Evaluation of Semi-Analytical Algorithms to Retrieve Particulate and Dissolved Absorption Coefficients in Gulf of California Optically Complex Waters

Two semi-analytical algorithms, Generalized Inherent Optical Property (GIOP) and Garver-Siegel-Maritorena (GSM), were evaluated in terms of how well they reproduced the absorption coefficient of phytoplankton (aph(λ)) and dissolved and detrital organic matter (adg(λ)) at three wavelengths (λ of 412, 443, and 488 nm) in a zone with optically complex waters, the Upper Gulf of California (UGC) and the Northern Gulf of California (NGC). In the UGC, detritus determines most of the total light absorption, whereas, in the NGC, chromophoric dissolved organic material (CDOM) and phytoplankton dominate. Upon comparing the results of each model with a database assembled from four cruises done from spring to summer (March through September) between 2011 and 2013, it was found that GIOP is a better estimator for aph(λ) than GSM, independently of the region. However, both algorithms underestimate in situ values in the NGC, whereas they overestimate them in the UGC. Errors are associated with the following: (a) the constant a*ph(λ) value used by GSM and GIOP (0.055 m2 mgChla−1) is higher than the most frequent value observed in this study’s data (0.03 m2 mgChla−1), and (b) satellite-derived chlorophyll a concentration (Chla) is biased high compared with in situ Chla. GIOP gave also better results for the adg(λ) estimation than GSM, especially in the NGC. The spectral slope Sdg was identified as an important parameter for estimating adg(λ), and this study’s results indicated that the use of a fixed input value in models was not adequate. The evaluation confirms the lack of generality of algorithms like GIOP and GSM, whose reflectance model is too simplified to capture expected variability. Finally, a greater monitoring effort is suggested in the study area regarding the collection of in situ reflectance data, which would allow explaining the effects that detritus and CDOM may have on the semi-analytical reflectance inversions, as well as isolating the possible influence of the atmosphere on the satellite-derived water reflectance and Chla.


Introduction
Ocean color remote sensors onboard satellites, such as the early coastal zone color scanner (CZCS) and the current Moderate Resolution Imaging Spectroradiometer (MODIS), have provided information on oceanographic structures and processes at different scales in the oceans, explaining a series of biological and ecological processes [1].The data from these sensors has been used in studies on ocean dynamics, biogeochemistry, and global climate change [2][3][4][5].
Specifically, these sensors have greatly improved the world's understanding of the properties of light absorption by water and particulate and dissolved material [6][7][8][9][10][11][12], and they have emphasized the importance of observing the properties routinely from space.These properties exercise an important influence on the function of marine ecosystems, determining, for example, the availability of solar radiation for phytoplankton growth [13], the effectiveness of visual predation [14], and the kinetics of photochemical processes [15].
The concentration of particulate material in water is important in coastal regions, with implications for coastal protection, shipping, and recreational activities [16].The analysis of absorption is necessary for identifying the water components that contribute to the process of light absorption.The total absorption can be described in terms of the additive contribution of different components [17]: where a(λ) is the light absorption coefficient at a given wavelength; a w (λ) is the light absorption coefficient by pure water; a p (λ) is the light absorption coefficient by particulate material, which in turn can be decomposed into the absorption by phytoplankton (a ph (λ)) and the absorption by detrital organic particles and minerals (a d (λ)); and, finally, a CDOM (λ) is the absorption coefficient by chromophoric dissolved organic material (CDOM).The coefficients a d (λ) and a CDOM (λ) have similar spectral shapes and they are evaluated as a sum (a dg (λ)) [16].Therefore, the total absorption a(λ) can also be expressed as follows: a(λ) = a w (λ) + a ph (λ) + a dg (λ) The absorption coefficients (a ph (λ), a dg (λ)) and the particulate backscattering coefficient (b bp (λ)) are referred to as inherent optical properties (IOPs) [18], and a variety of semi-analytical approaches have been proposed [16] to derive IOPs from the remotely measured "remote-sensing" spectral reflectance (R rs (λ)) [19], especially for optically complex waters [20].Two well-known-and widely used-semi-analytical algorithms have been proposed by Maritorena et al. [21] and Werdell et al. [22].The first algorithm, known as Garver-Siegel-Maritorena (GSM), was initially developed by Garver and Siegel [6] and it is based on a quadratic relationship between R rs (λ) and the absorption and scattering coefficients [23].It uses a semi-analytical approach and an optimization method to obtain estimates of chlorophyll a concentration (Chla), a dg (443), and b bp (443), assuming an underlying bio-optical model and using non-linear optimization [16].The GSM products generated by NASA's Ocean Biology Processing Group (OBPG) are described at https://oceancolor.gsfc.nasa.gov/products/eval/#GSM.The second algorithm, referred to as Generalized Inherent Optical Property (GIOP), also uses spectral optimization, but incorporates several ideas from previously published bio-optical models and methods, allowing the user to isolate and evaluate the individual differences between models in a controlled environment.GIOP products are standard NASA OBPG products; see https://oceancolor.gsfc.nasa.gov/atbd/giop/.GIOP was developed during two NASA-sponsored international IOP algorithm workshops at the Ocean Optics XIX (October 2008) and XX (September 2010) conferences.The international working group associated with these workshops proposed in consensus the preliminary configuration of GIOP, with alternative settings and characteristics of the model defined with the objective of applying continuous evaluations.
Brewin et al. [16], among others, have evaluated the semi-analytical algorithms available for the determination of IOPs, by means of an objective classification that allowed the grading of each one.Their results showed that the overall score obtained by the algorithms that estimated a ph (λ), when accounting for individual scores across all wavelengths, was higher in GIOP, followed by the others, among which was GSM.For the determination of a dg (λ), the slightly higher scores obtained were for the Quasi-Analytical Algorithm (QAA) [24,25] and the Hyperspectral Optimization Process Exemplar (HOPE) models [26], followed by other algorithms including GSM and GIOP.Meanwhile, none of the algorithms captured well the variability in S dg (spectral slope of a dg (λ)).In their study, the above authors indicated the need to use, in future inter-comparison exercises, an independent in situ dataset for testing algorithms (in this case, NASA bio-Optical Marine Algorithm Dataset, NOMAD).
In this study, the authors evaluated GSM and GIOP by comparing their results with an in situ database of a ph (λ), a d (λ), and a CDOM (λ) from an optically complex region, the northern part of the Gulf of California.The selection of the best model was done based on statistical tests, and the results of the analyses allowed the authors to identify the possible adaptations of the algorithm that could improve the retrieval in this type of region.

Study Area
The study area comprises the northern part of the Gulf of California (Mexico) and is located at 30.5 • N to 32 • N and −115 • W to −113.5 • W (see Figure 1).In previous studies, this area has been classified into two zones (Upper Gulf of California and Northern Gulf of California) according to hydrodynamic characteristics and bio-optical properties [27][28][29].The shallower zone (<30 m) is the Upper Gulf of California (UGC) and is characterized by high turbidity and strong water-column mixing [30], high chlorophyll a concentration (Chla), the dominance of microphytoplankton (diatoms and dinoflagellates), and a high contribution of detritus to total light absorption [29].The Northern Gulf of California (NGC) is a deeper region more oligotrophic than the UGC, dominated by picophytoplankton (cyanobacteria and green algae), with lower values of Chla and light absorption by detritus [29].A transitional zone separates both regions (see Figure 1), whose location can change according to differences in hydrodynamics.A detailed description of the particular bio-optical characteristics of each region can be found in Betancur-Turizo et al. [29].
Remote Sens. 2018, 10, x FOR PEER REVIEW 3 of 17 their study, the above authors indicated the need to use, in future inter-comparison exercises, an independent in situ dataset for testing algorithms (in this case, NASA bio-Optical Marine Algorithm Dataset, NOMAD).In this study, the authors evaluated GSM and GIOP by comparing their results with an in situ database of aph(λ), ad(λ), and aCDOM(λ) from an optically complex region, the northern part of the Gulf of California.The selection of the best model was done based on statistical tests, and the results of the analyses allowed the authors to identify the possible adaptations of the algorithm that could improve the retrieval in this type of region.

Study Area
The study area comprises the northern part of the Gulf of California (Mexico) and is located at 30.5°N to 32°N and −115°W to −113.5°W (see Figure 1).In previous studies, this area has been classified into two zones (Upper Gulf of California and Northern Gulf of California) according to hydrodynamic characteristics and bio-optical properties [27][28][29].The shallower zone (<30 m) is the Upper Gulf of California (UGC) and is characterized by high turbidity and strong water-column mixing [30], high chlorophyll a concentration (Chla), the dominance of microphytoplankton (diatoms and dinoflagellates), and a high contribution of detritus to total light absorption [29].The Northern Gulf of California (NGC) is a deeper region more oligotrophic than the UGC, dominated by picophytoplankton (cyanobacteria and green algae), with lower values of Chla and light absorption by detritus [29].A transitional zone separates both regions (see Figure 1), whose location can change according to differences in hydrodynamics.A detailed description of the particular biooptical characteristics of each region can be found in Betancur-Turizo et al. [29].

In Situ Data
Physical and biological data were collected during six oceanographic cruises in the study area performed during neap tides.Table 1 indicates the sampling dates, and Figure 1c the location of the stations.Surface water samples (approximately 0.50 m deep) were collected using 5 L Niskin bottles for the determination of phytoplankton (aph(λ)), detritus (ad(λ)), and CDOM (aCDOM(λ)) absorption

In Situ Data
Physical and biological data were collected during six oceanographic cruises in the study area performed during neap tides.Table 1 indicates the sampling dates, and Figure 1c the location of the stations.Surface water samples (approximately 0.50 m deep) were collected using 5 L Niskin bottles for the determination of phytoplankton (a ph (λ)), detritus (a d (λ)), and CDOM (a CDOM (λ)) absorption coefficients according to the protocol indicated in Mitchell et al. [17].Chla concentration was measured using High-performance liquid chromatography (HPLC) with the method proposed by Thomas [31].The specific absorption coefficient by phytoplankton (a* ph (λ), m 2 (mg Chla) −1 ) was calculated by normalizing a ph (λ) by Chla.More details of these analyses are provided in Betancur-Turizo et al. [29].The semi-analytical algorithms that determine the IOPs do not estimate the absorption coefficients of detritus a d (λ) and a CDOM (λ) independently, but as an integrated variable called a dg (λ) which represents their sum.For this reason, this variable was determined by the sum of each of the absorption spectra of a d (λ) and a CDOM (λ).The newly generated spectra were fitted to an exponential function y = Ae (−S*λ) between 250 and 500 nm using a nonlinear least square minimization routine.The exponent S of the equation was called S dg and corresponds to the spectral slope of the absorption spectrum of a dg (λ).Finally, given that the June 2008 and 2010 cruises did not have CDOM data, the analyses of this variable were applied only to the data of the four cruises taken between 2011 and 2013 (see Table 1).

Satellite Data
A selection process of MODIS-Aqua Level 1A files was done, in which scenes with less than 80% cloudiness and/or sun glint were selected for the study period.The result was a total of 48 images (see Table 2) with a spatial resolution of ~1.1 km at nadir.These files were extracted from the online OBPG Data Processing System database (https://oceancolor.gsfc.nasa.gov/cgi/browse.pl) in accordance with the available passes depending on the date of each analyzed cruise (see Table 2).For the processing of Level 1A archives to Level 2, the L2GEN program was used and its standard atmospheric correction scheme (SeaDAS version 7.4) was applied, selecting the IOP products a dg (λ) and a ph (λ) at 412 nm, 443 nm, and 488 nm in their default configuration for algorithms GIOP and GSM.After the generation of the L2 archives, the statistics median, the standard deviation, and the number of valid pixels were calculated.
An exclusion process for each geographical position extracted was applied in those cases for which one or more of the Level 2 L2GEN quality control indicators were not fulfilled (see Table 3).All Level 2 archive variables were extracted from 3 × 3 pixel windows, centered on the pixel closest to the in situ sample.For the analyses, only data with at least three valid pixels (out of a total of nine) were included, due to increased errors from pixels close to clouds or land.Only model data with quality control were paired with in situ information of the six cruises analyzed (see Figure 2).The MODIS-Aqua images for match-up analysis (one km spatial resolution) were processed for Chla estimation using SeaDAS V7 and using the OCx product with the OC3M algorithm.Average Chla from a box of 3 × 3 pixels centered at the station position was used for comparison between MODIS Chla and in situ Chla in order to evaluate its influence on the a ph (λ) estimation.
Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 17 nine) were included, due to increased errors from pixels close to clouds or land.Only model data with quality control were paired with in situ information of the six cruises analyzed (see Figure 2).The MODIS-Aqua images for match-up analysis (one km spatial resolution) were processed for Chla estimation using SeaDAS V7 and using the OCx product with the OC3M algorithm.Average Chla from a box of 3 × 3 pixels centered at the station position was used for comparison between MODIS Chla and in situ Chla in order to evaluate its influence on the aph(λ) estimation.

Semi-Analytical Algorithms
GIOP and GSM were used to retrieve the absorption coefficients from the satellite data, and the estimates were compared with in situ data.In GSM [21], the following parameterizations are used: A constant value for a*ph(λ)is specified as 0.055 m 2 mgChla −1 .S is the spectral decay constant for dissolved substances and detritus absorption [32], whose value has been specified in the GSM source code as Sdg = 0.02061 nm −1 [33].Using the spectral satellite radiance as input, the Levenberg-

Semi-Analytical Algorithms
GIOP and GSM were used to retrieve the absorption coefficients from the satellite data, and the estimates were compared with in situ data.In GSM [21], the following parameterizations are used: A constant value for a* ph (λ)is specified as 0.055 m 2 mgChla −1 .S is the spectral decay constant for dissolved substances and detritus absorption [32], whose value has been specified in the GSM source code as S dg = 0.02061 nm −1 [33].Using the spectral satellite radiance as input, the Levenberg-Marquadt nonlinear least squares procedure was employed to solve for the remaining unknown terms, namely Chla and a dg (λ) [32].
GIOP uses the same constant value for a* ph (λ) (0.055 m 2 mgChla −1 ) that is used in GSM, although S dg is specified as 0.018 nm −1 .The GIOP model [22] allows one to specify different parameterizations and optimization approaches, including the a* ph (λ) and S dg eigenvectors employed, the number of eigenvalues resolved, the optimization method selected, and the number of sensor wavelengths.All of these GIOP elements are therefore defined by specifying eigenvectors for each optically significant constituent assumed to exist in the water column [22].

Algorithm Evaluation Methodology
The degree of association between the IOP products and the in situ data was evaluated through the "match-up" technique [34].Variables graphed were the absorption coefficient of phytoplankton (a ph (412, 443, and 488)) and the absorption coefficient of CDOM and detritus (a dg (412, 443, and 488)) (y axis) against their respective in situ counterparts (x axis).These wavelengths were selected because they are representative of most remote sensors and in particular MODIS-Aqua.Below are the statistics that were used for the algorithm evaluation.

Pearson's Correlation Coefficient (r p )
The statistical validity of the models was determined through the Pearson's correlation coefficient (r p ), whose mathematical expression is as follows [35]: where Cov A,B is the covariance of A and B and SD A and SD B are the standard deviation of A and B. This coefficient is a measure of the correlation (linear dependence) between two variables A and B, giving a value between +1 and −1 inclusive (1 indicates a direct linear relationship, −1 indicates an inverse linear correlation, and zero indicates no linear relationship).The coefficient's significance is determined with a hypothesis test, known as correlation analysis [35]: To accept or reject hypothesis H 0 , the value r calculared was compared with the value r critical based on the degree of freedom (df = n − 1) and the error α (0.05).r critical was the minimum significant value of r p .If r calculated > r critical , H 0 was rejected and r p was statistically significant, but if r calculated < r critical , H 0 could not be rejected and r p was not significant [34].

Root Mean Square Error (RMSE)
The Root Mean Square Error (RMSE) is a frequently used measure of the difference between values predicted by a model (x i = satellite data) and the values actually observed (y i = in situ data) from the environment that is being modeled.It is calculated according to [35]: The RMSE can be confirmed using the sum of square errors (χ 2 ): this statistical test is the minimum error of the modeled data (satellite) with respect to the observed data (in situ).In the comparison between models, the lesser value of χ 2 is the one which better describes the answer and is calculated according to [35]: Bias Bias provides information on the tendency of the model to overestimate (Bias > 0) or underestimate (Bias < 0) a variable and is calculated according to [35]: Taylor Diagram The Taylor diagram illustrates a different set of statistics in terms of uRMSD* that is comprised of the standard deviation (σ) of the model output and in situ data, σ model and σ in situ , as well as the Pearson's correlation coefficient (r p ) between estimates and in situ measurements [36]: The Taylor diagram provides a way of 2-D graphing three statistical parameters (r p , σ, and RMSD) that indicate how closely a pattern matches observations.With these statistics in the same plot, it is easy to determine how much of the overall root-mean-square difference in patterns is attributable to a difference in variance and how much is due to poor pattern correlation [37].The statistical significance was evaluated using an α of 5%.

Phytoplankton Absorption Coefficient
Betancur-Turizo et al. [29] analyzed the spatial and temporal variability of light absorption properties in the study area.They observed that there was a strong temporal variability with a spatial pattern that allowed the definition of two bio-optical regions named Upper Gulf of California (UGC) and Northern Gulf of California (NGC), with particular characteristics that indicated that these regions were very different when evaluating the individual contribution by phytoplankton, detritus, and CDOM to total light absorption.In particular, in the UGC, a d (λ) contribution to total light absorption was most of the time higher than 40% followed by a CDOM (λ), whereas in the NGC, a co-dominium between a ph (λ) and a CDOM (λ) was observed most of the time.
In this study, a total of 150 a ph (412, 443, and 448) in situ data were collected, but because of clouds, atmospheric corrections failure, and other aspects described in Table 3, only 75 match-ups were generated for GIOP and 76 for GSM (see Figure 2a).The difference in the number of data used for GIOP and GSM was due to outliers that were excluded from the analysis.The data used for these analyses are listed in the Supplementary Material (see Table S1).Figure 3 presents the comparison between the in situ data and the algorithm output for the entire dataset and also by region (UGC and NGC).The performance statistics indicated that GIOP was in general a better a ph (λ) estimator than GSM regardless of the bio-optical region, although the differences were small.Special attention should be given to the strong underestimation of a ph (412) by GSM, independently of the bio-optical region (bias between −0.70 to −0.86) (see Figure 3d-f).However, both algorithms in general underestimated the in situ values (negative bias) in the NGC, whereas they overestimated them (positive bias) in the UGC, although the negative bias in the NGC was much lower than the positive ones in the UGC.Comparative analysis between in situ and satellite a ph (412, 443, and 488 nm) for GIOP and GSM models, with the statistics Root Mean Square Error (RMSE), bias, r p , and χ 2 ; the 1:1 line is indicated for reference.The green and blue colors correspond to the UGC and NGC regions, respectively.In the first column (a, d, g, j, m, p) the entire database was used, in the second (b, e, h, k, n, q) only data from UGC, and in the third (c, f, i, l, o, r) only data from NGC.
Taylor diagrams (see Figure 4) confirmed that the a ph (λ) derived from GIOP was slightly better than the GSM a ph (λ), with higher values of r p (≈0.45) and normalized standard deviations close to 1.0.This, in addition to the underestimation observed in the match-ups independently of the analysis applied (entire dataset and by bio-optical region) and the higher χ 2 value presented by the GSM model, support the conclusion that GIOP better derives a ph (λ) values for both bio-optical regions.As previously mentioned, GIOP and GSM use a constant value for a*ph(λ) (i.e., a*ph(443) = 0.055 m 2 mgChla −1 ), which is then scaled according to Chla concentration to derive aph (λ).Moreover, Chla is derived from empirical OCx, that is, some of the ocean color band ratio algorithms OC3 or OC4 [38,39].In this study's data, a*ph(443) values varied between 0.011 and 0.37 m 2 mgChla −1 , where most data were below 0.055 m 2 mgChla −1 (see Figure 5a), with the exception of the June 2013 cruise when values increased to up to 0.37 m 2 mgChla −1 .Variability in a*ph(λ) could be associated with changes in pigment composition and cell size [40], which varied among cruises and bio-optical regions [29].For example, in June 2013 the UGC region was dominated by fucoxanthin, a pigment that indicates the presence of diatoms and larger cells (i.e., microplankton) [41], whereas , in the NGC, zeaxanthin was the major pigment indicating the importance of cyanobacteria and a dominium of small cells (picoplankton) [29].At the same time, this cruise was the one with the highest number of stations dominated by zeaxanthin (i.e., cyanobacteria) that represented a group characterized by high light absorption efficiency (i.e., high a*ph(λ)) [42], which agreed with the study's results (see Figure 5a).Frequency histograms were also generated by region (see Figure 5b,c) to emphasize the differences between them.In the UGC (see Figure 5b), most data were between 0.025 and 0.125 m 2 mgChla −1 , whereas, in the NGC, most data were between 0.02 and 0.06 m 2 mgChla −1 .Furthermore, the most frequent value (mode) was 0.03 m 2 mgChla −1 in both regions.These results indicated that a change in the default input values used by GSM and GIOP should be considered in addition to a temporal adjustment of the same value in order to improve aph(λ) estimations in the study area.As previously mentioned, GIOP and GSM use a constant value for a* ph (λ)(i.e., a* ph (443) = 0.055 m 2 mgChla −1 ), which is then scaled according to Chla concentration to derive a ph (λ).Moreover, Chla is derived from empirical OCx, that is, some of the ocean color band ratio algorithms OC3 or OC4 [38,39].In this study's data, a* ph (443) values varied between 0.011 and 0.37 m 2 mgChla −1 , where most data were below 0.055 m 2 mgChla −1 (see Figure 5a), with the exception of the June 2013 cruise when values increased to up to 0.37 m 2 mgChla −1 .Variability in a* ph (λ) could be associated with changes in pigment composition and cell size [40], which varied among cruises and bio-optical regions [29].For example, in June 2013 the UGC region was dominated by fucoxanthin, a pigment that indicates the presence of diatoms and larger cells (i.e., microplankton) [41], whereas, in the NGC, zeaxanthin was the major pigment indicating the importance of cyanobacteria and a dominium of small cells (picoplankton) [29].At the same time, this cruise was the one with the highest number of stations dominated by zeaxanthin (i.e., cyanobacteria) that represented a group characterized by high light absorption efficiency (i.e., high a* ph (λ)) [42], which agreed with the study's results (see Figure 5a).Frequency histograms were also generated by region (see Figure 5b,c) to emphasize the differences between them.In the UGC (see Figure 5b), most data were between 0.025 and 0.125 m 2 mgChla −1 , whereas, in the NGC, most data were between 0.02 and 0.06 m 2 mgChla −1 .Furthermore, the most frequent value (mode) was 0.03 m 2 mgChla −1 in both regions.These results indicated that a change in the default input values used by GSM and GIOP should be considered in addition to a temporal adjustment of the same value in order to improve a ph (λ) estimations in the study area.
Another source of error in both algorithms could be the satellite estimation of Chla (i.e., OCx performance).To evaluate its influence in the a ph (λ) calculation, the satellite estimates were compared with in situ measurements (see Figure 6).Results for the entire dataset (n = 122) indicated an overestimation of in situ Chla (bias = 1.72) with a RMSE of 0.45 and a correlation coefficient of 0.76.The positive bias was larger for the NGC and smaller for the UGC.Another source of error in both algorithms could be the satellite estimation of Chla (i.e., OCx performance).To evaluate its influence in the aph(λ) calculation, the satellite estimates were compared with in situ measurements (see Figure 6).Results for the entire dataset (n = 122) indicated an overestimation of in situ Chla (bias = 1.72) with a RMSE of 0.45 and a correlation coefficient of 0.76.The positive bias was larger for the NGC and smaller for the UGC.
In summary, there was a slight underestimation of aph(443) in the NGC (GIOP bias = −0.02,GSM bias = −0.06)related to an underestimation of a*ph(443) and a strong overestimation of Chla (bias = 1.93).There was a strong overestimation of aph(λ) in the UGC (GIOP bias = 0.71, GSM bias = 0.65) related to the same underestimation of a*ph(443) and smaller overestimation of Chla (bias = 1.41).A positive relationship was expected between Chla and aph(λ) [40], i.e., an overestimation of in situ Chla would result in an overestimation of aph(λ).If it is assumed that the same error is associated with a*ph(443) in both regions, differences between them should be related to Chla.Our results suggest that in the NGC the effect of underestimating a*ph(443) somewhat compensated the effect of overestimating Chla.In the UGC, on the other hand, the fact that a*ph(443) was more variable than in the NGC should be taken into consideration, which would explain, at least partly, the inferior performance of both algorithms.

Absorption Coefficient of Dissolved and Detrital Matter
The total number of adg(412, 443, and 448) in situ data were 84; however, for the same reasons previously explained (Section 3.1), only 28 match-ups were generated for GIOP and 32 for GSM (see Figure 2b).The difference in the number of data used for GIOP and GSM was due to outliers that were excluded from the analysis.The data used for these analyses are listed in the supplementary material (see Table S2).The comparative analysis between the absorption coefficient adg(λ) (mg/m 3 ) In summary, there was a slight underestimation of a ph (443) in the NGC (GIOP bias = −0.02,GSM bias = −0.06)related to an underestimation of a* ph (443) and a strong overestimation of Chla (bias = 1.93).There was a strong overestimation of a ph (λ) in the UGC (GIOP bias = 0.71, GSM bias = 0.65) related to the same underestimation of a* ph (443) and smaller overestimation of Chla (bias = 1.41).A positive relationship was expected between Chla and a ph (λ) [40], i.e., an overestimation of in situ Chla would result in an overestimation of a ph (λ).If it is assumed that the same error is associated with a* ph (443) in both regions, differences between them should be related to Chla.Our results suggest that in the NGC the effect of underestimating a* ph (443) somewhat compensated the effect of overestimating Chla.In the UGC, on the other hand, the fact that a* ph (443) was more variable than in the NGC should be taken into consideration, which would explain, at least partly, the inferior performance of both algorithms.

Absorption Coefficient of Dissolved and Detrital Matter
The total number of a dg (412, 443, and 448) in situ data were 84; however, for the same reasons previously explained (Section 3.1), only 28 match-ups were generated for GIOP and 32 for GSM (see Figure 2b).The difference in the number of data used for GIOP and GSM was due to outliers that were excluded from the analysis.The data used for these analyses are listed in the Supplementary Material (see Table S2).The comparative analysis between the absorption coefficient a dg (λ) measured in situ and retrieved by GIOP and GSM was done with the entire dataset and by bio-optical region for wavelengths centered on 412, 443, and 488 nm (see Figure 7).In general, GIOP gave better results than GSM represented by lower RMSE and higher r p and χ 2 .Irrespective of the algorithm used, the best estimations were at 488 nm, whereas the poorest sensitivity was observed at 412 nm.When comparing algorithm performance in the UGC and the NGC, it was observed that estimations were more accurate in the NGC than in the UGC.
Taylor diagrams indicate that both algorithms were statistically significant (α = 0.05) when the analysis was done without distinguishing between bio-optical regions (Figure 8a compared with Figure 8b,c), with higher values of r p (>0.60) and normalized standard deviations around 0.8 for GIOP and with a higher dispersion for GSM.However, when data was analyzed by region, it was observed that in the UGC, r p were lower than the critical value (−0.60 and 0.60) for both algorithms, indicating that neither one was able to reproduce the in situ values of a dg (λ).In the NGC, r p were above 0.50 and statistically significant (r calculated > r critical , α = 0.05).
In conclusion, both GIOP and GSM performed poorly for a dg (λ) estimations.In the UGC region, they underestimated the in situ data and, according to r p , estimations were not statistically accurate.For the NGC region, the situation changed, given that the statistics were slightly better for GIOP than for GSM, with higher r p values (>0.29), normalized standard deviations close to 1.0, lower values of RMSE, bias close to zero, and the lowest values of χ 2 This indicates that the algorithm that best derives a dg (λ) for the NGC is GIOP.
Because a dg (λ) was calculated as the sum of a d (λ) and a CDOM (λ), it was considered important to analyze the average spectra of these individual variables for each cruise and bio-optical region.This analysis was conducted by comparing the values of a dg (λ) from GIOP and GSM at five wavelengths (412, 443, 448, 555, and 678), specifying the contribution given by detritus (a d (λ)) and CDOM (a CDOM (λ)) to the absorption coefficient a dg (λ).The underestimation associated with both algorithms appeared related to those cruises for which the contribution from detritus to a dg (λ) was greater than that from CDOM (see Figure 9b-d), independently of the bio-optical region.In conclusion, both GIOP and GSM performed poorly for adg(λ) estimations.In the UGC region, they underestimated the in situ data and, according to rp, estimations were not statistically accurate.For the NGC region, the situation changed, given that the statistics were slightly better for GIOP than for GSM, with higher rp values (>0.29), normalized standard deviations close to 1.0, lower values of RMSE, bias close to zero, and the lowest values of χ 2 This indicates that the algorithm that best derives adg(λ) for the NGC is GIOP.Because adg(λ) was calculated as the sum of ad(λ) and aCDOM(λ), it was considered important to analyze the average spectra of these individual variables for each cruise and bio-optical region.This analysis was conducted by comparing the values of adg(λ) from GIOP and GSM at five wavelengths (412, 443, 448, 555, and 678), specifying the contribution given by detritus (ad(λ)) and CDOM (aCDOM(λ)) to the absorption coefficient adg(λ).The underestimation associated with both algorithms appeared related to those cruises for which the contribution from detritus to adg(λ) was greater than that from CDOM (see Figure 9b-d), independently of the bio-optical region.The estimation of adg(λ) by GSM considers an Sdg value of 0.0206, whereas GIOP considers a value of 0.018.However, in situ data showed that most values were below 0.018 especially in the  Because adg(λ) was calculated as the sum of ad(λ) and aCDOM(λ), it was considered important to analyze the average spectra of these individual variables for each cruise and bio-optical region.This analysis was conducted by comparing the values of adg(λ) from GIOP and GSM at five wavelengths (412, 443, 448, 555, and 678), specifying the contribution given by detritus (ad(λ)) and CDOM (aCDOM(λ)) to the absorption coefficient adg(λ).The underestimation associated with both algorithms appeared related to those cruises for which the contribution from detritus to adg(λ) was greater than that from CDOM (see Figure 9b-d), independently of the bio-optical region.The estimation of adg(λ) by GSM considers an Sdg value of 0.0206, whereas GIOP considers a value of 0.018.However, in situ data showed that most values were below 0.018 especially in the The estimation of a dg (λ) by GSM considers an S dg value of 0.0206, whereas GIOP considers a value of 0.018.However, in situ data showed that most values were below 0.018 especially in the UGC where the mode was 0.012, whereas, in the NGC, it was 0.018 (see Figure 9).Lower values of S dg were related with a higher contribution by detritus, as was the case in August 2012, September 2012, and June 2013 in the UGC (see Figure 10).These results suggested that the input value for S dg should be modified for UGC to yield better a dg (λ) estimations.After using the in situ S dg as model input, the results were much improved (see Table 4).In the NGC, characterized by a greater dispersion of in situ S dg values, the statistical improvement was much more evident that in the UGC, especially with the GSM algorithm.
Sdg were related with a higher contribution by detritus, as was the case in August 2012, September 2012, and June 2013 in the UGC (see Figure 10).These results suggested that the input value for Sdg should be modified for UGC to yield better adg(λ) estimations.After using the in situ Sdg as model input, the results were much improved (see Table 4).In the NGC, characterized by a greater dispersion of in situ Sdg values, the statistical improvement was much more evident that in the UGC, especially with the GSM algorithm.

Conclusions
In this study, a statistical analysis was carried out to compare the performance of two semi-analytical algorithms (GIOP and GSM) to retrieve absorption coefficients in regions characterized by different bio-optical properties, namely the UGC and the NGC.GIOP was a better estimator for a ph (λ) than GSM, independently of the bio-optical region.Both algorithms, however, underestimated

Figure 1 .
Figure 1.(a) Study area map.(b) Transition zone between the Upper Gulf of California (UGC) and Northern Gulf of California (NGC) bio-optical regions, indicated by the dotted line.(c) Station location for each cruise.

Figure 1 .
Figure 1.(a) Study area map.(b) Transition zone between the Upper Gulf of California (UGC) and Northern Gulf of California (NGC) bio-optical regions, indicated by the dotted line.(c) Station location for each cruise.

Figure 2 .
Figure 2. Data of the six cruises that had in situ information on the coefficients (a) aph(λ) and (b) adg(λ) in the study zone.Black circles represent stations paired with the Generalized Inherent Optical Property (GIOP) algorithm, and red points represent stations paired with the Garver-Siegel-Maritorena (GSM) algorithm.The dotted black line represents the intermediate position of the transitional zone that separates the bio-optical regions UGC and NGC [29].

Figure 2 .
Figure 2. Data of the six cruises that had in situ information on the coefficients (a) a ph (λ) and (b) a dg (λ) in the study zone.Black circles represent stations paired with the Generalized Inherent Optical Property (GIOP) algorithm, and red points represent stations paired with the Garver-Siegel-Maritorena (GSM) algorithm.The dotted black line represents the intermediate position of the transitional zone that separates the bio-optical regions UGC and NGC [29].

Figure 3 .
Figure 3.Comparative analysis between in situ and satellite a ph (412, 443, and 488 nm) for GIOP and GSM models, with the statistics Root Mean Square Error (RMSE), bias, r p , and χ 2 ; the 1:1 line is indicated for reference.The green and blue colors correspond to the UGC and NGC regions, respectively.In the first column (a, d, g, j, m, p) the entire database was used, in the second (b, e, h, k, n, q) only data from UGC, and in the third (c, f, i, l, o, r) only data from NGC.

Figure 4 .
Figure 4. Taylor diagram illustrating the relative performance of the GIOP and GSM algorithms upon reproducing the absorption coefficient aph(412, 443, and 488 nm).Diagrams represent (a) the entire dataset and data collected in the (b) UGC and (c) NGC.The red line represents the critical value of Pearson's correlation coefficient and indicates the best-model performance.

Figure 4 .
Figure 4. Taylor diagram illustrating the relative performance of the GIOP and GSM algorithms upon reproducing the absorption coefficient a ph (412, 443, and 488 nm).Diagrams represent (a) the entire dataset and data collected in the (b) UGC and (c) NGC.The red line represents the critical value of Pearson's correlation coefficient and indicates the best-model performance.

Figure 5 .
Figure 5. (a) In situ a*ph (m 2 mgChla −1 ) variability for all cruises analyzed in this study, including the value used in GIOP and GSM (a*ph = 0.055 m 2 mgChla −1 , dotted line).Also indicated are the frequency histograms for (b) UGC and (c) NGC.

Figure 5 . 17 Figure 6 .
Figure 5. (a) In situ a* ph (m 2 mgChla −1 ) variability for all cruises analyzed in this study, including the value used in GIOP and GSM (a* ph = 0.055 m 2 mgChla −1 , dotted line).Also indicated are the frequency histograms for (b) UGC and (c) NGC.Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 17

Figure 6 .
Figure 6.Relationship between in situ chlorophyll data (Chla) and satellite chlorophyll data for the June 2008, June 2010, March 2011, August 2012, and June 2013 cruises, plotted on a logarithmic scale.The dashed line is the one-to-one line.RMSE is computed on log10-transformed data, and bias on original data.

Figure 7 .
Figure 7. Comparative analysis between in situ and satellite adg(412, 443, and 448) for the GIOP and GSM algorithms, with statistics Root Mean Square Error (RMSE), bias, rp, and χ 2 .The 1:1 is indicated for reference.The green and blue colors correspond to the UGC and NGC regions, respectively.

Figure 7 .
Figure 7.Comparative analysis between in situ and satellite a dg (412, 443, and 448) for the GIOP and GSM algorithms, with statistics Root Mean Square Error (RMSE), bias, r p , and χ 2 .The 1:1 is indicated for reference.The green and blue colors correspond to the UGC and NGC regions, respectively.In the first column (a, d, g, j, m, p) the entire database was used, in the second (b, e, h, k, n, q) only data from UGC, and in the third (c, f, i, l, o, r) only data from NGC.

Figure 8 .
Figure 8.Taylor diagram illustrating the relative performance of the algorithms GIOP and GSM in reproducing the absorption coefficient adg(412, 443, and 488 nm).Each diagram represents the analysis applied to (a) all of the data and by bio-optical regions (b) UGC and (c) NGC.The dotted red line represents the critical value of Pearson's correlation coefficient.

Figure 9 .
Figure 9. Average spectra of the absorption coefficient of dissolved and detrital matter (adg(λ)) calculated for each cruise in the UGC (a-d) and NGC (e-g).The pie chart inside diagrams represents the percentage contribution of detritus (ad) and chromophoric dissolved organic material (CDOM) (ag) to adg(λ).Open circles represent GSM adg(λ) values and black crosses represent GIOP adg(λ) values.Note: The August 2012 cruise was represented by a single station and was not included in the figure.

Figure 8 .
Figure 8.Taylor diagram illustrating the relative performance of the algorithms GIOP and GSM in reproducing the absorption coefficient a dg (412, 443, and 488 nm).Each diagram represents the analysis applied to (a) all of the data and by bio-optical regions (b) UGC and (c) NGC.The dotted red line represents the critical value of Pearson's correlation coefficient.

Figure 8 .
Figure 8.Taylor diagram illustrating the relative performance of the algorithms GIOP and GSM in reproducing the absorption coefficient adg(412, 443, and 488 nm).Each diagram represents the analysis applied to (a) all of the data and by bio-optical regions (b) UGC and (c) NGC.The dotted red line represents the critical value of Pearson's correlation coefficient.

Figure 9 .
Figure 9. Average spectra of the absorption coefficient of dissolved and detrital matter (adg(λ)) calculated for each cruise in the UGC (a-d) and NGC (e-g).The pie chart inside diagrams represents the percentage contribution of detritus (ad) and chromophoric dissolved organic material (CDOM) (ag) to adg(λ).Open circles represent GSM adg(λ) values and black crosses represent GIOP adg(λ) values.Note: The August 2012 cruise was represented by a single station and was not included in the figure.

Figure 9 .
Figure 9. Average spectra of the absorption coefficient of dissolved and detrital matter (a dg (λ)) calculated for each cruise in the UGC (a-d) and NGC (e-g).The pie chart inside diagrams represents the percentage contribution of detritus (a d ) and chromophoric dissolved organic material (CDOM) (a g ) to a dg (λ).Open circles represent GSM a dg (λ) values and black crosses represent GIOP a dg (λ) values.Note: The August 2012 cruise was represented by a single station and was not included in the figure.

Figure 10 .
Figure 10.(a) In situ Sdg variability for all cruises analyzed in this study, including the value used in GIOP (Sdg = 0.018, black dotted line) and GSM (Sdg = 0.02061, gray dotted line).Also indicated are the frequency histograms for (b) UGC and (c) NGC.

Table 4 .
Comparison between statistics applied to the in situ absorption coefficient adg(λ) and the outputs of the models in their default configurations (GIOP, GSM), and the outputs after adjustment with the in situ Sdg values (GIOP*, GSM*).The lowest values of RMSE and Least squares are indicated in bold letters.

Figure 10 .
Figure 10.(a) In situ S dg variability for all cruises analyzed in this study, including the value used in GIOP (S dg = 0.018, black dotted line) and GSM (S dg = 0.02061, gray dotted line).Also indicated are the frequency histograms for (b) UGC and (c) NGC.

Table 4 .
Comparison between statistics applied to the in situ absorption coefficient a dg (λ) and the outputs of the models in their default configurations (GIOP, GSM), and the outputs after adjustment with the in situ S dg values (GIOP *, GSM *).The lowest values of RMSE and Least squares are indicated in bold letters.GIOP GIOP * GIOP GIOP * GIOP GIOP * GIOP GIOP * GIOP GIOP *

Table 1 .
General information of the oceanographic cruises and measured variables.

Table 2 .
General information on the in situ database analyzed and effective monitoring days used for the extraction of Level 1A images.

Table 3 .
Level 2 flags used for excluding pixels from analysis.

Table 3 .
Level 2 flags used for excluding pixels from analysis.