Towards better representations of carbon allocation in vegetation: a conceptual framework and mathematical tool

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.

Contrasting carbon cycle along tropical forest aridity gradients in W Africa and Amazonia

“…Further differences between Amazonian and West African forest carbon cycling were revealed in an investigation of photosynthate allocation into canopy, fine root, and wood NPP and respiration (see Figure 3 for definition). Note that this is the partitioning of productivity and metabolic activity instead of the more commonly reported partitioning of biomass 48 . In both regions, the allocation pattern of autotrophic respiration is more homogeneous across plots than the allocation of NPP (i.e., points in Figure 3a are more clustered than in Figure 3b).…”

The fate and transit time of carbon in a tropical forest

“…ecosystem. Linear first order models of differential equations are the most common representation of carbon dynamics in ecosystem and land surface models (Luo and Weng, 2011;Luo et al, 2017;Huang et al, 2018;Ceballos-Núñez et al, 2020). These linear autonomous compartmental systems at equilibrium have steady-state carbon stocks equivalent to…”

“…Since we are concerned in this manuscript with tropical old‐growth forests at equilibrium, we will represent carbon dynamics with differential equations in multiple pools using a linear autonomous compartmental system of the formwhere the vector represents total carbon inputs from the atmosphere to ecosystem pools, and the matrix represents all cycling and transfer rates of carbon within the ecosystem. Linear first order models of differential equations are the most common representation of carbon dynamics in ecosystem and land surface models (Ceballos‐Núñez et al, 2020; Huang et al, 2018; Luo & Weng, 2011; Luo et al, 2017). These linear autonomous compartmental systems at equilibrium have steady‐state carbon stocks equivalent toAt this equilibrium point, where inputs from photosynthesis are balanced by losses from ecosystem respiration, it is possible to compute the fate of carbon inputs entering at an arbitrary time , defined as the trajectory of photosynthetically fixed carbon through the network of ecosystem compartments.…”

Matrix Approach to Land Carbon Cycle Modeling

“…Alternatively, μ ( t ) can be simulated by a “top‐down” approach based on the linear relationship between photosynthesis and canopy absorbed radiation (light‐use efficiency; Running et al., 2004), as in the CASA model (Potter et al., 1993). Plant carbon allocation B has been represented with diverse schemes, including fixed coefficients, functional relationships, resource limitation and optimization, for different models (Ceballos‐Núñez et al., 2020; De Kauwe et al., 2014; Xia et al., 2017). The carbon transfer elements of matrix A are usually fixed as constants or vary with plant traits or soil texture as in the CENTURY model (Xia et al., 2013).…”