Numerical Simulation of Illumination and Thermal Conditions at the Lunar Poles Using LOLA DTMs

We are interested in illumination conditions and the temperature distribution within the upper two meters of regolith near the lunar poles. Here, areas exist receiving almost constant illumination near areas in permanent shadow, which were identified as potential exploration sites for future missions. For our study a numerical simulation of the illumination and thermal environment for lunar near-polar regions is needed. Our study is based on high-resolution, twenty meters per pixel and 400 x 400 km large polar Digital Terrain Models (DTMs), which were derived from Lunar Orbiter Laser Altimeter (LOLA) data. Illumination conditions were simulated by synthetically illuminating the LOLA DTMs using the horizon method considering the Sun as an extended source. We model polar illumination for the central 50 x 50 km subset and use it as an input at each time-step (2 h) to evaluate the heating of the lunar surface and subsequent conduction in the sub-surface. At surface level we balance the incoming insolation with the subsurface conduction and radiation into space, whereas in the sub-surface we consider conduction with an additional constant radiogenic heat source at the bottom of our two-meter layer. Density is modeled as depth-dependent, the specific heat parameter as temperature-dependent and the thermal conductivity as depth- and temperature-dependent. We implemented a fully implicit finite-volume method in space and backward Euler scheme in time to solve the one-dimensional heat equation at each pixel in our 50 x 50 km DTM. Due to the non-linear dependencies of the parameters mentioned above, Newton's method is employed as the non-linear solver together with the Gauss-Seidel method as the iterative linear solver in each Newton iteration. The software is written in OpenCL and runs in parallel on the GPU cores, which allows for fast computation of large areas and long time scales.