## 2.8.1. Snow Covered Area Fraction[¶](#snow-covered-area-fraction "Permalink to this headline")
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The fraction of the ground covered by snow, \\(f\_{sno}\\), is based on the method of [Swenson and Lawrence (2012)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#swensonlawrence2012). Because the processes governing snowfall and snowmelt differ, changes in \\(f\_{sno}\\) are calculated separately for accumulation and depletion. When snowfall occurs, \\(f\_{sno}\\) is updated as

(2.8.1)[¶](#equation-8-14 "Permalink to this equation")\\\[f^{n+1} \_{sno} =1-\\left(\\left(1-\\tanh (k\_{accum} q\_{sno} \\Delta t)\\right)\\left(1-f^{n} \_{sno} \\right)\\right)\\\]

where \\(k\_{accum}\\) is a constant whose default value is 0.1, \\(q\_{sno} \\Delta t\\) is the amount of new snow, \\(f^{n+1} \_{sno}\\) is the updated snow covered fraction (SCF), and \\(f^{n} \_{sno}\\) is the SCF from the previous time step.

When snow melt occurs, \\(f\_{sno}\\) is calculated from the depletion curve

(2.8.2)[¶](#equation-8-15 "Permalink to this equation")\\\[f\_{sno} =1-\\left(\\frac{\\cos ^{-1} \\left(2R\_{sno} -1\\right)}{\\pi } \\right)^{N\_{melt} }\\\]

where \\(R\_{sno}\\) is the ratio of \\(W\_{sno}\\) to the maximum accumulated snow \\(W\_{\\max }\\), and \\(N\_{melt}\\) is a parameter that depends on the topographic variability within the grid cell. Whenever \\(W\_{sno}\\) reaches zero, \\(W\_{\\max }\\) is reset to zero. The depletion curve shape parameter is defined as

(2.8.3)[¶](#equation-8-16 "Permalink to this equation")\\\[N\_{melt} =\\frac{200}{\\min \\left(10,\\sigma \_{topo} \\right)}\\\]

The standard deviation of the elevation within a grid cell, \\(\\sigma \_{topo}\\), is calculated from a high resolution DEM (a 1km DEM is used for CLM). Note that _glacier\_mec_ columns (section [2.13.4](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Glacier/CLM50_Tech_Note_Glacier.html#multiple-elevation-class-scheme)) are treated differently in this respect, as they already account for the subgrid topography in a grid cell in their own way. Therefore, in each _glacier\_mec_ column very flat terrain is assumed, implemented as \\(N\_{melt}=10\\).

