by Norbert Schörghofer
This program collection contains:
- Semi-implicit one-dimensional thermal model for planetary surfaces (Crank-Nicolson solver with Stefan-Boltzmann Law boundary condition; flux-conservative spatial discretization)
- 3D model of direct insolation, terrain shadowing, and terrain irradiance for airless bodies, Mars, and Mauna Kea
- Monte-Carlo model for ballistic hops in the exospheres of the Moon and Ceres
- Miscellaneous
- incoming solar irradiance on Mauna Kea
- asynchronously coupled method for retreat of near-surface ice on asteroids
- lunar ice pump (boundary value formulation)
- vapor diffusion at lunar conditions (microphysical model)
The theory behind the numerical methods is described in UserGuide.pdf or in the individual journal articles cited below.
Standard thermal model for asteroidal surfaces. The one-dimensional heat equation is solved, based on solar energy input and thermal radiation from the surface to space. The solver for the one-dimensional heat equation is semi-implicit, with the Stefan-Boltzmann radiation law as upper boundary condition. The finite-difference method is flux-conservative even on an irregularly spaced vertical grid and the thermal properties of the soil can vary spatially and with time. (This is a simplified version of the Mars Thermal Model. They both use the same flux-conservative spatial discretization and the same Crank-Nicolson solver with nonlinear boundary condition.)
Directory: Asteroids/
The core subroutines for the thermal model are located in Common/ and available in Fortran, C, Matlab, and Python.
Common/Test/testcrankQ.f90 provides an example for how to call the semi-implicit solver for the heat equation.
Documentation: User Guide Part 1
Documentation: Schörghofer & Khatiwala (2024)
This set of models for asteroidal surfaces combines diurnally-resolved temperatures, the long-term loss of near-surface ice to space, and probabilistic impact stirring (only one-dimensional). It can be used to estimate long-term ice loss from near the surface due to sublimation as the orbit is changing, the Sun brightens, or ice is mixed due to impacts. A significant complexity in this model arises from partially ice-filled pore spaces (necessary to incorporate the consequences of impact stirring), because the re-distribution of ice within the pores due to vapor diffusion and deposition adds another partial differential equation. A simpler two-layer version, where pore spaces are either empty or full, is also implemented.
Directory: Asteroids/
Documentation: Schorghofer (2016)
Two types of models for water vapor migration in the shallow lunar subsurface are implemented. One is a particle-based microphysical model that follows water molecules that undergo a random walk. The other uses the time-averaged boundary value formulation for the same process. Both models are one-dimensional, and primarily intended for the low temperature regime, when molecular adsorption times are long.
Directory: Lunar/
Documentation for boundary-value model: Schorghofer & Aharonson (2014)
No documentation has yet been written for the random walk model.
Clear-sky direct and indirect short-wave irradiance on Mauna Kea summit, based on optical path length but an otherwise 0-dimensional atmospheric model. The incoming irradiance can be calculated for a flat unobstructed surface, but also for a tilted suface with horizons, i.e., 3D sky irradiance.
Directory: EarthAnalogs/
Documentation: User Guide Sections 3.1 and 2.5
This model of the three-dimensional surface energy balance calculates horizons from a digital elevation model for terrain shadowing calculations and, optionally, also view factors for use in terrain irradiance calculations. The surface energy balance model can then be coupled to the model of subsurface heat conduction introduced above. This then provides a complete thermal model for rugged terrain on Mars or airless bodies. The model is still at prototype stage, but has been used in several research studies.
Directory: Topo3D/
Documentation: User Guide Part 2
Ballistic trajectories of neutral molecules or atoms are modeled for large airless bodies (the Moon and Ceres). Individual molecules are launched with probabilistically distributed velocities. The model then computes the molecule's impact location and time analytically, using a closed-form solution for the intersection of an ellipse with a sphere, i.e., without numerical integration of the particle trajectory. An event-driven algorithm processes landing and launching events in time-order. Molecules may be lost or destroyed by photo-dissociation before they land. Surface temperatures are based on the thermal model for airless bodies.
Directory: Exospheres/
Documentation: User Guide Part 4
MSIM has moved to its own repository at https://github.com/nschorgh/MSIM and is no longer part of the Planetary-Code-Collection. In brief, MSIM contains a (semi-implicit) Mars thermal model, a vapor diffusion model for Mars, models for the equilibrium ice table, and implementations of a fast (asynchronously-coupled) method for subsurface ice dynamics on Mars. The three-dimensional surface energy balance model for Mars is still part of the Planetary-Code-Collection.
Third party source code from Numerical Recipes is covered by a separate copyright. These are files ending with .for. A few code snippets from other sources are also used, as documented in the source code.
The non-portable Fortran declarations real(8) and real*8 are meant to correspond to an 8-byte floating point number.
Sep 2023: Thanks to Alexander Smolka for catching and fixing an error in function hop1
May 2023: Thanks to Cyril Mergny for a major speed improvement of conductionQ.py
2019: Thanks to Sam Potter for comments that helped me speed up the view factor calculations
2016: Thanks to Lior Rubanenko for a bug report in cratersQ_*
2006: Troy Hudson discovered a grid-point offset in conductionT and conductionQ, which has been corrected.
Many Thanks to Andy Vaught for developing an open-source Fortran 95 compiler (G95). The early versions of this code were developed with this compiler.
2001: Samar Khatiwala invented an elegant implementation of the upper radiation boundary condition for the Crank-Nicolson method.
SUPPORT: This code development was supported mainly by NASA, and in smaller parts by Caltech and the University of Hawaii. Undoubtedly, some parts were written in my spare time.