Monte Carlo approach for solving the radiative transfer equation over mountainous and heterogeneous areas

Abstract

An algorithm based on the Monte Carlo method is developed to solve the radiative transfer equation in the reflective domain (0.4-4 microm) of the solar spectrum over rugged terrain. This algorithm takes into account relief, spatial heterogeneity, and ground bidirectional reflectance. The method permits the computation of irradiance components at ground level and radiance terms reaching an airborne or satelliteborne sensor. The Monte Carlo method consists of statistically simulating the paths of photons inside the Earth-atmosphere system to reproduce physical phenomena while introducing neither analytical modeling nor assumption. The potentialities of the code are then depicted over different types of landscape, including a seashore, a desert region, and a steep mountainous valley.

AMARTIS v2: 3D Radiative Transfer Code in the [0.4; 2.5 µm] Spectral Domain Dedicated to Urban Areas

“…Thus, it becomes necessary to use a new formalism adapted to those areas. The signal at ground and at sensor levels is the result of several radiative components as described in Figure 3 ( [24,25]). …”

“…The Earth-atmosphere coupling irradiance cannot be expressed by an analytical formulation because of the complex geometry of the scene. This is the reason why this component is computed by means of Monte Carlo methods [25]. The downward reflected irradiance might be calculated by an analytical method.…”

“…This Monte Carlo principle consists of modeling the radiometric flux by analyzing the propagation of a high number of photons (usually ~10 9 to 10 10 per simulation) in the Earth-atmosphere system. The phenomena of scattering and absorption by the atmosphere and of reflection and absorption by the ground are modeled by statistical laws [25]. As the Earth-atmosphere coupling irradiance and the downward reflected irradiance result from interactions with the ground, the neighborhood of the scene has an impact on the signal.…”

“…As for the Earth-atmosphere coupling irradiance, this term cannot be modeled by an analytic expression and is also solved with Monte Carlo calculations [25].…”

“…DART [23] can achieve such simulations but its main drawback is that it does not give access to all radiative terms at surface and sensor levels, which are essential to conduct radiative phenomenological studies. AMARTIS v1 (Advanced Modelling of the Atmospheric Radiative Transfer for Inhomogeneous Surfaces [24][25][26]) has been developed to this end. It can simulate every radiative contributor on these two levels.…”