### 2.12.5.8. Phase Change[¶](#phase-change "Permalink to this headline")

Phase change in the lake, snow, and soil is done similarly to that done for the soil and snow for vegetated land units (Chapter [2.6](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Soil_Snow_Temperatures/CLM50_Tech_Note_Soil_Snow_Temperatures.html#rst-soil-and-snow-temperatures)), except without the allowance for freezing point depression in soil underlying lakes. After the heat diffusion is calculated, phase change occurs in a given layer if the temperature is below freezing and liquid water remains, or if the temperature is above freezing and ice remains.

If melting occurs, the available energy for melting, \\(Q\_{avail}\\) (J m\-2), is computed as

(2.12.52)[¶](#equation-12-47 "Permalink to this equation")\\\[Q\_{avail} =\\left(T\_{i} -T\_{f} \\right)c\_{v,i}\\\]

where \\(T\_{i}\\) is the temperature of the layer after thermal diffusion (section [2.12.5.7](#crank-nicholson-solution-lake)), and \\(c\_{v,i}\\) is as calculated in section [2.12.5.6](#heat-capacities-lake). The mass of melt in the layer _M_ (kg m\-2) is given by

(2.12.53)[¶](#equation-12-48 "Permalink to this equation")\\\[M=\\min \\left\\{M\_{ice} ,\\frac{Q\_{avail} }{H\_{fus} } \\right\\}\\\]

where \\(H\_{fus}\\) (J kg\-1) is the latent heat of fusion of water ([Table 2.2.7](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Ecosystem/CLM50_Tech_Note_Ecosystem.html#table-physical-constants)), and \\(M\_{ice}\\) is the mass of ice in the layer: \\(I\_{i} \\rho \_{liq} \\Delta z\_{i}\\) for a lake body layer, or simply the soil / snow ice content state variable (\\(w\_{ice}\\) ) for a soil / snow layer. The heat remainder, \\(Q\_{rem}\\) is given by

(2.12.54)[¶](#equation-12-49 "Permalink to this equation")\\\[Q\_{rem} =Q\_{avail} -MH\_{fus} .\\\]

Finally, the mass of ice in the layer \\(M\_{ice}\\) is adjusted downwards by \\(M\\), and the temperature \\(T\_{i}\\) of the layer is adjusted to

(2.12.55)[¶](#equation-12-50 "Permalink to this equation")\\\[T\_{i} =T\_{f} +\\frac{Q\_{rem} }{c'\_{v,i} }\\\]

where \\(c'\_{v,i} =c\_{v,i} +M\\left(c\_{liq} -c\_{ice} \\right)\\).

If freezing occurs, \\(Q\_{avail}\\) is again given by but will be negative. The melt \\(M\\), also negative, is given by

(2.12.56)[¶](#equation-12-51 "Permalink to this equation")\\\[M=\\max \\left\\{-M\_{liq} ,\\frac{Q\_{avail} }{H\_{fus} } \\right\\}\\\]

where \\(M\_{liq}\\) is the mass of water in the layer: \\(\\left(1-I\_{i} \\right)\\rho \_{liq} \\Delta z\_{i}\\) for a lake body layer, or the soil / snow water content state variable (\\(w\_{liq}\\) ). The heat remainder \\(Q\_{rem}\\) is given by eq. and will be negative or zero. Finally, \\(M\_{liq}\\) is adjusted downwards by \\(-M\\) and the temperature is reset according to eq..

In the presence of nonzero snow water \\(W\_{sno}\\) without resolved snow layers over an unfrozen top lake layer, the available energy in the top lake layer \\(\\left(T\_{1} -T\_{f} \\right)c\_{v,1}\\) is used to melt the snow. Similar to above, \\(W\_{sno}\\) is either completely melted and the remainder of heat returned to the top lake layer, or the available heat is exhausted and the top lake layer is set to freezing. The snow thickness is adjusted downwards in proportion to the amount of melt, maintaining constant density.

