Full Implementation of Matrix Approach to Biogeochemistry Module of CLM5

Earth system models (ESMs) have been rapidly developed in recent decades to advance our understanding of climate change‐carbon cycle feedback. However, those models are massive in coding, require expensive computational resources, and have difficulty in diagnosing their performance. It is highly desirable to develop ESMs with modularity and effective diagnostics. Toward these goals, we implemented a matrix approach to the Community Land Model version 5 (CLM5) to represent carbon and nitrogen cycles. Specifically, we reorganized 18 balance equations each for carbon and nitrogen cycles among the 18 vegetation pools in the original CLM5 into two matrix equations. Similarly, 140 balance equations each for carbon and nitrogen cycles among the 140 soil pools were reorganized into two additional matrix equations. The vegetation carbon and nitrogen matrix equations are connected to soil matrix equations via litterfall. The matrix equations fully reproduce simulations of carbon and nitrogen dynamics by the original model. The computational cost for forwarding simulation of the CLM5 matrix model was 26% more expensive than the original model, largely due to calculation of additional diagnostic variables, but the spin‐up computational cost was significantly saved. We showed a case study on modeled soil carbon storage under two forcing data sets to illustrate the diagnostic capability that the matrix approach uniquely offers to understand simulation results of global carbon and nitrogen dynamics. The successful implementation of the matrix approach to CLM5, one of the most complex land models, demonstrates that most, if not all, the biogeochemical models can be reorganized into the matrix form to gain high modularity, effective diagnostics, and accelerated spin‐up. Plain Language Summary Land models are widely used in climate change research. Due to the complex system, the model is not easily comprehended, nor the results are easily interpreted, even by a specialist. Enhancing the model tractability is imperative to make climate change prediction more effective, especially as models become more and more complex. In this study, we developed a matrix model by reorganizing six carbon and nitrogenmodules of Community LandModel version 5 (CLM5) into four matrix equations to represent vegetation carbon, vegetation nitrogen, soil carbon, and soil nitrogen balance equations, respectively. The CLM5 matrix model gains high modularity, effective diagnostics, and accelerated spin‐up. The success of applying the matrix approach to CLM5, one of the most complex land models, support the theoretical analysis that the matrix approach is applicable to almost all land biogeochemical models.