Mixture density networks for re-constructing historical ocean-color products over inland and coastal waters: demonstration and validation
Authors: Balasubramanian Sundarabalan V. , O’Shea Ryan E. , Saranathan Arun M. , Begeman Christopher C. , Gurlin Daniela , Binding Caren , Giardino Claudia , Tomlinson Michelle C. , Alikas Krista , Kangro Kersti , Lehmann Moritz K. , Reed Lisa 
Published: February 2025

Ocean color remote sensing tracks water quality globally, but multispectral ocean color sensors often struggle with complex coastal and inland waters. Traditional models have difficulty capturing detailed relationships between remote sensing reflectance (Rrs), biogeochemical properties (BPs), and inherent optical properties (IOPs) in these complex water bodies. We developed a robust Mixture Density Network (MDN) model to retrieve 10 relevant biogeochemical and optical variables from heritage multispectral ocean color missions. These variables include chlorophyll-a (Chla) and total suspended solids (TSS), as well as the absorbing components of IOPs at their reference wavelengths. The heritage missions include the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Aqua and Terra, the Environmental Satellite (Envisat) Medium Resolution Imaging Spectrometer (MERIS), and the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (Suomi NPP). Our model is trained and tested on all available in situ spectra from an augmented version of the GLObal Reflectance community dataset for Imaging and optical sensing of Aquatic environments (GLORIA) (N = 9,956) after having added globally distributed in situ IOP measurements. Our model is validated on satellite match-ups corresponding to the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) database. For both training and validation, the hyperspectral in situ radiometric and absorption datasets were resampled via the relative spectral response functions of MODIS, MERIS, and VIIRS to simulate the response of each multispectral ocean color mission. Using hold-out (80–20 split) and leave-one-out testing methods, the retrieved parameters exhibited variable uncertainty represented by the Median Symmetric Residual (MdSR) for each parameter and sensor combination. The median MdSR over all 10 variables for the hold-out testing method was 25.9%, 24.5%, and 28.9% for MODIS, MERIS, and VIIRS, respectively. TSS was the parameter with the highest MdSR for all three sensors (MODIS, VIIRS, and MERIS). The developed MDN was applied to satellite-derived Rrs products to practically validate their quality via the SeaBASS dataset. The median MdSR from all estimated variables for each sensor from the matchup analysis is 63.21% for MODIS/A, 63.15% for MODIS/T, 60.45% for MERIS, and 75.19% for VIIRS. We found that the MDN model is sensitive to the instrument noise and uncertainties from atmospheric correction present in multispectral satellite-derived Rrs. The overall performance of the MDN model presented here was also analyzed qualitatively for near-simultaneous images of MODIS/A and VIIRS as well as MODIS/T and MERIS to understand and demonstrate the product resemblance and discrepancies in retrieved variables. The developed MDN is shown to be capable of robustly retrieving 10 water quality variables for monitoring coastal and inland waters from multiple multispectral satellite sensors (MODIS, MERIS, and VIIRS).