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.