## 2.7.5. Lateral Sub-surface Runoff[¶](#lateral-sub-surface-runoff "Permalink to this headline")
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Lateral sub-surface runoff occurs when saturated soil moisture conditions exist within the soil column. Sub-surface runoff is

(2.7.108)[¶](#equation-7-168 "Permalink to this equation")\\\[q\_{drai} = \\Theta\_{ice} K\_{baseflow} tan \\left( \\beta \\right) \\Delta z\_{sat}^{N\_{baseflow}} \\ ,\\\]

where \\(K\_{baseflow}\\) is a calibration parameter, \\(\\beta\\) is the topographic slope, the exponent \\(N\_{baseflow}\\) = 1, and \\(\\Delta z\_{sat}\\) is the thickness of the saturated portion of the soil column.

The saturated thickness is

(2.7.109)[¶](#equation-7-1681 "Permalink to this equation")\\\[\\Delta z\_{sat} = z\_{bedrock} - z\_{\\nabla},\\\]

where the water table \\(z\_{\\nabla}\\) is determined by finding the first soil layer above the bedrock depth (section [2.2.2.2](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Ecosystem/CLM50_Tech_Note_Ecosystem.html#depth-to-bedrock)) in which the volumetric water content drops below a specified threshold. The default threshold is set to 0.9.

The specific yield, \\(S\_{y}\\), which depends on the soil properties and the water table location, is derived by taking the difference between two equilibrium soil moisture profiles whose water tables differ by an infinitesimal amount

(2.7.110)[¶](#equation-7-174 "Permalink to this equation")\\\[S\_{y} =\\theta\_{sat} \\left(1-\\left(1+\\frac{z\_{\\nabla } }{\\Psi \_{sat} } \\right)^{\\frac{-1}{B} } \\right)\\\]

where B is the Clapp-Hornberger exponent. Because \\(S\_{y}\\) is a function of the soil properties, it results in water table dynamics that are consistent with the soil water fluxes described in section [2.7.3](#soil-water).

After the above calculations, two numerical adjustments are implemented to keep the liquid water content of each soil layer (\\(w\_{liq,\\, i}\\) ) within physical constraints of \\(w\_{liq}^{\\min } \\le w\_{liq,\\, i} \\le \\left(\\theta\_{sat,\\, i} -\\theta\_{ice,\\, i} \\right)\\Delta z\_{i}\\) where \\(w\_{liq}^{\\min } =0.01\\) (mm). First, beginning with the bottom soil layer \\(i=N\_{levsoi}\\), any excess liquid water in each soil layer (\\(w\_{liq,\\, i}^{excess} =w\_{liq,\\, i} -\\left(\\theta\_{sat,\\, i} -\\theta\_{ice,\\, i} \\right)\\Delta z\_{i} \\ge 0\\)) is successively added to the layer above. Any excess liquid water that remains after saturating the entire soil column is added to drainage \\(q\_{drai}\\). Second, to prevent negative \\(w\_{liq,\\, i}\\), each layer is successively brought up to \\(w\_{liq,\\, i} =w\_{liq}^{\\min }\\) by taking the required amount of water from the layer below. If this results in \\(w\_{liq,\\, N\_{levsoi} } <w\_{liq}^{\\min }\\), then the layers above are searched in succession for the required amount of water (\\(w\_{liq}^{\\min } -w\_{liq,\\, N\_{levsoi} }\\) ) and removed from those layers subject to the constraint \\(w\_{liq,\\, i} \\ge w\_{liq}^{\\min }\\). If sufficient water is not found, then the water is removed from \\(W\_{t}\\) and \\(q\_{drai}\\).

The soil surface layer liquid water and ice contents are then updated for dew \\(q\_{sdew}\\), frost \\(q\_{frost}\\), or sublimation \\(q\_{subl}\\) (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)) as

(2.7.111)[¶](#equation-7-175 "Permalink to this equation")\\\[w\_{liq,\\, 1}^{n+1} =w\_{liq,\\, 1}^{n} +q\_{sdew} \\Delta t\\\]

(2.7.112)[¶](#equation-7-176 "Permalink to this equation")\\\[w\_{ice,\\, 1}^{n+1} =w\_{ice,\\, 1}^{n} +q\_{frost} \\Delta t\\\]

(2.7.113)[¶](#equation-7-177 "Permalink to this equation")\\\[w\_{ice,\\, 1}^{n+1} =w\_{ice,\\, 1}^{n} -q\_{subl} \\Delta t.\\\]

Sublimation of ice is limited to the amount of ice available.

