1. Introduction

High-quality moderate resolution optical imagery over nearshore coastal and inland waters are becoming available from multiple satellite missions. With 10 to 300m nominal spatial sampling, missions like Landsat-8, Sentinel-2A/B, and Sentinel-3A/B allow for frequent observations of dynamic inland and nearshore aquatic systems. These missions carry sufficiently radiometrically sensitive instruments, including the operational Land Imager (OLI), the MultiSpectral Instrument (MSI), and the Ocean and Land Color Imager (OLCI), respectively, that enable measuring in-water optical properties [1–4]. In addition, the Visible Infrared Imaging Radiometer (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) also has the potential to provide valid observations over larger inland waters where adjacent land signals do not affect water-leaving radiances.

The spectral remote sensing reflectance $\left[{\text{R}}_{\text{rs}}(\text{λ})\right]$, which is defined as the ratio of water-leaving radiance to the total downwelling irradiance just above the water, is a key product derived through the atmospheric correction process [5]. The wavelength symbol ($\text{λ}$) is dropped for brevity hereafter. Satellite-derived ${\text{R}}_{\text{rs}}$ products are commonly validated with radiometric measurements made with the ocean color component of the Aerosol Robotic Network (AERONET-OC) [6]. Currently, these in situ measurements are made using radiometers with ~10nm wide square filters centered (nominally) at 412, 443, 490, 530, 555, and 670nm [7]. The OLI and MSI, however, measure visible/near-infrared spectral radiances using relatively broad spectral bands. Their channel widths range from 20 to 70nm measured at full-with-half-maximum (FWHM). In addition, VIIRS and OLCI’s spectral bands are not identical to AERONET-OC channels. Thus, when evaluating satellite-derived ${\text{R}}_{\text{rs}}$ with equivalent AERONET-OC data, there is often a spectral mismatch that increases uncertainties in matchup analyses.

In the earlier years, narrow-band (typically ~10nm) multispectral in situ radiometers were used for validating satellite-derived water-leaving radiances (${\text{L}}_{\text{w}}$). Although ocean color missions like the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) sample spectral radiances through relatively narrow bands, they commonly exhibit some degree of out of band responses [8]. To account for these out-of-band responses and minimize uncertainties in satellite matchup analyses, Wang, et al. [9] suggested using modeled hyperspectral ${\text{L}}_{\text{w}}$ [10] to compute per-band correction factors derived as a function of band ratios ${\text{L}}_{\text{w}}$. Currently, using a similar methodology, NASA’s ocean biology processing group (OBPG) has extended this work and pre-computed a set of sensor-specific quadratic polynomial coefficients to convert derived (full-band) satellite-derived ${\text{R}}_{\text{rs}}$ to nominal 10-11nm resolution bands. For instance, this procedure converts OLI-derived $R_{rs}$ (482) to an equivalent 10-11nm $R_{rs}$ (482). In this approach, hyperspectral ${\text{L}}_{\text{w}}$ is modeled a) using a limited set of chlorophyll-a concentrations, i.e., 0.03, 0.1, 0.3, 0.5, 1.0, and $3\text{mg}/{\text{m}}^3$, and b) varying a scattering-related parameter, i.e., ${\text{b}}^0$, ranging from 0.12 to 0.45 ${\text{m}}^{-1}$. In a more recent effort, Mélin and Sclep [11] used the quasi analytical approach (QAA) [12] to model hyperspectral ${\text{L}}_{\text{w}}$ from which band shifting corrections are derived. The methodology was tested with extensive in situ data and a set of limited synthetic data [13]. They also examined the impacts on SeaWiFS-MODIS Level-3 ${\text{R}}_{\text{rs}}$ products [14]. The results indicated significant improvements in the ocean color matchup analyses, however, it was recommended that future efforts be dedicated to waters of higher trophic states since QAA’s parameterization is not specifically tuned for these aquatic systems. Also, QAA requires ${\text{R}}_{\text{rs}}(410)$ to fully resolve all the inherent optical properties (IOPs) and enable reconstruction of hyperspectral $R_{rs}$. The moderate resolution imagers like OLI and MSI do not make measurements at ~410nm.

Furthermore, for a consistent multimission record of satellite products over coastal/inland waters, it is common to compare corresponding near-simultaneous $R_{rs}$ products [4]. In such cases, retrieved $R_{rs}$ differs from sensor to sensor due to inherent differences in their spectral sampling in addition to other factors, such as differences in spatial sampling [15]. To minimize uncertainties in such exercises, i.e., sensor-to-sensor comparisons, there is a need for a robust method that enables band adjustments that carry minimal errors and that works for OLI, MSI, OLCI, and VIIRS. Such a method will also facilitate merging of multisource data products [16].

The goal of this manuscript is to minimize uncertainties associated with a) AERONET-OC matchup analyses, and b) cross-mission product comparisons. This research ultimately ensures improved multimission product analyses for consistent monitoring of nearshore coastal and inland waters and aids in elucidating other sources of uncertainties (e.g., image artifacts). To do so, we simulate in situ multispectral ${\text{R}}_{\text{rs}}$ data from modeled and measured hyperspectral ${\text{R}}_{\text{rs}}$ spectra to represent simulated AERONET-OC and satellite-derived products. The simulated satellite sensors considered here are OLI, MSI, OLCI, and VIIRS. To account for differences in spectral sampling, this study introduces a novel machine-learning technique, i.e., deep neural networks (DNN) and compares its performance with existing methods [4, 11]. The DNN is trained using a large database of simulated hyperspectral ${\text{R}}_{\text{rs}}$ for a broad range of in-water optical conditions. The impacts of band adjustments are further examined and discussed for OLI, MSI, and VIIRS matchups at AERONET-OC sites. In what follows, we describe the data sets and methodology in sections 2 and 3 respectively. Section 4 includes the results and, in sections 5, we discuss the impacts of spectral band adjustments on actual AERONET-OC matchups. The manuscript ends with conclusions and discussions of future perspectives.

2. Data sets

Two sets of data are used in this study: simulated ${\text{R}}_{\text{rs}}$ spectra (FWHM = 5nm resolution), which will be used for training and in situ ${\text{R}}_{\text{rs}}$ spectra (FWHM = 1 to 3.5nm), which will be utilized for testing. Using these data sets, we simulate AERONET-OC radiometric data (hereafter referred to as AER_sim) and satellite-derived $R_{rs}$ spectra. The community-accepted simulated data [13] was not used here as the data are provided at 10-nm spectral spacing. In addition, this simulated database (n = 500) is not fully representative of various bio-optical and biogeochemical properties in inland and nearshore coastal waters, which is required for extensive training of algorithms like neural networks.

2.1 Simulated data

The core simulated data set for this study was generated using the widely used Hydrolight package [17]. To encompass a wide variety of water types, many of the input variables were varied using Hydrolight’s Case-II option. These include the specific absorption of chlorophyll-a (${\text{a}}_{\text{ph}}^{\text{*}}$), the specific absorption (${\text{a}}_{\text{NAP}}^{\text{*}}$) and backscattering (${\text{a}}_{\text{NAP}}^{\text{*}}$) of non-algal particles (NAP), near-surface concentrations of chlorophyll-a (Chl) and total suspended solids (TSS), the unitless backscattering ratio ($B_p=b_b/b$) [18], the absorption of colored dissolved organic matter at 440nm (${\text{a}}_{\text{cdo}m}$(440)), and the CDOM slope parameter (S) as:

The phytoplankton specific absorption spectra together with the distribution of $R_{rs}(443)$ and $R_{rs}(675)$ are shown in Appendix. The Chl, TSS, and $a_{cdom}$ (440) were allowed to vary from 0.01 to 100 $mg/m^3$, 0 to 98.4 $g/m^3$ and 0.01 to 6 $m^{-1}$, respectively. The backscattering ratio (B_p) were also varied from 0.012 to 0.03 for both Chl and non-algal particles (i.e., TSS). With various combinations of concentrations and optical properties, a database with nearly one million $R_{rs}$ spectra with FWHM = 5nm resolution was created. A summary of the range, mean, median, and standard deviations of the parameters are provided in Table 1.

Table 1. Summary of statistics for input parameters used in the simulations.

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The simulations were performed from the ultra-violet (350nm) to the near-infrared region (800nm) and for 15m-deep waters (i.e., no bottom reflectance was specified) with uniformly distributed Chl, TSS,${\text{a}}_{\text{cdom}}$ (440) for a solar zenith angle of $45°$. Following the creation of the database, the hyperspectral data were convolved with OLI, MSI, OLCI, and VIIRS relative spectral response (RSR) functions to compute weighted band-average ${\text{R}}_{\text{rs}}$ for each nominal band center (j) ($R_{rs}({\lambda }_j)$):

Table 2. The nominal band centers (nm) of in sit and satellite sensors.

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Fig. 1 The relative spectral response(RSR) functions of MSI, OLI, VIIRS, and OLCI in the visible spectrum. The broad spectral bands of OLI and MSI are evident in the three blue, green, and red channels, however, their 443nm bands are very similar to those of VIIRS and OLCI. Note the MSI’s non-uniform response within the 460-520nm region and OLCI’s four narrow red channels.

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2.2 In situ (test)data

The in situ hyperspectral ${\text{R}}_{\text{rs}}$ data were obtained from various regional campaigns in coastal and inland waters of North America. The database also includes radiometric data from the SeaWiFS Bio-Optical Archive and Storage System (SeaBASS) [20]. Note that the bandwidths of the hyperspectral in situ data collected mostly using Hyper-OCR radiometers (Satlantic) are estimated to be ~3.5nm. These data were visually inspected to identify poor quality (noisy) data, resulting in 980 ${\text{R}}_{\text{rs}}$ spectra available for testing. Similar to the previous section, the hyperspectral data were resampled to OLI, MSI, OLCI, VIIRS, and AERONET-OC radiometers (Eq. (2). Figure 2 illustrates the distribution of $R_{rs}$ (440) and $R_{rs}$ (555), $R_{rs}$ (670), and $R_{rs}$ (490) / $R_{rs}$ (555) for the in situ $R_{rs}$ data. The histograms confirm that the spectra are primarily representative of turbid/eutrophic bodies of water.

 

Fig. 2 The distribution of $R_{rs}$ spectra collected in situ in various aquatic systems in inland and nearshore coastal waters of North America. While most of the data are representative of turbid/trophic waters, a small percentage was measured in clear or moderately turbid waters.

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The Chl and TSS concentrations, which were not available for all the $R_{rs}$ spectra, ranged from 0.2 to 290 $mg/m^3$ and 0.15 to 127 $g/m^3$, respectively. The mean and median values for Chl and TSS were 9.6 and 3.5, and 8.9 and 5.2, respectively. The simulated and in situ hyperspectral ${\text{R}}_{\text{rs}}$ are provided in [21].

3. Procedure

Four different methods including the Deep Neural Networks (DNNs), spectral matching technique (SMT), QAA-based technique [11], and cubic splines are considered. The idea is to employ simulated AERONET-OC $R_{rs}$ ($\lambda$) (AER_sim) to predict $R_{rs}$ (${\lambda }_i$) for each satellite sensor (e.g., AER_sim > OLI), where i refers to each band, using the four different techniques. Note that the symbol “>” indicates the mapping direction. For example, OLCI > VIIRS indicates the use of OLCI-derived $R_{rs}$ to predict VIIRS-derived $R_{rs}$.Note that recorded AERONET-OC data or satellite retrievals have not been used for training. The impact of band-shifting algorithms on AERONET-OC matchups, however, are presented in section 5. We will also utilize a reference satellite-retrieved $R_{rs}$ ($\lambda$) to estimate $R_{rs}$ (${\lambda }_i$) for a target sensor (e.g., OLCI > VIIRS). While the simulated $R_{rs}$ database is used for extensive training of DNNs and as a look-up-table for the SMT, the in situ (test) $R_{rs}$ data are utilized to evaluate the performances of the methods.

For example, given a test hyperspectral ${\text{R}}_{\text{rs}}$ spectrum from which respective multispectral ${\text{R}}_{\text{rs}}$ can be computed for all the sensors, we will gauge the performances using statistical metrics provided in section 3.4. All the python scripts developed as part of this study are provided in [22].

3.1 Deep neural network (DNN)

Neural networks form a class of algorithms, which learn a function mapping $\text{F}\left(\text{x}\right)\to \text{ y}$ by iteratively improving upon a set of weights [23]. The structure of a standard feed-forward neural network, also known as a Multilayer Perceptron (MLP), consists of an input layer, a variable number of hidden layers, and an output layer – each containing a variable number of weights (Fig. 3).

 

Fig. 3 The architecture of the multilayer perceptron for spectral band adjustments. The input spectral bands (e.g., simulated AERONET-OC data; AER_sim) shown on left are applied to predict output spectral bands (e.g., four OLI bands) to the right. The Rectified Linear Unit is shown as the activation function.

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Beginning with the difference ($\Delta$) between the expected (${\widehat{R}}_{rs}$) and the observed ($R_{rs}$) output, the weights are gradually updated during training through a backward propagation of the error gradient with respect to subsequent layers. Here, the training is performed using our Hydrolight-simulated $R_{rs}$ spectra resampled to different sensors’ spectral responses.

Each layer in an MLP uses an activation function to modify the output signal, with functions such as sigmoid or hyperbolic tangent function being common. However, these activations have been shown to create convergence issues, especially when considering deep network implementations. Therefore, we specifically design a network with three considerations. First, following the results of Nair and Hinton [24], we use the Rectified Linear Unit (ReLU) as the primary network activation function. ReLU has been shown to be faster and better performing than the alternatives, especially with regard to networks with many layers [25–27]. The benefits in training come primarily from addressing the vanishing gradients problem, which arises from the shape and bounds of the activations. With ReLU, the output is instead clipped on the negative end, and unbounded on the positive.

Second, the initialization of the network weights has recently received significant attention in consideration of deep neural networks performance. Reflecting the notion that we do not have any a priori information to inject into the network, the standard practice is to distribute weights drawn from a Gaussian distribution with arbitrary variance (usually dependent on the data set). However, this can lead to poor performance due to improper gradient propagation and so, instead, we adopt the MSRA (Microsoft Research Asia) initialization scheme [26, 28], which accounts for the size of each weight layer ${\text{W}}_{\text{i}}$ by maintaining a constant variance ($\sigma$) through the network:

In summary, to optimize the learner, there are four relevant hyper-parameters we tune: the learning rate, the L2 normalization coefficient, the dropout rate, and the specific network architecture. These are found via a coarse cross validated grid search per target, over a random subset of simulated $R_{rs}$ data from the full training set. The best hyper-parameter set for each target spectral band is then used to fit a model to the full training data, which is taken as the final $R_{rs}$ estimation. To account for differences in spectral bands, the DNN accepts the multispectral $R_{rs}(\lambda )$ (e.g., AERONET-OC) and predicts $R_{rs}({\lambda }_i)$ for a desired sensor (for band i). Each channel for a given sensor has its own trained architecture.

3.2 Spectral matching technique (SMT)

Spectral matching has been widely used in the ocean color literature [31–33]. In this study, we use the Hydrolight-generated $R_{rs}$ database as a look-up-table, which encompasses all in-water conditions.

For in situ matchup exercises i.e., AERONET-OC > Sensor, (A2S) we first need to identify a hyperspectral $R_{rs}$ spectrum that best represents an observed AERONET-OC $R_{rs}$ spectrum. Here, we start with a simulated AERONET-OC $R_{rs}$ spectrum (AER_sim) obtained from our in situ database (n = 980). From the $R_{rs}$ database, a hyperspectral ${\text{R}}_{\text{rs}}$ curve (resampled to AERONET-OC bands;${\text{ R}}_{\text{rs}}^{\text{res}}$) is found such that it best fits AER_sim (e.g., ${\text{R}}_{\text{rs}}^{\text{AER}}$). The search is conducted by examining the root mean squared errors (RMSE) in the multispectral domain for all the records of our look-up-table:

A similar procedure is followed for sensor-to-sensor (S2S) spectral band mapping (e.g., OLCI > MSI). The only difference here is that the sensor with more number of spectral bands is used in the fitting process. For example, for intercomparisons of VIIRS and MSI, VIIRS products are used for fitting and reconstructions of hyperspectral spectra, i.e., VIIRS > MSI.

3.3 QAA-based approach

We further implemented the approach proposed by Mélin and Sclep [11]. To do so, we applied QAA(V6) [12] and tested the performance against DNN and SMT using in situ data. Given multispectral $R_{rs}$, this semi-analytical method estimates IOPs are derived (hereafter referred to as Mélin and Sclep [11]). This method first applies QAA to derive ${\text{b}}_{\text{bp}}$, ${\text{a}}_{\text{ph}}$, and ${\text{a}}_{\text{cdm}}$ at a reference wavelength, i.e, $\text{λ}=443\text{nm}$. Then ${\text{b}}_{\text{bp}}(\text{λ})$, ${\text{a}}_{\text{ph}}(\text{λ}$), ${\text{a}}_{\text{cdm}}(\text{λ})$ at any target (t) band center is computed as follows

3.4 Performance metrics

The root mean squared error (RMSE) is the main metric used to measure the performances of the four methods for the A2S experiments and is computed for N = 980 and band i as follows

4. Results

The results will be presented in two subsections explaining findings associated with a) AERONET-OC $R_{rs}$ ($\text{λ}$) to $R_{rs}$ (${\text{λ}}_{\text{i}}$) for each sensor (A2S) and b) predicting $R_{rs}$ (${\text{λ}}_{\text{i}}$) for a sensor from another sensor’s retrieved $R_{rs}$ ($\text{λ}$), i.e., S2S.

4.1 AERONET-OC > Sensor (A2S)

The normalized histogram distributions of the differences ($\Delta$) associated with A2S is illustrated in Fig. 4. For clarity in presentations, the x-axes are bound to $[-2{\text{e}}^{-4},2{\text{e}}^{-4}](1/\text{sr})$. In general, the Deep Neural Networks (DNN) was found to perform the best for almost all the A2S cases. The distribution peaks are, in general, < ${\text{e}}^{-4}$, which is less than the accepted uncertainties for satellite-retrieved $R_{rs}$ in oceanic waters i.e., $5{\text{e}}^{-4}$ [35]. The top row shows the distributions associated with AERONET-OC > OLCI band adjustments. Since OLCI’s narrow blue bands (Fig. 1) closely resemble those of the in situ radiometers, the predictions are generally good with DNN exhibiting the best performances. While more uncertainties are found when predicting OLCI’s $R_{rs}$ within the 500-700nm range, DNN still outperforms the other methods in all bands except for the 681nm channel for which Mélin and Sclep [11] approach (i.e., QAA) performs the best. The predictions of red bands using cubic spline indicate poorest performance. This is because of high spectral variations in this region. For the AERONET-OC > MSI and AERONET-OC > OLI, the DNN approach performs significantly better than the other methods. The QAA-based method performs equally well or better than the DNNs for the 412 and 487nm bands in AERONET-OC > VIIRS.

 

Fig. 4 The normalized histogram distributions of the differences ($\Delta$) for the predictions of satellite-derived R_rs from AERONET-OC R_rs. The distributions derived from DNN predictions (shown in solid red lines) clearly indicate better performances than the other methods in most cases. The QAA-based method (Mélin and Sclep [11]) outperforms DNN when predicting R_rs(412) and R_rs(487) bands of VIIRS. The performance of DNN, in particular, is significantly better than other methods, including the spectral matching technique and cubic splines. DNN Predictions of OLIC’s R_rs in the green and red bands carry highest uncertainties.

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That said, the DNN performance for predicting $R_{rs}$ (550) and $R_{rs}$ (670) is considerably better than those estimated by the Mélin and Sclep [11] approach. Comparing to DNN and Mélin and Sclep [11] methods, the spectral matching technique (SMT) was found to perform poorly in all cases.

The RMSE plots are provided in Fig. 5. The vertical axes are clipped to 0.001 1/sr above which the performance is regarded as poor. The poorest performance in the blue band is associated with the spectral matching technique (SMT). Further investigations of errors per test $R_{rs}$ spectrum indicated that SMT is very sensitive to $R_{rs}$ spectra not represented in our simulated $R_{rs}$ database. Amongst the 980 test spectra, it was found that the spectra collected in extremely turbid waters were not well represented in our database. It is further inferred that, amongst the four satellite sensors, VIIRS matchup analyses are expected to carry minimal uncertainties due to spectral band mismatches.

 

Fig. 5 The root mean squared errors computed from N = 980 test spectra for AERONET-OC > Sensor (matchup analyses). While the DNN shows (solid red bar) the best performance amongst all the methods, the spectral matching technique (SMT) indicates poorest performance. The SMT is very sensitive to the lack of representative R_rs spectrum in the reference database. The high RMSEs associated with SMT is due to erroneous predictions for highly turbid samples.

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The DNN and Mélin and Sclep [11] approaches can equally well predict VIIRS-derived $R_{rs}$ spectra. The RMSEs estimated for these two methods are < 2e⁻⁴. On the other hand, the expected noise in matchup analyses is high for OLI and MSI. Due to OLI’s wider bands in the green and red, the expected impacts are, on average, higher for OLI than for MSI.

The performance of DNN exceeds that of Mélin and Sclep [11] for all the bands and the RMSEs are, in general, found < 4e⁻⁴ except for the ~560nm band. The larger uncertainties in this band is due to large gradients in this portion of the spectrum and highly scattering waters, i.e., average $R_{rs}$ (555) of ~0.01 1/sr, (see Fig. 2) included in our test data set. Similar uncertainties are found for OLCI’s 560nm band. The relatively high RMSEs, i.e., percentage-wise (see Fig. 2 for average signals), in predicting OLCI’s 681nm band from AERONET-OC $R_{rs}$ (668) in situ radiometry may be attributed to uncertainties in modeled chlorophyll-a fluorescence signal [36] available for training in our database.

Note that the RMSEs associated with DNN and Mélin and Sclep [11] approaches when predicting OLCI’s 620nm band are ~0.0015 and ~0.002 1/sr, respectively. Needless to say, the lack of in situ measurements in 620nm band gives rise to these large uncertainties. This will, however, be resolved in future using new 12-band AERONET-OC radiometers equipped with 620nm filters.

4.2 Sensor-to-sensor (S2S)

In this section, we present the performances of different spectral band adjustment methods for predicting $R_{rs}$ (${\text{λ}}_{\text{i}}$) for a lower spectral resolution sensor (i.e., target) from $R_{rs}$ ($\text{λ}$) retrieved from a sensor with more spectral bands (i.e., reference). Figure 6 shows sensor-to-sensor (S2S) prediction errors (i.e., RMSD) in the form of a color-coded matrix with reference and target sensors shown on the left and right sides of plot.

 

Fig. 6 The color-coded matrix of RMSDs for sensor-to-sensor spectral band adjustments. The corrections use R_rs spectra from reference sensors to predict different bands of target sensors. Similar to the A2S results, the DNN yields smallest uncertainties. The performances of all methods are satisfactory when adjusting bands in R_rs(443). Note that the spectral band adjustments for OLI > MSI and MSI > OLI is not possible through Mélin and Sclep [11] method; thus no data are shown in the corresponding rows. On average, the spectral matching technique performs better than the Mélin and Sclep [11]

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The nominal band centers for each target sensor (right) are shown on the x-axes. For instance, the top row shows RMSDs given for OLCI-“derived” $R_{rs}$ spectra predicting MSI’s $R_{rs}$ (444), $R_{rs}$ (497), $R_{rs}$ (560), and $R_{rs}$ (664). Note that no predictions were made for OLI > MSI or MSI > OLI using the Mélin and Sclep [11] approach (due to the lack of $R_{rs}$ (410)) [12].

Overall, the Deep Neural Network (DNN) provides more accurate predictions of $R_{rs}$ for various sensor-to-sensor conversions. The most accurate predictions for all the methods are found when predicting $R_{rs}$ (~443), i.e., average RMSD of 8e-5. On the other hand, the largest RMSDs are found for the green and red bands.

The cubic spline and Mélin and Sclep [11] methods, on average, perform fairly poorly for predicting $R_{rs}$ ($\text{λ}>500$). By further visually inspecting the performance of DNN, it can be inferred that all the S2S mapping yield RMSDs < 5e⁻⁴ with the exception of the green bands in VIIRS > OLI and VIIRS > MSI. Analyzing test $R_{rs}$ set indicated that most uncertainties come from extremely turbid waters, i.e., $R_{rs}$ (550)> 0.02 1/sr. Therefore, avoiding such in-water conditions will ensure robust direct intercomparisons minimally influenced by differences in spectral response functions. The DNN performance for OLCI > VIIRS also indicates promise for low uncertainties in direct intercomparisons of the respective $R_{rs}$ products.

5. Discussion

From the results presented, it is clear that spectral band adjustments increase the rigor in matchup analyses. However, to further demonstrate the impacts of spectral band adjustments on the existing AERONET-OC matchups, we apply the DNN and Mélin and Sclep [11] algorithms to OLI-, MSI-, and VIIRS-derived R_rs retrievals. We utilize all the valid matchups for OLI (n = 69) and MSI (n = 52) published in [4, 37]. In addition, valid matchups at the Venise site (available in the 2012-2016 period) are examined for VIIRS products (n = 344). We use the SeaWiFS Data Analysis System (SeaDAS) for processing the imagery [1]. For the processing, the broadband-to-narrowband conversion [9] built into SeaDAS is not applied (i.e., the option was turned off; outband_opt = 0). For the DNN, we use the network trained using modeled R_rs spectra (section 3.1).

The per-band RMSE and slopes of linear fits for matchups are presented in forms of bar charts in Fig. 7. The statistics are associated with a) no spectral-band adjustments, b) correction using the Mélin and Sclep [11] method, and c) correction with our proposed DNN approach. Analyzing the RMSEs indicates how noise contributions in matchups change whereas examining slopes implies how performance evaluations may differ for the three scenarios. In general, the slopes tend to better exhibit the impacts of band adjustments and differences in the performances of DNN and Mélin and Sclep [11].

 

Fig. 7 Per-band statistics shown for evaluating the impact of spectral band adjustments on AERONET-OC matchups for OLI, MSI, and VIIRS data products. The RMSE and the slopes of linear fits are evaluated. The blue bars show matchup statistics for which no spectral band adjustments have been applied. In general, slopes better show the impacts of corrections. Overall, the statistics indicate that it is critical to perform band adjustments in the red bands for all the sensors. The impacts are also found noticeable for the OLI and MSI’s green bands due to their relatively broad spectral coverage. Note that all the available, valid matchups for OLI and MSI were utilized in the calculations. For VIIRS, only matchups (n = 344) at the Venise site were analyzed. The images were processed via SeaDAS for which the broadband-to-narrowband option [9] was turned off.

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The overall RMSEs (most-right panels in Fig. 7) indicate that the impact of corrections is < 5e⁻⁴ 1/sr. However, it is critical to correct OLI and MSI red channels where average R_rs is ~0.0013 1/sr. It is also noted that the Mélin and Sclep [11] method noticeably increases the RMSE for OLI’s green channel (561nm).

The slopes of the linear fits (Fig. 7), on the other hand, further highlights the need for applying adjustments for OLI’s red and green channels. A closer examination of the slopes for MSI and VIIRS’s red channels shows that there is a relatively significant impact on matchup analyses. The impacts of correction on the slopes in red channels range from 2% to 5%. Considering DNN performance as the baseline (since it provides best band adjustment according to section 4), it can be inferred that the Mélin and Sclep [11] approach yields significantly different slopes for OLI and VIIRS’s red channel conveying different matchup quality.

It should further be noted that the test data used for performance evaluations (section 4.1) constitute a very broad range of R_rs spectra, including clear and extremely eutrophic/turbid waters. The AERONET-OC matchups analyzed here do not fully represent inland waters where high-frequency variations in R_rs spectra, in particular, in red and NIR portions of the spectrum are commonly found. With future AERONET-OC sites expected in inland waters, it becomes more critical to apply DNN to account for differences in spectral bands. Furthermore, our study has demonstrated that the DNN outperforms Mélin and Sclep [11] approach when multi-mission product comparisons are desired over various inland and nearshore coastal waters (section 4.2).

While the Deep Neural Network (DNN) methodology introduced here shows very promising results for minimizing uncertainties in matchup analyses (section 4) and direct sensor-to-sensor comparisons of $R_{rs}$ products, there are still remaining ambiguities in accounting for differences in the spectral response functions. One way to further minimize these uncertainties is to expand the simulated database to enhance the training set enabling better predictions. For instance, it is possible to conduct simulations capturing extremely turbid conditions (beyond what is available in our database) because currently the majority of the uncertainties are attributed to these conditions. Such further expansions of the database will also enhance the performance of the spectral matching technique (SMT). Although our test set included $R_{rs}$ spectra representing areas with high sediment loads, the distribution of actual AERONET-OC $R_{rs}$ matchups are primarily skewed towards moderately turbid waters [38]. Hence, under such conditions, the SMT and Mélin and Sclep [11] methods can provide satisfactory corrections (as shown above for Mélin and Sclep [11]). We ran a test by removing extremely turbid waters from our test set (i.e., $\text{TSS}<70 g/{\text{m}}^3$ and $\text{Chl}<100 g/{\text{m}}^3$); reducing the set from n = 980 to n = 750. The performance of SMT for AERONET > OLI for $R_{rs}$ (560) was reduced from 0.0013 to 0.0004 1/sr. Therefore, it is further emphasized that the SMT and Mélin and Sclep [11] are expected to perform poorly in hypereutrophic or extremely turbid waters. The Mélin and Sclep [11] approach, i.e., QAA, in particular, is not parametrized for such in-water conditions normally present in inland waters. Expanding the simulated $R_{rs}$ database, on the other hand, may not guarantee significant improvements because Hydrolight-modeled $R_{rs}$ spectra may carry uncertainties due to both lack of comprehensiveness of the shapes of IOPs and inaccurate model performances [39]. This is likely to occur in turbid hypereutrophic inland systems. Such uncertainties in training result in unrealistic predictions.

Furthermore, uncertainties in R_rs can degrade the performance of DNN since the network is trained using modeled data. In fact, if the uncertainties in satellite retrievals are high, the spectral band adjustments using both DNN and Mélin and Sclep [11] are expected to fail. This was confirmed when attempting to perform spectral band adjustments for VIIRS-derived R_rs at the Palgrunden site, a typically eutrophic inland site. Therefore, for a reasonable performance of spectral band adjustments one needs to first ensure fairly good satellite retrievals.

6. Conclusion

A novel deep neural network (DNN) system was trained using a large database of simulated $R_{rs}$ spectra to account for differences in spectral bands of in situ and remote-sensing radiometers. The performance of the DNN for predicting $R_{rs}$ in a desired channel was compared against existing methods, including cubic spline, spectral matching, and Quasi Analytical Approach (QAA), using 980 hyperspectral in situ (test) data set. It was found that the DNN, on average, significantly outperforms the other methods with uncertainties generally < 5e⁻⁴ 1/sr in most bands. This was the case for spectral band adjustments for both AERONET-OC-to-sensor (A2S) and sensor-to-sensor (S2S) intercomparisons. Further analyses of actual AERONET-OC matchups for OLI, MSI, and VIIRS indicated the need for spectral band adjustments for the red bands. Relatively broad OLI and MSI’s green bands also require band adjustments. It is concluded that the DNN performance is, in particular, superior at eutrophic and very turbid AERONET-OC sites, which are under-represented in the existing network. Although DNN improves upon other methods, there are still uncertainties in accounting for differences in spectral bands in green bands over highly turbid/eutrophic waters. Future work may focus on training the neural networks using historic measured/retrieved $R_{rs}$ at AERONET-OC sites and expanding/enhancing the simulated training set.

Appendix

The simulated database includes varieties of in-water optical conditions. Amongst all the input variables allowed to vary were specific phytoplankton absorption spectra ${\text{a}}_{\text{ph}}{}^{\text{*}}(\text{λ})$. Several different laboratory cultures as well as in situ measured spectra used in this study are illustrated in Fig. 8. Note that ${\text{a}}_{\text{ph}}{}^{\text{*}}(\text{λ})$ with spectral resolutions < 1nm were normalized to within the range of 0.06-0.09 $[{\text{m}}^2/\text{mg}]$ at 443nm when supplied to Hydrolight. The field spectra are named after the respective cruises. For instance, GOCI-XXX spectra were collected in Korean waters, GOMI data were collected in Gulf of Mexico, and Muri-XXX were collected around Hawaiian Islands.

 

Fig. 8 Normalized ${\text{a}}_{\text{ph}}{}^{\text{*}}(\text{λ})$ collected during various field cruises and/or grown in laboratory conditions. The field spectra are named after the respective cruises. For instance, GOCI-XXX spectra were collected in Korean waters, GOMI data were collected in Gulf of Mexico, and Muri-XXX were collected around Hawaiian Islands.

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The distribution of simulated $R_{rs}(443)$ and $R_{rs}(675)$ (n > 900,000) are provided in Fig. 9. The large dynamic ranges indicate the breadth of water types captured in our database. The database may also be improved in red part of the spectrum, in particular, where $6e^{-4}<R_{rs}\left(675\right)<0.0015 1/sr$, i.e., there is a lack of representative $R_{rs}$ spectra.

 

Fig. 9 The distribution of simulated ${\text{R}}_{\text{rs}}(443)$ and ${\text{R}}_{\text{rs}}(675)$ available in our database. The database may also be improved in red part of the spectrum, in particular, where $6{\text{e}}^{-4}<R_{\text{rs}}\left(675\right)<0.0015 1/sr$, i.e., there is a lack of representative $R_{rs}$ spectra.

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Funding

The National Aeronautics and Space Administration (NASA); Research Opportunities in Earth and Space Science (ROSES-15); new investigator program (NNX16AI16G).

Acknowledgments

The authors are grateful to Ryan Vandermeulen (NASA Goddard Space Flight Center), Zhongping Lee and Jianwei Wei (University of Massachusetts Boston), and Mike Ondrusek (NOAA) for sharing in situ radiometric data. We are also grateful to Aimee Neeley (NASA Goddard Space Flight Center) and Sherry Palacios (NASA Ames) for providing $a_{ph}{}^{*}(\lambda )$_. We also thank Sundarabalan Subramanian for his support of the matchup analyses.

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