We have computed two geophysical model functions (one for the vertical and one for the horizontal polarization) for the NASA scatterometer (NSCAT) by using neural networks. These neural network geophysical model functions (NNGMFs) were estimated with NSCAT scatterometer &sgr;0 measurements collocated with European Center for Medium-Range Weather Forecasts analyzed wind vectors during the period January 15 to April 15, 1997. We performed a student t test showing that the NNGMFs estimate the NSCAT &sgr;0 with a confidence level of 95%. Analysis of the results shows that the mean NSCAT signal depends on the incidence angle and the wind speed and presents the classical biharmonic modulation with respect to the wind azimuth. NSCAT &sgr;0 increases with respect to the wind speed and presents a well-marked change at around 7 m s-1. The upwind-downwind amplitude is higher for the horizontal polarization signal than for vertical polarization, indicating that the use of horizontal polarization can give additional information for wind retrieval. Comparison of the &sgr;0 computed by the NNGMFs against the NSCAT-measured &sgr;0 show a quite low rms, except at low wind speeds. We also computed two specific neural networks for estimating the variance associated to these GMFs. The variances are analyzed with respect to geophysical parameters. This led us to compute the geophysical signal-to-noise ratio, i.e., Kp. The Kp values are quite high at low wind speed and decrease at high wind speed. At constant wind speed the highest Kp are at crosswind directions, showing that the crosswind values are the most difficult to estimate. These neural networks can be expressed as analytical functions, and FORTRAN subroutines can be provided. ¿ 1999 American Geophysical Union