Under the hood of satellite empirical chlorophyll a algorithms : revealing the dependencies of maximum band ratio algorithms on inherent optical properties

Empirically-based satellite estimates of chlorophyll a [Chl] (e.g. OC3) are an important indicator of phytoplankton biomass. To correctly interpret [Chl] variability, estimates must be accurate and sources of algorithm errors known. While the underlying assumptions of band ratio algorithms such as OC3 have been tacitly hypothesized (i.e. CDOM and phytoplankton absorption covary), the influence of component absorption and scattering on the shape of the algorithm and estimated [Chl] error has yet to be explicitly revealed. We utilized the NOMAD bio-optical data set to examine variations between satellite estimated [Chl] and in situ values. We partitioned the variability into (a) signal contamination and (b) natural phytoplankton variability (variability in chlorophyll-specific phytoplankton absorption). Not surprisingly, the OC3 best-fit curve resulted from a balance between these two different sources of variation confirming the bias by detrital absorption on global scale. Unlike previous descriptions of empirical [Chl] algorithms, our study (a) quantified the mean detrital:phytoplankton absorption as ~1:1in the global NOMAD data set, and (b) removed detrital (CDOM + non-algal particle) absorption in radiative transfer models directly showing that the scale of the remaining variability in the band ratio algorithm was dominated by phytoplankton absorption cross section. © 2012 Optical Society of America OCIS codes: (280.4991) Passive remote sensing; (010.4450) Oceanic optics; (010.1690) Color; (010.1030) Absorption; (010.1350) Backscattering. References and links 1. J. A. Yoder, “An overview of temporal and spatial patterns in satellite-derived chlorophyll-a imagery and their relation to ocean processes,” in: Satellites, Oceanography and Society D. Halpern, ed. (Elsevier Oceanography Series, 2000), pp. 225–234. 2. W. W. Gregg, N. W. Casey, and C. R. McClain, “Recent trends in global ocean chlorophyll,” Geophys. Res. Lett. 32(3), L03606 (2005). 3. J. H. 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McClain, “SeaDAS: a data analysis system for ocean color satellite sensors,” in EOS, Trans. Am. Geophys. Union, (2000). #163481 $15.00 USD Received 22 Feb 2012; revised 11 Jul 2012; accepted 11 Jul 2012; published 29 Aug 2012 (C) 2012 OSA 10 September 2012 / Vol. 20, No. 19 / OPTICS EXPRESS 20921 36. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). 37. A. Morel, “Optical properties of pure seawater,” In: Optical Aspects of Oceanography N. G. Jerlov and E. Steemann Nielsen, eds. (Academic Press Inc., 1974), pp. 1–24. 38. H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975). 39. Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. 2. 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Introduction
Over the last 30 years, a major focus of the interpretation of ocean color has been estimating the surface concentration of chlorophyll a, the major light absorbing pigment in phytoplankton and proxy for phytoplankton biomass.Synoptic empirically-based satellite estimates of chlorophyll a concentration (mg m −3 ; [Chl]), such as those obtained with the sequencing maximum band ratio algorithms OC3 (MODIS) and OC4 (SeaWiFS), provide important indicators of the condition of marine ecosystems.The ubiquitous use of empirical satellite [Chl] estimates and their importance as a phytoplankton biomass index [1,2] despite confounding issues of photadaptation [3][4][5] dictates that the estimates must be accurate and that knowledge of the errors and biases are necessary in order to correctly interpret [Chl] variability.This is all the more important given the inclusion of empirical satellite [Chl] estimates in the NASA Earth System Data Record.
The task of estimating [Chl] from remotely-sensed ocean color has been considerably difficult at regional and local scales because the spectral inherent optical properties (IOPs) of the ocean influencing the color of the ocean are both diverse and complex.Major sources of variation in the bulk IOP signals are due to the quantity and spectral quality of dissolved and particulate material which are a function of the variability in phytoplankton community composition, inorganic suspended particles, chromophoric dissolved organic material (CDOM), and non-algal particles (NAP).The shape of the chlorophyll a-specific phytoplankton absorption spectrum (m 2 mg chl −1 ; a ph * (λ)) has been shown to be widely variable, dependent on pigment complement ([Chl] + accessory pigments), pigment packaging, physiological state of the cell, and community composition [6][7][8][9][10].Detrital absorption, characterized by a wavelength dependent exponentially decreasing spectrum, are often defined as the combination of CDOM, NAP and inorganic particles.Both inorganic particle and detrital absorption have been found to be non-covarying factors in the open ocean [11,12].The lack of covariance between bio-optical components and their common strong absorption of blue and blue-green light are confounding influences on empirical satellite [Chl] estimates [11][12][13][14][15].The magnitude of the upwelling light field measured in remotely sensed applications is dominated by light scattered in the backward directions.Backscattering has been shown to globally covary with [Chl] in the surface waters, although the variations in the global relationship are large [16][17][18].Spectral particle backscattering (m −1 ; b bp ) has minimal wavelength dependence relative to absorption and is characterized by a slope of λ -n where n varies from 0 to 2 suggesting that the spectral slope of backscattering plays a minor, secondary role in determining the spectral variability of global ocean color [19].
Ocean color varies approximately with backscattering and inversely with absorption [20,21], which globally, depends primarily on phytoplankton community structure.Since chlorophyll a is the main phytoplankton absorbing pigment, ocean color is indirectly dependent on [Chl] to first order such that as the ocean shifts from oligotrophic (low [Chl]) to eutrophic water (high [Chl]), a gradient of blue to blue-green color is traversed [21].Empirical algorithms exploit this absorption dependency, statistically linking changing remotely-sensed reflectances (sr −1 ; R rs (λ)) with the gradient in [Chl].For example, the OC3 (Fig. 1) empirical [Chl] algorithm use maximum band ratios (MBRs) of blue to blue-green (443 or 490nm) wavelengths, where phytoplankton absorption is strong, to green (547nm) wavelengths where phytoplankton absorption is relatively weak.Because phytoplankton and detrital matter absorption overlap in the blue to blue-green, however, MBRs do not carry unique information about [Chl].
As such, the success of empirical algorithms rests on the global mean covariation of phytoplankton with detrital absorption and particulate backscattering.This indicates that errors in the estimates of [Chl] may occur wherever and whenever the standard of component absorption covariation is not met [14,15].Consequently, [Chl] empirical algorithms approach only 35% accuracy in Case 1 water and may be worse in Case 2 waters [19].This disagreement with the 'bio-optical covariation assumption' was thought to only occur only in Case 2 waters where optical constituents vary independently.However, the lack of covariation has been shown in many different Case 1 ocean environments [11][12][13][14][15], suggesting that the well-recognized variability feature of empirical algorithms relates to cases where second order variability exists.
Clearly, satellite empirical [Chl] algorithms are complicated in their IOP dependencies.The details of the foundation of the [Chl] empirical algorithms have been tacitly hypothesized (i.e CDOM absorption covaries with phytoplankton), and the dispersion patterns within the   [23,24], Brown et al. [22] found the impact of b bp spectral slope, n, on the OC4 MBR algorithm to be ten times less than b bp (λ) and a dm (λ).Brown et al. [22] also suggested that the anomaly patterns in the MBR-[Chl] polynomial regression were related to differences in particulate backscattering rather than phytoplankton absorption.This is contrary to previous results attributing the anomaly patterns in b bp to functional group differences in Alvain et al. [25][26][27].More recently, Loisel et al. [14] and Szeto et al. [15] confirmed the well-known detrital absorption bias in OC3 or OC4 and its impact on [Chl] retrievals.However, both of these studies stop short of quantifying the covariance structure of phytoplankton and detrital absorption, or the impact of a ph * and b bp probability on the shape of OC3 or OC4.
In this study, we confirm and quantify the impacts of the component absorption bias.We expand the analysis by looking under the hood of the MODIS OC3 empirical [Chl] algorithm and exploring the relationships between remote-sensing MBRs, in situ [Chl], and the discrete IOP measurements found in the in situ NOMAD training data set used to develop the biooptical algorithm.First, we provide an IOP perspective of the OC3 empirical model similar to previous studies [13][14][15] but with attention to defining and quantifying the extent of the correlation between phytoplankton absorption and detrital absorption.Second, we further explore the basis of the algorithm by examining the global variability of a ph * that underlies the OC3 empirical model after removal of the detrital absorption component.Third, we test the sensitivity of MBR empirical models to variability in a ph * and backscattering probability through radiative transfer simulations.These extra steps go beyond recognizing the pattern of impact that detrital absorption has on empirical algorithms by observing and quantifying the impact of each component separately on the structure of the empirical algorithm.

Methods
Our approach is divided into three sections: (1) analysis of component absorption and backscattering within the NOMAD data set where the interrelationship between IOPs are both confirmed and quantified, (2) development of a detrital absorption free radiative transfer model derived from NOMAD in situ data for exposing how detrital absorption influences the curvature of OC3 and for determining the range of variability leftover in the model without detrital influence, and (3) development of a Hydrolight model of reflectances based on models of a ph * and bb p to isolate the influence of phytoplankton absorption and particle size on empirical algorithms.The overarching analysis is focused on identifying trends that affect global retrieval of [Chl] and are inherent in the NOMAD data set.While previous work has explored (1) [14,15,[17][18][19]22], to our knowledge, analyses such as (2) and ( 3) have yet to be executed.

NOMAD in situ Data set -Component Relationships
The NOMAD data set was compiled using the NASA SeaWiFS Bio-optical Archive and Storage System (SeaBASS) [23,24] and was developed as part of the NASA Sensor Intercomparison and Merger of Biological and Interdisciplinary Ocean Studies (SIMBIOS) Program [28][29][30] for supporting present and future satellite ocean color missions.The data set includes both open ocean and coastal data sets [31,32].
The global bio-optical data set used in this study is a subset of NOMAD that includes in situ measured above water remote sensing reflectance and a set of matching depth-weighted discrete samples (n = 771) of coincident phytoplankton absorption and detrital absorption (CDOM + NAP) plus particulate backscattering (n = 331) (for information on database quality control, depth-weighting, and processing see [31,32]).This subset of NOMAD also includes co-located and depth-weighted measurements of [Chl].These measurements were a combination of HPLC [Chl] (primary) and fluorometric [Chl] (secondary).Component (phytoplankton and detrital (CDOM + NAP)) absorption was compared with [Chl] and between each component to determine relative variability and covariation in the NOMAD data set.
Because original b bp measurements were limited in quantity (n = 331) and geographic distribution relative to absorption measurements (n = 771), sample numbers of b bp were augmented to match sample numbers of in situ absorption measurements.We used the Garver-Siegel-Maritorena (GSM) semi-analytic algorithm [33,34] to estimate b bp (λ) (Table 4.2) employing standard coefficients set from the SeaWiFS Data Analysis System [SeaDAS ; 35].Realizing that the use of modeled data could introduce biases into our analyses, we confirmed that the GSM modeled b bp at 443, 489, and 547nm matched closely to in situ measured values (443nm, slope (s.d).= 1.06 (0.03); 489nm, slope = 1.05 (0.03); 547nm, 1.03 (0.03).We further verified that biases were not introduced by GSM modeling of b bp (λ) by confirming the dynamic ranges of the in situ and modeled data sets aligned (data not shown).

Forward Model of Detrital Absorption Free Reflectance
Reflectance spectra, from which the contribution by detrital matter absorption was removed, were calculated from the remaining NOMAD IOPs in the following manner.Phytoplankton absorption measurements from the NOMAD data set and particulate backscatter measurements derived from NOMAD and GSM retrievals were combined with spectral water absorption [36] and backscatter measurements of water [37] at MODIS wavelengths (443, 490, 547nm) in a forward model.All particles were assumed to be of phytoplankton origin.Detrital (CDOM + NAP) absorption-free reflectances (a dm -free) were then derived according to Gordon et al. [38] and Morel and Prieur [21]: where g 0 = 0.0949, g 1 = 0.0794, and r rs (0-, λ) indicates the remote-sensing reflectance just below the air-seawater interface.Below water remote-sensing reflectance was transferred across the seawater interface following Lee et al. [39]: Similar to the OC3 algorithm, a fourth order modified polynomial fit (OC3") was applied to the a ph and b bp dependent [Chl] where (r) corresponds to the blue-green MBR defined as:

Radiative Transfer Model Computations of Detrital Absorption -Free Reflectance
The radiative transfer model software package Hydrolight was used to compute above-water reflectances from a vertically homogeneous water column for a series of [Chl] (0.005-50 mg m −3 ), in an infinitely deep water column during clear sky, low wind (5 m/s), and annual averaged sunlight conditions.Each set of [Chl] model runs included a series of a ph * (0.11, 0.050, 0.022, 0.018 m 2 mg chl −1 at 444nm) computed from the power law model of Bricaud et al. [10,40] and corresponding to [Chl] (0.005-10mg m −3 ).Contributions of detrital (CDOM, NAP) and inorganic particles were not added to the absorption model such that above-water radiative transfer modeled reflectances were dependent only on absorption and scattering by water and phytoplankton.
Spectral scattering was derived from the difference of attenuation and absorption where attenuation was modeled based on [Chl] following the near-surface model developed by Loisel and Morel [41; their Eq.( 5)]: where c 0 = 0.407, n = 0.795 and v is a function of Backscattering probability, bb p , was parameterized based on Morel et al. [42] Case 1 Small/Large particle scattering phase functions constituting backscatter proportions of 1.40% and 0.19% respectively.This corresponded to particle sizes ranging from 0.02 to 14µm (diameter of equivalent sphere with equal geometric cross-section) for phytoplankton-like particles with a refractive index of 1.06.Additionally, all model runs were made incorporating Raman scattering.
Each model computation in Hydrolight was preset to be run to a depth of at least 2/K d (min) to ensure the capture of all photons influencing the surface ocean color, where K d (min) is the minimum value of K d (λ) estimated following Kirk [43]: where

Statistical Evaluation
Slopes and intercepts of the regressions between OC3 estimated and in situ [Chl] as well as between IOP components were based on log-transformed data.This transformation is necessary because [Chl] has been shown to be more normally distributed when transformed [44] and the dynamic range of the biogeochemical variables is large.Analyses were made using Type II (major axis) regressions because sampling and systematic errors were present in both abscissa and ordinate variables and each paired variables were of the same unit and scale [45].

IOP Relationships within the OC3 Algorithm
Phytoplankton absorption in the in situ NOMAD subset exhibited a stronger least-squares power law relationship with [Chl] at 443 and 489nm than did detrital absorption (Fig. 2).Dispersion in a dm around the best fit line relationship with [Chl] was ~2 orders of magnitude compared to ~1 for a ph .In both a ph and a dm , the range of dispersion was mostly conserved throughout the range in [Chl].Log-transformed phytoplankton and detrital absorption at 443 and 489nm were significantly correlated (r = 0.78 at 443nm; r = 0.76 at 489nm; p<0.001 for both) with similar slopes at different wavelengths (Fig. 3).The distribution of a dm vs.
[Chl] (Fig. 2) indicates that variability in a dm was the primary source of dispersion in the a ph :a dm relationship at both 443 and 489nm.Variability in the a ph :a dm relationship was limited at high a ph (e.g high [Chl]) as the number of observations with relatively high a ph with low a dm was not present in the NOMAD data set at either wavelength.In contrast, at low a ph , relatively high and low a dm were both found.This suggests that non-covariance in the NOMAD data set was most likely to occur at low [Chl] where the dynamic range of a dm was greatest.Higher amplitudes of b bp were associated with increased levels of phytoplankton and detrital absorption.However, with respect to [Chl], highest amplitudes of b bp were associated with a ph :a dm ratios that were <1 (Fig. 3) suggesting that non-algal particles and detrital material play a large role in high backscattering, high [Chl] waters.An independent analysis of component IOP contributions by Babin et al. [46] in European waters also show a similar dependence of a dm , where the upper range of [Chl] was associated with an a dm signal dominated by NAP.This is consistent with post-phytoplankton bloom samples where nonalgal particles increased after peak phytoplankton biomass had been reached [47][48][49].Once the component IOP relationships are displayed against the OC3 model curve, the absorption bias in the empirical [Chl] model becomes evident (Fig. 4).Above the OC3 model line, a ph is the dominant absorption signal (a ph :a dm >1), while a dm dominates below the best fit line (where a ph :a dm <1).At the ends of the data distribution, the lowest [Chl] are dominated by a dm and very low b bp while the highest in situ [Chl] is dominated by a ph .Similar to Fig. 2 2 for regression results.Removal of detrital absorption (a dm -free) from the reflectance signal revealed a 4th degree polynomial (OC3") that was a better fit (see Table 1) to [Chl] (Fig. 5) than OC3 (Fig. 4).The new relationship between MBRs and [Chl] was independent of a ph :a dm ratio suggesting that component absorption bias was removed in the OC3" empirical model.The correlation between b bp and [Chl], however, remained in the empirical model relationship.

Empirically estimated [Chl] vs. in situ [Chl]
OC3 is a two-wavelength (max 443>490nm) switching MBR algorithm with different [Chl]estimate statistical performance when evaluated individually by wavelength used in the MBR rather than as a pooled population (see Fig. 1; Table 1).Overall, the algorithm performs best (slope is ~1) when estimating [Chl] over a broad range of MBR values including data sets from both wavelength ratios.The overall pooled statistical success, however, disguises its relative shortcomings in oligotrophic 'blue' ocean conditions, below [Chl] of ~0.5-1.0 mg m −3 , when the algorithm switches to 443/547 rather than 490/547.The differences in the regression slopes between the two MBRs imply that the underlying IOP relationships of absorption and scattering with [Chl] and ocean color are presumably different along the gradient in the model.There was a clear component absorption based bias in the distribution of estimated [Chl] from OC3 (Fig. 6(A); Table 1; r 2 = 0.85 for full NOMAD or IOP subset) while the relationship between OC3" estimated [Chl] and in situ [Chl] was tighter with little or no component absorption bias (Fig. 6(B); Table 1; r 2 = 0.88).High a ph :a dm was associated with underestimated [Chl] and low a ph :a dm with overestimated [Chl].This was an expected result because OC3 inherently assumes some covariation between a ph and a dm .Consequently, when there is relatively very low a dm , OC3 attributes a portion of the reflectance signal to a dm rather  [Chl] suggest that the spectral slope of b bp drives these biases.Where [Chl] is low and b bp slope increasingly negative, reflectance at 443nm is increased relative to 547nm driving the color of the ocean towards shorter wavelengths and lower estimated [Chl] than expected from a global mean spectral b bp .For higher [Chl], the opposite is expected, as b bp at 547nm is increased relative to 443 or 490nm, b bp spectral slope is flattened, and MBR is reduced driving the ocean toward a green color.While it appears that spectral slope does exert an influence on the shape of OC3 and [Chl] errors, the Brown et al. [22] model analysis of MBR anomalies based on b bp spectral slope suggests that it is relatively minor influence.While the errors in OC3 were unequal, the a dm -free modeled data set showed uniform error across the dynamic range of [Chl] (Fig. 7).This suggests, as implied by the individual wavelength MBR regression coefficients, that OC3 might perform well on balance (overestimate ~underestimate), biases due to underlying variability in a ph :a dm and b bp exist in the model.This absorption bias suggests that the distribution of satellite estimated [Chl] is only comparable in a global sense where variability in a ph :a dm is averaged.Consequently, these biases also indicate that when moving between global to smaller regional and local scales, comparisons of [Chl] will be at a greater risk of error as the IOP relationships may be significantly different between two different regions or between the same region at a different time.

Radiative Transfer Model of Reflectance
The purpose of our Hydrolight modeling of computed reflectances was to provide a perspective on the expected, average global a ph * and a measure of the sensitivity of empirical algorithms to changes in bb p which is linked to particle size [42].By using a series of increasing [Chl] associated with defined a ph * shapes provided by the model of Bricaud et al. [10] and two extreme bb p as input to Hydrolight, we bracketed the MBR variability between very small and large theoretical phytoplankton-like cell sizes (Fig. 8).While the same a ph * dependence would be expected to be found in OC3, it is well masked by the influence of a dm variability on ocean color particularly for [Chl] below ~5 mg/m 3 (compare OC3 trend lines in Fig. 5).This is not surprising considering that a dm variability exceeded a ph variability relative to [Chl] in the NOMAD in situ data set (Fig. 2).In addition, the masking of a ph * dependent modulation in OC3 agrees with the Brown et al. [22] assertion, based on a different NOMAD ocean color statistical approach, that chromophoric dissolved matter absorption (our a dm ) is the most important secondary influence on the shape of OC3.
In contrast to a ph * we found that our Hydrolight MBR model was relatively insensitive to bb p providing little impact on the shape of OC3" (data not shown).These results suggest that, despite the extreme range of size implied by b bp spectral slope in the model, particle size would have a relatively minor influence on OC3.This implies that there is little opportunity to identify particle size class differences from ocean color through an MBR empirical methodology.Instead, the derivation of IOPs from remote-sensing reflectances first, should provide better insight into the biogeochemistry of dissolved and particulate matter in the ocean.

Conclusion
Our analyses of the NOMAD data set confirmed and quantified the sources of bias with regard to the IOPs that defined the NOMAD global training data set.Furthermore, unlike previous studies, we revealed the variability attributed to phytoplankton absorption in OC3 and the impact of a ph * and bb p variability on the structure of empirical algorithms.Phytoplankton and detrital absorption were similarly correlated in the NOMAD global ocean data set at 443 and 490nm, however, the variability in a dm at both wavelengths relative to [Chl] in the global data set was approximately double that of a ph indicating that ocean color variability in the NOMAD data set was dominated by a dm .
The distribution of the ratio a ph :a dm in the NOMAD data subset indicated that the OC3 curve represents a best fit approach to encapsulate inherent (e.g., global) a ph and a dm in situ variability.But, while the best fit approach works reasonably well when considering the full dynamic range of MBR reflectances and [Chl], over smaller ranges (e.g., regional scales), the inherent IOP component variability limits the accuracy of MBR models to estimate [Chl].At high MBRs and low [Chl], waters were weakly backscattering irrespective of whether absorption was dominated by a ph or a dm .In contrast to absorption, the distribution of b bp magnitude remained similar in both OC3 and OC3" substantiating the covariation of b bp with [Chl].Expectedly, absorption component bias resulted in [Chl] underestimates of a ph dominated samples and overestimates where a dm dominated.
Our a dm -free Hydrolight radiative transfer model covered a wide range of a ph * and bracketed a two order of magnitude variation in particle size revealing substantial modification in the shape of OC3".The variability in a dm -free OC3" was found to be driven primarily by a relatively narrow order of magnitude window in a ph * with further minor variations due to changes in bb p .While our model results indicated that shape modification of OC3" by both a ph * and bb p could potentially be used to identify changes in phytoplankton functional groups (see [25][26][27]), our study suggests that the influence of a dm and b bp on the shape of OC3 would most likely prohibit a statistical approach from identifying phytoplankton groups based on pigment characteristics and packaging.
Our study directly shows that IOP biases are contained within the foundation of ocean color data sets used to develop MBR-[Chl] algorithms.Empirical [Chl] estimates using these MBR algorithms whether on local, regional, or global spatial scales or for weekly, seasonal, or annual time-scales must assume that the mean IOP characteristics of their data set are similar to that of the IOP algorithm training set.This match in IOP component covariance allows for the most reduced set of remotely-sensed [Chl] estimate errors when considering a global scale of oceanic environments.However, consistent component absorption covariation is elusive in any of these cases exposing the weaknesses in empirical [Chl] algorithms.Extending satellite capabilities for ocean color biology requires recognizing the limitations of empirical algorithms to estimate [Chl] not only in complex coastal seas but also in global ocean settings.Due to natural IOP variability and the noncovariance observed on many spatial and temporal scales, the potential for large [Chl]  This demonstrates that the utilization of empirical methods could lead to substantial [Chl] estimate errors and the potential for implausible conclusions regarding long-term trends in phytoplankton productivity.Moving towards understanding the sources of variability in absorption (as well as other inherent optical properties) and its influence on ocean color should be a primary focus.Semianalytical algorithms that decompose the absorption signal into phytoplankton and detrital components represent an approach that allows for a direct relationship between [Chl] and phytoplankton absorption to be established.A reduction in error at local and regional levels for estimating biogeochemically important variables such as [Chl] is suggested as an outcome of this approach.Alternatively, establishing [Chl] estimate uncertainties for empirical algorithms based on the variability (dispersion) of [Chl] per reflectance ratio and uncertainties in sensor radiance measurements is vital to accurately portraying spatial and temporal differences in [Chl].
, at high [Chl], high b bp values are found dominating the region below the OC3 model line for very low MBRs.

Fig. 5 .
Fig. 5.The detrital-free OC3" colored by in situ aph:adm at 443 or 490 determined by maximum MBR wavelength (A) and bbp (B, 443nm).The OC3 model fit is provided for comparison.
(443>489)/ R rs (547) #163481 -$15.00USD Received 22 Feb 2012; revised 11 Jul 2012; accepted 11 Jul 2012; published 29 Aug 2012 (C) 2012 OSA than a ph , and [Chl] is underestimated.Similarly, when more a dm is present than expected OC3 overestimates [Chl] by assuming some of the a dm signal is due to a ph .Low b bp waters (in situ [Chl] range from 0.01 to ~5 mg m −3 ) underestimated [Chl], while high b bp waters ([Chl] range ~0.1 to 20 mg m −3 ) generally overestimated [Chl].Under or overestimates corresponding to b bp amplitude and low or high

Fig. 7 .
Fig. 7. [Chl] estimate error fields.Relative error in [Chl] from OC3 (A) and OC3" (B) vs. bbp (443) and color coded by in situ [Chl].OC3" had smaller, balanced relative errors while the error in OC3 was larger and biased.The model demonstrates that variability in a ph * determined the shape of OC3", moving smoothly along the gradient in the OC3" curve over a decreasing range of a ph * at 444nm (0.050-0.022 m 2 mg/chl) specified by increasing [Chl] of ~0.5-5.0 mg chl/m 3 .This suggests that a relatively narrow window of a ph * spectral shapes was sufficient to match the average global [Chl] estimated by OC3".Considering the full distribution of MBRs in OC3", our Hydrolight model found that the OC3" data dispersion was bounded by only an order of magnitude in a ph * (0.11-0.018 m 2 mg/chl at 444nm) specified by [Chl] from 0.05 to 10 mg chl/m 3 .

Fig. 8 .
Fig. 8. Modeled in situ [Chl] vs. MBRs from Hydrolight aph-based modeled Rrs using high backscattering probability (Hydrolight Case 1 Large particle) relative to OC3" curve and data dispersion.OC3 provided for comparison.Colors specify 'OC3′ fits dependent on Chl-specific phytoplankton absorption (magnitude at 444nm shown to the side of plots).Data dispersion from in situ [Chl] vs. adm-free MBRs used to generate OC3" was bracketed by an order of magnitude range of Chl-specific phytoplankton absorption.