sense the MTF may be understood as “a measure of the transparency of the medium to images of a target with long sinusoidally graded
stripes at range R, oriented any direction, and having a spatial frequency of
$/R cycles per unit length” (Hodara, 1973). It follows that a direct
measurement of the MTF is accessible.
MTF meter
MTF meters are described by Wells and Todd (1970) and by Hodara
(1973) (Fig. 92). It is principally a beam transmittance meter, the receiver
-
Deteclor
\
Source
-
Blur Circle
Resolved \
Spatial Freque
B a r Chart
,
Oscilloscope
Unresolved
Fig. 92. Modulation transfer function meter. (After Hodara, 1973.)
162
is provided with a reticle analyser made up of alternate opaque and transparent bars with exponentially changing width spaced around the wheel.
When the wheel revolves a Fourier analysis of the blur is obtained. The
envelope of the record on the oscilloscope yields after calibration the MTF,
F ( $ , R ) for square waves which can be converted to sine-wave MTF by a
simple transformation (Coltman, 1954).
From the measured F( $ , R ) or rather the spatial frequency decay function
D($) (for a collimated beam) the point spread function f ( 6 , R ) and the
volume scattering function p ( 6 ) are computed using the relations:
F ( $ , R ) = e-D($)R
0(2.rrO,$) +d$
P41
CHAPTER 1 3
COLOUR OF THE SEA
DEFINITIONS
The discussion of the colour problem brings a special aspect t o marine
optics. We have now t o deal exclusively with light, i.e., the radiant energy
which is capable of stimulating the human eye. The visible spectrum is
regarded as covering the small band between 380 and 770 nm, but its limits
are ill defined.
Definitions of the fundamental colorimetric concepts are not included in
Chapter 1,which gives an account of the radiometric terms only; for detailed
information about colorimetry the reader is referred t o the publication by
the Commission Internationale d e 1’Eclairage (Anonymous, 1957). In the
context of colour it is proper t o speak about luminance and illuminance
instead of radiance and irradiance.
PERCEPTION O F COLOUR
Colour is not a question of the physics of light only, but is also a sensation.
In the perception of colour the retina image is the immediate stimulus which
creates a response process involving a chain of physiological events. The last
stage is the mental interpretation, which is complex and affected by experience and associations of different kinds. A characteristic feature is that
colour is considered as belonging t o the object in view or caused by the
illuminant. In regard to its psychological aspect, it is no wonder that the
colour problem has been the subject of a great number of theories (Born,
1963). Attention is drawn t o some significant facts about colour vision.
Colour perception is most highly developed in the central part of the retina,
which contains only cones. The rods are used mainly for low-intensity vision,
which is in monochrome. It has been known for a long time, already formulated in the Young-Helmholtz’ theory, that the normal human eye is
trichromatic. Recent colour research has detected the presence of three
independent receptors as discrete units in the cone’s outer limbs, and their
spectral response is becoming known. In essence, trichromaticity implies that
any colour can be matched with a mixture of three independent colours
provided that no one of these can be matched by mixing the other two.
164
TABLE XXXIV
The C.I.E. colour mixture d a t a for equal energy spectrum
Wavelength
(nm)
Wavelength
(nm)
ZA
380
390
0.0023
0.0082
0.0000
0.0002
0.0106
0.0391
580
590
1.8320
2.0535
1.7396
1.5144
0.0032
0.0023
400
410
420
430
440
450
460
47 0
480
490
0.0283
0.0840
0.2740
0.5667
0.6965
0.6730
0.5824
0.3935
0.1897
0.0642
0.0007
0.0023
0.0082
0.0232
0.0458
0.0761
0.1197
0.1824
0.2772
0.4162
0.1343
0.4005
1.3164
2.7663
3.4939
3.5470
3.3426
2.5895
1.6193
0.9313
600
610
620
630
640
650
660
670
680
690
2.1255
2.0064
1.7065
1.2876
0.8945
0.5681
0.3292
0.1755
0.0927
0.0457
1.2619
1.0066
0.7610
0.5311
0.3495
0.2143
0.1218
0.0643
0.0337
0.0165
0.0016
0.0007
0.0003
0.0000
500
510
5 20
530
540
550
560
570
0.0097
0.0187
0.1264
0.3304
0.5810
0.8670
1.1887
1.5243
0.6473
1.0077
1.4172
1.7243
1.9077
1.9906
1.9896
1.9041
0.5455
0.3160
0.1569
0.0841
0.0408
0.0174
0.0077
0.0042
700
710
720
7 30
740
750
760
770
Totals :
0.0225
0.0117
0.0057
0.0028
0.0014
0.0006
0.0003
0.0001
0.0081
0.0042
0.0020
0.0010
0.0006
0.0002
0.0001
0.0000
21.3713
21.3714
21.3715
COLORIMETRIC SYSTEM
A colour specification aims a t expressing colour as synonymous with a
dominant wavelength of light on the basis of a system which considers any
colour as synthesized by a mixture of three components which may be
described as red, green and blue. The C.I.E. (1957) standard colorimetric
system for evaluating any spectral distribution of energy is generally
employed. The sequence of basic definitions is briefly outlined here.
The numerical description of colour is based on the tristimulus values of
the spectrum colours, o r the colour mixture data which are given the symbols
X A , Y h and Z;, . These are hypthetical standard values chosen so that YA is
identical with the standard luminosity curve for photopic vision by the
normal eye (see also Committee on Colorimetry, 1963). The standard
functions are shown in Table XXXIV for an equal energy spectrum.
For any coloured light source the spectral properties of which are given by
E A , the tristimulus values X, Y and 2 are determined by the following
165
integrals :
Z =
1
EkTkdh
These components can be added, and the ratio of each component to the
sum of the three form the chromaticity coordinates x, y and z :
x=
X
X+Y+Z
+ +
Y =
Y
X+Y+Z
z =
z
X + Y S Z
Since x y z = 1, two coordinates suffice to represent the colour in a
chromaticity diagram. Usually x and y are plotted in a rectangular diagram.
For a constant value of E A, t h e chromaticity coordinates x = y = z = 0.333
define the white point or the achromatic colour S in the diagram. The
numerical value of colour is geometrically derived by drawing a line from the
white point S through the plotted colour Q (see Fig. 94). The intersection A
of this line with the locus curve of the spectrum specifies the dominant
wavelength. The other significant factor, purity, is equivalent to the ratio
QSIAS.
THEORIES O F THE COLOUR OF THE SEA
Many theories have been advanced to explain the blue colour of clear
ocean water and the change of colour caused by increasing turbidity. It is
nowadays generally accepted that the blue colour owes its origin to selective
absorption by the water itself, which acts as a monochromator for blue light.
The old absorption theory of Bunsen (1847) thus affords the principal
explanation as far as it concerns the blue colour of clear water. The Soret
theory (1869), which attributes the blue colour entirely to scattering, contains a part of the truth. As emphasized by Raman (1922), molecular
scattering plays a significant role. It is borne out by radiance and irradiance
measurements (Chapter 10) that the clearest waters display a backscatter
which emanates to a great extent from multiple molecular scattering, and
therefore shifts the colour towards shorter wavelengths, Shuleikin (1923) has
given a complete explanation of the colour of the sea; he deduced a formula
which takes all colour-producing agencies into account: light scattering by
water molecules and large particles (air bubbles, suspended matter), and
absorption by molecules and dissolved substances. Unacquainted with this
166
work, Kalle (1938, 193913) has critically examined existing theories. He
has emphatically proved the role of molecular scattering in clear water
and presented the new idea that yellow substance is largely responsible for
the change of colour towards longer wavelengths in turbid waters. Lenoble
(1956d) has made colour computations applying Chandrasekhar's method
with the assumption of non-selective scattering. For clear water illuminated
by a uniformly white sky, it was proved that the colour is close t o the
transmittance peak of water and thus essentially an absorption effect.
COLOUR OBSERVED ABOVE THE SEA
The colour of the sea viewed from a point above the surface is spectacularly beautiful. Several factors conspire t o make the sea a scene of incessant
colour changes: white glitter from the sun, reflected blue skylight, dark
shadows of clouds and the blue or green light scattered back from subsurface
levels. In clear weather the last component produced by sunlight lends a
distinct colour t o the sea, whereas with diffuse conditions the light nonselectively reflected dominates and the sea looks colourless and grey (Kalle,
193913). Rippling and ruffling of the surface greatly enhances the colour
because of reduced reflection (Raman, 1922). Likewise, waves seen from the
lee side are more intensely coloured than from the windward side (Shuleikin,
1923). Hulburt (1934) has pointed out that for a breezy sea the blue in the
reflected skylight which emanates from the sky at 30" (Chapter 5) is usually
bluer than that which comes from near the horizon. Hence a colour contrast
arises between the sea and the horizon.
COLOUR OBSERVED I N SITU
The oceanographic concept of colour refers more adequately t o colour in
situ, which does not involve light reflected from the water surface. The
initial investigations by Kalle apply the tristimulus system of Haschek and
Haitinger, which employs colour mixture data different from those of C.I.E.
The triangular representation in Fig. 93 exhibits colour values from various
areas and reveals several fundamental features. The colour of such relatively
turbid waters as the North Sea and the Baltic is a mixture of colours of
various components, and its purity is therefore low. The colour from below
in the Sargasso Sea is more shortwave and more saturated than is the colour
in the horizontal direction because selective scattering is more active in the
upwelling light. Chromaticity coordinates for the fluorescence of Baltic
water are also inserted in the diagram which determines the fluorescent
colour at 488nm. However, the contribution of fluorescence t o colour of
the sea has so far been little studied.
167
Fig. 93. Haschek-Haitinger chromaticity triangle showing loci of colours for various
regions of t h e sea. (After Kalle, 1939b.)
01
0.2
I
,
03
Fig. 94. C.I.E. chromaticity diagram showing loci of t h e colours a t different depths of
downward illuminance (longer curve) and of upward illuminance (shorter curve) in t h e
Sargasso Sea.
168
Wholly objective colour information is furnished by spectral distribution
of irradiance and radiance subjected t o a colour analysis in terms of the C.I.E.
chromaticity coordinates. As an example, a chromaticity chart for the
Sargasso Sea data in Fig. 9 4 exhibits the typical features of clear water. In
this case we have in view the colour of a horizontal surface facing upwards
for downward irradiance and downwards for upward irradiance. The figures
marked a t the colour loci indicate the depths in meters.
This diagram offers a perspective on colour as a function of depth. The
curvature of the locus of the downward component is indicative of the
selective absorption process effected by the water. The colour at the surface
is 491 nm. Such a greenish-blue hue can be observed in shallow waters with a
reflecting bottom (Duntley, 1963), or against a blue background in
propeller-disturbed water where air bubbles reflect light t o the observer. It is
noted in Fig. 94 that at small depths, even a t 10 m, blue light (482 nm) falls
on the horizontal surface and the blue colour becomes gradually saturated
down to the last measured point of 1 0 0 m ( 4 6 6 n m ) . The locus of the
upward component, on the other hand, is a short and nearly straight line
representing a colour change from 470 nm at the surface t o 464 nm at 100 m.
As we have seen, this colour is t o some degree the result of selective multiple
scattering by the water.
Fig. 95. C.I.E. chromaticity diagram showing loci of the colours of downward illuminance
at different depths in optical water types.
169
TABLE XXXV
Colour evaluated f r o m spectral energy distribution of upward irradiance
Station
Position
Solar
elevation
Depth
(m)
Colour
(nm)
Purity
2
5
10
25
50
473
47 3
47 3
472
469
85
87
89
92
95
50
2
10
25
50
10
472
4 69
474
47 3
472
469
90
97
84
87
92
94
(%)
(O)
Pacific Ocean
142
s01°201
E l 67' 2 3'
61
Indian Ocean
191
192
S11'25'
E102' 1,3'
S11'25
E102'08'
31
Mediterranean
277
N33'54'
E28'17'
74
0
5
10
25
50
47 3
473
473
472
470
83
86
87
92
95
Atlantic Ocean
off Bermuda
N32'
W65'
70
0
483
71
Sargasso Sea
N26'50'
W63'30'
62
2
10
25
50
100
1
10
25
50
100
470
470
468
467
465
471
470
4 69
468
466
86
88
92
95
97
85
88
91
93
95
0
10
20
540
551
553
24
73
87
80
25
Baltic Sea
N60'
E19'
55
The two loci for downward and upward illuminance are close, and seem t o
converge towards a colour of 462 nm with 100% purity. In other words, the
final outcome of the colour selective process at 300-400m is blue light of
462 nm from all directions around the observation point. The wavelength of
the residual light at these levels is obviously equivalent t o the wavelength of
maximum transmittance. Attention is called to the fact that an isotropic
170
colour distribution prevails at levels where the approach t o an asymptotic
radiance distribution is not yet complete.
The chromaticity diagram in Fig. 95 exhibits loci of downward illuminance
for the existing water types. It is noted that the oceanic colour is close t o
470 nm, whereas the colour of coastal waters of types 1-9 is conspicuously
changed towards longer wavelengths on account of the selective action of
particles and yellow substance.
TABLE XXXVI
Colour evaluated from spectral energy distribution o f irradiance
Second column contains depths where t h e energy (400-700 n m ) is 10% of t h e surface
value
(After Morel and Caloumenos, 1974).
Area
EU
Ed
Sargasso Sea
South Pacific
Galapagos
Off Mauritania
Off Senegal
depth
(m)
colour
(nm)
purity
(%)
depth
(m)
colour
(nm)
purity
(%)
47
29
20
10
8
473
484
492
5 09
513
88
68
53
36
18
0
0
0
0
0
473
482
487
491
510
81
63
49
39
14
I
'
I
500
0.5
I
700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7x0.8
Fig. 96. C.I.E. chromaticity diagram showing loci of colours of E u / E , f o r surface waters
off West Africa. (After Morel and Prieur, 1975.)
171
Since a special interest attaches t o the colour of upwardly scattered light,
colour data evaluated from upward irradiance at different depths are
assembled in TableXXXV. The numerical value of colour at the surface
extends from 4 6 2 n m in the clearest waters t o 540nm in the most turbid
(Baltic Sea). Decreasing solar elevation tends t o change colour and purity in
the same way as does increasing depth (Chapter 1 0 ) . Table XXVI contains an
informative exposition of the colours of various waters comprising practically
the whole range of optical water masses in the ocean (Morel and Caloumenos,
1974). Two colour series are presented, one for upward irradiance just below
the surface, the other for downward irradiance at the depth where it is
reduced to 10% of the surface value. The numerical colour values for each
area compare fairly well indicating that the spectral composition of Ed at the
10% level is similar t o that of E, at the surface.
TABLE XXXVII
Colour evaluated from spectral energy distribution of radiance in surface water
Region
Solar
elevation
("1
Sargasso Sea
North Sea
Baltic Sea
Gulf Stream
Californian coast
60
27
Vertical angle
of radiance
Colour
(nm)
Purity
(%)
Reference
1 8 0 (nadir)
475
482
502
512
478
519
85
80
37
32
84
8
Lundgren and
Hdjerslev( 1 9 7 1 )
Kalle ( 1 9 3 9 b )
("1
+90
180
180
180
90
+
Duntley ( 1 9 6 3 )
Tyler (1964)
Morel and Prieur (1975) have derived numerical values of E,/E, which are
independent of the colour of the incoming radiation. Their results (Fig. 96)
represent waters off West Africa which show large variations in the spectral
composition of E,/E, (Fig. 67). Accordingly the group of plots extends
from the blue region t o the vicinity of the white point S.
In situ colour varies with the direction of observation. An analysis of
spectral radiance rather than irradiance, gives some insight into colour as a
function of vertical and azimuthal angle. Table XXXVII summarizes some
data obtained from spectral radiances. It is evident that the angular distribution of colour has not yet been scanned in detail. It may be anticipated
that a fine structure occurs in the refraction cone 2 48.6", which includes
white sunlight as well as blue skylight.
-
ABSORPTION B Y PARTICLES AND YELLOW SUBSTANCE
The influence on colour of particles and coloured dissolved matter, chiefly
yellow substance merits particular attention. Overall decreased transmittance
172
is accompanied by a shift of peak transmittance toward longer wavelengths,
which appears as a colour change from blue via green t o brown. There is
evidence that this is a consequence of increased selective absorption by
particles and yellow substance. Kalle (1938) and Joseph (1955) have
thoroughly investigated the significant role of yellow substance as an
absorbing medium for shortwave light. Atkins and Poole (1958) believe that
the reversal and variations in the green/blue attenuation coefficient ratio is
partly due t o absorption by chlorophyll, carotenoids and xantophylls in the
phytoplankton. Contributions by Yentsch and Ryther (1959) and Yentsch
(1960) stress the importance of absorption in the blue by photosynthetic
pigments of phytoplankton. As will be remembered, coloured particles cause
wavelength selectivity in absorption and, to some extent, in scattering
(Table XI).
DISCOLOURATION O F THE SEA
Discolouration of the sea visible t o an observer above the surface is
commonly caused by exceptionally dense populations of marine phytoplankton, sometimes by swarming zooplankton and, very rarely, by air-borne
sand or volcanic dust. The well-known phenomena of red tides and marine
water blooms are generally due t o various species of phytoplankton.
It follows from what has been stated about upwelling light in the sea that
the amount of back-scattered light is proportional t o the total cross section
of the particles. The size of the dominant organism is therefore important.
Hart (1966) mentions that 20 cells/ml of Noctiluca, 570 filaments/ml of
Trichodesmium , and 6,000 cells/ml of the small thecate dinoflagellate
Peridinium triquetrum are each capable of producing visible discolouration.
For further details the reader is referred t o Hart’s complete description of
the phenomenon of discoloured water.
CHAPTER 14
APPLICATIONS TO PHYSICAL OCEANOGRAPHY
OBJECT O F OPTICAL APPLICATIONS
The optical properties of sea water and the propagation and distribution
of underwater light are dependent on the physical, chemical and dynamic
conditions of the sea. As a consequence optical data may be utilized in various ways to gain information about oceanographic conditions, in particular
dynamic conditions. Rewarding efforts at implementation have been made,
and optical applications in oceanographic research are rapidly gaining
ground. It has become clear that scattering and beam transmittance measurements supply substantial knowledge about two constituents in the sea, viz.
particles and yellow substance. The oceanographic interest in the distribution of these components is dictated by the desire to find suitable parameters for characterizing water masses. The primary advantage of optical
methods is the relative ease by which data can be obtained even in rough
weather.
The supreme importance of underwater light for marine biological studies
merits treatment in a special Chapter (15). It is also clear that the absorption
of the radiant energy by the sea is a fundamental factor in the thermodynamics of the sea. As already mentioned, however, we must refrain from
dealing with thermodynamical transfer processes and related problems of
heat economy, since this subject is too Iarge to be embraced by the present
account .
REFLECTION AND REFRACTION
The reflection and refraction of sunlight at the sea surface are indicative
of the state of the surface. This is brought out in the aforementioned glitter
theories (Chapter 5, p. 77). The deductions of the slopes of the sea surface
made by C. Cox and Munk (1956) show that the observed, nearly Gaussian
distribution of slopes is consistent with a continuous wave spectrum of arbitrary width or with a large number of discrete frequencies. Such slope distributions and wind velocity can be determined by using sun glitter viewed
from a synchronous satellite (Levanon, 1971). Theories are also available of
utilizing powerful coherent light sources for measuring wave statistics
(Krishnan and Peppers, 1973).
176
The refracted glitter is also dependent on wave action. Schenck Jr. (1957)
has studied the phenomenon of bright bands of light moving across a shallow
sea bottom at the same velocity as the waves. The intensification of radiance
is ascribed t o lens action by the waves. In this context, it may be mentioned
that the heights of water waves produced in a laboratory tank can be
observed by fluctuations in the absorption of light passing vertically through
the water (Faller, 1958).
DISTRIBUTION OF PARTICLES
Scattering measurements
There is adequate ground for treating separately the oceanographic application of scattering observations, since they provide the most sensitive means
of exploring the particle distribution as was first demonstrated by Kalle
(1939a). Some conspicuous results indicate that the particle content may be
considered to be an inherent property of the water mass. An example of
clear identification is given in Fig. 97. The Pacific water present below 1,000
m depth has passed severals sills before reaching the deep Flores Basin. In
spite of the long duration of this transport, it has apparently maintained its
integrity and remained unaffected by the turbid water in the surface layers.
It seems that the refractive index is joining the group of optical parameters useful for characterizing water masses. For computing the “bulk”
refractive index of marine particles Zaneveld and H. Pak (1973) have developed a method considering the fact that the index shows appreciable variations in the sea. They use the Mie theory and presume that the particle-size
distribution and the scattering function at two different wavelengths are
known. In the representation of computed refractive indices shown in Fig.
98 a marked zone of maximum in index appears which is attributed to interaction of the equatorial undercurrent with the Galapagos Islands.
30
Scattering coefficient I km-71
LO
50
60
70
80
90
2,000
3,000
L,OOO
5,000
Fig. 97. Particle statification in the Flores Basin, showing the inflow of clear Pacific water
between 800 and 1,400 m. (After Jerlov, 1959.)
177
92
I
1
92
90
88
I
I
I
I
90
88
86OW
I
86OW
84
Fig. 98. “Bulk” index of refraction of particles on the 250-m level east of the Galapagos
Islands. (After H. Pak and Plank, 1974.)
An important aspect of the particle problem is the formation of optical
scattering layers frequently encountered at various levels in the sea. Riley et
al. (1949) have considered theoretically the distribution of phytoplankton in
an uppermost layer of the ocean with a constant eddy diffusion, and found
that a maximum is developed near the lower limit of the photic zone. Wyrtki
(1950) has discussed the significant role of the vertical gradient of the eddy
diffusion in forming the particle distribution pattern. Below the photic zone,
the mechanism at which a maximum is developed requires not only that the
eddy diffusion increases with depth but also that the sinking rate of the particles be reduced, i.e., their buoyancy be improved (Jerlov, 1959). The
necessary conditions are generally fulfilled for a discontinuity layer which
shows high vertical stability. Neuymin and Sorokina (1964) and Paramonov
(196 5) have thoroughly investigated the relation between stability and distribution of particles. They found that in the upper layers down t o 150 m the
predicted distribution does not invariably correlate with stability, on
account of migrations of living organisms. Neuymin (1970) points out that
inhomogeneities of optical properties may also occur in deep water. Vertical
movements of water occurring at upwellings or at divergences and convergences are generally indicated by the particle content; upwelling leads t o
salient changes of the productivity of the sea (see Fig. 131). A conformity
between the trends of the temperature and scattering profiles is often found
because the upwelling water is heated in the upper strata (Fig. 99).
178
0
m
20
60
60
80
100
120
140
..
160
0< 25
25-30
30-40
Fig. 9 9 . Conformity between depth profiles for temperature T oand scattering coefficient
b for the upwelling area off West Africa. (After G. Kullenberg, 1974c.)
Fig. 100. Stratum with high particle concentration in t h e salinity minimum. Tongue of
high-salinity water from t h e subtropical convergence rich in particles. Meridional section
near longitude 15OoW in t h e Pacific. (After Jerlov, 1 9 5 9 . )
The spreading of water masses in the deep sea is often reflected in particle
diagrams (Jerlov, 1959). A conspicuous situation in Fig. 100 demonstrates
that the tongue of high-salinity water from the subtropical convergence in
the Pacific is fairly rich in particles. The intruding water mass as a rule has
higher particle content than the surrounding water. It is difficult t o judge t o
what extent this is an inherent property of the water mass originating from
surface levels or an effect of the turbulence created by the flow of the water
masses. The occurrence of strata of such high particle concentration as that
extending at the 6" level in Fig. 100 is in many cases associated with a
defined water mass. In other instances one fails t o find any relationship. The
initial scattering data obtained by Kalle (1939a) in deep Atlantic water indicate several particle maxima (Fig. 101). Carder and Schlemmer (1973) found
a well-defined maximum in the high-stability portion of the subtropic underwater in the eastern Gulf of Mexico (Fig. 102). From scattering observations
in the Puerto Rico trench Tucholke and Eittreim (1974) report a maximum
near the south slope of the trench which is associated with the existing
western boundary undercurrent; the bottom scattering layer found here is
attributed t o the westward-flowing Antarctic Bottom Current.
Some indication of average or typical vertical distributions as derived from
179
rJrJamm
0-25
2.5.5
5-10
10-20
10-30
m
>50
30-50
Fig. 101. Particle maxima in a west-east
Atlantic. (After Kalle, 1939a.)
vertical section near the Tropic of Cancer in the
0
m
100
200
300
-1
LOO
50 0
I
600
Fig. 102. Distribution of the scattering f ~ n c t i o n p ( 4 5(~ )
m-lstr-') in a section in the
eastern Gulf of Mexico, (After Carder and Schlemmer, 1973.)
scattering observations may be found in Fig. 103. The profiles, which represent exclusively the equatorial regions, indicate that at great depths the
western Atlantic has the highest relative particle concentration, whereas
minimal amounts are encountered in the western Pacific.
In areas where water masses of different particle content meet, light
180
Scattering coefficient [km-11
30
SO
50
50
50
50
50
7
East Atlantic West Atlantic
East Pacific West- Pacific East Indian
I
I
,
I
,
!
1
,
,
1
,
1
,
,
,
,
Fig. 103. Depth profiles of scattering in the oceans, indicating spreading of Antarctic
Intermediate (A.I.) and Antarctic Bottom water (A.B.). (After Jerlov, 1959.)
St 1251
0
4253
1252
L251
L250
L7l.Q
rn
1,000
2,000
3,000
OGO
@ LO-55
55-70
70-90
290
Fig. 104. Scatterance distribution in two sections through the Strait of Gibraltar, viz., the
“Albatross” section 306-309 in June, 1948 (Jerlov, 1953a) and the “Discovery 11” section 4249-4254 in September, 1960 (Jerlov, 1961.)
scattering becomes a useful parameter. This application is beautifully developed for the Strait of Gibraltar (Fig. 104) where salt Mediterranean water
flows across the ridges, sinks a t the Atlantic side and is replaced by an inflow
of Atlantic water in the upper layers. It is interesting to note that depth profiles (Fig. 105) obtained by Matlack (1974) at a station near 4252 conform
quite well to the distribution in Fig. 104; even the maximum at 400m due
to Mediterranean intermediate water appears in both representations. A
181
0.01
005
010
0.03 O(33'1
0.02
7
015
025
020
030
m-1str-1
c rr
m
500
1,000
1,500
6
8
10
12
14
T
Fig. 105.Depth proliles of temperature T , scattering function p ( 3 3 ' ) and attenuation
coefficient c(478 n m ) near S t . 4252 in Fig. 104. (After Matlack, 1974.)
(6635
(6636
46637
(6638
46639
m
200
400
600
Fig. 106. Distribution of the scattering function p(90") (m-') a t 546 n m in t h e channel
between Sicily and Tunisia. (After Morel, 1969.)
similar exchange of water takes place across the submarine ridges between
Tunisia and Sicily. The particle maximum found here between 500 and 600 m
(Fig. 106; Morel, 1969; Ivanoff, 1973) is probably formed by a mechanism
analogous t o that in the Strait of Gibraltar (Morel, personal communication,
1975).
182
rn-l str-l) on the 3-m surface
Fig. 107. Distribution of the scattering f ~ n c t i o n P ( 4 5(~ )
in the Columbia River plume region. (After H. Pak e t al., 1970.)
Rivers are important sources of particulate matter and in consequence the
river water can by scattering measurements be traced over long distances
from the mouth. Ketchum and Shonting (1958) have studied the flow of the
turbid Orinoco water in the Cariaco Trench. Particle distributions from off
the Po river prove the existence of a countercurrent of clear water which
flows against the turbid surface drift (Jerlov, 1958) by which the salt balance
is maintained. Such a system is also encountered in the Columbia river
plume; here major surface flow forms a tongue-shaped plume extending
toward the south and southwest on account of northern winds and windinduced upwelling along the coast (Fig. 107; H. Pak et al., 1970). An investigation by Gibbs (1974a) shows that the immense quantities of turbid
Amazon river water are chiefly transported northwestward along the SouthAmerican coast for about 2000 km (Fig. 108).
The introduction of particulate matter into a saline environment starts
precipitation and settling of particles. In the Nile river estuary these processes are intense t o the degree that at only 50 km from the Nile mouth the
water has clarified and the surface water has almost attained the high clewness characteristic of the eastern Mediterranean (Fig. 109; Jerlov, 1953a,
1969).
183
t
(25
25-50
m 5 0 - 7 5
a 7 5 - 9 0
0 > 9 0
i
20N
O0
2OS
56"
52'
AMAZON 5 O o W
Fig. 108. Percentage of transmittance ( T =e-") of surface waters during high river discharge of the Amaqon. (After Gibbs, 1974a.)
st
J LOO
Fig. 1 0 9 . Scatterance distribution in the Nile estuary northwards from Port Said on 8
May 1948. (After Jerlov, 1953a.)
Beam transmittance measurements
The beam transmittance meter has developed into a powerful tool for
identifying water masses, as evidenced by a great number of investigations
(Joseph, 1955, 1959, 1961; Nishizawa et al., 1959; Wyrtki, 1960; Pavlov,
1961; Schemainda, 1962; Dera, 1963, 1967; Neuymin et al., 1964; Ball and
LaFond, 1964; Malmberg, 1964; Hdjerslev, 1974a; Matlack, 1974).
184
N
30.
25.
20'
15.
10.
5.
0.
5.
10'
15O
20.
25.
30.
35. S
0
rTr sz " t n
Fig. 110. Distribution of beam transmittance in a meridional section near longitude
1 7 1 O W in the Pacific. (After Kozlyaninov, 1960.)
Beam transmittance, if recorded in the red, is a measure of the particle
content, though it is a less sensitive parameter than scatterance. Its relation
to dynamics is analogous t o that of scatterance.
A section of vertical particle distribution in Fig. 110 serves t o illustrate
the usefulness of beam transmittance as an oceanographic parameter. Note
that the prominent features of the section in Fig. 100 are only vaguely indicated in Fig. 110 which is situated farther t o the west. Instead, attention is
drawn t o the huge stratum of turbid water present at 2,000-2,500m. It is
interesting t o note that the profiles in Fig. 1 0 3 display similar maxima. Both
Jerlov (1959) and Kozlyaninov (1960) think that they result from the flow
of Antarctic water. Furthermore, a large-scale comparison between dynamic
sections and distributions of beam transmittance made by Kozlyaninov and
Ovchinnikov (1961) shows correlations between the structure of the current
pattern and the broad outlines of the beam transmittances.
Convincing proof of the capability of the beam transmittance meter t o
detect the discontinuity layer and record its movements is furnished first and
foremost by Joseph (1955). A section between the Dutch and Norwegian
coast (Fig. 111)shows that the thermocline is associated with a layer rich in
particles. This is not split up until over the deep Norwegian trench where the
Baltic current influences the structure of the surface water. On the basis of
beam transmittance measurements, Joseph and Sendner (1958) have elaborated a new approach t o the problem of horizontal diffusion in the sea and
have induced a fruitful development in this domain. Voitov (1964) has
utilized the transmittance method t o measure vertical eddy diffusion as a
function of depth.
Further proof of the usefulness of the transmittance meter in stratified
water is provided by Gohs' (1967) measurements. His profiles in Fig. 112
demonstrate the association between temperature, salinity and optical
parameters. It seems that significant information on the particulate matter
can be gained by combining optical measurements with observations of
sound velocity. An example of pioneer work in this domain is presented by
Kroebel and Diehl(l973) in Fig. 113.
0
m
M
100
mO10-015
> 075
Fig. 111.Turbidity layer associated with the thermocline. Section from t h e Norwegian to t h e Dutch coast. (After Joseph, 1955.)
01
5
lore,s%,
I '
o
0.1
0.2
(c-cw)
rn-f
/
530
0
0
N
0
2 00
1
Fig. 1 1 2 . Comparative observations of temperature T , salinity S , scattering function P(6O0) and t h e attenuation coefficient ( c - c , )
for three wavelengths in t h e Baltic Sea. (After Gohs, 1967.)
UI
186
0.6
I
s
Fig. 113. Comparative measurements of attenuation coefficient c and sound velocity V in
waters off Cadiz. (After Kroebel a n d Diehl, 1973.)
Particle distribution near the b o t t o m
From a systematic study of near-bottom scattering distributions in the
equatorial parts of the oceans Jerlov (1953a, 1969) has drawn the following
conclusions. The turbulence effected by bottom currents generally leads t o
an increase of scattering or particle content towards the bottom i.e., to a
bottom scattering layer (BSL). Only if currents vanish, or if the bottom is
bare of fine sediments, is the bottom layer uniform in particles. The existing
turbulence is obviously much influenced by topographic features. Maxima in
the vertical particle distribution are frequently encountered at levels above
the bottom. This can often be interpreted as an effect of lateral transport
from adjacent topographic heights (Fig. 114).
The vast literature on the subject of BSL (e.g., Ivanoff, 1961; Neuymin,
1970; Plank et al., 1972; H$jerslev, 1973; Matlack, 1974; Fukuda, 1974)
cannot be discussed here. Reference is made t o recent reviews by H. Pak and
Plank (1974) and in Gibbs (197413). Only a few relevant facts are adduced.
Three typical examples of the BSL are depicted in Fig. 115 (Ewing and
Thorndike, 1965). Feely et al. (1974) have shown that clouds of particles
above the bottom can be several hundred meters thick. On the whole, the
particle distribution near the bottom confirms the deep-sea circulation
(Hunkins et al., 1969; Plank et al., 1973). On the other hand Pickard and
Giovando (1960) and Eittrem et al. (1969) stress the role of turbidity currents as a source of the sediment in the water column. It is established by
Plank et al. (1973) that bottom erosion occurs at two sites on the Carnegie
Ridge (Fig. 116).
187
Scatterance
Depth
2060m
S c a t t e r i n g coefficient ( k m - ' )
37001
20
I
V
LO
60
80
I
I
I
100 120 140 160
I
I
'
1
Fig. 114. Examples of particle clouds above the bottom. (After Jerlov, 1953a.)
Fig. 115. Examples of bottom scattering layers. (After Ewing and Thorndike, 1965.)
S t a t i o n number
0
km
0.6
1.2
1.8
2.4
3.0
1
3OS
O0
Lat i t udc
5'N
Fig. 116. Meridional section of the scattering function p(45u) in the Panama Basin. (After
Plank et al., 1973.)
188
20
50
100 200
500 1,000 t
.ta
m
50 -
100 -
150 -
1875 -r-
.8 '10. S
421
6
.8
130
.2
1
30
LO
53
60
70
80 90 100 110 b
~,
-r
7 1
i - 7 - 7 -
6
-7
200
t
I
\
\
Fig. 1 1 7 . Particle accumulation in t h e high-salinity water near t h e b o t t o m of t h e Red Sea.
(After Jerlov, 1 9 5 3 a . )
Fig. 118. Logarithmic increase of particle content towards t h e b o t t o m in the Baltic and in
t h e Adriatic Sea. (After Jerlov, 1 9 5 5 a , 1958.)
A peculiar phenomenon with a high load of scattering particles is met with
near the bottom in the Red Sea (Fig. 117). In this case the abundance of particles is an inherent property of the extremely salt water present in the deep
basins of the Red Sea.
In shallow waters a logarithmic increase towards the bottom is evidenced
in some cases (Fig. 118). The distribution below the layer of the thermocline
in the Bothnian Gulf indicates slow settling of organic material under the
influence of semi-permanent horizontal flow (Jerlov, 1955a; Fukuda, 1960).
This material originates from rapid precipitation, under saline conditions, of
high-molecular weight humus matter from limnic waters entering the Baltic
Sea (M. Brown, 1975). Variable logarithmic increases in the North Sea (Fig.
119; Joseph, 1955) and in the Adriatic Sea (Fig. 118; Jerlov, 1958) are controlled by the tidal currents which cause periodic rising and sinking of sediments.
POLLUTION RESEARCH
Extensive applications of scatterance and beam transmittance meters and
also of fluorometers are found in pollution research (FAO, 1971). Their
potential role for assessment of water pollution largely depends on defining
or classifying different types of pollutants. The detection of pollutants
involves an identification of the substances by their spectral absorption and
emission. The optical methods for particle tracing rest on the finding that
the attenuation or the scattering coefficient in the red in many cases is
189
0
m
5
10
15
20
25
60
06h
15.3.53
lZh
18."
OOh
16.3
06h
Fig. 119. Periodic rising and sinking of sediment in t h e North Sea caused by tidal currents.
(After Joseph, 1955.)
proportional to the particle concentration expressed as mass per unit volume
(Wyrtki, 1953; Joseph, 1955; Jones and Wills, 1956; Ochakovsky, 1966a;
Pustelnikov and Shmatko, 1971; Gibbs, 1974a; Carder et al., 1974; Tucholke
and Eittreim, 1974).
REMOTE OPTICAL SENSING
The potentialities of oceanographic observations from manned satellites
by means of visible light have in some detail been discussed by Duntley
(1965). The development of remote optical sensing shows that by visual
observations or multispectral photography a considerable amount of detail
on the water surface can be observed. The great advantage of this method is
its capability of repeated synoptic coverage of vast oceanic areas. The use of
remote optical sensing is, however, restricted by several factors:
(1)First by the obvious effect of cloud cover.
(2) Oceanographic information is obtained from the surface layer only.
H.R. Gordon and McCluney (1975) have found that the upwelling field
above the surface can provide information only about the upper 20-25 m of
clear ocean water.
( 3 ) Light specularly reflected by the surface (Chapter 5 ) may be included
in the field of view. This effect can practically be eliminated by using a
polarizer on the receiving aperture of the instrument and tilting it at 53"
(Brewster angle) from the vertical opposite the sun. This, however, increases
air mass t o 1.67 (Austin, 1974). Reflected skylight is not believed to affect
seriously the signal from the water.
190
(4) The most severe restriction of remote optical sensing stems from the
interference of the atmosphere. Light is scattered by air molecules and particles into the path between the sea surface and the sensor. Austin (1974)
mentions that this component, which is highly wavelength selective, may be
4-5 times larger than the radiance emitted from the ocean. He concludes
that remote optical sensing is highly dependent on the ability of the atmosphere at a particular time and location t o transmit the signal t o the sensor.
Despite these restrictions remote optical sensing has contributed a great
deal of valuable information about the oceans e.g., for determining surface
slope distributions and for detecting current boundaries, upwelling areas
and depth contours in shallow water. Vortices, slicks, swells and other visible
lines reveal current direction, internal waves, and regions of convergence and
divergence (La Violette, 1974). A technique of remotely sensing oil spills by
laser-excited fluorescence has been developed (Fantasia et al., 1971). It has
the advantage - contrary t o other methods - that different oil types can be
distinguished as each type has a distinct fluorescent spectral signature.
DISTRIBUTION O F YELLOW SUBSTANCE
Yellow substance may be treated as a semi-conservative concentration
which is readily determined by means of beam transmittance measurements.
The analysis presumes its presence in fairly high concentrations such as are
generally encountered in coastal waters. Original experiments in the Baltic
conducted by Kalle (1949) and corroborated by Jerlov (1955a) prove that
diagrams of the content of yellow substance plotted against salinity yield
excellent information about the water masses and the mixing between them
(Fig. 120). The very first scattering and beam transmittance measurements
made by Pettersson (1936) showed that the Baltic water flowing northwards
along the west coast of Sweden is clearly identified by its colour due t o
yellow substance. It is evident from Fig. 121 which represents these results,
that the upper layer of water of partly Baltic origin absorbs more strongly in
the blue than does the underlying Skagerrak water of higher salinity; an
accumulation of particles occurs at the boundary between the two water
masses.
DISTRIBUTION OF FLUORESCENCE
The use of fluorescent dyes as tracers in order t o study diffusion in the sea
is another beautiful example of an optical method applied t o significant
dynamical problems. Rhodamine B is generally selected as a suitable dye on
account of its relatively low cost, high detectability and relatively good stability.
191
--surface
A
0
2
1
3
4
water) Gulf of
5
6 7
Salinity
8
z
.-.
0
-"
9 10 11%.
Central SdtlC
B 0
5
10
15
20
25
30 %.
20
35
100
60
LO
80
120
Fig. 120. Relationship between salinity and amount of yellow substance in the Baltic.
A. After Kalle (1949). B. After Jerlov (1955a.)
Fig. 121. Comparison of scatterance and beam transmittance (in the blue) for water off
the Swedish west coast indicating stronger absorption in the t o p layer of partly Baltic
water than in the underlying Skagerrak water. (After Pettersson, 1936.)
1 1 5 0 cm
i
r
/
10
> 6
:5-
ILL
0 3
I
-+=-
1 2 5 0 cm
22
0
1
2
3
L
5
Sclinity
6
7
8
9%.
Fig. 122. Profiles of dye and temperature from the western Mediterranean after 1.8 (top)
and 1.9 (bottom) hours of tracing. (After G. Kullenberg, 1974a.)
Fig. 123. Relationship between salinity and ratio of amount of fluorescent matter t o
amount of yellow substance in the Baltic. (After Kalle, 1949.)
The method is recently reviewed by Weidemann (1974). The technique
involves the following working principles: The rhodamine dye must be
excited preferably by the green mercury line which can be isolated by suitable combination of Schott filters. The emitted light is filtered so that light
scattered by particles is eliminated. Observations are usually made by means
of a laboratory meter on collected water samples or on water brought up
under positive pressure with the aid of a pumping system. More adequate in
situ measurement is hampered by the superposed effect of ambient natural
light. This difficulty is overcome for a meter which is provided with two
192
12 $10
-
c
f 8-
-$ 6 U
L -
Fig. 1 2 4 . Fluorescence-salinity relation characterizing continental coastal water in t h e
southern North Sea. (After Otto, 1967.)
measuring units; both of them face downwards but with only one receiving
the fluorescent light (G. Kullenberg, 1974a). It may also be expedient t o use
a chopped light source in the fluorometer. The capability of the dye method
for studying turbulent diffusion is amply illustrated in Fig. 122.
It follows from Chapter 3 that natural fluorescence is a characteristic
property of the same utility as yellow substance. Kalle (1949) has proved
that in the Baltic the ratio of fluorescent substance t o yellow substance is a
suitable parameter to be plotted against salinity (Fig. 123). The small variations of this ratio in the area is further confirmed by Karabashev and
Zangalis (1972). Also in other regions, where fluorescence stems from terrestrial humic acids, fluorescence can be employed as a semi-conservative
property with success. This is clear from investigations by Otto (1967) in the
southern North Sea (Fig. 124) and by Zimmerman and Rommets (1974) in
the Dutch Wadden Sea and the adjacent North Sea.
This distribution of fluorescence in oceanic areas may help t o reveal significant features in the circulation pattern. An attempt t o realize this view
has been made by Karabashev and Solov'yev (1973). The grouping of isolines
in Fig. 125 indicates a fluorescence minimum in the surface water of the
Antilles current which, being a branch of the North Equatorial Current, has a
low biological productivity.
COLOUR INDEX
The usefulness of the colour index defined as F = L(450 nm)/L( 520 nm)
(Jerlov, 1974b) for characterizing water masses is demonstrated by a distribution in the western Mediterranean (Fig. 126). This is consistent with the
circulation pattern, showing inflowing Atlantic surface water of high and
fluctuating turbidity which is mixed with clear Mediterranean water during
its flow eastward near t o the African coast.
The colour index is found t o be closely linked to other apparent optical
193
30° N
zoo
Fig. 1 2 5 . Distribution of fluorescence a t a depth of 1 0 m in t h e Antilles region. (After
Karabashev and Solov’yev, 1 9 7 3 . )
Fig. 1 2 6 . Regional distribution of colour index in t h e western Mediterranean. (After
Jerlov, 197410.)
194
0.5
10
Colour index
15
20
25
3.0
7
Im
Off West A f r i c a ( 2 0 ’ N 1
_____lj\
Gibraltar S t r a i t
East o f G i b r a l t a r
E a s t of S a r d i n i a
L
I
i
1:
10
I
Fig. 127. Relationships between colour index and depths at which the percentage o f surface quanta irradiance (350-700 nm) is 10%.(After Jerlov, 1974a.)
properties in the upper layer of the sea. This is amply illustrated in Fig. 127,
by comparing the index with a relevant parameter as the depth at which the
percentage of surface quanta is 10%. The clear association between these two
quantities goes t o prove that a simple colour meter may be an efficient tool
for indirect evaluation of photosynthetic light parameters.
CHAPTER 1 5
APPLICATIONS TO MARINE BIOLOGY
PRIMARY PRODUCTION
Light p e n e tra tio n
The physics of radiant energy is of direct importance for evaluating the
result of the photosynthetic activity in the sea. The penetration of light
defines the photic zone, the lower limit of which is generally marked by the
depth where surface irradiance is reduced t o 1%.This significant level is
depicted in Fig. 1 2 8 as a function of the wavelength for the different types
of ocean water classified in Chapter 10 (p. 135). It is clear that the zone is
shallow in the red, and that overall increased turbidit,y reduces the shortwave
part of the spectrum more strongly than the longwave part. This diagram, in
conjunction with the regional chart of distribution of optical water types,
yields general information about the depth of the photic zone in some
oceanic areas. With a dense station net, it is possible t o represent the topography of the 1%level. Such a pattern off the Strait of Gibraltar (Fig. 129)
illustrates the presence of turbid water along the coasts, and the extension of
clear water from west-northwest close to the Strait consistent with the
general flow. Another significant parameter is the attenuation of energy in
the interval 350--700nm, which is found t o be active in photosynthesis.
Relevant information for the different water types is given in terms of
percentage of surface irradiance by the family of curves in Fig. 130.
Distribution of particles and yellow substance
The question arises whether the total particle content as determined by
scattering measurements could be indicative of the distribution of oceanic
productivity. There is ample evidence that the horizontal particle pattern is
largely effected by dynamical processess, especially upwelling. As an example, results from the equatorial Pacific are adduced which exhibit a close
congruence even in details between the particle distribution and the topography of the depth of the thermocline or the topography of the sea surface
(Fig. 131). An abundance of particles occurs in the upwelling area near the
Galapagos, which merges into the sharply defined equator divergence region.
Even the divergence at the northern boundary of the countercurrent at 1 0 ° N
shows up clearly in this picture. Another upwelling in the divergence
196
I
300
I
I
400
I
I
I
500
l
1
I
600 nm 700
1
I
Fig. 128. Depths a t which downward irradiance is 1 % of t h e surface value in t h e different
water types.
Fig. 129. Topography of t h e level of 1%of surface downward irradiance ( 4 6 5 nm) off t h e
Strait of Gibraltar. (After Jerlov and Nygird, 1961.)
between the south equatorial current and the countercurrent in the Indian
Ocean is also clearly established by the high particle content which is
obviously due to phytoplankton or remnants of phytoplankton (Jerlov,
(19 53a).
Among the dissolved substances only yellow substance plays an important
optical role. It is manifest that the wavelength selective absorption due t o
particles and yellow substance determines the transmittance of daylight and
ultimately the colour of the sea. So far we know little about yellow substance as a constituent part of the total dissolved matter. On the other hand,
recent findings indicate that the conversion of organic particulate material
into dissolved material is a reversible process. In an attempt t o link the
physical factors to the biological factors we may venture t o suggest the
following chain of direct and casual relationships:
stock of phytoplankton-particulate
dead- - -transmittance of
daylight
f
/
primary production
dissolved matter ’
partly yellow substance
\
\
\
N
colour
Such a model fivds considerable support in the finding of Steemann Nielsen
(1963) that the regional distribution of colour in the South Atlantic according to Schott’s chart conforms in considerable detail t o the observed regional
distribution of primary production.
Quanta measurements
Several examples of depth profiles for quanta irradiance have been presented in Chapter 10. Supplementary information is given for different water
197
05
PERCENTAGE OF SURFACE IRRADIANCE [350-700nml
1
2
5
10
20
50
100
Fig. 130. Depth profiles of percentage of surface downward irradiance (350-700 n m ) f o r
different water types.
types in Fig. 132, which is the counterpart t o Fig. 130 representing energy
irradiance. The significant ratio E/Q has been calculated by Jerlov and
Nyggrd (196913) (Fig. 133). These curves approach a constant value with increasing depth for each water type on account of the narrowing of the
underwater spectral band. For coastal types (1, 3 ) with maximum transmittance in the green the variation of the ratio is inconsiderable, whereas the
oceanic types, which more effectively transmit the shortwave light, display
some increase of the ratio from the surface to 2 0 m . The total variation of
the ratio E/Q is however only
8%. This is corroborated by Morel and
Smith (1974) who on the basis of many experimental results also from
the Sargasso Sea derived a variation of 5 10%.
In view of the difficulties involved in the construction, calibration and
*
198
Fig. 131. Particle content in the uppermost 50 m in the Pacific. (After Jerlov, 1964.)
1.00
EIO
1.05
1.10
1.15
rn
Percentage of surface quanta
I
10
20
1350-700 n m )
50
20
100
O
m
LO
20
60
LO
80
60
100
80
120
I00
140
120
I
Fig. 132. Depth profiles of percentage of surface quanta (350-700 nm) for different
water types.
Fig. 133. The ratio of energy irradiance t o quanta irradiance in the spectral range 350700 nm as a function of depth in different optical water masses (normalized at the surface).
use of quanta meters it seems important t o find experimental alternatives. In
practice, it is possible t o evaluate underwater quanta by measuring blue light
only. The depth profile in Fig. 134 (Jerlov, 1974a) based on numerous data
shows that for types I , I1 and I11 the ratio of Q (350-700 nm) t o E (465 nm)
199
Fig. 134. The observed ratio of quanta irradiance Q (350-700 n m ) to blue irradiance E
( 4 6 5 n m ) as a function of depth for water types Z-ZZZ.
is the same function of depth in the quanta interval 100 t o 1%.
The function
can be described by the simple expression: Q = E [0.23 5.6/(z 7.3)]
valid for solar elevations > 10". It is also quite feasible to record quanta with
a blue meter above the surface.
Biologists often employ pyranometer data, taking half of its value t o
represent the photosynthetic energy incident on the surface. Investigations
by Shifrin et al. (1962) and Szeicz (1961) indicate that the percentage is
more precisely 43%:
+
+
= 0.43 E (350-3000)
~961
If the spectral distribution of radiant energy is known, the corresponding
quanta distribution is found from the relation:
E (350-700)
1quantum sec-' = 1987/A *
W ( A in nm)
Using this equation the following conversion factor for the visible regon is
obtained :
Q (350-700) quanta m-2 sec-' = 2.75 * 10'' E (350-700) Wm-2
WI
and hence :
Q (350-700)
=
1.2 * 10l8E (350-3000)
~981
200
c
Fig. 135. Diurnal variation of quanta just below t h e surface off Sardinia on 13 J u n e 1971.
which is valid for a Raleigh atmosphere and high solar elevations but which
changes little with turbidity of the air. The ratio Q / E (eq. 97) agrees remarkably well with that experimentally derived by Morel and Smith (1974):
2.77 2 0.16 * 10'' (in air)
irrespective of solar elevation (above 22") and meteorological conditions.
The described methods can be employed t o record the diurnal variation
of irradiance. A specific example is presented in Fig. 135.
Remote colour measurements
Ocean colour is largely determined by the spectral changes imposed on the
incoming radiation by water, as well as by various suspended and dissolved
substances in the sea. It is clear from the scheme presented on p. 196 that
201
Chlorophyll
A Slope water
0.3 r n g l r n 3
B Transition
0.6
-51C Georges Bank
1 3 -11D Georges Shoals 3.0 -152 L
Fig. 136. Spectra of upwelling radiance obtained a t 3 0 5 m above t h e sea o n 27 August
1968. (After Clarke e t al., 1970.)
colour is indirectly related t o the concentration of chlorophyll which is an
index of the amount of phytoplankton. An aspect of remote optical sensing
which has come into prominence during the last decade has been an attempt
t o model this relationship (Ramsey, 1968; White, 1969; Clarke et al., 1970;
Duntley, 1971; Clarke and Ewing, 1974). The method has the great advantage that it makes possible repeated synoptic surveys over extensive areas of
the sea. Fig. 136 showing some pioneer research by Clarke et al. (1970)
demonstrates the changes in the spectral response of the ocean for different
chlorophyll concentrations. Their recording procedure includes the elimination of disturbing light reflected from the surface by using a polarization
filter on the receiving aperture of the spectrophotometer and tilting of the
instrument at 53" (Brewster angle) from the vertical opposite the sun.
Despite the restrictions of remote optical sensing (Chapter 14) Curran
(1972) concludes from calculations of scattering and absorption properties
of the atmosphere that useful measurements may be made at satellite altitude to indicate strong gradients in chlorophyll concentration.
The shape of the spectrum of upwelling light can be described by the
colour ratio C (540)lL (460) (Strickland, 1962; Clarke et al., 1970; Arvesen
et al., 1971; Curran, 1972). This ratio is nearly the inverse of the abovementioned index used by Jerlov (Chapter 14). These wavelengths have been
chosen t o represent positions of low (540 nm) and high (460 nm) absorption
by chlorophyll. Obviously the ratio is not a measure of chlorophyll only but
202
is also sensitive t o the wavelength-selective effect of other particulate and
dissolved matter. The thorough investigation made by Morel and Smith
(1974) confirms the well-recognized fact that a vague relation exists between
chlorophyll concentration and the apparent optical properties. It should be
recalled that type 111 shows indication of chlorophyll absorption.
COO
500
600nm 700
Fig. 137. Attenuation spectrum of sea-water suspension of P h a e o d a c t y h m tricornutum.
Opal-glass technique. (After Yentsch, 1962.)
Absorption measurements
In laboratory studies of absorption spectra for translucent biological
material it is desirable t o bring out a strong absorption effect. The discussion
in Chapter 3 maintains that a part of the transmitted light is direct and has
not been scattered by suspended particles; the scattering, on the other hand,
is chiefly due t o diffraction at small angles and t o refraction and reflection
at greater angles. Since refraction is associated with absorption, a scattering
cone of considerable angle should be recorded in order t o improve the
absorption effect. This condition is simply fulfilled by placing a diffusing
glass before or after the sample cell. This principle long utilized in the ZeissPulfrich photometer has been investigated by Shibata (1958). Murchio and
Allen (1962) stress that fact that a similar high resolution is attained by
using a wide beam. Yentsch (1962) has applied Shibata’s method on natural
plankton populations, obtaining excellent absorption reliefs as evidenced in
Fig. 137.
BIOLUMINESCENCE
The generation of light or luminescence is a common characteristic of
marine fauna. The activity of many organisms in the sea is controlled by the
ambient light emanating from sun and sky, and the diurnal migration of the
sonic scattering layers occurs according t o changes in the ambient light level.
Animals with sensitive eyes may perceive daylight at 1000 m in the clearest
waters and may detect luminescent flashes at distances of 40 m (Clarke and
203
Denton, 1962). The complicated photic relation between migration, amount
of luminescent flashing and ambient light changes cannot be discussed in the
present context. Interested readers are referred, for instance, to the publications of Boden and Kampa (1964,1974) and Clarke and Kelly (1965).
Biologists have contributed considerable data about irradiance in the sea,
especially for deep strata. This information is incorporated in the discussion
of irradiance distribution (Chapter 10). It may be added that the proper
functioning of meters specialized for measuring bioluminescence requires
high sensitivity, great speed and preferably logarithmic response as the
flashes are quite intense (Clarke and Hubbard, 1959). In deep layers it is
often difficult to distinguish the biological and the physical phenomenon,
since bioluminescence creates a background of light which mixes with the
ambient light penetrating from the surface.
ANIMAL 0 RIENTATION
It has been demonstrated that certain aquatic animals can use the sun for
visual navigation (Waterman, 1959). This specific ability of determining
direction in the sea involves an internal clock mechanism which compensates
for the sun’s movements through the sky. The usefulness of the sun as an
accurate compass is somewhat restricted by the fact that the in situ sun
seldom appears as an image but is disintegrated in a glitter pattern which subtends a fairly large angle. On the other hand, recent research testifies that
directionality (in the apparent direction of the sun) of the radiance distribution persists down to greater depths than hitherto anticipated.
An exciting aspect of visual orientation in the sea concerns the polarization of underwater light. There is now conclusive evidence that in arthropods
and even in cephalopods the plane of oscillation (e-vector) of linearly
polarized light in the sea is perceived by a visual mechanism different from
that which senses radiance patterns (Waterman, 1959; Jander et al., 1963).
The fact that polarization is an environmental factor adds further importance to such measurements. The recent development in the field is described by Waterman (1974).
205
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INDEX
Absorption, 3, 8 3
-bands, 53, 54, 127, 128, 133
-coefficient, 48, 51, 87, 88, 89, 90, 120,
121,132
_ - of particles, 57-61
_ - _ yellow substance, 56-62
- meter, 51
-,particle, 41, 94, 127, 131, 171, 172,
202
-, pure water, 53, 54
_ ,_ _ , in the infra-red, 53, 139
_ ,- - , in the ultra-violet, 5 3
-, yellowsubstance, 55, 56, 57, 127, 131,
171,172
Adriatic Sea, 188
Adsorption, 26
Air light, 190
Albedo, 78, 79, 95
Algae, 57, 172
Allard’s law, 47, 157
Amazon river, 182, 183
Animal orientation, 203
Antarctic Bottom Current, 178
-Intermediate water, 178, 180
Apparent optical depth, 150
- properties, 8, 51, 97
Arago point, 72
Atlantic, 24, 38, 41, 65, 178, 179
-,North, 24, 27, 60, 127, 137, 140, 143,
148
-, northeastern, 24, 37, 69
- off Bermuda, 58, 59,143,149, 169
_ _ Cadiz, 186
_ _ Madeira, 143
_ _ New York, 143
_ _ the Antilles, 193
_ _ _ West Indies, 149
_ _ West Africa, 127, 130, 144, 169, 178
-, South, 137, 196
-, western, 179
Attenuance of particles, 54, 55
_ _ pure sea water, 54
_ _ _ water, 51, 54
_ _ - - in the infra-red, 53, 54
_ _ _ _ in the ultra-violet, 53
_ _ - - , temperature effect, 54
Attenuation coefficient, 48, 51, 52, 89,
99,181,185,186,188,189
Aureole effect, 79, 117
Average cosine, 89, 123
Babinet point, 72
- principle, 31
Bahamas, 25
Baltic, 38, 41, 60, 61, 62, 65, 88, 98, 122,
127, 128, 144, 166, 169, 171, 185,
188,190,191
Band-width error, 101, 106, 107
Bay of Biscay, 143
Beam attenuation, 3, 47, 66
Beam transmittance meter, 2, 3, 89
---, laboratory, 49
_ _ _ , in situ, 49-51
---,calibration, 50
Bioluminescence, 140, 202, 203
Black Sea, 41, 152
Bocaiuva, 76
Bothnian Gulf, 188
Bottom erosion, 186
Brewster point, 72
Brewster’s law, 73, 189
Brillouin scattering, 39
Cariaco Trench, 182
Caribbean Sea, 59, 127, 128, 129
Carnegie Ridge, 186
Chandrasekhar’s method, 92, 93, 166
Chesapeake Bay, 36
Chlorophyll, 55, 130, 131, 172, 201, 202
Chromaticity coordinates, 167, 168, 170
Collection, cosine, 88, 102
-, equal, 88,102
Collectors, fish-eye lens, 101, 108, 117
-, hemispherical, 102
-, irradiance, 102-104
-, radiance, 101
228
-, spherical, 102
Colorimetric concepts, 1 6 3
Colour, fluorescent, 166
- from downward irradiance, 168, 169,
170,171
, influence of solar elevation on,
171
_ _ upward irradiance, 168, 169, 170,
171
index, 115, 192, 1 9 3
-, influence of waves on, 1 6 6
- irradiance ratio, 1 7 1
-, isotropic, 169
-meters, 115
- mixture data, 164
-, numerical aspects of, 165, 166, 167,
168,169,170,171
- o f the sea, 115,163-172,190,196
-purity, 165, 166, 167, 168, 169, 170,
171
Columbia river, 1 8 2
Committee on Colorimetry, 1 6 4
Commission Internationale d’Eclairage
(CIE), 2, 1 6 3
Contrast, apparent, 157, 158
-, inherent, 167, 158
Cosine emitter, 17
--law (Lambert), 9, 1 0 2
Coulter Counter, 25
~
Definitions, 3
Detectors, photoelectric, 15, 16, 17, 18,
105,107,111, 113,114, 115
-, photographic, 17, 24, 101, 113
-, visual, 24, 101, 1 1 3
Diffraction, 26, 28, 39, 202
Diffusion, 177, 1 8 4
Discolouration, 172
Discontinuity layer, 177
East China Sea, 36, 41
Efficiency factor, 29, 30, 31, 32
English Channel, 36, 37, 42, 66, 152
Filters, blocking, 66
-, colour, 106, 107
-, differential, 106
-, interference, 107, 110
-, neutral, 105, 1 0 6
-, Polaroid, 113, 189, 201
-, Schott, 106, 111, 113, 115, 191
Flocculation, 23, 26, 56
Flores Basin, 1 7 6
Florida Current, 1 4 3
Fluctuation theory, 20
Fluorescence, 55, 63-66, 107, 190, 192
Fluorometers, 63, 192
Fraunhofer lines, 69, 127
Galapagos, 59, 170, 176, 177
Geometric optics, 26
Gershun’s equation, 87, 90, 110, 111, 1 4 5
Gibraltar Strait, 88, 180, 181, 195, 1 9 6
Glitter, reflected, 77, 78, 166, 175, 1 7 6
-, refracted, 82, 117, 203
Global radiation, 69-72
_ - , polarization of, 72
- _ , spectral distribution of, 70, 7 1
Golfe du Lion, 142, 1 4 3 ,
Great Belt, 51, 6 3
Gulf of Mexico, 178, 179
Gullmar Fjord, 118, 121, 1 2 2
Gulf Stream, 1 7 1
Haschek-Haitinger colour system, 166,
167
Illuminance, 1 6 3
Imaging systems, 1 6 0
Immersion effect, 1 0 2
Indian Ocean, 146, 148, 169
--, western, 1 4 3
Inherent properties, 57, 66, 89, 97, 100
- _ , ultra-violet, 92
International Association of Physical
Oceanography (IAPSO), 2
International Dictionary of Physics and
Electronics, 2
Inverse-square law, 9
Irradiance, 3, 8, 9, 10, 47
-attenuation coefficient, 86, 130, 131,
132,133,135,136,147
-, downward, 83, 9 3
-, --, effect of waves on, 150
-, -, in deep water, 139, 1 4 0
-, -, - upper layers, 127, 150
_ , _ , influence of solar elevation on, 86,
145, 146
_ ,- , photosynthetic, 197, 198, 199
_ ,- , spectral distribution of, 128, 129,
1 3 0 , 1 3 3 , 1 3 4 , 1 3 6 , 1 4 2 , 1 9 6 , 197
_,- , total, 139, 140, 1 4 1
-, -, transmittance of, 1 3 4
-, -, ultra-violet, 127, 131
-, horizontal, 140
229
-, inverse-square law of, 9
-meters, 3, 51, 109-111
- _ , calibration of, 114
_ _ , ultra-violet B, 111
-, monopath, 147
-, multipath, 47
- ratio (reflectance), 88, 94, 95, 143,
146, 148, 149,171
- _ , influence of solar elevation on, 148
- _ , internal, 95, 148
-,scalar, 2, 10, 87-90, 102, 144, 145
-, spherical, 10, 87, 102, 145
- theory, 83-90
- _ of scattered light, 84, 85, 86
-, upward, 142-144
_ , _ , in deep water, 144
, -,- upper layers, 142-144
- ,_ , influence of solar elevation on,
146-1 49
- ,_ , near bottom, 94, 95, 149
_ , _ , spectral distribution of, 144
-vector, 103, 111,1 4 5
Isochrysis galbana, 24
Kattegat, 60, 62
Kuroshio diving chamber, 25, 113
Lake Hefner, 79,
- Pend Oreille, 91, 118, 121, 122
- Winnipesakee, 37
Lens-pinhole system, 16, 101
Light leakage, interference filters, 107
_ _ , irradiance meters, 110
Luminance, 163
Mediterranean, 27, 36, 37, 38, 41, 98,
119, 123, 169
-, east, 127, 128, 129, 137, 182
- Intermediate water, 180
- off Corsica, 93, 1 2 1
_ _ France, 120
_ _ Monaco, 37, 45, 46, 93
_ _ Sicily, 181
_ - South Sardinia, 147, 154, 200
-,west, 34, 35, 38, 60, 191, 192, 193
Mie theory, 28-33, 43, 176
Modulation transfer function, 160-162
- _ _ meter, 161-162
Monte Carlo techniques, 93, 94, 95, 100
Muller matrix, 100
Neutral points, 70, 152
Nile river, 182, 183
Noctiluca, 172
North Sea, 65, 166, 171, 184, 185, 188,
189,192
Norwegian Sea, 65
Oil spills, 190
Optical classification, 131-137
-types, 132-138,197,198
Orinoco river, 182
Pacific, 27, 42, 137, 169, 178, 184, 195,
198
-, central, 24, 59
-, east, 54
-off California, 37, 143, 171
_ - Japan, 25, 36, 118, 128
_ _ South America, 56, 59, 170
-- Tahiti, 143
-, west, 27, 179
Panama Basin, 187
Particle distribution, 176-188, 195, 198
_ - and stability, 177
_ _ in a monodisperse system, 28, 30
- - - - polydisperse system, 29, 31, 32
- -~ near bottom, 186-188
- shape, 24-26, 44
-size, 24-27, 30, 41, 44, 176
- _ , hyperbolic distribution of, 25, 26, 32
Particles, concentration and nature of, 22,
23
-, coloured, 41, 42
-, refractive index of, 23, 24, 176
Path function, 89, 9 1
Peridinium triquctrum, 172
Phaeodactylum tricornutum, 202
Photic zone, 177, 195
Phytoplankton, 23, 55, 172, 177, 196
Po river, 182
Point spread function, 160, 161
Polarimeter, 46, 113
Polarization, asymptotic state, 153, 154
-, circular, 43
-, defect term, 20, 44
-, effect of solar elevation on, 151
-, elliptical, 43, 74
-, linear, 43, 73
-, negative, 152, 153
-, reflected glitter, 78
-, refracted glitter, 81
-, scattered light, 28, 32, 33, 43-46
-, skylight, 82, 151, 153, 189
-, sunlight, 81, 151
230
-, underwater energy, 113,151-155, 203
Pollution, 188, 189
Potomac river, 49
Primary production, 130, 177,195
Puerto Rico trench, 178
Pumping system, 14, 191
Quanta irradiance, 137, 139, 194, 196,
197, 198, 199
- _ , dependence on solar elevation of,
147, 200
-meters, 111-113
Radiance, 8, 9, 10, 117-125, 176, 179
-, asymptotic distribution of, 96, 97, 98,
99,100,120-125,145
- attenuation coefficient, 96, 97, 120,
158
-, dual nature of, 8
-, field, 157, 158
-meters, 3, 107, 108, 109
- _ , calibration of, 114
-,target, 157, 158
-theory, 83-95
Radiative transfer equation, 89, 90, 92,
97, 98,161
Rayleigh scattering, 19, 30, 31, 39, 43, 83,
92, 94
- _ atmosphere, 200
Raman scattering, 65
Red Sea, 65,131, 188
Red tide, 172
Reflectance for diffuse radiation, 74
_ _ direct radiation, 73
- _ global radiation, 75, 76
- - _ - , effect of waves on, 76, 77
Reflection at surface, 73-80, 86, 175,
189
-, dependence on wavelength of, 80
-, Fresnel, 73, 74, 75, 79, 8 1
- from bottom, 94, 95
-, internal, 81, 86
-, particles, 26, 28, 38, 39, 43, 150, 202
Refraction at surface, 73, 81, 82, 150, 175
---, effect of waves on, 82
-by particles, 26, 28, 38, 39, 43, 150,
202
-cone, 81,117,151
Refractive index of particles, 23, 24, 29,
31, 33, 44
--sea water, 22, 23, 81, 82
- - - - -, dependence on wavelength of,
22, 23
_ _ _ - _ , salinity effect on, 22, 23
_ _ - - - , temperature effect on, 22, 23
Remote colour measurements, 200, 202
- optical sensing, 189
Rhodamine B, 190
Romanche deep, 59
Sagitta, 25
Sargasso Sea, 19, 32, 33, 36, 37, 38, 41,
59, 60, 65, 123, 125, 130, 133, 137,
142, 143, 144, 147, 166, 167, 168,
169,170,171,197
Scatterance meters, 2, 3
--, fixed angle, 14
_ _ , free angle, 14
_ - , in situ, 15-17
--, integrating, 14, 17-19
_ _ , laboratory, 1 5
_ _ , small angle, 16, 1 7
Scattering, 3, 13-46
-, anisotropic, 20, 43, 44, 45, 46
-, coastal, 39
-coefficient, 18, 39, 40, 48, 51, 58, 59,
60, 61, 99, 120, 121, 188
-, dependence on wavelength of, 40-42
-function, 15, 21, 22, 32, 33-39, 79,
87, 91, 97, 131, 176, 178, 180, 181,
182,183,185,188
_ _ , backward, 34, 85
_ - , forward, 34, 39, 40, 8 3
-, independent, 28
-, isotropic, 20, 28, 43, 44, 45, 46, 83,
100
-layers, 177, 178, 179, 180, 181, 184,
190,191
_ _ near bottom, 178, 179, 180, 181,
183,185,186,187,188,189
- matrix, 44, 45, 46, 100
-, multiple, 30, 42, 83, 89, 94, 157, 165,
168
-, particle, 13, 26-33, 41, 94
-, primary, 83, 84, 157
-, pure water, 13, 19-22, 41
-, -sea water, 21
Shading error, 114
Sighting ranges, 159
Skagerrak, 60, 65, 94, 131, 190, 191
Skylight, clearsky, 69, 74, 75, 76, 77, 92
-, _ - , angular distribution of, 69, 71
-, - -, percentage of global radiation of,
69, 70
-, _ - , spectral distribution of, 70, 71
231
-, overcast sky, 70
-, _ _ , spectral distribution of, 70, 71
Snell, law of, 81, 82
-circle, 153
Sound, 62,63, 65
Special Committee on Oceanographic
Research (SCOR), 111
Stoke parameters, 44
Sunlight, 76, 83, 92
-, spectral distribution of, 70, 71
Transmittance, beam, 3, 52, 183, 184,
190,191
-, underwater energy, 129, 131, 133, 134,
136,139,141,145,146,147
Trichodesmium, 172
Trichromatic colour system, 163, 166
Turbid suspensions, 45, 124, 154
Turbidity currents, 186
Tyrrhenian Sea, 65
Upwelling, 177, 190, 195
Visibility, 157-162
-, field radiance, 160, 203
- Laboratory, 89, 90, 157, 159
Working Group 1 5 (IAPSO, SCOR) on
photosynthetic energy in the sea, 111
Yellow substance, 55, 57, 63, 166, 190,
195
Zooplankton, 23, 172