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Effective reflectance of oceanic whitecaps

Peter Koepke

The effective reflectance of the foam on the ocean surface together with the fraction of the surface coveredwith foam describes the optical influence of whitecaps in the solar spectral range. This effective reflectanceis found to be -22% in the visible spectral range and is presented as a function of wavelength for the solarspectral range. With the fraction of the surface covered with foam, taken from the literature, the resultslead to a good agreement with satellite measured radiances and albedo values. The effective reflectance ismore than a factor of 2 lower than reflectance values used to date in remote sensing and radiation budgetstudies. Consequently, the optical influence of whitecaps can be assumed to be much less important thanformerly supposed.

1. Introduction

In the solar spectral range the reflectance of the oceanincreases with the proportion of whitecaps. Conse-quently, the variability of whitecaps gives rise to avariation in the radiance and the radiant flux densitiesat the bottom and the top of the atmosphere.'

So, the correct optical influence of whitecaps must betaken into account, both for remote sensing and in ra-diation budget (climate) studies. In remote sensingmeasurements, where the actual optical influence ofwhitecaps is not precisely known, there is an equivalentuncertainty in the remotely sensed quantity.2-4 Inclimate studies the correct optical influence of white-caps should be taken into account, since oceanic foamhas an effect on the albedo of the ocean, affecting thesolar heating of its upper boundary layer which mayresult in an alteration of the water temperature and thedepth of the mixed layer.

Austin and Moran5 have characterized the reflectionproperties of the ocean surface with foam by deter-mining the fraction of the surface with reflectancewithin a given interval (a histogram of the surface areaas a function of the surface reflectance). Unfortunatelythey have analyzed too few cases to establish a quanti-tative relationship between reflectance of the sea surfaceand wind speed.

However, statistical data are available which give .thefraction covered with foam, W as a function of windspeed U.6-11 In computations of radiance or radiantflux over an ocean surface, whitecaps are usually taken

The author is with Universit~t Mnchen, Meteorologisches Institut,D-8 Mnchen 2, Federal Republic of Germany.

Received 2 November 1983.0003-6935/84/111816-09$02.00/0.© 1984 Optical Society of America.

into account as the product of their percentage area anda reflectance value between 0.5 and 1.0.1,4,12 Theserather high foam-reflectance values are in the rightorder of magnitude for fresh, dense foam but not for realfoam on water surfaces with patches of all ages andconsequently very different reflectances.

The aim of this paper is to determine the effectivereflectance of whitecaps which allows one to use theW(U) values from the literature to describe the opticalinfluence of whitecaps.

11. Reflectance of Ocean SurfaceIn the solar spectral range the reflectance of an ocean

surface, Roc, is composed of three components: re-flection at foam, specular reflection, and underlight:

R.c = Rfstt + (1 - W) R. + (1 - Rftot) Ru. (1)

The first term in Eq. (1) gives the reflectance of the totalnumber of foam patches and streaks, Rf,tot. It is theproduct of the fraction covered with whitecaps and thereflectance of the whitecaps. It is described in detailin the next section.

The second term describes the specular reflectanceat the water surface without foam. This component canbe calculated for a flat surface with the Fresnel formulaand therefore depends on the angles of incidence andreflection and on the refractive index of the water.Small spectral variations of this refractive index in thespectral range between 0.4 and 1.5 m (Ref. 13) resultin an unimportant decrease of the R values in thisrange. The slope of the waves of the usually roughocean reduces and broadens the glint,14 15 an effectwhich must be taken into account in R, e.g., with dataafter Cox and Munk. 16 The R value in Eq. (1) isweighted by (1 - W), the area not covered with white-caps, since specular reflection is possible only at thatpart of the surface.

1816 APPLIED OPTICS / Vol. 23, No. 11 / 1 June 1984

The third part describes the reflectance due to un-derlight R,. Although the underlight is scattered atwater molecules and suspended material in the water,it can be described as a reflectance. 1 7 To take into ac-count the reduction of underlight due to whitecaps, RUin Eq. (1) is weighted by the factor in the parentheses.This factor is based on the assumption that the reflec-tance of whitecaps is the same for light coming fromabove or below. The reflectance due to underlight canbe assumed to be isotropic1 7 1 8 due to the multiplescattering processes inside the water and to thespreading of the radiance field emerging upwardthrough the water surface. The RU values show strongspectral behavior,17 depending on the material in thewater. In ocean water RU can be neglected at wave-lengths longer than 0.7 ,um due to the spectral absorp-tion of the water. In turbid waters with high sedimentload, however, underlight is possible even at wave-lengths above 1.0 Mm.17' 19

The contributions due to whitecaps and underlightare of the same order of magnitude. As mentionedabove, they depend on the wavelength, on the waterquality, and on the foam coverage. If an angle-depen-dent reflection function of the ocean surface is used tocalculate radiances, Eq. (1) is also valid, but instead ofreflectances the angle-dependent reflection functionmust be introduced. In this case, in directions outsidethe sun glint where the specular reflected componentis low, the contribution due to the diffuse componentsunderlight and whitecaps becomes important.Therefore their exact values must be used and the ef-fective reflectance of the whitecaps is required.

Ill. Reflectance of Whitecaps

The spectral reflectance of dense foam of clear water,Rf, is -55% in the visible part of the spectrum as mea-sured by Whitlock et al. 2 0 in laboratory conditions.The value of -55% is valid up to 0.8-Mtm wavelength;toward longer wavelengths the reflectance decreases dueto absorption of liquid water. The reflectance has tworelative minima at 1.5 and 2 ,m and can be assumed tobe zero at 2.7 MAm. Calculations with a simple model fora whitecap consisting of more than twenty-five uniformbubble layers also give a reflectance value of -55% inthe spectral range below 1 Mm.21

The angle-dependent reflection function of whitecapshas not yet been studied. Usually they are assumed tobe isotropic reflectorsl4 2 2 ,23 which is in agreement withvisual inspection.

The relative area covered with whitecaps, W, is de-termined by different authors 6 -11 as a function of the10-m elevation wind speed U. They use photos of theocean surface where the outline of the white area istraced, more or less, and the area is measured.8 Thesurface is divided into subregions that are deemed, inthe judgment of the investigators, to contain whitewater, all other regions are consequently dark water.5

However, the threshold reflectance value that the in-vestigators used as their decision criteria for white is notknown. The white water must stand out against thewater without foam. Consequently the threshold re-

flectance for white increases toward the horizon, andlittle account is taken of the less dense wind-generatedfoam streaks.24 Each of the photos contains whitecapsof different ages; it follows that in the published W( U)values whitecaps of different ages are taken into ac-count.

The fraction covered with whitecaps, however, notonly depends on the wind speed but also on the fetch 9

and on the factors altering the mean lifetime of thewhitecaps, such as water temperature25 and thermalstability of the lower atmosphere.11 Consequently, anexpression for W(U) only as a function of the windspeed, in the form given by Eq. (2),

W = a- U, (2)

has a large uncertainty; different authors or differentstatistical methods give different results.10 11 Never-theless, due to the lack of appropriate additional data,the user will usually take an expression like Eq. (2) todetermine the area covered with whitecaps. In thispaper, the optimal W(U) expression by Monahan andO'Muircheartaigh, 11

W = 2.95 10-6. U3.52, (3)

is used, which is valid for water temperatures higherthan 14°C.

The optical influence of all the individual whitecaps,the total foam reflectance Rfatot, is obviously the sum ofthe optical influence of the individual whitecaps. Theoptical influence is given by the product of the area ofeach individual whitecap with its corresponding re-flectance. These individual data are not, in general,available; as mentioned above, usually a fixed RJ valuebetween 0.5 and 1.0 independent of wavelength or awavelength-dependent Rf after Whitlock et al. 2 0 iscombined with W(U) to describe the optical influenceof whitecaps:

Rttot = W Rf. (4)

However, the area of an individual whitecap increaseswith its age while its reflectance decreases. An exampleof this well-known behavior is shown in the photos inFig. 1 taken at 1-sec intervals. The figures to the leftof the fields give the age of the dominant whitecap withan uncertainty of 0.5 sec.

Since whitecaps of different ages are taken into con-sideration in the W values, the combination of W withRf values valid for dense, fresh foam gives Rf,tot valuesthat are too high. Consequently, a lower effective re-flectance Ref must be used [Eq. (5)]:

Rftot = W Ref- (5)

The available photos yield Ref values only in thespectral range up to 0.8 m. But they can be used todetermine an efficiency factor fef, independent ofwavelength, which allows the combination of spectralRf values, as measured by Whitlock et al.,2 0 with the Wvalues depending on wind speed:

Rf,tot( ) = W * fef Rf (X) (6)

1 June 1984 / Vol. 23, No. 11 / APPLIED OPTICS 1817

4.5

5.5

Fig. 1. Examples of the variation of a whitecap at1-sec intervals, beginning at an age of 0.5 sec with anuncertainty of ±0.5 sec: wind speed, 7.5 m sec';water temperature, 15.7 0C; viewing elevation, 600;

distance to foam patch, 35 m.

7.5

IV. Method

The variation in the size and reflectance of individualwhitecaps as a function of time was determined fromseveral series of photos. They were made from theupper deck (30-m height) of the research platform"Nordsee" in the German Bight at 50'43'N and 710'Ebetween 22 Aug. and 21 Sept. 1978. The reason forworking on the platform was to obtain ground truthmeasurements to calibrate the European satelliteMeteosat. 2 6 This was done mostly in summer in lowcloud coverage conditions and, unfortunately, also lowwind speed conditions. Only a few series of photo-graphs were made, but the material allows determina-tion of an approximate value of the effective reflec-tance.

Meteorological and oceanographic parameters, suchas wind speed and direction, wave height and period,and water and air temperature, were continuously re-corded by the equipment on the platform. The windspeed at the 10-m level was estimated from that mea-sured at the 47-m level using the logarithmic law witha roughness length of 0.15 mm.27 The water tempera-ture was between 15 and 160C.

The camera was a 6- X 6-cm2 Hasselblad equippedwith a motor drive, a red filter to enhance the contrast,

and a wide-angle lens with a focal length of 50 mm. Thephotos were taken as a series of -10, at intervals of 1 secand facing away from the sun. The elevation angle ofthe camera was varied between 450 and 60°, resultingin a distance to the analyzed whitecaps of between 33and 60 m.

An analysis was made of the lifetimes of thirteen in-dividual whitecaps, resulting from winds of 8 m sec',and of six individual foam streaks from winds between14 and 15 m sec'. Each whitecap detected for thefirst time in a series must have been formed the secondbefore, since it was not present in the preceding photo.Consequently, its age is 0.5 sec with an uncertainty of+0.5 sec, as is also true for all the following pictures

taken at 1-sec intervals. Due to a restriction of thelengths of the series, not all the whitecaps could be fol-lowed until they vanished.

Figure 1 shows an example of the lifetime of an indi-vidual whitecap. Figure 2 shows 10 sec of the lifetimesof different foam streaks. The streaks are fairly stableand only vary slightly in size and reflectance. Since thelifetime of such foam streaks is longer than 10 sec, nei-ther their beginning nor their end can be seen. Due tothis lack of information, in the evaluation it is assumedthat all foam streak were seen for the first time at an ageof 3.5 sec.


age inseconds

0.5

1.5

2.5

3.5

Fig. 2. Examples of the variation of an ocean sur-face with foam streaks at 1-sec intervals: windspeed, 14.5 m sec'1, water temperature, 15.70 C;viewing elevation, 500; distance to the center of the

image, 50 m.

To determine the area covered by a particularwhitecap, a common method was used: The photoswere projected onto graph paper, the outline of thewhite area was traced, and the area was measured. Thearea of each whitecap was normalized to be one at itsmaximum. So normalized values of the area of foamas a function of its age, a(t), are the results presentedin Figs. 3 and 4. It can be seen that the area of the foampatches increases during their lifetime.

The reflectance of the whitecaps was analyzed fromthe film density, similar to the method described byAustin and Moran.5 If the reflectance of two points inthe target can be established, the density curve can begraduated. These two reflectance values are theFresnel reflectance of the nonwhite vicinity of thewhitecap and the maximum diffuse reflectance of thedense, fresh whitecap. To analyze the reflectance offoam streaks, it was assumed that small portions foundwith density values comparable with that of densewhitecaps really have the maximum reflectance of densewhitecaps. Due to the wide variation of the reflectanceover the area of the foam patches 5 the film density wasmeasured at many positions, and mean values weredetermined. A mean value also was used as the densityof the film in the vicinity of the whitecap to try to ac-

count for the variability of the reflectance due to thescope of the wave without foam. The camera trans-mittance curve was not taken into account, since thewhitecap in each series was placed in a fixed position.

The maximum reflectance was taken to be 55% asmeasured by Whitlock et al.2 0 and as calculated byStabeno and Monahan2l for the spectral region of thefilm material. Since this value was used as the meanvalue for the total area of the fresh, dense foam patches,it is also in agreement with the value found by Austinand Moran.5

It can be assumed that the slope of the film densitycurve is stable for at least ten pictures. So this slope,starting at density values of the reflectance of darkwater in the vicinity of the whitecap, was used to de-termine the reflectance of the whitecap, r(t), in eachpicture of the series. Figures 5 and 6 show the decreasein the reflectance as the whitecaps age.

Over a large area of the ocean, as analyzed in theW(U) determination, it can be assumed that the agedistribution of the whitecaps does not alter with time.Consequently, the mean effective reflectance of all thewhitecaps in the area can be determined as the effectivereflectance of an average whitecap, taking into accountits total lifetime.


seconds

0.5

1.5

4.5

5.5

2.5

3.5

6.5

7.5

1.0

0.4

0.2

0 2 4 6 5 10ange in second s

Fig. 3. Normalized area of whitecaps (foam patches) as a functionof their age. The thicker stripes give the mean values. Wind speedbetween 7.5 and 8.5 m sec'; water temperature between 15 and16'C. The curve is calculated from Eq. (10) with =0.25

and~y= 1.

1.0-

0.4/

0.2

N

0-

0 2 6 8 12 14age in seconds

Fig. 4. Normalized area of foam streaks as a function of their age.The thicker stripes give the mean values. Wind speed between 14and 15 m sec; water temperature between 15 and 16°C. The curve

is calculated from Eq. (10) with a = 0.4.

But in the W(U) determination, whitecaps were ig-nored if they were decayed to a reflectance less than thethreshold reflectance for white, which occurs at an ager of the average whitecap. It follows that the integra-tion to determine Ref ends at time r, since the values ofthe effective reflectance will be used in Eq. (5) in com-bination with W( U) values. The effective reflectancecan be evaluated with Eq. (7):

f a(t) r(t) dtRef = * (7)

| a(t) dt

In the numerical solution, the products a (t) r(t) of eachindividual whitecap are calculated and the integral isdetermined from the mean values of these products.The integration is performed as a sum with steps of dt= 1 sec.

The reduction of the effective reflectance of white-caps due to the expansion of their area and the thinningof the foam can be assumed to be independent of thewavelength. The effective reflectance Ref determinedin the visible (and valid only for this spectral range if notwritten as a function of A) can be converted to otherspectral regions or wavelengths with an efficiency factorfef, which is derived as the ratio of the effective reflec-tance to the reflectance of dense foam:

Ref RefRef R 0.55 (8)

Consequently, this efficiency factor can be combinedwith spectral reflectance values Rf (X) of fresh, densefoam as measured by Whitlock et al. 20:

Ref(X) = fef Rf (),

resultingtance.

(9)

in spectral values of the effective reflec-

60-

50-

C

0Ca

us ~~ ~ . a I 0 2 4 6 B 10

age in seconds

Fig. 5. Reflectance of whitecaps (foam patches) in the visible spectralrange as a function of their age. The thicker stripes give the meanvalues. Maximum reflectance of fresh dense foam Rf = 55% after

Whitlock et al.2 0 Other data as in Fig. 3.

60-

50-

40-C

0iUC4a

a,a,

30-

20-

1 0-

0I .T M I-I I I

2 4 6 8 10 12 14age in seconds

Fig. 6. Reflectance of foam streaks in the visible spectral range asa function of their age. Other data as in Fig. 4.


-

us l w g . w w

-v z

-.1

Table I. Effective Reflectance in the Visible Spectral Range andEfficiency Factor Independent of Wavelength as a Function of Age T of

Individual Whitecaps (See Text)

T Foam patches Foam streakssecond Refp (%) fef,p Refs (%) fef,s

1 41 0.75 10 0.182 35 0.63 10 0.183 30 0.55 10 0.184 28 0.50 10 0.185 25 0.45 9.9 0.186 23 0.41 9.6 0.177 21 0.38 9.5 0.178 19 0.35 9.4 0.179 18 0.32 9.2 0.17

10 16 0.29 9.0 0.16

V. Result

Figure 3 shows the normalized area a (t) of individualfoam patches as a function of their age, together withthe mean values and the standard deviation. The largestandard deviation arises not only in the high variabilityof the individual whitecaps and in the relatively lownumber of series analyzed but also in the subjectivejudgment used to determine the values. The uncer-tainty in the age is ±0.5 sec, as explained above. Theincrease of the area a(t) can be described by an expo-nential function of the form

a(t) = 1 - exp(-0 ty), (10)

which is presented in Fig. 3 with : = 0.25 and -y = 1.Figure 4 shows the a(t) values determined for foam

streaks. As mentioned above, they start with an as-sumed age of 3.5 sec. The streaks spread fastest whenthey have just been generated and spread more slowlyas they grow older, as the figure shows. Taking this intoaccount leads to values of = 0.7 and -y = 0.4 in Eq. (10)which gives the curve in Fig. 4.

The reflectance of individual whitecaps and foamstreaks is shown in Figs. 5 and 6 as a function of time,together with mean values and standard deviations.Again, the large standard deviation originates in thevariability in the reflectance of individual whitecapstogether with subjective judgment.

The reflectance of foam patches, seen in Fig. 5, hasits highest value at -1.5 sec after generation. Since theindividual whitecaps reach their maximum reflectancevalue at different ages, the mean value of r(t) is alwayslower than 55%. But, as mentioned above, to calculateRef with Eq. (7) the r(t) values of the individual white-caps are used, which reach 55% as a maximum.

The reflectance of foam streaks shown in Fig. 6 hasvalues of -10%, in agreement with the result for a singlebubble layer found by Whitlock et al. 2 0 It slowly de-creases with age. For the integration [Eq. (7)], thevalues are extrapolated to 10% at t = 1 and 2 sec.

In Table I the effective reflectance Ref in the visiblespectral range and the efficiency factors fef are givenseparately for foam patches (subscript p) and foamstreaks (subscript s). They are calculated with Eq. (7)as a function of time r, the last age at which the foam istaken into account in the W(U) values. The r values

used in the different W(U) determinations are notknown. Assuming a reflectance of 10% as the thresholdvalue for white, one can work back to r = -7.5 sec forthe patches from Fig. 5 and to -4.5 sec for the streaksfrom Fig. 6.

The values for the patches clearly decrease with in-creasing r, as expected from the strong variation overtime of the properties of the whitecaps. Due to theirmore stable behavior, the values for the foam streaksdepend only slightly on r in the first 10 sec.

The resulting average values are for foam patches(whitecaps)

Refp = (22 ± 8)%,

fef,p = 0.4 ± 0.15.

The values are given with high uncertainty, to take intoaccount both the uncertainty of the individual data andthe uncertainty due to the lack of knowledge of the rvalue used in the determination of W(U). Foamstreaks9 contribute to the area of white water at windspeeds higher.than -9 m sec-. The resulting valuesare for foam streaks

Refs = (10 + 4

fef,s = 0.18 ± 0.07.

In this case, the uncertainty is stated to be even higherthan the variability in Table I, to take into account theuncertainty due to the unknown real age of the streaksand the extrapolation back to the time t = 0 in additionto the uncertainty of the measured data.

In actual cases where the patches and streaks arehighly variable, the total reflectance should be summedfrom a histogram giving the fraction of the surfacehaving a particular reflectance value.5 Since these dataare not available, the total reflectance is summed fromonly two terms [Eq. (11)], with Wp the fraction of foampatches and W, the fraction of streaks:

Rtatot = Rf (Wp fef p + Ws fefs)

1.0-

.8-

.6 -

.4

.2-

(11)

fef, p ef,

0.55 0.250.4 0.180.25 0.11

- - -,C- -. -.-. -.

L~:! .. Z -.- --- -- y .

0.5

A/ , lb . . . . .~ .8 10 15u in m-s~

120

Fig. 7. fef values as a function of wind speed U. The numbers at thecurves indicate what proportion x of the fraction of foam streaks is

assumed to be taken into account in the W( U) values; see text.


o . ,s . . . . . . . ,, . . . .

- /V-=

Since the goal of this article is to use available W(U)data, Wp and W, must be explained by W(U). This ispossible using a streak-to-whitecap ratio SP9 :

Table II. Wind Speed Dependent Values of the Area Covered with FoamW(U), the Efficiency Factor f(U), the Effective Reflectance in the

Visible Spectral Range R61( U), and the Total Reflectance Due to FoamR,,tt(U) in this Spectral Range

sP = ws/Wp. (12)

The equation for SP, recalculated from Fig. 4 in Rossand Cardone9 and converted to a wind speed U (in m -sec-1 ) at the 10-m level, is given in Eq. (13):

SP = 0, U 8.5 m sec1,SP =-2.1 + 0.24 U U < 8.5 m sec-. (13)

However, as mentioned in Sec. III, in the W(U) valuesdetermined by different authors, not all the streaks aretaken into account,2 4 since the reflectance of the streaksmay be less than the threshold value for white. Thefraction taken into account, called x, may vary between0 and 1:

W(U) = Wp(U) + x W8 (U).

Combining Eq. (14) with Eq. (12) gives

W'(U) = W(J)/[1 + x SP(U)],

Ws(U) = W(U) SP(U)/[1 + X SP(U)].

(14)

U(m/sec)

456789

101112131415161718192025

W(%)

0.00.10.20.30.50.71.01.41.92.53.24.15.16.37.79.4

11.224.6

(15)

Using Eq. (11) gives the total reflectance due to foamas a function of wind speed,

Rftot(U) = W(U) fef(U) Rf = W(U) - Ref(U), (16)

with a wind-speed-dependent efficiency factor fef(U):

fef(U) = [ef,p + fef,s - SP(U)]/[1 + SP(U)]. (17)

As may be seen in Eq. (7),fef(U) depends on the frac-tion of foam streaks assumed to be considered in W(U).If x is small, the streaks not taken into account give anadditional increase in the reflectance, resulting in a highfef(U) value. If all streaks are taken into considerationin W(U), the increasing streaks-to-whitecap ratio withincreasing wind speed results in a dominance of streaksat higher wind speed, resulting in a low fef(U) value.Figure 7 shows this behavior for fef(U) values calculatedfrom maximum, minimum, and the means fef,p andfefs -

The right x value depends on the criteria used in thedifferent W(U) determinations.24 To determine an xvalue, different photos made at the "Nordsee" platformwere analyzed for W(U) values. The results agree wellwith values calculated with Eq. (3) when half of the areacovered with streaks is taken into account. So x is as-sumed to be 0.5, in agreement with the data shown byRoss and Cardone.9 Due to subjective judgment bothin the W(U) and in the W and Wp values, other xvalues may occur. But the use of other x values seemstoo sophisticated compared with the approximate fef,pand fef,s values.

Consequently, the results are an efficiency factor andan effective reflectance that only decrease slightly withwind speed, as seen in Fig. 7:

fef(U) = 0.4 0.2, Ref(U) = (22 11)%. (18)

In spite of that, in Table II fef is presented as a functionof wind speed, together with Rf(U) after Eq. (8), with

.

C

0

1

e

Z

S

S

fef

0.40.40.40.40.40.40.390.390.390.390.380.380.380.380.380.380.380.37

1.0 1.2

wavelength In pm

Ref Rftot(%) (%)

22 0.022 0.022 0.022 0.022 0.122 0.221.7 0.221.5 0.321.4 0.421.3 0.521.2 0.721.1 0.921.0 1.120.9 1.320.8 1.620.8 2.020.7 2.320.6 5.1

Fig. 8. Effective reflectance of oceanic foam as a function of wave-length, after Eq. (9).

W(U) calculated from Eq. (3) and the total reflectancedue to foam after Eqs. (16) and (17) using x = 0.5.

The effective reflectance as a function of wavelength,Ref(X), is calculated with Eq. (9) from the average effi-ciency factor given in Eq. (18) together with the spectralreflectance values from Whitlock et al.20 The resultingspectral effective reflectance of oceanic foam, patchestogether with streaks, is presented in Fig. 8. As men-tioned above, this effective reflectance is nearly inde-pendent of wind speed.

The large uncertainty of the results in Eq. (18) andconsequently in Fig. 8 (but not shown there) takes intoaccount the variability Of fef due to x, presented in Fig.7. The reasons for this uncertainty are discussed above;they are the same as those which result in the high un-certainty of the empirical formula that describes theW(U) relations. Nevertheless, the new effective re-flectance is an improvement on the values of the re-flectance currently used, since these values were muchtoo high.


VI. Comparison with Data in the Literature

Only a few works were found which give data onmeasured radiances or albedo values as a function of theamount of whitecaps or the wind speed. These data arecompared with radiances or albedo values, calculatedwith the corresponding atmosphere model, using Eq.(1) as the ocean reflection function. The calculationstake into account multiple scattering and absorption ofatmospheric gases as described by Koepke.2 6

For a first comparison, the results found by Austinand Moran5 seem appropriate. Unfortunately, theirreflectance cumulative-distribution function gives thefraction of the surface having a reflectance less than thevalue shown at the abscissa and not the mean reflec-tance of a fraction of the surface. But this reflectancecan be calculated from the histogram given in their Fig.6. In this histogram the fraction a of the surface isgiven as a function of the surface reflectance ri. Addingthe columns of the histogram up to a specific column I,with reflectance r, gives the fraction of the surface awhich has reflectance values less than r. The meanreflectance r of this surface fraction is the weighted sumof the reflectance values in the histogram:

Ia= ai

I Ir = E ai ri/ E a (19)

i=1 i=1

The data from Austin and Moran originate from a windspeed of 25 m - sec 1, which results in W(U) = 0.246after Eq. (3) and consequently in the fraction of thesurface without foam (1 - W) of 0.754. Adding theareas of the columns in the histogram, this value isreached at the 22nd column at a reflectance of 10%. Sothe use of Eq. (3) with the Austin and Moran valuesgives the result that a reflectance of 10% is the thresholdvalue between a surface covered with foam and that freeof foam. The mean reflectance of the surface withoutfoam is 5.5% from Eq. (19). This value is in goodagreement with literature data for a rough ocean inovercast conditions. 2 8 Adding all columns of the his-togram gives a surface fraction of 100% with a meanreflectance of 7.73%. This value can be understood asthe total reflectance of the analyzed ocean surface Roc.It is used with Eq. (1), neglecting the underlight, tocalculate Rftot, the total reflectance due to foam being0.036. Using Eq. (16) gives an efficiency factor of fef =0.265 and, equivalently, an effective reflectance of Ref= 14.6%. These values confirm the need to use an ef-ficiency factor in foam reflectance calculations. Thevalue of the efficiency factor determined from theAustin and Moran data is even lower than the factorproposed in this paper, but it is well within the givenuncertainty range. Better agreement cannot be ex-pected, since at the high wind speed in the Austin andMoran data,5 the W(U) values are questionable and theproblem of the fraction of streaks in the W(U) databecomes especially important.

At lower wind speed conditions, the .extensive mea-surements by Payne2 8 allow a check of the efficiency

coefficient. He found that in the albedo of the sea sur-face, effects of whitecaps are not noticeable at windspeeds up to 30 knots, the highest observed in thatstudy. His measurements of the albedo are made forthe total solar spectral range from 0.28 to 2.8,Mm. Somy calculation of the albedo values requires computa-tions in this broad spectral range and is made only forone mean turbid, cloudless atmosphere at a solar zenithangle of 32.50. The rms error which Payne found forthis condition leads to an uncertainty in the measuredalbedo value of ±0.003. The wind speed of 15 Insec 1

gives W = 4.1%. Compared with the case withoutwhitecaps, such a fraction of whitecaps would lead toan increase in the calculated surface albedo of 0.017, ifthe literature data of W and Rf(X) are used without theefficiency factor. Including the efficiency factor (TableII) reduces the increase in the calculated albedo to 0.006,which is still higher than the rms error found by Paynebut well inside his range for single data points.

The Landsat data published by Maul and Gordon12

allow another check on the influence of whitecaps on theocean surface. They report an increase from digitalnumber 20 to 22 in channel MSS-4 due to an increasein the fraction of whitecaps from 5% to 10%. With thespectral transmission curve of the filter and the equiv-alent-radiance resolution,29 the resulting spectral ra-diances are determined to be 37.2 and 40.9 W . m-2 sr-1Mm 1 , respectively. Nadir radiances, calculated for thesun elevation of 53.90, including the different amountof foam as well as the different underlight reported byMaul and Gordon12 but without the efficiency factor,are 42.3 and 50.9 W m-2 sr- 1 Mm-1, respectively. Thatmeans the values are too high and, moreover, they in-crease too strongly with increasing amount of whitecaps.However, if the efficiency factor is used, the calculatedradiances for both of the foam fractions coincide withthe measured values. They are within the digitizationuncertainty of the measured radiances.

A last comparison is made with radiances measuredby CZCS published by Viollier.30 In a clear atmo-sphere, he found an increase of the ocean reflectance of0.02 due to foam from 20 m sec 1 wind. This is in verygood agreement with radiances calculated with thecomplete model, if the efficiency factor is used. It canbe seen from Eq. (1) with data from Table II that thefoam reduces the specular reflection by 11% but givesan additional total reflectance of 0.023, resulting in anincrease of the reflectance of 0.02, as measured.

VII. Conclusions

The effective reflectance of ordinary foam on theocean is lower than the reflectance of fresh, dense foam.In the visible spectral range it was found to be only-22%, nearly independent of wind speed; the efficiencyfactor was determined to be 0.4 which is used, togetherwith the reflectance of fresh foam, to calculate thespectral effective reflectance in the solar spectralrange.

The combination of the effective reflectance (Ref inTable II) with the fraction of the surface covered with


foam [Eq. (3)] gives the wind-speed-dependent reflec-tance due to the total foam coverage (Rftot in Table II)and so the optical influence of oceanic whitecaps on theradiation field over the ocean.

The values of the effective reflectance and the effi-ciency factor have a rather high uncertainty, as do thevalues of the fraction of the surface covered withwhitecaps presented by different authors, due to thewide variation of the data and the subjective judgmentin the analysis. Moreover, the quantities depend onparameters other than just the wind speed, such asfetch, thermal stability, and water temperature. Theeffective reflectance should be determined with moredata in different conditions. Nevertheless, radiancesand fluxes calculated with the results given in this paperare in good agreement with measured values presentedby different authors.

The effective reflectance is more than a factor of 2lower than reflectance values used to date in remotesensing and radiation budget studies. Consequently,the optical influence of oceanic whitecaps can be as-sumed to be much less important than was formerlysupposed.

I want to thank E. Thomalla for helpful discussionsand the crew of the "Nordsee" platform, D. Matthies-Tschernichin and H. Kremser, for technical assis-tance.

Financial support for parts of this research undergrant MF-0235 from the German Minister for Researchand Technology is gratefully acknowledged.

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effective reflectance of oceanic whitecapsvijay/papers/brdf/koepke-84.pdf · a reflectance value...

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