Revisiting the vegetation hot spot modeling: Case of Poisson/Binomial leaf distributions

Abstract

The accuracy of spaceborne/airborne sensor measurements in the solar domain keeps increasing over time. High resolution, multi-directional and hyperspectral image acquisitions start to be abundant. With regard to the multi-angular remote sensing data, the hot spot, i.e. the exact backscattering direction of direct sunlight together with its neighboring directions, is of special interest. Accurate hot spot models have to be used to adequately simulate the hot spot signature and to allow reliable inversion of multi-angular data. In this paper, we propose a physical hot spot model (Leaf Spatial Distribution based Model, LSDM) assuming that for a given point inside the vegetation to be sunlit (respectively, observed) it should be located within a cylinder free from leaf centers. The cylinder is oriented to the sun (respectively, sensor) direction. Assuming a leaf random, regular or clumped spatial distributions, the gap probabilities in the sun and sensor directions are expressed as a function of these cylinder volumes. Based on the same hypothesis, the bidirectional gap probability is estimated as a function of the total volume of the two cylinders. The evaluation of the needed common volume of two cylinders having different radii is reduced to calculation of some elliptic integrals. Finally, the hot spot signature is estimated based on the bidirectional gap probability distribution. Different model versions with different leaf spatial distribution functions are compared. Particularly, it is shown that compared to the random distribution, the regular (the clumped, respectively) distribution increases (decreases, respectively) the reflectance due to single scattering contribution from foliage. The proposed model is validated using the ROMC web-based tool and its better performance compared to the Semi-Discrete Model and Kuusk's model is confirmed.