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TITLE AND SUBTITLE 5a. CONTRACT NUMBER Estimating The Underwater Light Field from Remote Sensing of Ocean Color 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0602435N 6. AUTHOR(S) 5d. PROJECT NUMBER Cheng-Chien Liu, Richard L. Miller, Kendall L. Carder, Zhongping Lee, Eurico J. D'Sa, James E. Ivey 5e. TASK NUMBER 5f. WORK UNIT NUMBER 73-6802-06-5 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION Naval Research Laboratory REPORT NUMBER Oceanography Division NRL/JA/7330-06-6145 Stennis Space Center, MS 39529-5004 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR*S ACRONYM(S) Office of Naval Research ONR 800 N. Quincy St. Arlington, VA 22217-5660 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release, distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT We present a new approach that incorporates two models to estimate the underwater light field from remote sensing of ocean color. The first employs a series of analytical, semi-analytical, and empirical algorithms to retrieve the spectrum of inherent optical properties (lOPs), including the absorption and backscatter coefficients, from the spectrum of remote sensing reflectance. The second model computes the profile of photosynthetically available radiation EO,PAR(z) for a vertically homogeneous water column using the information of the retrieved lOPs and the ambient optical environment. This computation is based on an improved look-up table technology that posesses high accuracy, comparable with the full solution of the radiative transfer equations, and meets the computational requirement of remote sensing application. This new approach was validated by in situ measurements and an extensive model-to-model comparison with a wide range of lOPs. We successfully mapped the compensation depth by applying this new approach to process the SeaVWiFS imagery. This research suggests that EO,PAR(z) can be obtained routinely from ocean-color data and may have significant implications for the estimation of global heat and carbon budget. 15. SUBJECT TERMS photosynthetically available radiation, ocean color, radiative transfer, ocean optics, compensation depth 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT OF Zhongping Lee PAGES Unclassified Unclassified Unclassified UL 19b. TELEPHONE NUMBER (Include area code) l14 228-688-4873 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 DISTq1BUTION STATEW711T A Journal of Oceanography,V ol. 62, pp. 235 to 248, 2006 Approved for Public Release UistriOutilol Udh-m-iited 11 Estimating the Underwater Light Field from Remote Sensing of Ocean Color CHENG-CHIEN LIuI*, RICHARD L. MILLER2, KENDALL L. CARDER3, ZHONGPING LEE4, EURICO J. D'SA5 and JAMES E. IVEY3 'Department of Earth Sciences, National Cheng Kung University, Tainan, Taiwan 701, R. 0. C. also at DisasterP revention Research Center and Earth Dynamic System Research Center, National Cheng Kung University, Tainan, Taiwan 701, R. 0. C. 2NASA, Earth Science Applications Directorate,S tennis Space Center, MS 39529, U.S.A. 3College of Marine Science, University of South Florida,S t. Petersburg,F L 33701, U.S.A. 4Naval Research Laboratory, Code 7340, Stennis Space Center, MS 39529, U.S.A. JDepartmento f Oceanographya nd Coastal Sciences, Louisiana State University, Baton Rouge, LA 70803, U.S.A. (Received 15 September 2005; in revised form 12 December 2005; accepted 12 December 2005) We present a new approach that incorporates two models to estimate the underwater Keywords: light field from remote sensing of ocean color. The first employs a series of analytical, •P hotosynthetically semi-analytical, and empirical algorithms to retrieve the spectrum of inherent opti- available radiation, cal properties (lOPs), including the absorption and the backscatter coefficients, from ocean color, the spectrum of remote sensing reflectance. The second model computes the profile of •r adiative transfer, photosynthetically available radiation EOAR(Z) for a vertically homogeneous water ••c oocmeapn enospattiicosn, column using the information of the retrieved lOPs and the ambient optical environ- depth. ment. This computation is based on an improved look-up table technology that pos- sesses high accuracy, comparable with the full solution of the radiative transfer equa- tion, and meets the computational requirement of remote sensing application. This new approach was validated by in situ measurements and an extensive model-to-model comparison with a wide range of lOPs. We successfully mapped the compensation depth by applying this new approach to process the SeaWiFS imagery. This research suggests that EO0PAR(Z) can be obtained routinely from ocean-color data and may have significant implications for the estimation of global heat and carbon budget. 1. Introduction efforts have focused on relating radiative signals to pig- Observing ocean color from space is an important ment concentration (Gordon et al., 1988; O'Reilly et al., international tool in resource management and scientific 1998; Carder et al., 1999). Maps of satellite-derived pig- investigations. Currently, there are ten space-borne ocean- ment concentration (e.g., biomass) have been widely used color sensors orbiting the Earth operated by various space to estimate global ocean carbon content and productivity agencies in the United States, Asia and Europe. Another (Longhurst, 1995; Platt et al., 1995). However, rates of six satellites with ocean-color sensors onboard are sched- phytoplankton photosynthesis are regulated by many fac- uled to be launched in the next four years (http:// tors, including light availability. Hence, an accurate esti- www.ioccg.org/sensors-ioccg.html). A major goal of these mation of ocean primary production and carbon flux re- missions is to assess the role that the ocean plays in the quires a thorough description of the underwater light field. global carbon cycle and to examine the factors that affect Compared to advanced methods for retrieving pig- global climate change (Hooker et al., 1992). To attain this ment concentrations from ocean color (Gordon et al., goal, the amount, distribution and productivity of 1988; O'Reilly et al., 1998; Carder et al., 1999), meth- phytoplankton must be estimated from space. Many past ods for estimating the underwater light field from space have not progressed very far. A common approach is to diminish the surface solar irradiance based on satellite- derived estimates of the diffuse attenuation coefficient • Corresponding author. E-mail: [email protected] for the downwelling planar irradiance KEd (symbols used Copyright©The Oceanographic Society of Japan/TERRAPUB/Springer in this paper are summarized in appendices) at 490 nm. 235 Table 1. Various values of the coefficients used in Eq. (1) taken from various past works. KE,,,.(490) A B 2A, Source 0.022 0.088 -1.491 443 550 (Austin andPetzold, 1981) 0.022 0.0984 -1.403 443 550 (Mueller, 1995) 0.022 0.1 -1.3 443 555 (Mueller and Trees, 1997) 0.016 0.15645 -1.5401 490 555 (Mueller, 2000) Based on a simple linear regression analysis on the data tempted to conduct global simulations at the spatial reso- set, Austin and Petzold (1981) proposed the first empiri- lution of ocean-color sensors, mainly due to the signifi- cal algorithm of K5a(490) of the form: cant computational effort required to solve the full radiative transfer equation. We present a new approach that incorporates two KEd(490) = KEdww, tr(490) + A[w(L) (1) models to estimate the underwater light field from remote [L 2 'sensing of ocean color. The first employs a series of ana- lytical, semi-analytical and empirical algorithms to re- where KEdwul,,(490) is the diffuse attenuation coefficient trieve the spectrum of inherent optical properties (TOPs), for pure w, a ter at wavelength 490 nm, L,,,) and L.(X9 including the absorption and the backscatter coefficients, faorreap uwrea wteart-eler-alveainvgin grraaddiiaaatnn cceess at 4tthhwfereoa rrvmeeess plpe encgttihvsee wavelengths a. t0h2e. Tsepseccntr um of remootee s ensoipntgs terepfoleiecotance (Lee et of A, and X2. After new profiles were added to the data al., 2002). The second model computes the profile of set, the values of the coefficients used in Eq. (1) had to photosynthetically available radiation EOPAR(z) for a ver- be revised to maintain a better model-to-data fit. Table I mticaatilolyn hoof mthoeg reenterioeuvse dw laOtePr s caonldu mthne baamsebdie notn otphteic ailn feonr-- lists various results of regression analysis from a series of works performed in the past. vironment (Liu et al., 2002). This computation is based There are four major known sources of error, how- on an improved look-up table (LUT) technology that pos- evrst, invshoulvd n usingthisly dependent.Measuremaeo f ns sestshees raa dhiiagthiv aec ctruarnascfye,r ceoqmuaptaioranb laen dw mithe etthse t hfue llc osmolpuutitoan- First, K~Ea should be spectrally dependent. Measurements tinlrqrentormtessngapcto. of KEd at one spectral band (e.g. 490 nm) cannot repre- tional requirement of remote sensing application. sent the spectrally dependent absorption of short- and This new approach was first validated against in situ long-wave components of light, even in the upper 10 m measurements. To further examine the applicability of this of the ocean (Soifm ptes ono eaaannn d(S iDDpisicokk eeyy, 1199811)).. SSeecconnddK, ~KEad nteenwsi vaep pmrooadcehl -tfoo-rm ao dlaerl gec ovmapriaertiys oonf wwaast etrh etyn ppeesr, foarnm eexd- should be a function of depth even in a homogeneous fonside rane of OP combations the reslsso medium (Zaneveld, 1989). Taking an average value of for a wide range of IOP combinations. The results show medim( aneeld,1a9k8in). anaveage alu ofthat the KEd approach generates substantial errors under KEd over the first optical depth to propagate the light field different a caol ndtins ilerorm oder thwroteghrcoto ltem n my gnerte arg erors different computational conditions, while our model re- thwroteghrcoot tlem n my gnerte arg erors duces the errors significantly. This new approach was also at greater depths. Third, light absorption by phytoplankton apled the erro Fs imagery To nerate a apso or other water constituents generally have no preferen- applied to the SeaWiFS imagery to generate a map of the tial direction (Kirk, 1994). Current KEd models only cal- compensation depth. The premise assumptions of the set culate the downwelling planar irradiance Ed, yet should of three-variable bio-optical model and the vertically ho- include the scalar irradiance E0 for heat and carbon budg- mogeneous water column have been carefully discussed. ets. Fourth, the underwater light field is closely related This research suggests that EOPAR(z) can be obtained rou- to the sky radiance (diffuse) distribution at the sea sur- tinely from ocean-color data and may have significant face, which is very sensitive to solar position (Liu et al., implications for the estimation of global heat and carbon 2002). A value of KEd obtained during a satellite over- budget. pass provides no information on the underwater light field 2. Methods at other times during the day. Over the past two decades, major advances in 2.1 Fast, accurate model of underwater scalar irradi- radiative transfer theory have enabled a realistic numeri- cal simulation of the underwater light field (Mobley et Liu et al.( 2002) employed four strategies to accel- al., 1993), provided that the inherent optical properties erate the simulation of the underwater light field without (lOPs) and the ambient optical environment are given. lo si muration of the late st versio ut These radiative transfer models, however, have not at- losing accuracy compared with the latest version 4.2 of 236 C.-C. Liu et al. Hydrolight (H42). They demonstrated that the sky radi- 0.75 ance can be reallocated to the plane of the Sun and de- composed into ten independent sources of light incident , 0 ! from ten different zenith angles. EopAR(z) can then be 0.65 f! " obtained by summation of contributions from these light sources. For each incident light source with unit inten- (cid:127) 0.60 sity, they constructed a look-up table (LUT) for quick .5 reference to a set of parameters (B0, Bl, P, B2, Q) that are 0 required by a five-parameter model (McCormick, 1995) -C 0.50so P for specifying the vertical profile of the average cosine jl(z). Finally, Gershun's equation (Gershun, 1939) was 0.45 used to convert ,7 (z) to Eo(z). They also developed an empirical approach to correct the effects of a wind-rough- 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 ened surface and the contributions from an extra CDOM component. Their model runs more than fourteen thou- Original values of a(670) sand times faster than the full Hydrolight code, while lim- Fig. 1. Comparison of derived a(670) (Eq. (1)) and original iting the percentage error to 2.20% and the maximum er- values of the simulated data. ror to less than 4.78%. Detailed procedures are illustrated in the block of Step 3 of Fig. 2. To construct a LUT of t (z), Liu et al. (2002) em- ployed a set of bio-optical models to parameterize lOPs, b (,A)- bp(A) - . ( including absorption, scattering, and the phase scattering /3 +(Ab)(+ll/rp;()v-lb; A), (4) function. The absorption coefficient a(A) is obtained us- ing the models of Morel (1991) and Prieur and Sathyendranath (1981): where V is the scattering angle and bp(A) is the spectral scattering coefficient of particles. &lw(Va)n d fp(y, A) a(A) = a.(A) + 0.06a*(A)Chl°'65 are calculated from the analytic Fournier-Forand phase a C(2u) function (Fournier and Forand, 1994) by specifying the +F-0.06.a ,(440)Chl°65 exp(-0.014(A-440)), (2) backscatter fraction of water BFw and particles BFp, re- spectively. The value of BFw is set to be 0.5 (Mobley and where aw(A) is the absorption coefficient of pure water, Sundman, 2001). ChI is the chlorophyll-a concentration (mg m-3), F speci- This set of three-variable (Chi, F, BFp) bio-optical fies how CDOM absorption is set to be proportional to models gives a flexible parameterization of lOPs repre- chlorophyll absorption at a reference wavelength 440 nm, sentative of a large variety of water types. The current and a,*(A) is the normalized chlorophyll-specific absorp- LUT is constructed by changing variables within certain tion coefficient. a,,(A) is taken from Pope and Fry (1997). ranges: A. (400-700 nm), Chi (0-10 mg m-3) and BFp ac*(A) is given by Morel (1988) and is equal to unity at a (0.01-0.04) (Liu et al., 2002). Note that there is no limi- reference wavelength 440 nm (i.e. ac*(440) = 1). Although tation on the range of F by employing an empirical ap- F is usually set at a fixed value of 0.2 for Case 1 waters proach to correct the contributions from an extra CDOM (Prieur and Sathyendranath, 1981; Morel, 1991), it may component. vary within a range around 0.2 (Liu et al., 1999). We de- In principle, the model of Liu et al. (2002) can be termine F from an estimate of the CDOM absorption co- integrated with any ocean color algorithms. We present efficient at 440 nm ag(440). The scattering coefficient b(X) here the integration of their model and the quasi-analyti- is derived from the model of (Gordon and Morel, 1983): cal algorithm (QAA) (Lee et al., 2002), with the goal of improving the retrievals of Chi, F and BFp, and hence, the estimation of EOPAR(z) from the spectrum of remote = b,9.()+ 0.30(51o)Chlo62, (3) sensing reflectance measured above the surface R,,r). 2.2 Quasi-analyticala lgorithm where bQ(A) is the spectral scattering coefficient of pure A full description of the QAA is presented by Lee et water as taken from (Morel, 1974). The normalized phase al. (2002). Briefly, the QAA employs a series of analyti- scattering function /3 is the sum of the contributions by cal, semi-analytical and empirical algorithms to convert pure water and particles (Mobley, 1994) Rr(AQ) to a(2L) and bb(;). Multiple H42 simulations were done to derive the empirical relationship between a(670) Estimating the Underwater Light Field from Remote Sensing of Ocean Color 237 Start Step 1: Multi-band Quasi-analytical Algorithm R, (.(cid:127)2)S--l- r, (3) 05 "2 ~ +~ 1 (cid:127) '7R ' ( A ) | " r(A)=0.0895u(.)+0.1247u(A)2_ a(670)=049035r ,(670)] '-t a(670)---u2 2' 670) -b -6 7 0 = (cid:127) '(6 7 0) +b6( 6 70) - (6 7 0 ) (cid:127)- u (6 70 ) , ( 7( J az(670) + b,, (670) br (670)L "(cid:127)b,,(,t)=b(cid:127),(670)(ý.-7-J-b(")"b()b,()b()- bh(A)- Sa i' b,h(A) S--- --- ---- I - - - - - - - - -- --- --- -- - - - - - - - - - - -- HF ~b'~F 006(40)hI~ep(0.i a(2-44) u) = bh,( 443) a(1) (43 Chi F [Look.-up tablel Sbw2 + F.0.0( -a: ()Chl" + B P exp+(4-P(,1) p( Qc)) accrat moe oFEoL iiz dz / L / 7(z) * E~)~-.~/_ )E(Z)h. E()step 3"Fast and Fi(g) . 2. Processing steps to convert R.,() to E(z). and the ratio of rrs(670) and rrs(443) by varying the three The comparison of the derived a(670) and their original variables within the ranges Chl (0-1I0 mag.m-3), F (0-i1.0) values of simulated data is shown in Fig. 1. Even at band and BFp (0.005-0.05), where rrs stands for the remote 670 nm, where absorption is mainly dominated by water, sensing reflectance measured just below the surface. A varying the volume scattering phase function (VSF) regression analysis gives through BFp has an effect on rrs, and hence the derived a(670). The simple regression analysis shown here (Eq. a(670) = 0.439 + 0.305/r(670) 1-0.".3|. 2 (5) (b5y) )L eper oavnidd eSs aan dgiodogde e(2st0i0m3a)t ieomn polof yae(d6 7a0 )n. euRreacl ennet twwoorrkk L[r.A 443)J approach to relate a to the spectral ratio of rrs. Therefore, 238 C.-C. Liu et al. 10 (a) Table 2. Accuracy of retrievals for simulations shown in Fig. 3. SIndex Chi F BF, Pearson correlation coefficient 0.998 0.998 0.967 4 Average value of relative error (%) 5.19 1.73 6.78 0 accuracy of QAA in retrieving (Chl, F, BF ) was first 0 2 4 6 8 10 examined by use of Hydrolight-simulated Rrs(A) curves. InpUt Chl (mg m3") Detailed procedures are illustrated in the block of Step 1 of Fig. 2. t.0 A total of 100 cases were simulated by randomly specifying values of seven parameters (see caption of Fig. 3 for details). For each case, H42 was run to simulate Rrs at 20 wavebands in the PAR range (default setting in H42 So00..6for simulating SeaWiFS). Note that all processes of in- S0.4 elastic scattering are considered and the fluorescence efficiencies are the default settings in H42. The simulated 0.2 Rrs(A) were then used as input to QAA for converting Rrs(A) to a(A) and bb(A). The algebraic solutions of Chl, 0.0.o F and BFp canbe obtained from a(412), a(443) and 0.0 0.2 0.4 0.6 0.0 1.0 bb(443) (see the block of Step 2 of Fig. 2). The retrievals InputFpo f Chl, F and BFP and their original values are compared in Fig. 3, and the average values of the relative error for 0.030 (c) retrieving Chl, F and BFp are listed in Table 2. 0.025 2.3 Field data S..""In situ data were collected during EcoHAB cruises .020 .-." between March 1999 and October 2001 on the West Florida Shelf, and the Coastal Benthic Optical Properties (CoBOP) experiment from 1998 to 2000 in late May to 0.015 early June around Lee Stocking Island in the Bahamas. Rs(A) was determined by correcting for the surface-re- 0.010 flected skylight and solar glint from the above-surface 0.010 0.015 0.020 0.025 0.030 total reflectance, which is measured from a hyper-spec- InputBF tral handheld radiometer (Spectrix) developed by the Fig. 3. Comparison between retrieval of (a) Chl, (b) F and University of South Florida. The details of the method (c) BF, using QAA and original values used in H42 are given in Lee etal. (1998). The vertical profile of Ed(z) simulations. A total of 100 cases were compared by ran- was measured using a submersible hyperspectral radiom- domly specifying values of the solar zenith angle (0°-450), eter that was also developed by the University of South percent cloud cover (0-50%), surface wind speed (0-15 Florida. This instrument, together with two ac-9TM ab- m/s), chlorophyll concentration (0-9 mg m-3), visibility (5- sorption meters (WET Labs) and a Hydroscat-6TM 50 km), the CDOM ratio F (0.15-1.0) and backscatter frac- backscattering meter (HOBI Labs) were deployed on a tion BF, (0.015-0.025). slow-drop package and allowed to drift away from the boat to minimize ship shadow. Surface water samples were collected at each sta- tion. The spectrophotometric methods consisted of sum- the deviations shown in Fig. 1 can be reduced. ming the particulate absorption (ap) as determined by the QAA was derived from a large combination of IOPs quantitative filter pad method (Bissett et al., 1997) and for a wide variety of water types. It should be applicable the absorption of the 0.22 /m filtrate (ag) as measured to Case 1 waters of which the IOPs are described by a set using a 10 cm cell in a Perkin Elmer Lambda 18 spectro- of three-variable biooptical models (Eqs. (2)-(4)). The photometer (Spec). The accuracy of the ag measurement Estimating the Underwater Light Field from Remote Sensing of Ocean Color 239 Table 3. Descriptions of the in situ data used in the model-to-data comparison (Figs. 4 and 5). Originator identifier LSD52601 LK404U Mirirl Mirir2 Location LSI WFS (23.81°N, 76.06°W) (26.98°N, 83.30-W) (28.79°N, 89.84°W) (28.68°N, 89.90-W) Water type Low Chl-a Moderate Chl-a High Chl-a Moderate Chl-a Moderate CDOM Moderate CDOM High CDOM High CDOM Date 26-May-00 22-Apr-01 7-Apr-00 26-Oct-00 Time (GMT) 13:57 18:03 14:10 16:37 Solar zenith angle (degree) 34.9 27.48 58.6 44.2 Cloudiness (%) 10.0 5.0 30.0 5.0 Mean wind speed (m/s) 6.00 7.96 10.0 5.0 Average BP ("Hg) 29.92* 30.26 29.92* 29.92* Air mass type 1 * 1 * 1 * 1* Average relative humidity (%) 80* 79.7 80* 80* Precipitable water content (cm) 1.5* 1.5* 1.5* 1.5* Visibility (km) 15.0* 15.0* 15.0* 15.0* *Default values used in Hydrolight. is ±0.046 m-1 as reported by the manufacturer's specifi- lected in these four stations are valid inputs for the model cations. Chlorophyll concentrations were determined from of Liu et al. (2002) to estimate the underwater light field. the same samples using a Turner fluorometer (Holm- Hansen and Riemann, 1978). Details of the instruments 3. Results and Discussion and data processing of these two stations are described in Ivey et al. (2002). 3.1 Model-to-data comparison To validate our approach, we need a set of field data Here we present the results of model-to-data com- with biological measurement of Chl-a(z), the above-wa- parison at all stations. Following the Steps 1 and 2 illus- ter measurement of Rs(;L), and the in-water measurement trated in Fig. 2, the spectrum information of Rrs(G) is sub- of lOPs(z). Apart from the profiles of a(z, ALa)n d c(z, A) stituted into QAA to retrieve Chl, F, and BFP. Since Rrs(A) from the ac-9TM absorption meter (WET Labs), we espe- is a weighted average signal over depths, the mean (hol- cially need the backscattering coefficient bb(z, A) for cal- low symbols) as well as the standard deviation (error bars) culating the backscatter fraction BF(z, A). At the time of of the in situ measurements are calculated over the e-fold- writing, there are only two stations (LSD52601 and ing depth and compared to the retrievals of QAA (filled LK404U) with bb profiles measured from the newly in- symbols), respectively (Fig. 4). The e-folding depth is stalled Hydroscat-6TM backscattering meter (HOBI Labs). defined as the depth where EoPAR(z) has decreased to l/e Therefore, we add the data from other two stations (Mirirl of its surface value. Note that we compare BFp at band and Mirir2) that have all measurements except for bb(z, 488 nm because it is the first waveband that both ac-9 A). These measurements were obtained during a cruise in and Hydroscat-6 have. We also compare the total absorp- the northern Gulf of Mexico in 2001. Details of the in- tion coefficient at 440 nm, which takes into account the struments and data processing of these two stations are CDOM absorption through the value of F (Eq. (2)). For described in D'Sa and Miller (2003). the case of the most turbid water at station Mirirl (Fig. All field data were obtained from coastal regions, 4(c)), the deviations between the QAA retrievals and the where LSD52601 and LK404U represent more clear wa- means of in situ measurements taken within the e-fold- ters with moderate chlorophyll and sediment loading, ing depth (only 1.8 m) are apparent. The deviation can be while Mirirl and Mirir2 represent more turbid waters with reduced if the means are taken over more depths. How- high chlorophyll and sediment loading. A detailed descrip- ever, there is no way to determine to what depths the tion of all stations, including their locations and water means should be taken simply based on the existing meas- types, is given in Table 3. Note that the model of Liu et urements, because RrsL) is a weighted average signal over al. (2002) can be applied to Case I waters as well as to depths. Nevertheless, Fig. 4 demonstrates that QAA pro- Case 2 waters that is gelbstoff rich, and the volume-scat- vides reasonable retrievals of bulk lOPs both for verti- tering phase function can be generated dynamically based cally well-mixed waters (Fig. 4(a)) and for those cases on the backscatter fraction. Therefore, all field data col- with vertical structure (Figs. 4(b), (c), (d)). These 240 C.-C. Liu et al. 00 00 0 * 0000 * I000 T .a 00 W9 0 0 0 ,9 00 Z0 tn .0 ri2 .0 kn0 00 ocg 0 CD L 0 0 C )I 8~* ' 8 4 4 00 00C 4 0 v4f. -r C- 0 4 0 - W0 . 0oo 0 0 00 o0A V - eq 0 1 0 0 - eq M Ei ns t mt h aM ne w t r L g t F e d f o e m t e s n f O e n C l r 2 0 (a) 2 4 ----- E4,,,,(z) from in situ measurement 5 S - Ed,,,A(Z) from Hydrolight 10 30 --- E.^,,A(:) from Hydrolight 9 o EvAra(z) from Hyperlight 12 I7 14 0 500 1000 1500 2000 2500 0 10 20 30 40 50 At mol photons m- s-1 W m_' (b) 0 (d) 10 '5 410. 20 8 Cie 30 20 25 30 0 500 1000 1500 2000 2500 3000 0 100 200 300 400 u tool photons ms2 s- w m-1 Fig. 5. Model-to-data comparison of the underwater light field. (a) LSD52601, (b) LK404U, (c) Mirirl and (d) Mirir2. retrievals are used as inputs to the model of Liu et al. of Rrs. The spectrum of Rrs should be signals weighted by (2002) to calculate EOPAR(z), which corresponds to the in Kd(AL) over the first optical attenuation length, dependent situ measurements well (Fig. 5). on wavelength and the optical properties of the water at As mentioned, light absorption by phytoplankton or that wavelength (Platt and Sathyendranath, 1988). Nev- other water constituents generally have no preferential ertheless, both the OC2-v4 algorithm and our approach direction (Kirk, 1994). Therefore, we should take the sca- provide good retrievals that represent the bulk properties lar irradiance E0 rather than the downwelling planar irra- in the upper ocean. The model-to-data comparison dem- diance Ed into account. Because the in situ measurements onstrates that a good estimate of E0,PAR(z) at depth can be are EdPAR(Z) which cannot be compared directly to our obtained, as long as the bulk values of IOP are retrieved model output EOPAR(z), we use H42 as a surrogate to simu- for the important surface layer. A detailed distribution of late both EOPAR(z) and EdPAR(Z) under the same computa- the lOPs in the vertical direction would be of great help tional conditions. Figure 5 shows that, using the retrievals in estimating EOPAR(z) at depths. However, such informa- of Chl, F and BF., from QAA, H42 offers a simulation of tion usually derives from simulations of biogeochemical EdPAR(Z) that corresponds closely to the in situ measure- models rather than remote sensing (e.g. see Bissett et al., ments. In the meantime, the results from the model of 1999). The model of Liu et al. (2002) needs to be further Liu et al. (2002) are virtually identical to H42 simulations expanded to deal with a stratified water column, if the of EOPAR(z). This comparison verifies our approach. goal is to incorporate the optical model into a A major premise of this work is the vertical homo- biogeochemical model. geneity of IOPs, which is not always valid (e.g. Figs. 4(b) Figure 5 also illustrates the difficulties in obtaining and (c)). There is currently no practical way to resolve a smooth profile of EdPAR(Z) from in situ measurements. the vertical structure simply from surface observations The irradiance fluctuation is a typical phenomenon that 242 C.-C. Liu etal. EOXA (ut mol photons m,2 s-1) 0 10 10 10 0 20 OS\ 00 t 0 S 0. o0 o02 00 S ~\ 3 \ A 0(cid:127) 40 .\ 30 1142 40 K114K(490) 40 o K0,(A) 50 A . * LL iu et al -40 -30 -20 -10 0 10 20 30 40 50 60 so 0(b) Liu eltat Fig. 6. Model-to-model comparison of Eox ,(z), where Xrep- 20 resents various approaches, including H42 (Hydrolight ver- U ------ 0,-30' sion 4.2), KEd(490) (Mueller, 2000), KEd(A) (Eq. (6)), and (cid:127)"20 1 - - - -e =40o' Liu etal. (this work). --- e- S30 is not due to small-scale vertical variations in the IOPs ;k i\ but almost entirely due to the wavy surface (Zaneveld et 40 Ai\ al., 2001). Another limitation of the model-to-data com- 0 parison is that the dataset collected from in situ measure- I0 ments only covers a limited range of IOPs. To further -40 -30 -20 -10 0 10 20 30 40 50 60 verify our approach for a large variety of water types, we Relative error e(%) conducted the following model-to-model comparisons. Fig. 7. Model-to-model comparison of the relative errors E(z) in predicting EOpAR(z) by use of (a) KEJA() approach, and 3.2 Model-to-model comparison (b) Liu et al. approach. The controlled variable 0, is varied The procedure used for model-to-model comparisons from 0° to 60'. is briefly as follows. For a set of computational condi- tions of IOPs and the ambient optical environment, the H42 radiative transfer model (Mobley and Sundman, 2001) is used to simulate L,(490), LJ(555) Han4dO ,RP rAs(RA ). A fore, another profile E K,'(cid:127)() (z)jc cnabn be obbtaainnedd bb y att- detailed vertical profile of EopAR(z) is also generated to tenuating the below-surface value of EOpAR(O-) by KEda(). represent the simulated underwater light field derived Finally, the H42 simulated Rr,(L) and EdA(, 0÷) curves from a full solution of the radiative transfer equation. The are used to calculate E (z) following the approach latest formula (Mueller, 2000) is used to calculate illustrated in Fig. 2. OPAR KEd(490) from L,,(490) and L,,(555). The ratio of EGEd is We start from a simulation of a typical Case I water nominally 1.4-1.8 up to 2.0-2.5 in very turbid waters and compare the predictions of EOPAR(z) using different (Kirk, 1994). Therefore, KEd(490) is assumed to approxi- approaches (Fig. 6). A detailed description of this set of mate KoPAR averaged over the entire PAR spectral range computational conditions is given in the caption of Fig. and depth, and EOPARK (z) is estimated by attenuating 6. The relative errors of E(cid:127),(R9") (z) are as high as 188.0% the below-surface value of EOPAR(O-) by KEd(490). (38.0 in), wi a l Austin and Petzold (1986) found a relationship: at the euphotic depth (38.0 m), wh2 ile 0,PAR (z) closely pH42 matches the full H42 solution EPAR(z) (8.1% at the same KEd(2)- KEdwafer,(,I) depth). E;,P (z) indeed gives a better prediction than KEd (490) - KEdwaer, (490) = M(A), (6' l E0,PA(R90 ) (z) by taking the spectral variation of KEd(Q) into consideration. However, apparent deviations between which allows us to estimate KEQ(;L) from KEd(490). There- E (,PA(z)) and E,-Aj(Z) can still be seen from 5 m to 30 Estimating the Underwater Light Field from Remote Sensing of Ocean Color 243