SuspendedSolidAndCDOM

8/7/2019 SuspendedSolidAndCDOM

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Effect of suspended particulate

and dissolved organic matter on

remote sensing of coastal and riverine waters

Michael Sydor and Robert A. Arnone

We use remote sensing reflectance RSR together with the inherent optical properties of suspendedparticulates to determine the backscattering ratio bbb for coastal waters. We examine the wavelengthdependence ofbb and fQ and establish the conditions when C in RSR Cbba canbe treated as a constant. We found that for case 2 waters, RSR was insensitive to the natural fluctu-ations in particle-size distributions. The cross-sectional area of the suspended particulate per unitvolume, xg, showed an excellent correlation with the volume scattering coefficient. 1997 OpticalSociety of America

Key words: Particle-size distributions, remote sensing reflectance of coastal waters, backscatteringcoefficient, upwelling irradiance-to-radiance ratio.

1. Introduction

In remote sensing of turbid waters, it is commonpractice to assume that the remote sensing reflec-tance RSR is given by RSR Cbba,where bb is the volume backscattering coefficientat wavelength , a is the volume absorption coef-ficient, and C is a proportionality function that isoften presumed constant. The difficulty with thisexpression is the fact that bb generally is unknownand difficult to measure, and the product of the pre-sumed constant C and bba cannot be testedagainst RSR separately. We examine the behav-ior of RSR and C in terms of easily measuredparameters such as b, a, particle-size distribu-tion, and the diffuse attenuation coefficient Kd.

For any given , C is defined by the ratio C fTQ, where f relates diffuse reflectance R to bband a, Q is the upwelling irradiance-to-radianceratio, and T is the reflectionrefraction factor.1,2

C is constant under stringent observational con-ditions,1,2 but may actually vary with water turbid-

ity.2 Although several numerical simulations ofRSR and C have been made, the simulations gen-erally apply to clear waters. There is little in theway of theory or experimental data that shows howRSR and C behave for turbid waters, say as a func-tion of dissolved organic matter DOM, particleconcentrations, and particle-size distributions.The question of dependence of RSR on particle-sizedistribution for case 2 waters is important. Intheir simulation of light scattering from ocean wa-ters Ulloa et al.3 pointed out that the shape ofparticle-size distributions could have a profound in-fluence on RSR. On the other hand, for turbid case3 waters, Stumpf and Pennock4 suggest that Rshould depend only on the total cross-sectional areaof particulate per unit volume, xg, and on K, thediffuse attenuation coefficient. Neither hypothe-sis has been verified experimentally.

We investigate the implications of particle-size dis-tributions on RSR for St. Louis Bay, Miss., and the

Mississippi Sound at Gulfport, Miss. The studyarea is typical of coastal and estuarine environment,varying from highly absorbing DOM waters to clearercoastal waters, with suspended solids ranging from 1to 10 gm3. In such waters light scattering is gen-erally dominated by suspended particulates, largelysilt and clay, whereas absorption is dominated byDOM. We examine how C changes with DOMand determine the conditions under which it may betreated as a constant.

M. Sydor is with the Department of Physics, University of Min-nesota Duluth, Duluth, Minnesota 55812. R. A. Arnone is withthe Naval Research Laboratory, Stennis Space Center, Mississippi39529.

Received 27 November 1996; revised manuscript received 27May 1997.

0003-693597276905-08$10.000 1997 Optical Society of America

20 September 1997 Vol. 36, No. 27 APPLIED OPTICS 6905


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2. Symbols

Photon wavelength nanometers, dependenceand value specified when needed;

a, a volume absorption coefficient inverse meters;c, c beam attenuation coefficient inverse meters;b, b c a volume scattering coefficient in-

verse meters;bb, bb volume backscattering coefficient inverse

meters;RSR vertically emerging radianceabove-surface

downwelling irradiance inverse steradians;C, C proportionality function relating RSR to bba

inverse steradians;R, R diffuse reflectance;f, f proportionality function relating R to bba;Q, Q irradianceradiance ratio steradians;T 0.54 nominal transmission factor including all re-

flection and refraction effects at the waterairinterface;

Kd, Kd diffuse downwelling attenuation coefficient in-verse meters;

Ku, Ku diffuse upwelling attenuation coefficient in-verse meters;

Bb

, Bb

irradiant backscatter coefficient relating R to1Kd Ku inverse meters;

photon scattering angle measured from the di-rection of propagation of the incident photon;

azimuthal scattering angle about the directionof propagation of the incident photon;

r radius of a polystyrene sphere meters;r, differential scattering cross section for photons

by a polystyrene sphere of radius r squaremeters per steradians;

p, differential scattering cross section for photonsby an unknown particle square meters persteradian;

nri number of particlesunit volume with effective

radius ri inverse cubic meters;xg cross-sectional area of particulate treated asspheres per unit volume inverse meters;

Ck proportionality constant relating RSR to bKdinverse steradians;

Cb light-field distribution factor steradians;Lw water-leaving radiance.

3. Theoretical Background

We outline some of the results needed to analyze ourdata. The theory of ocean color has been treatedextensively by several authors.510 In general, R atany wavelength can be expressed as a polynomial inbbbb a or as

R f bba. (1)

Usually a bb, and f is a proportionality functionthat has a value of 0.33.2,6,7 Similarly, RSR isapproximated by1

RSRCbba

or

RSR 0.051bba, (2)

where C is a function of the zenith solar angle, theobservation angle, atmospheric turbidity, and surfaceroughness.1,2 A detailed discussion of all the termscontributing to C and the variability of C withthe observational geometry and atmospheric condi-tions is presented by Morel and Gentili.2 The au-thors applied their calculations to clear ocean waters,but their results indicate that C changes with wa-ter turbidity as well as with the observational condi-tions. In arriving at the nominal value of C in

relation 2, we take T 0.54 and fQ 0.094, thenC fTQ 0.051.

An alternative formulation of R is given by Phill-pot,5 in which the angular distribution of the down-welling and upwelling radiance is incorporated intothe downwelling and upwelling diffuse attenuationcoefficients Kd and Ku. When the irradiant back-scatter coefficient Bb Kd, Phillpots relation-ship for R reduces to

R BbKdKu. (3)

Using Phillpots result, Stumpf and Pennock4 showedthat R for turbid waters is independent of particle-

size distribution. For turbid waters, Kd Ku,and relation 3 reduces to

R Bb2Kd. (4)

We use relations 1, 2, and 4 together with ourexperimental results to estimate the magnitude ofbbb at 660 nm. Subsequently, we determine bband fQ over the entire 400750-nm range.

4. Experimental Details

A preliminary set of measurements was made on 24June 1995 at four stations in the Gulf of Mexico.The stations were located roughly 3, 6, 15, and 25 kmfrom the shoreline along the commercial shipping

channel to Gulfport, Miss. Partly cloudy conditionsat the start of the preliminary cruise quickly changedto overcast; thus the RSR data were marginal. How-ever, the preliminary cruise measurements of aand b were crucial in corroborating the overallrelationship between b and xg.

For the actual test, a set of six stations roughly 2km apart was chosen along a transect running thelength of St. Louis Bay, Miss. Station 1 was locatednear the mouth of St. Louis Bay in the Gulf of Mexico;Station 6 was chosen well up the estuary in the Jour-dan River. The stations were located over deepchannels well away from vegetation. The experi-mental cruise occurred from 10 a.m. to 2 p.m. on 26

July 1995, under calm conditions with less than 10%cloud cover.

At a later date, two similar sets of measurementswere obtained to confirm the results presentedhere.11 The general character of water in St. LouisBay is typical of coastal waters. For St. Louis Bay,a was dominated by the absorption that is due todissolved organic material. The combined absorp-tion by chlorophyll and suspended particulates wasless than 0.1 m1 at 660 nm. The absorption by

6906 APPLIED OPTICS Vol. 36, No. 27 20 September 1997


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DOM was a factor of 510 higher than the combinedabsorption by particulates and chlorophyll.11 Theshapes of the absorption spectra for the sediment andchlorophyll were comparable with those reported byTassan.12

5. Method

We used a portable spectrometer Analytical Spectral

Devices with calibrated white and gray diffuse re-flectors Spectralon to determine RSR and Kover the entire 380 800-nm spectral range. Mea-surements of RSR followed the techniques em-ployed by Arnone et al.13 We used polarizedforeoptics with 18 acceptance angle to minimizeglint. Polarized foreoptics are essential for properelimination of surface reflectance from dark riverinewaters. To determine Kd we measured the lightreflected from a submersible diffuse white reflector.The reflector was mounted horizontally and wasviewed by a fiber optics probe that had a 22 field ofview. The probe was mounted 3 cm above the whitereflector. Measurements of K

d were taken at

points 10 cm above and 10 cm below the water surfaceand at 0.5-m depth intervals thereafter. Measure-ment of the upwelling light was made in the samemanner using the same probe but with the whitereflector taken off.

We used two AC9 meters WETLabs to make insitu measurement of a and c. The water in-takes for the AC9 meters were located at a depth of1 m. The values ofa and c were determinedat 412, 456, 488, 520, 560, 650, 660, 676, and 715 nm.Grab samples for chlorophyll and for particle-sizeanalysis were taken at 0.5-m depth. We madestandard spectrometric absorption measurements on

0.5-m glass microfiber filter pads to determine therelative concentration of the yellow substance, theabsorption by chlorophyll, and the absorption by par-ticulates. Light transmission measurements werealso performed on 0.2- and 0.5-m filtrates to deter-mine the relative absorption by DOM at each station.Half-liter samples for particle-size measurementswere cured with 0.5 ml of methyl alcohol, refriger-ated, and analyzed the next day using a laser particlecounter Spectrex calibrated against known solu-tions of polystyrene spheres. The determination ofparticle sizes was based on 520 forward scatteringfrom individual particles. Pulse heights from indi-

vidual particles of the sample were compared withequivalent scattering from known sizes of polysty-rene spheres. The relative suspended solid concen-tration at each station was determined from particle-size distribution referenced to two samples whosesuspended solids were determined by filtering andweighing. We made duplicate measurements ofRSR and particle-size distributions at two stationsto check for repeatability and for temporal variations.Both sets of measurements showed good agreement.

6. Particle-size Distribution and Determination of xg

In optical measurement of particle-size distributionwe equated the scattering from natural particulateswith the scattering by polystyrene spheres. We took

5

20

0

2

p, , sin dd

2 5

20

r, sin d,

where r, is the differential scattering cross sec-tion for a spherical particle of radius r at angle

measured relative to the direction of propagation ofthe incident photon. p is the differential scatteringcross section for a particle in the sample. We com-pute xg for the sample according to

xgi1

30

nri ri2,

where nri is the number of particles per unit volumewith an effective radius ri. The sum signifies thatwe subdivided particle sizes into 30 intervals.

Figure 1 shows a typical distribution of particlesizes for St. Louis Bay. The distribution is slightly

bimodal with a distinct inflection at 2.5 m. Thedistribution of particle sizes in the study area wasgenerally exponential, as shown in Fig. 2. The vari-ations in particle-size distribution from station to sta-tion appeared mainly in the sizes above 10 m. Thetotal scattering coefficient b fell off as 1 anddisplayed a similar dependence with at all stations,as shown in Fig. 3. The mean particle diameter Dranged around 2 m. The distribution of xg withparticle size is shown in Fig. 4. Determination ofxg

Fig. 1. Particle-size distribution in St. Louis Bay has a slightlybimodal shape with an inflection at 2.5 m. The mean particlediameter ranged from 1.8 to 2.1 m. The dotted curves representthe resolution of particle sizes into two component distributions.



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was truncated at 1 m. However, the logarithmic

distribution shown in Fig. 2 indicates that the con-tribution to xg that is due to the submicrometer par-ticles was negligible. This is confirmed by the closerelationship between b and xg as exemplified at650 nm in Fig. 5. Whereas xg is truncated and de-rived from 5 to 20 forward scattering, b mea-sured with AC9 meters includes the total scatteringfrom all particle sizes.

7. Determination of bbb at 660 nm and theEffect on RSR that is due to Particle-size Distributions

We can utilize measurements of a to test the de-pendence of RSR on particle-size distribution. To doso, we consider the instances when a is nearly

constant. We see in Fig. 6 that, for 650 nm, ais almost the same for all stations in St. Louis Bayindependent of particle concentration and particle-size distributions. Thus, if we assume that relation2 holds and RSR is proportional to 1a, then,

for the wavelength region where a is nearly con-stant, RSR should be proportional to scattering, say

as measured by xg.4

We see from Fig. 7 thatRSR660 is proportional to xg, independent of parti-cle concentration and the inherent differences inparticle-size distributions from station to station.Figure 8 shows further that RSR 0.00062ba at 660 nm.

The results in Figs. 5, 7, and 8 imply that, forconstant a, the ratios xgb, RSRxg, and RSRb areindependent of particle concentration and particle-size distribution. In terms of the scattering processthis implies that at 660 nm forward scattertotalscatter, backscatterforward scatter, and back-scattertotal scatter are independent of station lo-cation, i.e., the shape of the scattering function for

particulates in St. Louis Bay was insensitive to thedifferences in particle-size distribution from station

Fig. 2. Particle-size distribution, which is seen to behave accord-ing to lnn 109 0.51x 3.9, is typical of coastal waters.

Fig. 3. Plots ofb reveal an 1 dependence with wavelength.

Fig. 4. Main contribution to xg comes from the 25-m particles.

Fig. 5. xg and b correlate with r2 0.9. The linear relationship

appears to hold for three geographical areas: Camp LejeuneCamp Les., N.C., the Gulf of Mexico, and St. Louis Bay,Miss.



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to station. Using the slope in Fig. 8 and taking C 0.051 from Eq. 2, we obtain bbb 0.0125 at 660

nm, in agreement with previously reported results forthe Mississippi Sound.1

8. Spectral Dependence of bb and fQ

Thus far we have shown thatbbb 0.0125 at 660 nm.The technique worked because absorption by particu-lates was small at 660 nm. For 650, absorptionby particulates becomes appreciable, then RSR is nolonger linear with ba and fand Q become functions ofturbidity. Thus, the quotient ofba becomes of littleuse in correlation with RSR. On the other hand,RSR is directly proportional to the quotient bKd independent of because Kd incorporates the

variability of Ca with .4,5 The results for RSRversus bKd are shown in Fig. 9, where we ob-serve that the relationships between RSR and b

Kd are quite similar for two widely differingstations, one in the Mississippi sound, with xg 3m1, the other a riverine station with xg 2 m

1.The values ofa for the two stations differ by an orderof magnitude, as can be seen from curves 1 and 3 inFig. 6. Based on this result, we propose that the prod-uct RSRKd can be identified with bb alonethrough a geometric factor Cb according to

CbRSR Kd bb. (5)

For St. Louis Bay stations Cb 12.5. The resultsfor bb obtained in this manner are shown in Fig.10. The spectral dependence and the magnitude ofbb

in Fig. 10 is comparable to the values of bb

measured at 90 for a variety of case 2 waters,including DOM-laden harbor waters.14 The signif-icance of Cb can be interpreted roughly as follows:

Fig. 6. a has an exponential behavior for 600 nm: curve1, a for the Jourdan River station high DOM, 2-gm3 sus-pended solids; curve 2, a at the mouth of St. Louis Bay, lowerDOM, 10-gm3 suspended solids. The Gulf of Mexico stationsare shown by curves 3 and 4. Curve 4 can be considered typical ofthe relatively clear seawater having a Secchi transparency of 3 m.

Fig. 7. RSR at 660 nm at constant a shows a linear relationshipwith xg for six St. Louis Bay stations independent of the suspendedsolids concentration and the inherent fluctuations in particle-sizedistribution from station to station.

Fig. 8. RSR versus ba is also linear at 660 nm according toRSR 0.00062ba. The linear relationship breaks down for 650 nm because C becomes a function of turbidity.

Fig.9. For case2 waters, Kd and Ku are nearly the same andRSR is linear with bKd for all independent of DOM. RSR CkbKd, where Ck is the slope. Curve 1, the Mississippi Soundlow DOM, 3 gm3; curve 2, Jourdan River, high DOM, 2 gm3.



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The product RSRKd is equal to RSR2RBb,5 andcan be approximated by

CbRSR2RBb Cb

Lw, cosd

0

2

d 0

2

2Lw, cossindBb. (6)Lw is the water-leaving radiance at angles relative tothe zenith, is the unit solid angle at the zenith.For perfectly diffuse Lw, the integral term withinbrackets in relation 6 becomes 14, giving Cb4

1, then Eq. 5 reduces to Bb bb. These condi-tions are never met,1,2,5 but the approximation givesa rough explanation for Cb.

In Fig. 10 the departure of bb from the magni-tude of 0.0125b is within 10%, indicating thatbbb is independent of for case 2 waters.

Since a is largely a function of DOM concentra-tion, and bbb is constant, we can use the dependenceofa and Kd on to examine the spectral behav-ior offQ as a function of DOM. From the radiativetransfer theory we have RRSR QT. Further-more, the experimental relationship RSR CkbKd, where Ck is the slope in Fig. 9, and R fbba combine to give fQ CkTbbbaKd. Using the experimental val-ues for Ck, taking bbb 0.0125 and T 0.54, weobtain fQ, shown in Fig. 11. Note in Fig. 11that fQ has an average value of0.09 and appearsreasonably constant in the 450 600-nm range.This result is expected because the variability in fand Q as a function of the sun angle compensate eachother at the short wavelengths.2 fQ in Fig. 11 hasa trend with comparable to the zero solar zenithangle fQ discussed in Ref. 2.

9. Remote Sensing Reflectance as a Function of

Dissolved Organic Matter and Particle Concentration

We now consider RSR as it applies to satellite remotesensing of DOM and xg. To examine how satelliteremote sensing behaves, we average RSR and xga at each for three stations that could representa satellite pixel of a 1-km2 area. A plot of the area-averaged RSR versus xga shows the behaviorof satellite RSR with 1a, as displayed in Fig. 12.We see a pattern of experimental points in Fig. 12that fall in a narrow loop depending on. In Fig. 12,the slope of RSR versus xga is proportional toC. We observe that the slope is constant for 450

Fig. 10. Spectral dependence of bb derived from the measure-ments of RSR and Kd: curve 1, a station with 10-gm

3

suspended load; dotted line, curve 2, 0.0125b for the same sta-tion; curve 3, bb for the Mississippi Sound; curve 4, bb for theJourdan River.

Fig. 11. Spectral dependence offQ for the Jourdan River,curve 1 and for the Mississippi Sound, curve 2. fQ is reasonablyflat in the 450620-nm range but deviates markedly from theaccepted value in the long wavelength region. The dotted lineshows a nominal value of fQ 0.094 used in satellite remotesensing of turbid water.

Fig. 12. Area-wide average of RSR versus xga for 1 km2

representative of case 2 pixel with an average suspended load of4 gm3. RSR falls along a distinct loop of points dependingon , as marked. The slopes of the dashed lines correspond to Cin the range 0.046 C 0.063. The accepted value ofC is 0.054.For St. Louis Bay bb 0.15xg.



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560 nm. Thus, for 450 560 nm, we can treatC as a constant and expect that the ratio RSR1RSR2 a2a1. We can use the ratios of ab-sorption coefficients a2a1 to determine the

concentration of DOM by using satellite DOM algo-rithms.1,12 However, the ratio technique should notbe extended to wavelengths outside the 450560-nmrange where C is no longer constant.

Figure 12 provides a qualitative explanation of howsatellite RSR changes with DOM concentration.Keeping the suspended solids concentration fixed butincreasing DOM makes the 412-nm point in Fig. 12move down toward the origin, but the 715-nm pointremains fixed since a715 is mainly due to the absorp-tion by water. In general, the presence of DOM re-sults in lower overall values of RSR, but the values ofRSR in the highly absorbing waters are nearly linear,with the suspended solids as much as 10 gm3. On

the other hand, keeping DOM fixed but increasing theconcentration of suspended solids makes the entireloop in Fig. 12 move up from the origin, as indicated inFig. 13. The two cases shown in Fig. 13 demonstratewhat happens to RSR as we move down the JourdanRiver toward the mouth of St. Louis Bay to an area oflarger b and lower DOM. For low concentrations ofDOM, RSR increases rapidly with the suspended load,but the relationship between RSR and xga becomesnonlinear at a few grams per cubic meter.14

We can examine further the linearity of RSR withxga by averaging RSR for each interval of xgaregardless of . The results are shown in Fig. 14.The experimental points in Fig. 14 lie along a straight

line to xga 0.6, or roughly, to bba 0.09. SinceC is proportional to the slope of the line in Fig. 14, wecan state that it can be treated as a constant providedthat xga 0.6 and provided that falls in the range450 560 nm.

10. Discussion

The results in Figs. 10 and 11 show that, for 660nm, bbfQ is a function of particle concentration notDOM. Thus, RSR at the longer wavelengths pro-

vides a good reference as to what RSR should be atthe shorter wavelengths if DOM were absent. Thedifference RSRexpected RSRactual at the shorterwavelengths should depend only on the concentrationof DOM.11

11. Summary

1 Natural fluctuations in particle size distribu-tions do not affect RSR for case 2 waters provided themean particle diameter does not vary by more than15%.

2 RSR for case 2 waters comes mainly from the23-m particles.

3 A linear relationship between xg and c aholds for different geographic areas. Thus, xg deter-

mined from the 520 forward scattering offers a goodcheck on the AC9 measurement ofb.4 The close correlation between xg and RSR for all

stations indicates that the contribution to bb that isdue to submicrometer particles is negligible. Other-wise, the submicrometer component contributing toRSR would have to vary in unison with the 25-mcontribution to xg. The bimodal character ofparticle-size distribution in Fig. 1 implies that this isunlikely, especially since the inflection at 2.5 mwas absent at some stations.

5 Assuming that C is a constant, the riverinewaters and the near-shore waters in St. Louis Bayyield a bbb 0.0125.

6 The relationship for satellite RSR Cbba holds provided xga 0.6 and 450 560nm. Under these conditions, C can be treated as aconstant in the ratio-based algorithms for the deter-mination of DOM.1,12

We express our sincere appreciation to co-workers,students, and government personnel at the Univer-sity of Minnesota Duluth, NRL Stennis Space Center,Southern Mississippi State University, and the U.S.Coast Guard. Our thanks to Howard Mooers, and

Fig. 13. RSR versus ba for two stations: curve 1, JourdanRiver station 2 gm3, highDOM; curve 2,St. Louis Bay 5 gm3,lower DOM.

Fig. 14. RSR versus xga regardless of . The dotted line rep-resents a linear region where C is a constant the slope of the linefor xga 0.6 corresponds to C 0.055. The solid line gives asecond-order polynomial fit according to RSR 0.0093 xga0.0018xga

2. The nonlinear region, xga 0.6, indicates theonset of multiple scattering and corresponds to bba 0.09.



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Brian Edgar; Charles Walker, Gregory Terrie, RickGould, Alan Weidemann, and Tod Bower; D. G. Re-dalje, Ken Matulewski, and Jim Ivey; and to BMCBrown and his crew. This project was funded by theNaval Research Laboratory NRL 6.2 program, McMCoastal Optics P.E. 627354, directed by D. Rams-dale and the 6.1 Spectral Signature Program P.E.601153N, directed by E. Hartwig. This contribu-tion is part of the NRLAmerican Society for Engi-neering Education summer faculty program.

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