Modeling soil CO2 production and transport with dynamic source and diffusion terms: Testing the steady-state assumption using DETECT v1.0

The flux of CO₂ from the soil to the atmosphere (soil respiration, R_soil) is a major component of the global carbon (C) cycle. Methods to measure and model R_soil, or partition it into different components, often rely on the assumption that soil CO₂ concentrations and fluxes are in steady state, implying that R_soil is equal to the rate at which CO₂ is produced by soil microbial and root respiration. Recent research, however, questions the validity of this assumption. Thus, the aim of this work was two-fold: (1) to describe a non-steady state (NSS) soil CO₂ transport and production model, DETECT, and (2) to use this model to evaluate the environmental conditions under which R_soiland CO₂ production are likely in NSS. The backbone of DETECT is a non-homogeneous, partial differential equation (PDE) that describes production and transport of soil CO₂, which we solve numerically at fine spatial and temporal resolution (e.g., 0.01m increments down to 1m, every 6h). Production of soil CO₂ is simulated for every depth and time increment as the sum of root respiration and microbial decomposition of soil organic matter. Both of these factors can be driven by current and antecedent soil water content and temperature, which can also vary by time and depth. We also analytically solved the ordinary differential equation (ODE) corresponding to the steady-state (SS) solution to the PDE model. We applied the DETECT NSS and SS models to the six-month growing season period representative of a native grassland in Wyoming. Simulation experiments were conducted with both model versions to evaluate factors that could affect departure from SS, such as (1) varying soil texture; (2) shifting the timing or frequency of precipitation; and (3) with and without the environmental antecedent drivers. For a coarse-textured soil, R_soil from the SS model closely matched that of the NSS model. However, in a fine-textured (clay) soil, growing season R_soil was  ∼ 3% higher under the assumption of NSS (versus SS). These differences were exaggerated in clay soil at daily time scales whereby R_soil under the SS assumption deviated from NSS by up to 35% on average in the 10 days following a major precipitation event. Incorporation of antecedent drivers increased the magnitude of R_soil by 15 to 37% for coarse- and fine-textured soils, respectively. However, the responses of R_soil to the timing of precipitation and antecedent drivers did not differ between SS and NSS assumptions. In summary, the assumption of SS conditions can be violated depending on soil type and soil moisture status, as affected by precipitation inputs. The DETECT model provides a framework for accommodating NSS conditions to better predict R_soil and associated soil carbon cycling processes.