Where does oxygen extinction occur in a soil profile?

Abstract

The problem of where and under what circumstances oxygen extinction (concentration in gas phase, C =0) in a soil profile is of increasing interest, due to the effect of nitrous oxide and methane fluxes on atmospheric chemistry (Ravishankara et al., 2009) climate change (Forster et al., 2007). The oxygen concentration profile is also of importance as the biogeochemical processes in soils are mainly mediated by oxidation/reduction reactions. In soil there are two main sinks for oxygen (O2), microbes and plant roots. Cook and Knight (2003) developed an analytical model for the steady-state transport of oxygen into a uniform soil by use of transformations of the independent variables, the concentration (C) and spatial dimension (z). The transformed concentration is C ' = C - Cr / a ; Cr is the critical concentration in the water phase at the root surface and a is the Bunsen coefficient. The spatial transform is X = 2Zr exp(- z / 2Zr ) g with g = 2pa Dl L0 / [Da ln(R / a)], Zr the scaling depth for an exponentially decreasing root length density with z, Dl is the diffusion of O2 in soil water, Da is the diffusion of O2 in soil air, R is the radius of the root plus saturated soil around the root, a is the root radius and L0 is the root length density at z = 0. This model could not calculate the depth at which either C or C ' went to extinction. A subsequent extension was able to calculate the depth (X1) when C ' = 0 and the air-filled porosity (?) was less than a critical value (?c) but with the restriction that dC '/ dX X1 = 0. Here (Figure Presented) we remove this restriction and by coupling with model of Cook (1995) where the only O2 sink is microbes are able to determine the depth (Z0) at which C = 0. This requires solving a set of five boundary condition equations and a recursive method is presented. The extension to dC '/ dX X1 < 0 results in essentially the same critical air-filled porosity (?c) below which C ' = 0 at a finite depth. When ?