Studies on accuracy of numerical simulations of emission from rough ocean-like surfaces

Numerical simulation of passive microwave remote sensing of ocean surfaces has a strict requirement of accuracy. This is because the key output of the simulations is the difference of brightness temperature between a rough surface and a flat surface. Since the difference can be as small as 0.5 K, it is important to simulate the scattering and emission accurately. In this paper, we perform accurate simulations of transverse electric (TE) and transverse magnetic (TM) waves for ocean surfaces with relative permittivity = 28 9541 + 36 8430 at 19 GHz. Because ocean permittivity is large, we used up to 80 points per free space wavelength. Furthermore, accurate numerical integration is also performed to obtain accurate impedance matrix elements. To ensure accuracy, a matrix equation obtained from the surface integral equation formulation is solved by matrix inversion. Conservation of energy is required to be accurate to a relative error of 0.001, which corresponds to 0.3 K in brightness temperature. Numerical results are illustrated for rough surfaces with Gaussian spectrum and bandlimited ocean spectrum and bandlimited fractal surfaces. We show convergence with respect to the density of sampling points and with respect to raising the upper limit of the bandlimited ocean spectrum. Comparisons are also made with results with an impedance boundary condition approximation. Numerical results indicate that fine discretization is required for ocean-like surfaces with fine scale roughness.