Analytical Solutions for Steady-State Oxygen Transport in Soil With Microbial and Plant Root Sinks

Abstract

A complete model using analytical solutions for one-dimensional oxygen transport from the atmosphere into soil with microbial and root sinks that builds on work over 30 years is developed. This new model uses concepts from a previously published model for one distributed sink and two sinks with a distributed (microbial) and line (root) sink. It removes the problem, in previous publications, of matching the flux at the joining point between the two sink solution where the root sink ceases and the single sink at a finite depth. Analytical solutions are developed for integer values of p = Z_r/Z_m, where Z_m is the scaling depth for microbial respiration and Z_r is the scaling depth for root length density. The solutions allow two critical diffusivity (D) values to be defined (D_c) and (D_c2). When D_c2 ≤ D < D_c, a procedure is presented to calculate the depth, z₁, where C^′ = 0 and this is the depth where root uptake of oxygen ceases and is shown to be related to D/D_c. When D < D_c2, a procedure is presented to estimate the depth, Z₀, at which the oxygen concentration = 0 and is shown to be related to D/D_c2. These results have useful applications in determining soil aeration, soil biogeochemical reactions, soil surface flux of oxygen and carbon dioxide, and the effect of climate change on these processes through the temperature dependence of the solution. These results suggest the oxygen diffusion rate (ODR) is likely to be the best estimator of soil aeration but there will not be a universal value for all plants. The surface flux density of oxygen into the soil for both the microbial sink (S_m) and total sink (f₀) are presented and the ratio is shown to be related to $D/D_a^0$ ($D_a^o$ is the diffusivity in air). The possible range in S_m/f₀ is shown to be compatible with measured values from the literature. The solutions have many applications in environmental science.