Atmospheric correction over coastal waters using multilayer neural networks

Highlights

• A neural network based atmospheric correction method for coastal water was developed.

• Method based on radiative transfer simulation of a coupled atmosphere-ocean system

• Validation with AERONET-OC measurements showed great improvement in R_rs retrieval.

• Algorithm showed better separation between atmospheric and marine features.

• Algorithm is robust and resilient to adjacency effect and sunglint.

Abstract

Standard atmospheric correction (AC) algorithms work well in open ocean areas where the water inherent optical properties (IOPs) are correlated with pigmented particles. However, the IOPs of turbid coastal waters may independently vary with pigmented particles, suspended inorganic particles, and colored dissolved organic matter (CDOM). In turbid coastal waters standard AC algorithms often exhibit large inaccuracies that may lead to negative water-leaving radiances (L_w) or remote sensing reflectance (R_rs). We introduce a new atmospheric correction algorithm for coastal waters based on a multilayer neural network (MLNN) method. We use a coupled atmosphere-ocean radiative transfer model to simulate the Rayleigh-corrected radiance (L_rc) at the top of the atmosphere (TOA) and the R_rs just above the surface simultaneously, and train a MLNN to derive the aerosol optical depth (AOD) and R_rs directly from the TOA L_rc. The method is validated using both a synthetic dataset and Aerosol Robotic Network – Ocean Color (AERONET–OC) measurements. The SeaDAS NIR algorithm, the SeaDAS NIR/SWIR algorithm, and the MODIS version of the Case 2 regional water - CoastColour (C2RCC) algorithm are also included in the comparison with AERONET–OC measurements. The performance of the AC algorithms is evaluated with four statistical metrics: the Pearson correlation coefficient (R), the average percentage difference (APD), the mean percentage bias, and the root mean square difference (RMSD). The comparison with AERONET–OC measurements shows that the MLNN algorithm significantly improves retrieval of normalized L_w in blue bands (412 nm and 443 nm) and yields minor improvements in green and red bands compared with the other three algorithms. On a global scale, the MLNN algorithm reduces APD in normalized L_w by up to 13% in blue bands and by 2–7% in green and red bands when compared with the standard SeaDAS NIR algorithm. In highly absorbing coastal waters, such as the Baltic Sea, the MLNN algorithm reduces APD in normalized L_w by more than 60% in blue bands compared to the standard SeaDAS NIR algorithm, while in highly scattering coastal waters, such as the Black Sea, the MLNN algorithm reduces APD by more than 25%. These results indicate that the MLNN algorithm is suitable for application in turbid coastal waters. Application of the MLNN algorithm to MODIS Aqua images in several coastal areas also shows that it is robust and resilient to contamination due to sunglint or adjacency effects of land and cloud edges. The MLNN algorithm is very fast once the neural network has been properly trained and is therefore suitable for operational use. A significant advantage of the MLNN algorithm is that it does not need SWIR bands.

Introduction

Atmospheric correction (AC) is the first and a very important step in many ocean color algorithms. Ideally, it should remove the radiance contribution of the atmosphere (including that of air molecules and aerosols) and surface reflection from the satellite measured radiances to produce water-leaving radiances (L_w), which can be used to derive ocean color products such as the chlorophyll-a concentration (CHLa). The atmosphere may contribute about 90% to the TOA radiance measured by a satellite sensor, and in coastal areas this contribution could be even higher, especially in the blue bands, or way less in sediment dominated extremely turbid waters, especially in red and NIR bands (Wang, 2010). Therefore, an accurate AC algorithm is crucial to ocean color data processing. Standard AC algorithms (Gordon and Wang, 1994b, Gordon, 1997) describe the radiance measured by the satellite sensor as:

$$L_{\mathrm{t}}(\lambda )=L_{\mathrm{r}}(\lambda )+L_{\mathrm{a}}(\lambda )+T(\lambda )L_{\mathrm{g}}(\lambda )+t(\lambda )L_{\text{wc}}(\lambda )+t(\lambda )L_{\mathrm{w}}(\lambda )$$

where λ is the wavelength, L_t is the total radiance measured by the ocean color sensor, L_r is the radiance contributed by Rayleigh scattering by atmospheric molecules, L_a is the radiance contributed by aerosol scattering/absorption including the aerosol-Rayleigh interaction, L_g is the radiance contributed by sunglint, L_wc is the radiance contributed by surface whitecaps, L_w is the radiance backscattered by the upper water column that leaves the ocean surface, commonly referred to as the water-leaving radiance. Note that L_w does not include radiance (Fresnel) reflected by the water surface. T and t are the atmospheric direct and diffuse transmittance, respectively. It is important to note that Eq. (1) is valid only in the single-scattering limit (Gordon and Wang, 1994b, Zhang et al., 2007).

Conventional atmospheric correction algorithms derive the water-leaving radiance (L_w) by quantifying the first four terms in Eq. (1). The Rayleigh scattering radiance (L_r) needs to be computed accurately (Gordon and Wang, 1992, Wang, 2002) because it constitutes a major proportion of the atmospheric radiance, especially for open ocean waters in the ultraviolet-visible bands. Generally, it can be simulated using a radiative transfer model with an uncertainty lower than 0.5% (Wang, 2005). Sunglint is due to specular reflection of direct sunlight by the surface. It can be avoided by tilting the sensor away from the direct reflection of sunlight, as specifically done with a dedicated OC instrument like the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS). For sensors that do not have tilt capability such as MODIS, a 1-D version of the Cox and Munk model (Cox and Munk, 1954) is commonly used to compute the sunglint radiance (L_g) for situations with low sunglint contributions (Wang and Bailey, 2001). A recent study by Lin et al. (2015) suggests that a 2-D Gaussian slope distribution is needed in order to simulate the sunglint radiance accurately. The radiance due to surface whitecaps (L_wc) is usually estimated from the wind speed (Gordon and Wang, 1994a, Frouin et al., 1996, Stramska and Petelski, 2003). The aerosol radiance (L_a) which includes the aerosol-Rayleigh interaction is highly variable due to the complexity of the micro-physical properties (i.e. particle size distribution and refractive index) of the aerosols. For open ocean water, the AC algorithms estimate the aerosol radiance by assuming the water-leaving radiance to be negligible (black ocean assumption) at near-infrared (NIR) wavelengths due to the strong absorption by pure water.

The aerosol model is determined from the radiance measured at two NIR bands, and then used to estimate the contribution of aerosols to the radiance in the visible bands. This method works well in open ocean areas but is challenged in coastal areas where the black ocean assumption often fails. Several modified algorithms (Siegel et al., 2000, Ruddick et al., 2000, Wang and Shi, 2007, Wang et al., 2012, Brajard et al., 2008, Brajard et al., 2012, Bailey et al., 2010, He et al., 2012, Singh and Shanmugam, 2014, Jiang and Wang, 2014) among others were developed for coastal waters to correct for the non-zero NIR water-leaving radiances. An alternative AC algorithm developed by Wang and Shi (2007) estimates the aerosol contribution to the radiance using shortwave IR (SWIR) bands (1240 and 2130 nm for MODIS), where the black ocean assumption may still hold, and then obtains L_w values in the visible bands by extrapolation. Most of these algorithms showed improvements, at least for selected calibration/validation areas.

However, these modified or alternative AC algorithms may still yield questionable results in coastal water areas (Zibordi et al., 2006b, Jamet et al., 2011, Goyens et al., 2013b, Singh and Shanmugam, 2014). The reason is that both the water and the aerosols are optically more complex in coastal regions. Therefore, the NIR water-leaving radiance correction algorithms predict incorrect water-leaving radiances resulting in an over-estimation of the aerosol radiance.

To address this problem, we introduce a different approach. Since the problem arises because it is difficult to remove the aerosol contribution to the spectral radiance in coastal water areas, an alternative approach is not to attempt removing it, but to use the combined aerosol and water-leaving radiances together. This combined radiance is called the Rayleigh-corrected TOA radiance (L_rc), defined as

$$L_{\text{rc}}=L_{\mathrm{a}}(\lambda )+t(\lambda )L_{\mathrm{w}}(\lambda ).$$

Since, as noted above, Eq. (2) is valid only in the single-scattering approximation, it was not used in this study. Instead, a radiative transfer model for the coupled atmosphere–ocean system was used to simulate L_rc values. The information about aerosol optical depth (AOD) and water-leaving radiance is embedded in the L_rc signal. Our radiative transfer simulations show that there is a spectral similarity between the Rayleigh-corrected radiance and the water-leaving radiance (L_w), as shown in Fig. 1. This spectral similarity allows us to use a multilayer neural network (MLNN) method to find a relation between L_rc and L_w. Also, the correlation coefficient between spectral L_rc and the spectral aerosol optical depth (AOD) is about 0.5, implying that it should be possible to develop a MLNN method to retrieve spectral AOD values from spectral L_rc data.

The feasibility of applying a neural network method to atmospheric correction has been investigated in several previous studies. Jamet et al., 2005, Brajard et al., 2008 used a trained neural network to replace the radiative transfer model in the forward simulation to obtain TOA radiances. Schiller and Doerffer, 1999, Doerffer and Schiller, 2007 showed that a neural network can be directly applied in the inverse process to derive AOD and L_w from satellite measured TOA radiances. However, these methods did not use coupled atmosphere–ocean radiative transfer models to simulate TOA radiances. Schroeder et al. (2007) used a coupled radiative transfer model to simulate the TOA radiance and demonstrated that direct inversion of the total TOA signal was feasible for atmospheric correction and simultaneous AOD retrieval and that application to MERIS data was successful. This algorithm has been applied by Goyens et al. (2013b) to MODIS images and validated using AERONET-OC data.

The MLNN method described in this paper is different from previous methods in terms of neural network structure, the use of Rayleigh-corrected TOA radiance as input, and training procedures. First, we use a coupled atmosphere–ocean radiative transfer model (RTM) to compute L_rc and L_w at both visible and near infrared (NIR) bands to ensure that NIR L_w values are correctly simulated. Second, AODs and marine particle IOPs at 443 nm are extracted from a statistical analysis of 8-day averaged MODIS L3 products over 5 coastal areas (see Fig. 2), in order to obtain realistic “concentration" ranges that are representative of a variety of situations encountered in nature. These values become the input to the aerosol and marine IOP models described in Section 2 to compute IOPs at other wavelengths as required in the RTM simulations. Third, the major difference of our neural network method is the independent training of two multilayer neural networks separately: the AOD MLNN retrieves AODs from L_rc while the R_rs MLNN retrieves remote sensing reflectances, where R_rs(λ) = L_w(λ)/E_d(0 ⁺,λ) and E_d(0 ⁺,λ) is the downward solar irradiance just above the surface. This separation has two advantages, (i) each MLNN is focused exclusively on learning one type of spectral shapes, thereby reducing the training difficulty and likely increasing the accuracy of retrieved quantities, (ii) errors in one MLNN do not necessarily affect the results of the other. However, the AOD and R_rs MLNN algorithms are not completely independent because both are trained with the same L_rc data which include contributions to the radiance from both the aerosols and the water. In other words, the trained R_rs MLNN takes into account aerosol information in L_rc implicitly, and the AOD MLNN takes into account the spectral shape of water-leaving radiance implicitly as well. Validation of the MLNN method is carried out with a synthetic dataset as well as field measurements from seven Aerosol Robotic Network – Ocean Color (AERONET–OC) stations (Zibordi et al., 2006a, Zibordi et al., 2009) over the 2002–2015 period. Detailed validation results and some discussions are presented in the following sections.