A Monte Carlo Study of Altimeter Pulse Returns and the Electromagnetic Bias

The electromagnetic (EM) bias is an important error term in sea-surface height estimation from satellite radar altimetry. While the EM bias has been studied extensively, previous studies have utilized hydrodynamic and EM models that require an a priori separation of the sea surface into “long” and “short” waves that are then treated separately. This paper presents a study of the EM bias that avoids this decomposition by employing a Monte Carlo procedure with numerical nonlinear hydrodynamic simulations coupled with numerical physical-optics methods for EM scattering from the sea surface. Due to the computational complexity of the approach, only long-crested surfaces (i.e., 2-D scattering problems) are considered. The formulation of the physical-optics model utilized is presented, along with a derivation of the standard Brown model for the long-crested surface case for comparison. The simulated pulse returns generally are in good agreement with the Brown model using the specular surface height probability density function. However, the influence of the EM frequency on the EM bias obtained is much smaller than that reported from satellite observations. Predicted biases are also examined as the range of length scales included in the surface profile is varied, in order to determine any apparent cutoff or length-scale separations that occur. It is found that the bias continues to increase as additional short waves are included in the surface spectrum, although a saturation occurs for surface length scales shorter than the EM wavelength.