## Diffusion and water content

Methane diffuses from the atmosphere to methanotrophic bacteria contained within a semi-porous soil matrix. A gradient of decreasing methane with depth is usually evident, declining from a mixing ratio of about 1.75 ppmv at the soil surface often to <0.5 ppmv at 10-30 cm depth (Born et al., 1990; Whalen et al., 1992; Adamsen and King, 1993; Dörr et al., 1993; Koschorreck and Conrad, 1993; Dunfield et al., 1995). Methane oxidation must therefore be diffusion-limited, because if the movement of methane from the atmosphere were much faster than microbial oxidation, no gradient would be evident. Net diffusion along a linear gradient (i.e. downward into a soil) can be described by Fick's law:

J = DcHsoil xd[CHJ/dz

where J is flux (e.g. mmol/m2/day) and DCH soU is the binary diffusion coefficient of CH4 in soil matrix air (e.g. m2/day) and z is the depth (m).

Soil is a three-phase system composed of water, air and solids. Diffusion of a gas in water is 10,000 times slower than diffusion in air, so the critical factor controlling the diffusion rate of methane into the soil column is the gas-filled porosity of the soil. DCH4soil can be adequately estimated by the following empirical formula:

^CH4soil= DCH4air X aj

where DCH4air is the temperature-dependent diffusion rate in air (1.95 m2/day at 22.5°C; Striegl, 1993), j is fractional gas-filled soil porosity, and a and b are empirical factors to compensate for soil-dependent tortuosity. The actual values of these coefficients will vary with soil type, but estimated average values of a = 0.9 and b = 2.3 work well with many soils (Campbell, 1985; Dunfield et al., 1995; Price et al., 2004). The dependence of the diffusion rate on gas-filled pore space should therefore be an exponential rise to a maximum, the maximum rate occurring where all pore space is gas-filled (Fig. 10.1) (Dunfield et al., 1995).

One corollary of this diffusion model is that coarse-textured soils have higher potential methane uptake rates than fine-textured soils, because there is more gas-filled pore space and less water retention capacity (Born et al., 1990; Dörr et al., 1993). Another is that soil methane uptake decreases with increasing water content

(Whalen et al., 1990; Adamsen and King, 1993; Dunfield et al., 1995; Sitaula et al., 1995; Kruse et al., 1996). In addition, soil compaction decreases methane oxidation (Hansen et al., 1993; Ruser et al., 1998; Sitaula et al., 2000). This is primarily a diffusion effect, but a long-term decline of methanotrophic populations may also be caused by the decreased methane supply to compacted soil (Sitaula et al., 2000). Forest harvesting decreases the soil methane sink, or converts it to a methane source, probably because of reduced transpiration and the resulting increase of soil water content (Castro et al., 2000; Kähkönen et al., 2002).

At extremely high and extremely low water contents this physical diffusion model is complicated by biological factors. Methane oxidation, like any micro-bial activity, becomes limited by water stress (osmotic stress) under very dry conditions (Whalen et al., 1990; Nesbit and Breitenbeck, 1992; Schnell and King, 1996; Prieme and Christensen, 1999). A hump-shaped dependence of methane uptake on water content may therefore be observed, with an optimum at 20-50% of waterholding capacity (or water-filled pore space), bordered by a zone of diffusion limitation at higher water contents, and a zone of desiccation stress at lower water contents (Torn and Harte, 1996; Gulledge and Schimel, 1998a). At high water contents diffusion of O2 is also limited, resulting in anaerobiosis and potentially in methane production (Fig. 10.1).