Land ecosystems absorb approximately 30% of the anthropogenic carbon dioxide emissions. This estimate has been deduced indirectly: combining analyses of atmospheric carbon dioxide concentrations with ocean observations to infer the net land carbon flux. In contrast, when knowledge about the land carbon cycle is integrated into different models they make widely different predictions. It is urgent to improve land biogeochemical models in order to accurately predict future changes in ecosystem services and feedback to climate change.
In general, land models represent carbon and nitrogen cycles by a series of carbon balance equations to track its influxes into and effluxes out of individual pools. This representation matches our understanding of biogeochemical processes well but makes it difficult to track model behaviors and computationally costly for spin-up and sensitivity analysis.
Results/Conclusions
We have recently reorganized the carbon balance equations in original ecosystem or earth system models into matrix equations without changing any modeled biogeochemical processes and mechanisms. We have developed matrix equations of several global land carbon cycle models, including Community Land Model (CLM) version 3.5, 4.0, 4.5, and 5.0, CABLE, LPJ-GUESS, and OCHIDEE. We have also developed matrix representation of coupled carbon and nitrogen models, such as CLM5.0 and TECO. Indeed, this matrix representation is generic and can be applied to almost all land biogeochemical models.
With the matrix equation, we have developed new theory, such as dynamic disequilibrium, predictability, and transient dynamics of land carbon storage. In addition, the matrix approach has several applications. First, it accelerates spin-up by ten or hundred times, which is extremely meaningful for computation of earth system models. Second, it offers a suite of new diagnostic tools, such as the 3-dimensional (3-D) space to evaluate all model outputs and traceability analysis to pinpoint uncertainty sources. Third, it makes pool-based data assimilation computationally possible so as to constrain highly uncertain components with data. Fourth, it makes the computer source code much shorter, more tractable, more portable, and easier to learn for novices. Overall, the matrix approach has the potential to transform biogeochemical research to more theory-based science, offers a suite of new tools for uncertainty analysis, and provides clear directions for model improvement and future research.