Using model reduction to predict the soil-surface C¹⁸OO flux: an example of representing complex biogeochemical dynamics in a computationally efficient manner

Abstract. Earth system models (ESMs) must calculate large-scale interactions between the land and atmosphere while accurately characterizing fine-scale spatial heterogeneity in water, carbon, and other nutrient dynamics. We present here a high-dimension model representation (HDMR) approach that allows detailed process representation of a coupled carbon and water tracer (the δ¹⁸O value of the soil-surface CO₂ flux (δ F_s)) in a computationally tractable manner. δ F_s depends on the δ¹⁸O value of soil water, soil moisture and temperature, and soil CO₂ production (all of which are depth dependent), and the δ¹⁸O value of above-surface CO₂. We tested the HDMR approach over a growing season in a C₄-dominated pasture using two vertical soil discretizations. The difference between the HDMR approach and the full model solution in the three-month integrated isoflux was less than 0.2% (0.5 mol m⁻² ‰), and the approach is up to 100 times faster than the full numerical solution. This type of model reduction approach allows representation of complex coupled biogeochemical processes in regional and global climate models and can be extended to characterize subgrid-scale spatial heterogeneity.