A dynamical systems analysis of the data assimilation linked ecosystem carbon (DALEC) models

Abstract

Changes in our climate and environment make it ever more important to understand the processes involved in Earth systems, such as the carbon cycle. There are many models that attempt to describe and predict the behaviour of carbon stocks and stores but, despite their complexity, significant uncertainties remain. We consider the qualitative behaviour of one of the simplest carbon cycle models, the Data Assimilation Linked Ecosystem Carbon (DALEC) model, which is a simple vegetation model of processes involved in the carbon cycle of forests, and consider in detail the dynamical structure of the model. Our analysis shows that the dynamics of both evergreen and deciduous forests in DALEC are dependent on a few key parameters and it is possible to find a limit point where there is stable sustainable behaviour on one side but unsustainable conditions on the other side. The fact that typical parameter values reside close to this limit point highlights the difficulty of predicting even the correct trend without sufficient data and has implications for the use of data assimilation methods. We show that the DALEC model contains a transition point where, for parameters on one side forests thrive, but on the other they die. Analysing data from two forests we find that they sit near the transition point, and we hypothesize that this is a natural consequence of a tree's need to optimize its resources.Such transition points are important because, in a changing world, we expect parameter values to drift. Drifting across a transition point can have serious consequences and results in "tipping" from one kind of behaviour to another.For example, a shift in the amount of rainfall could induce tipping from a sustainable forest to a forests that dies. The presence of such transition points also has important consequences for prediction. Models often contain many parameters that need to be determined, usually by fitting to data. Different algorithms used to fit models to data typically lead to slightly different values for parameters.Away from transition points for non-chaotic systems, this usually means that there is some small uncertainty in the parameter values that leads to a small uncertainty in prediction. However, near transitions points, small differences in parameter values can lead to very different predictions.

Balancing multiple constraints in model‐data integration: Weights and the parameter block approach

“…DALEC considers a labile pool in vegetation, which is replenished by carbon from leaves before senescence and fuels the leaf production in the next spring. The labile pool is largely decoupled from forest biomass dynamics [ Chuter , ].…”

Constraining DALEC v2 using multiple data streams and ecological constraints: analysis and application

“…As shown in Chuter et al (2015) for the previous DALEC evergreen and deciduous models, the evolution of the carbon pools for DALECv2 show a tipping point which depends on the parameters 490 p 1 to p 17 . Given a set of parameters p the fast carbon pools C lab , C f , C r and C l grow or decay rapidly to an equilibrium state.…”

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

“…The work of Williams et al (2005) established the benefit of using DALEC together with net ecosystem exchange (NEE) of CO 2 measurements in a Bayesian framework to estimate initial carbon stocks and model parameters, to improve flux predictions for ecosystem models and to quantify uncertainties. Inter-comparison experiments (Fox et al, 2009;Hill et al, 2012) have then demonstrated the relative merit of various inverse modelling strategies using NEE and MODIS leaf area index observations: most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. Other studies have tried to overcome this difficulty by adding complementary data streams (see Richardson et al (2010)) or by considering longer observation windows (see Hill et al (2012)).…”