Model function development for GPS reflection measurements

Empirical model functions are derived for the retrieval of surface winds from the post-correlation waveform of scattered GPS signals. A geometric optics model is applied to generate model waveforms from the the surface slope probability density function (PDF). Batches of experimentally recorded waveforms are then processed to estimate parameters defining the PDF (ie., up-wind and cross-wind slope variances and the direction of the principal axes). A nonlinear least squares method is used to perform this estimation. Experimentally measured PDFs from this method are then compared with independent measurements of surface wind conditions obtained from the TOPEX altimeter. Linear and a logarithmic forms are assumed for the functional dependence of apparent slope moments on wind speed. The coefficients of each of these functions are determined by weighted linear least squares. The limitations and uncertainty in these models are discussed.