Integration of the thermodynamic equation over an entire drainage basin\ud yields a fairly simple expression for the steady-state heat balance.\ud This stems from the fact that dissipative heating can be calculated\ud directly from the release of gravitational energy. When mass balance,\ud surface temperature and geothermal input are known, the mean ice\ud temperature at the grounding line can be obtained as a residual.\ud The procedure is applied to the drainage basin feeding the Ross Ice\ud Shelf. The resulting mean outlet temperature is -16.2 oC. The heating\ud rates making the balance turn out to be (in 0.0001 K/yr): dissipation\ud 8.2, advective flux divergence -13.5 and geothermal heating 5.3. The\ud method also reveals how the mean outlet temperature depends on mass\ud balance, surface elevation, etc
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