The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in land C cycle models. This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original land C cycle models into one matrix equation without changing any modeled C cycle processes and mechanisms. We have applied the matrix approach to three global land C models: CABLE, LPJ-GUESS, and below-ground part of the Community Land Model (CLM3.5, CLM4.0 and CLM4.5) and ORCHIDEE‐MICT; and two ecosystem models: TECO and BEPS. The matrix equation exactly reproduces C dynamics of the original models. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. In addition, the matrix tool can accelerate model spin-up, permit thorough parametric sensitivity tests, enable pool-based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective.
