### 2.8.6.2. Overburden pressure compaction[¶](#overburden-pressure-compaction "Permalink to this headline")

The compaction rate as a result of overburden \\(C\_{R2,\\; i}\\) (s\-1) is a linear function of the snow load pressure \\(P\_{s,\\, i}\\) (kg m\-2) ([Anderson (1976)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#anderson1976)):

(2.8.35)[¶](#equation-8-45 "Permalink to this equation")\\\[C\_{R2,\\, i} =\\left\[\\frac{1}{\\Delta z\_{i} } \\frac{\\partial \\Delta z\_{i} }{\\partial t} \\right\]\_{overburden} =-\\frac{P\_{s,\\, i} }{\\eta }\\\]

The snow load pressure \\(P\_{s,\\, i}\\) is calculated for each layer as the sum of the ice \\(w\_{ice,\\, i}\\) and liquid water contents \\(w\_{liq,\\, i}\\) of the layers above plus half the ice and liquid water contents of the layer being compacted

(2.8.36)[¶](#equation-8-47 "Permalink to this equation")\\\[P\_{s,\\, i} =\\frac{w\_{ice,\\, i} +w\_{liq,\\, i} }{2} +\\sum \_{j=snl+1}^{j=i-1}\\left(w\_{ice,\\, j} +w\_{liq,\\, j} \\right) .\\\]

Variable \\(\\eta\\) in [(2.8.35)](#equation-8-45) is a viscosity coefficient (kg s m\-2) that varies with density and temperature as

(2.8.37)[¶](#equation-8-46 "Permalink to this equation")\\\[\\eta = f\_{1} f\_{2} \\eta\_{0} \\frac{\\rho\_{i}}{c\_{\\eta}} \\exp \\left\[ a\_{\\eta} \\left(T\_{f} -T\_{i} \\right) + b\_{\\eta} \\rho\_{i} \\right\]\\\]

with constant factors \\(\\eta \_{0} = 7.62237 \\times 10^{6}\\) kg s\-1 m\-2, \\(a\_{\\eta} = 0.1\\) K\-1, \\(b\_{\\eta} = 0.023\\) m\-3 kg\-1, and \\(c\_{\\eta} = 450\\) kg m\-3 ([van Kampenhout et al. (2017)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#vankampenhoutetal2017)). Further, factor \\(f\_1\\) accounts for the presence of liquid water ([Vionnet et al. (2012)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#vionnetetal2012)):

(2.8.38)[¶](#equation-8-46b "Permalink to this equation")\\\[f\_{1} = \\frac{1}{1+ 60 \\frac{w\_{\\mathrm{liq},\\, i}}{\\rho\_{\\mathrm{liq}} \\Delta z\_{i} }}.\\\]

Factor \\(f\_2\\) originally accounts for the presence of angular grains, but since grain shape is not modelled \\(f\_2\\) is fixed to the value 4.

