Ocean color algorithms in optically shallow waters: Limitations and improvements

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1 Ocean color algorithms in optically shallow waters: Limitations and improvements Kendall L. Carder *a, Jennifer P. Cannizzaro a, Zhongping Lee b a University of South Florida, th Ave. S, St. Petersburg, FL, USA 33701; b Naval Research Laboratory, Code 7333, Stennis Space Center, MS, USA ABSTRACT Current ocean color algorithms based on remote-sensing reflectance spectra, R rs (λ), overestimate chlorophyll a concentrations, Chl, and particulate backscattering coefficients, b bp (λ), in optically shallow oceanic waters due to increased bottom reflectance. Since such regions often contain important ecological resources and are heavily influenced by human populations, accurate estimates of Chl and b bp (λ) are essential for monitoring algal blooms (e.g. red tides), detecting sediment resuspension events and quantifying primary productivity. In this study, a large synthetic data set of 500 R rs (λ) spectra is developed to examine limitations of ocean color algorithms for optically shallow waters and to develop alternative algorithms that can be applied to satellite (e.g. SeaWiFS and MODIS) and aircraft ocean color sensor data. R rs (λ) spectra are simulated using a semi-analytic model for optically shallow waters. The model is parameterized with sand bottom albedo spectra, ρ(λ), using a wide range of chlorophyll a concentrations ( mg m -3 ), bottom depths (2-50m) and bottom albedos (ρ(550)-0.30) to provide a robust data set that accurately represents and complements shipboard R rs (λ) data from the Gulf of Mexico and Bahamian waters. The accuracy of a remotely-based technique developed recently from shipboard R rs (λ) data is tested on the synthetic data for identifying waters with bottom reflectance contributions at R rs (555) greater than 25%. Limitations and improvements regarding this method are discussed. Keywords: remote sensing, chlorophyll a, bottom albedo, backscattering 1. INTRODUCTION Shallow, estuarine and coastal environments in the Gulf of Mexico and Bahamas are under threat from several sources: anthropogenic pollutants cause eutrophication; red tides threaten fisheries, public health, and endangered species (e.g. manatees) and affect tourism; and hurricanes threaten benthic habitats causing erosion/deposition and increased turbidity sometimes hindering navigation. As important as these waters are to humans, they can be difficult to assess remotely for numerous reasons (atmospheric correction 1, Case 2 waters 2, and bottom reflectance 3,4 ). Optically shallow waters perturb standard chlorophyll a concentration 5,6, Chl, and backscattering 7 algorithms by differentially enhancing reflectance at wavelengths (e.g. green) in the transparency window 3,4,8-11. A method is needed of providing accurate and quick assessments of bottom reflectance contributions to water-leaving radiance imagery for satellite and aircraft retrievals of water column optical properties (i.e. absorption and backscattering) and constituents such as chlorophyll a concentrations in shallow coastal environments. Empirical chlorophyll algorithms strongly depend upon correlations between chlorophyll concentrations and remotesensing reflectance, R rs (λ), ratios. In traditional blue-to-green reflectance-ratio algorithms 5, the green or reference waveband is located in a region of minimal phytoplankton absorption (~ nm) that can be heavily influenced by bottom reflectance. Alternatively, the blue waveband is located near the phytoplankton absorption peak where chlorophyll a absorbs maximally (~440nm). Studies have shown that shifting the blue waveband from 443nm to 490 and 510nm may improve estimations of chlorophyll concentrations by minimizing interference due to CDOM absorption and signal-to-noise errors that occur with increasing chlorophyll concentrations 6,7. The standard empirical chlorophyll algorithm for the Sea-viewing Wide Field-of-View Sensor (SeaWiFS) (OC4) employs a maximum band-ratio approach with a fourth-order polynomial function 6,12. *kcarder@marine.usf.edu; phone ; fax

2 An empirical algorithm for estimating particulate backscattering coefficients 7 also involves a green reflectance wavelength (R rs (555)) taking advantage of a spectral region with relatively low phytoplankton and gelbstoff absorption and high signal-to-noise ratios. Once again, however, since this wavelength is located within the most transparent spectral region for coastal waters, bottom reflectance will increase the apparent backscattering coefficient derived using R rs (555). Algorithms for chlorophyll and backscattering using red wavelengths 13,14 are less subject to bottom effects due to a large increase in absorption by water molecules. However, signal-to-noise may be problematic for such wavelengths. More complicated algorithms (e.g. optimization 15, spectral look-up tables 16, and neural networks 17 ) that specifically take bottom reflectance into consideration are computationally less efficient as they require hyperspectral data, making them unsuitable for processing large satellite and aircraft images. The goal of this study is to analyze how bottom reflectance perturbs empirical chlorophyll 6,12 and backscattering 7 algorithms. Analysis of a large in situ dataset (Gulf of Mexico and Bahamas) has shown that optically shallow waters can be discriminated from optically deep waters using the relationship between R rs (412)/R rs (670) and [R rs (412)*R rs (670)]/ R rs (555) 2, and chlorophyll concentrations for mixed environments can be calculated more accurately using a combination of standard and alternative reflectance ratio algorithms 18. While the technique has potential, limitations in the range of optical properties and bottom depths for the in situ dataset necessitate testing of this scheme with a synthetic dataset containing most combinations of water column optical properties, bottom depths, and bottom albedos. 2. DATA The synthetic dataset contains 500 remote-sensing reflectance spectra generated using a semi-analytic reflectance model 15 with water column optical properties (e.g. absorption and backscattering) modeled using global models 19. Chlorophyll concentration is used as the free parameter to define different waters and is set in a range of mg m -3 with 20 steps. For each chlorophyll step, 25 different absorption and backscattering spectra were created. Terms for chlorophyll and gelbstoff fluorescence and water Raman scattering are omitted, and the bottom is assumed to be a Lambertian reflector 20. Total absorption, a(λ), and backscattering, b b (λ), spectra are a = a + a w p + b b = b bw + b bp. (2) where the subscripts w, p, and g represent water, particles, and gelbstoff (or colored dissolved organic matter), respectively. Wavelengths are omitted except where deemed necessary for clarity. a w (λ) and b bw (λ) are constant and known 21,22. Particulate and gelbstoff absorption coefficients at 440nm and particulate backscattering coefficients at 550nm are 23, a p ( 440) = 0.06C, a g ( 440) = p1 *a p ( 440), 0.62 b ( 550) = { [ log( C) ]}*p *C. Further, a a bp p g ( λ) = a p ( 440) A 0 ( λ) + A1( λ) ln a p ( 440) ( λ) = a ( 440) exp[ 0.015( λ 440) ], g a g [ ( )], 550 b bp ( λ) = b bp ( 550), λ where values for A 0 (λ) and A 1 (λ) were generated from Gulf of Mexico and Bahamian in situ data 18 and n is the spectral shape of the particulate backscattering spectra. Values for p 1, p 2, and n were perturbed to expand the dataset to represent both Case 1 (p 1 0.8, p 2 0.3, and n 1.0) and Case 2 23,24 waters and are 19 n 2 (1) (3) (4)

3 = R R n = C where R 1, R 2, and R 3 are random values between 0 and 1. p p R1 *a = a 2, 3, p ( 440) ( 440) p, (5) The subsurface remote-sensing reflectance, r rs (λ), can be separated into two components due to the water column and bottom reflectance and is expressed as 15 C 1 D 1 B 1 D dp u u rrs rrs 1 exp H exp H (6) κ + ρ + κ π where r dp rs is the subsurface remote-sensing reflectance for optically deep waters, κ is equal to the sum of the total absorption and backscattering coefficients, H is the bottom depth, ρ is the bottom albedo spectra, and D C u and D B u are the optical path elongation factors for the water column and bottom, respectively. Bottom albedo spectra are generated by multiplying a 550nm-normalized sand albedo spectra 15 by, the bottom albedo value at 550nm. For each chlorophyll step, every different combination of bottom depth (2, 5, 10, 20, and 50m) and (0.01, 0.05, 0.1, 0.2, and 0.3) is used. Since the angular distribution for molecular backscattering due to water differs from that of particulate backscattering, subsurface remote-sensing reflectance for optically deep waters is 25 b dp b bw bp rrs = g w + g p (7) a + b b a + b b where g w and g p are known model-derived parameters for molecular and particle scattering, respectively. The optical path elongation factors for the water column and bottom are 15 respectively, where C 0.5 B 0.5 ( u) and D 1.04 ( 1 5.4u), (8) D u 1.03 u + b b u = a + b Remote-sensing reflectance spectra above the air-sea interface, R rs (λ), is related to that below the sea surface as rrs R rs (10) rrs for a nadir-viewing sensor. This expression accounts for the water-to-air divergence factor and internal reflection of the water-air interface 26. b 3. RESULTS Since the intent of using a large synthetic R rs (λ) dataset is to complement and expand the Gulf of Mexico and Bahamian in situ dataset 18, parameters used to generate the synthetic data are first compared to those measured (or derived in the case of ρ(550)) for the in situ data (Fig. 1). Chlorophyll concentrations for both the synthetic and in situ datasets span ~3 orders of magnitude. While low-chlorophyll (~ <1mg m -3 ), synthetic particulate absorption coefficients at 440 and 555nm and gelbstoff absorption coefficients at 440nm are similar to the in situ data, synthetic values generated from global models are slightly lower than in situ values for higher chlorophyll concentrations (Fig. 1a,b). Particulate backscattering coefficients at 550nm for the synthetic data center about the Case 1 (i.e. low backscattering/chlorophyll) in situ data (Fig. 1c). High-chlorophyll (~ >1mg m -3 ), high-backscattering estuarine waters represented by the in situ dataset are not represented by the synthetic data. The synthetic dataset adequately represents the range in bottom depths observed for the in situ data and expands the dataset to include even shallower data (H=2m) inaccessible by most large research vessels (Fig. 1d). Although high-. (9)

4 chlorophyll data were typically observed naturally in shallow coastal waters and in blooms of red tides, the synthetic data set includes such data for deeper waters (>20m). Bottom albedos at 550nm derived from shipboard R rs (λ) data by optimization 15 ranged from 0 to 0.5 and exhibit decreasing values with increasing chlorophyll concentrations (Fig. 1e). The five ρ(550) levels (0.01, 0.05, 0.1, 0.2, and 0.3) chosen for the synthetic data adequately represent these in situ values. While certain combinations of the synthetic parameters may not exist naturally (e.g. high-chlorophyll deep and high-albedo data; shallow, low-chlorophyll, high albedo data), such water types are still examined in this exercise. Synthetic remote-sensing reflectance spectra, equal to the sum of the light reflected by the bottom and the water column (e.g. Eq. 6), are shown for various combinations of chlorophyll concentrations (0.1, 1.0, and 10.0 mg m -3 ), bottom depths (5 and 20m) and bottom albedo coefficients at 550nm (0.01 and 0.2) (Fig. 2). Reflectance peaks shift from blue to green with increasing chlorophyll concentration. Spectral reflectance values are relatively low when the bottom albedo and hence bottom reflectance contributions are low. Increasing the bottom albedo at 550nm from 0.01 to 0.20 and shortening the water column from 20m to 5m increases total reflectance values for blue and green wavelengths due to bottom reflectance. Note that even when the chlorophyll concentration is 10 mg m -3, a 5m water column and a bottom albedo at 550nm of 0.20 causes 46% of the light reflected at 550nm to be due to bottom reflectance. Maintaining the same chlorophyll concentration and bottom albedo and increasing the bottom depth from 5m to 20m causes bottom reflectance contributions at all wavelengths to become negligible. Figure 3 shows, for each wavelength, the number of synthetic data points (out of 500) where light reflected by the bottom contributes greater than 25% to the total R rs (λ). A threshold of 25% is chosen because above this value, chlorophyll concentrations derived using standard empirical algorithms are overestimated for the Gulf of Mexico and Bahamian in situ data 18. In this figure, the spectral transparency window is clearly visible between ~500 and 600nm. This spectral region is most transparent because phytoplankton/gelbstoff strongly absorb blue light and water molecules strongly absorb red light. Sharp decreases in bottom reflectance contributions are especially apparent at ~600 and 710nm where water absorption increases significantly. Since most empirical chlorophyll reflectance-ratio algorithms 5,6,12 and reflectance-based backscattering algorithms 7 strongly rely upon R rs ( ), and because this is a spectral region most strongly influenced by bottom reflectance (Fig. 3), the synthetic R rs (λ) data are sorted for the remainder of this study by the percentage that bottom reflectance contributes to R rs (550). These spectra are then separated into four groups: <25%, 25-50%, 50-75%, and >75%. All of the synthetic remote-sensing reflectance spectra generated with 50m bottom depths had bottom reflectance contributions at 550nm less than 4%, indicating that bottom reflectance is insignificant for such deep waters. For bottom depths equal to 2, 5, 10, and 20m, the percentage of data points with bottom reflectance contributions at 550nm greater than 25% were 98, 80, 55, and 23%, respectively (Fig. 4). Generally, increasing bottom reflectance contributions at 550nm were observed for decreasing chlorophyll concentrations and increasing ρ(550) values. The influence that bottom reflectance can have on the performance of standard reflectance-ratio, chlorophyll algorithms with R rs (550) as the reference waveband 6 and alternative algorithms with R rs (670) as the reference waveband is shown in Figure 5. Cubic polynomial regression functions were fit between log-transformed reflectance ratios and chlorophyll concentrations for data with bottom reflectance contributions at 550nm less than 25% (Table 1). For reflectance ratios with R rs (550) in the denominator, these functions are very similar to the functional relationships (OC2-type) developed for a large, global, optically deep dataset 6, demonstrating the consistency of the synthetic data to natural data. Root-mean-square errors (RMSE log10 ) calculated for log-transformed data with bottom reflectance contributions at 550nm less than 25% using the best-fit algorithms were actually lower for reflectance ratios with R rs (670) than those using R rs (550) (Table 1). For highly absorbing data, total absorption algorithms including wavelengths longer than 600nm outperformed those with only wavelengths shorter 560nm[Carder, 2005, in prep., in prep.]. This is because molecular absorption due to pure water, which is constant 21, dominates the total absorption coefficient at red-orange wavelengths whereas it does not always dominate below 560nm. On the other hand, a lack of signal-to-noise errors for perfect synthetic data eliminates the uncertainty normally found in natural measurements, so care must be taken in interpreting these results for oligotrophic waters where signals are small. Applying these best-fit functions to the entire dataset (n=500), including points with high bottom reflectance, increases RMSE log10 some 3- to 5-fold for all reflectance ratios (Table 2). While reflectance ratios decrease systematically with

5 increasing bottom reflectance contributions for reflectance ratios involving R rs (550) because of the water transparency window centered there, reflectance ratios involving R rs (410)/R rs (670) mostly cluster together about one upper relationship regardless of the bottom reflectance contribution (Fig. 5e). Data that form a lower relationship between R rs (410)/R rs (670) and chlorophyll concentrations were all derived using shallow bottom depths (2m) and exhibit bottom reflectance contributions at 670nm greater than ~80%. Omitting these extremely shallow (H=2m) data, RMSE log10 values calculated using R rs (410)/R rs (670) and R rs (440)/R rs (670) (Table 2) increase only by a factor of 1.5 to compared to errors calculated for the optically deep data only (Table 1). For estimating particulate backscattering coefficients at 550nm, Figure 6a shows how a deep-water, empirical algorithm 7 that uses R rs (555) will significantly overestimate b bp (550) due to bottom reflection and underestimate values for optically deep data with extremely high absorption-to-backscattering ratios. The latter problem can be minimized by using algorithms that include both R rs (555) and a red waveband (e.g. R rs (670)) to estimate b bp (550)[Carder, 2005, in prep., in prep.]. An alternative algorithm is suggested by Figure 6b where a quadratic polynomial regression function fit to logtransformed data relating R rs (670) to b bp (550) is shown. Data for optically shallow waters with bottom reflectance contributions at 550nm greater than 75% (H=2m), however, continue to be overestimated using this approach due to extremely small water column contributions to R rs (λ). Using the band-ratio R rs (412)/R rs (670) as a surrogate for chlorophyll concentration (e.g. Fig. 5e) and the spectral curvature about 555nm ([R rs (412)*R rs (670)]/R rs (555) 2 ) as an indicator of bottom reflectance contributions, shipboard R rs (λ) data from the Gulf of Mexico and Bahamas were successfully separated into optically deep, optically shallow, and transitional waters 18. Chlorophyll a concentrations were then derived for these water types more accurately from R rs (490)/R rs (555), R rs (412)/R rs (670), and a blend of these retrieved values, respectively, compared to when a single band ratio was used alone. Plotting the synthetic R rs (λ) data in the same fashion as the in situ data (replacing R rs (412) with R rs (410) and R rs (555) with R rs (550)) (Fig. 7), the classification scheme developed for the in situ data is tested for the synthetic data and limitations are discussed. For data with R rs (410)/R rs (670) values greater than ~10 (e.g. low-chlorophyll data; Fig. 5e) and bottom depths greater than 5m, curvature values decrease systematically with increasing bottom reflectance contributions at 550nm similar to trends observed for the in situ data (not shown). Remote-sensing reflectance data generated for waters with bottom depths equal to 2m, however, exhibit low R rs (410)/R rs (670) values and high curvature values indicating that these data cannot be discriminated using this technique because R rs (410) and R rs (670) values are no longer unaffected by bottom reflectance. These data can be omitted using a bathymetric flag since they are nondiscriminable using this technique. The remainder of the results will focus on data with bottom depths greater than 5m. A quadratic polynomial regression function was fit to the log-transformed R rs (410)/R rs (670) and [R rs (410)*R rs (670)]/ R rs (550) 2 data for data with bottom reflectance contributions at 550nm less than 25% (Fig. 7). Dividing this best-fit relationship by a series of factors (1, 1.5, 3, 6, 12, and 65), various threshold functions were generated below which data contaminated by bottom reflectance were flagged and excluded from statistical analysis. Chlorophyll concentrations and b bp (550) values were then derived using various existing and newly developed empirical algorithms and compared to known values for data located above these threshold functions. Chlorophyll concentrations estimated for the 5m data using the best-fit R rs (440)/R rs (670) relationship exhibit error values that are approximately half of those calculated using best-fit R rs (440)/R rs (550) and R rs (490)/R rs (550) functions (Fig. 5, Table 3). RMSE log10 values decrease by 25% and 60% using R rs (440)/R rs (670) when 18% and 67% of the most optically shallow data are omitted and 82% and 33% of the data are retained, respectively. Particulate backscattering coefficients at 550nm calculated using R rs (555) 7 exhibit a high RMSE log10 (65%) and show only minor improvements when data with increasing bottom reflectance contributions are omitted (Table 3). This occurs because data with extremely high a:b b values cause R rs (555) values to decrease per unit backscattering leading to large underestimations in derived values[carder, 2005, in prep., in prep.]. Errors for calculating b bp (550) from R rs (670), however, are more than three times lower for the 5m dataset compared to when values are derived from R rs (555). Errors decrease three-fold using R rs (670) when 18% of the most optically shallow data are excluded using the band ratio versus spectral curvature filter (Fig. 7, Table 3).

6 4. DISCUSSION Remote-sensing reflectance in the transparency window near 550nm for productive coastal waters is much more strongly affected by bottom-reflected radiance than are red wavelengths, making 670nm a less perturbed wavelength to use for evaluating optical properties by remote sensing for shoal waters. For waters at least 5 m deep, algorithm accuracies improve 3-fold and 2-fold in estimating particulate backscattering coefficients and chlorophyll, respectively, when R rs (670) is used as the reference wavelength. These accuracies improve even more (up to 8-fold retaining 76% of the data) if a numerical filter is used to omit data manifesting the most egregious bottom effects. The numerical filter, consisting of a curvature algorithm centered at 550nm compared to a chlorophyll concentration estimated using a R rs (410):R rs (670) algorithm, operates on the basis that the curvature algorithm over the transparency window is much more affected by bottom reflectance than is the ratio algorithm that straddles the transparency window. This filter is effective for waters 5m or deeper, but it is ineffective at 2 m depth where the bottom-reflected radiance dominates the water path radiance. Thus, the first filter to apply is a bathymetric filter for points shallower than 5 m where depths are known. Using various discrimination thresholds for the curvature filter, the backscattering RMSE log10 drops three-fold to about 6% while retaining 82% of the original data points. The filtered 18% of the points could then, in theory, be addressed with an alternative algorithm using a model-optimization approach 15. Since optimization approaches are computationally inefficient, it is best to discriminate first the points requiring this special attention using a numerical filter. The significant improvements observed in retrieved chlorophyll a concentrations and backscattering coefficients resulting from algorithm ratios using 670nm as a reference wavelength rather than 550nm, even for deeper waters, was surprising because the R rs (670) signal is typically about 5 times smaller than is R rs (550). On the other hand, for synthetic data there is no noise. Thus the inherent functionality of an empirical algorithm uncontaminated by noise was observed. Nevertheless, in the real world there is chlorophyll fluorescence to be considered as well as measurement and/or atmospheric-correction-induced noise. The synthetic dataset examined in this study is reasonably representative of natural waters. Certain combinations of synthetic data, however, are unlikely to be found in nature. These include chlorophyll a values lower than 0.10 mg m -3 in shallow waters and bottom albedos of 0.3 in highly productive waters with chlorophyll a values > 10 mg m -3. The dataset at present includes only a sand type of bottom albedo. Additional bottom-albedo spectra (e.g. seagrass) can be considered in the future analyses along with realistic noise estimates. Use of actual shallow field reflectance data for retrieval of optical properties and chlorophyll concentrations is a step that has already been taken 18,27. This data set includes of course natural covariance relationships among constituents and optical properties, and it includes natural fluorescence effects that can affect R rs (670). Adding noise representative of atmospheric correction to the field data set is a step still awaiting implementation. ACKNOWLEDGMENTS Financial support was provided by the National Aeronautics and Space Administration (NNG04ZL55G) and the Office of Naval Research (N ). REFERENCES 1. Siegel, D.A., M. Wang, S. Maritorena, and W. Robinson, "Atmospheric correction of satellite ocean color imagery: the black pixel assumption", Appl. Opt., 39, , Siegel, D.A. and A.F. Michaels, "Quantification of non-algal light attenuation in the Sargasso Sea: implications for biogeochemistry and remote sensing", Deep-Sea Res., II, 43, , Carder, K.L., Z.P. Lee, and F.R. Chen, "Satellite pigment retrievals for optically shallow water", SPIE Ocean Optics XV, 1-9, Lee, Z., K.L. Carder, R.F. Chen, and T.G. Peacock, "Properties of the water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data", J. Geophys. Res., 106, 11,639-11,651, Gordon, H.R., et al., "Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates", Appl. Opt., 22, 20-36, O'Reilly, J.E., et al., "Ocean color chlorophyll algorithms for SeaWiFS", J. Geophys. Res., 103, 24,937-24,953, 1998.

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8 Table 1. Cubic polynomial regression coefficients derived empirically between log-transformed chlorophyll concentrations and reflectance ratios, R ij (where i and j are wavebands #1-6 equal to 410, 440, 490, 510, 550, and 670nm, respectively) for data with bottom reflectance contributions at R rs (550) (%bt550) less than 25%: Chl=10^[a 0 +a 1 log(r ij )+a 2 log(r ij ) 2 +a 3 log(r ij ) 3 ]. Root-mean-square errors (RMSE log10 ) calculated on logtransformed data using these best-fit functions are shown. Band ratio a 0 a 1 a 2 a 3 RMSE log10 (%bt550<25%; n=241) R R R R R R R R Table 2. Root-mean-square errors (RMSE log10 ) calculated on all (n=500) and the 5m (n=400) data using the best-fit cubic polynomial functions derived from the %bt550< 25% data. Band ratio RMSE log10 (all data; n=500) RMSE log10 (H 5m; n=400) R R R R R R R R Table 3. Root-mean-square errors (RMSE log10 ) calculated for Chl as a function of R 25, R 35, and R 26 (Table 1) and b bp (550) as a function of a R rs (555) 7 and b R rs (670) (Fig. 6b). Errors were calculated for data located above threshold functions (see Fig. 7) that were generated by dividing the best-fit relationship between R rs (410)/R rs (670) and [R rs (410)*R rs (670)]/R rs (550) 2 for optically deep data by a series of factors: 1, 1.5, 3, 6, 12, and 65. RMSE log10 RMSE log10 RMSE log10 RMSE log10 RMSE log10 Factor n % of data Chl 25 Chl 35 Chl 26 b bp (550) a b bp (550) b % % % % % %

9 a p (λ) m -1 a g (440) m -1 b bp (550) m -1 1e+0 1e-1 1e-2 1e-3 1e-4 1e+0 1e-1 1e-2 1e-3 1e-2 1e-3 a) d) 150 syn. 440: 550: in situ 440: 550: in situ syn. in situ syn. 1e H (m) 50 0 b) e) 0.4 c) ρ(550) 200 in situ syn Chl (mg m-3) in situ syn. Figure 1. Comparison between semi-analytical remote-sensing reflectance model input parameters and in situ (Gulf of Mexico and Bahamas) data 18. ρ(550) values for the in situ data were derived by optimization C=0.1 C=1.0 C=10.0 R rs (λ) (sr -1 ) C=0.1 C=0.1 C=1.0 C=1.0 C=10.0 C= C=0.1 C=1.0 C= Wavelength (nm) Figure 2. Example synthetic remote-sensing reflectance spectra (solid) decomposed into bottom (dotted) and water column (dashed) reflectance spectra for various chlorophyll a concentrations (0.1, 1.0, 10.0mg m -3 ), bottom depths (5, 20m), and (0.01, 0.20).

10 # of points a w (λ) (m -1 ) Wavelength (nm) Figure 3. Spectral distribution of the number of data points (out of 500) with bottom reflectance contributions at 550nm greater than 25% (solid). Pure water absorption spectra (dashed) 21 is shown for comparison H (m) <25% 25-50% 50-75% >75% Figure 4. Distribution of synthetic data with percent bottom reflectance contributions to total remote-sensing reflectance at 550nm <25%, 25-50%, 50-75%, and >75% for various combinations of chlorophyll concentrations (Chl), bottom depths (H), and bottom albedos ( ). R rs (λ)/r rs (670) R rs (λ)/r rs (550) a) b) c) d) < 25% 25-50% 50-75% > 75% λ=410nm λ=440nm λ=490nm λ=510nm e) f) g) h) Figure 5. Relationships between chlorophyll a concentrations and (a-d) R rs (λ)/r rs (555) and (e-h) R rs (λ)/r rs (670) where λ is (a,e) 412nm, (b,f) 443nm, (c,g) 490nm and (d,h) 510nm for synthetic data. Symbols are the same as in Figure 4. Cubic polynomial regression functions (solid) were fit through log-transformed data with bottom reflectance contributions at 550nm less than 25%. Global OC2 algorithms 6 (dotted) are shown in (a-d) for comparison.

11 R rs (550) (sr -1 ) 1e+0 1e-1 1e-2 < 25% 25-50% 50-75% > 75% (a) 1e-3 1e-2 (b) R rs (670) (sr -1 ) 1e-3 1e b bp (550) (m -1 ) Figure 6. Relationships between particulate backscattering at 550nm and a) R rs (550) and b) R rs (670). Symbols are the same as in Figure 4. An empirical backscattering function 7 (dashed) is shown in (a). A best-fit quadratic polynomial regression function generated for R rs (670) (solid) for data with bottom reflectance contributions at 550nm less than 25%: b bp (550) =10^( log(r rs (670)) log(r rs (670))^2) is shown in (b). [R rs (410)*R rs (670)]/R rs (550) m data omitted <25% 25-50% 50-75% >75% R rs (410)/R rs (670) Figure 7. Relationship between R rs (410)/R rs (670) and [R rs (410)*R rs (670)]/R rs (550) 2 for data with bottom depths greater than or equal to 5m. Symbols are the same as in Figure 4. A quadratic polynomial function (solid) was fit through logtransformed data with bottom reflectance contributions at 550nm less than 25%: y=10^( log(x) log(x) 2 ). Lines parallel and below this best-fit function (dashed) were generated to filter optically shallow data by dividing the best-fit function by the following factors: 1.5, 3.0, 6.0, 12.0, and 65.0, respectively.