Subgrid Slopes in the Mars PCM

Purpose

In order to study surface processes in the Mars Planetary Climate Model (e.g., gully formation, glacier evolution, ...), a representation of the sub-grid slopes has been introduced in the Mars PCM. This parametrization is detailed in Lange et al., 2023, "Modelling Slope Microclimates in the Mars Planetary Climate Model" https://arxiv.org/pdf/2306.12449.pdf.

For each GCM mesh, we decompose the cell as a distribution of sloped terrains (defined by characteristic slopes) and a flat terrain. On each sub-grid terrain, we let the microclimates evolve so that the slope-specific features (e.g., condensation of volatiles, formation of glaciers, migration of subsurface ice, etc.) can be simulated. The portion of the atmosphere above the ground within the cell sees an average of these surface microclimates, and all sub-grid terrains see the same ”shared atmosphere”.

Practical Implementation

The practical implementation is detailed in section 3. of Lange et al., 2023. In short:

• The mesh can be divided in 1, 5, or 7 sub-grid slopes that are North - South facing. Then, using MOLA data (resolution: 64 pixel per degree), the distribution of sub-slope within the mesh is computed.

• All the surface quantities have now a dimension nslope: qsurf, watercap, tsurf, tsoil, albedo, emis, inertiesoil

• The radiative transfer is computed with grid-box albedo, emissivity, temperature. Then, the values are adapted for-each sub-grid slopes following Spiga & Forget 2008 (section 2. of physiq_mod, param_slope).

• The turbulent exchanges (vdifc_mod) are solved with the predominant sub-grid surface (i.e., the sub-grid surface which has the largest cover within the grid box).

• Water and CO2 ice condensation are computed for each sub-grid slopes (vdifc_mod, co2_condens)

• Grid box averaged values are then computed using the specific computation detailed in the dedicated section.

How to run with sub-grid slopes ?

By default, the model runs with only 1 sub-slope (i.e., a flat surface). If one wants to use this sub-grid parameterization, then one must use newstart and choose the option to add sub-slopes. FYI: The CPU time is increased by ~20% with 7 sub-slopes (64x48x26 grid).

Post Processing

In order to go from the sub-grid surface quantity to the grid-box value, the following computations are done:

• For albedo and emissivity:

\begin{align} X = \sum_{i=1}^7 X_i \delta_i \label{eq:opticalproperties} \end{align} where $$X$$ refers to the grid parameter, $X_i$ the sub-grid parameter of slope $$i$$, $$\delta_i$$ the cover fraction (subslope_dist in the code).

• For surface tracers, to ensure mass conservation:

\begin{align} X = \sum_{i=1}^7 X_i \frac{\delta_i}{\cos(\mu_i)} \label{eq:traceurs} \end{align} where $$\mu_i$$ is the slope angle of the sub-grid slope (def_slope_mean in the code)

• For surface temperature, we average the surface flux:

\begin{align} \epsilon T_{\rm{surf,grid}} = \sum_{i=1}^7 \epsilon_i T_{\rm{surf,i}}^4 \delta_i \label{eq:Tsurf} \end{align} where $$\epsilon$$ (1) is the grid emissivity, $$T_{\rm{surf,grid}}$$ (K) the grid surface temperature