# Modeling conservation of energy¶

In normal use PISM solves the conservation of energy problem within the ice, the thin subglacial layer, and a layer of thermal bedrock. For the ice and the subglacial layer it uses an enthalpy-based scheme [28] which allows the energy to be conserved even when the temperature is at the pressure-melting point.

Ice at the melting point is called “temperate” ice. Part of the thermal energy of temperate ice is in the latent heat of the liquid water stored between the crystals of the temperate ice. Part of the thermal energy of the whole glacier is in the latent heat of the liquid water under the glacier. The enthalpy scheme correctly models these storehouses of thermal energy, and thus it allows polythermal and fully-temperate glaciers to be modeled [65].

The state of the full conservation of energy model includes the 3D enthalpy variable plus the 2D bwat and tillwat subglacial hydrology state variables (subsection Subglacial hydrology), all of which are seen in output files. The important basal melt rate computation involves all of these energy state variables, because the basal melt rate (bmelt in output files) comes from conserving energy across the ice-bedrock layer [28]. Fields temp, liqfrac, and temp_pa seen in output files are all actually diagnostic outputs because all of these can be recovered from the enthalpy and the ice geometry.

Because this part of PISM is just a conservation law, there is little need for the user to worry about controlling it. If desired, however, conservation of energy can be turned off entirely with -energy none. The default enthalpy-based conservation of energy model (i.e. -energy enthalpy) can be replaced by the temperature-based (i.e. “cold ice”) method used in [22] and verified in [23] by setting option -energy cold.

The thermal bedrock layer model is turned off by setting -Mbz 1 (i.e. zero spaces) while it is turned on by choosing a depth and number of points, as in -Lbz 1000 -Mbz 21, for example, which gives a layer depth of 1000 m and grid spaces of 50 m (= 1000/20). The input geothermal flux (bheatflx in output files) is applied at the bottom of the bedrock thermal layer if such a layer is present and otherwise it is applied at the base of the ice.

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