Two dimensional diffusion theory of trace gas emission into soil chambers for flux measurements

Chamber-based techniques have been widely used over the past several decades to measure the soil–atmosphere exchanges of trace gases. Despite numerous publications on this topic, it still remains controversial as to which chamber deployment strategy and non-steady state model should be used to retrieve the pre-deployment flux from the observed headspace concentration data. As a consequence, the flux estimation models used in chamber studies to date have been either empirical or, at best, based on one dimensional (1-D) diffusion theory. While the validity of empirical models to aid the interpretation of headspace concentration data is questionable because they are not process-based, the 1-D models are crucially based on assumptions regarding the chamber insertion depths and deployment durations which may or may not be met in practice especially on untested soils. To resolve these issues, we develop here a two dimensional (2-D) non-steady state theory by considering both lateral and vertical diffusion as the post-deployment mechanism of trace gas emission into a chamber deployed at the surface of the soil matrix. This theory provides an accurate framework for interpreting the concentration data derived from surface deployed chambers without having to worry about insertion depths or deployment durations. Three major contributions of the theory are: (i) development of an analytical formula for the instantaneous flux drop due to a change in the gas mixing processes in the headspace immediately following chamber deployment, (ii) derivation of a rigorous formula, valid without time restrictions, to describe the non-linear increase in the chamber headspace concentration as a function of soil properties and chamber dimensions, and (iii) prediction of a saturation steady state concentration in the headspace. From the exact solutions, an exponential approximation was also developed as a simple fitting function for extended deployments for practical applications. The performance of the 2-D model was evaluated successfully against experimental observations on radon (222Rn) using two chambers having different dimensions. These experiments demonstrated the usefulness of the model for estimating not only the pre-deployment flux, but also the soil diffusion coefficients by utilizing data from extended periods of observations. They also demonstrated, for the first time, that chambers now may be allowed to operate in both NSS and steady state (SS) modes attributable purely to diffusion. The practical implications of the results are discussed.