### 2.25.7.4. Boundary Conditions[¶](#boundary-conditions "Permalink to this headline")

We assume the CH4 and O2 surface fluxes can be calculated from an effective conductance and a gaseous concentration gradient between the atmospheric concentration and either the gaseous concentration in the first soil layer (unsaturated soils) or in equilibrium with the water (saturated soil\\(w\\left(C\_{1}^{n} -C\_{a} \\right)\\) and \\(w\\left(C\_{1}^{n+1} -C\_{a} \\right)\\) for the fully explicit and fully implicit cases, respectively (however, see [Tang and Riley (2013)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#tangriley2013) for a more complete representation of this process). Here, _w_ is the surface boundary layer conductance as calculated in the existing CLM surface latent heat calculations. If the top layer is not fully saturated, the \\(\\frac{D\_{m1} }{\\Delta x\_{m1} }\\) term is replaced with a series combination: \\(\\left\[\\frac{1}{w} +\\frac{\\Delta x\_{1} }{D\_{1} } \\right\]^{-1}\\), and if the top layer is saturated, this term is replaced with \\(\\left\[\\frac{K\_{H} }{w} +\\frac{\\frac{1}{2} \\Delta x\_{1} }{D\_{1} } \\right\]^{-1}\\), where \\({K}\_{H}\\) is the Henry’s law equilibrium constant.

When snow is present, a resistance is added to account for diffusion through the snow based on the Millington-Quirk expression [(2.25.13)](#equation-24-13) and CLM’s prediction of the liquid water, ice, and air fractions of each snow layer. When the soil is ponded, the diffusivity is assumed to be that of methane in pure water, and the resistance as the ratio of the ponding depth to diffusivity. The overall conductance is taken as the series combination of surface, snow, and ponding resistances. We assume a zero flux gradient at the bottom of the soil column.

