-Rig? 89 REMOTE SENSING OF ATMOSPHERIC OPIA HWCMs N /

SEA-URTER ATTENUATION. (U) SCRIPPS INSTITUTION OFOCEANOGRAPHY LA JOLLA CA VISIBILITY LA

UNCLASSIFIED T J PETZOLD ET AL JUL 87 SIO-REF-87-18 F/G 2/6 U

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MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARD 1963-A

IEFILE Copy

E SIO Ref. 87.18 July 1987

Remote Sensing of Atmospheric Optical Thickness

and Sea-Water Attenuation when Submerged:

Wavelength Selection and Anticipated Errors

S IMoo10 D T.J. PetzotdR.W. Austin

S A N D I G 0Supportod by:Orflcc of Naval Roaarh

Conutrat N(X)1471-C0556

" Approved~ for -

IuntI A

U Unclassified A ~ ,q oSECURITV CLASSFICATION Of THIS PAGE I

REPORT DOCUMENTATION PAGEI&a REPORT SECURITY CLASSIFICATION lb. RESTRICTIVE MARKINGS

Uniclassif ied Nn21L SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTIONIAVAILAIyITY OF REPORT

2b.OECASSFICTIOIDONGRDIN ~ApprcoVed for publIc release;21L DELASSIICATIN10010distrihG SHEDUL is unlimited

SaPERFORMING ORGANIZATIONREPORT NUMUIER(SI 5. MONMITORING ORGANIZATION REPORT NUMBER(S)

SIO Ref 87-186*& NAME OF PERFORMING ORGANIZATION b. OFFICE SYMBOL 74L NAME OF MONITORING-ORGANIZATION

Uni esity of California, (If APPOC961 ffi Of

6c. ADDRESS (City. Sift and ZIP Code) 7b. ADDRESS (City. Seate nd ZIP Cadet

La Jolla, CA 92093-0703 800 N Quincy St.Arlington, VA 22217-5000

S e. NAME OF FUNOINGISPONSORING SB. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER

Office of 'Naval Research N004N0014-78--C-0556&c. ADDRESS (City. Stoa and ZIP Cod.j 10. SOURCE OF FUNDING NOS. ___________

Dp'ofteNvy, Office of Naval Resac PROGRAM PROJECT TASK IWORK UNIT80 unyS.ELEMENT NO. NO. NO0. No.

4 Arlington, VA 22217-5000 2E0 631 650 NR395-62511.TILE(liddeSecriy ~w~i~ Paij wte Sensin of At nop ic optjicai. j_______

12-PESOAL UTORS)T. J. Petzold and R. W. Austin13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Yr.. Mo.. Day) S5. PAGE COUNT

F inal IF ROM 1 Jl .78 TO 19.wpL 6 1987, July 1 T 8416. SUPPLEMENTARY NOTATION

17. COSATI CODES IS. SUBJECT TERMS lCentinue on mwuera if necemwry and identify by block aumbruiU FIELD GROUP SU.01. GA. ReTmte Sensing, atnxospheric attenuation; sea-waterattenuationi,

19. ABSTRACT IC.. linus on merse if neceaaary and identify by block number)

1,f'Pror analysis and experiimentation has provided strong support for determining the attenuation of optical radiation for theatniosphere and the water colum above a submerged platform by measuring tie absolute downwelling irradiance at twowavelengths. The technique requires ktnowing the two irradiance values x~mdko 1) the spectral irradiance of the sunoutside the anmospherA, (2) the soLar zenith angle and (5) the depth at which the iradianices wre measured.

With this capability in handthe questions considered in this report are which wavelengths to use and the effect of errors in themeasurement of irradiance and other pawres.

S20. OiSTRIBUTIONIAVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION

UNCLASSIFIED/UNLIMITEOI SAME AS RPT. 0 OTIC USERS 0 Unclassified22a. NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE NUMBER 22c. OFFICE SYMBOL

(include A me Codef

Dr. Matthew B. White (617)-451-3172 N00014

DO FORM 1473, 83 APR EDITION OF IJAN 125I OBSOLETE. unclassified ----SECURITY CLASSIFICATION OF THIS PAGE

University of California, San DiegoScripps Institution of Oceanography

Visibility LaboratoryLa Jolla. California 92093

Remote Sensing of Atmospheric Optical Thickness andSea-Water Attenuation when Submerged:

Wavelength Selection and Anticipated Errors

TJ. Petzold and R.W. Austin

S10 Ref. 87-18

July 1987

Supported by:

Office of Naval ResearchContract #N00014-78-C-0556

Approved:- Approved:

Uowe W. Austin. Director Edward A. Friernan. DirectorVisibility Laboratory Scripps histitudont of Ocemography

II

TABLE OF CONTENTSI

LIST OF TABLES AND ILLUSTRATIONS ............................................................................ v

FORW ARD .................................................................................................................................. ix

I ABSTRACT .................................................................................................................................. I

1.0 INTRODUCTION ................................................................................................................. I

2.0 M ETHOD .............................................................................................................................. 22.1 The Forward Calculation ......................................................................................... 221. The Inverse Calculation ......................................................................................... 4

3.0 CONSIDERATIONS IN THE SELECTION OF WAVELENGTHS ............................... 4

4.0 OTHER SOURCES OF ERROR ..................................................................................... 74.1 Radiomemic Error (other than wavelength .................................................................... 74.2 Depth Efor ............................................................................................................... 74.3 Solar Zenith Angle E ror ......................................................................................... 74. Error Inarduced by the Model used for Sea Water Optical Ptpeies ............................... 7A44.5 Solar and Aunospheric Constants ............................................................................ 7

5.0 DIFFUSE ATTENUATION COEFFICIENT OF THE WATER ...................................... 8

6.0 SUM M ARY AND COM M ENTS .......................................................................................... 9-

7.0 RECOM M ENDED W AVELENGTHS .............................................................................. 9

8.0 REFERENCES ..................................................................................................................... 9

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LIST OF TABLES AND ILLUSTRATIONS

TABLE PAGE

Table A Recommended Wavelengths............................................................................ 11

Table B Wavelength error, X,-420, X2.30nm. Maximum error caused by a ±t 2nm offset inIwavelength calibration.............................................................................. 11Table C Wavelength error tar X, and X2 in table. Maximum error causcd by a 2nm offict

in wavelength calibration using XI and X2to obtain greater depth capability ....................... 12

Table D Maximum error caused by a 5% offset in the measured irradiance, Ez(k). at XIorX2Calculated at X.=459nm ............................................................................ 12

Table E Error caused by a I meter offset in depth. Calculated at kc-459nm................................. 13

Table F Error caused by a +5% offset in solar zenith angle, Gs ............................................. 13

Table G Error caused by a ±t5% offset in the solar irradiance, E0Q.L). Calculated at X.-459nm................ 14

FIGURE PAGE

Fig. la Extra terrestrial Solar Irradiance. Neckel and Labs Ref. 5 .............................................. 15

Fig. lb Table showing the effective extra-terrestrial solar irradiance in a l~nm bandcentered at the wavelength in column 1, and the optical depths rR(;L)(Rayleigh or molecular component), c(;L) (ozone), and ta(;) (aerosol).Uniform sensor response over the pass band an @ ta(490) - 0.01 were assumed...................... 15

Fig. 2 Ozone spectral absorption. Data and model ........................................................... 16IFig. 3 Values of K(X) for Jerlov water types 1-1ll and 1 & 2. See Ref. 3 ..................................... 17

Fig. 4 Optimum wavelengths for maximum depth vs K((490)................................................1

Fig. S Depth limit (for 0.2gtw .cm-2 nw-1) vs wavelength when K(490)n0.067m 1 .... . . . . . . . . . . . . . . . . . . . . . . 19

Fig. 6 Sensitivity of proposed method to changes in water type (K(490)) when wavelengthsare X1=480 and X2 -500nm. Depth in example is 100m ............................................... 20

Fig. 7 Same as Fig. 6 except wavelengths are XI-460 and X2a510nm (A;L=50nm) ........................... 21

Fig. 8 Same as Fig's. 6 & 7 except wavelengths are X.l=440 and %2 .54Onm. (AX - 100nm) ................. 22

Fig. 9 Sensitivity to changes in depth with wavelengths X 1 460 and X2-5 IOnm. Water typeK(490).0.067 ...................................................................................... 23

Fig. 10 Same as Fig. 9 except K(490).0.038 .................................................................. 24

Fig. 11 Same as Fig's. 9 & 10 except K(490).0.115 .......................................................... 25

-V.

Fig. 12 Sensitivity to wavelength error. K(490)s0.067, 03 - 30*. Curve iablcd "I for haze,Ta-0 .O. --1.00. Curves labeled "2" for overcast Ta -10-20, X.=0.0. Results shownfor X--459nm and unit air mass. Measurement wavelengths ).LI420, )L2 .490nm.Error +2nm in )L2................................................................................... 26

Fig. 13 Same as Fig. 12 except error is -2nm in 12........................................................... 27

Fig. 14 Same as Fig. 12 except )L=46O. ) 2 =510. Error is +Znm in L2 ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Fig. 15 Same as Fig. 14 except error is -2nm in )L2 ................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Fig. 16 Same as Fig. 12 except K(490).0.248, X1l=420, X2-550. Error is +2nm in ;L2 ...... . . . . . . . . . . . . . . . . . 30

Fig. 17 Same as Fig. 16 except error is -2nm in )L2 .................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Fig. 18 Same as Fig. 16 except )LI=527am, X2 .577nm. Error is +e2nm in .................................. 32

Fig. 19 Same as Fig. 1S except error is -2nm in X2...........................................................3

Fig. 20 Sensitivity to Radiometric error, K(490)=0.022m" 1 , )Xi=420, ;L2 =470nm.Error is -5% in E,()LI). Other conditions as in Fig. 12................................................ 34

Fig. 21 Same as Fig. 20 except )X1.420, )L2 .530am........................................................... 35

Fig. 22 Same as Fig. 20 except K(490)..125................................................................. 36

Fig. 23 Same as Fig. 22 except Xl =420, XL2 -53OnW ......................................................... 37

Fig. 24 Sensitivity to errors in depth of u/w sensor. K(490)ui.038m-1, X1=420, X250

Error is I meter offset in Z. Other conditions as in Fig. 12 ........................................... 38

Fig. 2S Same as Fig. 24 except K(490).0.250m-1 ................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Fig. 26 Same as Fig. 24 except 1% error in Z.................................................................... 40

Fig. 27 Same as Fig. 26 except K(490).250m-1 ................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Fig. 28 Sensitivity to error in solar zenith angle. K(490)-0.038, )Lq- 42 0, )L2w53Onm, es-300.

Error. 5* offset in 9B.......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Fig. 29 Same as Fig. 28 except OS-600....................................................................... 43

Fig. 30 Sensitivity to errors in solar spectral irradiance. K(490)=0.022rn- 1, )L=420, ).2 =470nm.Error: 5% in E0()LI). Other conditions same as in Fig. 12............................................. 44

Fig. 31 Same as Fig. 30 except K(490).0125m- 1 ................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Fig. 32 Same as Fig. 30 except %1lu420, X2.530 ............................................................. 46

Fig. 33 Same as Fig. 32 except K(490)=0125m'l.................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Fig. 34 Sensitivity of K determination to errors in wavelength, K(490).0.067m1 )L1.420, X2 m530nm.Error +2nm in X, (a) Haze ('Ta-0inO.1 -0), (b) Overcast (Ta-1O2O, ot=0).Other conditions as in Fig. 12 ........................................................................ 48

Fig. 35 Same as Fig. 34 except: (a) K(490).0.038m 1 ,. (b) K(490).0.152m1................................. 49

I

I Fig. 36 Sensitivity of K determination to radiometric error. I .420, X. 30nm.Error. -5% in Ez(XLl). (a) K(490)-O.038m"1. (b) K(490).0.152m " 1.3 Other conditions as in Fig. 12 ......................................................................................... 50

Fig. 37 Sensitivity of K determination depth of u/w sensor. ). 1-420, X2 .530.Error. 1 meter offset in Z, (a) K-0.038m" 1, (b) K.0.152m" 1.Other conditions as in Fig. 12 ......................................................................................... 51

Fig. 38 Same as Fig. 37 except +5% error in Z .............................................................................. 52

Fig. 39 Sensitivity of K determination to error in solar zenith angle.es=300, error 50 offset in Gs, (a) K(490)=0.038m"1, (b) K(490)=0.152m "1 .Other conditions as in Fig. 12 ......................................................................................... 53

Fig. 40 Same as Fig. 39 except Os=60 ° . ...................................................................................... 54

Fig. 41 Sensitivity of K determinations to errors in solar spectral irradiance. X=420, X2=530.Error -5% in Eo(.l). (a) K(490)=0.038m"1 , (b) K(490)=0.152m " 1.Other conditions as in Fig. 12 ......................................................................................... 55

I

I

II

I

-.vii-

IFOREWORD

The remote sensing technique which is discussed in this report represents a new capability which couldpotentially have several important applications. The use of the term "remote sensing" we believe is appropriatesince a sensor unit, located at a known depth in the ocean is used (during daylight hours) to determine the opticalattenuation properties of the water above the sensor and of the atmosphere above the water. Knowing the time, date,latitude, longitude, and the extra-terrestrial solar spectral irradiance, (all easily obtained) it is a straightforward matterto compute the ga pith transmittance at a single wavelength, i.e. a single value representing th combined waterand atmospheric attenuation. The problem of determining the two component parts of the attenuation separately wasthe challenge.

Our approach was to make measurements at two or more wavelengths and use these measurements in a set ofequations which can be solved for the separate attenuations. This required models describing how the attenuationcoefficients of sea water and of the atmosphere varied with wavelength for various turbidities. Atmospheric modelsexisted which had been used successfully by the Visibility Laboratory and others to infer and remove the effects ofthe atmosphere on the water-leaving radiances arriving at the Coastal Zone Color Scanner satelite sensor. Simplifiedversions of these atmospheric models worked satisfactorily. The problem was that there was no existing comparableanalytic model for seawater. The often quoted and used water types of Jerlov are described by a table of attenuationvalues specified at 25nm intervals throughout the visible spectrum for 5 oceanic and 5 coastal water types. Todevise a model around the Jerlov table would have required fitting analytic functions to his attenuation values,putting the model another step removed from the actual data set upon which the table was based. Furthermore wehad available to us a large and high quality data base of spectral irradiance profiles which had been obtained byinvestigators at the Visibility Laboratory, in France at Prof. Morel's laboratory, and by Okami and his colleagues inJapan. These data, which were obtained in a wide variety of oceanic and coastal waters, were acquired at wavelengthintervals of approximately 5 nm thus permitting a better representation of the shape of the spectral attenuationcoefficient in the resulting model. That model, described in Austin and Petzold, 1984 (Ref. 2 and Appendix 2,attached), allows the complete specification of the diffuse attenuation coefficient at all wavelengths in the visiblespectm, given the value of the coefficient at any one wavelength in that spectral region.

The technique which was developed uses that analytic model for the spectral attenuation of the water and theresults have been very promising indeed. This report describes the technique and examines the errors that might beexpected due to errors in radiometric calibration, wavelength assignment, depth, solar zenith angle, and in solar andatmospheric constants. It also addresses the matter of optimum wavelength selection. A subsequent report willprovide an evaluation of the technique using data sets obtained from various cruises on surface ships. Among theapplications we see for this remote sensing technique are the following.

* The determination of the amount of attenuation above a submerged sensor from a set of measurementsmade at a single point in time and space. Separate determinations of the amount of attenuation due to thewater and due to the atmosphere are provided.

• A rather precise assessment of the mean diffuse attenuation coefficient, K, from the ocean surface to thedepth of the sensor can be obtained on a continuous basis.

• The technique is particularly useful for applications involving installations on towed sensor systems andon unattended buoys or bottom mounted sensor systems.

For the genesis of this technique we must credit Dr. Matthew B. White of the Office of Naval Research. It washe who asked the critical question: "Isn't there some way you can determine, using a submerged sensor, the separatelosses due to the water and to the atmosphere without moving the sensor vertically? Perhaps use more than onewavelength." or words to that effect. With that challenge we have proceeded to develop the Submerged Remote

VSensing (SRS) technique together with the required water attenuation model, both of which potentially haveimportant future applications.

R.W. Austin

-iX-

14

III

REMOTE SENSING OF ATMOSPHERIC OPTICALTHICKNESS AND SEA-WATER ATTENUATION WHEN SUBMERGED:

WAVELENGTH SELECTION AND ANTICIPATED ERRORS

TJ. Petzold and R.W. Austin

Prior analysis and experimentation has provided strong support for determining the attenuation of optical radiation for theatmosphere and the water column above a submerged platform by measuring the absolute downwelling irradiance at twowavelengths. The technique requires knowing the two irradiance values and in addition (1) the spectral irradiance of the sunoutside the atmosphere, (2) the solar zenith angle and (3) the depth at which the irradiances are measured.

With this capability in hand the questions considered in this report are which wavelengths to use and the effect of errors in themeasurement of irradiance and other parameters.

S 1.0 INTRODUCTION

The concept and theory for the determination of the optical properties of the atmosphere above the ocean's surface fromspectral measurements of the natural light made below the surface was presented in detail in Ref.l*.

One requirement to achieve a solution is that there be a known spectral relationship between the diffuse attenuation~ coefficient, K() for at least two wavelengths which is valid for the various "types" of natural waters found in open oceans.

Preferably, a way of relating K(Q) for all wavelengths over the range of interest would allow flexibility in the choice ofwavelengths at which to make the measurement. From the results, the K(X) at any other wavelength, within the rangecovered, could be determined. A study of a large body of spectral K(Q.) data obtained by several investigators has yielded aI model which can be used for these purposes. The model and its basis are presented in Ref. 2.

The scheduling of a field experiment prompted asking the question of what wavelengths to select. Five photometers wereavailable for this experiment and as a result five wavelengths were selected. Unfortunately, there is not a straightforwardanswer that is "best" for all situations. The "type" of water is critical to the selection of wavelengths and since this isunknown the selection must be based on predictions of the type of water expected. The effect of errors, particularlyphotometric, has played a large role in the wavelength selection. If the photometric measurements could be made withouterror, then the criteria for wavelength selections could be, by and large, those that would allow useable results to be acquiredat maximum depth. Perversely, the use of wavelengths which would allow the system to perform at greater depths tend tomake the system very sensitive to photometric error. As we gain more field experience and develop more precise and stable

S radiometers for this application, we can expect to obtain greater depth capability.

*Ccpf ofRd. 1. and 2 a ppdedodo mspat% %

-I-*ii

2.0 METHOD

Using our knowledge of the optical characteristics of the atmosphere and seawater it is possible to compute, for a given

wavelength, X, the transmission of light downward thro,,-h the atmosphere, the air-water interface, and through the water tosome depth, z, for a given set of conditions. Using known values for the spectral irradiance from the sun outside theatmosphere, Eoa), we can obtain an estimated value for the downwelling irradiance at depth z, E,(.), for any wavelength forthe given set of conditions. This is done at two wavelengths to produce a pair of irradiance values E,(X1), 2 Then, usingonly these values, the procedure given in Refs. I & 2 is used to perform the inverse computation to calculate the diffuseattenuation of the water, K(X), and the optical depth of (or transmission through) the atmosphere at either of the wavelengths.These computed attenuation values are then compared with the original given or "true values" to get an estimate of themagnitude of error. This is the error which exists for a perfect system and results from assuming for the inverse computationthat the optical properties of the aerosols in the atmosphere are not wavelength dependent This assumption is necessary toenable the solution from measurements at two wavelengths.

Other sources of error will be present in a real system due to such causes as radiometric accuracy, errors in the values used forthe solar input, solar zenith angle, depth measurement, etc. Offsets commensurate with those types of errors have beeninserted into the calculations to find the sensitivity of the system to each of those sources of error.

Note: In the figures which follow the "true" values are indicated by a straight solid line, the computed values for a perfecttwo wavelength system are shown with a diamond (0) symbol, and the results of applying an error to some particularparameter are plotted using (+).

2.1 The Forward Calculation

The two values for E(XI) and E().o are determined as follows:

For values of (I) :1 the transmittance for irradiance through the atmosphere is taken to be

TA (X) = exp - [.48-TR(X) + TOOL) + 0.5(1-g)a(X)]/po (1)

whereX indicates wavelength

TA(X) is the total path transmission through the atmosphere

po is the cosine of the sun's zenith angle

TR(X), To(X), a (X) are the optical depths for unit air mass due to:air molecules (Rayleigh scattering),ozone absorption, andaerosols respectively

g is an asymmetry factor for aerosol particles and isapproximately equal to 2/3.

The transmittance for irradiance through the water column is

Tw(L) = e-K0X)z (2)

where

K(X) is the diffuse attenuation, andz is depth of water over sensor.

"See Ref. 5

.2.

Iif A value of 0.98 is used for the irradinace transmittance through the air-water interface for all wavelengths. While this is not

strictly true, any variation from this value will not be large and would have a very small effect upon the final results.

The irradiance at depth z is then:

Ez(.) - 0.98- TA(X) •Tw(.) Eo(X) . (3)

where

Eo(X) is the solar irradiance outsidethe atmosphere at a nominal wavelength Xand over the band width of the sensor.

In this simulation two wavelengths are selected and a spectral bandwidth is chosen for the radiometric measurements. Theradiometric response is taken to be uniform within this band width. In a real system the spectral response of the radiometerswill have to be carefully determined and the mean, or effective wavelengths calculated. Also it will be necessary to calculate

~ the proper effective values for the spectrally dependent parameters used such as E,(%).

The value for Eo()) was obtained from the work of Neckel and Labs Ref. 4. Figure I is a plot of these data. The dataS fluctuate markedly with wavelength and can not be represented by simple curve fitting procedures. Therefore, EoQ.) is

calculated by interpolation at one nanometer increments over the passband and the average value used.

S The Rayleigh (molecular) optical depth, TR(X), for diffus propagation of light through the atmosphere varies very nearly withthe inverse fourth power of wavelength and is calculated using

clt(;L) - 0.044070).4 .

The effective value, XR()-over the pass band .t to X2 is:

=TO- -0.044(X2 -L,5)' • , d , - 2.956 10' (X_ 1t)-. 0' - A,2' (4)

S The work of Klenk et a, Ref. 3. is used to find the spectral absorption coefficicent for ozone as a function of latitude andseason. Figure 2 shows the spectral data (+) and a function curme which adequately describes the absorption per unitatmosphere - centimeter, ( alatm-cm). The total spectral absorption coefficient may be found by multiplying these values by

I "total ozone" which is a function of latitude and season. A value of 0.300 atm-cm was used as representative for mid-

latitudes. The optical depth ;(X) is taken to be equal to the total absorption coefficient and may be calculated from:

ro(X) = 0.300. 0.13879. e-A() (5)

A - 0.0014717 . (I;X - 589.751)1 .5301. (6)

Whe the effective value, T over the pass band X, to X2 is

TOO) -(A2 -;.0" 1 f o(X) • d. (7)

-3-

The summation is done at one nanometer increments over the bandwidth and the average value used for %o(.)

The optical depth for the aerosol, ?a(X) has a spectral dependency which appears to follow the power law

'CAO = (X/X,)-• ( , .1 (8)

The exponent, a, known as the Angstrom exponent, is dependent upon the amount and quality of the aerosol. It falls in therange of 1.1 to 1.4 for clear atmospheres and, approaches zero for very large aerosols (fog, overcast).

Two types of atmosphere are used for illustration purposes, as follows:

Number Type IDesignation Designation Ta(4 9 0) a

1 Haze 0.10 1.02 Heavy Overcast 10-20 0

For the "Heavy Overcast" case, the term 0.5 (1-g) ;,(X) in Eq. (1) for transmittance (see Section 2.1) does not hold true. Thetransmittance of diffuse light is nearly spectrally independant for a heavy overcast consisting of fog or complete cloud cover.For this case the transmittance of diffuse light through the aerosol is taken to be 10% and the constant 2.3 i.e. -In 0.1, issubstituted for the term involving ;(T.).

In some of the figures the number(s) appearing on the right side are the number designation for the type of aerosol for whichthe information displayed applies.

The calculations used to obtain the irradiance values at the two wavelengths at depth z, viz. E(X.) and E(X2) and then using* only these two values to estimate the atmosphere and water properties, require that a relationship exist between the diffuse

attenuation coefficients, K(X.), of the water at these two wavelengths. For the forward calculation, i.e., propagating the lightdownward, a "type" of water must be selected. The value of K(490) is used to specify the water type and from this, values forK (X ) and K (X2) may be calculated using the model and procedure presented in Ref. 2.

2.2 The Inverse Cakulation

The model from Ref. 2 is also used to obtain the function relating K(XI) and K%) required for the inverse solution to theproblem, given only E.(XI) and E(k).

Neither of the wavelengths X, or X2 at which the two irradiance measurements are made needs to be at the wavelength forwhich we would like to know the atmospheric and water optical properties. To estimate the diffuse transmission of lightthrough the atmosphere at some other wavelength, X3, we may use the same approximate assumption used to enable the

* inverse solution of the problem which is that the optical depth of the aerosol, %(X), is independent of wavelength, hence,%(LI) =r,(X,) - ',(X). In effect the calculated t,(X) applies equally well at any wavelength. The erro, caused by thisassumption is not large enough to preclude the usefulness of the procedure. Using Eq. (4) and (5) we can calculate rRa() and?.(X3). From Eq. (1) for diffuse atmospheric transmittance and using the approximation that the aerosol term is constant wecan derive:

TA(W) -TA(L) • exp - [ .48['C(X) - a T)]L + 'Co(3) - TC.M) }(9)

Thus we can obtain an estimate for the vertical diffuse transmittance through the total atmosphere at wavelengths other than

the measurement wavelengths. For the water we can find K(X.) from K(Xt) or K(X2) using the model for K().

3.0 CONSIDERATIONS IN THE SELECTION OF WAVELENGTHS

Two criteria were considered in making the wavelength selection. The first and most obvious was to achieve maximum depthat which the radiometric measurements can be made. The second was to minimize the sensitivity to system error. The best

-4-

pair of wavelengths to use is highly dependent on the type of water for both of these criteria. The wavelengths which mightbe chosen for use in clear waters would not be a good choice for more turbid waters. Also these two criteria are notcompatible. Using wavelengths to achieve maximum depth capability can result in the system being very sensitive toradiometic error, particularly those induced by wavelength calibration, and using wavelengths which minimize sensitivity tosystem error will lessen the depth at which the radiometric measurement can be made.

It is felt, at this time, that the second criteria should be dominant in the wavelength selection, i.e, do the best we can toenhance the probability of acheiving good results. After it has been demonstrated that the radiometric measurements can bemade with the precision required to obtain satisfactory results over the long path lengths and high attenuations involved, thenwe can work toward greater depth capability.

To illustrate the effect of wavelength selection on sensitivity to radiometric error, water with a diffuse attenuation coefficientof K(490) = 0.067 (Jerlov Type II) will be used. If we are trying for greatest depth capability we should choose wavelengthsin the region where light penetration is the greatest. Figure 3 shows typical values of K(.) plotted as a function ofwavelength, X, for seven Jerlov water types. Figure 4 shows the "optimum" wavelength, i.e., the wavelength at which theminimum K(.) occurs, for water types in the region from pure sea water, K(490) = 0.022, to K(490) - 0.250. Consideringonly the water transmission properties we find that for water with a K(490) - 0.067 the "optimum" wavelength is in theregion of 489nm and we would select two wavelengths on either side of this value. Figure 5 gives, as a function ofwavelength, the depth at which the downwelling irradiance is 0.00021LW • cm-2. nm-l*.

This somewhat arbitrary number allows depth limit computations which are useful in wavelength selection. Ideally, in a"balanced" system both photometers would run out of adequate signal at the same depth. Figure 5 helps in the selection oftwo wavelengths in an attempt to acheive this, for water with a K(490) - 0.067. The solar input outside the atmosphere,EoQ.), and the diffuse transmittance through the atmosphere are included in the computations used for Fig. 5. The spectralsolar irradiance, Eo(X), and the effective spectral diffuse optical depths, TR(X) (Rayleigh), %(ozone), and ;,(aerosol) are all, inthis case, computed over a l0nm pass band. Also a clear air case has been used with ,(490) being set to be 0.01 and the sunis at the zenith.

If the separation between the wavelengths selected is not large enough, the system will be insensitive to the spectralproperties of the diffuse attenuation coefficient, K(X), of the water and poor results will be obtained. For a separation of20nm Fig. 5 indicates that 480 and .0nm are nearly "balanced" wavelengths for K(490) - 0.067 type water. The sensitivityof measurement at these two wavelengths to change in water type, K (490), is demonstrated in Fig. 6. The value "Q" is a"figure of merit" where:

Q - 2.3026. [log R2 - log R1]/[K(490)2 - K(490)1] • z (10)and

R - Ez(X2) / EzO.1) . (11)

The statement "if AK(490) -. 001 then AR = 1.019" in Fig. 6, indicates that a change in K(490) of .001 will result in achange in the ratio of the irradiances, R - E,(500YE5(480), at depth z (100 meters in this case) of 1.9%. It can also beinferred from this that an error in the determination of the ratio, R, of 1.9% will cause, approximately, an error or .001 in thecomputation of K(X). In a similar manner but using wavelength separations of 50 nm and 100 nm, the results shown inFigs. 7 & 8 are obtained. It is seen that increasing the separation markedly improves the sensitivity to change in the waterquality. This improved performance comes at the cost of depth capability. Again using Fig. 5 we can estimate the depthlimitation; i.e., the depth at which the irradiance, E5(X), arriving at one or both photometers is 0.00024LW cm- 2 . nmt'.To summarize:

For Water Type K(490) - 0.067

Sensitivity Approximatechange in DR with Depth Limitation

l(m) Vll(nm) 0.001 change in K( 49 0 ) (meters)

480 500 1.019 200460 510 1.049 180440 540 1.092 160

The is t. level ; %1hidh a phlrtom employin a hil quality photomultiplier tue having an iradiance collector with a 3/4 inch dianate, a baud pm of IOam, and aUseimaguseUihr9 Uh optical pe of 1%, mnSltbe mpeced to have a signal to Doug rio in cee Often.

-S-

The above selection process could be used to obtain maximum depth capability for any one water type. Using 460 and510nm, Fig. 9 explores how the E,(460) and E,(510) values and their ratio would change with depth in K(490) - 0.067 typewater. Since K(460) = 0.0759 and K(5 10) = 0.0739 are not greatly different, the ratio does not change much with depth.Figures 10 and I I are similar, using the same two wavelengths, but in water types K(490) = 0.038 (Jerlov Type IB) andK(490) = 0.115 (Jerlov Type I). Note that the arbitrary irradiance limit of 0.0002gw • cm2 nm- is reached at a depth ofabout 100 meters at X-460nm when K(490) - 0.115 and has not been reached at 200 meters when K(490).0.038.

The selection of wavelength based on the second criteria, minimum sensitivity to system error (primarily wavelength), leadsto a different set of wavelengths and some loss in depth capability. By wavelength error is meant the difference between thewavelength at which we think the radiometer is making the measurement, (the assigned wavelength used in thecomputations), and the actual effective or mean wavelength to which the radiometer responds. For instance if the radiometer'seffective response was at 492nm and we used 490nm in the calculations the wavelength error would be -2nm.

To acheive minimum sensitivity to wavelength error we must find a wavelength where K(k) (and to a much lesser extentE0(X), RL(X), To(X) and ,(X)) is not changing rapidly with wavelength over the channel band width. We also need to do this attwo wavelengths which are far enough apart and in regions which will give good responsivity to the quality of the water.Observation of the K(X) vs X curves, Fig. 4, is helpful in the selection for this criteria and also shows the difficulty in such aselection. Certainly the selection of the "optimum" pair of wavelengths is highly dependent upon water type.

To illustrate the difference in sensitivity to wavelength error between wavelengths selected with this in mind as opposed towavelengths selected to obtain maximum depth capability, the use of wavelengths 420 and 490nm will be compared with 460and 510nm when the water type is again K(490)-0.067. In the figures starting with Fig. 12, the solid lines are the "true"

* •values; the points indicated by diamonds (0), are values which would be calculated if the system were perfect. i.e. had noerrors including the values used for E0 (X), R(X) and ;(X); and crosses (+), are values which would be calculated if the errorshown in the heading under "error factors" is introduced. The small error of the "perfect" system is due to the assumption,made to allow the inverse problem to be solved, that the diffuse transmission properties of the aerosol, -%(X) are spectrallyindependent, i.e. ;,(X) is the same at all wavelengths. Two "types" of aerosol are used: (1) haze, T,(490)-0.10 and cx-1.00,and (2) overcast ,(490)-10-20 and ct-0.00. The type of aerosol is indicated on the graphs by the numbers 1,& 2 on the righthand side. In all cases 30' is used for the solar zenith angle and l0nm for the radiometric bandpass. Frequently we would liketo know the atmospheric and water attenuations at a wavelength other than either of the two at which the measurement ismade. In these figures two wavelengths have been used for the measurement wavelengths, the problem solved at one of thesewavelengths, both with and without the applied eiror, and then the results transferred to a third "wavelength of interest" A, viathe model(s). The figures have three graphs: (1) transmission through the total atmosphere. This is the verticaltransmission, i.e. for unit air mass. It is shown for both atmospheric types. (2) Logarithm of the transmission through thetotal path. This is the vertical transmission through the atmosphere, the air-water interface and the water column. It isshown for both atmospheric types. (3) The ratio of the calculated transmission to the true transmission for the total verticalpath. It is shown for one atmospheric type*. All of these values are plotted as a function of depth, and are the resultsobtained for the third wavelength, the "wavelength of interest".

In Fig. 12 the photometric measurement wavelengths are 420 and 490nm and the wavelength of interest is 459nm. A* wavelength error of +2nm has been applied to the photometric measurement at X2(490nm). The problem is solved to obtain

the results at 490nm and the values for X-459nm calculated. To calculate the effect of the applied error, values indicated bycrosses (+), the problem is solved using 492nm, the erroneous wavelength, in place of 490im, the true wavelength. Figure13 is a repeat of Fig. 12 except that the error applied to X2 is -2nm. Figuresl4 and 15 show the effect of the same wavelengtherror offsets when 460nm and 510nim, the wavelengths arrived at previously to obtain greater depth capability, are used for themeasurement wavelengths.

Oi

Comparison of Fig. 12 & 13 with Fig. 14 & 15 demonstrates that the sensitivity to wavelength error is highly dependent on

wavelength selection. The penalty for lower wavelength sensitivity is loss of depth capability. In this case the depth limit,

(K (490)-0.067 type water and again using 0.0002gtW • cm-2 • nm-1 for the photometer's limit of sensitivity), is about 140meters at 420nm when 420nm and 490nm are used and about 180 meters when 460nm and 510nm are used. This sensitivityto wavelength error becomes even more drastic in more turbid waters. Figures 16 through 19 is another case with the samemagnitude of wavelength error applied for water type K(490)-0.248 (Jerlov Type 2). For maximum depth, 527nm and577nm would be used (Fig. 18 & 19) and the depth limit would be about 64 meters. For the other wavelengths used, 420 &

I"M =ft pimmiad ha way am newly identl for all amophac typs.

-6-

BS 550nm, the depth limit is about 33 meters (see Figs. 16 & 17).

4.0 OTHER SOURCES OF ERROR

4.1 RADIOMETRIC ERROR (other than wavelength)

S Two measurements of the absolute downwelling irradiance at some depth, z , are required. An error in these measurementsproduces a corresponding error in the determination of the atmospheric and water diffuse attenuation properties. Theradiometric error is the sum of the error in calibration, drift in sensitivity with time, and change in sensitivity withtemperature. The effect of this error is a function of the two wavelengths used and in general is lessened by increasing theseparation between the wavelengths. This is illustrated in Fig. 20 where XI,420nm and X2t=470nm, the water is pureseawater, K(490)=0.022, and an error of -5% is applied to the irradiance measurement at XI; and in Fig. 21 where the sameerror is applied but the wavelengths used are 420nm and 530nm. Figures 22 & 23 are similar to Figs. 20 & 21 but for water

S type K(490)=0.125. The effect of this type of error is independent of depth and essentially independent of water type.

4.2 DEPTH ERROR

S A one meter offset in the depth value used in the computations will cause the errors shown in Figs. 24 & 25 for water typesK(490)=0.038 and 0.250 respectively. The errors caused by a 1% non-linearity in depth are shown in Fig. 26 & 27 for the

I same water types. In all cases 420nm and 530nm were used for the two photometric wavelengths. An offset produces errorsin TA, total atmospheric transmisssion, and T, total transmission atmosphere and water, which quickly reach an asymptoteand become essentially independent of depth. A non-linearity, of course, produces an error which is proportional to depth.

I! ,4.3 SOLAR ZENITH ANGLE ERROR

The error caused by using an incorrect zenith angle, 0, for the sun is a function of the cosine of the zenith angle. It is smallfor high suns, (small zenith angle) and large for low suns, (large zenith angle). Two examples ae given in Figs. 28 & 29 for0.=30 and 0,=60' both with an applied error of +5'. This error is independent of depth and water type.

4.4 ERROR INTRODUCED BY THE MODEL USEDFOR SEA WATER OPTICAL PROPERTIES

To use this system it is necessary to use a relationship which allows the determination of the diffuse attenuation coefficientof the water at a second wavelength, K(X2), from knowledge of the value at some other wavelength, K(,I) (Ref. 1 & 2). Forflexibility it is most desirable that this can be done between any two wavelengths within a span of practical values. The

S model used for this pupose is presented in detail in Ref. 2. To obtain good results over the long water path lengths desired,it is necessary to determine accurately the K(X) values involved. The prospect of doing this depends to a large extent on howwell this model matches the spectral character of the water in which the system is being used. The data on which the modelis based is not very precise. It is subject to usual experimental errors and adversely affected by difficult, at sea, environmental

S operating conditions. It can be hoped that the fairly large data base used in forming the model, resulted in statisticallysignificant smoothing of the data base and that the model is satisfactory for this application.

S The correctness of the model and the uniformity of fairly clear deep oceanic water such that the model will match all suchwaters can only be determined by future experimentation and testing. The model remains a potential source of error, themagnitude of which, at this time, is unknown.

4.5 SOLAR AND ATMOSPHERIC CONSTANTS

S The sun is used as a known source of irradiance outside of the atmosphere. The absolute spectral level of this irradiance,E, ,). is a primary input for this system. Much effort has been put into determing the correct values for this spectral solarirradiance. It is believed the values of Neckel and Labs (1981) are correct within approximately one percent. However, this

.7.

must be considered a potential source of error. Figures 30 & 31 show the results of a +5% error in EQL) at 420nm using420nm and 470nm for the measurement wavelengths. Figure 30 is for pure sea water, K(490)-0.022 and for Fig. 31K(490)=0.125. Figures 32 & 33 are for the same water types and error offset but 420nm and 530nm are the wavelengthsused. This type of error is independent of depth and water type and has less effect, at least on the atmospheric transmissioncalculated, when the wavelengths used are farther apart

5.0 DIFFUSE ATTENUATION COEFFICIENT OF THE WATER

The ability to determine the effective diffuse attenuation coefficient, K(.), of the water at any wavelength of practical interestfrom the measurement of downwelling irradiance at two wavelengths is a significant secondary objective of this type ofsystem. Examples are given, all using 420nm and 530nm for the measurement wavelengths and the results shown for thecomputed K(A) at 459nm. The computed K0.) vs depth for water type K(490)=0.067 with an applied error of 2nm atX.(420nm) is shown for two types of atmosphere in Fig. 34. Figure 35 has the same error applied at 420nm but for watertypes K(490)=0.038 and K(490)-0.152 with atmosphere No. 2 (overcast). Figures 36 through 41 all show examples usingthese same two water types. In Fig. 36, the error applied makes the irradiance measurement at 420rum low by 5%.Figure 37 has a depth offset error of +I meter at all depths and Fig. 38 has a depth non-linearity of +5%. The effect of a +5*error in the solar zenith angle is shown in Fig's. 39 & 40; with the "true" zenith angle 30* in Fig. 39 and 60° in Fig. 40.Figure 41 has an error of -5% in the assumed solar irradiance at 420nm.

When a fairly long path length is used (2-4 attenuation lengths; transmission about 2 to 10%), the theoretical computationsproduce, even with these applied errors, values which are closer to the real value than can be expected from the usual in-situmethods normally employed to get this type of data. How well this works in the real world needs to be determined. Theaccuracy of the K(.) calculated is subject to degradation by all the errors discussed in previous sections. It is largely the errorinvolved in determining K() which will cause an eror in the calculated atmosphere and water path transmissions.

6.0 SUMMARY AND COMMENTS

Wavelen Selectin - There are two consideration in selecting the two wavelengths: (1) maximum depth at which thephotometers will have adequate signal and (2) sensitivity of the system to radiometric and other error sources. These twocriteria do not lead to the same wavelengths. Selection of "optimum wavelengths" to satisfy one has an adverse effect on theother and both wre highly dependent on the type of water. There is no one "best choice". The choice is a matter ofcompromise, judgement and pratical considerations. Large separation between the wavelengths in most cases will improvesystem performance.

Radmetry - If adequate system performance is to be achieved, good radiometric calibrations and stability are required. Theabsolute responsivity, linearity and "effective mean wavelength" for both radiometers must be known. The radiometers needto be stable with respect to time, environment, and temperature. The spectral filters may degrade with time and thesensitivity of the radiometer may change. This suggests that periodic "re-calibration" should be done. The sensor,particularly if a photomultiplier tube, may suffer a change in spectral response with changes in temperature. Some methodmay be required to stablize or correct for such changes in sensitivity. A stable internal reference light source could be used tocorrect the readings for changes in sensitivity.

Ero - The system can be very sensitive to wavelength and the wavelength at which the measurements are made must beclosely known to avoid possible large errors. Absolute radiometric error has less significance if both radiometers are in errorin the same direction. The inherent error of the two wavelength system is small relative to the probable error caused by othersources such as radiometric measurement accuracy, the values used for the other inputs, and the fidelity of the K(') modelused.

ater B=Sia - The system can be a useful tool for the determination of the spectral diffuse attenuation properties ofnatural oceanic waters.

Atmsjg- It appears that an estimate of the optical depth of the atmosphere can be obtained which is adequate forassessing the total atmospheric transmittance loss.

-8-0

Totl Tranmision- When the total spectral diffuse transmission, i.e., the transmission through the total atmosphere, the air-water interface and the water path, is examined, it becomes apparent that for any appreciable water path (i.e., depth) theattenuation through the water is predominate over the loss in the atmosphere. In estimating the total attenuation it appearsthat this type of system may produce very satisfactory results.

Final Cmment - The inherent error in the computations which results from the assumption that the portion of theatmospheric attenuation caused by the aerosol is constant at all wavelengths is very small. For atmospheres which are not

cloudy, heavily overcast, or foggy (a<l), the term for the aerosol in Eq. (1) for the atmospheric transmittance given insection 2.1. i.e. 1/2 (l-g)r,(.) is approximately 1/6 • ;a.) and has a minor effect on the results. For aerosols of greaterdensities a is very small and the aerosol attenuation though large is essentially independent of wavelength.

All that has been presented in this report assumes perfection, other than for the errors intentionally introduced. In a realsystem the final results will be the summation of all sources of error. The goodness of the match between the K(X) watermodel and the actual waters is a source of error the magnitude of which is yet to be determined.

7.0 RECOMMENDED WAVELENGTHS

For a field test, five photometers were available allowing the choice of five different wavelengths. Two of those photometershad a linear response with auto-ranging. The remaining three had a pseudo-logrithmic response.

Using the approach presented in this report, five wavelengths were selected: 420,470, 490, 530, and 550nm with 420nm and530nm assigned to the linear photometers. Table A gives the selected combinations and lists the water types for which it isrecommended these wavelengths be used. The first choice for wavelength pair is 420 and 530nm. Table B gives an estimateof certain errors that might be anticipated for a 2nm wavelength calibration offset, when using these two wavelengths in fivedifferent types of water. Table C gives the second choice of wavelength pairs which could be used to increase depthcapability. Again the same estimates of error are given for the five types of water. The error values in Table C can bedirectly compared with the values in Table B where 5-4S9. Tables B and C also give the depth limits which can beanticipated for the various pairs of wavelengths.

A photometric error of 5% in the measurement of the irruiance, E,(X), can cause the resultant errors shown in Table D for thevarious recommended wavelength combinations. Similarly the effect of a I meter offset in depth is shown in Table E. TableF gives the errors which can result from a +5% offset in solar zenith angle. This eror can be severe for large zenith angles(low sun). The errors indicated in Table G can result from a 5% error in the value used for Eo(L), the extra-terrestrial solarirradiance arriving outside the atmosphere.

Table H is a listing of the solar irradiance, Eo(ltW • cm-2. nm-t), outside the atmosphere and the optical depths TRQL)(Rayleigh), ro().) (ozone) and %()L) (aerosol); calculated a discussed in this report. A 10im bsndpass, uniform responsefrom X.-5nm to X.+Snm and a value of ?,(490)uO.01 (clear atmosphere) was used.

8. REFERENCES

I. Petzold, TJ. (1983), VisLab Tech Memo EN-001-83:, University of California, San Diego, Scripps Institution ofOceanography, Visibility Laboratory.

2. Austin, R.W. and TJ. Petzold (1984), "Spectral dependence of the diffuse attenuation coefficient of light in ocean water",Proc. of the SPIE, Ocean Optics VII, Vol. 489, pp. 168-178, Monterey, California.

3. Klenk, K.F., P.I. Bharia, E. Hilsenrath and AJ. Fleig, "Standard ozone profiles from balloon and satellite datasets, Journal of Climate & Applied Meteorology, December, 1983, Vol. 22, #12, pp. 2012-2022.

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4. Neckel, H. and D. LAWs. -Improved data of solar spectral irradiance from 0.33 to 1.25sL". Solar Physics, Vol. 74 (1981).pp. 23 1-249.

5. Tanre, D.. M. Harman, P.Y. Deschamnps and A. de Leffe, "Atmospheric modeling for space measurements of groundreflectances, including bidirectional properties". Appi. OpL. Vol. 18. #21 (Nov. 1979), pp. 3587-3594.

-106

Table A. Recommended wavelengths.

11 (nm) X- (am) Water Type, K(490), Range (m"') Depth Range(m)

420 530 .022 - .50 260 - 333 420 490 .022 - .046 620 - 229470 530 .046 - .125 197 - 97490 550 .125 - .250 109 - 55

NOTES: The cominatiom .=420 and X.30 is the fir romnended choice. Theother combinatiou should be u n oly if aceary to obtain atequate ipal.

The &th ang given is for the conspooding water type range and is the depth atwhich the inadiace, Ez. ). a either , or Xtita readies 0.002LW • c-z • n-r witha cler aanfaqah and the sun at Oh zenith.

Table B. Wavelength error, 'i 420. X=530nm. Maximum error caused by a t 2am offset in

wavelength calibration.

Max I %EROR IN T"A AT %ERROR IN1"AT Trane d o En r AppliedK(490) Depth 25m 50m 100m 200m 25m 50m 100m 200m TO Cowputs At At

.. l (Gm) x(m) Veto)

.022 260 4 1 17 37 -0.5 -0.5 -0.5 -0.5 420 & 530 420 A 530 530(+2)4 8 17 37 0.5 1 3 7 459 420 530(+2)

.046 200 2 5 11 24 -0.5 -0.5 -0.5 -0.5 420 & 530 420 & 530 530(+2)2 5 11 24 0.5 1 2 5 459 420 530(+2)

.077 120 1 3 7 - 1 1 1 1 420 A 530 420 a 530 420(+2)1 3 7 - 1 2 2 - 459 420

.125 70 3 6 - - 1 1 - - 420 & 530 420 530 420(+2)3 6 - - 1 2 - - 459 420

.250 33 9 - - - 2 - - - 420 A 530 420 a 530 530(-2)9 - - - 2 - - - 459 420

Notes: (1) Depth at which E,(%).0.0002 ILW .cm . nm-' (clew atmosphere, sun at the zenith).(2) Transmnance thmuh atmosphere at wavelength X(3) Trnsmiuance through real path (atmosphere + water) at wavelength ,,(4) Wavelength and diecoo (1) Wa which 2am offset causes maximum error

-11.

Table C. Wavelength error for X,~ and X2 in table.Maximum error caused by a 2am offset in wavelength calibration using X, and X. to obtain greater depth capability.

K(011 011 01DfK(9)A Max DpthI! %ERROR IN TA AT %ERRORINtrAT IEffor Applied

M1 (am) (nm) (mn) 25m 50m 100m 200m 25m 50m 100m 200m ).(Gm)

.022 400 490 620 12 1 20 48 -3 -4 -4 14 1 490(+2)

.046 420 490 229 0.5~ 2 6 20 -2 -3 -4 -9 490(+2)

.046 40 50 197 3 7 16 351.1 -t -2 -3 1 530(+2)

.125~~~ 97 a 1 3 1 2 - 470(+2)

.177 470 530 951 8 16 34 - -1 -2 -2 - 470(+e2)

.125 490 550 1 09 6 0 1.- - 5 .8 - V 490(.2)

.250 490 5501 16 31 : i -: -10 - i 49 %+42)

Notes: (1) Depth at which 04.0002 jLW -cm~l nm-' (clear atmosphere, sun a the zenith).(2) Transmittance through atmosphere at X.-u4S9om.(3) Transmittance through total path (atmosphere + water) at Xw459nm.(4) Wavelength and direction (t) at which 2am offset cause maxinum error.

Table D. Maximum emo consed by a 5% offset in she menused iredimoc, 4k)4, at AL1 or X.CalculMd a A-9.m

0 0)I )L2 W&We Type. K(490) Maximum Emo Maximum Error

(nm) (11m) from 10 in rA.(%) in_____M

420 530 .022- IM 9 4420 490 =f - .046 13 3470 530 .046-.125 13 7490 550 .125 -250 13 9-

Note: (1) Xi. X2 am the two wavelselghe as witich the bleme EZM.. tm umaan imi. (nIn aim m claim for tmmlin anme to Xe-0i9em)

(2) Thoams -I attmiue a XenS5Pin.(3) Tsuammmic bII taal pob (atmoqphu + wate) a ).e.459am.

(2),(3) Eiudasmptem of do^h

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Table L Em caused by a 1 meter offset in depth. Calculated at 4,459am

X,;L! Water Type K(490) EFfor i I A Efor in

(am) (mn) m" (%) ()

420 530 .022 8 3

420 530 .046 8 7

420 530 .077 a 11

420 530 .125 8 18

420 530 .250 8 39

420 490 .022 3 2

420 490 .046 3 5

470 530 .046 11470 530 .125 11 16

490 S50 .125 13 13490 550 .250 13 33

Nots: (1) 4, X at the tw wavelengts at which the iradiance, F, (.)arem nasud.(The mors no calculmaed for osuw trmsfened to 4-459nm).

(2) Trummiu m bough amosphem at A g59nm.(3) Trmsmiume thruug total path (aumosphem + water) a Ae45 m.

(2),(3) Ermr sidepeodeu of deph.

ITable F. Er caused by a +5% offset n solar unith angle. O

ERROR IN r'A(%) ERROR IN T'(%)

3 0, (d.) Han Overas Hm Overcast

2.5 3 10 3 1030 5 19 5 1945 7 32 8 3360 9 $5 11 S9

'75 10 133 25 !'70

Note: (1) Em is indepemrt of depth.

(2) The waveilngh at which the comPuta o am made, A,has negligble effect on th eror (-,02%).

(3) The nwmmt w wlougihs, X, X2ued have a smaneffect oo the f=mitmt amo (a ,0.4%).

(4) The em is independent of yp. of water.

(5) TA = mUMuIMCC ftugh the amsphere.(6) ra so indfloac thouglh the tMWa path (+mhee wat).

E -13-

Table G. ETnr caused by a ±5% offset in the solar irradiance,4(Calculated at k-459a

)L(I X2 (m) Eor in IA% Error in T'(%)

420 530 9. 3420 490 14 3470 530 13 7490 550 14 10

Notes: (1) ~,~ are the tm wavelengths at which the irradima, E, (X). a esured.(Th camr am calculated for results transferred to 4.459=m).

(2) Transmittance through atmopheiu at k-459am(3) Tranminance throgh total path (atmsphere + water) at k.459a.

(2),.(3) Euo in IrA and I- am independent of depth.(3) Errn in r can be larger or smaller if another "wavelength of interest, A,

is used.

044

Ia

0

C

a,

309 480 5N 600 700

Wavelength (original)

Fig. la. ExtaterrestrialSolar Irradiance. Neckei ad Labs Ref. 4.

E0 r

416 7 l ?9 0 1584 O.eC22 0 6:!'413 173 29 0 1509 0.0826 0.014420 172 62 0 14?9 e e e el,:425 165 80 0 1372 0 0037 0,0120

430 162.49 0 1309 0 0044 0 0113435 168 47 0 1230 0 0052 0 0117440 1a3.93 & 1194 eO 9 9 1 olt445 192 73 0 1141 0.007t 0 O113

S450 200 19 0 1091 0 0063 0.011Z

455 203 39 0.1944 0 9097 0.9110460 2e3.37 0.0999 9 9112 0 0109465 t$S 82 0 0937 0 0130 0 9107470 199.14 0 0917 0 0150 0 0106473 201 19 0 099 0 173 0 0164480 N01.86 9 Sa43 0,9198 0 e1OZ4aS 194 04 e 909 9 0227 0 0101490 189 03 0 07-6 0 625 0 0109493 193 68 9 0745 0 0293 a 099500 192 48 0 0716 0,9332 0 0097505 191 29 9 0688 0 0374 0 009

Dr 510 191 4S $ 0641 0 0421 0 90991vtl 515 132 72 0 0636 0 0471 0 oe94

s2e ta1i . a eg12 9 @5;s a q@935' 196 34 a 0599 0 05;3 0 981

PUO S 167 SS 0 0567 0 0644 0 00175 13 43 0 034 0 0709 a soi:?540 185 90 0 0526 0.0777 0 0088545 185 16 0 6507 9 c4 0 09975 1ai 29 0 04e9 6 091; a 6986555 133 iS 0 0472 e 0992 0 005569 192 39 8 0433 9 1065 0 084

56 177 42 0 0439 e 1136 0 0083570 174 It 9 0424 0 1294 0 00O2575 181 7;, 0 0409 0 1266 0 09158S 133-24 9 0395 0 1321 0 0080

Fig. lb. Table showing the effective extwternesrial solff iffadince in a 100M band centered at the wavelength in column 1,

and the optical depths -.i(X) (Rayleigh or molecular component, to(k) (ozone), and ta(X) (aeosol). Uniform sensor responseova the pas bond and @% (4") a 0.01 was assumed.

,I I

4 i 0 6 II7I

V1

II v' ,

II '

P2-. I 4

P3 ," 5 S 10;0

.. o.

40N i O. 700

5370 0=P'13 EXP-(P(2nFE$'.H-P':.

P5 = ..389E-001- 1 4717E-003P3 =5.8975E802 -.

P4 = 1 .5301E+000

NO LIMIT

- DATA CURVE DIF

40'3 0.300030 .001.5 0 0015450 0 00350..0083 013048500 0.0345 0 0331 -. 0014550 0.0920 ..99- 00600 0.1320 0131* -. 00032

650 0.0620 0.0637 0.3017700 0.0230 0"8195 -.0035

NO. POINTS 7

DIFF

MEAN .0004

SDEV . 0026

L~ 2. Ozone spectral absOption. Daa and model.

0, -16

0rJ E.". ML. , . . 6- .

. E. L It, -

-Y i::E K..,.4 '.:.

3 e. e

3 0ML 7 .612"

T .' 7.:

.60

.20

300 400 500 600 700

;I MLC76 1625

S.40 --4

30

Ill ...'......... . ..0 0 LA. AI

00400 500 6000

4v 0

Fig. 3. Vulmuaof KQk)for JNlov watya sIM and 1 2. SeeRef. 2.

-17.

MODEL Mt'6 C76 . 6-5

OPTIMUM WRI'.ELENGTH

K , 4 ¢, ,,, r:r, : I:,,-4 922 450 k -'..

cl C130 47'3 0 o'27A. 040 47:: - 0. 0390 050 483 0.0490 .060 4:87 O F,00 070 490 '3 0700.080 494 0.0:300 C.90 496 0.089C .100 499 0, 09 90.110 501 0.1080. 120 50 0. 1170.130 COW 0. 1260.140 54. 0 1320.150 -45 0.138r-.160 547 A-1450.170 548 0.1500.180 550 0.1560.190 551 0.1620.200 552 0.168-0.210 553 0.1740.220 554 0.1790.230 555 0.1850' 240 556 0.1910.250 557 0.196

LiiM CEL L P1_LC7IS16_._ , 5

45A

0 0 10 .2;0 3

Fig. 4. Optimum wavelengths for maximum depth vs K (490).

.18-

"O £L r --~; = '-

R C P."Fq.,40 1173 - .

DEPTH T WHICH FRADI 0FINCE I.E = O.,@2 v wu:

Q.r 3 3. .4 6

~~ 1471- .Ao 6 ,-:4n

43 5 0677 154J 45 C.1 :,." 0 1 "4

4!. 0 , 087 1704 ! .0703 1754 6 k 0 0759 1:i ~ 16".- .,.77_-.5 S?6

5 70 70.14 ? 1-475 C.0695 1975:4.0 6. PA2 20 14!15 0A 677 105490 0 0670 2 044 -1'5 03 07 74 203500 0 0 o.- S 199

505 O.0708 1'9560 0 0939 1:35515 0.0781 174520 0.08.6 163SZ5 0.082" 16550J a 083!5 16:3

535 0. 0846 161'540 0 asp;@ 15e.

545 0.987 155fi 550 0 92 151555 O0930 14 6

560 0.0966 140

565 0.10!2 133570 0.1072 1265"5 0.1155 11,7

580 0 1285 105

MODEL: MLC761625

K(, 490) -.

4' 0"0

r.ri

SD i r 49" * .a 67w Er -. 0002 viW/em1nm

4Onr50 600

3Fig. S. Depth limit (for O.24&&w • cm: omr) vs# wavelength when K(490)-.067mt .

E -19-

M 0, ~CE L M1L C: 7. I 25,

0 M'3 rE TE P'-0,

W

0w 1 2!

-'. 4 '9 C1

WAELENC;T4: 4-,C AND 500 ~nDEPTH4 eZ.! 10q, METERS

IF -I-.'49'3.= '0: THENI LPml1-?

' 3.4 - PV V: . 0 02skiA~ 040A0 ' 3 P4.~ P5 00440J

C3 ~ ' 067.c '3 0 -1! 6o- O-Soe 0 0,024 a.oe05.3 13 00 A3.112:4 7 e3 e9'8713 1200, 0. 121' 3 1170?13 14C0 ' 14~: A 1,352

A- 00 0 17 00 0 135A- 180e '3 192A 6 17170 .20e 0 Z139 '. 18:99'3 2200? '3 417 5 61 2.6leA. 2 400 0 Z5 ! 1 2.264r3.200 ID29 ~ ' 2446

A3 172.-4 26c.'E$00 I @&E-kl''3 C4400 3A-77E'3fr 2 038E+000'0' 04300 4 2:=-'36i 3 M-003 '3808 4 72i-0062 5 42E-OP2e 1000 5 27E-6003 8 76E-003'3 1.200 5 90ES-094 1 41E-036 1460 6.59E-003 22'E-004

* .31600 VS7-096 3 69E-005* 6 1800 8.24E-997 5 95E-6

p 0 606 21E-098 9.61E-00762200 1 63E-668 1 SSE-001

'3 240A 1 1!E-069 2 !OE-00e0.2600 1.29E-613 4 04E-909

Fig. 6. Sensitivity of proposed method to changes in water type (K(490)) when wavelengths are X148 and X2.SO0nm.Depth in example is lO0m. For definition of Q see text.

-20-

M 0C, L r- L C 7. 1E 5

Tr

W

w4

-ADAS 10 1o 25,90)z

490E.ENTf. 4EO N (5 10

0 04PL-4 10.0406'9t) 0.01

0. A1re 0 "9 .4

0 1408 83.1713 13461

8.1888 0.195 e15120 .1288 22375 0.1188

8.2008 8.2NIPS 0 18448 2288 0 1.60 8e28118.2488 8.3821 0.2177

Kf 49e. E="'46', :- 51A

0 0224 3.09S+O81 4 23E.08809 0408 3.99E+000 9 S1E-00i08 8600 2.26E-881 I 96E-O8818.88 1 66E-092 3.53E-9820.1880 1.21E-883 6.7@E-Oe38.1288 8.95E-805 1.27E-0930.140e 6.4eE-006 2.41E-0940-1686 4.74E-007 4 5SE-9058 1888 3.46E-99S 8.9-88 28889 2.57E-009 1.65E-0960.220e 1.85E-BIB 3 13E-9e70.2488 1.3!E-011 5 94E-088ID.-2688 9.91E-913 1.13E-98

Fig. 7. Sam a Fig. 6 except wavelengths ame ;.ln46O and ).2.SlOnm (A)WmOnm).

-21-

MODI~EL - MLC 1 1 Fe-_5

Z t C' C M E TE PS15

:4

144

DET (Z) 1 15 2~

SAHOPASS; 10 no fb'4?0' .0

0 a 882

IF &K(490>) 001 THEN &P=1.92

K (491D~ - 14412. P 54A

0.0224 0.0'77 0.95 7713.0400 0 0444 0 06989e 0600 A..0748 eimo Aeoo 0 10 A51 0. 09430-196e 0 1 ?NJ! 0,107eo 1200 0.1658 0 11970 1400b 0 16 8 17248 1400 0 -226-5 0.1451O 1680 0.24368 01578a 2000 0.2872 0.1750 2200 0.3175 0 :83a0 2400 0.34?q. 0.19590 2600 0.37S2 19.298#5

K. 40) E:i446) Ez'540"'

.0224 2.71E+081 4 99E-A0I0400 1.87E+009 I 63E-0010600 9.02E-002 4 ISE-002

8.089a 4.34E-003 I 29E-0020 .1I080 2.99E-004 3.EI61E-e0030. 1200 l-OIE-095 1,91E-0030 1400 4 84E-00? 2 85E-e@40.1600 2.37E-009 8.OOE-0050.1800 1 ZE-099 2.25E-0050.2000 5.4@E-011 6.31E-6060.2200 2.68E-012 1.77E-0060 2400 1 2!E-013 4.99E-e97

F~g 3.Sw F .60 6.:2E-015 :.40:-eel* 7)

V. ( 4EL Q-1 1 H 3 10 0 C1D0 7

BAtiOPA$E: 10 fr i'4O 0 0

UNITS FOR E-6: uW.'cm*nn

DEPTH E(490'- E--(510'- RATIO

0 1.SE+002 1 7E+002 9.5E-001708 3.,-E+001 3.SE.001 9.SE-803148 8.5E+0003 8 7E+@Oe 1 OE4480060 1.9E+000 Z.OE.000 1.1E+00088 4.1E-001 4.SE-001 1 1E+000100 8.9E-8S2 1.@E-001 1.ZE.O00120 2.SE-002 2.3E-Se2 1.2E+Se140 4.3E-e83 5.4E-003 1.2E+809160 9.4E-eS4 1.2E-eS3 1.3E~eeeI180 2.IE-004 2-8E-004 1.3E+Se@29e 4.5E-905 6.3E-905 1.4E+Q0

1 MODEL! MLC761625

ID K(9'I0- /

DEPTH - Z (enrz'

Fig. 9. Sensitivity to changes in depth with wavelengths X,0460 and X2uS10u Water type K(490).0.067.

-23-

MODE'. MLC.611

WRVELENGTH:S 4-0 ND !5 ',n,

K'4.? . = 038 1 .m

K ,4 60 -> 0. 3-80 K 51 0, 0 4 .?

BAh4DPASS: 10 nm r'498) =

UNITS FOP Ez: L.."cm~nm

DEPTM Ez468. Ez'510) PRTIO

8 1.-SE+02 1 7E+e# 9 5E- I20 S 3E+001 6.2E+001 '.sE-09148 3.9E+001 2 3E+081 5.gE-00160 1 8E+0018 4E+0 4.6E-09180 S.5E+.091 3.IE+80 3.7E-001108 4.@E+09 1.IE+00 2 9E-901120 1 9ES0 4.2E-001 2.3E-001140 8.7E-001 1.6E-001 1 8E-001160 4.1E-01 5-8E-002 I 4E-001180 1.9E-001 2.E-02 iE-Ol200 8.9E-002 7.9E-003 S.SE-002

MODEL! MLC7616251

K<490) * .038 1/M

w

5 30 100 150 0 250300DEPTH - Z .M*ttr )

Fig. 10. Sam as Fig. 9 except K(490)mO.038.

-24-

Wfl'.JELENGT'H? 4tE'EI RND a-:*.( Pir

BANOPASS: 10 is(444 0

U NITS POR Ez -w, m* i

DEPTH EZC(460:' Ez(510, PRTICt

'3 1.8E4-0'2 1 7E+802 9 4E-04211.20 1.IE+001 1.7E+001 I -SE4400040 7.OE-001 1.SE+000 .5 E+010060G 4.4E-002 I SE-001 4.2E+e00080 2.7E-0303 1.9E-002 6 .9E+00eOlee 1.7E-004 1.9E-983 l.1E+0301120 1.IE-095 Z.OE-004 l.9E+e01140 6.6E-0107 2 OE-005 3.1E+001160 4.2E-0138 2.IE-806 5 SE*001

203 .6E-QI 2-21E-e08 1.4E.02

3 4 MODEL: MLC7619234 rV'490 - 115 1-M

:3

: 3DEPTH - Z(#~

Fig. 1.Sam u Fig'&. 9 & 10 except K(490)sO.I IS.

.25.

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I = ~~~~CL _ _ _ _ _ _ _ _

I p% I :~~ -M

I U') ''JZ2 - I .

CL~ CL .- 0.

IMIP-- llZ I 11 II I- 1Ix ~ .-

CLIZ T Oz I 11 7.-

-j LX-) ( I . IDW U. -. T Ir-i-- 0 *C'i w CLl I .4

-M -i .i w

IL0 W 1 11 ow

aI.

Izim:cm

* *D.X'I I ca

I . ' 1 'i- *

4zIe I.NJ U.1

BWi 10 gmw I

'0 I

0. tzg w L1

x *U II Q, II x~r

0 0l **.IL~ - I I 0 A 7 rVi

Lai T 0 UW'a .Z 1

'NJ X w I '.1) ,40 4

Ll.'rf I l A - ...~ W1111 1i LLL1C I W I

olo .1..

A LL1*~1 r

- - rLadW % t '

QCI w U

w-IX J Q ~ W -I a

ZWWWC&UOQ to I r cJ

L .Z 'Z T Im CL *I"AC! g

-i .7 I

C9 C

ww

-II .1= -

,i -To .' oi~

U...I I) -

*ZL 1 . LuA

-e -. = 0 L-

0) o j o..4 I- I 1T ! Xw Q I v..1

(-)i w * W ii

EWWWGLIOi)I O UI CI-a. nwr, T W 0 I 0 a~'..I

2 ' Ce 1X 0 0.- &o La s It1 r inui I__0_ _ __ix I

n 0i =::>

1.0 INTRODUCTION

This brief study was made in response to the question: From opticalmeasurements made at an arbritay depth Wz in the open oceans, can the

~optical character of the atmosphere existing at the time of the measurement(s)

! be determined? That is, can we conceive of a technique which, using the

ambient light at some depth in the ocean, will provide information from whichwe can determine the type of atmosphere (clear, hazy, overcast, etc.) existingoverhead? It is assumed that the depth r, at which the measurement is made,

and the zenith angle of the sun (6s) (i.e. time of day and latitude etc.) are

~known.

2.0 CONCEPT

Prior work indicates that there exists an apparent spectral relation-

~~ship between the diffuse attenuation coefficient, K( ,),and the various "types"of natural waters found in the open oceans. The attenuation, n vrie! with

~wavelength and its spectral form is quite different for clear water than formore turbid water. If this relationship is consistent and known for thewaters of interest, then by making measurements of the ambient spectralirradiance at depth we should be able to determine the attenuation characteris-

tics of the water column. Assuming we can determine the diffuse attenuationof the water above the instrument and that the instrument measures the absolute

downwelling irradiance, the downwelling irradiance at the surface can be com-puted. Frome the diu e atteion cethe attenuation through the atmos-

phere can be found using established values of the solar irradiance outside

the atmosphere.

-%IV.'F.H\IT Y I IV A1,1!1 'IA I A Lot J l -'~ /i

p.%

2. .. qC WAVELENGTH MODEL

A two wavelength model is used to illustrate the procedure. The

dwavelengths () used, A = 490 nm and 520 nm, were chosen to take advan-

tage of a fairly large body of data which has been processed by the Visibility

Laboratory to yield the spectral relationship of the diffuse attenuation co-

efficient KF at these specific wavelengths. These may not be the optimum

wavelengths, but they serve well to illustrate the mechanism of the concept.

3.1 K( ) Relationships

(1)

A study at the Visibility Laboratory has developed the

• following relationships:1.491

K(490) 083 ss(443 + 0.022 (1)= 0 .0883 Lss (550 1

K(520) = 0.0663 LSS -1.398 0.044FLss (443);4 2

LLss(550)J

Where Lss( ) is the subsurface upwelling radiance at

wavelength A.

From this it follows that

r 0.9376

K(520) = 0.0663 11.325 x K(490) - 0.2492 + 0.044 (3)

3.2 Propagation of the Light Downward

.et:

TA = the transmittance through the atmosphere

T,= = the transmittance through the water surface

(1) Ref. R.W. Austin; Remote Sensing of the Diffuse Attenuation Coefficient of

Ocean Water, Visibility Laboratory, 29th Synposium of the AGARr Electromagnetic

Wave Propagation Panel; Monterey, Calif., Anril 1981.

e,

B3

3 TW = the transmittance through the water to depth z

, o = cosine of solar zenith anqle

All transmittances are for diffuse light.

Then the irradiance at deoth z is

E = ~ T < T (.T(. E C.) where Cz A S W o

E = the solar irradiance outside the atmosphere.0 r

- T r (\ (X) + T ()TA (,\) e o a ( (5)

k-, Where R, To and T are the optical depths of the atmosphereR 0 a

for unit air mass for Rayleigh (air molecules , for ozone, and for

the aerosol, respectively. The values for T R(",) and , (.,) are fairly

well known and are essentially fixed, appearing to vary slightly with

season and latitude. The aerosol component has a wavelength dependency

which appears to follow a power law so that

= • ('N2) .(G)

The exponent, , is known as the Angstrom exponent and is commonly

taken to be in the range of 1.1 -1.4 for fairly clear atmospheres and

it will, we believe, be around zero for very heavy (fog, overcast)

aerosols.

TS = 0.98 (7)

T W eK() z (8)

And we get

1 R + To + 'T()J -(zEz(,) LI.±0 (0.98) e- *e E (9)

0 .9)

-4-

3.3 Solving the problem

The above (section 3.2) is used only to calculate the irradiance

E, ,. which would arrive at depth z for various types of atmospheric

conditions and sea water,to use for inputs in solving the problem.

At this juncture we are at depth z with an instrument which measures

E *(- at two wavelengths 490 and 520 nm. From these two measurements

we wish to determine the type of atmosphere overhead.

Let 1 be the first wavelength, (, = 490 nm and be the second

(2 = 520 rum). From (9) we can get the ratio

E (!) -I 1 P1o (1) - - (2) + T (1) T(2) ( ,

2 1o JR R 0 ( ,e

z

e (l-K (21. (10)

T (\) and '(7 ) are very nearly constant so letR o

o-- ( R() TR (2) T() o (2C1 =e

T (1) and T (2), the ontical thickness due to aerosols and clouds,a a

are unknowns which we are seeking to establish. However, since I and

A2 are close together and the Angstrom exponent in Eq. (6) is small

(<1.4) we assume that they are equal and then

1 L (l)-r(2.

e 0o a a 1.0

thus

E (1) -(K(-K(2)• z

E (2) z C, e

z

* See section 4 for a discussion of the nannitude of error caused by

this assumotion.

.. - .. . . . .4*.~

-5-

1 z

1h C ___ (12)z 1 E(1

Substituting Eq. (3) into (12)we get

K(.)-0.0663 (11. 325) K (I)-. 249 0.37 0.044

1 Z ) (13)in 1 (1)

Where K (1)is a calculated value as opposed to K(1; the "true"

value.

From Eq. (13) by successive approximation K(i) can be calcu-

lated and if desired K(1) can be calculated using (3).

The irradiance at the surface can now be estimated using K(A),

i.e.,

1 I(X) - zElS M -0.98 e.Ez

The calculated atmostpheric transmittance is then

T MX = 1 *A l io E (A)

0

and since

then

Ta = -,-o.]n X -ln T"A R0

E C= -uo ln0

-6-

'1 K (")"z ____

i) = - • in *e C) - - T)a' 998" 7 E R, 0

0

-o K ( z + in7o (14)a" ~0.98",-o E ( ) (4

The magnitude of T (X) is an indicatQr of the aerosol density.aFor examole:

CaG) 3 .1 Clear - fairly clear

.5 Haze - light overcast

> 1 Overcast - heavy overcast

4.0 COMMENTS

4.1 The duffuse attenuation coefficents, K(M), are the mean or

"effective" values over the total water column above depth z. The

models used for K(490) and K(520) were developed using data roughly

over one attenuation length (z =r/K(X)) from the surface downward.

It has been assumed that these relationships hold for the mean K(X)

over greater depths ( 1 - 200 meters). This needs to be verified.

4.2 The solution determines the optical thickness normalized to

one air mass but from conditions mainly in the direction of the sun

0 not directly overhead.

4.3 Assuming a non-spectrally dependent aerosol in going from (10) to

(12)(Section 3.3)results in an error, at this point, of approximately

1% for Hi sun and clear air; 2% for Hi sun and heavy overcast. The

worst case would be with a low sun and hazy sky where the error (at

this point) for a sun zenith angle of 800 would be approximately

10%. A choice other than zero might be slightly better here. Also,

an itterative process could be used where the"-" exoonent is estimated

from the 7 found and the computations repeated, etc.a

-7-

4.4 Errors of ± 5t in the measurement of the irradiances Ez()

and E do not seriously degrade the ability to estimate the r;_u

of atmosphere present.

4.5 The precision with which the attenuatigr. coefficients K(X)

are determined is increased with increased path length (z). On

the other hand over long path lengths the effect of error in K(X)

becomes more detrimental to the final results. These two things

are somewhat compensating.

4.6 The place where this model is weakest is probably in the

K() relationships used. Although it is based on a fairly large

body of data (88 points for X = 490 and X - 520) the precision

and variability of the data base, as is always the case with this

type of in-situ measurement, is not as good as we would like. We

are left with questions. Will this K() model or some variation of

it work adequately over the distances contemplated and how well

will it work when used under actual in-situ conditions. These

and other questions are best, and perhaps can only, be answered

by field work in the ocean.

4.7 The wavelengths used here are not necessarily the optimum

wavelengths. In choosing wavelengths we wish to work with those

which will provide the best determination of the attenuation of

the water so that our extrapolation back to the surface is most

accurate. We must also not forget the approximation made in Section

3.3 which becomes less significant with less separation between the

wavelengths used.

4.8 Examples of the two wavelengths scheme have been worked up for

a variety of input conditions. The spectral irradiances at depths

z, i.e. E (A1) and Ez 2) , were computed using Eq. (10) for the set of

assumed input parameters (i.e. all water, atmospheric and geometric

variables are known and the underwater irradiances computed. Using

the values of E (X1 ) and E (N ) that were computed above and a knowledgez 1 z 2

Ivan-

of depth beneath the surface, time, date, latitude, and longitude,

appropriate values of uc, ('R(\ ), R(Al)), T- (0 ), and r o(,\2 ) may be

determined,and from Eq.(!l), K'(\i), the estimate of the diffuse

attenuation coefficient at i may be determined. K (N ) may then

be inserted in Eq. (14) to obtain an estimate of the aerosol optical

thickness . (N). With only two wavelengths, hence two equations, ita

is not possible to solve completely for K, T , and =, the threeaunknown variables in the complete radiative transfer equation. Hence

the necessity to assume 7(A) - Ta(A ), i.e. that the Angstroma 2 a 1

exponent, is sufficiently small and - is sufficiently close to

1 that 1. This assumption is not correct in the general

case and in order to obtain a solution when Ta )I 2 Ta(,2 ) we must

resort to measurements at a third wavelength for which we must obtain

a relationship similar to that of Eqs. (1) and (2). We would then have

three equations of the form of Eq. (9) and three unknowns and could

solve for Ta (X ) the optical thickness of the aerosol component of

the atmosphere at the wavelength of interest with K(X) and as

byproducts.

r--w

N

A r

-9-S

K x

(A) OL + (A)

Figur 1

Appendix 2

A Reprint from the

~~O SNET. Internationa Society for Optica Erlieerin5

Volume 489

Ocean Optics V1I

June 25-28, 1984Monterey, California

Spectral dependence of the diffuse attenuation coefficient of light in ocean waters

p R. W Austin, T. J. PetzoldVisibility Laboratory, Scripps Institution of Oceanography

University of California, San Diego, La Jolla. California 92093

SI1984 to the. Socwft of Photo-Optical Iwtumetatiof Engneesson, 0. Bellingham, Washnfgton 98227 USA Telgehone 206/676-32W0

Irs

SPECTRAL DEPENDENCE OF THE DIFFUSE ATTENLATIONCOEFFICIENT OF LIGHT IN OCEAN WATERS

R. W. Austin and T J. Petzold

Visibility LaboratoryScripps Institution of OceanographyUniversity of California. San Diego

La Jolla. California 92093

Abstract*A study of the spectral nature of the diffuse attenuation coefficient of light, K (W). for various types of oceanic waters

has been performed. These attenuation spectra were computed from downwelling spectral irradiance data, E, (A). obtainedby U.S., French and Japanese investigators, working in widely separated oceanic regions and using different measuringtechniques and equipment. Attenuation properties were calculated over the spectral region from 365 to 700nm and fordepths from near-surface to in excess of 100 meters.

Examining the K (A) data, we find strong, simple, and useful relationships exist between the value of K at someselected reference wavelength. k., and the value of K at some other wavelength such thatK(X) - M(.) [K(Xo) - K,(X,)I + K(k) , where K. is the attenuation coefficient for pure sea water. For oceanicwaters (for example, Jerlov types I through i1) the relationships are linear. These relationships appear to be usefulthroughout the entire spectral range examined and are particularly good between 420 and say 580 nm.

The significance of the existence of such relationships is that they allow the inference of the spectral attenuationcoefficient at all wavelengths from the attenuation value at a single wavelength, and provide analytical expressions for

*modeling the spectral nature of the attenuation in ocean and clear coastal water.

IntroductionThe need for information with respect to the optical properties of ocean water greatly exceeds its availability. For

example, little data exists on the spectral diffuse attenuation coefficient of sea water, if one insists on data based on in situmeasurements. If we examine such attenuation spectra, however, we find that they behave in a well ordered and regularfashion over most of the spectrum, particularly if we restrict our attention to the open ocean where the water may beclassified as Jerlov Types I through III (Jerlov 1976). The concept of the Jerlov water types itself is based on aspecification of attenuation spectra. For many applicatons the Jerlov classification may. in fact, provide an adequatedescription of the spectral nature of the water attenuation.

We have reexamined the problem using new spectral data as obtained by a variety of investigators, working in vari-ous geographical regions, using different types of equipment and varied methods. The results which we have obtained aresimilar in many respects to those presented by Jerlov but show some important differences in detail. The method ofpresentation of the results allows the user to estimate attenuation spectra for ocean water knowing only the value of thediffuse attenuation coefficient. K. at a single wavelength. Thus, the value of K at any wavelength that may be availablefor a particular water may be used to:

(a) estimate the value of K at any other wavelength of interest.(b) estimate the complete spectral characteristics of the diffuse attenuation coefficient for the water, or(c) determine the Jerlov water type.

Discussion

It is helpful conceptually to partition the diffuse attenuation coefficient into components associated with known con-stituent components of the water. For example, subtracting K., the K associated with pure sea water, leaves the contri-bution to K resulting from all material suspended and dissolved in the water, denoted here as K'. Thus if K (A) is thetotal diffuse attenuation coefficient at wavelength A, then

K'(.)- KI0)- K ) . (I)

K (k) may be further subdivided into contributions from components due to say. (a) the presence of phytoplanktonand the detrital material that is associated with it- (b) to the absorption of dissolved yellow substance which is found invarying concentrations in ocean water; and (c) to the suspended particulates which do not co-vary with phytoplankton or itsrelated pigment concentrations.

Smith and Baker (1978), for example, used a model wherein K' was composed of two components, i.e. one propor-tional to concentration of chlorophyll-like pigments and the other. K, (\). *... a variable representing the average contribu-tion to spectral attenuation not directly attributable to chlorophyll-like pigments. They successfully reproduced the generalshape of measured spectral attenuation spectra using empirically derived values of K. (W). K, (A) and the specific spectralattenuation coefficient for chlorophyll, , (A). together with a knowledge of the pigment concentrations.

F68 / SP Vo. 49 Ocen Optics V flM4j

If one attempts to model the attenuation K'(A) using varying amounts of two or three component spectra, eachdependent on a concentration, then one must know the value of K'(A) at a minimum of two or three wavelengths in orderto solve for the various concentrations and specify the complete K (k) spectrum. Such a technique has the potential advan-

, age thai the concentrations of these constituents may be determined provided that a unique set of specific attenuationspectra has been determined. We have elected in this study. however, to attempt to determine a single spectral componentK '(A) which when added to K. (A), the spectral attenuation of pure sea water, will provide the complete diffuse attenuationcoefficient specification of the water, K (A).

The Data Base

Downwelling spectral irradiance data from various sources were first examined for general suitability, spectral range,and availability of contemporaneous data at other depths. Irradiance data from 148 stations each having measurements atfrom 2 to 12 depths were interpolated to provide values of irradiance, & (A). at uniform 5 nm steps. Various pairs of thesespectra at each station were then used to compute the K (A) for the selected depth interval using the relationship.

K(A)- - In Ed (,k.:2) (2)

These K (A) spectra were then examined for artifacts such as might be attributable to changes in environmental con-ditions during the acquisition of the irradiance data, ship shadows, etc.. and a selection made of the spectra to be used as a

,i .'. data base. No more than one spectra was selected from a station". The value of K at 490 nm was used as a classificationindex for the spectra. No data were used if the K(490) value exceeded 0.25(m-'). This limit excluded relatively few sta-tions in areas such as enclosed bays and in coastal areas of very high productivity or regions of high terrigenous input.

N ~ Those excluded data do not affect the generality of the results for applications to the open ocean and many coastal regions.For the special cases where K (490) exceeds 0.25(m-i) the shapes of the spectra are more disparate and there is real meritto using a multicomponent model as suggested above to obtain a better fit to the data and to obtain a measure of the con-centration of the several constituents of the water**.

Table I lists the sources of the data used in the present study. The three groups of investigators that acquired theirradiance spectra were Smith and his colleagues at the Visibility Laboratory of the Scripps Institution of Oceanography;Morel and his colleagues at the Laboratoire de Physique et Chemie, Villefranche-suI-Mer. and Okami, Kishino and Sug-ihara at the Physical Oceanography Laboratory of the Institute of Physical and Chemical Research in Japan. The geograph-ical regions include open ocean, upwelling areas, coastal waters and marginal seas. The irradiance spectra were obtained atdepths from I to I18 meters. The K's were calculated using irradiance data separated in depth by from 5 to 78 meters.Because the absorption of water becomes particularly significant at the longer wavelengths, the spectral range varied withthe depth of the deeper of the two irradiance spectra used to calculate K(A). The values of the classification index,

S., K (490), varied from a very clear 0.025m - I in the Sargasso Sea to a turbid 0.245 near the mouth of the Mississippi River.A total of 76 K (A) spectra were selected for the data base from the 148 stations examined.

Diffuse attenuation coefficient of pure sea waterThe process of isolating the attenuation effects of the material suspended or dissolved in the sea water required a

knowledge of the attenuation due to the base sea water to which these materials were added. Excellent reviews of theknowledge of the attenuation properties of clear natural waters have been provided by Morel (1974) and by Smith andBaker (1981). Briefly K. for pure water may be approximated by the sum of the absorption coefficient. a., and the back-

;,. scattering coefficient b ',. In "pure sea water the scattering would be molecular or "Rayleigh" with a phase function havingI' equal forward and backward lobes. The backscattering coefficient was thus assumed to be one half the total scattering

" ~coefficient and K. (k). therefor. determined as

4-K. (A) - a. + zb5,. (3)

Using a. (A) as given by Morel and Prieur (1977) and values for b,., (A). the sea water scattering coefficient, presented byMorel (1974). we have arrived at the K.(W) values listed in Table 2 in the column labeled "Morer. These values havebeen smoothed and interpolated to orovide estimates of K,(A) every 5nm (only IOnm intervals are presented in thetable) The entries differ by a small amount from those given by Smith and Baker in their Table I (usually less than one

*unit in the third decimal place) due to procedural differences.Because subsequent processing of the data was to be performed by a computer, it was deemed desirable to find an

>:' analytic fit to the K. (A) curve. As can be seen in Fig. I (a). the curve does not lend itself to fitting with a single function.

on the S Co R DISCOVERER expedione Motre aid South lhmiteUfd SIgarsl ltrrdinm using dlervinit equmnm and mihob. Of ih It seM Weed ftro. Mols weeknd theI S tins leled fromt Sm I's. ine the seli. Fot tlrein of thO. dilerlst depth Intervals wees us ; on ofe saticon the S1 mete dewt intervd welted rfioi Steih's

work i cluded the O meter interval of elll's. on ihe firth stlicei the tine inteli w ell itd.A itttlticomnPonent mnodell hn feen tried with excellent sumin tuM I cottlum spectr (f or ote ta rm Morel aviii Pritew (19771 Ussieg tim fusscttcro .54 '.wn of K (A) aI

property Ch . wslet h. aid W auWp of shoo of the meetl EtA) spectra could be ropredum aid relative amounts of the coe¢elratices of chloropittd-ke Ieets. yelo.

$PIE VoE 409 O ,0. eies Vw(IS41 / in

I te 1. Uata base for K..(A I i udy

14# 1 dYEAR EXPEDITION LOCATION '40 STATIONS DEPTHS WAVELEGTH K 1490) RANGE REFERENCE

bor esoel) USED Iml RANGE (.m) MI)

1 967 OLIVER Gulf Sireati 1 5-15 3111-4190 0039 Tyler A Smith1970)

2 1968 FRESNEL 14ll Gulf of C~liorna 6 3-20 365-695 0 049.0 Is# Tyler & SmithI Tres M5artuts 11970)

3 1970 DISCOVERERI jfCanbuan" 17 5r 400-90 0025-0 119 Tyler(Moell Sa aa 119731

4 970 DISC! RR Gl fPnm 6-17 365-660 0029-0073 Tyler(Smisth I ( uaor, ac 4 119131

1911 HARMATTAN Central E Atliantic 12 2.118 40o.610 0038-0 1"4 rel & Cjlounenon41971)

6 1974 CIECA S/ LitelIlns off Is 4-40 400-685 0109-0220 More$ & PriourCHARCOT Mauritania (19761

1974 SEIYO-MARU Saaml fty.Japan 3 5-30 420-46 0 030.00ON Ollarrin. a

119731

8 1976 TANSEI-MARU Sagemi Rev. isown 3 5-20 420-670 0o09"227 Okhm. ev el

(19781

9 1976 SHINYO4MARL Seaof awm 3 5-20 420-6W0 002840058 Okamx. e ul(19781

to' 1977 RESEARCHER Gulf ofMeaco, 2 1-11 390.690 0206-0243 VaisLab4unpublisahdi

11 1973 GYRE Gulf ofMexico 1 1.11 3"S68 0094 Visals* l(unpublmaltedl

12 1979 N4EW HORIZON California bpit 6 1-13 175-7110 0 0434 227 VisLablafpublilkil)

(at Numbeir of su14(1061 ~agd 76 stations letgeed from0total of(148 i lthOe data but.I1ti Range of depths (or the E,(A) spetral gMM used trom each1 expedition FormI number is the mimmun s econd ithe maximum : 2lo Ranse of aelanghs for the E,(Al spectral Poen used trom each expedition Firat number as the amalleu of all miimumn wavelietha.

weond is 1he largust of the mesnam we36*60116s

(dl Range of K valuesat 4qsww toe Ihe net of K (j, I sectra ulecid for eac lizipell06

Diffuse Attenuationa Coefficiuunt of Pure Sea Wateir. K,,A t" More Rauio Diff I k MII&I or Ratio Dig I A Moesa Moail IRatio IDig1

350 0011 0"34 - M3 470 0.0179 0.0192 0.904 - 003 3S0 01373 0.13 .0003 +000130 00403 0.0403 I 10052 +0002 410 0.01") 0.0191 0.111111 - 0002 600 0.2409 0.2457 0.911113 -0099

370: 003311 0 032n 10073 .0003 490 0.0224 0.0216 10373 .0008 610 02M9 0.260 099S2 -0014

330 00278 00277 1 0040 1 *0001 50 0,0230 0-0275 10101 .0005 620 0.3124 03106I 10036 *0011390 00242 00242! 0911011 -O0000 $10 00369 0037) 0968 -000 630 03196 0.320611 01111611 -0010400 00217 0021II1 099484 -0001 520 0 04"60 04912 10114 1 -00061 640! 0329 0330S 099541 -0015

410 0 0200 00204 09*12 -0(041 330 0,05261 0.0321 110096 -.0003 650 0359 0350S 1 10155 1.-0054 i'20 001"9 00191 0 9903 -00021 540 00$77 00371 110100 .0006 6410 04105 0.4105 09999 - 00430 00182 0017131 10226 1 .0004 5 50 0 06401 0,0630 0"531 -0010 670 0.4271 041 0,9103 -00261

Q 007 007 10143 .00031S) 023!01 10033 .0006 6W0 04521 0.41,111 1,0038 *.0017500001 07 10145 ' 00031 370 0.0642 006 1027 .0034 690 051164 0.9M3 10224 *.0112

Cut 414Ratio column 2 te~de4 by column 3Cal 5 DINi column 2 minus column 3

770 /SMI Vol 409 Maew Optics VI (794)

It was subdivided into 5 wavelength intervals. (1) 350 to 445 nm. (2) 445 to 520nm. (3) 520 to 590nm. (4) 590 to 660nmand (5) 660 to 700nm. and best least square fits obtained to parabolic functions. The values obtained from the model arelisted in Table 2 in the "moder column. The model reproduces the values derived from Morel's work with a standarddeviation of 0.013 as determined from the ratios of the Model to the Morel values (4th columns in Table 2) and the stan-dard deviation of the differences (columns 5) was 0.0022. Figures I (b-f) show the values plotted (+) and the analytic fitsobtained (solid line) for each of the 5 spectral regions.

06 o

*MOREL - MOREL - MOREL

- MODEL 0 - MODEL 05 - MODEL

04' 04-

03 ' 03

)( (a) 2 b) 02 - (c)

0. 01 . . . . 0' ,_ ,_, _, _,_,_ _

300 .400 500 600 700 350 400 450 400 450 500

A Inm) X(nm) Afrim)

20*MOREL , MOREL 6" MOREL

-MODEL 40- MODEL - MODEL

30- 55.

05 20o I 4(d) (e) (1

_ 0 , ,_ ,_ . . . . 10 . . . ._ , _. . . . 35500 550 600 550 600 650 650 700

A minm) A (nm) A(nm)

Fig. I. Companson of values of K. as determined by means of Eq. (3) (points marked +) and the fitted functions or "Modet (shown athe continuous line) Panels b-f show the 5 subregions that were individually fitted to the points using a least squares technique.

Data AnalysisIf one plots all the available K (A) values at each of the 68 wavelengths from 365 to 700 nm against the correspond.

ing values of the classification index, K (490). one finds that these scatter diagrams provide strong evidence that there is alinear relationship between the two variables up to some maximum value of K (490). Figure 2. for example, shows suchscatter plots for wavelengths of 400, 440, 520 and 560nm. We have noticed that for the shorter wavelengths there is atendency for the data to depart from linearity at the larger values of K (490). As a result we have used only data whereK (490) < 0.160 for fitting purposes when working at wavelengths below 580 nm. No significant lessening of linearity wasfound for longer wavelengths when all K (490) < 0.250 were included.

The linear equation is of the form

K(t) - l(A) + M(\) K(490) (4)

and since K. (A) is a special case of K(t), i.e., the lower limit, we see that we can determine a set of values for K.(A)from a knowledge of the slopes. M(A), the intercepts, AXt), and a value of K. at some reference wavelength, say

K. (490) This technique has been tried and provides values very close to those shown in Table 2. We have chosen to usein our analysis, however, the K. (A) values in the columns labeled "Model (Col. 2) in Table 2. The slopes that were calcu-lated for each of the 68 wavelengths were based on fitting, by least squares technique, a linear equation of the form,

K ) -M(A) [K (490) - K. (491 + K. W (5)

SPIE VoL 489 Oe~n Optics W (IU4j / 17?

4060'

30. 30 bI.40.

30- 0 --30]7"

2 0 M Ct o10 * r.I

0 to 20 0 10 20

K (401) K 4901M(400) - I 7313 %140 - 15169

25 20

20 - to 1d1

S0.19 to

O ..- 0 CI0 .. . . . . . . . . . . .0 1 - I.. . . . . . . .0 tO 20 0 10 20

0K K14901 K 1490)%1 (520) - 0 7A78 M .5601 - 0$457

Fig. 2. Examples of scatter plots of K (A) vs K (490). for wavelengths shownare 400. 440. 520 and 56Onm.

to the data in the scatter plots. By using the tabulated values of K. () as the intercept in the linear equation, we have inessence assumed that the K. (A) values are correct. The effect of this was to decrease the excellence of the fit sligihtly overthat which would be obtained had we used the data to determine the values of K.. At most wavelengths the effect wastrivial. Those few wavelengths where the effect seemed noticeable were at the extremes of the wavelength range where theenvironmental and instrumental problems associated with field measurements were greater and the number of samples wassmall or, in a few instances, at wavelengths where the data was "noisier than usual.

Figure 3 is a plot of the values of the slopes, M(W), at each of the 68 wavelengths as determined by the proceduredescribed above. A piecewise least squares fit was made to these data providing analytic relationships that could be usedfor further computational analysis. Figures 3(b) to 3(d) show the details of the three spectral sections- (1) 365-420nm,(2) 420-620nm, and (3) 625 to 700nm. Both the data and the mathematical fit to these data are shown. The fitting pro-cess not only facilitates the use of the model by the computer but also provides additional smoothing to the overall dataset, essentially enlarging its size on a local basis thereby providing better estimates of the slope than can be obtained from aregression at single wavelength. Table 3 lists the values of the slopes as determined from the individual fits to the K'() VsK'(490) plots (Col. 3. headed *Daal) and the values determined from the fitted mathematical functions (Col. 2. headed

*"Moder). The fourth column in each panel is the ratio of the value from column 2 divided by column 3 and provides ameasure of the relative agreement between the model and the data used to construct the model. The fifth column is thedifference between the model and the data and is thus a measure of the absolute agreement. Slopes were calculated forevery 5 nm. The table lists values at 10nm intervals.

ApplicationsA major application of the tables is the estimation of K (A) at a wavelength other than that for which data may be

0- available. For example, if the value of K (490) is known then Eq. (5) may be used directly to compute K (A). Values forM(A) and K.(\) are provided in Table 4 at every 5nm from 350 to 700nm. (The values of M(A) for 350. 355, and360nm contained in the table were estimated by extrapolation using the fitted mathematical function and should be usedwith caution.)

Similarly, if the known K is at any wavelength, k1, then the unknown K at wavelength x,2 is,

KUI) M(- K L " 1) - K.(x 1) + K.(A2 ) (6)

772 / SPAI Vo 49 Om Oprtin v (In)

91scadihpaw~d swumU64dUA~d ALAAmu

2 ~DATA 20 DATAi

00 400500 600 100 350 0

20 0 (d)

DATA *DATA

-MODEL 8 * MODEL

'44

2

0 _ __ __ __ __

400) 500 600 600 650 700k(nmi) A (nml

Fig. 3. Slopes M(A). as determined from individual scatter plots of K Gk) is K (490)shown as (+). Solid lines show the piecewise fits of the parabolic expressions to thethree sections of the spectrum.

Table 3. Slopes of K(X) iwsmK'(490)

SLOPE loo (A)I

Mome Ome Roig D&E 4 MomI Due Rato. 0,1f Ak Itidl Ome Ratio MT

360 0 "'Iloss owiss -05011 ON!0 04"1; 049701 09665 -0067370 1911,1 19706 0"9O 00"6 490 1000091 0000 00N 0 =i 6100iO 05M0 0422~ io0s2 -02.a

360I 18"2 1 %5309552 -Owi so 09ill 091"9 oqq 1 -00i1 620 05160 05260 10223, -0120,

19 h10111Iis$ 09913 -01491150030 08571 09*95 1-0261, 630' 06231 06*1 1020 i 0AM 113. 1M.N 0011 :20 0757 1 O7253 06 03 51 1;0 106 06i -0325'

410 17591: 174671 10060 , 01041 o3 0*924! 066141 10i*01 .01091 6501 07M0 O6ij (096J 0661420 16914 1 V7044 0995111 -00701 540 0*6350, .079 62160016 40' 0730I1 074641 0 9762, OilS430 1610 16175 00999 -00 7 1 :" $86 603 9714701 0700 07517 1029 - osn

Q 15169 I 5169 0000o -0am01 1401 05457 051 loll,! 0160 06245 062i4 (10 M1 0031450 4158 1(3911 10127 . 0177 1 570 05146, 05011* 10270 1. 0135 1 ow0 041110 05121 09571 - 0220.1*0 :1307' 1291119 10064 -010611 510 04935 05071 097186 -0143 1700' 02691 016*8 (5$476 .1023

CIA I A *ia~olerolhti in nanetimll

Col 2 Model ireu %4mm III of 1105 incolumnif 3 fDul to Waol~c fulrcleofs of(4fl3111gt isee test)

Coo J Data %ioo determined from lite! (lo squerea fi o( ,wer lott of K (A i vs 9 (4901Col 4 Ratio .column I divWde by column 3Col 5 DIN column 2 nus$ column 3

SPIE Vol 4f Ocew ts em W(INS) n17

Table 4. Values of the slope function .M (W)and K. (A for use in Eqs. 5 and 6

vJ,A. (am)w W A) K.IA) A IRMOw W 4A) K. (A) 1. I (am)IW 00 K. Al

350 2 12 00510 470 I 1932 00179 59 04840 0 1571355 20963 00453 475 I 1440 00114 545 04853 0 43360 20504 00405 480 10955 00193 600 04903 02409365 20051 00365 485 10469 00206 605 04963 02168

370 19610 00331 490 10000 00224 610 05090 02192375 19113 00302 ' 495 095S0 00248 615 05223 03040380 18772 I 00278 500 09118 00230 620 05380 03124385 I (379 00258 505 081704 00320 625 05659 03174

390 1 IM, 0.0242 510 04310 00369 630 06231 03196395 17671 00221 515 07934 00423 635 0.83 03227400 17313 00217 520 07578 0096 640 07001 03290405 ( 7463 00203 525 07241 0054 645 07201 03397

410 17591 00200 530 06924 00526 650 07300 03559415 ( 7312 00194 535 06627 00550 655 0'323 037"9420 (6974 0.019 540 06350 00577 660 07301 04105425 16550; 00115 545 060 00607 665 07205 04206

4:0 16106 0012 550 0530 00640 670 0700 04278435 1%48 00110 555 05647 00673 675 06693 04372440 51(69 I 00178 50 0.54S7 00723 680 06245 0452(415 (4673 00176 56 05289 00776 615 05651 04755

450 14158 00176 570 05146 00142 690 04"01 05116455 13627 00175' 575 05027 00931 695 03984 0567144o I(37 00(7 no 04935 0(065 me00 02891 06514465 12521 0.0177 515 04871 01341

Values for M(A) and K. (A) should be interpolated when precise wavelengths are defined. Equation (5) or (6) and Table 4

are all that are needed to estimate entire K (A) spectra if the known value of K indicates the water to be oceanic ormoderately clear coastal water, for example Jerlov Type I through III oceanic or Type I coastal, or if K (490) < 0.16 m- I

Figure 4(a) is a plot of the model K(K) versus wavelength with K (490) as a parameter. In Fig. 4(b) K'(A), i.e.K (A) - K. (A), is plotted for the same K (490) values. In Table 5 values of K (A) are listed for each 10 nm from 350 to700 nm, inclusive, for a variety of values of the water classification index. K (490). from 0.03 to 0.18 m-1 Figure 4 andTable 5 comprise a summary of the results of the model.

(a) (b)6?OK40 50 4,,60 ,u 40 '•,-

- 0 30 16

,300 400 500 600 '00 300 400) .O0 600 "00

A 1Inm1 A Iul

Figuare 4. Plots of the water model wulh values of K(490) as a parameter. Bottom curve K(490) -0.022 is K (A)

,Ox Filgure 5 shows plots of the model superimposed on K (A) values calculated from the measured downwelling irradi-~ance spectra at S of the stations used in the original data base. The K (490) values range from 0.033 for Fig. 5(a) to 0.116

for Fig. 5(e). The comparison between the model and the measured data provides examples of the manner in which themodel represents the data from which it wa formed. Figure 6 provides another measure of the deglree of the fit betweenthe model and the data. Figure 6(a) shows the standard deviation of the ratio of the K values calculated from the modelto those obtained from the measured irradiances. Figure 6(b) shows the standard deviation of the differences between thetwo. Faigure 7 presents the number of points used at each of the 681 wavelengths between 365 and 700 in the oripp.al dataset.

-! t 174 / SPIf VeA 489 Ocean Optics VI (1994l

004

Tabl S. Values of K (A) for selected K 1490). the water classification index

.-IS0 00510 00672 00617 0 1101 0 1316 023530 021,4S 021950 0' 3 0 2*02 03031 034*0 03369360 00405 005*1 00766 00971 01176 0111 0156 0 1 91 0199 02.4* 0.1810 03226 0 3636370 00331 00100 00676 00672 01018 012' 0 14*0 02*5*6 0 1152 0 2244 02637 03029 03421

P,360 00278 00421 006011 0079* 00961 022172 021359 02IS47 0 03S 02110 0 .48* 023.W 03236A 30 00242 00379 00559 0 0739 00919 02109 0127 014)9 0216J9 0 1999 023*,0 0 2'20 03060

* .400 00217 00349 00123 00*97 00670 01014 0122 021392 02)1" 0 1913 02261 023091 029)4* F.420 00200 00334 00)10 00*N* 00161 021037 0 1213 01369 0215*5 0 1917 02269 02621 02972

420 00239 00313 00116 0 06 0062Z7 00997 0211*7 03* 02)0* 0134* 0218) 02525 026430 00102 0030W 004OW 00*27 0 0736 009*9 02220 02271 024132 0217)4 02076 0 23"6 0272140 00176 00293 0 06 00Oft 0074 00399 021051 01203 0213)5 01*53 01961 0226S 0 25*8R4)0 0027* 00263 00425 00146 00706 00349 00992 02233 021274 021)57 01640 02224 024074*0 0 0276 0027) 00Oft 00)36 00447 00796 00929 010*0 02290 014)2 021723 0297) 02236470 00279 00270 0039 00)10 00630 00749 006*9O 009619 02209 02349 01)36 0128 020*7480 00293 00276 00311 0 019 00*0) 00714 00624 00933 021063 026*2 02482 021700 01919

490 00224 0 0300 00400 00M00 040 00700 0060W0 09010 01000 01200 0240 02600 01300

'00 002O0 00349 0 060 00)32 00623 00724 00605 0 069 00967 022170 023352 02)S35 021727$10 003*9 00432 00525 00)96 00*81 00764 00647 00920 01013 01260 01234* 0)512 02*673520 0 009 00)55 00*31 00707 00713 00353 00934 02010 0206 02237 0 136 02540 01692530 00526 00)79 00111 00727 0076 0016 009M 0 0906 010*3 02202 02340 02479 02*17

li- 40 0057? 00*23 0 0*9 0075 0 W6* 00179 00943 0100* 02070 02297 02324 02452 01)73.P550 00*40 00*63 00743 0030 001*1 00929 0097 01036 01095 0212 01329 024 0"? 5*4

SOO.. * 00723 00764 00629 00673 0092 0036 02037 02092 02244 02255 01364 02474 0253)'0 00342 00662 00933 00664 01036 02061 02239 01190 01241 02345 02448 021551 0163Sao 010*4 02202 02252 0201 01230 0129 02349 02390 02447 0154* 02645 02744 02642590 01573 02*24 0216*3 02722 0.17" 026N$ 0215* 0290) 0213 02030 02147 02243 02340:a00 02436 0234411 0 249 02544 02393 02*42 02691 02740 0 2769 0267 02965 03063 0322*10 02692 02931 02932 03033 0 303 03134 03235 03236 03217 0 3369 03491 03592 03694*20 03123 031*4 03226 03272 0332* 03379 0343) 0347 03542 03643 0375* 03164 03972*3o 0319* 03243 0320* 03346 03430 03493 03555 03617 0 3*10 03304 03929 04053 04273640 0329 0 3343 03423 0 3463 03553 03623 03493 037*3 03833 03973 04223 04253 04M9*50 03559 0315 03*6 037*2 0 36341 03907 0 3960 04053 0426* 04272 0442 0 4114 047106 '440 0420)5 0412*0 04233 040% 04379 04452 04525 0 4596 04472 04627 049*3 05209 05255670 04278 04332 04401 044712 0 44 014611 04*1 04752 04622 049*2 05202 05242 05312*o0 04522 043491 04*32 04*93 0475* 0483 04862 04943 0 500* 05232 01256 05360 053063 90 0512* 05254 05203 05252 015302 05330 05399 03S446111 05497 0559) 0)4 93 05792 03369'M0 06513 0*535 06W* 0*593 0*622 06651 0440 0*709 0*731 0*79* 0*153 06911 0*6W

a"DtacoIII Sia. 10 Eip 2 Nout Slsunyo.Maru Ste. 4 Oliami.e a/e Discovurer St. 9 5.1*212

K (490) -0033. Depth: 1 -4&n K (490) -0053. Depth 10.- 19 6M K (490) -0.073. Dbosh. 10 -20 1im

14/912- 30 .. 0

06 2020

30 30 4 0 2004 10

02 (a) (b[ WC50 00 600 700 400 500 600 70411 o 0 0

A, I III A (nmI Inmit

New Horizon Sta. 9 SfihIh FmiWe1. Gulf of Califortia, SrmthK (490) -0076. Depth: 5,2 -12.4tm K24(M)-0 116. Depth 6.16

70 7060- 60,

40 -50

20 - 2

I0-

400 500 600 700 400 Soo 60 700V.1 I A I, I

jFig. S. Examples of K (A) spectra as determined from irradianCe data at 5 selected locations (+I Solidcurve is plot of model using K (490) values determined from~ data-

SPValet 4" OceenOwxscsW t "4) 175

WIN

'480 12 4

(a) (b) 4

:1- - -O5

-z . -. -

4 .o

. ' 0, - 0 o i" - . -- °350 400 450 500 550 600 650 '00 350400450 00 50 60 650 -00

X trim) A (nmi

Fig. 6. Approximate standard deviations of comparisons between model and measureddata at each of the 68 wavelengths examined between 365 and 700nm (a) Standard.deviation of the ratio K. (A)/K, (A) where K. is the value calculated from the model andK.,, is the value determined from measured Ed (A,: . (b) Standard deviation of the dif-

ferences K, (A - K,, (A)

S<O6 <025-

so0-

z 0350 400 450 500 550 600 650 '00

A (nrn

Fig. 7. Number of K,,, (A) samples used at each wavelength to form t.he data base for the model

Comparison with Jerlov water typesIt is interesting to compare our results with those presented by Jerlov (1976). The Jerlov water types were designed

to be used as a general means of classification the upper, usually well mixed, 10 meters of the ocean. The oceanic watertypes I, IA. IB, 11, and III have a minimum K (k) at about 475 nm as may be seen from Jerlov's Table XXVII and Fig. 70.Using 475 nm as a reference wavelength we have plotted K (A) Ys K (475) using our model and the values of K (475) fromJerlov's Table XXVII. Figure 8 is a plot of K(A) from 350 to 600nm showing the manner in which the attenuationchanges for the 5 Jerlov oceanic water types. We observe that our model shows the minimum attenuation shifting tolonger wavelengths as the water turbidity increases which is consistent with most observations. We also call attention tothe fact that some of the attenuation values for Type I oceanic water as given by Jerlov are less than the values we suggestfor K. (W). In fact, at some wavelengths the values given by Jerlov for K are less than the values of absorption alone pub-lished by Morel and Prieur (1977). We recommend, therefore, that the values of K () as published by Jerlov be replacedby those in Table 6. The values for Type I water given in the table are those of pure sea water, K.. The other tabulatedvalues were computed using our model and the values for K (475) given by Jerlov in his Table XXVII. The form of Table6 allows direct comparison with Jerlov's table. Figure 9 presents a comparison between the K (A) values at the wavelengthin Jerlov's table and our model for oceanic water types IA, 1I and Ill. The disagreement between the two is generallygreater in the blue. This would be consistent with our finding less evidence of yellow substance in the data which we used

* 0_as a basis for our model than Jerlov had in the data upon which he based his work.

20

to . ... ........

1A .

300 40 0 600

Fig. 8. Spectral diffuse attenuation coeffcients for Jerlov water types I-Ill.

176 /SPRt VL 489 Ocean Optics V11 17984/

Table 6. Downward irradiance auIenuatt~n coefficients K ix I for Jerbo1. water tYpe

WIer WA1. ELENGTHi4

T, Ve is 1. 400 425 As0 4,5 00 i2s 550 5'j 6W0 625 650 675 "00

1 0510 001302 00217 00185 00176 00134 0 030 00504 00640 00931 0.2403 0 3174 03559 04372 0651314 '0632 10412 0)0316 00230 00257 00250 00332 00545 00674 00960 0 2437 03206 03601 04410 06530

0 1012 : 10546 00413 Q03OW 00355 00330 00396 00596 00715 0 095 0 .471 o33245 03652 04457 0655011 1132 31031 0 0373 0011 00714 00620 00627 00779 00363 0 1122 021595 03389 03337 04626 06623

~ . I 13' 11935 0 1697 0 1544 0 1331 01160 0 1056 0 1120 0 1139 0 1359 02326 03655 04131 04942 06760

0 11341 32839 0 2516 02374 02043 0 1'00 0 1486 01461 0 1415 0 1596 03057 03922 04525 0 5257 06396

1.i.ue-, ,,I K IA iI n body of Table ha~e uni. m, Compare with. Table XXVII Jerloul 1976)

IL(b) (c)

12 >~30-

-06 J09 20- .

0 IA whnt

A lnrfl A (nm) X (nm)

Fig. 9. Comparison between Jerlov oceanic Types IA, 11 and III with the present modelwhnK(475) set equal to Jerlov's tabulated values.

Figure 10 is a plot of K (A) versus K (475) for each 25 nm from 350 to 700 nm. This plot is direcly comparable toFigure 70 in Jerlov (1976). The slopes associated with each of the lines in the plot were taken from the present model and

inmi Slope 11.41

351) 1 871 Io 3a I315 1 674 .1 17

475 1170 30 -5 60

525 163 444450 '1 3 [if475 1)3 00 35 50-

202 -)9 304

'1)4 025245b- -

4' I

(1439 1075

IFs 058

SKI V448975n pic I (94 7

SummaryThe spectral characteristics of the diffuse attenuation coefficient of oceanic water behave in an orderly predictable,

fashion. The complete spectra may be predicted knowing the value of the diffuse attenuation coefficient at a singlewavelength through the use of a model based on the analysis of many such spectra. Regressions of the attenuation

*' coefficient at any wavelength from 365 to 700nm against the corresponding value of the coefficient at a second referencewavelength show a linear relationship between the two variables (Eq. (4), Fig. 2(a-d)). From the slopes and intercepts oflinear equations fitted to these regressions the value of the attenuation of pure sea water. K,. (k) may be inferred. Suchvalues were found to be very close to the values obtained using Eq. (3) with the spectral absorption and scattering valuespublished by Morel and Prieur (1977) and Morel (1974). Using these latter values for K.(k) and Eq. (5), new slopes..Nf (.), were calculated which with K. () form the basis for the model of spectral diffuse attenuation coefficient. Table 5lists the values of K. and V, at 5nm intervals from 350 to 700nm. These values may be used in Eqs. (5) or (6) to pro-vide estimates of K (W) at any wavelength, given the value of K at a second, reference wavelength. Table 5 lists values ofK (k) calculated as described using selected values of K (490) from 0.03 to 0. 18 m- I as a water classification index.

Jerlov water types may be redefined using the model presented here. Table 6 presents values of the diffuse attenua-ton coefficient at the same wavelengths as published by Jerlov for oceanic Types I. [A, lB, 11. III and coastal Type I. Thetabulated values at 475 nm are the same as those used by Jerlov.

An alternative to the use of Jerlov water types would be the use of a classification index such as the value of K at aselected reference wavelength (e.g. our K (490)). This has the advantage that the value of the index provides a quantita-tive indication of the water clarity (i.e. attenuation coefficient) and allows the user to classify the water by selecting anyrange of values of the classification index that may be appropriate to the particular application.

We observe that the spectral nature of the attenuation coefficient did not appear to be dependent on the geographicallocation of the water investigated nor on the depth of the observation in the water column providing the classificationindex, K (490) was less than approximately 0.16m - '. We believe, therefore, that the model can be considered as generallyapplicable for water at the surface or at depth as -ong as K (490) < 0.16 m - .

References

Jerlov, N.G. (1976), "Marine Optics," in Elsevier Oceanography Series, vol. 14, Elsevier Scientific Publishing Co., Amster-dam, Oxford, New York.

Morel, A. and L. Caloumenos (1971), "Mesures D'enclairements Sous Marins Flux De Photons Et Analyse Spectrale,"Centre De Recherches Oceanographiques, Report No. 11, La Darse - 06230 Villefranche-sur-Mer. De Villegranche-Sur-Mer, France.

Morel, A. (1974), "Properties of Pure Water and Pure Sea Water," in Optical Aspects of Oceanography, eds. N.G. Jerlov andB. Steemann Nielsen, pp. 1-24, Academic Press, New York, N.Y.

Morel, A. and L. Prieur (1976), "Irradiation Journaliere En Surface Et Measure Des Eclairements Sous Marins: Flux DePhotons Et Analyse Spectrale." Resultats De La Campagne Cineca 5 -J. Charcot Capricorne 7403, Report No.10,Serie: Resultats des Campagnes a la Mer, Groupe MEDIPROD, Centre National Pour L'Exploitation Des Oceans

*. (CNEXO).

.,i Morel, A. and L. Prieur (1977), "Analysis of Variations in Ocean Color," Limnol. Oceanogr., 22 (4), pp. 709-722.

Okami. N., M. Kishino, and S, Sugihara (1978), "Measurements of Spectral Irradiance in the Seas Around the JapaneseIslands," Technical Report No. 2, The Physical Oceanography Laboratory of the Institue of Physical and ChemicalResearch, Tokyo. Japan.

Smith, R.C. and K.S. Baker (1978), "Optical Classification of Natural Waters," Limnol. and Oceanogr., 23, pp. 260-267.Also issued as University of California, San Diego.'Scripps Institution of Oceanography. Visibility Laboratory, SIORef. 77.4.

Smith, R.C. and K.S. Baker (1981), "Optical Properties of the Clearest Natural Waters (200-800nm)." Appl. Opt., 20. pp.177-184.

Tyler, J.E. and R.C. Smith (1970), in Measurement of Spectral Irradiance Underwater, pp. xii - 103. Gordon and Breach,New York, London, Paris.

Tyler, I.E. (1973), "Data Report of the Discoverer Expedition." SIO Ref. 73.16. pp. 1.1000. University of California, SanDiego, Scripps Institution of Oceanography, Visibility Laboratory.

AcknowledgmentThis work was supported by the Office of Naval Research under contract N ()O 14-78-C-O.66, This support is

gratefully acknowledged.

778/ SPIE Vol. 489 Ocean Optcs VII (7984)

,LOW#

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6R%