Technical Note: Simple formulations and solutions of the dual-phase diffusive transport for biogeochemical modeling
Representation of gaseous diffusion in variably saturated near-surface soils is becoming more common in land biogeochemical models, yet the formulations and numerical solution algorithms applied vary widely. We present three different but equivalent formulations of the dual-phase (gaseous and aqueous) tracer diffusion transport problem that is relevant to a wide class of volatile tracers in land biogeochemical models. Of these three formulations (i.e., the gas-primary, aqueous-primary, and bulk tracer based formulations), we contend the gas-primary formulation is the most convenient for modeling tracer dynamics in biogeochemical models. We then provide finite volume approximation to the gas-primary equation and evaluate its accuracy against three analytical models: one for steady-state soil CO2 dynamics, one for steady-state soil CO2 dynamics, and one for transient tracer diffusion from a constant point source into two different sequentially aligned medias. All evaluations demonstrated good accuracy of the numerical approximation. We expect our result will standardize an efficient mechanistic numerical method for solving relatively simple, multi-phase, one-dimensional diffusion problems in land models.