Terrestrial carbon cycle: Ecological and mathematical properties

Background/Question/Methods:

Terrestrial ecosystems play a crucial role in the global carbon cycle and in the regulation of climate change. Anthropogenic CO₂ emissions increased from 2.4 Petagram (Pg) C in 1960 to 8.7 Pg C per year in 2008 while terrestrial ecosystems absorbed roughly 30% during that period. If that absorption capacity were to change, in either direction, it would have a large impact on atmospheric CO₂ concentrations, resulting in a strong feedback effect on climate.  It is, therefore, imperative to accurately predict dynamics of the terrestrial carbon cycle in order to accurately predict future changes in the Earth’s climate. To date, the magnitude of the terrestrial carbon sink has been deduced indirectly: combining analyses of atmospheric carbon dioxide concentrations with ocean observations to infer the net terrestrial carbon flux. In contrast, when knowledge about the terrestrial carbon cycle is integrated into different terrestrial carbon models they make widely different predictions and fit observations poorly. The lack of predictive ability of the terrestrial carbon cycle models prompts us to examine the ecological and mathematical properties of the terrestrial carbon cycle so as to understand fundamental constraints on model predictions.

Results/Conclusions: Phenomenologically, the dynamics of the terrestrial carbon cycle appear very rich, exhibiting fluctuations, directional changes, and tipping points. These occur because multiple environmental forcing variables interact with internal carbon cycle processes to cause diverse dynamics over different temporal and spatial scales. However, the internal processes are in fact relatively simple and can be characterized by five fundamental properties: (1) compartmentalization of carbon within distinct pools; (2) photosynthesis as the dominant carbon input; (3) partitioning of that photosynthetic input between the various pools; (4) donor pool-dominated carbon transfers between pools; and (5) the first-order decay of litter and soil organic matter to release CO₂ via respiration.  These fundamental properties are common to all ecosystems on Earth. The five properties together define a general mathematical model and result in an emergent constraint that carbon pools tend to converge monotonically over time to some form of equilibrium. The mathematical model describes a nonautonomous system that is strongly regulated by time-varying inputs and influences of external forcing. This model has opened up many new ways to analyze the terrestrial carbon cycle and its responses to climate change.