Improved electromagnetic bias theory: Inclusion of hydrodynamic modulations

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Abstract
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 here under a two‐scale two‐dimensional 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 help to explain the role of long‐wave slope and orbital velocity fields within the EM bias problem. Simplified analytical expressions are derived using linear Gaussian statistics for both modulating and modulated waves. For the sake of completeness an outline of the possible extension to nonlinear interacting waves is provided.