Matrix Approach to Land Carbon Cycle Modeling

Yiqi Luo, Yuanyuan Huang, Carlos A. Sierra, Jianyang Xia, Anders Ahlström, Yizhao Chen, Oleksandra Hararuk, Enqing Hou, Lifen Jiang, Cuijuan Liao, Xingjie Lu, Zheng Shi, Benjamin Smith, Feng Tao, Ying Ping Wang

Research output: Contribution to journalReview articlepeer-review

7 Scopus citations


Land ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin-up of land carbon cycle models by tens of times. The accelerated spin-up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever-increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.

Original languageEnglish (US)
Article numbere2022MS003008
JournalJournal of Advances in Modeling Earth Systems
Issue number7
StatePublished - Jul 2022


  • biogeochemistry
  • carbon cycle
  • dynamical equation
  • terrestrial ecosystems
  • uncertainty analysis

ASJC Scopus subject areas

  • Global and Planetary Change
  • Environmental Chemistry
  • General Earth and Planetary Sciences


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