Exploring the Sensitivity of Paleo-PCO2 Models Based on δ13C of Pedogenic Gibbsite to Changing Soil Variables with Depth Using Numerical Methods

Soil respiration on geologic time scales and resultant depth-dependent δ¹³C soil gas signatures preserved in the rock record have been predominantly based on models using analytical solutions to the one dimensional Fickian diffusion equation. Numerical models and Monte Carlo simulations allow for sensitivity testing of δ¹³C affecting variables for which analytical solutions are not possible. A computer program has been developed, based on the finite difference method and is used to explore variability in depth dependent factors such as bulk density, rates of CO₂ production, and boundary conditions. Comparison of the analytical and numerical model solutions with literature data for soil CO₂ compositions reveals discordance between the solution soil property parameters and measured physical properties of the soil. Variables used to calculate the δ¹³C of soil CO₂ with the analytical solution indicate that the δ¹³C of the soil biomass and the rate of CO₂ production are the most sensitive parameters. The analytical solution indicates that the majority of the variability occurring within the first 20 cm of depth is related to soil CO₂ production rate and bulk density. Specifically, the shape of the δ¹³C profile and depth of maximum inflection is controlled by the rate of CO₂ diffusion, i.e. the CO₂ production rate or bulk density. The δ¹³C of the soil biomass and the P_CO2 of the atmosphere are responsible for variability at depths greater than 20 cm. The numerical model solutions allow for differences in bulk density, δ¹³C of biomass, and soil CO₂ production rate with depth. This model was also used to perform a Monte Carlo analysis of the interdependence of model solutions on these variables.

Ultimately, these models will have application for paleobarometry studies, which use stable carbon isotopes occluded in pedogenic gibbsite and goethite and assumed climatic conditions at the time pedogenesis.