Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

In radar altimetry, the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs; thus, the average sea surface height is underestimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this paper, the EM bias is computed using numerical simulations. To do so, a time-dependent synthetic non-Gaussian sea surface is created using the Pierson-Moskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets and illuminated using a right-hand circular polarization GNSS signal, previously recorded by an up-looking antenna connected to a data logger. The waves scattered from each facet are then computed using the physical optics method under the Kirchhoff approximation, and the radar cross section of each facet is computed. The scattered electric fields are collected by a down-looking left-hand circular polarization antenna, and the EM bias is computed based on its fundamental definition. The numerical model is validated against Millet's model (a combined model of the weakly non-linear and modulation transfer models) with real data at C-and Ku-bands. Then, the numerical model is applied at L-band, for bistatic configurations, including different azimuth angles and different wind speeds. It is found that the EM bias is almost insensitive to the sea surface spectra selected and increases with increasing wind speed and incidence/scattering angle (up to similar to-20 cm at theta(i,s) = 45 degrees and U-10 = 12 m/s), and it also exhibits a non-negligible azimuthal dependence, which must be accounted for in the error budgets of upcoming GNSS-R altimetry missions.