| Abstract: |
Formation of whitecaps (WCs) due to waves breaking on a wind roughened sea surface facilitates the exchange of mass, momentum and heat between the atmosphere and ocean. It thus influences processes governing weather and climate such as gas exchange, tropical convection, storm development, and ocean currents. At moderate wind speeds, breaking waves produce air bubble plumes near and below the surface, resulting in transient (active breaking) and persistent foam patches. In high winds, water droplets injected above the surface form spray layers that may obscure the surface. Previous laboratory, field and remote sensing studies have empirically quantified WC parameters such as coverage and scale, foam layer thickness, and bubble plume profiles, but only a few have simulated foam layer or WC microwave reflectivity and emissivity using analytical and numerical electro-magnetic E-M models.
We report the development and application of a Finite-Difference Time-Domain (FDTD) E-M model to investigate the emissivity, reflectivity and detectability of WCs. The model solves Maxwell’s equations directly for an arbitrary free space and dielectric configuration. This rigorous solution allows single- and multiple surface scattering, volume scattering and edge diffraction effects of WCs to be modeled, consistent with the Yee cell second order explicit numerical approximations, and limited only by grid resolution and available computing power. The model, written in optimized MATLAB (The Mathworks Inc.) code, runs on an 8-cpu PC workstation with 24 Gbytes of RAM and a GPU. It features an accurate E-M plane wave source with highly-absorbing boundary conditions, and an auxiliary near-to-far-field transformation for computing bistatic radar cross sections (BRCS) and emissivity.
The FDTD model is applied to multiple dielectric layers representing foam and spray overlying a rough sea surface. The foam layer profiles are adapted from Anguelova’s L-band radiative transfer model (RTM), and the rough surface is a statistical realization of the Kudryavtsev wave spectrum model (alternative spectral models are available). The FDTD model generalizes the 1-D RTM layer structure to a 2-D space, which allows foam layers of finite horizontal extent to be investigated. The WCs, represented by foam patches having specified void fraction profiles and associated dielectric layer characteristics, are randomly superimposed on the rough sea surface. The mean sea surface slope, and WC coverage and scale, are prescribed empirically for given wind speeds. Runs are performed at L-band for calm, moderate and high winds (up to 15 m/s), and the resulting emissivities are validated by running the analytical SSA/SPM E-M model with the Kudryavtsev wave spectrum. The precision of model emissivity estimates, the roughness emissivity increment, and detectability of WCs using L-band radiometry, are assessed under these conditions. Possible enhancements using stochastic Monte-Carlo 2-D simulation and more deterministic 2- and 3-D simulations of E-M interactions with active breakers and WCs of various void fractions, shapes and scales, are also considered. |
