Multi-layer diffusion model and error analysis applied to chamber-based gas fluxes measurements

Chambers are widely-used for measuring greenhouse gas emission from soil surfaces. Current chamber methods are generally based on constant production within the soil, both before and after the placement of the enclosed chamber, and well-mixed chamber systems. The objective of this study is to present an analytical solution for either perfectly mixed or non-mixed non-steady-state (NSS) chamber systems with a depth-dependent gas production term. Parameters such as the decreasing production rate (k), the distance from soil-atmosphere interface to the water table (l ₁), the height of chamber (l ₂ - l ₁), the diffusion coefficient in the chamber (D ₂), and the air-filled porosity (ε) were included in our model. This was accomplished by using a one-dimensional multi-layer transient diffusion model with a production term. If we know k, l ₁, l ₂ - l ₁, D ₂, and ε, the pre-deployment flux density f ₀ can be obtained by fitting the new solution to experimental concentration curve. The analytical solution can be applied to various case scenarios from pure diffusion to perfectly mixed systems, by adjusting D ₂. The widely-used linear and nonlinear regression models are subsets of the solution. The proposed solution indicates the importance of the initial concentration distribution f(x) and production term g(x) in emission rates. Without measuring g(x), a large error in estimated pre-deployment flux density f ₀ could result. Without knowing the parameters k, l ₁, l ₂ - l ₁ and D ₂, a large error in estimated f₀ could result. If the well-mixed model is used for modeling diffusion in not perfectly mixed chamber headspace, the magnitude of the error in f ₀ increases monotonically with the increase in heights of sampling ports above l ₁ and can be larger than 60% at x = l ₂. The error caused by using the well-stirred approximation increase with decreases in D ₂ and can be significant for chambers when there are no external mixing devices. The well-mixed solution could not be fitted well to the pure diffusion concentration curve, and vice versa. The solution may be helpful for better evaluating f ₀ of trace gases from soil, carrying out the errors analysis and reducing the uncertainty in measured greenhouse gas emissions from soil.