Constrained linear inversion of satellite ocean-color data

An inversion methodology, based on least squares minimization, is proposed to retrieve spectral marine reflectance from top-of-atmosphere reflectance measurements in the visible and near infrared. The problem is first made linear by decomposing into principal components the additive contributions of the water body (the signal of interest) and of the atmosphere and surface (the perturbing signal), after subtraction of molecular effects and proper normalization. For realistic geometric and geophysical conditions, the two contributions can be described adequately by a few eigenvectors. This yields generally (i.e., for current satellite ocean-color sensors) an over-determined system of linear equations, in which the unknown parameters are the coefficients associated with the eigenvectors. The problem is ill conditioned, since the measurements are noisy, the signal of interest is small compared with the top-of-atmosphere reflectance, and some of the eigenvectors of the atmosphere/surface signal are correlated with those of the water-body signal. The system of linear equations is solved in the least squares sense using a regularization scheme, in which a regularization parameter is introduced to stabilize the solution. Once the coefficients are determined, they are used to reconstruct the water-body signal, basically the marine reflectance, and the perturbing signal. Performance is evaluated theoretically for the Sea-viewing Wide Field-of-view Sensor, using a comprehensive non-noisy simulated data set. The inversion scheme yields acceptable root-mean-squared errors of 0.0034, 0.00228, 0.00132, 0.00102, 0.00081, and 0.00021 on the retrieved water-body signal at 412, 443, 490, 510, 555, and 670 nm (Case 1 waters). Performance could be improved by using additional wavelengths in the near infrared, but more eigenvectors might be required to describe the atmospheric/surface signal.