### 2.8.6.3. Compaction by melt[¶](#compaction-by-melt "Permalink to this headline")

The compaction rate due to melting \\(C\_{R3,\\; i}\\) (s\-1) is taken to be the ratio of the change in snow ice mass after the melting to the mass before melting

(2.8.39)[¶](#equation-8-48 "Permalink to this equation")\\\[C\_{R3,\\, i} = \\left\[\\frac{1}{\\Delta z\_{i} } \\frac{\\partial \\Delta z\_{i} }{\\partial t} \\right\]\_{melt} = -\\frac{1}{\\Delta t} \\max \\left(0,\\frac{W\_{sno,\\, i}^{n} -W\_{sno,\\, i}^{n+1} }{W\_{sno,\\, i}^{n} } \\right)\\\]

and melting is identified during the phase change calculations (section [2.6.2](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Soil_Snow_Temperatures/CLM50_Tech_Note_Soil_Snow_Temperatures.html#phase-change)). Because snow depth is defined as the average depth of the snow covered area, the snow depth must also be updated for changes in \\(f\_{sno}\\) when \\(W\_{sno}\\) has changed.

> (2.8.40)[¶](#equation-8-49 "Permalink to this equation")\\\[C\_{R4,\\, i} =\\left\[\\frac{1}{\\Delta z\_{i} } \\frac{\\partial \\Delta z\_{i} }{\\partial t} \\right\]\_{fsno} =-\\frac{1}{\\Delta t} \\max \\left(0,\\frac{f\_{sno,\\, i}^{n} -f\_{sno,\\, i}^{n+1} }{f\_{sno,\\, i}^{n} } \\right)\\\]

