An inverse analysis reveals limitations of the soil-CO₂ profile method to calculate CO₂ production and efflux for well-structured soils

Abstract. Soil respiration is the second largest flux in the global carbon cycle, yet the underlying below-ground process, carbon dioxide (CO₂) production, is not well understood because it can not be measured in the field. CO₂ production has frequently been calculated from the vertical CO₂ diffusive flux divergence, known as "soil-CO₂ profile method". This relatively simple model requires knowledge of soil CO₂ concentration profiles and soil diffusive properties. Application of the method for a tropical lowland forest soil in Panama gave inconsistent results when using diffusion coefficients (D) calculated based on relationships with soil porosity and moisture ("physically modeled" D). Our objective was to investigate whether these inconsistencies were related to (1) the applied interpolation and solution methods and/or (2) uncertainties in the physically modeled profile of D. First, we show that the calculated CO₂ production strongly depends on the function used to interpolate between measured CO₂ concentrations. Secondly, using an inverse analysis of the soil-CO₂ profile method, we deduce which D would be required to explain the observed CO₂ concentrations, assuming the model perception is valid. In the top soil, this inversely modeled D closely resembled the physically modeled D. In the deep soil, however, the inversely modeled D increased sharply while the physically modeled D did not. When imposing a constraint during the fit parameter optimization, a solution could be found where this deviation between the physically and inversely modeled D disappeared. A radon (Rn) mass balance model, in which diffusion was calculated based on the physically modeled or constrained inversely modeled D, simulated observed Rn profiles reasonably well. However, the CO₂ concentrations which corresponded to the constrained inversely modeled D were too small compared to the measurements. We suggest that, in well-structured soils, a missing description of steady state CO₂ exchange fluxes across water-filled pores causes the soil-CO₂ profile method to fail. These fluxes are driven by the different diffusivities in inter- vs. intra-aggregate pores which create permanent CO₂ gradients if separated by a "diffusive water barrier". These results corroborate other studies which have shown that the theory to treat gas diffusion as homogeneous process, a precondition for use of the soil-CO₂ profile method, is inaccurate for pore networks which exhibit spatial separation between CO₂ production and diffusion out of the soil.