A system of conservative regridding for ice-atmosphere coupling in a General Circulation Model (GCM)

The method of elevation classes, in which the ice surface model is run at multiple elevations within each grid cell, has proven to be a useful way for a low-resolution atmosphere inside a general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields for use in one-way studies coupling atmospheres and ice flow models. Past uses of elevation classes have failed to conserve mass and energy because the transformation used to regrid to the atmosphere was inconsistent with the transformation used to downscale to the ice model. This would cause problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded and five transformations between those grids required by a typical coupled atmosphere-ice flow model. This paper develops a theoretical framework for the problem and shows how each of these transformations may be achieved in a consistent, conservative manner. These transformations are implemented in Glint2, a library used to couple atmosphere models with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.