Optical properties of the clearest natural waters(200-800 nm)

Raymond C. Smith and Karen S. Baker

A new UV submersible spectroradiometer has been employed to determine the diffuse attenuation coeffi-cient for irradiance in the clearest natural waters [K;(X)] with emphasis on the spectral region from 300 to400 nm. K (X) can be related to the inherent optical properties of pure water, in particular the total absorp-tion coefficient a,,(X) and the molecular scattering coefficient bm(X), by means of equations derived fromradiative transfer theory. We present an analysis showing that limiting values of K. (X) can be estimatedfrom aw(X) and vice versa. Published a (X) data, which show discrepancies much larger than their estimat-ed accuracies, are briefly reviewed and then compared, via our analysis, with K, (X) data (our own new andpreviously published data as well as relevant data of others). This comparative analysis and new data allowa consistent and accurate set of optical properties for the clearest natural waters and for pure fresh water andsaltwater to be estimated from 300 to 800 nm.

1. Introduction

The optical properties of both pure liquid water andthe clearest natural fresh waters and saltwaters havebeen investigated by numerous authors. Recent criticalreviews of experimental data include those by Irvine andPollack, 1 Jerlov,2 Hale and Querry, 3 Kopelevich, 4

Morel,5 Smith and Tyler,6 and Querry et al. 7 Mostrecently, measurements of the optical absorptioncoefficients of pure water (usually doubly distilled inquartz) have been made in selected regions of the visiblespectrum by Morel and Prieur8 by absorption spectro-photometry, Hass and Davisson9 by adiabatic lasercalorimetry, Querry et al.7 (using deionized filteredwater) by a split-pulse laser method, and Tam andPatel10 by laser optoacoustic spectroscopy.

Most early absorption measurements were made byemploying conventional absorption spectrophotometertechniques. These techniques require careful evalua-tion of the optical characteristics of the transmission celland preparation of water free from contaminant scat-tering and absorbing material. The large discrepanciesamong the experimental data of this early work havebeen noted in the above reviews, and possible reasonsfor these discrepancies are discussed at length.6 The

The authors are with University of California at San Diego, Visi-bility Laboratory-SIO, La Jolla, California 92093.

Received 28 July 1980.0003-6935/81/020177-08$00.50/0.©) 1981 Optical Society of America.

latest data, save for the careful work of Morel andPrieur, involve new techniques that avoid many of theexperimental problems associated with the earliermethods. Thus there is less discrepancy among thelater data, although the agreement is not as good as thepublished accuracies would suggest. As a consequence,there is still uncertainty in the choice of the most reli-able data set.

Researchers concerned with the penetration of solarradiation into natural waters have a keen interest in theinherent optical properties of pure water, since, inprinciple, these inherent optical properties can be usedto calculate the apparent optical properties of theclearest natural waters.2 11 1 2-14 These properties can,in turn, be used to describe quantitatively the maximumpenetration of solar radiation to depths in natural wa-ters for the estimation of a variety of aquatic photo-processes. 15,16

Conversely, experimental values of the apparentoptical properties for the clearest natural waters can beused to estimate theoretically values of the inherentoptical properties of pure water. In the following wesummarize both the most recent and the most reliabledata of the total absorption coefficient of pure wateraw(X), in the 200-800-nm spectral region. By means ofsimple approximations derived from radiative transfertheory, these data are then compared with values of thediffuse attenuation coefficient K(X) determined forthe clearest natural waters. The comparison demon-strates that some laboratory determinations of a(X)are inconsistently large. From our own experimentalKW (A) data, which includes the UV region from 300 to

15 January 1981 / Vol. 20, No. 2 / APPLIED OPTICS 177

400 nm and from the published a (X) data, we haveselected a consistent set of data for the optical proper-ties of the clearest natural waters. This selection pro-vides upper bound estimates for the absorption coeffi-cient of pure water.

the explicit ) dependence unless it is necessary forclarity.)

When discussing natural waters the attenuationcoefficient can be written

c = c + bp + ap + ay,

I. Theoretical Background

The optical properties of the sea can be divided intotwo classes, the inherent and the apparent opticalproperties of the medium. 11 1 2 An optical property isinherent if its operational value at a given point in amedium is invariant with changes of the radiance dis-tribution at that point. Inherent optical properties(IOP) directly specify the true scattering and absorbingcharacteristics of the medium and are dependent uponthe dissolved and suspended material in the water andthe electromagnetic properties of the medium. Theseproperties are of particular practical importance whenconsidering high-resolution image transmittancethrough ocean waters.

An optical property is apparent if its operationalvalue at a given point in a medium is dependent uponthe radiance distribution at that point. Apparent op-tical properties (AOP) can be related to IOP by meansof radiative transfer theory and, like the IOP, are de-pendent on the dissolved and suspended material in thewater in addition to the geometry of the lighting dis-tribution. AOP are of particular importance whenconsidering the penetration of radiant energy to depthsin ocean waters.

The diffuse attenuation coefficient for irradianceK(X) is the AOP that provides the most direct measureof the penetration of radiant energy in ocean water,i.e.,

E(X,z) = E(XO-) exp[-K(X) z], (1)

where E(X,z) is the spectral irradiance at depth z andE(A,O-) is the irradiance just beneath the surface. K(X)is the ocean optical property necessary for the solutionof a wide range of ocean scientific and engineeringproblems, is measurable in situ by appropriate instru-mentation, is directly related to the inherent opticalproperties, 1 2 1 3 and has been shown to be quasi-in-herent. 17

A number of experimental and theoretical studieshave shown or derived relationships between the diffuseattenuation coefficient and the inherent optical prop-erties of natural waters. 2 11-14 18 19 Preisendorfer 12 forexample, derived a set of inequalities and approxima-tions,

c K+ bf >K=D a+ bb >a+ bb >a, (2)

where c = a + b is the total beam attenuation coeffi-cient, a is the total absorption coefficient, b = bf + bbis the total scattering coefficient, b is the forwardscattering coefficient, bb is the backscattering coeffi-cient, and D is the distribution function. All thesecoefficients are a function of wavelength. (We suppress

(3)

where c, is the attenuation coefficient for pure water,bp is the scattering coefficient for particles, ap is theabsorption coefficient for particles, and ay is the ab-sorption coefficient for dissolved organic material(yellow substance).

Optically pure water is defined as a medium that isdevoid of dissolved and suspended particulate material(bp = ap = ay = ). Thus

cw = aw + bn, (4)

where a, is the absorption coefficient for pure water,and bm is the molecular scattering coefficient for purewater. Morel 5 has determined (and reviewed previousvalues for) the total scattering coefficient for both purefreshwater bw and pure saltwater (35-39%o) b as afunction of wavelength. Compared with a (), bm (A)is accurately known.

From the above relations we can obtain the in-equality,

Kf.' 2 aw + '/2bf(m, (5)

where KfW is the diffuse attenuation coefficient for theclearest natural freshwaters (e.g., Crater Lake, Ore.20),and 1/2bf' is the backscattering coefficient for molecular(Rayleigh) scattering in freshwater. Thus, Kf',, = a,+ 1/2bl' represents the lowest experimental value onecould expect to encounter in natural freshwater basedon laboratory measured values of the inherent opticalproperties for pure water.

An analogous argument holds for the clearest oceanwaters if we assume that the absorption of freshwaterand saltwater is the same so that a minimum expecteddiffuse attenuation coefficient for seawater (e.g., Sar-gasso Sea2 ) is

K'mIn = a,, + 1/2bsm (6)

If the salts in seawater cause a weak absorption in theUV region, slowly increasing with shorter wave-lengths,21 22 the inequality corresponding to Eq. (6)holds even more strongly.

A further refinement to Eq. (6) can be made. Thetotal backscattering coefficient for clear ocean waterscan be written

B-b =B-bb +B. b (o) n (7)

where B = bb/b is the backscattering function, and n isan exponent defining the wavelength dependence ofparticle scattering. For the Sargasso Sea bp (515) 0.023 (m-1 )2 3 24 and B 0.044 (Ref. 25) so that

K"ml = a + 1/2 b"' + 0.0010 ()n (8)

The procedure described above for estimating a valueof Kmin from the inherent optical properties can be re-versed by rewriting the inequality, i.e.,

178 APPLIED OPTICS / Vol. 20, No. 2 / 15 January 1981

a,,, K - /2bm. (9)

Thus given experimental values for Kw (X) from veryclear ocean waters a maximum value for a,,(,) can beestimated by setting amax = K - 1/2bm (or K. -B b).In other words, if reliable field data from the clearestnatural waters are available, an upper bound for theabsorption of pure water can be estimated.

Ill. Brief Review of aw(X) Data

Figure 1 presents the results from a selected numberof investigators2 2 2 6-32 from a previous review6 plus morerecent results.7 -1 0 In anticipation of the discussion tofollow, the data of Morel and Prieur8 and Tam andPatel1 0 are indicated by solid and dashed lines, re-spectively. The other data are indicated by symbols asnoted in the figure caption. For this figure we haveconverted cw (X) (when that is what was experimentallydetermined) to a, (X) by means of Eq. (4) using Morel's5

bfw(X) data.Critical observations with respect to Fig. 1 are as

follows: the data agree reasonably well (roughly within+10%) for wavelengths >600 nm; a marked disagree-ment (at some wavelengths nearly an order of magni-tude) among the data exists at wavelengths <600 nm,

in spite of claims of higher accuracies; the recent dataof Morel and Prieur8 (MP) and Tam and Patel'0 (TP)generally agree within ±10% except between 446 and480 nm and between 515 and 546 nm; the other recentdata of Querry et al. 7 are high compared with mostother data for wavelengths less than -580 nm; the fewdata points of Hass and Davisson agree with TP andMP at 488 nm but fall below these workers at 515 nmand below most other data at 633 nm.

IV. Experimental Results [K,(X) Data]

Before continuing a discussion of the laboratory a, (X)data displayed in Fig. 1, we now introduce experimentaldata of the diffuse attenuation coefficient for irradianceobtained at sea in clear ocean waters. Some of thesedata were obtained with the original Scripps submers-ible spectroradiometer, 3 3 whereas our more recent datahave been obtained with a new underwater spectrora-diometer capable of measuring spectral irradiance E(z)throughout the near UV and visible region of the spec-trum. This instrument, designed especially to includethe mid UV region from 280 to 340 nm, and our methodfor determining K, (A) by means of Eq. (1) are describedin detail elsewhere.3 4 3 5

10

E

HzLU

UU-LU0z0a-

0

I-

0H_

1.0

0.10

0.01 _200 800

A, WAVELENGTH [ nm ]

Fig. 1. Total absorption coefficient for pure freshwater [a.(X)(m-1)] vs wavelength [X(nm)I as given by various authors: solid line, Moreland Prieur8; dashed line, Tam and Patel' 0; v, Querry et al. 7; 1, 2, Hass and Davisson 9 ; X, Sawyer2 6 ; +, Dawson and Hulburt 2 7 (200-400 nm)

and Hulburt 2 8 (400-700 nm); A, Lenoble and Saint-Guilly 3 l; 0, James and Birge2 9 ; 0, Clark and James3 0 ; A, Curcio and Petty 40 ; 0, Sullivan3 2 ;*, Armstrong and Boalch.2 2

15 January 1981 / Vol. 20, No. 2 / APPLIED OPTICS 179

400 600

Figure 2 presents K(X) data from various workers forclear ocean water. These data are distinguished bybeing from remote open ocean areas, where the ab-sorption and scattering of dissolved and suspendedparticulate material are very low (e.g., chlorophyllconcentrations of <0.04 mg chl m-3); and the opticalproperties are relatively uniform to depths over whichoptical measurements were made. The solid circles,from 350 to 700 nm, show our determination of K (X)from earlier data obtained in the Sargasso Sea36 asreanalyzed and augmented with data from the sameregion using both the new and old submersible spec-troradiometers. The solid circles from 300 to 340 nmare our data from the Central Equatorial Pacific.16 Thesolid boxes are our most recent data from the SargassoSea, and + and X indicate our recent data from otherclear ocean areas. Also shown in Fig. 2 are Jerlov's K(X)values for his water type I solid v. An early determi-nation of K(310) for clear ocean water by Jerlov3 7 O anda more recent determination by Hojerslev3 8 0 are in-dicated, and a recent value of K(315) by Calkins3 9 isindicated by o. Data of Lenoble 2 ' for clear ocean wa-ters lie significantly above the data shown.

It should be noted that the precision in determining

10

E

U-UI

LL

0C,zZ0

LU

:DLLLLLL

y'

1.0

0.10

0.01 200 400

Kw (X) can be quite good (5% with cooperative envi-ronmental conditions). This is because our opticalmeasurements can be, and generally are made to depthsof several diffuse attenuation lengths KW1(X) by meansof a number of independent determinations of E(z). Aleast squares fit to these independent determinationsof lnE(z) vs depth z provides a precise determinationof

-1 dE(z) -1 E(z2)Kw (A) = - ln

E(z) dz z2 -z 1 E(zl)

The absolute accuracy in determining KW (X) is poorerthan the precision because K (X), being an apparentoptical property, is dependent on the radiance distri-bution of solar energy and hence has a slight functionaldependence with depth even for uniform waters.However, it has been shown17'38 that K (A) displaysquasi-inherent characteristics, showing a relative in-sensitivity with sun angle. Thus absolute uncertaintiesin estimating KW (X), save for very near surface values,are generally less than ±25% even under moderatelyadverse conditions. Given relatively calm seas, a clearsky, and a small sun zenith angle the accuracy in de-termining Kw (X) improves.

600 800

A, WAVELENGTH [ nm]

Fig. 2. Diffuse attenuation coefficient for irradiance [K.(X)(m')] vs wavelength [X(nm)] as determined by various authors for clear oceanwaters: 0, (350-700 nm), present work plus Smith and Baker3 4 ; 0, (300-350 nm) Smith and Baker' 6 ; *, +, and X, present work; 0, Jerlov3 7

and Hojerslev 3 8 ; 0, Calkins3 9 ; v, Jerlov water type J.2

180 APPLIED OPTICS / Vol. 20, No. 2 / 15 January 1981

X00.0$

X 0

.;.004e

O~~~~~~~~~~~~~~~~~ **0 R ~~~~~~~~~~~~~~~0

Xs 4,0~~~~~~~~~~~00

"~~~e x ,.. ~ ~ ~ ~ ~ ~ ~ X..** gOy -@ *v v

I IlI I I

These comments with respect to the accuracy andprecision of KW (X) refer to a source free medium. It isknown that underwater irradiance measurements in theneighborhood of 675 nm detect in vivo fluorescence ofchlorophyll (even for downward irradiance measure-ments) in waters containing moderate amounts ofchlorophyll. As a consequence the simple equationsgiven above do not hold for this spectral region in waterswith high chlorophyll concentrations. For the veryclear water data considered here fluorescence due tochlorophyll is negligible, and the equations are valid.

V. Comparison of a(X) and Kw(X) Data

Figure 3 presents K(X) data derived from severalsources. First, the light dashed curves give variousvalues of K'Mwj(X) derived from the a, (X) data shown inFig. 1 by means of Eq. (6). No attempt has been madeto identify individually these data except those of Moreland Prieur (heavy pluses) and Tam and Patel (heavycrosses). Second, clear ocean water K (X) data aregiven (with the same symbols) as described for Fig. 2.The solid curve is discussed below.

A number of observations with respect to Fig. 3 canbe made: (1) In the 380-700-nm spectral region our

10

IE

H

zLU

C,

ULLLU0

0

LU

LUU-

1.0

0.10

0.01 200

K (X) values, those of Jerlov, and those values ofK"'i,(X) derived from Morel and Prieur are in sub-stantial agreement (25%). Furthermore, these dataagree within this accuracy with the data of Tam andPatel except in the 446-480- and 515-546-nm regions.(2) Most of the remaining data are incompatible withthese data in the wavelength region below 580 nm.Based on the analysis summarized by Eq. (9), we mustsuspect those laboratory data falling significantly abovethe ocean measured values of KW (X) as being system-atically in error. (3) By means of our analysis and thisconsistent data set (our data plus that of Jerlov, MP,and TP), we can estimate a(X) values in the 350-380-nm region where recent reliable laboratory data arelacking. (4) Values of a, (X) estimated in this way (anddiscussed below) for the near UV and the blue region ofthe spectrum are as much as an order of magnitudelower than reported laboratory determinations of a, (X)for both pure freshwater and pure saltwater.22 27'31

In Fig. 4 we present additional K(X) data (from 300to 460 nm) determined for a range of ocean water typesvarying in chlorophyll concentration from 0.06 to 5.0(mg chl m-3). These data are superimposed on valuesof K' n(X) derived from the a (X) data, shown in Fig.

800

A, WAVELENGTH [ nm ]

Fig. 3. Diffuse attenuation coefficient for irradiance [Kmwj(X)(m-') vs wavelength [X(nm)] as derived from various sources: values of Kswn(X)derived using Eq. (6) from a(X) data of Morel and Prieur,8 +, Tam and Patel,10 X, and others (dashed lines) as given in Fig. 1; measured valuesof Kw (X) for clear ocean waters (with the same symbols) as given in Fig. 2; solid curve, our selected estimate of Kw (X) for clear ocean waters

(see text for discussion).

15 January 1981 / Vol. 20, No. 2 / APPLIED OPTICS 181

400 600

10

EI

zLU

UU-

IL

LU0z0

zLU

U-U-

1.0

0.10

0.01 .260 360 460

A, WAVELENGTH (nm)

Fig. 4. Diffuse attenuation coefficient for irradiance [K(X)(m'1)]vs wavelength [(nm)]. Solid curves, measured values of K(X) fromocean waters of different chlorophyll concentrations. Data points,K'M'n(A) values derived using Eq. (6) from a,(X) data given (with same

symbols) in Fig. 1.

1 (and similarly labeled), by means of Eq. (6). Theprimary observation, with respect to this figure, is thatmuch of the laboratory determined a (X) data aresystematically high, with respect to Kw (X) values for theclearest ocean waters and ocean waters containing sig-nificant concentrations of chlorophyll. Based on theresults shown in Figs. 3 and 4 and the analysis presentedabove, it is our hypothesis that laboratory a,(A) data,which lie appreciably above K. (X) data, are probablyin error.

VI. Discussion and Summary

There is need for an accurate and consistent set ofdata for the optical properties of the clearest naturalwaters and for optically pure water. Such a set of datawould help to resolve the present large discrepancies inpublished data and would be useful for a range ofpractical applications. We believe our results plusthose of Jerlov, MP, and TP form an accurate and

X(nm)

200210220230240250260270280290

300310320330340350360370380390

400410420430440450460470480490

500510520530540550560570580590

600610620630640650660670680690

K-(m- 1 )

3.142.051.360.9680.7540.5880.4810.3940.3060.230

0.1540.1160.09440.07650.06370.05300.04390.03530.02670.0233

0.02090.01960.01840.01720.01700.01680.01760.01750.01940.0212

0.02710.03700.04890.05190.05680.06480.07170.08070.1090.158

0.2450.2900.3100.3200.3300.3500.4000.4300.4500.500

700 0.650710 0.834720 1.170730 1.800740 2.380750 2.47760 2.55770 2.51780 2.36790 2.16800 2.07

182 APPLIED OPTICS / Vol. 20, No. 2 / 15 January 1981

Table 1. Diffuse Attenuation Coefficient for Irradiance for Clearest OceanWaters [K.'(X)] and Absorption [a,(X)] and Scattering [b'.(X), b"(X)]

Coefficients for Pure Water

a. (m-l)

3.071.991.310.9270.7200.5590.4570.3730.2880.215

0.1410.1050.08440.06780.05610.04630.03790.03000.02200.0191

0.01710.01620.01530.01440.01450.01450.01560.01560.01760.0196

0.02570.03570.04770.05070.05580.06380.07080.07990.1080.157

0.2440.2890.3090.3190.3290.3490.4000.4300.4500.500

0.6500.8391.1691.7992.382.472.552.512.362.162.07

bm (m-')

0.1510.1190.09950.08200.06850.05750.04850.04150.03530.0305

0.02620.02290.02000.01750.01530.01340.01200.01060.00940.0084

0.00760.00680.00610.00550.00490.00450.00410.00370.00340.0031

0.00290.00260.00240.00220.00210.00190.00180.00170.00160.0015

0.00140.00130.00120.00110.00100.00100.00080.00080.00070.0007

0.00070.00070.00060.00060.00060.00050.00050.00050.00040.00040.0004

bf'(m-1

0.1160.09350.07700.06350.05250.04430.03750.03200.02720.0235

0.02010.01760.01530.01340.01180.01030.00910.00810.00720.0065

0.00580.00520.00470.00420.00380.00350.00310.00290.00260.0024

0.00220.00200.00190.00170.00160.00150.00140.00130.00120.0011

0.00110.00100.00090.00090.00080.00070.00070.00070.00060.0006

0.00050.00050.00050.00050.00040.00040.00040.00040.00030.00030.0003

--

Table II. Diffuse Attenuation [K-w(X)] and Absorption Coefficient [a,(,)] Compared to Total Backscattering Coefficient b",\(X) = B bsw(X) = B-bm(X) + B b,(Xo) * (X/X o) for Zero Particle Scattering (b. = 0) and for Particle Scattering with Wavelength Dependence of n = 0 and n = -1

b X 103 (-1 b"b/s %X(nm) Kw(m-') aw(m' ) 'I2bsw B-b- o) B b- =_) 1/2 b B b"=o) B b

200 3.14 3.07 75.4 76.4 78.0 2.40 2.43 2.48250 0.588 0.559 28.8 29.8 30.8 4.90 5.23 5.23300 0.154 0.141 13.1 14.1 14.8 8.51 9.15 9.6350 0.0530 0.0463 6.73 7.74 8.21 7.03 14.6 15.5400 0.0209 0.0171 3.78 4.79 5.08 18.1 22.9 24.3450 0.0168 0.0145 2.27 3.28 3.43 13.5 19.5 20.4500 0.0271 0.0257 1.46 2.45 2.48 5.31 9.04 9.15550 0.0648 0.0638 0.97 1.98 1.91 1.09 3.05 2.95600 0.245 0.244 0.71 1.72 1.57 0.29 0.70 0.64650 0.350 0.349 0.48 1.49 1.29 0.14 0.43 0.37700 0.650 0.650 0.355 1.36 1.09 0.05 0.21 0.17750 2.47 2.47 0.26 1.27 0.95 0.01 0.05 0.04800 2.07 2.07 0.20 1.21 0.845 >0.01 0.06 0.04

consistent set of data. Table I presents a summary ofour best estimate for this consistent data set, whichgives K"'(X) (also shown as the solid curve in Fig. 3)values for the clearest ocean waters and aw(X), bfw(X),cw(X) for pure water.

The selected K"w (X) values are derived from the fol-lowing: (1) The data of Morel and Prieur from 380 to700 nm. These data are consistent with our own, withthose of Jerlov,2 and with those of Tam and Patel andhave the merit that they comprise a continuous andconsistent data set within this spectral range. (2) Anaverage of the data of Curcio and Petty,40 James andBirge,2 9 Clark and James,3 0 and Sullivan,3 2 payingparticular attention to curve shapes in the 650-800-nmregion. (3) A low limit fit to our own data from 300 to400 nm. (4) An extrapolation of our own data (and thedata points near 310 nm of Jerlov,37 Hojerslev,38 andCalkins39), which follows the shape of Armstrong andBoalch's2 2 data, below 300 nm.

Our estimation of the uncertainties of the selectedKw () curve is as follows: (1) The wavelength regionbelow 300 nm is merely an educated estimate. Becauseof the sharp drop in solar radiation (due to stratosphericozone) near 300 nm, K () measurements using naturalsunlight become increasingly difficult in this wavelengthregion and below. (2) In the 300-380-nm region thereis a spread of 15% between the high and low Kw(X)data. We have chosen the lower limit of these data butrecognize that we could have selected a curve -30%higher. (3) In the 380-480-nm region our data, and tosome extent those of Tam, Patel, and Jerlov, are -30%higher than those of Morel and Prieur. Again a highervalued curve could have been selected. (4) There is amarked change of slope of the data curves in the 515-nmregion. By selecting Morel's data here we are agreeingwith our own work and choosing values -10% aboveTam and Patel. (5) In the region above 580 nm theselected curve is probably on the higher side of a ± 15%spread in the data.

The a () values are derived so as to be consistentwith these selected KsVW(X) values using the bw(X) dataof Morel,5 as extrapolated by a power law fit to his datato longer and shorter wavelengths. That is, we have

derived aw(A) by means of Eq. (6) with the assumptionthat particle backscattering for clear natural waters isnegligible.

Table II presents these K'W (A), aw(X) and the back-scattering coefficient derived in three ways to displaythe consequences of this assumption. In column 4 thebackscattering coefficient is calculated as one-half themolecular scattering for seawater (i.e., assuming bp =0 as for Table I). In the next two columns the totalbackscattering coefficient is calculated according to Eqs.(7) and (8) with n = 0 (column 5) and (n) = -1 (column6). Thus, these columns display the relative magni-tudes of pure water molecular backscattering withoutand with the inclusion of particle backscattering forclear ocean waters. The next three columns in TableII give the ratio (expressed as percent) of these back-scattering coefficients to Kw (X).

From Table II we can conclude that (1) inclusion ofthe particle backscattering coefficient, B bw, to ourcalculations would increase KsW(A) values by -6% in the440-500-nm regions, -4% in the 350-440- and 460-500-nm regions, and only a few percent elsewhere; (2)inclusion of a wavelength dependence (difference be-tween n = 0 or n = -1) for particle scattering wouldmake a negligible difference to our selected Kw(X); (3)inclusion of particle backscattering of our results canbe accomplished by the addition of 0.001 m- 1 [i.e., Eq.(8) with n = 0] at all wavelengths.

While we have distinguished between freshwater andsaltwater when discussing the scattering coefficient wehave not done so when dealing with the absorptioncoefficient. There is strong evidence that there is nosignificant (<10%) difference between aw (X) for fresh-water and saltwater30 32 for wavelengths longer than-375 nm. The evidence for a possible difference atshorter wavelengths is inconclusive: the work ofLenoble21'31 and Armstrong and Boalch22 suggests thatsea salts cause a slowly increasing absorption with de-creasing wavelengths in the near UV region and below;our own Kw (X) measurements as well as those byCalkins3 9 and Hojerslev3 8 plus the aw (X) data of Moreland Prieur8 at wavelengths of <400 nm are inconsistentwith these laboratory results. Because of this uncer-

15 January 1981 / Vol. 20, No. 2 / APPLIED OPTICS 183

tainty we have chosen to rely on our own data in the300-400-nm region. We do not have clear freshwaterdata with which to make a judgment regarding a pos-sible distinction between a(A) and a(X) in thisspectral region. Also it should be noted that if there isa difference in the near UV absorption of freshwatersand saltwaters it would indicate an even greater dis-crepancy between a (A) values estimated from oceandata and the reported laboratory measurements.

In summary, selected data are presented with an ac-curacy estimated to be within +25 and -5% between300 and 480 nm and +10 and -15% from 480 to 800 nm.We stress the continued need for an accurate and con-sistent set of optical data for pure water as well as theclearest natural waters. Table I represents our presentbest estimate for such a data set, and we emphasize theneed for more reliable laboratory measurements atwavelengths below 500 nm.

This work was supported by EPA grant R806-4-89-02for the Stratospheric Impact Research and AssessmentProgram of the U.S. Environmental Protection Agencyand in part by NOAA grant 04-6-158-44033. The studyis also a contribution to the research encouraged by theIAPSO Working Group on Optical Oceanography. Weexpress our thanks to the crews of the R/V Knorr, R/VNew Horizon, and R/V Oceanus, A. L. Chapin and G.D. Edwards for help at sea, and R. W. Austin for usefuldiscussions.

References1. W. M. Irvine and J. B. Pollack, Icarus 8, 321 (1968).2. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968);

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