Inclusion of hydrodynamic modulations to the improved electromagnetic bias theory

The modulation of short ocean waves by longer ones is a likely contributor to the radar altimeter´s electromagnetic ranging bias (EM-bias). An analytic model to account for this component of the EM bias is developed under a two-scale hydrodynamic assumption. Following the principle of wave action balance, a standard hydrodynamic modulation transfer function is used to establish that the longer modulating waves enter the EM-bias formulation not only through their elevation and slope variables but also through their quadratures. These latter contributions explain the implication of long wave slope and orbital velocity fields in the EM-bias problem. To first order in complexity, analytical expressions are derived using linear Gaussian statistics for both modulating and modulated waves. For sake of completeness, an outline of the possible extension to nonlinear interacting waves is provided