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Module thk

This IGM module solves the mass conservation equation for ice to update the thickness based on ice flow (computed by the iceflow module) and surface mass balance (provided by any module that updates smb). The equation is solved using an explicit upwind finite-volume scheme on the 2D working grid. Ice transport is computed from edge-defined fluxes derived from depth-averaged velocities and ice thickness in the upwind direction. To reduce numerical diffusion while preserving monotonicity, a piecewise-linear reconstruction of the ice thickness at cell edges is performed using the Superbee slope limiter (Roe, 1986)1, which satisfies the total variation diminishing property.

The scheme is mass-conservative and parallelizable due to its fully explicit nature. However, it is subject to a CFL condition, meaning the time step (defined in the time module) is constrained by the parameter processes.time.cfl. This parameter represents the maximum number of cells crossed in one iteration and cannot exceed one. For more details, refer to the documentation of the time module. Additional information about the scheme can be found in the following paper: (Jouvet et al., 2021)2.

State variables

Reads: thk, topg, ubar, vbar, smb, dt

Writes: thk, usurf, divflux

Parameters

thk:

  slope_type: superbee                 # slope limiter for the thickness equation (superbee or godunov)
  ratio_density: 0.910                 # rho_ice / rho_water for flotation

Description of the parameters:

Name Description Default value Units
slope_type Type of slope limiter for the ice thickness equation (godunov or superbee). superbee —
ratio_density Density of ice divided by density of water (used by the flotation term). 0.91 —

Contributors: Guillaume Cordonnier, Guillaume Jouvet.

  1. Roe, P. L. (1986). Characteristic-based schemes for the Euler equations. Annual Review of Fluid Mechanics, 18, 337--365. https://doi.org/10.1146/annurev.fl.18.010186.002005 ↩

  2. Jouvet, G., Cordonnier, G., Kim, B., Lüthi, M., Vieli, A., & Aschwanden, A. (2021). Deep learning speeds up ice flow modelling by several orders of magnitude. Journal of Glaciology, 68(270), 651--664. https://doi.org/10.1017/jog.2021.120 ↩