Spectral and spatial kernel water quality mapping

An empirical approach through remote sensing generally produces a robust data model of water quality for inland and coastal water. Traditional regressions in water quality mapping fail because the bio-optical relationship of turbid water exhibits nonlinear and heterogeneous patterns. In addition, in situ data are generally insufficient in the water quality mapping. Mapping based on a relatively small amount of water quality samples is considered a practical issue in environmental monitoring. Learning-based algorithms that require a large amount of data are inapplicable in this case. According to the concept of Nadaraya–Watson estimator, the kernel model can estimate nonlinear and spatially varying water quality maps effectively in turbid water. Experiments indicate that the kernel estimator provides better goodness-of-fit between the observed and derived concentrations of water quality parameter, e.g., chlorophyll-a in turbid water. The kernel estimator is feasible for a relatively small size of ground observations. Approximately 30% improvement of cross-validation error was identified in this approach when compared with traditional regressions. The model offers a robust approach without further calibrations for estimating the spatial patterns of water quality by using remote sensing reflectance and a small set of observations, considering spatial and spectral information, e.g., multiple bands and band ratios.