Mathematical Reconstruction of Land Carbon Models From Their Numerical Output: Computing Soil Radiocarbon From C Dynamics

摘要

Radiocarbon (14C) is a powerful tracer of the global carbon cycle that is commonly used to assess carbon cycling rates in various Earth system reservoirs and as a benchmark to assess model performance. Therefore, it has been recommended that Earth System Models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 report predicted radiocarbon values for relevant carbon pools. However, a detailed representation of radiocarbon dynamics may be an impractical burden on model developers. Here, we present an alternative approach to compute radiocarbon values from the numerical output of an ESM that does not explicitly represent these dynamics. The approach requires computed 12C stocks and fluxes among all carbon pools for a particular simulation of the model. From this output, a time‐dependent linear compartmental system is computed with its respective state‐transition matrix. Using transient atmospheric 14C values as inputs, the state‐transition matrix is then applied to compute radiocarbon values for each pool, the average value for the entire system, and component fluxes. We demonstrate the approach with ELMv1‐ECA, the land component of an ESM model that explicitly represents 12C, and 14C in 7 soil pools and 10 vertical layers. Results from our proposed method are highly accurate (relative error 0.01%) compared with the ELMv1‐ECA 12C and 14C predictions, demonstrating the potential to use this approach in CMIP6 and other model simulations that do not explicitly represent 14C. Plain Language Summary Models representing ecosystem carbon dynamics are generally complex and difficult to analyze. Comparing different models with different structures is even more challenging due to the variety of processes represented in the models. However, it is possible to use the numerical output of models to reconstruct the original structure using a common mathematical framework. In this manuscript, we demonstrate this approach and apply it to compute radiocarbon dynamics of a land carbon model. The proposed approach can reconstruct the carbon and radiocarbon dynamics of the original model very accurately and can be used to study system‐level dynamics of complex contrasting models.