Journal cover Journal topic
Biogeosciences An interactive open-access journal of the European Geosciences Union
Biogeosciences, 14, 145-161, 2017
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
12 Jan 2017
Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications
Yiqi Luo1,2, Zheng Shi1, Xingjie Lu3, Jianyang Xia4, Junyi Liang1, Jiang Jiang1, Ying Wang5, Matthew J. Smith6, Lifen Jiang1, Anders Ahlström7,8, Benito Chen9, Oleksandra Hararuk10, Alan Hastings11, Forrest Hoffman12, Belinda Medlyn13, Shuli Niu14, Martin Rasmussen15, Katherine Todd-Brown16, and Ying-Ping Wang3 1Department of Microbiology and Plant Biology, University of Oklahoma, Norman, Oklahoma, USA
2Department for Earth System Science, Tsinghua University, Beijing, China
3CSIRO Oceans and Atmosphere, Aspendale, Victoria, Australia
4School of Ecological and Environmental Sciences, East China Normal University, Shanghai, China
5Department of Mathematics, University of Oklahoma, Norman, Oklahoma, USA
6Computational Science Laboratory, Microsoft Research, Cambridge, UK
7Department of Earth System Science, Stanford University, Stanford, California, USA
8Department of Physical Geography and Ecosystem Science, Lund University, Lund, Sweden
9Department of Mathematics, University of Texas, Arlington, TX, USA
10Department of Natural Resource Sciences, McGill University, Montreal, Canada
11Department of Environmental Science and Policy, University of California, One Shields Avenue, Davis, CA 95616, USA
12Computational Earth Sciences Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
13Hawkesbury Institute for the Environment, Western Sydney University, Penrith NSW 2751, Australia
14Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China
15Department of Mathematics, Imperial College, London, UK
16Biological Sciences Division, Pacific Northwest National Laboratory, Richland, Washington, USA
Abstract. Terrestrial ecosystems have absorbed roughly 30 % of anthropogenic CO2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times.

Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Overall, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.

Citation: Luo, Y., Shi, Z., Lu, X., Xia, J., Liang, J., Jiang, J., Wang, Y., Smith, M. J., Jiang, L., Ahlström, A., Chen, B., Hararuk, O., Hastings, A., Hoffman, F., Medlyn, B., Niu, S., Rasmussen, M., Todd-Brown, K., and Wang, Y.-P.: Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications, Biogeosciences, 14, 145-161, doi:10.5194/bg-14-145-2017, 2017.
Publications Copernicus
Short summary
Climate change is strongly regulated by land carbon cycle. However, we lack the ability to predict future land carbon sequestration. Here, we develop a novel framework for understanding what determines the direction and rate of future change in land carbon storage. The framework offers a suite of new approaches to revolutionize land carbon model evaluation and improvement.
Climate change is strongly regulated by land carbon cycle. However, we lack the ability to...