Surface Roughness Retrieval By Inversion Of Hapke Model: A Multi-scale Approach

Abstract:

Surface roughness is a key property of soils that affects the various processes involved in their evolution such as solar absorption, erosion or moisture, both on Earth and other Solar System surfaces. In the 80's, B.Hapke provided an approximate analytic solution for the bidirectional reflectance distribution function (BRDF) of a particulate medium and, later on, included the effect of surface roughness as a correction factor for the BRDF of a smooth surface. The effect of roughness on the BRDF is modeled as a shadowing function of the so-called roughness parameter, which is the mean slope angle of the facets composing the surface integrated over all scales from the sub-millimeter to the kilometer scales.

Hapke model is widely used in planetary sciences to retrieve the roughness parameter from observed BRDFs. Yet the physical meaning of the retrieved roughness is not clear as the scale at which it happens is not defined. This work aims at understanding the relative impact of the roughness defined at each scale to the BRDF in order to test the ability of the singly retrieved roughness parameter at describing the ground truth.

We propose to perform a wavelet analysis on meter-sized digital elevation models (DEM) generated from various volcanic and sedimentary terrains at high-mm-scale spatial resolution. It consists in splitting the DEM in several spatial frequencies and in simulating the BRDF at each scale with a ray-tracing code. Also the global BRDF is simulated so that the relative contribution of each scale can be studied. Then the Hapke model is fitted to the global BRDF to retrieve the roughness parameter. We will expose and discuss the results of this study.

Figure: BRDF of a’a lava DEM simulated at varying azimut (φ_i) and incidence angles (i), in the principal plan. The direction of the light source is given by the colored squares. Mean slope angle of the surface is 36°.