Stochastic model for posttillage soil pore space evolution

Tillage operations disrupt surface layers of agricultural soils, creating a loosened structure with a substantial proportion of interaggregate porosity that enhances liquid and gaseous exchange properties favorable for plant growth. Unfortunately, such desirable soil tilth is structurally unstable and is susceptible to change by subsequent wetting and drying processes and other mechanical stresses that reduce total porosity and modify pore size distribution (PSD). Ability to model posttillage dynamics of soil pore space and concurrent changes in hydraulic properties is important for realistic predictions of transport processes through this surface layer. We propose a stochastic modeling framework that couples the probabilistic nature of pore space distributions with physically based soil deformation models using the Fokker-Planck equation (FPE) formalism. Three important features of soil pore space evolution are addressed: (1) reduction of the total porosity, (2) reduction of mean pore radius, and (3) changes in the variance of the PSD. The proposed framework may be used to provide input to hydrological models concerning temporal variations in near-surface soil hydraulic properties. In a preliminary investigation of this approach we link a previously proposed mechanistic model of soil aggregate coalescence to the stochastic FPE framework to determine the FPE coefficients. An illustrative example is presented which describes changes in interaggregate pore size due to wetting-drying cycles and the resulting effects on dynamics of the soil water characteristic curve and hydraulic conductivity functions.