### 2.8.6.4. Compaction by drifting snow[¶](#compaction-by-drifting-snow "Permalink to this headline")

Crystal breaking by drifting snow leads to higher snow densities at the surface. This process is particularly important on ice sheets, where destructive metamorphism is slow due to low temperatures but high wind speeds (katabatic winds) are prevailing. Therefore a drifting snow compaction parametrization was introduced, based on ([Vionnet et al. (2012)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#vionnetetal2012)).

(2.8.41)[¶](#equation-8-50 "Permalink to this equation")\\\[C\_{R5,\\, i} = \\left\[\\frac{1}{\\Delta z\_{i} } \\frac{\\partial \\Delta z\_{i} }{\\partial t} \\right\]\_{drift} = - \\frac{\\rho\_{\\max} - \\rho\_i}{\\tau\_{i}}.\\\]

Here, \\(\\rho\_{\\max} = 350\\) kg m\-3 is the upper limit to which this process is active, and \\(\\tau\_{i}\\) is a timescale which is depth dependent:

(2.8.42)[¶](#equation-8-50b "Permalink to this equation")\\\[\\tau\_i = \\frac{\\tau}{\\Gamma\_{\\mathrm{drift}}^i} \\quad \\mathrm{,} \\:\\; \\Gamma^i\_\\mathrm{drift} = \\max\\left\[ 0, S\_\\mathrm{I}^i \\exp(-z\_i / 0.1) \\right\].\\\]

Here, \\(\\tau\\) is a characteristic time scale for drifting snow compaction and is empirically set to 48 h, and \\(z\_i\\) is a pseudo-depth which takes into account previous hardening of snow layers above the current layer: \\(z\_i = \\sum\_j \\Delta z\_j \\cdot (3.25 - S\_\\mathrm{I}^j)\\). The driftability index \\(S\_\\mathrm{I}\\) reflects how well snow can be drifted and depends on the mobility of the snow as well as the 10 m wind speed:

(2.8.43)[¶](#equation-8-50c "Permalink to this equation")\\\[\\begin{split}\\begin{array}{rcl} S\_\\mathrm{I} & = & -2.868 \\exp(-0.085 U) + 1 + M\_{\\mathrm{O}} \\\\ M\_\\mathrm{O} & = & -0.069 + 0.66 F(\\rho) \\end{array}\\end{split}\\\]

The latter equation (for the mobility index \\(M\_\\mathrm{O}\\)) is a simplification from the original paper by removing the dependency on grain size and assuming spherical grains (see [van Kampenhout et al. (2017)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#vankampenhoutetal2017)).

