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

Abstract

Models representing exchange of carbon between the atmosphere and the terrestrial biosphere include a large variety of processes and mechanisms, and have increased in complexity in the last decades. These models are no exception of the simulation versus understanding conundrum previously articulated for models of the physical climate, which states that increasing detail in process representation in models, and the simulations they produce, hinders understanding of holistic system behavior. However, recent theoretical progress on the mathematical representation of the carbon cycle in ecosystems may help to provide a general framework for the qualitative understanding of models without compromising detail in process representation. Here we (1) briefly review recent ideas on the theory of transient dynamics of the terrestrial carbon cycle and its matrix representation, pointing out issues of interpretation, (2) show that these ideas can be further generalized in the mathematical concept of nonautonomous compartmental systems, and (3) provide thoughts on how this framework can be used to address a new set of questions in carbon cycle science.

Changes in Biomass Turnover Times in Tropical Forests and Their Environmental Drivers From 2001 to 2012

“…On the other hand, it is still disputable in how to represent τ , and most studies used mass/flux as an approximation, which may largely reflect the changes in turnover rate. To better represent τ , differences in turnover processes among various carbon pools (Lu et al., 2018; Sierra et al., 2018) should be considered. To our knowledge, there is no large‐scale observation based data to explicitly represent turnover processes of multiple pools and the carbon transit time is only possibly calculated by some process‐based models, some specific field experiments or with the help of stable isotopes (Lu et al., 2018).…”

Accelerated terrestrial ecosystem carbon turnover and its drivers

“… is the total system influx. It should be noted that this is a general linear nonautonomous system representation for dynamic carbon cycle processes, and vectors in the matrix equation are time dependent (Sierra, Ceballos‐Núñez, Metzler, & Müller, 2018). Furthermore, the matrix expression can be applied to the ecosystem, or separately for the vegetation or soil systems.…”

The climate benefit of carbon sequestration

“…System age and transit time are closely related to the complexity of the ecosystem and its process rates, which are affected by the environment (Luo et al, 2017;Rasmussen et al, 2016;Sierra et al, 2017;Lu et al, 2018). Mean system ages of carbon are consistently greater than mean transit time (Lu et al, 2018;Sierra et al, 2018b), suggesting that once a mass of carbon enters an ecosystem a large proportion gets quickly released back to the atmosphere, but a small proportion remains for very long times. Furthermore, differences in transit times across ecosystems suggest that not all carbon sequestered in the terrestrial biosphere spends the same amount of time stored; e.g., one unit of photosynthesized carbon is returned back to the atmosphere faster in a tropical than in a boreal forest (Lu et al, 2018).…”