## 2.8.3. Water Content[¶](#water-content "Permalink to this headline")
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The conservation equation for mass of water in snow layers is

(2.8.15)[¶](#equation-8-26 "Permalink to this equation")\\\[\\frac{\\partial w\_{liq,\\, i} }{\\partial t} =\\left(q\_{liq,\\, i-1} -q\_{liq,\\, i} \\right)+\\frac{\\left(\\Delta w\_{liq,\\, i} \\right)\_{p} }{\\Delta t}\\\]

where \\(q\_{liq,\\, i-1}\\) is the flow of liquid water into layer \\(i\\) from the layer above, \\(q\_{liq,\\, i}\\) is the flow of water out of layer \\(i\\) to the layer below, \\({\\left(\\Delta w\_{liq,\\, i} \\right)\_{p} \\mathord{\\left/ {\\vphantom {\\left(\\Delta w\_{liq,\\, i} \\right)\_{p} \\Delta t}} \\right.} \\Delta t}\\) is the change in liquid water due to phase change (melting rate) (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)). For the top snow layer only,

(2.8.16)[¶](#equation-8-27 "Permalink to this equation")\\\[q\_{liq,\\, i-1} =f\_{sno} \\left(q\_{grnd,\\, liq} +\\left(q\_{sdew} -q\_{seva} \\right)\\right)\\\]

where \\(q\_{grnd,\\, liq}\\) is the rate of liquid precipitation reaching the snow (section [2.7.1](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Hydrology/CLM50_Tech_Note_Hydrology.html#canopy-water)), \\(q\_{seva}\\) is the evaporation of liquid water and \\(q\_{sdew}\\) is the liquid dew (section [2.5.4](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Fluxes/CLM50_Tech_Note_Fluxes.html#update-of-ground-sensible-and-latent-heat-fluxes)). After surface fluxes and snow/soil temperatures have been determined (Chapters [2.5](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Fluxes/CLM50_Tech_Note_Fluxes.html#rst-momentum-sensible-heat-and-latent-heat-fluxes) and [2.6](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Soil_Snow_Temperatures/CLM50_Tech_Note_Soil_Snow_Temperatures.html#rst-soil-and-snow-temperatures)), \\(w\_{liq,\\, snl+1}\\) is updated for the liquid precipitation reaching the ground and dew or evaporation as

(2.8.17)[¶](#equation-8-28 "Permalink to this equation")\\\[w\_{liq,\\, snl+1}^{n+1} =w\_{liq,\\, snl+1}^{n} +f\_{sno} \\left(q\_{grnd,\\, liq} +q\_{sdew} -q\_{seva} \\right)\\Delta t.\\\]

When the liquid water within a snow layer exceeds the layer’s holding capacity, the excess water is added to the underlying layer, limited by the effective porosity (\\(1-\\theta \_{ice}\\) ) of the layer. The flow of water is assumed to be zero (\\(q\_{liq,\\, i} =0\\)) if the effective porosity of either of the two layers (\\(1-\\theta \_{ice,\\, i} {\\rm \\; and\\; }1-\\theta \_{ice,\\, i+1}\\) ) is less than \\(\\theta \_{imp} =0.05\\), the water impermeable volumetric water content. Thus, water flow between layers, \\(q\_{liq,\\, i}\\), for layers \\(i=snl+1,\\ldots,0\\), is initially calculated as

(2.8.18)[¶](#equation-8-29 "Permalink to this equation")\\\[q\_{liq,\\, i} =\\frac{\\rho \_{liq} \\left\[\\theta \_{liq,\\, i} -S\_{r} \\left(1-\\theta \_{ice,\\, i} \\right)\\right\]f\_{sno} \\Delta z\_{i} }{\\Delta t} \\ge 0\\\]

where the volumetric liquid water \\(\\theta \_{liq,\\, i}\\) and ice \\(\\theta \_{ice,\\, i}\\) contents are

(2.8.19)[¶](#equation-8-30 "Permalink to this equation")\\\[\\theta \_{ice,\\, i} =\\frac{w\_{ice,\\, i} }{f\_{sno} \\Delta z\_{i} \\rho \_{ice} } \\le 1\\\]

(2.8.20)[¶](#equation-8-31 "Permalink to this equation")\\\[\\theta \_{liq,\\, i} =\\frac{w\_{liq,\\, i} }{f\_{sno} \\Delta z\_{i} \\rho \_{liq} } \\le 1-\\theta \_{ice,\\, i} ,\\\]

and \\(S\_{r} =0.033\\) is the irreducible water saturation (snow holds a certain amount of liquid water due to capillary retention after drainage has ceased ([Anderson (1976)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#anderson1976))). The water holding capacity of the underlying layer limits the flow of water \\(q\_{liq,\\, i}\\) calculated in equation [(2.8.18)](#equation-8-29), unless the underlying layer is the surface soil layer, as

(2.8.21)[¶](#equation-8-32 "Permalink to this equation")\\\[q\_{liq,\\, i} \\le \\frac{\\rho \_{liq} \\left\[1-\\theta \_{ice,\\, i+1} -\\theta \_{liq,\\, i+1} \\right\]\\Delta z\_{i+1} }{\\Delta t} \\qquad i=snl+1,\\ldots ,-1.\\\]

The liquid water content \\(w\_{liq,\\, i}\\) is updated as

(2.8.22)[¶](#equation-8-33 "Permalink to this equation")\\\[w\_{liq,\\, i}^{n+1} =w\_{liq,\\, i}^{n} +\\left(q\_{i-1} -q\_{i} \\right)\\Delta t.\\\]

Equations [(2.8.18)](#equation-8-29) - [(2.8.22)](#equation-8-33) are solved sequentially from top (\\(i=snl+1\\)) to bottom (\\(i=0\\)) snow layer in each time step. The total flow of liquid water reaching the soil surface is then \\(q\_{liq,\\, 0}\\) which is used in the calculation of surface runoff and infiltration (sections [2.7.2.1](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Hydrology/CLM50_Tech_Note_Hydrology.html#surface-runoff) and [2.7.2.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Hydrology/CLM50_Tech_Note_Hydrology.html#infiltration)).

