### 2.7.3.1. Hydraulic Properties[¶](#hydraulic-properties "Permalink to this headline")

The hydraulic conductivity \\(k\_{i}\\) (mm s\-1) and the soil matric potential \\(\\psi \_{i}\\) (mm) for layer \\(i\\) vary with volumetric soil water \\(\\theta \_{i}\\) and soil texture. As with the soil thermal properties (section [2.6.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Soil_Snow_Temperatures/CLM50_Tech_Note_Soil_Snow_Temperatures.html#soil-and-snow-thermal-properties)) the hydraulic properties of the soil are assumed to be a weighted combination of the mineral properties, which are determined according to sand and clay contents based on work by [Clapp and Hornberger (1978)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#clapphornberger1978) and [Cosby et al. (1984)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#cosbyetal1984), and organic properties of the soil ([Lawrence and Slater 2008](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#lawrenceslater2008)).

The hydraulic conductivity is defined at the depth of the interface of two adjacent layers \\(z\_{h,\\, i}\\) ([Figure 2.7.2](#figure-water-flux-schematic)) and is a function of the saturated hydraulic conductivity \\(k\_{sat} \\left\[z\_{h,\\, i} \\right\]\\), the liquid volumetric soil moisture of the two layers \\(\\theta \_{i}\\) and \\(\\theta\_{i+1}\\) and an ice impedance factor \\(\\Theta\_{ice}\\)

(2.7.47)[¶](#equation-7-85 "Permalink to this equation")\\\[\\begin{split}k\\left\[z\_{h,\\, i} \\right\] = \\left\\{\\begin{array}{lr} \\Theta\_{ice} k\_{sat} \\left\[z\_{h,\\, i} \\right\]\\left\[\\frac{0.5\\left(\\theta\_{\\, i} +\\theta\_{\\, i+1} \\right)}{0.5\\left(\\theta\_{sat,\\, i} +\\theta\_{sat,\\, i+1} \\right)} \\right\]^{2B\_{i} +3} & \\qquad 1 \\le i \\le N\_{levsoi} - 1 \\\\ \\Theta\_{ice} k\_{sat} \\left\[z\_{h,\\, i} \\right\]\\left(\\frac{\\theta\_{\\, i} }{\\theta\_{sat,\\, i} } \\right)^{2B\_{i} +3} & \\qquad i = N\_{levsoi} \\end{array}\\right\\}.\\end{split}\\\]

The ice impedance factor is a function of ice content, and is meant to quantify the increased tortuosity of the water flow when part of the pore space is filled with ice. [Swenson et al. (2012)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#swensonetal2012) used a power law form

(2.7.48)[¶](#equation-7-86 "Permalink to this equation")\\\[\\Theta\_{ice} = 10^{-\\Omega F\_{ice} }\\\]

where \\(\\Omega = 6\\)and \\(F\_{ice} = \\frac{\\theta\_{ice} }{\\theta\_{sat} }\\) is the ice-filled fraction of the pore space.

Because the hydraulic properties of mineral and organic soil may differ significantly, the bulk hydraulic properties of each soil layer are computed as weighted averages of the properties of the mineral and organic components. The water content at saturation (i.e. porosity) is

(2.7.49)[¶](#equation-7-90 "Permalink to this equation")\\\[\\theta\_{sat,i} =(1-f\_{om,i} )\\theta\_{sat,\\min ,i} +f\_{om,i} \\theta\_{sat,om}\\\]

where \\(f\_{om,i}\\) is the soil organic matter fraction, \\(\\theta\_{sat,om}\\) is the porosity of organic matter, and the porosity of the mineral soil \\(\\theta\_{sat,\\min,i}\\) is

(2.7.50)[¶](#equation-7-91 "Permalink to this equation")\\\[\\theta\_{sat,\\min ,i} = 0.489 - 0.00126(\\% sand)\_{i} .\\\]

The exponent \\(B\_{i}\\) is

(2.7.51)[¶](#equation-7-92 "Permalink to this equation")\\\[B\_{i} =(1-f\_{om,i} )B\_{\\min ,i} +f\_{om,i} B\_{om}\\\]

where \\(B\_{om}\\) is for organic matter and

(2.7.52)[¶](#equation-7-93 "Permalink to this equation")\\\[B\_{\\min ,i} =2.91+0.159(\\% clay)\_{i} .\\\]

The soil matric potential (mm) is defined at the node depth \\(z\_{i}\\) of each layer \\(i\\) ([Figure 2.7.2](#figure-water-flux-schematic))

(2.7.53)[¶](#equation-7-94 "Permalink to this equation")\\\[\\psi \_{i} =\\psi \_{sat,\\, i} \\left(\\frac{\\theta\_{\\, i} }{\\theta\_{sat,\\, i} } \\right)^{-B\_{i} } \\ge -1\\times 10^{8} \\qquad 0.01\\le \\frac{\\theta\_{i} }{\\theta\_{sat,\\, i} } \\le 1\\\]

where the saturated soil matric potential (mm) is

(2.7.54)[¶](#equation-7-95 "Permalink to this equation")\\\[\\psi \_{sat,i} =(1-f\_{om,i} )\\psi \_{sat,\\min ,i} +f\_{om,i} \\psi \_{sat,om}\\\]

where \\(\\psi \_{sat,om}\\) is the saturated organic matter matric potential and the saturated mineral soil matric potential \\(\\psi \_{sat,\\min,i}\\) is

(2.7.55)[¶](#equation-7-96 "Permalink to this equation")\\\[\\psi \_{sat,\\, \\min ,\\, i} =-10.0\\times 10^{1.88-0.0131(\\% sand)\_{i} } .\\\]

The saturated hydraulic conductivity, \\(k\_{sat} \\left\[z\_{h,\\, i} \\right\]\\) (mm s\-1), for organic soils (\\(k\_{sat,\\, om}\\) ) may be two to three orders of magnitude larger than that of mineral soils (\\(k\_{sat,\\, \\min }\\) ). Bulk soil layer values of \\(k\_{sat}\\) calculated as weighted averages based on \\(f\_{om}\\) may therefore be determined primarily by the organic soil properties even for values of \\(f\_{om}\\) as low as 1 %. To better represent the influence of organic soil material on the grid cell average saturated hydraulic conductivity, the soil organic matter fraction is further subdivided into “connected” and “unconnected” fractions using a result from percolation theory ([Stauffer and Aharony 1994](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#staufferaharony1994), [Berkowitz and Balberg 1992](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#berkowitzbalberg1992)). Assuming that the organic and mineral fractions are randomly distributed throughout a soil layer, percolation theory predicts that above a threshold value \\(f\_{om} = f\_{threshold}\\), connected flow pathways consisting of organic material only exist and span the soil space. Flow through these pathways interacts only with organic material, and thus can be described by \\(k\_{sat,\\, om}\\). This fraction of the grid cell is given by

(2.7.56)[¶](#equation-7-97 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{lr} f\_{perc} =\\; N\_{perc} \\left(f\_{om} {\\rm \\; }-f\_{threshold} \\right)^{\\beta\_{perc} } f\_{om} {\\rm \\; } & \\qquad f\_{om} \\ge f\_{threshold} \\\\ f\_{perc} = 0 & \\qquad f\_{om} <f\_{threshold} \\end{array}\\end{split}\\\]

where \\(\\beta ^{perc} =0.139\\), \\(f\_{threshold} =0.5\\), and \\(N\_{perc} =\\left(1-f\_{threshold} \\right)^{-\\beta\_{perc} }\\). In the unconnected portion of the grid cell, \\(f\_{uncon} =\\; \\left(1-f\_{perc} {\\rm \\; }\\right)\\), the saturated hydraulic conductivity is assumed to correspond to flow pathways that pass through the mineral and organic components in series

(2.7.57)[¶](#equation-7-98 "Permalink to this equation")\\\[k\_{sat,\\, uncon} =f\_{uncon} \\left(\\frac{\\left(1-f\_{om} \\right)}{k\_{sat,\\, \\min } } +\\frac{\\left(f\_{om} -f\_{perc} \\right)}{k\_{sat,\\, om} } \\right)^{-1} .\\\]

where saturated hydraulic conductivity for mineral soil depends on soil texture ([Cosby et al. 1984](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#cosbyetal1984)) as

(2.7.58)[¶](#equation-7-99 "Permalink to this equation")\\\[k\_{sat,\\, \\min } \\left\[z\_{h,\\, i} \\right\]=0.0070556\\times 10^{-0.884+0.0153\\left(\\% sand\\right)\_{i} } .\\\]

The bulk soil layer saturated hydraulic conductivity is then computed as

(2.7.59)[¶](#equation-7-100 "Permalink to this equation")\\\[k\_{sat} \\left\[z\_{h,\\, i} \\right\]=f\_{uncon,\\, i} k\_{sat,\\, uncon} \\left\[z\_{h,\\, i} \\right\]+(1-f\_{uncon,\\, i} )k\_{sat,\\, om} \\left\[z\_{h,\\, i} \\right\].\\\]

The soil organic matter properties implicitly account for the standard observed profile of organic matter properties as

(2.7.60)[¶](#equation-1-101 "Permalink to this equation")\\\[\\theta\_{sat,om} = max(0.93 - 0.1\\times z\_{i} / zsapric, 0.83).\\\]

(2.7.61)[¶](#equation-1-102 "Permalink to this equation")\\\[B\_{om} = min(2.7 + 9.3\\times z\_{i} / zsapric, 12.0).\\\]

(2.7.62)[¶](#equation-1-103 "Permalink to this equation")\\\[\\psi\_{sat,om} = min(10.3 - 0.2\\times z\_{i} / zsapric, 10.1).\\\]

(2.7.63)[¶](#equation-1-104 "Permalink to this equation")\\\[k\_{sat,om} = max(0.28 - 0.2799\\times z\_{i} / zsapric, k\_{sat,\\, \\min } \\left\[z\_{h,\\, i} \\right\]).\\\]

where \\(zsapric =0.5\\) m is the depth that organic matter takes on the characteristics of sapric peat.

