### 2.3.2.3. Snow Aging[¶](#snow-aging "Permalink to this headline")

Snow aging is represented as evolution of the ice effective grain size (\\(r\_{e}\\)). Previous studies have shown that use of spheres which conserve the surface area-to-volume ratio (or specific surface area) of ice media composed of more complex shapes produces relatively small errors in simulated hemispheric fluxes (e.g., [Grenfell and Warren 1999](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#grenfellwarren1999)). Effective radius is the surface area-weighted mean radius of an ensemble of spherical particles and is directly related to specific surface area (_SSA_) as \\(r\_{e} ={3\\mathord{\\left/ {\\vphantom {3 \\left(\\rho \_{ice} SSA\\right)}} \\right.} \\left(\\rho \_{ice} SSA\\right)}\\), where \\(\\rho\_{ice}\\) is the density of ice. Hence, \\(r\_{e}\\) is a simple and practical metric for relating the snowpack microphysical state to dry snow radiative characteristics.

Wet snow processes can also drive rapid changes in albedo. The presence of liquid water induces rapid coarsening of the surrounding ice grains (e.g., [Brun 1989](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#brun1989)), and liquid water tends to refreeze into large ice clumps that darken the bulk snowpack. The presence of small liquid drops, by itself, does not significantly darken snowpack, as ice and water have very similar indices of refraction throughout the solar spectrum. Pooled or ponded water, however, can significantly darken snowpack by greatly reducing the number of refraction events per unit mass. This influence is not currently accounted for.

The net change in effective grain size occurring each time step is represented in each snow layer as a summation of changes caused by dry snow metamorphism (\\(dr\_{e,dry}\\)), liquid water-induced metamorphism (\\(dr\_{e,wet}\\)), refreezing of liquid water, and addition of freshly-fallen snow. The mass of each snow layer is partitioned into fractions of snow carrying over from the previous time step (\\(f\_{old}\\)), freshly-fallen snow (\\(f\_{new}\\)), and refrozen liquid water (\\(f\_{rfz}\\)), such that snow \\(r\_{e}\\) is updated each time step _t_ as

(2.3.72)[¶](#equation-3-72 "Permalink to this equation")\\\[r\_{e} \\left(t\\right)=\\left\[r\_{e} \\left(t-1\\right)+dr\_{e,\\, dry} +dr\_{e,\\, wet} \\right\]f\_{old} +r\_{e,\\, 0} f\_{new} +r\_{e,\\, rfz} f\_{rfrz}\\\]

Here, the effective radius of freshly-fallen snow (\\(r\_{e,0}\\)) is based on a simple linear temperature-relationship. Below -30 degrees Celsius, a minimum value is enforced of 54.5 \\(\\mu\\) m (corresponding to a specific surface area of 60 m2 kg\-1). Above 0 degrees Celsius, a maximum value is enforced of 204.5 \\(\\mu\\) m. Between -30 and 0 a linear ramp is used.

The effective radius of refrozen liquid water (\\(r\_{e,rfz}\\)) is set to 1000\\(\\mu\\) m.

Dry snow aging is based on a microphysical model described by [Flanner and Zender (2006)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#flannerzender2006). This model simulates diffusive vapor flux amongst collections of ice crystals with various size and inter-particle spacing. Specific surface area and effective radius are prognosed for any combination of snow temperature, temperature gradient, density, and initial size distribution. The combination of warm snow, large temperature gradient, and low density produces the most rapid snow aging, whereas aging proceeds slowly in cold snow, regardless of temperature gradient and density. Because this model is currently too computationally expensive for inclusion in climate models, we fit parametric curves to model output over a wide range of snow conditions and apply these parameters in CLM. The functional form of the parametric equation is

(2.3.73)[¶](#equation-3-73 "Permalink to this equation")\\\[\\frac{dr\_{e,\\, dry} }{dt} =\\left(\\frac{dr\_{e} }{dt} \\right)\_{0} \\left(\\frac{\\eta }{\\left(r\_{e} -r\_{e,\\, 0} \\right)+\\eta } \\right)^{{1\\mathord{\\left/ {\\vphantom {1 \\kappa }} \\right.} \\kappa } }\\\]

The parameters \\({(\\frac{dr\_{e}}{dt}})\_{0}\\), \\(\\eta\\), and \\(\\kappa\\) are retrieved interactively from a lookup table with dimensions corresponding to snow temperature, temperature gradient, and density. The domain covered by this lookup table includes temperature ranging from 223 to 273 K, temperature gradient ranging from 0 to 300 K m\-1, and density ranging from 50 to 400 kg m\-3. Temperature gradient is calculated at the midpoint of each snow layer _n_, using mid-layer temperatures (\\(T\_{n}\\)) and snow layer thicknesses (\\(dz\_{n}\\)), as

(2.3.74)[¶](#equation-3-74 "Permalink to this equation")\\\[\\left(\\frac{dT}{dz} \\right)\_{n} =\\frac{1}{dz\_{n} } abs\\left\[\\frac{T\_{n-1} dz\_{n} +T\_{n} dz\_{n-1} }{dz\_{n} +dz\_{n-1} } +\\frac{T\_{n+1} dz\_{n} +T\_{n} dz\_{n+1} }{dz\_{n} +dz\_{n+1} } \\right\]\\\]

For the bottom snow layer (\\(n=0\\)), \\(T\_{n+1}\\) is taken as the temperature of the top soil layer, and for the top snow layer it is assumed that \\(T\_{n-1}\\) = \\(T\_{n}\\).

The contribution of liquid water to enhanced metamorphism is based on parametric equations published by [Brun (1989)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#brun1989), who measured grain growth rates under different liquid water contents. This relationship, expressed in terms of \\(r\_{e} (\\mu \\text{m})\\) and subtracting an offset due to dry aging, depends on the mass liquid water fraction \\(f\_{liq}\\) as

(2.3.75)[¶](#equation-3-75 "Permalink to this equation")\\\[\\frac{dr\_{e} }{dt} =\\frac{10^{18} C\_{1} f\_{liq} ^{3} }{4\\pi r\_{e} ^{2} }\\\]

The constant _C_1 is 4.22\\(\\times\\)10\-13, and: \\(f\_{liq} =w\_{liq} /(w\_{liq} +w\_{ice} )\\)(Chapter [2.8](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Snow_Hydrology/CLM50_Tech_Note_Snow_Hydrology.html#rst-snow-hydrology)).

In cases where snow mass is greater than zero, but a snow layer has not yet been defined, \\(r\_{e}\\) is set to \\(r\_{e,0}\\). When snow layers are combined or divided, \\(r\_{e}\\) is calculated as a mass-weighted mean of the two layers, following computations of other state variables (section [2.8.7](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Snow_Hydrology/CLM50_Tech_Note_Snow_Hydrology.html#snow-layer-combination-and-subdivision)). Finally, the allowable range of \\(r\_{e}\\), corresponding to the range over which Mie optical properties have been defined, is 30-1500\\(\\mu\\) m.

