Towards better representations of carbon allocation in vegetation: a conceptual framework and mathematical tool
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ORIGINAL PAPER
Towards better representations of carbon allocation in vegetation: a conceptual framework and mathematical tool 1 · Carlos A. Sierra1 ´ ˜ 1 · Markus Muller ¨ Veronika Ceballos-Nu´ nez
Received: 8 April 2019 / Accepted: 3 March 2020 © The Author(s) 2020
Abstract The representation of carbon allocation (CA) in ecosystem differs tremendously among models, resulting in diverse responses of carbon cycling and storage to global change. Several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems of model structure. We analyzed the mathematical representation of CA in models using concepts from dynamical systems theory; we reviewed a representative sample of models of CA in vegetation and developed a model database within the Python package bgc-md. We asked whether these representations can be generalized as a linear system, or whether a more general framework is needed to accommodate nonlinearities. Some of the vegetation systems simulated with the reviewed models have a fixed partitioning of photosynthetic products, independent of environmental forcing. Vegetation is often represented as a linear system without storage compartments. Yet, other structures with nonlinearities have also been proposed, with important consequences on the temporal trajectories of ecosystem carbon compartments. The proposed mathematical framework unifies the representation of alternative CA schemes, facilitating their classification according to mathematical properties as well as their potential temporal behaviour. It can represent complex processes in a compact form, which can potentially facilitate dialog among empiricists, theoreticians, and modellers. Keywords Carbon allocation · Ecosystem models · Nonlinearities · Compartmental systems
Introduction Current and expected changes in climate and atmospheric CO2 concentration have prompted the study of the mechanisms used by vegetation to survive to changing environmental conditions. One of these mechanisms is the adjustment of their carbon allocation scheme (Lacointe 2000; Franklin et al. 2012; Xia et al. 2017). Carbon allocation is a concept that involves all carbon cycle– related processes that take place within vegetation such as the following: the assimilation of atmospheric CO2 Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12080-020-00455-w) contains supplementary material, which is available to authorized users. Ver´onika Ceballos-N´un˜ ez
[email protected] Carlos A. Sierra [email protected] 1
Max Planck Institute for Biogeochemistry, Hans-Kn¨oll-Str. 10, 07745, Jena, Germany
via photosynthesis; the partitioning of the photosynthetic assimilates to vegetation parts (from here on compartments) for growth or for other processes such as maintenance, defence, and storage; and the time carbon atoms remain in the vegetation before being released back to the atmosphere (Lacointe 2000; Schimel et al. 2001; Trumbore 2006; Canadell
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