### 2.25.7.3. Aqueous and Gaseous Diffusion[¶](#aqueous-and-gaseous-diffusion "Permalink to this headline")

For gaseous diffusion, we adopted the temperature dependence of molecular free-air diffusion coefficients (\\({D}\_{0}\\) (m2 s\-1)) as described by [Lerman (1979)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#lerman1979) and applied by [Wania et al. (2010)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#waniaetal2010) ([Table 2.25.2](#table-temperature-dependence-of-aqueous-and-gaseous-diffusion)).

Table 2.25.2 Temperature dependence of aqueous and gaseous diffusion coefficients for CH4 and O2[¶](#id15 "Permalink to this table")   
| \\({D}\_{0}\\) (cm2 s\-1)
 | CH4

 | O2

 |
| --- | --- | --- |
| Aqueous

 | 0.9798 + 0.02986_T_ + 0.0004381_T_2

 | 1.172+ 0.03443_T_ + 0.0005048_T_2

 |
| Gaseous

 | 0.1875 + 0.0013_T_

 | 0.1759 + 0.00117_T_

 |

Gaseous diffusivity in soils also depends on the molecular diffusivity, soil structure, porosity, and organic matter content. [Moldrup et al. (2003)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#moldrupetal2003), using observations across a range of unsaturated mineral soils, showed that the relationship between effective diffusivity (\\(D\_{e}\\) (m2 s\-1)) and soil properties can be represented as:

(2.25.12)[¶](#equation-24-12 "Permalink to this equation")\\\[D\_{e} =D\_{0} \\theta \_{a}^{2} \\left(\\frac{\\theta \_{a} }{\\theta \_{s} } \\right)^{{\\raise0.7ex\\hbox{$ 3 $}\\!\\mathord{\\left/ {\\vphantom {3 b}} \\right.}\\!\\lower0.7ex\\hbox{$ b $}} } ,\\\]

where \\(\\theta \_{a}\\) and \\(\\theta \_{s}\\) are the air-filled and total (saturated water-filled) porosities (-), respectively, and _b_ is the slope of the water retention curve (-). However, [Iiyama and Hasegawa (2005)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#iiyamahasegawa2005) have shown that the original Millington-Quirk ([Millington and Quirk 1961](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#millingtonquirk1961)) relationship matched measurements more closely in unsaturated peat soils:

(2.25.13)[¶](#equation-24-13 "Permalink to this equation")\\\[D\_{e} =D\_{0} \\frac{\\theta \_{a} ^{{\\raise0.7ex\\hbox{$ 10 $}\\!\\mathord{\\left/ {\\vphantom {10 3}} \\right.}\\!\\lower0.7ex\\hbox{$ 3 $}} } }{\\theta \_{s} ^{2} }\\\]

In CLM, we applied equation [(2.25.12)](#equation-24-12) for soils with zero organic matter content and equation [(2.25.13)](#equation-24-13) for soils with more than 130 kg m\-3 organic matter content. A linear interpolation between these two limits is applied for soils with SOM content below 130 kg m\-3. For aqueous diffusion in the saturated part of the soil column, we applied ([Moldrup et al. (2003)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#moldrupetal2003)):

(2.25.14)[¶](#equation-24-14 "Permalink to this equation")\\\[D\_{e} =D\_{0} \\theta \_{s} ^{2} .\\\]

To simplify the solution, we assumed that gaseous diffusion dominates above the water table interface and aqueous diffusion below the water table interface. Descriptions, baseline values, and dimensions for parameters specific to the CH4 model are given in [Table 2.25.1](#table-methane-parameter-descriptions). For freezing or frozen soils below the water table, diffusion is limited to the remaining liquid (CLM allows for some freezing point depression), and the diffusion coefficients are scaled by the volume-fraction of liquid. For unsaturated soils, Henry’s law equilibrium is assumed at the interface with the water table.

