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Abstract
Abstract. 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 that 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 CH4 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.
Highlights
The interest in predicting fluxes of various biogenic greenhouse gases and their interactions with climate change has motivated the development of many terrestrial biogeochemical models; e.g., ecosystem methane models (Walter and Heiman, 2000; Zhuang et al, 2004; Tang et al, 2010; Riley et al, 2011), nitrification-denitrification models (Venterea and Rolston, 2000; Maggi et al, 2008), water-CO2 isotope models (Riley et al, 2002), and generic reactive transport models that attempt to integrate as many biogeochemical processes and chemical species as possible (e.g., Simunek and Suarez, 1993; Grant, 2001; Tang et al, 2013)
Ecosystem models would benefit from a simple mechanistic formulation and numerical implementation of the dualphase diffusion problem
The 20- and 100-layer simulations predict a surface CO2 efflux of about 1 and 0.03 % accuracy, respectively, with respect to the analytical flux. These results indicate our numerical technique is sufficient for most soil dual-phase diffusion modeling applications
Summary
The interest in predicting fluxes of various biogenic greenhouse gases and their interactions with climate change has motivated the development of many terrestrial biogeochemical models; e.g., ecosystem methane models (Walter and Heiman, 2000; Zhuang et al, 2004; Tang et al, 2010; Riley et al, 2011), nitrification-denitrification models (Venterea and Rolston, 2000; Maggi et al, 2008), water-CO2 isotope models (Riley et al, 2002), and generic reactive transport models that attempt to integrate as many biogeochemical processes and chemical species as possible (e.g., Simunek and Suarez, 1993; Grant, 2001; Tang et al, 2013). To resolve the depthdependent dynamics, these models in general represent multiphase (aqueous and gaseous phase) diffusion processes and often assume negligible advection. The numerical implementation of the equation is often vaguely described (either by referring to other publications or by mentioning the numerical scheme) or is convolved with other technical details, making the model difficult to understand or replicate by other researchers. One does not need to represent all the processes typically included in a complicated reactive transport model to understand a particular problem. When soil moisture and temperature data are available together with soil respiration, one only needs a diffusion model to evaluate belowground CO2 dynamics (Davidson et al, 2006). Ecosystem models would benefit from a simple mechanistic formulation and numerical implementation of the dualphase diffusion problem
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