Remote sensing of phytoplankton chlorophyll-a concentration by use of ridge function fields

A methodology is presented for retrieving phytoplankton chlorophyll-a concentration from space. The data to be inverted, namely, vectors of top-of-atmosphere reflectance in the solar spectrum, are treated as explanatory variables conditioned by angular geometry. This approach leads to a continuum of inverse problems, i.e., a collection of similar inverse problems continuously indexed by the angular variables. The resolution of the continuum of inverse problems is studied from the least-squares viewpoint and yields a solution expressed as a function field over the set of permitted values for the angular variables, i.e., a map defined on that set and valued in a subspace of a function space. The function fields of interest, for reasons of approximation theory, are those valued in nested sequences of subspaces, such as ridge function approximation spaces, the union of which is dense. Ridge function fields constructed on synthetic yet realistic data for case I waters handle well situations of both weakly and strongly absorbing aerosols, and they are robust to noise, showing improvement in accuracy compared with classic inversion techniques. The methodology is applied to actual imagery from the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS); noise in the data are taken into account. The chlorophyll-a concentration obtained with the function field methodology differs from that obtained by use of the standard SeaWiFS algorithm by 15.7% on average. The results empirically validate the underlying hypothesis that the inversion is solved in a least-squares sense. They also show that large levels of noise can be managed if the noise distribution is known or estimated.