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Abstract
With the increasing interest in ocean color remote sensing in polar oceans and geostationary ocean color satellite with diurnal observations, it is unavoidable to encounter ocean color retrievals under high solar zenith angles. Under these scenarios, the capability of current remote sensing algorithms is poorly known. In this study, the performance of the two widely used semi-analytical algorithms for the water inherent optical properties (QAA and GSM01) under high solar zenith angle conditions were firstly evaluated based on global in situ data set (SeaBASS-NOMAD). The results showed that the performances of both QAA and GSM01 degraded significantly with the increasing in solar zenith angle (SZA), and the biases increased about 1.3-fold when SZA varied from 30° to 80°. The high uncertainties at high SZA was mainly induced by the systematic overestimation of the key parameter u (ratio of backscattering coefficient to the sum of absorption and backscattering coefficients) at high solar zenith angles. Based on the Hydrolight-simulated data set, a new model (NN-algorithm) for retrieving u from remote sensing reflectance was developed for high solar zenith angle conditions using the neural network method. The validation results revealed that the NN-algorithm could improve the estimation of parameter u and further ocean color products. In addition, our results indicate that a more accurate atmosphere correction is needed to deal with ocean color remote sensing data acquired under large solar zenith angle conditions.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ocean color remote sensing from both sun-synchronous (or polar orbit) and geostationary satellites provides valuable data for extracting information on the spatial distributions and temporal variations of phytoplankton and associated components in the regional and global oceans [1]. Recently, ocean color remote sensing at polar oceans becomes more and more important, because of the possible rapid changes of marine ecologic system in response to global warming as well the diurnal dynamic monitoring of ocean phenomena in coastal regions by geostationary satellite [2,3]. Thus, it is unavoidable to encounter ocean color retrievals under high solar zenith angle (SZA) for both polar orbit and geostationary satellites.
A number of algorithms have been developed to retrieve bio-optical and geophysical variables (i.e., chlorophyll, suspended sediments and colored dissolved organic matter contents), as well as the bulk and specific inherent optical properties (“IOPs” such as absorption, particulate scattering and backscattering) of the water components from normalized water-leaving radiance (Lwn) or remote sensing reflectance (Rrs) [4,5], which are obtained using an atmospheric correction scheme applied to satellite measured top-of-atmosphere (TOA) radiance data [6,7]. These algorithms are based on empirical and semi-analytical (or quasi-analytical) approaches.
The empirical model is simple as it is based on statistical regression between water constituents’ concentration and remote sensing reflectance derived from the in situ measurement data. The empirical models are relatively successful for estimating chlorophyll a concentration (Chla) in some regional waters and global open oceans [8–10], but the estimation accuracy is found to be lower in turbid coastal waters due to the limited historical data and the reflectance band architecture used to build the model [11]. Thus, the applicability of these models is limited in terms of temporal and geographic spread [12]. The advantageous of the empirical methods are that they can be recalibrated and further improved based on a larger in situ data set in question and can provide robust estimates within the regions from where the in situ data were collected and used for calibration. Numerous studies reported that empirical models have the limited applicability in terms of temporal coverage and yield large errors toward the larger solar zenith angles. For instance, empirical models when applied to MODIS-Aqua data in the western Arctic Ocean and Mediterranean Sea [13,14] were positively biased and presented the lowest accuracy at high solar zenith angles. Recently, we have evaluated the ability of seven empirical algorithms for Chla retrieval under different solar zenith angles based on an extensive global in situ data set, and found that there was a significant decrease in performance of all seven algorithms under high solar zenith angles [11].
In contrast, semi-analytical algorithms are based on solutions for radiative transfer equation and involve empirical solutions which make these models to have the geographic and temporal flexibility and a wider applicability [2,15]. The semi-analytical models have the advantage of being applicable to different satellite sensors, geographic locations and water regimes, and can overcome the confounding effects of multiple components present in optically complex waters within coastal and inland environments. The success of the semi-analytical algorithms is highly dependent on the foundational relationship between remote sensing reflectance and the key parameter u (ratio of backscattering coefficient to the sum of absorption and backscattering coefficients), which might also be sensitive to the solar zenith angles. However, to date, no major study has been undertaken for evaluating semi-analytical models’ performance under high solar zenith angle conditions.
This study is focused to evaluate the performance of two well-known semi-analytical algorithms – Quasi-Analytical Algorithm (QAA) and Garver–Siegel–Maritorena model (GSM01) under high solar zenith angles. The analysis is performed using a global in situ data set (i.e., SeaBASS-NASA bio-Optical Marine Algorithm Data set). Then, based on the Hydrolight radiative transfer simulations, a neural network model (NN-algorithm) for retrieving the (ratio of backscattering coefficient to the sum of absorption and backscattering coefficients) from remote sensing reflectance was developed to improve the performance of the semi-analytical algorithms at high solar zenith angles. Finally, the NN algorithm is applied to the geostationary satellite observation data from the Geostationary Ocean Color Imager (GOCI) and the results are further discussed.
2. Data and methods
2.1 In situ data
The in situ data of bio-optical properties representative of a wide range of water types, trophic status, and geographic locations in open ocean waters, estuaries and coastal waters were obtained from the NASA Ocean Biology Processing Group (hereafter referred to as SeaBASS-NOMAD in situ data) [16] and used to evaluate performance of the semi-analytical models. The SeaBASS-NOMAD in situ data comprise a large number of coincident radiometric observations, inherent optical properties and phytoplankton pigment concentrations. The latest version of SeaBASS-NOMAD includes more than 3400 samples (stations) collected at different latitudes from equator to polar regions with water types varying from turbid coastal waters to clear open ocean waters. This is a high-quality in situ data set suitable for satellite ocean color algorithm development and product validation. A careful screening of these data based on the requirement of this study yielded 1243 samples consisting of coincident Chla and remote sensing reflectance (Rrs) at six wavelengths (e.g., 412 nm, 443 nm, 490 nm, 510 nm, 555 nm and 660 nm) for both low and high solar zenith angle conditions (Fig. 1) (When the data set contains chlorophyll concentration, six bands remote sensing reflectance data, station latitude and longitude, and measurement time at the same time, moreover, the remote sensing reflectance data are all positive, the data are selected. The bands used in the semi-analytical model are slightly different from those in the NOMAD data set, so we use 411nm and 489nm data of NOMAD data set replace the 412nm and 490nm in the semi-analytical model. Because of the small amount of data in 670 nm band, some stations use 665 nm band data to replace them.). Many of the samples included here come from coastal and estuarine waters that are characterized by multi-constituent systems.
Fig. 1 Map showing the sampling stations for the SeaBASS-NOMAD in situ data set. The cruise names are shown along transects and sample stations. The background color represents the bathymetry.
Since there was no record of solar zenith angle for the SeaBASS-NOMAD samples, we need to calculate the solar zenith angle for each sample. To accomplish this, a simple method proposed by Woolf [17] was used in this study. It takes the form
where is the solar zenith angle, is the sampling latitude, is the sun declination, and is the hour angle. Figure 2 shows the distribution of solar zenith angle for the chosen NOMAD samples. It can be seen that 28.84% of the samples were measured under low solar zenith angle conditions (SZA<40°), 55.88% of the samples were measured under moderate solar zenith angle conditions (SZA = 40°–70°), and 15.28% of the samples were measured under high solar zenith angle conditions (SZA>70°).2.2 Simulated data set
The Hydrolight-based radiative transfer model was utilized to simulate 5000 remote sensing reflectance in a spectral range of 400-800 nm (Δλ = 1 nm) for different water types, given the sun position, the water constituents’ concentrations (Chla, concentration of the total suspended particle-TSM, absorption coefficient of CDOM- aCDOM) and surface and bottom boundary conditions. In these simulations, Chla ranged from 0~100 mg/m3, aCDOM (443nm) from 0~10 m−1, and TSM from 0~100 g/m3. Each set of the data was generated randomly within these ranges of constituents, and all of data were exponentially distributed within this range. To examine the influence of solar zenith angle, each set of data was assigned a random solar zenith angle. Given these inputs, the Hydrolight produced radiance distributions enabling other related quantities to be derived from these radiance data (e.g., remote sensing reflectance, diffuse attenuation coefficient) with different water types.
2.3 Satellite data
To demonstrate the impact of solar zenith angle on satellite estimation of Chla, GOCI Level 2 data for a region of the Sea of Japan were downloaded from the Korea Ocean Satellite Center (KOSC) (http://kosc.kiost.ac/) and processed to generate Chla products using semi-analytical algorithms. The GOCI offers moderate spatial resolution data (500m × 500m) for eight spectral bands (centered around 412 nm, 443 nm, 490 nm, 555 nm, 660 nm, 680 nm, 745 nm and 865 nm) every hour during the day time [18,19]. Several studies have utilized GOCI data for monitoring the short-term coastal ocean phenomena, suspended sediment dynamics, red tide occurrence, river plumes and tidal variability [20–22]. In this study, all the 8 times observation data from the GOCI on 2 February 2015 were obtained for a region of the Sea of Japan which is a semi-enclosed deep marginal sea in the Northwestern Pacific (Fig. 3). The reason to choose this area is that the sun zenith angle often exceeds 70° in the first-time and last-time GOCI observations in the winter season. Moreover, in the basin of this area, waters are stable within a day, including the phytoplankton biomass.
2.4 Semi-analytical algorithms for Chla retrieval
Semi-analytical algorithms utilize approximate solutions of the radiative transfer equation (RTE) (analytical part) together with assumptions about the spectral shapes of IOPs (empirical part). Unlike purely empirical algorithms, semi-analytical algorithms are generally less sensitive to disparate geographical regions or water types. The semi-analytical algorithms are based on the foundational relationship between apparent optical properties (AOPs) and IOPs, as shown in Eqs. (2) and (3) as
where is the sea–air transmission factor; are the coefficients derived from the Monte Carlo simulations for an idealized ocean [23]; is the total absorption coefficient; is the total backscattering coefficient; is the refractive index of water; is the wavelength. Using the normalized water-leaving radiance, the total absorption and backscattering coefficients of water can be obtained using inversion models. The total absorption coefficient includes absorptions by pure water, phytoplankton pigment and CDOM (or colored dissolved organic matter). Similarly, the total backscattering coefficient is the sum of backscattering by pure water and suspended particulate matter. Currently, the quasi-analytical algorithm (QAA) and Garver-Sigel-Maritorina (GSM01) model are well known semi-analytical inversion models originally proposed by Lee et al. [15,24,25] and Maritorena et al. [8], and both of them were incorporated into the SeaDAS processing system for regional and global applications. These models use different techniques to achieve reasonable retrieval accuracy for the absorption and backscattering coefficients of individual water components. The QAA model returns reasonable estimates of bio-optical properties, including the absorption coefficients and particulate backscattering coefficient based on remote sensing reflectance data. Moreover, the QAA uses the spectral models derived from some empirical relationships to spectrally decompose the total absorption coefficient to absorption by phytoplankton pigment and dissolved plus detrital matter (CDOM and detrital). In this study, the latest version of QAA was downloaded from the IOCCG website (http://ioccg.org/group/lee/) and used to derive the absorption coefficients of individual water components from remote sensing reflectance (at six wavelengths 412 nm, 443 nm, 490 nm, 510 nm, 555 nm, and 670 nm). For estimations of Chla concentration, the specific absorption coefficient for phytoplankton () is a required parameter and can be estimated with a reasonable accuracy at a short wavelength (443 nm) as [26,27]where A and D are the parameters that describe the ordinate and abscissa of the point of symmetry for the curve, B describes the asymptotes of the graph, and C depicts how quickly the curve approaches the asymptotes (A = 0.44,B = 1.05,C = −0.60,D = 0.7). Note that is estimated at a shorter wavelength (443nm) where phytoplankton absorbs light strongly than at other wavelengths. This formulation takes into account the variability of that can result from changes in the magnitude of absorption associated with pigment concentration, composition, and cell size/ the package effect. Here the interests in retrieving is to estimate Chla concentration which is used as an index for phytoplankton abundance [28,29].On the contrary, GSM01 employs a fixed set of parameters derived based on in situ measurement data using a statistical optimization procedure. This model was evaluated using synthetic data and model parameters were adjusted to maximize its performance for the global ocean. With the tuned parameters, the accuracy of retrievals found with this globally optimized model was reasonably good. The advantage of GSM01 model is its ability to produce simultaneous retrievals of the absorption and backscattering coefficients that enable us to extend and explore the nature of applications in global oceans. In this study, the GSM01 version was downloaded from the IOCCG website (http://ioccg.org/group/lee/) and used to estimate Chla concentration from the remote sensing reflectance data.
2.5 Neural network model for retrieving u from remote sensing reflectance
Conveniently, the above-surface remote-sensing reflectance Rrs can be converted to the below-surface remote-sensing reflectance (rrs) using [24]
where with the radiance transmittance from below to above the surface and the irradiance transmittance from above to below the surface; is the water-to-air internal reflection coefficient. Please note that is omitted in Eq. (5) for brief. Then, using Eqs. (2) and (3), absorption and backscattering coefficients can be derived from rrs. In another way, rrs can be estimated from . In earlier studies, the model parameters were considered as T≈0.52, γQ≈1.7, g0 = 0.0949, and g1 = 0.0794 [23] or g0 = 0.0895, and g1 = 0.1247 [24]. These model parameters may vary with the solar zenith angle and the particulate scattering phase function and are not remotely measured, which indicates that the accuracy of retrieved bio-optical properties from satellite data may be impacted or influenced by those parameters operating as a function of the solar zenith angles.Another key to reliable retrieval of IOPs is the normalized water-leaving radiance (Lwn) or the remote sensing reflectance (Rrs). In principle, the more accurate Lwn (or Rrs) will yield the more accurate biogeochemical products. The normalized water-leaving radiance can be defined as [23]
where is the Fresnel reflectance of the sea surface; is the Fresnel reflection albedo of the sea surface for irradiance from the sun and sky; is the mean extraterrestrial sun irradiance; R is the irradiance reflectance just beneath the sea surface; Q is the ratio of the upwelling irradiance to the upwelling radiance just beneath the sea surface. The value of depends on the solar zenith angle. The BRDF effect was studied by Morel and colleagues in a series of papers [30], where they used numerical radiative transfer models to compute correction factors that would transform a measurement made for a particular solar zenith angle, viewing direction, wind speed, and atmospheric conditions and water IOPs into a measurement that corresponds to a zenith Sun and nadir viewing direction for a typical marine atmosphere and for a Case 1 water with a given chlorophyll value. Morel et al. [31,32] examined R and its variations with solar zenith angle based on Monte Carlo simulations and found that R is linearly related to , with a slope that varies strongly with the ratio of molecular backscattering to total backscattering. In Eq. (6), the Q function is also dependent on the Sun's position which indicates that the Lwn has dependence on the sun zenith angle despite its strong correlation with the water-column inherent optical properties.Due to the complex influences of solar zenith angles, it is difficult to establish an empirical model to estimate the key parameter u from remote sensing reflectance at high solar zenith angles. Here, the Neural network (NN) method was used instead of polynomial regression. It has been demonstrated that any continuous function can be represented by one-hidden-layer NN with sigmoid functions [33,34]. The underlying characteristics of the radiative transfer under high solar zenith angles can be assimilated into the NN algorithm architecture. A NN architecture consists of an input layer, intermediary or hidden layer(s) and an output layer. Once the input training data is given into the network, the neurons in the hidden and output layers transform the input signal by an activation function. If the NN architecture, number of hidden layers and number of neurons, is established, the association between the input and the output ultimately depends on the weighting functions associated with each connection. These values are obtained by a supervised learning technique, using a priori information about the actual output that corresponds to a set of input data. Finally, the network is adjusted, so that the optimum estimate to the actual output is achieved.
In this study, a simple one hidden layer NN was trained to establish the relationship between input Rrs and output parameter u at high solar zenith angles. The NN has three layers: one input layer, one output layer, and one hidden layer with 10 neurons. The input layer has two parameters, including the solar zenith angle and the remote sensing reflectance at a specific band (one of the 412nm, 443nm, 490nm, 510nm, 555nm and 660nm). The output layer has one element which is the u(λ) value. The network was trained with Levenberg-Marquardt backprogation algorithm. The transfer (activation) function of the neurons is taken to be the hyperbolic tangent sigmoid function. The output layer uses a linear transfer function to link the hidden layers to the output. The training data was based on a randomly selected data set consisting of 70% of the total simulation data (5000 samples), and was tested using the remaining 30% simulation data. Moreover, to make the NN algorithm more robust and less sensitive to noise, 10% uniformly distributed noises were added to the training data set [35,36]. The parameters in the simulated data set random vary in the following ranges: For ocean color constitutes, Chla: 0-100 mg/m3, CDOM: 0-10 m−1, TSM: 0-100 g/m3; For solar zenith angle, SZA: 25-85°. The scattering phase function measured by Petzold was used for both the phytoplankton and mineral particles. (Now, users can download the model from the website: http://www.soed.org.cn/en/index.php/scientific/data)
2.6 Assessment method
The major steps in the assessment process are described in Fig. 4. The assessment of the semi-analytical models is performed using typically statistical parameters: root mean square deviation (RMSE), absolute percentage deviation (APD), and relative percentage deviation (RPD). These matrices are defined as
where Yi, Xi, and N represent the algorithm-retrieved Chla, in situ Chla, and sample number, respectively. RPD is a predictor of the systematic error or mean relative bias, while APD gives the absolute accuracy of derived products relative to the known data (in situ or simulated reference data).3. Results and discussion
3.1 Effects of the SZA on the performances of the semi-analytical algorithms
In situ Rrs from the SeaBASS-NOMAD data set were used as inputs to QAA and GSM01 models, and the model-retrieved Chla were compared to concurrent in situ values. The evaluation data sets consisted of 1114 observations for the QAA model and 1074 observations for the GSM01 model, wherein the number of samples varied depending on the model parameterizations. Model performance over the entire range of Chla from regional and global waters was evaluated by using a linear regression analysis between estimated Chla and in situ Chla concentrations (Fig. 5). Both QAA and GSM01 models performed fairly well and consistently returned reasonable Chla for most of the samples from open ocean waters (as demonstrated by a one-to-one correlation in Fig. 5 for Chla <1 mg/m3). In turbid coastal waters, QAA significantly overestimated Chla, whereas GSM01 returned typically lower Chla concentrations for many samples. Low accuracy of Chla returned by QAA and GSM01 models in coastal regions could result from the fact that the bio-optical properties of these waters differed from those of the open ocean samples used in the original QAA and GSM01 models. In addition, in turbid coastal waters, were less well constrained leading to overestimations or underestimations of Chla by these models.
To further examine the uncertainty of these models due to high solar zenith angles, model results were compared with in situ observations based on the different SZA ranges of 0-30°, 30°–40°, 40°–50°, 50°–60°, 60°–70° and 70°–90° with sample numbers of 211, 195, 265, 223, 193, and 156, respectively. Figure 6 shows the APDs under different SZA ranges. When SZA<30°, QAA presented the lower error (APD = 33.5%) relative to the GSM01 model (APD = 40%). However, the APDs of the QAA model increase significantly with the SZA, i.e., APD rapidly increased from 33.5% to 50.1% when SZA increased from 30° to 70°, resulting in a 1.5-fold bias for Chla. For SZA within 60°, GSM01 presented similar but larger APDs (a 1.3-fold increase of APD relative to QAA). At high solar zenith angles (SZA>60°), GSM01 presented similar error increase as QAA did, with an APD reaching up to 40-51%. For statistical comparison of the models, samples recorded for high SZA conditions (>70°) were discarded to avoid the discrepancy and results for the rest of the samples are presented in Table 1. Note that QAA presented the lowest APD and RPD as compared to the GSM01 model although a slight difference in the magnitude of RMSE for these models. These results indicate good performance of the semi-analytical models for estimating Chla over the low to moderate SZAs, and performance degrading over the high SZAs.
Table 1. Statistical results for the QAA and GSM01 models
3.2 Performances of the semi-analytical algorithms under high SZAs
Model performance under high solar zenith angle conditions was independently evaluated by using a suite of 156 in situ observations with solar zenith angles larger than 70°. Another suite of 195 samples corresponding to the solar zenith angles between 30° and 40° was used to compare to the samples observed under high SZAs. Results showed that QAA underestimated Chla in low Chla waters (< 1 mg/m3) and overestimated Chla in high Chla waters (>1 mg/m3) when SZA is in the range of 30°-40° (Fig. 7). QAA exhibited a similar trend at high solar zenith angles (>70°), but greatly overestimated in high Chla waters (>1 mg/m3) when SZA>70°. On the contrary, model performance over the moderate and large solar zenith angles was found to be consistent for GSM01 as demonstrated by data around the one-to-one line between estimated and measured Chla concentrations. However, this model did not produce the same satisfactory results for high Chla waters (>1 mg/m3) under high SZA (>70°) (see the data spreading farther away from the 1:1 line). The statistical values produced by QAA and GSM01 models in estimating Chla for both the SZA regimes (low-moderate SZA = 30°–40°; high SZA = 70°–90°) are given in Table 2, where the number of samples chosen was dependent on the availability of data and allowed a reasonable comparison between the model results and in situ data. Overall, QAA exhibited a smaller RPD, while GSM01exhibitted a larger RPD for moderate solar zenith angles (30°–40°). For the larger solar zenith angles (70°–90°), these results were reversed due to a large overall bias (overestimation) associated with the QAA model. The RMSE and APD values produced by QAA and GSM01 were found to be nearly identical despite their overall better performance at the lower sun zenith angles. The difference in the statistical performance of the models (i.e., good for the smaller SZAs and poor for the larger SZAs) could result from the influence of solar zenith angles and the inaccuracy/inadequacy of the parameterizations of these models for turbid and productive waters.
Fig. 7 Comparisons of the results of QAA and GSM01 models and in situ Chla for two solar zenith angle regimes (30°–40°; 70°–90°).
Table 2. Comparison of the model performances at two different solar zenith angle regimes (30°-40°;70°-90°)
3.3 NN-algorithm for estimating parameter u from Rrs at high solar zenith angles
Theoretically, the influence of SZA emerges from the conversion process between remote sensing reflectance and the ratio of backscattering coefficient to the sum of absorption and backscattering coefficients (u(λ)), as shown in Eqs. (2) and (3). To demonstrate this effect, Hydrolight simulations were performed to simulate the remote sensing reflectance at 443nm for a variety of water types under two solar zenith angle conditions (SZA = 30°, 80°). Then, the simulated Rrs(443nm) were used to calculate the u(443nm) (using Eqs. (2) and (3)). Figure 8 shows the comparison of the retrieved u(443nm) between SZA = 30° and 80°. Ideally, if the SZA has no effect, u(443nm) at SZA = 30° and 80° should have the same value since of the same inputted water optical properties. However, the difference of the retrieved u(443nm) between SZA = 30° and 80° can be up to 20% depending on the water types, indicating that the gi coefficients in Eq. (2) may not suitable for high SZAs.
The BRDF correction is the key for the application of the QAA and GSM models to high solar zenith angle (e.g. lager than 70°). Ideally, if the BRDF correction is perfect, then the derived normalized Rrs values are the same for all solar and viewing geometries. However, the exact BRDF correction is still difficult especially under high solar zenith angles. For an example, based on the NOMAD data set, Fig. 6 reveals the good performance of the semi-analytical models over low to moderate SZAs, but the performance degrades largely under high SZAs. Currently, the developed BRDF correction models can only deal with the Rrs observations under solar zenith angles less than 75° [37]. Therefore, it needs to develop new model for high SZA cases. In this study, a neural network (NN) approach was adopted to overcome the difficulty for retrieving the key parameter u(λ) from the Rrs(λ) under high solar zenith angles. The performance of the NN-algorithm was tested using independent simulated data and in situ data. Figure 9 shows comparison of the inverted u(443nm) and known u(443nm) (based on the inputted absorption and backscattering coefficients for the simulation) with the different levels of noise (0%, 10%, 20% and 30%) added to the simulated Rrs data. For this comparison, the simulated data independent of the training samples were used. The “known” values of u(443nm) were calculated from Eq. (3) using the inputted a(λ) and b(λ) in the simulations. The results revealed that even for the input data with a noise level of 30%, the retrieved u(443nm) values were better compared to their u(λ) counterparts, with a determination coefficient (R2) of 0.9999, 0.9955, 0.9822 and 0.961 for the noise level of 0%, 10%, 20% and 30%, respectively. Under the noise level of 10%, the retrieved u(λ) at typical wavelengths (412 nm, 443 nm, 490 nm, 510 nm, 555 nm, 660 nm) generally yielded R2 > 0.97, APD (%) < 13%, Intercept < 0.004 and Slope > 0.96 (except λ = 555, Slope = 0.876), as shown in Table 3, indicating that the NN is nearly insensitive to the reasonable noise levels. When compared to the retrieved u(443nm) based on NN, it was found that the traditional conversion methods returned unreasonable estimates of u(443nm) under different SZA conditions and showed a slight underestimation at 443 nm, whereas the NN approach provided estimates of u(443nm) closely consistent with the known u(443nm) values (as demonstrated by the closeness of data around the 1:1 line), as shown in Fig. 10. Further comparison based on the available in situ data (SeaBASS-NOMAD, N = 78) also showed that u(443nm) retrieved by the NN-algorithm were again closely consistent with in situ u(443nm) which were obtained from in situ a(λ) and b(λ) (Fig. 11). It should be noted that in consideration of the measured error, the precision of inversion is good and the retrieved u(λ) by NN-algorithm can be inputted to the semi-analytical models for estimating IOPs and further water constituents under the high SZA conditions.
Fig. 9 Comparisons between the retrieved u(443nm) by the NN-algorithm and the “known” u(443nm) values. The inputted Rrs data were the independent simulated data (not used in the NN training process) with different noise levels (ε) from 0% to 30% adding to the simulated Rrs.
Table 3. Comparison of the retrieved u(λ) by NN-algorithm (with 10% noise adding to the Rrs) with the inputted u(λ) at different wavelengths
Fig. 10 Comparison of the performances of the retrieved u(443nm) between the NN-algorithm and the traditional conversion method (Eqs. (2)-(3)). The input Rrs are the simulated data set which are not used in the NN training.
Fig. 11 Comparison between the retrieved u(443nm) by NN-algorithm and in situ u(443nm). The SeaBASS-NOMAD data set consisting of 78 samples was used here.
Using the NN-algorithm retrieved u(λ) as inputs, Chla were further estimated from QAA-NN and GSM01-NN models and compared with results obtained from those u(λ) values calculated using the traditional method based on the SeaBASS-NOMAD data set (Fig. 12). As expected, the QAA-NN and GSM01-NN models significantly improved the estimation of Chla for a variety of samples from both coastal and open ocean waters (top panels). Comparing the results obtained with standard and new u(λ) values for high SZA (>70°), it can be seen that QAA-NN and GSM01-NN exhibited slight improvement upon QAA and GSM01 models in terms of R2, RMSE, APD and RPD (Table 4). The slight improvement of Chla is also visible on scatterplots (Fig. 12, bottom panels) when Chla>1 mg/m3. QAA-NN and GSM01-NN presented similar improvements for the intermediate Chla regimes (0.1<Chla<1 mg/m3) as compared to the QAA and GSM01 models with the standard u(λ) values as inputs. These findings indicate that the NN-algorithm retrieved u(λ) are more suitable for the semi-analytical models to produce more accurate Chla concentrations under high solar zenith angle conditions.
Fig. 12 Comparison of the retrieved and in situ Chla for the SeaBASS-NOMAD data set. Top panels represent the results at all SZA conditions, whereas bottom panels represent the results for SZA>70°.
Table 4. Comparison of the performance of the retrieved chla between the original models (QAA and GSM01) and the improved models (QAA-NN and GSM01-NN) under high SZA (>70°).
3.4 Application to satellite data
Practical applications of the original (QAA and GSM01) and adjusted (QAA-NN and GSM01-NN) semi-analytical models were evaluated using hourly GOCI images that were observed over a region of the Sea of Japan during winter (2 Feb. 2015) (Fig. 3). This period was devoid of algal blooms in this region (generally characterized by Chla <1 mg/m3), which made it as an ideal case to examine the model performance. As expected, all four models (QAA, GSM01, QAA-NN and GSM01-NN) provided nearly consistent results around noon local times (Fig. 13), comparable to generally observed Chla patterns within this region [38]. However, QAA and GSM01 models returned abnormally high Chla in either morning or later afternoon local times. Comparing to the original QAA and GSM01 models, QAA-NN and GSM01-NN could reduce the overestimations of the Chla at the morning or later afternoon which have high solar zenith angles, indicating that NN-algorithm retrieved u value can improve the performance of the semi-analytic models at high SZAs. Nevertheless, there was still a large discrepancy in magnitude of Chla for near noon local times and morning/later afternoon local times due to their highest overestimation of Chla in the larger solar zenith angles, which is caused by the high uncertainties of atmospheric correction under high solar zenith angles [39]. Therefore, more accurate algorithm for the atmospheric correction under high solar zenith angles should be developed in the future.
Fig. 13 Comparison of the GOCI-retrieved hourly Chla by the QAA, GSM01, QAA-NN and GSM01-NN models in the basin of the Sea of Japan on 2 Feb. 2015.
4. Conclusion
This work was aimed at evaluating and improving the performance of two widely-used semi-analytical models (QAA and GSM01) under high solar zenith angle conditions. A global in situ data set (SeaBASS-NOMAD) representing diverse water types in coastal and open oceans and wider geographic locations at low and mid latitudes was used to evaluate the model performance. Both QAA and GSM01 provided reasonable estimates of Chla in clear oceanic waters (Chla<1 mg/m3) under low to moderate solar zenith angles. However, for the larger solar zenith angles, these models yielded an increased APD (by a factor of 1.3), one of the reasons is the influence of solar zenith angle on the conversion process between remote sensing reflectance and the ratio of backscattering coefficient to the sum of absorption and backscattering coefficients (u(λ)). To examine this effect, Hydrolight radiative transfer simulations were performed to generate remote sensing reflectance given the appropriate input parameters and boundary conditions to form a training data set and an evaluation data set for the neural network method to improve the model performance for high solar zenith angle conditions. The results showed that the QAA and GSM01 with new inputs (u(λ)) from NN-algorithm improved the estimation of Chla and substantially reduced the associated errors for the larger solar zenith angles when compared to the original QAA and GSM01 models. The practical applications of these models were further evaluated using diurnal GOCI imageries in the basin region of the Sea of Japan during a non-bloom period, and it was found that all four models (QAA, GSM01, QAA-NN and GSM01-NN) yielded nearly consistent and exhibited satisfactory results around near noon local times, but QAA and GSM abnormally overestimated Chla yielding the highest errors in morning and later afternoon local times. On the other hand, Chla returned by the QAA-NN and GSM01-NN models were significantly improved although, being abnormal or erroneous in the larger solar zenith angles (morning and late afternoon local times). The high uncertainties for these model products are likely associated with atmospheric correction problems under high solar zenith angles. This indicates that atmospheric correction algorithms will need to be improved for high solar zenith angle conditions so that the full potential of diurnal geostationary ocean colour data can be exploited and utilized for operational applications.
The NN-algorithm could be applied to the polar orbit ocean color satellite data to retrieve the IOPs and further water components in the polar oceans when the solar zenith angles are usually large in winter half years. Moreover, it could be applied to the geostationary ocean color satellite data to deal with the early morning or later afternoon observing data. The improved diurnal ocean color products will in turn provide the opportunity for extracting new information from the coastal and open-ocean waters and investigating dynamical biogeochemical and oceanographic processes at regional and global scales.
Funding
National Key Research and Development Program of China (grant #2017YFA0603003); National Basic Research Program (973 Program) of China (grant #2015CB954002); Public Science and Technology Research Funds Projects for Ocean Research (grant #201505003); National Natural Science Foundation of China (grants #41676172, #41676170, #41825014 and #41621064); Global Change and Air-Sea Interaction Project of China (grants #GASI-02-SCS-YGST2-01, #GASI-02-PAC-YGST2-01 and #GASI-02-IND-YGST2-01); Project of State Key Laboratory of Satellite Ocean Environment Dynamics (grant #SOEDZZ1801).
Acknowledgments
The authors would like to thank all participants in the NASA SIMBIOS program as well as all voluntary contributors for collecting data that have been assembled in the NOMAD data set (http://seabass.gsfc.nasa.gov/cgi-bin/nomad.cgi). We also thank W. Balch, F. Chavez, L. Harding, S. Hooker, G. Mitchell, R. Morrison, F. Muller-Karger, N. Nelson, D. Siegel, A. Subramaniam, R. Stumpf, and all of their co-investigators for releasing their SeaBASS data contributions to the public ahead of schedule.
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