The enthalpy method for the thermodynamics of polythermal glaciers and ice sheets is tested and verified by aone-dimensional problem (parallel-sided slab). The enthalpy method alone does not include explicitly the transitionconditions at the cold-temperate transition surface (CTS) that separates the upper cold from the lower temperatelayer. However, these conditions are important for correctly determining the position of the CTS. For the numericalsolution of the polythermal slab problem, we consider a two-layer front-tracking scheme as well as three di erentone-layer schemes (conventional one-layer scheme, one-layer melting CTS scheme, one-layer freezing CTS scheme).Computed steady-state temperature and water-content profiles are verified with exact solutions, and transient solutionscomputed by the one-layer schemes are compared with those of the two-layer scheme, considered to be a reliablereference. While the conventional one-layer scheme (that does not include the transition conditions at the CTS) canproduce correct solutions for melting conditions at the CTS, it is more reliable to enforce the transition conditionsexplicitly. For freezing conditions, it is imperative to enforce them because the conventional one-layer scheme cannothandle the associated discontinuities. The suggested numerical schemes are suitable for implementation in three dimensionalglacier and ice-sheet models.
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