PB83-2381Q8
Effects of Suspended Sediments on
Penetration of Solar Radiation into
Natural Waters
California Univ., Santa Barbara
Prepared for
Environmental Research Lab., Athens, GA
Jul 83
U.S. Department of Commerce
Technical information Service
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EPA-60,0/3-83-060
July 1933
EFFECTS OF SUSPENDED SI DIMENTS ON PENETRATION
Of SOLAR RADIA110N INTO NATURAL WA1ERS
by
Raymond C. Smith1'2
Karen S. Baker ^
J. Benjamin Fahy1
•^Department of Geography
University of California at Santa Barbara
Santa Barbara, California 93106
2lnstitute of Marine Resources
Scripps Institution of Oceanography
University of California at San Diego
La Jolla, California 92093
Grant No. 806372019
Project Officer
Ric-hard G. Zepp
Environmental Processes Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMLNTAL RESIARCH LABORATORY
OFFICE Of RESEARCH AND DEVELOPMENT
U.S. ENVIRONMEN1AL PROTECTION AGENCY
ATHENS, CEOIU.LA 30613
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TECHNICAL REPORT DATA
(/'/ £!( nail tiu'nii inns on i/u nu;u ">< Ion i
NO
EPA-600/3-83-060
J TITLE A\D SUBTITLE
Effects of Suspc-nde^ Sednents on Penetration
of Solar Radiation into .Natural Waters
Nl t, ACCES<;iOr#NO
ft $ ?5818K
b REI'OIU DA IK
July 1983
6 PERFORMING ORGANIZATION CODE
Raymond C. Smith1'? Karen S. linker2, and J. Benjamin
8PEHIORMINGOIIGANIZA1IONIUIOHINO
Fay
ir-*-
•3 PERFORMING ORGANIZATION NAME AND ADDRESS
•1-L'nivcrsity of California at Santa Barbara, Santa
Barbara, CA 93106
2Scripps Institution of Oceanography, University of
California at Fan Diego, La Jolla, CA 92093
12 SPONSORING AGENCV NAME AND ADDRESS
Environmental Rcse rch Laboratory—Athens GA
Office of Research and Levelopment
U.S. Environmental Protection Agency
Athens, GA 30613
10 PROGHAM ELEMENT NO
CCUU A
11 CONTI'ACT/GHANT NO
80f> "J7-J019
13 TYPI Ol nU'ORT AND PERIOD COVCHF.O
Final, 2/79-12/92
14 SPONSORING AGENCY CODC
EPA/600/01
IE SUPPLEMENTARY NOT?S
16 ABSTRACT
Aquatic photochcn-Lcal and photobiolrgical processes depend on both the .unount
and the spectral compot>ition of solar radiation penetrating to depths in natural wa-
ters. In turn, the depth of penetration, ar a function of wavelength, depends on the-
dissolved and suspended material in these waters. As a consequence, the rates of
photochemical transformation as well as the impact on photobiological processes, de-
pends on the optical properties, of these water bodies as determined by their dissolve.
and suspended material. In particular, because pnoto-chemical processes are frequent
ly governed b> radiation in the ultraviolet region of the spectrum, the optical pro-
perties of natural wacers in this spectral region are especially important. In this
study, several theoretical models were developed and some unique experimental data
were developed for the purpose of characterizing the optical properties of various
natural waters. Particular e-.i,>hasis was placed on optical properties in the ultra-
violet region of the spectrum. Optical properties of water bodies were modeled in
terms of their dissolved materials and suspended sediments so that the solar radiant
energy penetrating to dept."- in tnese waters can be calculated from available, or
easily collected, experimental uita. The theoretical models, with imput of these
data, can then be used to calculate the rates of photochemical and photobiological
processes in various aquatic environments.
KEY WOHOS AND DOCUMENT ANALYSIS
DESCRIPTORS
h IDENTIFIERS/OPEN ENDED TERMS
COSATI I ltlll/(.liill|i
14 DISTRIBUTION STATCMfcNI
RELEASE TO PUBLIC
SECURITY CLASS /Ilin K,f/
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EPA Form 2220-1 (9 73)
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DISCLAIMER
Although the research described in this report ha.s been funded
wholly or in part by the United States Environmental Protection Agency
through Grant No. 8063720J9 to the Universit> of California at San
Diego, it has not been subjected to the Agency's required peer and
policy review and therefore does not necessarily reflect the views of
the Agency and no official endorsement should be inferred.
ii
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FOREWORD
Environmental protection efforts are increasingly dliecteu towards
prevention of adverse health and ecological effects associated with specific
compounds of natural or hutvan origin. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and
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PREFACE
Within an aquatic environment the presence ot solar rauiation as in
cneigv source is ot fundamental importance. Uur ability to unuer&iand anu
manage our aquatic resources is theretore strongly linked to our aoility to
understand the penetration of radiation into a body ot water acd its appor-
tionment among various components of dissolved and suspended material in the
water. This report presents a study in hydrologic optics which included
assembling t data base of relevant optical measurements, deriving mathematical
models for the solution of the equation of radiative transfer, and deducing
from these both simplified theoretical and practical results. This study will
have long term benefits, not only to the investigators of hydrologic optics,
but also to a wide variety of other fields concerned with understanding and
predicting phutoprocesses in an aquatic environment.
iv
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AU SIR ACT
The relationsnip oetween dissolved and suspti.dcd cons t1 tucr.t s in water
and the optical properties ol a range oi water types has been investigated and
anlytically characterized using several approaches. This characterization
permits the spectral radiant energy throughout the water column to be predic-
tive ly modeled. This in turn provides a basis for the quantitative calcula-
tions of photo processes such as photolysis rates, in aquatic environments.
A series of new laboratory experiments has provided a set oi data upon
which the Bio-optical Component Model (Baker and Smith. 1981) could be further
dej^ioped. The investigation into the humic acid component has been contin-
ued. A new component dealing with a terrigenous clay has been added. Both of
these components are parameterized and hence remain within the intended sim-
plicity of the original model.
A briet introduction to underwater modeling is presented as an introduc-
tion to the development of a Monte Carlo model. The Uio-optical Component
Model allows calculation of the diffuse attenuation coefficient of Irradiance.
howeNPr it does not permit calculations with respect to sun angle or investi-
gations into the changing light field as a function of depth. The Monte Carlo
method is a photon tracking technique, essentially a random walk procedure,
using the apparent optical properties ot the water. Ibis oojc 1 can then be
used to investigate the influences of depth and sun au^lo on the lijut field.
Technical anu practical considerations limit the collection ot aata pertinent
to all lijjht conditions. Indeed, this is the advantage ot a model. It can
serve as an organizational tool as well as a deductive and predictive tool.
To organize field data to test the developed models, it v.as first neces-
sary to uecermine the best available values tor the optical properties ot the
clearest natural waters. An extension and a completion of the set 01 apparent
anu iniicrent optical properties for the clearest natural waters has been
described. Also, other optical field data sets have been collected and organ-
ized.
This report was submitted in fulfillment of grant //S06-372-019 under the
sponsorship of the U.S. environmental Protection Agency. This report covers a
period from February 1979 to December 1982 and v/ork was completed as of
December 1982.
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TABLE OF CONTENTS
List 01 Figures .................................................. v'
List of Tables [[[ j .•
I . INTRODUCTION .................................................. 1
II . CONCLUSIONS .................................................. 4
III . RECOMMENDATIONS ............................................. 5
IV . liXPUlLMLNTAL ................................................. 7
A. Tan* Data ............................................... 7
U. DOil [[[ 10
C. Other Field Data ......... . ............................... 11
V . Til^OiiiiTlCAL [[[ 12
A. '1 10 Code ............................................. 13
J . Jjvc LOce ............................................. 13
L. .on '« Cjrlo noc!eliii{, .................................... 14
D. POOP [[[ 15
i). >>iocel Cnecjts ............................................ 16
VI. liESULTS [[[ 18
.i. vuuosj-acre ............................................. 12>
J. TII..J data - . lejr viator ................................ iy
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LIST OF FIGURLS
I-igure 1. ite lationsnips between experimental tielu liata and toisputcr aodcls. 24
Figure 2. The spectral l.ght attenuation in each ot the Clay Group water
types #1 - #8 listed in Table 1. 25
Figure 3. The spectral light attenuation in each of the DOM Group water types
#9 - #16 listed in Table 1. 25
"Mg'.re -! . "he spectral Kclay component for each of the Clay Group water types
,'2 - J 8 1 -iied in Table 1. 26
5. Int Kclay component for the wavelength range from 275nu to 74Snm. 26
Fifui > The Kclay component for the wavelength 550am for a range of clay
Ippm] where *h: x s are experimental data and the line is a polynomial fit. 27
Figure 7. The Kclay component for five wavelengths where 5B300niL. ll»450nm,
13=550nn, and 15=650nm where these points represent data and the solid line is
the model fit. - 27
figure 8. ihe spectral u'uoa component (with scattering material still
present; see teit) for a UXI Group water types >/ll - £16 listed in Tablo 1. 28
Figure 9. The spectral iCdco component for the DOM Group water types #11 - #16
listed in Table 1. 28
Figure 10. The Kdotn component tor two wavelengths where the points are data
and the solid line is a fit. 29
Figure 11. The spectral (kaoa^&clay ) component where the x's are data aad the
line is the aodel fit. 29
Figure 12. The spectral Ktot data points and analytic model fit as solid
lines for the Clay Group. 30
Figure 13. The spectral Ktot data points and analytic model fit as solid
lines for the DOM Group. 30
Figure 14. The total scattering b for a variety of water types from molecular
scattering to clear water to ocean to river. 31
Figure 15. The spectral a (solid line), b (dashed line), c (dash dashed
line), and b/c (notched line) for SCOR Discoverer station 21 Sargasso Sea
waters. The D points are the field data measurements ot total diffuse
attenuation coefficient whereas the 1,6 are the Monte Carlo calculations of K
for 10 degree and 60 degree sun angles. 32
Figure 16. 'Ihe a (solid line), b (dashed line), c (dash dashed line), and b/c
(notched line.) for San Vicente waters. The circled 1,6 points are the field
measurements of total diffnse attenuation coefficients for tun angles 10
degrees and 60 degrees whereas the 1,6 points are the Monte Carlo predictions. 33
VI11
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Figure 17. The particle volume scattering function for fairly clear ocean
water (Oceanus cruise station 4) tor wavelengtns 440nm, 490nm, 520nra, 610nm,
and 670nn. J4
Figure 18. The calculated total volume scattering function for very clear
ocean water (SCOR Discoverer station 21) for wavelengths 440nm, 490run, 520nm,
6lOno, and 670nn. 35
Figure 19. The Baker-Smith III component model prediction of spectral Ktot
(X) for a range of chlorophyll, dissolved organic material and clay. The fol-
lowing explains the composition: 36
line
chl
DOM
.,,
solid
0 .5 5.
000
000
dashed
0 0
.5 5.
0 0
dashed dot
0 0
0 0
5 25
hatched
.5 5
.5 5
5 25
r--g. 20. The Monte Carlo calculation of KO..z,0) for waveler.gth S50"-« for
son angles 10, 30, 60, 70, SO degrees plotted versus optical depths cz when
using only a direct oeaa input to the water column. 37
Fig. 21. The Monte Carlo calculation of Jx(X, z.O) tor wavelength 55Own for
sun angles 10. 30, 60, 70, 80 degrees plotted versus optical depths cz when
using both a direct and a diffuse input to the water column. 38
Fig'-re 22. The 'lonte Carlo calculation of HO., z. 0) for cleir waters of SCCK
Discoverer for sun angle 10 degrees (solid line) and 40 degrees (broken line)
for wavelengths 440nm, 490iun, 515nm, and 550nn. The straight line j-uperim-
posed is the field measured value which is an average for the day. 39
Figure 23. The Monte Carlo calculation of K(X.z.O) for San Vicente waters for
sun angles 10, 30. 60, 70, 80 degrees for wavelengths 440nm, SSOnm, and 670nm.
The straignt lines superimposed are the field measured values for 10 and 60
degree sun angles. 40
LIST OF TABLES
Table 1. Tank study water types.
23
ix
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ACKNOWLEDGEMENT
Xichard Zcpp recognized the recessity for those studies and acted as pro-
ject officer during the course ot this research. Uc continually encouraged
our researcn and provided valuable scientific input through informal discus-
sions and the practical utilization of oui results. An earlier EPA grant
RG806489010, under the BAGIil program and concerned with the penetration of UV
radiation into natural waters, supported the development of the UV spectrora-
diometer used in this research.
The tank data were obtained with the help of the Marine Application*
Group at NASA Langley Research Center, especially Wayne Esaxas. Lament Poole,
and Charlie Whitlock - who made the facilities available - and Al Gurganut
and Jim Usry who helped obtain the data. Lamont Poole also collaborated in
the development of the Monte Carlo modeling. This node ling built upon tag
earlier work of J.V. Oave and John Kirk.
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SECTION 1
INfiiODUCTlUN
Aquatic photochemical and photob loiog ical processes depend upon both the
amount of solar radiation penetrating to depths in natural waters as well as
upon its spectral composition. It is the influence ot dissolved and suspended
material in the water combined with the characteristics ot clear water which
determine the attenuation ot light in a water column. Our maiu research
objective was to characterize varuus natural waters, in terms of their con-
stituents and consequent optical properties so that the spectral radiant
energy versus depth can be estimated. Waters containing humic acid and
suspended sediments were of particular interest. This characterization can
then be used to calculate rates of photochemical and photobiological processes
in aquatic environments. This in turn allows a quantitative assessment of tae
photochemical process that may account for the transf ormai j on of pollutants in
aquatic environments. Some new r ad i one trie laboratory field studies have been
made and combined with information from previous bio-optical field studies.
This has allowed the further development cf models and theory which can in
turn be defined and checked by tae data.
Pre iseadorier '1976) has defined the inherent optical properties of a
uetliou to be those itnuch are iuue pendent of the lignt-iield within the vatcr.
iuciuueu witiim tais set are tne beam absorption toei i ice int c. tae bean
scattering coefficient b. and the total attenuation coefficient c, wnere c =
ai-b. The parameter b is actually the integral over all angles ot another
inherent optical property, the volume scattering coefficient
b = / k (0) dU . <1)
Preisendorf er has shown the set (c, p) of inherent optical properties to be a
sufficient and complete set for describing the optical properties of the opti-
cal medium under any circumstances. That is, knowing (c,p), and an input
radiance distribution illuminating the optical medium, which is arranged
within some known geometry, one can in principle deduce the resulting radiant
ilux distribution.
If an optical property does vary with respect to cnanges in the radiance
distribution, it is said to be an apparent optical property. To describe the
penetration of solar radiation into natural waters, we use the diffuse
attenuation coefficient for irradiance, which is an apparent optical property,
K(z.X) = -1/EU.X) dE(z.X)/dz (2)
or alternatively,
E(z2,X) =E(zrX) expt-K(z.X) • (Zj-Zj)] (3)
wnere K has units of reciprocal length, z. and z, are the depths which
increase positively with increasing depth at which E(z.) aid E(z_) are meas-
ured. In particular, if the spectral downward irradianco just beneath the
water surface, b(0~, X), and K(z,X) are known, tnen the spectral irraaiance at
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depth, z. can be calculated.
E«z.X) = fc(0~, X) expl-K(z.A) »zl. 14)
Miller and Zepp (1979) have shown that the average photolysis rate at
depth z and wavelength X can be expressed by
-UP/dt) , = 2.303 / * • eU) • L(z,X) • D(t) * [P] * dX (5)
z. X z
where 6 is the quantum yield for the reaction, e is the molar absorptivity of
the pollutant, E(z,X) * L)(z) is the scalar irradiauce at depth z, 0(z) is the
distribution function at depth z. and IP] is the pollutant concentration at
depth z. Thus. given the chemical characteristics of the pollutant and its
concentration, a knowledge of E(z.X), or oquivalently k(z,*.), is sufficient to
quantitatively calculate the photolysis rato of the pv/llutant under considera-
tion.
The diffuse attenuation coefficient is a function of the total attenua-
tion and scattering coetf ic icnts. It provides a way <.i crura. tuti..us variOL->
natural waters lu terns of the dissolved and suspended uutoriai in tticse
waters. \iuile the potential for character iz ing waters in tins way is widely
recognized, there are very few data relating the diftuso attenuation coeffi-
ceint for irradiance to the concentration of suspended material in waters con-*
tainiuj relatively nigh concentrations. The spectral diffuse attenuation
co«tficieat. X(z,X), can be expected to be dependent upon the sizes, shapes
and, concentration of suspended catena!. Thus, beiore natural waters of this
type can be characterized by an appropriate K-fuDctiou, iI is necessary to
obtain concurrent K(z, X) and suspended material data.
There are few data available in the ultraviolet portion of the spectrum,
the spectral region most critical for modeling photolysis rates. The UV radi-
ation is important for studies of pbotoreactions because many pollutants
absorb sunlight most strongly in this wavelength region. Hence, particular
eupnasis has been put on collecting data in several water typos in tne UV
region and decking the snort wavelength predictions of uodels.
• >
Modeling has been used to organize data into a classification scheme as
well as to permit predictive estimates to be made, blnco the diversity of
possible water types and ot radiant energy geometries is so large. it is
necessary to augment data gathering with the development of predictive models
which will allow limited data to be extrapolated to situations which have not
been defined by a complete set of field measurements.
The component model developed by Saith and Daker (1978n, 1978b, 1982)
presents the diffuse attenuation coefficient of irradiance as a function of
wavelength defined by water constituents of clear water, chlorophyll and dis-
solved organic material. This oodel defines an average Ktot(X) which
represents an intcgxated value of K to the ISo light level. Tank studies have
furthered the development of this model. New information regarding the dis-
solved orcanic material has been gathered and a new clay component has been
added. The use of this modal is enhanced by the fact that it is simple, and
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easy to use.
Uowcver, a core coup.eto understanding rec,uni,s uout Is wnich can oe used
to predict behavior of light as a function of angie and depth as well as a
tunction of wavelength. Existing radiative transfer theory and variations ot
Mio scattering theory as well as Monte Carlo modeling have been investigated.
This has resulted in the development of a phenomenological model of radiative
transfer which permits calculations of upwelling and dowuwelling radiance and
irradiance.
An important test of the limits of such models is comparison with
clearest natural waters as well as with turbid waters. Since the clear water
optical properties are one of the components of all other water types, it is
important to have as complete a set of these properties as possible. The
angular scattering and total scattering data for such waters have been incom-
plete. In the work reported herein these daca have been assembled anu
extended thus completing the set of inherent and apparent optical properties
tot the clearest waters. When inherent optical properties are input to the
Monte Carlo model, it has been shown to reproduce the apparent optical proper-
tic*. The oouel is usea to extend our knowledge of the beuavior ot apparent
optical properties as a function of wavelength, of depth, and of solar zenith
angle.
To simulate realistic and quantitative aquatic lignt fields, it is r.ei.es-
sary to define an input light tiold to the surface of the water column. This
requirement uas stiaulateu research into the etlcct ot varying solar angle aud
atmospheric condition* on the underwater light fi.:ld.
l-igure 1 summarizes the relationship between the experimental anu the
theoretical WOIK discussed hero. Tic triangles represent, licld aata. They
serve as inputs and cuecks on the classification schcucs and predictive nouels
wuich are portrayed as boxes. The calculated parauetcrs are represented by
circles. In this diagram, the lower dashed area relers to the UaLcr-Smith
component model of the diffuse attenuation coefficeint of irradiance. Tne
upper dashed box describes oar Monte Carlo modeling showing its inherent opti-
cal property inputs along with the atmospheric lighting geometry, LO, input.
The output iron tais model is the apparent optical properties, MX,z,0) and
hence E(X. z.O) aud K(X,z,0). Tae left Band side of the diagram snows water
type constituents wneroas the right hanu siue ot tiie diagram snows tne node Is
with their inputs and outputs.
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SECTION 2
CONCLUSIONS
The organization and further analysis of data lias allowed a full suite of
inherent and apparent optical properties tor clear waters to be deduced. In
addition, laboratory investigations of clear water with additions of clay as
well as humic acid have allowed the further development ot the Uio-optical
Component Model. Although this model is sinplo and easy to use in predicting
the light field underwater, it deals only with an average K and does not per-
mit a further understanding of the underlying processes contribution to light
attenuation. The development of the Monte Carlo model has furthered our
understanding of both the inherent and the apparent optical properties of
natural waters.
The Bio-optical Model III is described by liquation 9. With this taodel
and a knowledge of the chlorophyll, bunic acid, and the clay content of a
water system, the average diffuse attenuation coefficient for irradiance can
be calculated. Given an input irradiance field, it is then possible to esti-
mate the light field at any point in the water coluun. Having thus defined
the environment in terms of the light present, it is possible to investigate
various photo processes such as that describee by equation 5.
It xus oi:t,n demonstrated taut the ilonte Carlo uouci provides closure uuen
applied -0 the problem of calculating the apparent optical^properties of an
underwater light field when given the inherent optical properties. Further.
by use of the model we have uncovered several important facts. The importance
of dealing with the total light field (direct and diffuse) has been discussed
and explained. lUc diffuse attenuation coefficient has, oeeu »noun to be rela-
tively insensitive to the act-al cot-position of thu luul li^Jt fiulJ la n-rj;,
of the ratio oi direct sunlight to diftuso i».> light. Further, k has been
louna to be only weakly sensitive to the wavelength dependence of the volunc
scattering tunction. This has the important consequence that the data from a
volume scattering meter at one wavelength may be reliably extrapolated to
obtain K estimates at another wavelength.
Uy use oi the model we have demonstrated, with more completeness, -than is
practical with field data, that the diffuse attuuuatiou coefficient for irra-
diance will ruacu an asymptomatic value wuen the gvviaging ettcct ot depth on
the direct and diffuse components begins to take effect. bioilarly, it has
been shown that there is a significant change in K ai a function of sun angle.
This effect is more pronounced in turbid waters than in clearer wacers.
The investigations that are summarized are being described in detail in
several publications. Manuscripts currently in preparation are summarized in
the Appendix.
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SECTION 3
The data gathering, description and predictive modeling of environmental
processes 11 practical situations is complex and expensive. The research
sponsored here has demonstrated the cost ef tectiveness of an integrated
theoretical and experimental program where limited, but specifically chosen.
data have been utilized to test and refine models. These models are in turn
utilized to simulate realistic field data for sensitivity analyses and further
invesitgation and predictive modeling of the fundamental processes of
interest. Given todays limited resources allocated to the study of important
environmental problems, ve strongly recommend (.bat the methodology demon-
strated in this research program be utilized more frequently.
Our investigations have obtained valuable new data and created theoreti-
cal models which will provide solutions to a wide range of environmental prob-
lems dealing with natural waters. This work also suggests new directions for
iurther productive research. Specific recommendations include: (1) more com-
plete experimental work in controlled environments (such as tank experiments),
especially to obtain the optical properties of important organics and clays
and the optical effects when these are •ai.xed,- (2) work to increase the speed
anil cificicucy of the !>.outo Carlo model and tne use ol this uouel tor contin-
ued sensitivity analysis uirecteu toward speciiic practical problems,- (3) the
development and application of other solutions of the radiative transfer equa-
tion wuich can be expected to provide increased insight into the fundamental
processes underlying practical environmental problems: (4) the use of Hio
scattering theory to compute the inherent optical properties dop) of various
natural sediuents and tiic subsequent use ot these lop's in our component model
to1 compute the apparent optical properties (aop) for haters of interest.
The quantity and quality of valuable data that was efficiently obtained
in our tank experiments demonstrates the usefulness of this approach. New
valuable data could be obtained if similar experiments were performed using a
range of dissolved organics (especially different humic acids) and different
suspended clays and other materials. Future investigations should also
induce investigation ot the eifccts ol the mutual interaction of organic
material on the optical properties of «ator. Such tank experiments are essen-
tial in order to define the relationship between optical properties and tne
constituents of our water systems and for a more complete understanding of
photolysis in natural waters.
Considerable value, both for theoretical development and the solut en of
practical problems, can be obtained from the use and further development of
our Monte Carlo model. Increasing the efficiency of the model will propor-
tionally increase its usefulness. Valuable future applications of the model
include sensitivity studiei. of atmospheric parameters influencing the under-
water radiant energy distribution,- of variability in the volume scattering
function, due to chemical and physical modification of suspended particle size
and morphology, and how this influences the distribution of radiant energy; of
key variables for the purpose of parameterizing the most important effects
into simple practical mouols of photolysis 'rates; of the scattering and
absorption properties of various waters containing representative sediments
and how these inherent optical properties effect the distribution function in
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these waters.
The usefulness ot tnlie scattering theory, inputting the relatively large data bases ot
total suspended and particle size information for natural waters, to calculate
the innerent optical properties dop) for these waters. The lop's can in turn
be utilised to calculate the apparent optical properties (aop) and then input
to our bio-optical component model for the estimation of radiant energy pene-
tration into these waters.
The "trade-otf" between computing po»er and flexibility has led the
authors into the consideration of another approach to the problem of finding
one model which is capable of providing both power and flexibility at the same
time. It is our conclusion that perhaps the ideal solution lies within the
realm of "semi-analytic" models which have the merit of focusing computational
power where it is most needed but which still retain the flexibility of bring
easily adaptable to diverse geometries.
Finally it should be noted that we believe in many cases tliat investiga-
tions which are still in an exploratory stage are best served by approximate
methods such as Delta-Hddington approximations. These models provide quick.
albeit rough results, which allow the the investigator to determine whether a
given path of inquiry if likely to be fruitful. Once an approximate method
has been used to determine a basic level feasibility, a Monte Carlo model can
be applied to provide extensive theoretical understanding into the nature of
the phenomenon of interest. If the results of such an understanding then war-
rant continued ivestigation where the utmost efficiency and accuracy is
required, either a matrix operator, spherical harmonic, or similar analytic
method, should be specifically adapted to solve the problem more rigorously.
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SECTION 4
Considerable work has been done in Che past using optical instruments in
acquatic field work. However, as waters become more turbid (hence often more
complex anu variable), a more controlled investigation of the water types is
warranted. Several optical studies of turbid witters simulated in a defined
tank environment have been carred out. This information, in addition to our
own previous optical data base as well as the data base of colleagues who have
worked in more turbid river environments, has yielded a relatively complete
picture of the optical properties for a broad range of water types.
TANK DATA
iutown amounts of dissolved organic material (DOM) and terrigenous
material (clay) were added to a tank of filtered water while the optical pro-
perties were continually monitored. These data may be used then to describe
the influence of each substance individually on the attenuation of radiaut
energy in water. A further analysis yields possible par ame tcr izations of each
attenuating component. This series of experiments was run using the Luugley
Research Center tank facility and solar simulator.
The tan.it facility consists ot an enclosed labor itory, the tank and asso-
ciated filtering and pumping capabilities, and a solar simulator. The tank is
a stainless steel cylinder paintea black on the inside. The diameter is 2.4
meters; the depth is 3 meters/ the volume is approximately 11,600 liters.
Siu.-e the measurements used were relative, the absolute spectral output of the
solar simulator was not critical. However, becauic tue simulator had a hi{,'>
0V output, optical data coulo be obtained in this spCvlral region whicu woulu
otherwise have been impractical under natural conditions.
The organic material added came from the Aldrich Chemical Company. It
was listed as a humic acid vith catalog 111, 675-2 in crystalline form. Tiiese
crystals were dissolved in filtered deionized water before adding the tank
water. The terrigenous material added was a calvert clay which in powdered
form had a readi&h tinge cnarac ter istic of some soil sites in the eastern
United States. A summary of all water types created is given in Table 1.
Note tnat measurements
-------
1979) capable of measuring at any chosen wavelength in the range froti 270
nanometers to 750 nanometers. This inscrucunt has a 1 nm lull width at halt
i_ax pass oanu ana »a:> uc signed spec il ica 1 lj to er.aoli, accurate uudt iwa tor
measurements in the ultraviolet region to be cade.
The component model defines
Ktot(X) = (1/z )/ftQaX £(z.X) dz (6)
ciai 0
where z is the lv> light level. Equation (4) reduces to
Ktot(X) = (-1/z ) • lnU(z ,X)/Eo(0,X)J (7)
max max
Thus from tie E(X) versus depth measurements, a total diffuse attenuation
coefficient may be calculated by making a linear least squares fit through the
data.
The spectral diffuse attenuation coefficient for tne irradiance can oe
partitioned into components:
) -i- tCw(/.) + iic(A) + Kt(X, (u;
.w(X) is the attenuation due to pure seawatcr, Lc(X) is the attenuation
due to chlorophyll, Ku(X) is the attenuation duo to DOM and kt(A) is the
attenuation due to terrigenous material. The Kw component has been measured
ana 'uiscusscu previously (Suitu and Uaicr, 19bl; uaicer and Smitn, iyii2). Ine
.>.c component lias oecn parameterized based u(-on extensive ticld cata (liuith anu
lialer, 197oa,o,' L>a^er ana Smith, 19(52). taom component investigations have
oeen carried out based upon spectral irradiance ficlu measurements (llaker and
Smith, 19S2) wnich were limited due to lack of quantitative bio-chenical meas-
urements Of the IX) 11 present. And finally, the Kt component has not been
investigated previously by these authors. The present data set permits inves-
tigation into the Kd(/J and Kt(X.) components.
Equation 8 will be written for this work
KtotU) = KwU) + KcU) + Kclay(X) (9)
ir order to emphasize that the terrigenous component investigated consists of
only one type of clay. Until further such studies are completed, one can not
be sure what the influence of different terrigenous materials will be on the
light attenuation.
In the Clay Group of measurements made, we may assume that Kc(X) ° 0 and
the twd(X) = 0. Any attenuating substances that are present in the initial
filtered water are thus lumped into the Kw(X) base line measurement:
Kclay(X) = Ktot(X) -Kw(X) * ' (id)
-8-
-------
Thus the Kclay component for measurements #2 through /<8 ol Table 1 can be
caluclated. f plor fur tni: resultant clay coraponn*-s is shown in Figure 4
lais component can jc «riitea
KclayU) = itclayU) • T (11)
where kclayU) is the specific attenuation coefficient of irradiance due to
clay and T is the measure of clay particles in parts per million [pprnj. 1'tg-
ure 5 plots this data for all wavelengths in the range from 2/5 nm to 745 am
as a function of the amount of clay present. To look in more detail, the
wavelength 550 on is shown in Figure 6 where the actual data points are given
as x's. The form of this curve suggests a polynomial fit of the form:
KclayU) = (BU) + CU) » T) * T (12)
This fit is forced through the origin in order to conform to the reality that
•when there is no terrigenous material present, there can be no attenuation due
to the terrigenous component. When such a fit is made, the resulting CU) •»
found to be relatively constant such that
CO.) = -.0043 (13)
waich is wavelength independent. When this assumption i« presumed true, a now
linear least squares regression can be made to obtain a new set of BU). Thit>
parameter can be described by a line fit:
3(X) = A + B * (X) (14)
wnere a linear least squared fit yields
A = .408
B = -.000317.
In succiary. this gives
KclayU) = [.408 -,000317*U) ] *T -.0043*T*T (15)
where kclay = (.408 -000317*U) -0043) «T which is the specific attenuation
coefficient for this clay. To indicate the accuracy of this fit. Figure 7
shows the original data as points and the parameterized fit as a solid lino.
Because of the nature of the data, an inverse wavelength dependence was also
investigated in order to see whether a better fit could be obtained. Using a
technique similar to that described above, it was found that
KclayU) = [.119 -.201*(X/Xo)(-1) ] *T -,0043*T»T *" (16)
where Xo = 375 in this case. This parameterization did not improve the fit to
the data.
-9-
-------
DOM
Note chat the DOM Croup contains what night be called two sets ol ouse-
ll ne measurements. The //9 in Table 1 is the filtered clear water case. How-
ever, a small amount of clay has be in added to all 1X)M waters in order to
increase the light absorption and thus decrease the possible influence ot the
tank walls. The diameter of the tank is approximately 1.2 meters. The
instrument was no longer visible at 1.2 m when 6.47 ppm was in the water.
Thus the amount of clay added was chosen to be the #4 case of the Clay Group.
The Kdom component can be calculated
KdomU) = KtotU) - [KwU) + KclayU)] (17)
where the case #10 in Table 1 is taken to represent Xw + Kclay for the OOfl
Group of vater types. The plot of the DOM components is shown in Figu/.e 8.
Previous workers have investigated the DOM absorption and have always found
that the absorption approaches zero as the 650 run wavelength is reached. This
certainly is not the case with the curves in Figure 8. Instead, these curves
would lead cue to believe that there is a scattering agent present in the
hucic acid added to the water. This in fact agrees with observations frcr
i ther investigators wno have used siuilar sources of L0'
-------
la[Kdon.U)/«LoUo)»U)J = kd'(X-Ao). (21)
Solving this equation ,*itli a linear Jcast squares lit through tnu origin gives
a s.'ope of kd' = ~.01C4 wuich is found to be relatively wavelength independent.
Thil is exactly the value for the slope toucd by Zepp (1981) in bis laboratory
wor) Jt has been found mth ocean field data (Haker and !-rnit.h, 1982) that
kd' ranges froia -.014 to -.020.
This then gives us a defined component for tue Aldrich uumic acid
KdoinU) = D • 1.54 • expi-.0104»U-375) i. (22)
The extent to which this reproduces the original uata is shown 12 Figur. 11
where the points are the actual data and the solic line is deiivca froc. equa-
tion 22 with the appropriate D.
A final look at the fit., of the analytic model io the experimental d*ta
is shivn in Figures 12 and 13 *here the total attenuation coefficient K(X) is
plotted versus wavelength. The x's represent actual data whiK the solid line
i« the nouel prediction.
^
OTUCa FIELD DA.TA
The data collected oy Smith and others at the Visibility Laboratory at
Scripps Institution of Oceanography covered a wide range yt oceanic water
types. Measurements maue in a local reservoir aeipou extend tue 1'iruiu water
types. At the NASA Langley research Center, instr--L.cr.ts Lave \,atiz devulopeu
for (he express purpose of measuring optical properties in turuid waters.
Through collaboration with this group, -\n extensive set ot data for a wider
range of water types was available for our. modeling studies. Figure 14 give*
a sacpling of this data from very clear waters to quite turbid waters.
-11-
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SECTION 5
TliEOltETItAL
Modeling has played, and will continue to play, an important rclc in the
understanding and prediction of spectral radiation behavior underwater. This
is because field data is difficult and relatively expensive to obtain. Also
once a working model exists, it can be useu to extend a.id extrapolate the
necessarily limited field data sets. Use of the node Is also pernits one to
investigate problems that are particularly difficult in the field (i.e., low
sun angles or great depths), and to investigate unsampled water types, to
simulate variations in o/c or >, and to do general sensitivity studies. Such
modeling helps verify our understanding of sub-microscopic processes and pro-
vides an important theoretical link between the constituents of an optical
medium end its resultant optical properties.
Much of radiative transfer modeling has been concerned with the atmo-
sphere. An excellent summary ot atmospheric work is given by the IAMAP Radia-
tion Commission (1977). TLene models were studied to determine their adapta-
bility to our needs for a flexible yet accurate solution to the problem of
propagation of radiation within a variety of aquatic environments.
Atuospnuric nouels jay be classified m several *uys. Tor instant.)., a
few ncthoti are suuuarizeo acre with notes inclaaec to oriel ly mencion ioue ot
the investigators using the techniques. It is mentioned whether the investi-
gator has #orked on tae method in ihe past, uas a currently working uouel, or
is developing it now.
i^xact Anal) tic .Method*
1. Singular tigeafunction method
2. Wiener-ilopf technique
Computational Analytic Methods
I, Spherical liarmonics (Dave now)
2, Matrix Upcrutor method (Plass-tattawar now, Gordon now)
3. Doubling or adding method (Herring, Fitch)
4. Iteration Methods (Dave past)
Computational ("non-analytic") Methous
1. Monte Carlo (Plass-Kattawai past, Gordon past. Kirk, Fahy-Poole)
2. Successive Orders of Scattering or natural solution
(Preisneuorfer).
Approximate Methods
1. Eudington approximations (Delt&-Eddington)
2. single scattering - approximate Monte Carlo (Gordon past)
3. two stream approximations
4. approximate diffusion theories
The above lift is by no means complete but does pcntion the models we
have devoted the most time to e-xplor.ing, and which appear to be receiving the
most attention in the literature. It should be noted that tha approximate
methods usually yield only an irradiance solution nhereas the others give
-12-
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radiance solutions. Our investigation of computational methods focused oo
Dave's coue for an iterative solution and a Monte Carlo code adapted from ilirk
wuich oad cue adued virtue oi being a .vator model rather than an atnoi, j/acr ic
taoue1. Both of these codes were extensively moditied to suit our purposes:
the Dave code became it did not directly apply to aquatic media and the Kirk
code because it was comparatively <.nef f icient. It should be recognized that
despite the adaptability of the Monte Carlo code to the demands of aquatic
geometry. the spherical harmonics and matrix operator methods are more effi-
cient in terms of computation tine.
We have also utilized the solution to the Mie scattering • of light with
which we can deduce the inherent optical properties from particle size of
suspended sediments. This in turn can be used as inputs to either of the
above two models. An overview of our modeling to date is summarized in Figure
1.
MIE CODE
Hie scattering theory represents an analytic solution of the scattering
of light by small spherical particles. The solution due to Mie dates back to
the turn of the century and relies solely on Maxwell's discovery that light
may be represented in teras of corresponding electric and magnetic fields.
Given a spnencal particle of a given inuei ot refraction, one may calculate
the absorbing and scattering effects of that particle. Given a distribution
of such particles, one nay build up a model of the particular component* of
absorption and scattering, within
-------
t).c Rayleigh-scattoring optical depth oi tne atmosphere. This code was modi-
fied so that the bottom was made Frcsnul, which is appropriate for an aquatic
interlace. Ihe changes required v,ere not trivial siuce tne Uave coilo had par-
titioned photons into unreflected and reflected histories, and for reflected
photons used the Lambert tan assumption to remove the azimuthal dependence of
the reflected radiance. The objective in modifying this coue was to use it to
obtain accurate input radiance distributions to a water model which would then
be able to calculate the desired optical properties within the water column.
The separation of the atmosphere/ocean problem into first an atmosphere and
then a water problem requires the assumption that photons which backscatter
from water to air and back into the water represent a negligible 'contribution
to the flux received by the water. The functional layout of the Dave code was
presented in a previous report (Interim Progress Report, EPA Grant #806-372-
010), and thus it will not be repeated here. This converted version of the
Dave code for the atmosphere was running on the IBM 360.
MONTE CARLO JiODELING
Because the Dave code requires inputs which are not routine measurements
for most investigators, an alternative modeling approach was followed in
parallel with the modification of the Dave Code. This alternative apprcach
wai to pursue the development of a lioaie Carlo procedure whicii would use as
inputs the innerent optical properties wuicii had been measured previously oy
our group; ana whose outputs, or "predictions", could be checLed against a
corresponding set of apparent optical properties also available from earlier
studies.
j.lonte Carlo solutions for the atmosphere-ocean system were reported in
the literature in 1969 by Plass and ilattawar. The .Monte Carlo u.etlioU is fun-
damentally less accurate than the analytic methods but was among the first to
be adapted to an atmosphere-ocean system because of its flexibility. The
early calculations were restricted to sun positions directly overhead and
input phase functions were calculated from Rjyleigh and Hie scattering theory.
Over time, solutions have oeen carried out by several authors under a wide
variety of conditions (Plass and Kattawar, 1969; Gordon, 1975. 1977; Kirk,
1981). Indications of the power of such simulations have been demonstrated in
the form of papers which propose empirical relations between the inherent aau
apparent optical properties, as derived via uionte Carlo exploration (Ooraon et
al.. 1975; Kirk, 1981). Yet due to problems strictly associated with obtain-
ing sufficiently complete data sets, none of these authors have been able to
confirm the model within a comprehensive set of water types as found within
nature.
Briefly, a. Monte Carlo technique is a "random walk" procedure in which a
computer simulates and keeps track of the path of a large number of individual
photons as they scatter through, and are eventually absorbed by, the optical
medium. It is the set of inherent optical properties of the water, i.e., a.
b. and JJ, which define the probabilities of events, i.e., scattering and
absorption, within a given photon's "life history". Thus the input to the
Kuk code was exactly what we were looking for:- the inherent optical proper-
ties of the water.
-14-
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The meaning of the tern "large number of photons" is defined operation-
ally. As with any statistical sampling procedure involving the avenge of a
tatasured quantity over uany trials, tne variance ol Cue output decreases wita
the number of samples. Thus, tor example, perfectly smooth curves 01 li versus
depth aie expected if an infinite number of photons are run. If less photons
are run, less than perfectly smooth curves are obtained. In practice a large
number of photons are run and the resultant curves examined. If the curves
arc not considered smooth enough, more photons are 'uii. The number required
to achieve some arbitrary standard of "smoothness" is a function of the ratio
of absorption to scattering as well as of the optical property being
estimated. High absorption will generally require more photons to get the
some smoothness, au.d upwelling properties will almost always require many more
photons than their downwelling counterparts. Thus the number of photons
required to get good estimates of a given parameter may be anything from a tew
tens of thousands up to the hundreds of taousaads. Uue can understand that an
iterative solution of the equations of radiative transfer, such as used by
Dave, is inherently more accurate than the Monte Carlo type solution since it
is an exact solution.
A copy of Kirk's lionte Carlo procedure was gratefully obtained from Dr.
Kirk and modified. Th«. Kirk Monte Carlo code is ruu'.^ug on a Prime 550, 750.
The results were cneckcd against lira's, and were fotnd to agree.
PUGF
It was decided that the Monte Carlo technique -,vjs an appropriate method
to investigate further the attenuation of light underwater, liowever, it was
I'o mi u necessary to sake ^ajor Alterations to cue original uirk code in orucr
to improve cor.puta t lona 1 effic:ency. Further, the original Uirk eout a^^ro^i-
natet! the i..put radiaac-' U.L str loutiou as a uelta function, which is appropri-
ate for sun high in the sky out w'uicn is known to be a pool approximation for
low sun. After considerable improvements baa been made, we cooperated with
another researcher in the field (Poole. 1932) in oruer to proauce an effi-
cient, state-of-the-art vionte Carlo code. THIS code is a significant improve-
ment upon the original code and is detailed elsewhere (Fahy and Poole, in
prepartion). It is iiaceu POOF after its authors (Poole anu Fahy).
uses an important approximation ol the input rauiance uistriuution
by approximating it as a delta function plus a diffuse "skylight" component.
The method by which it incorporates data measured in the field to produce a
representative input distribution is discussed below, in the results section.
A severe problem with the Kirk model was the number of photons required
as input at the surface in order to obtain a usable number at depths below a
tew attenuation lengths. A photon was highly unlikely to survive long, enough
before absorption to reach significant depths. To address this problem pho-
tons were given statistical weights which are decremented at each interaction
with the medium. The decrement factor is simply b/c, which gives the proba-
bility of scattering (i.e., surviving) instead of absorbing in a given
interaction. Thus. a photon does not perish by being absorbed but rather,
lives on, albeit with a lower weight than before. Eventually the weight of
the photon becomes insignificant aad the photon is discarded and a new photon
is sent on its way.
-15-
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Other improvements fall under the category ot precalculating information
that i» needed repeatedly. l-or instuucc at cvcrv collision the collection
"sins" in wcicb a photon oclongs uust be v.,)Ua.tevi. \iLcrc tut: puoton ociun,,^
typically involves taking an arcsin or arc<.o*. wtiich is a lengthy computat 101. .
But since we know in advance which bins correspond to which cosines, it is
possible to pre-ct Iculate a mapping from thi direction cosines of the photon
(which describe its direction) to the bin in which it belongs. This saves
considerable time. Another example is the not hod by wkica a scattering anglo
is determined. It involves sampling froct a unilorm ranuom variable and then
doing a table look-up to get a corresponding angle. Hut the table loot-up
procedure aay be represented as a mapping which cau also be precalculated. A
table look~up can thus be reduced to sampling withiu a linear array, the ele-
ments of which correspond to values of the uniform random variable.
The most significant improvement of 1\X)F over previous efforts is it*
partitioning of the problem mto two separate "passes "; the first of wLich
aepends only on the volume scattering function, and the secon. which uses the
output of the first, and the remaining input (a.b) to obtain the final solu-
tion. The product of the first phase is a series of count arrays, which in a
very real sense contain the same sort of iiuornatiou as is calculated by the
so-called Natural Solution of radiative transfer, also known as the Successive
Uroers of bcattenns Solution. Thus, 1HX)1" nay accura to !;• be cclloii a cci.'ji.'a-
tico at ..omo Carlo
-------
lience, we will show here a comparison of the Mcnto Carlo lesults with both
clear water field measurements and ban Vicente tield iacas irctacuts wnich arc a
core turoiu *ater type. fhc rcseivoir is representative ot core productive
waters !icv mg a chloropayll concentration of approximately 7 nj, v,nl/n3 and an
attenuation length of 1/3 meter.
The consistency of tk? model's predictions with values of K measured in
clear waters is demonstrated by Figure 15. Plotted versus wavelength are
several inherent and apparent optical properties ot the water. Also plotted
arc the model's predictions of the value of K at one optical depth for zenith
angles 10 and 60 degrees (labeled '!' and '6', respectively), along with the
measured values of K from the cruise data. Note that the values over the
water column, because technical difficulties maae it impossible to measure an
instantaneous value of K at any given depth. 1'urther, the k's obtained trotu
the data represent averages over suti angle, since measurements were taken
slowly compared to the movement ot' the sun. With these limitations ot the
cruise data in mind, one sees that the model compares extremely well with the
field data, wuich in every case fall between the 10 degree and 60 degree pred-
ictions. This is to be expected since measurements were only taken for a
range of sun angles within these lioits.
T'.ie consistency of the model's predicitons for a tore turbiu vatcr is
sho»u 1.1 Figure 16. In this li^uru tuo uasheu liuoi give cue pruumuu
(uuucl) vaiuos 01 average attenuation uott i ic lent o\«.r tue tir»t seven tauter*
obtained by fitting a straight line to the log of the irradiance predictions
given by the siouel. The solid linos give the values obtained in a similar
manner frou the data. Note the wide variance in value* of & over wavelength,
and the ability of the model to truck this variance. even the turn-aiouna
wjvo Icnjih ol uini.ua 1 'L, 550 nm.
-17-
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SJCCTiON 6
RLSULIS
The results of this work can be broken into several related sections.
fust a con;ideration of atirnsphcnc influences of light was made. '1 ho input
irradiance alfects the underwater ligl>t fieJd and thus affects both tho field
data and the modeling of such data. Next, the field data needed was taken
and/or analyzed. including specifically an investigation of clear witer
scattering, of clay and UOM attenuation from a series of tank experiments, and
of the suite ot data with complete sets ot inherent optical properties avail-
able. Finally, the results of the Monte Carlo Model, which involves knowledge
both of the atmosphere and of the field data, are given.
AIMOSPUERE
In developing models of aquatic environments, one must first consider the
input radiance distribution. We have considered two quite dill irent
approaches; an an I ay tit. approach and an experimental approach. The analytic
method is that of Dave, an iterative solution to radiative transfer aquations
discussed earlier. This code has the advantage that it allows definition of
the atmosphere oased on its coustituleuts.
The second technique involves definition of the input radiance distr-bu-
tion as a delta function plus a uniform diffuse component. This however is a
crude approximation of the sky component. In fact, the Dave code will serve
as a useful check of the validity of this distribution assunption since the
Dave code gives an "exact soJition". However, the field tia'a ?vnilaole
describes a sky and a direct beam, he ace the cn.puasis on the e*pcr i»ik..tal
approach.
The total atmospheric radiation at the water surface nay be approximated
as a direct solor beam plus a diffuse sky component.
Etot(0, A.) = Edirect •*• Esky (23)
It is possible to measure Esky ana Ltot in the field. It is the ratio of
these quantities
y " Esky/Etot
that the model uses to approximate an input xadiance distribution. It is pos-
sible to pick an arbitrary Esky and then to calculate
Edxrect = (1-y) • Etot = (1-y) • (Esky/y) (24)
.We then integrate Esky using a uniform radiance and add this to Edirect and
propagate through the surface using Frosnel transmittance.
-18-
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Field measurements of y in both an oceanic atmosphere as »ell as in a
desert-like atmosphere nave been made. These measurements were available onl>
tor «ravti Ici.gths above 400 nci. Using another uoue) loreer. e_t u 1., 197b; uater
o t a 1.. 1981), this aata can be extended to the 2i>0 nu region. Using both of
these sets of data as surface irradiance input to the Monte Carlo model, the
influence of two very different atmospheres could be detected.
FIELD DATA - clear water
The measurements in the clearest natural wacers of the inherent and the
apparent optical properties are limited. As a result, we combine data from
the laboratory with uata fron the field. Our objective is to obtain a data
set representative of the clearest waters one might expect to find naturally
in the environment.
Tbe most recent and most reliable data of the total absorption coeffi-
cient of pure water, aw(wl) in the 200-800 nm spectral region are summarized
in Table 1 (from Smith and Baker. 1981). There is no such information regard-
.1 g the scattering of clear water. The total volume scattering function can
be descried as composed of two components, one due to molecular scattering of
pure sea wter, pia, and one aue to all other cocpcr.er.ts -vaicn we will refer to
as "particles", pp.
p(e. x) = pm(y. x) + pp(e, /.) * (25)
where Morel has shown
>
(,3(9.30 = b=(X)/16.06 * (1 + .S4cos2(H)) (26}
The molecular scattering of clear water, bm (X) is given elsewhere (Smith and
Baker. 1981).
A comparison of all currently available clear water scattering measure-
uenti uas snown tuat the SCCii Discoverer Station 21 uata (1973) is the most
accurate and representative r-casurcucct of p(/J for the clear waters. This
station was in the Sargasso Sea wnicu is rccognizec to be among tne clearest
of ocean waters. Since the scattering data in this set exists only for the
wavelength 515 nm, it is necessary to find an extrapolation technique to
obtain p(0) at other wavelengths. Tbe volume scattering function at the
wavelengths 440, 490. 520, and 670 no, exists for the Uceanus Station 4 data,
as is shown in Figure 17, where the molecular scattering has been removed. A
very simple method which is consistent with a "diluted water" treatment,
assuming that the data sets dealt nth are essentially the same water type,
has been adopted. Suppose we have two water samples, the second of which is a
simple dilution of the first. Thus the first sample has an instantaneous par-
ticle size distribution of N.(D), and the second has a distribution N_(D),
where D refers to particle diameter. Then
N2(D) = K21 • N1(D) (27)
-19-
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where i^.. is a constant which does not depend on L>. Let p(A,D, 0) be the
scattering Jue to a particle oi diameter L). m direction 0, at waveleijth >..
Tu en
d(J jU.y) = d(X.U,9)*N1(D) dU (28)
and it can be shown
p-U,W) = K • (JU.e) (29)
Since this result is wavelength independent, we can use it to extrapolate the
water dependence of water sample 2 to water sample 1 by
where
:-ue) = j, 2Uo.e)/(, jUo.e) (3D
Giver. Cue similarity ot \«ater samples taKeu on the so two cruises, we tell tue
diluted solution approximation to oe a reasonable approximation. The validity
of tins technique was checked using several other complete uata sets. iJencc
the extrapolation from one data set to tue next could be checked since the
second set of measurements had been made. When such comparisons were made
betueeu sirailar water types, tue uctnod prouucod vcr> accurate reproduction:,.
Given Equation 30, we can no-* caKulatt, tlio voluuc ;>wa ttLriiig Tuiiotiou for
other wavelengths for clear water as is shown in Figure 18.
FICL1J DATA - tank
Figure 19 shows what the Baker-Smith component model gives for a range of
C, U, and f values. The experiuent.il component analysis has tuus yielueu not
only a cescription of a set of water types, out the ability to generate a
range of tauter types oaseo upon a 'cuoice ol culropiiy 11> iXA>i, anu clay.
FIELD DATA - other
All of the field measurements of scattering must be integrated over all
angles to yield a total volume scattering function. This was done using a
program designed to take into account the geometry ot the scattering instru-
ment used (Petzold, 1972). This program was converted to the RilME 750. 550,
from an IBM 360.
POOF fcODEL
The limitation of cruise data is that the values of K usually represent
averages over depth and sun angle due to changing light and water conditions.
-20-
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The model is not confined by such problems and thus it becomes possible to
look in detail at the variation of tue apparent optical properties with sun
angle and with depth.
Figures 20 and 21 demonstrate a need to include a sky component in model-
ing calculations. The graphs ot i.d, the downwelling diffuse attenuation coef-
ficient, show a much greater variance with solar z;nith angle for a model
using input of a direct beam only. .Jan is evidenced in the POOF calculation.
Direct comparisons for solar zoutih ^nrlcs of 5 to 35 degrees show little
difference bjtvcec the t>o models while the models differ significantly for
solar zenith aiiglei. of 75 to 85 degrees. Of particular interest is the rever-
sal of order of tht» vertical positioning of the 70 and 80 degree curves in
Figure 16. For tae direct beam model, the 80 degree curve lies above the 70
degree curve. whilo for POOF the 80 degree curve is less extreme than the 70
degree curve. This is oeiause in POOF, the model takes into account that
alnost all the input into the uater for the 80 degree curve is diiiuse
skylight/ the Fresnel transiaittance through the water at 80 degrees zenith
angle being extremely low. 'Ihe gsneral pattern of light entering the water
therefore, closely resembles tho diffuse skylight, which represents something
of an average of the direct bo am results for solar zenith angles from 0 to 90
degrees.
that the values for £ in these figures lor SO degrees are less
extreme than are the values tor the 60 degree curve. It can ue snowu that it
increases with theta until a thota-max at which poiut it decreases since an
averaging effect swamps out the direct beam. That is. there are few of the
photons entering the water that are actually due to the direct solar bean. as
is understandable witrin the context of Freshnel's law; the dominant source of
iiynt is diffuse styiigi.t wun.li represents an aveargt: of Direct solar beuoj
t'ron 0 to 90 degrees. This effect lias not previously been rc^urccu since uuch
of our previous understanding comes trom field data which is limited by the
instrument technology which takes finite time to make measurements. During
this time interval, the lighting conditions can change rapidly. It is diffi-
cult to measure values of k over largo depths and for instantaneous solar
positions when the sun is low in the sky. Such an effect is important to take
into consideration when one is calculating the total availability of energy
ever one day.
The change in K as a function ol depth is illustrated in Figures 22 and
23. Such calculations provide previously unavailable insifht into depth
dependence of K. For instance, Figure 23 shows three different wavelengths at
several solar zenith angles. It should be noted that the spread between the
10 degree and the 60 degree curves decreases with depth, demonstrating that K
approaches an asymptotic value at great depths which is wholly independent of
the input radiance distribution.
The dependence of K on solar zenith angle is seen to be small here.
agreeing with previuus observations (Daker and Smith, 1979) that X is quasi-
inherent for this type water. Uaker and Smith fit a straight line through the
log of the downwelling irradiance measurements to obtain Kd and as such the
single value of Kd m&v be seen to be an average of Kd over the top 7-10 motors
of -the water column. Clos* scrutiny of the curves reveals that the asymptotic
value of lid, known as £00, is reached extremely rapidly. as early as 4-5
meters depth. Thus, the average computed by Baker and Smith to represent Kd
-21-
-------
is swamped out by Ldo, which is ot course independent ot solar zenith anlge.
This explains the "quasi-inherent" nature of .-id as reported previously.
It is now important to note that for 80 degrees, the asyuptotic value is
reached almost immediately. This suggests that scientists taking ucasureme-.s
in tne fielu would do well to take data for low sun positions, in order to
measure directly this nighly important parameter.
The sensitivity of the model to Y is very small wnen a dry desert atno-
sphere was used compared with a coastal ocean atmosphere. It is only at low
sun angles approaching 80 degrees that the atmospheric component ratio is
found to have aoro than a 3 per cent influence on the resultant apparent opti-
cal properties. It is also found that !£ is relatively insensitive to
wavelength variation in p. especially at the surface where the effect is less
than 1 percent.
-22-
-------
TABLE 1. TANK STUDY WAfFIl IM'CS
tt
I/
2/
3/
4x
5/
6x
7/
Sx
9x
ID/
1 I/
12'
lix
I4x
15'
16/
fi le
1
4
5
6
. 8
10
11
12
13
14
1*
17
13
19
20
21
gm
0
25
50
75
125
175
225
275
0
75
75
75
75
75
75
75
CLAY
ppm
0
. , 2. 16
4.31
6.47
10.78
15.09
19.40
23.71
0
&. 47
(-.4?
c.47
o.47
6.47
•5.47
ۥ. 47
gru
0
0
e
o
0
0
0
0
0
e
^
5
10
15
10
40
DOM
frig/ 1
0
3
e
0
0
0
0
0
0
f)
0.17
0.4:
0. ?6
1.2?
1.71
3.45
aate
- ?o;t32
3octS2
9oct32
13oc to2
1 4 o c t : 1
Reproduced from
best available copy
-23-
-------
I
Figure 1. Relationships between experimental field data
and computer models.
-24-
-------
CLRY
#l-#8
10
E
\
o
•p
y.
350 450 550 650 750
hflVELEN'GTM Cnm3
Tiguru 2. The spectral light attenuation in each of the
Clay Cro'ip water types //l-#8 listed in Table 1.
CLRY+DOM
-tie
trS
10F
350 450 550 650 750
WnVELENGTH CnrrD
Hyurc 3. The spectral light attenuation in each of the
OOM Group water types //9-//16 li:,ted in Table 1.
-25-
-------
CLRY
o
10
9
B
7
250 350 450 550 650 750
WRVELENGTH Lnm3
Figure 4. The spectral Relay component for each of the
Clay Group water types IU-tl8 listed In Table 1.
CLRY
#2-t8
10
9
8
i-i
£ S
X5
2
I
0,
0 5 10 15 20
CLflY CppmD
25
Figure 3. The Relay component for the wavelength range
from 275 ran to 745 rim.
-26-
-------
CLflY
WRVELENGTH-550
E
\
X
* 4
u
0
'0
5 10
CLRY
15
20
Figure 6. The Relay component for the wavelength 550 nm
for a range of clay (ppm) where the x's are experimental
data and the line is a pol>nonial fit.
CLRY
a
"o 2
0 5 10 15 20
CLflY CppmJ
25
Figure 7. The Relay component for five wavelengths where
5=300 nm, 11=450 nm, 13=550 nm, and 15=650 nm where these
points represent data and the solid line is the model fit.
-27-
-------
DOM
#1 1-#16
250 350 450 550
650 750
HflVELENGTH Cnm]
Figure 8. The spectral Kdom component (with scattering
material still present; see text) Cor a DOM Group water
types //11-//16 listed in Table 1.
10
9
8
•i 7
^ 6
L-l
5
£
O 4
* 3
2
1
DOM
#11-#16
250 350 450 550 650 750
WRVELENGTH Lnm]
Figure 9. The spectral Kdom component for the DOM Group
water types //11-//16 lisccd In lable 1.
-28-
-------
BOM
10
9
8
£ 7
^ 6
i_i
5
£
O 4
T3
* 3
2
I
0
X 375 NM
0 450 NM
012345
DOM Cmg/ll
Figure 10. The Kdom component for two wavelengths where
the points arc data and the solid line Is a fit.
DOM
#11-#16
\
250 350 450 550 650 750
WRVELENGTH Cnm!)
Figure 1J. The spectral (Kdom+Kclay) component where the
x's are d.ita and the line is the model fit.
-29-
-------
E
\
o
+J
*
CLflY
#2-#8
350 450 550 650 750
WRVELENGTH
Figure 12. The spectral Ktot data points and analytic nodcl
fit as solid linos for the Clay Croup.
CLRY+DOM
#11-#16
10
350 450 55' 650 750
WRVELENGTK CnmJ
Figure 13. Die sptctuU KLot dat.i points and analytic model
fit as solid lines for llie DOM Croup.
-------
1E+02
1E+01 t
san Vicente
1E+00 -
1E-01 r
I EH
•theoretical mo'^cu'ar
300 400 503 600 700 800
WRVELENGTH
Figure 14. 'Ihe total seal tor UIR b for a variety of water
f'pes from molecular scattering to clear watoi to ocean
to river.
-3L-
-------
1E+0B
1E-01
SCOR/DISCOVERER
b/c
1E-0H
400
500 600
WHVELENGTH Cnm]
700
I'lgurc 15. The spectral a (solid line), b (dashed line) c
(dash dashed line), and b/c (notched line for SCOK Discovers
suition 21 Sargasso Sea waters. The }) points are the field data
measurements of. total diffuse attenuation coefficient whereas
the 1,6 are the Monte Carlo calculations of K for 10 degrees
and 60 degrees sun angles.
-32-
-------
1E+01
SRN VICENTE
500 600 _
NRVELENGTH Unroll
700
Figure 16. Ihe a (solid line), b (dashed line), c (dash dashed line)
and b/c (notched line for San Vicente waters. The circled 1,6
points are the field measurements of total diffuse attenuation
coefficients for sun angles 10 degrees and 60 degrees whereas
the 1,6 points are the Monte Carlo predictions.
•-33-
-------
• 1E+00
0 20 40 62 80 183 123 140 160 160
RNGLE [decrees3
N^
Tigure 17. The particle volume scattering function for fairly
clear ocean water (Occanus cruise station 4) for wavelengths
440 nm, 490 urn, 520 nra, 610 nm, and 670 nm.
-34-
-------
SCOR/DISCOVEPER
0 20 40 60 80 100 120 M0 160 180
RNGLE [degrees]
Figure 18. The calculated total volume scattering function
for very clear ocean water (SCOR Discoverer station 21) for
wavelengths 440 nm, 490 nm, 520 nm, 610 nm, and 670 nm.
-35-
-------
BSIII MODEL
353 453 550 653 753
HL
Figure 19. The Uakor- Smith III component model orcdiction of
spectral Ktot (A) for a range of Chlorophyll, dissolved organic
material and clay. The following explains the composition.
1 line
1
1
1 chl
1 DOM
I clay
1
I
1
1 0
1 0
1 0
solid
.5
0
0
1
1
1
5. 1
0 I
0 1
dashed
0
.5
0
0
5.
0
dashed
0
0
5
dot
0
0
25
hatched
.5
.5
5
5 1
5 1
25
-36-
-------
SRN VICENTE DIRECT
N
U
0
8
10
12
14
16
18
10 30"
UO- TO"
.4
.6
.8
K
Figure 20. The Monte Carlo calculation of K (A,z,0) for
wavelength 530 nm for sun angJcs 10, 30, 60, 70, 80 decrees
plotted versus optical depths cz wlicn using only a diiecl l>uam
input to the water column.
-37-
-------
SRN VICENTE
N
U
0
8
10
12
14
16
IB
10" 30*
.4
.5
.7
.8
K
Figure 21. The Monti! (,arlo calculation of K(A,z,0) for wavelength
550 nm for sum nnj'.los 1.0,30, 60, 70, 80 degrees plotted versus
optical depths a. wlu'n using botli a direct and a diffuse Jnput
to the water colu.in.
-38-
-------
N
U
0
16
18
0
DISCO
.02
04
.06
.08
.1
K
Figure 22. The Monce Carlo calculation of K(A,z,0) Cor clear
waters of SCOR Discoverer for sun angle 10 degrees (solid line)
and 40 demises (broken line) for wavelengths 440 nm, 490 nm,
515 nm, and 550 nm. The straight line superimposed is the
field measured value which is average for the day.
-39-
-------
SfiN VICENTE
N
U
0
14
16
18
0
.4
,8
1.2
K
1.6
2.4
Figure 23. The Monte Carlo calcualtiuu of K (X,z,0) for San
Vicente waters for sun angles 10, 30, 60, 70, 80 degrees for
wavelengths 440 nm, 550 nm, and 670 ran. Tbe straig'it lines
superimposed are the field measured values for 1U and 60
degree sun angles.
-40-
-------
KEFLRlINCLS
uakor, K.2>. and ii.C. buitn (1979). U uasi-iunon-t-t: ci^arac ttr i it ics ot :..«. ,_.:'-
lu,sc attenuation coefficient for irrauiancc. bl'iu, Vol. 2l)fc, Ocean
Optics VI.
Ba^er, ii.J>., i£.C. Smith, and /i.c.S. Green (ii)oO). ilmdle ultraviolet radia-
tion Beaching the ocean surface. Phot delicti. Photobiol., 32 .367-37«».
Uajter. K.S. and tt.C. Smith (1982): Uio-optical classification and uodel ot
natural waters II. Lionel. Ueeanogr. 27(3) 500-509.
Bice, K..L. and S.C. Clement (1981): Mineralogical, optical, geocheroical anu
particle size properties oi four sediment samples for optical pny»ies
research. NASA Contract Report 165663.
Chapman, R.S. (1977): Particle size and x-ray analysis ->f feldspar, calvert,
ball and jordan soils. NASA tech. memorandum, NASA TM x-73941.
Dave, J.V. (1968): Subroutines for computing the parameters of tue elec-
tromagnetic radiation scattered by a sphere. JLU.'l Report 320-3237, ISM,
Federal Systems Division, 18100 Frederick Pise. Oai thur sour 5, .II) 2076',',
Dave, J.V. (1972) Developueat oi prograns for computing th^racteribtics 01
ultraviolet radiation. 13M Tech. Report. ItiM. Federal .Systems Division,
1S1UO I'retierici: PiJce, Gaithersburg, liD 20760.
Green, A.E.S., T. Sawada and C.P. Shettle (1974). The middle ultraviolet
reaching the ground. PUotoche^. PLotobiol., 19 251-259.
Ooraon, U.U. 11975): Uiftuse relectance of the octan: sorae effects of verti-
cal structure. Appl. Opt., 14.2892-2895.
Gordon, U.R.. O.U. Brown, and il.il. Jacobs (1975): Computed relationship*
between the inuerent and apparent optical properties of a flat homogene-
ous ocean. Appl. Opt., 14:417-427.
Gordon, li.H. (1977). Albedo of the ocean atmosphere system, influence of sea
foaii. upul. Opt., 16:2257-2260.
International Association of ileteorology and Atmospheric Physic* (A1LAP) radia-
tion commission. Standard procedures to compute atmospheric radiative
transfer in a scattering atmosphere. (1977), NCAli. Boulder. CO 80307.
Kirk, J.T.O. (1981): A Monte Carlo procedure for simulating the penetration
of light into natural waters. Division of Plant Industry Technical 1'aper
No. 36, Commonwealth Scientific and Industrial Research Organization,
Australia.
Kirk. J.T.O. (1981): A ilonte Carlo study of the nature of the underwater
light field in, and the relationships between, optical properties of tur-
bid yellow waters. Australian Journ. Mar. Freshwater lies., 32:517-532,
Mie. G. (1908): Annil. Physik.. 25:377.
-Al-
-------
Miller, (».C. and K.G. iepp (1978): Effects of suspended sediments on photo-
lysis rates of dissolved pollutants. Water ives. 13 453-459.
Pctzold. T.J. (1572): Volume scattering functions for selected ocean waters.
University of California at San Diego, Scripps Institution of Oceanogra-
phy, Ref. 77-78.
Plass, G. and G. uattawar (1969). Radiative transfer in an atmosphere-ocean
system. Appl. Opt., 8:455—»66.
Plass. G. and G. Kattawar (1972): Monte Carlo calculations of radiative
transfer in the earth's atnospiicre ocean system: I tlux in the atno-
sphere and ocean. Jour. Phy*. Oceanogr., 2:139-145.
SOUR Data Report of the Discoverer Expedition »lay 1970 (1973). J.H. Tyler
(ed.). University of California at San Diego, SlORef. 73-16 (1000
prges).
Poole, L.R., W. Esaias, J. Campbell (in press). A semi-analytic wonte Carlo
radiative transfer aoael for oceanographic lidar systems.
Preisendorfer, R.W., 1976: uydrologic Optics, vol. I-VI, U.S. Dept. of Co~-
uercc, NOAA.
Smith, R.C. and K.S. Baiter (1978a). The bio-optical state of ocean waters and
remote sensing. Litanol. Oceanogr., 23(2):247-259.
Smith. R.C. and K.S. Daker (197Sb). Optical classification of natural waters.
Liunol. Oceanogr., 23(2) .260-267.
bairn. it.C., R.L, Ensminger. 11.W. Austin, J.D. ilailey, G.D. Edwards, (1979):
Ultraviolet submersible spectroradioueter. Proceedings of the Society of
Photo-optical instrumentation engineers (SP1D). Ocean Optics VI, Vol.
208.127-140.
Smith. R.C. and K.S. Baker (1981): Optical properties of the clearest natural
waters (200-oOOnu). Applied Optics, 20.177-1S4.
Wiscuuioc, n.J. (1979). ^iic scattering calculations, auvauced tecuiiKjues and
vector-space computer codes. NCAR Tech. note NCAR/Tf<-140+STR.
Zepp, R.C. and P.F. Schlotzhauer (1981): Comparison of photochemical behavior
of various hum.ic substances in water: III. Spectroscopic properties of
humic substances in Chemosphere, vol. 10, 5:479-486. Pergamon Press.
-42-
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