Fine Scale Partial Coherent Model Based on lidar Elevation Measurements for GNSS-R Applications

In GNSS-R (Global Navigation Satellite System Reflectometry) land applications, bistatic scattering occurs in the vicinity of the specular direction, and the scattered waves can include both coherent and incoherent components. A description of land surfaces roughness is required to predict GNSS-R specular scattering. Here we consider roughness on three distinct length scales: a microwave roughness f 1 (x, y) with correlation lengths of ~ 10 centimeters, a coarse scale 30-meter planar topography f 3 (x,y) based on digital elevation model (DEM) data, and a fine scale topography f 2 (X,y) between these two length scales. The fine scale topography represents the length scales in which scattered waves can transition from coherence to partial coherence to incoherence. In this paper, we investigate f 2 (x, y) using recent airborne lidar measurements of land surface heights. Using f = f 1 + f 2 + f 3 , fine scale partial coherent FPCN and FPCP models are applied to predict bistatic scattering coefficients near the specular direction for 30m surface area. Here “fine scale” means the fine scale topography of f 2 (x, y) is included. The model uses complex electric field summation and Monte Carlo simulations within a large area. For non-overlapping large areas, we use intensity summations as in radiative transfer theory. We consider a fine scale partial coherent numerical model (FPCN) that applies numerical integration to the Kirchhoff integral using 2 cm discretization. The fine scale partial coherent patch model (FPCP) uses planar patches o fL size, where L is less than the correlation length of f 2 . Numerical illustrations show that the results of the FPCN and FPCP are in good agreement with each other. Comparisons are also made with geometric optics model (GO) with and without the attenuation factor of microwave roughness.