Error estimates for a histogram in scatterometer geophysical model function estimation

The relationship between the normalized radar cross section σ° and the ocean surface wind field, i.e., the geophysical model function, is a key element in scatterometry. Due to many unsolved physical modeling problems, only a semi-empirical approach can be used to quantitatively relate the observed σ° to the wind field. Once the appropriate functional form has been selected, a model calibration procedure based on colocated σ° measurements and external wind field observations/determinations is accomplished. To this end, a σ° data grouping (binning) is performed to limit measurement uncertainties and reduce data volume. On this note, the binning procedure is revisited as an histogram estimation procedure and the relevant errors are determined. It is shown that in the best case of wind field error-free model the bias error introduced by the binning is negligible (but for low wind regimes) while the variance error is significant