Determination of soil carbon dioxide source-density profiles by inversion from soil-profile gas concentrations and surface flux density for diffusion-dominated transport

Abstract This paper presents the mathematical derivation and evaluation of a suite of inversion techniques that determine the instantaneous soil carbon dioxide source-density distribution from corresponding values of soil carbon dioxide concentration at the 0, 0.1, 0.2, 0.4, and 0.8 m depths and additionally, for some methods, the surface carbon dioxide flux density. These concentrations and the surface flux density were simulated artificially whereas in real field applications they would be available from measurements. All methods assume that the vertical transfer of carbon dioxide within the soil profile is by molecular diffusion within the air-filled pore space. Simulations utilized the steady-periodic part of the forward solution of the standard carbon dioxide conservation equation that uses Fick’s law to drive diffusion and accounts for storage and an assumed carbon dioxide source-density distribution in the soil. Boundary conditions were a constant carbon dioxide concentration at the soil surface and zero flux density at the base of the soil profile, which was at the 2 m depth. Values of porosity, volumetric water content (both assumed constant with time for the 1-day period considered), and soil temperature (time series) at the 0, 0.1, 0.2, 0.4, 0.8, 1.6, and 2 m depths, the functional dependence of soil carbon dioxide diffusivity on air-filled porosity, and the Q 10 temperature parameter (equal to 2) in the assumed carbon dioxide source-density function were known a priori for the inversion calculations, which determined the two remaining unknown parameters in this function diurnally every 900 s. Maximum and mean inversion errors for the two parameters were determined for all methods with two levels of solar irradiance, three levels of soil moisture, both random and systematic measurement errors in the input data, and an incorrect form for the shape factor (which is usually associated with the vertical profile of organic matter and root density) in the assumed source-strength function.