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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

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