Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications

Abstract

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 timedependent 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 threedimensional (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 computationPublished by Copernicus Publications on behalf of the European Geosciences Union. 146Y. Luo et al.: Land carbon storage dynamics ally 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.

Soil Organic Carbon Stabilization in the Three Subtropical Forests: Importance of Clay and Metal Oxides

“…Previous studies found that carbon input through aboveground litter to soil increased in the coniferous or mixed forests, but decreased in the broadleaved forest over the last three decades, while the soil carbon accumulation was greatest in the broadleaved forest among the three forests (Tang et al, ). This result contradicted the proportionality of soil carbon change with carbon input, which is used in most global land carbon models that use the first‐order kinetics of soil carbon dynamics (Luo et al, ). Furthermore, evidence showed that the old forests in both temperate and subtropical regions accumulated SOC at quite high rate (Carey et al, ; Luyssaert et al, ; Zhou et al, ).…”

Representing and Understanding the Carbon Cycle Using the Theory of Compartmental Dynamical Systems

“…Bolin () was one of the first to write a simple carbon cycle model in matrix form. However, this form of representing carbon models has become more common recently by the development of the dynamic disequilibrium (Luo & Weng, ), traceability framework (Xia et al, ), and the transient dynamics theory (Jiang et al, ; Luo et al, ) of the terrestrial carbon cycle. Within these frameworks, carbon stocks in ecosystem pools x are represented as where is a vector of carbon pool sizes; U ( t ) is a scalar function that represents photosynthetically fixed carbon; b is a vector of partitioning coefficients of the photosynthetically fixed carbon to plant pools (e.g., leaf, root, and woody biomass).…”

“…By expressing models in this general and compact form, it is possible to better understand holistic behaviors of terrestrial carbon cycle models. For instance, the framework can be applied to better trace different components of the carbon cycle (Xia et al, ), determine timescales of different processes (Huang et al, ; Yan et al, ), determine the predictability and dynamic disequilibrium of the carbon cycle (Luo et al, ; Luo & Weng, ), and assess carbon storage capacity and potential (Jiang et al, ; Luo et al, ; Luo & Weng, ).…”

“…The model of equation proposed for the disequilibrium, traceability, and transient dynamics frameworks (Jiang et al, ; Luo et al, ; Luo & Weng, ; Xia et al, ) can be classified as linear nonautonomous because there are no dependencies on the vector of states, but rates and inputs are time‐dependent. We will see below that this classification is of fundamental importance to study the qualitative mathematical properties and overall behavior of ecosystem models.…”

“…Issues of interpretation are evident in the recent theory of transient dynamics of the carbon cycle (Jiang et al, ; Luo et al, ). For instance, if we adopt the notation of the linear nonautonomous system of Table , we can rewrite it as …”