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

Abstract

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.