The electromagnetic (EM) bias is an important error term in sea surface height estimation from satellite radar altimetry. Although numerous theoretical studies of the EM bias have been performed in the past, most are based on low-order hydrodynamic and electromagnetic models that impact the results obtained. This dissertation attempts to improve understanding of the underlying physical mechanism of the EM bias through both numerical and analytical approaches, so that EM bias correction algorithms for satellite missions can be improved. The first part of the dissertation employs a Monte Carlo procedure with numerical nonlinear hydrodynamic simulations coupled with numerical physical optics methods for electromagnetic scattering from the sea surface to produce a deterministic set of sea surface profiles and the corresponding altimeter pulse returns. This numerical approach allows studies of the impact of various physical effects on the EM bias including long wave and short wave effects. Results have shown that short sea waves can play an important role for the EM bias; these effects are not fully captured by previous low-order EM bias theories.
The second part of the dissertation involves the development of an improved analytical model of the EM bias in order to capture and explain effects obtained previously in the numerical Monte Carlo study. The analytical model utilizes the same formulation as used in the computation of pulse returns in the previous Monte Carlo simulation and has a final form that involves an integral containing the correlation and reduced bicorrelation functions of the sea surface. The surface reduced bicorrelation functions due to the effects of nonlinear long waves and modulated short waves are derived from the weakly nonlinear theory of Longuet-Higgins and the hydrodynamic modulation transfer function respectively. It can be shown that, in the geometrical-optics limit, the developed analytical model yields previous models of altimeter pulse return and EM bias when appropriate. Comparisons of the results obtained analytically to the empirical EM bias model for Jason-2 satellite mission show reasonable agreement. Effects of sea swell and shallow water depth are also considered.