@Article{Luo_Biogeosci_20170112,
 author		= {Yiqi Luo and Zheng Shi and Xingjie Lu and Jianyang Xia and Junyi Liang and Jiang Jiang and Ying Wang and Matthew J. Smith and Lifen Jiang and Anders Ahlstr{\"{o}}m and Benito Chen and Oleksandra Hararuk and Alan Hastings and Forrest Hoffman and Belinda Medlyn and Shuli Niu and Martin Rasmussen and Katherine Todd-Brown and Ying-Ping Wang},
 title		= {Transient Dynamics of Terrestrial Carbon Storage: Mathematical Foundation and Its Applications},
 journal	= Biogeosci,
 volume		= 14,
 number		= 1,
 pages		= {145--161},
 doi		= {10.5194/bg-14-145-2017},
 day		= 12,
 month		= jan,
 year		= 2017,
 abstract	= {Terrestrial ecosystems have absorbed roughly 30\% of anthropogenic CO$_2$ 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.}
}