Bayesian calibration of the Pasture Simulation model (PaSim) to simulate European grasslands under water stress
Introduction
Efforts to model the inherently unknown future behavior of complex, inter-related systems have led to a focus on the uncertainties associated with framing possible future realizations (Butler et al., 2014, Schwanitz, 2013). Ecosystem models are widely used to project impacts of climate changes and to examine options for adaptation by local stakeholders and policymakers (White et al., 2011). The advantage of biophysically complex models is that they provide an integrated system perspective in which vegetation, soil, weather, and management factors dynamically interact to simulate system feedbacks and revise management alternatives. Quite a number of issues have been raised on the uncertainties of the use of ecosystem models in simulating climate change impacts (e.g. Soussana et al., 2010). Reducing uncertainties in model parameters has the potential to reduce the uncertainty in model projections but the knowledge about parameters is often incomplete as the uncertainty inherent in available data to calibrate them is high, and data series are often limited. Moreover, impact assessments often implicitly assume that parameters calibrated under current climate will remain valid under far future conditions. Given fundamental system changes that occur at these time scales, this can be an unrealistic assumption. Complexity of the system and incomplete knowledge about its basic parameter values thus give rise to output variables that are laden with uncertainties and can provide a biased picture of the impacts. Parameter calibration can help in reducing model uncertainties under projected future conditions. The challenge here is in combining techniques to ensure robust parameter estimates in modeling approaches suitable for use under changing conditions, and well-designed experimental trials to represent such conditions.
Grassland ecosystems are the core of our study. Grasslands are a widespread vegetation type, with about 24 million km2 covering nearly one-fifth of the world's land surface (Suttie et al., 2005). They provide a broad range of agronomic services, including the provisioning of forage and, hence, of milk and meat (Huyghe, 2008). They also play a considerable role in Earth cycles by mitigating greenhouse gas emissions through soil organic carbon and nitrogen sequestration (Ciais et al., 2010). In addition, they can be hotspots of biodiversity, which contributes to the temporal stability of these services (Marriott et al., 2004). Grasslands are complex ecosystems, given the many interactions between herbivores, vegetation, soil and the atmosphere, and the role of agricultural practices. Process-based simulation models, providing insight and understanding of these interactions, are therefore widely used in climate change impact projections. We focus our work on the Pasture Simulation model (PaSim) (Ma et al., 2015). Including both grazing and cutting management options, PaSim is able to simulate a variety of grassland ecosystems and has been used in impact studies (e.g. Graux et al., 2013, Vital et al., 2013). Here we extend the uncertainty analysis of PaSim, using a set of experimental sites and Bayesian calibration capabilities. Computational methods rooted in Bayesian statistics have gained popularity, in particular for the analysis of complex problems arising in biological sciences (e.g. in population genetics, Beaumont et al., 2002). There is ever more evidence (e.g. Ramin and Arhonditsis, 2013) that Bayesian tools can provide an effective statistical framework for model calibration. The exercise is done to incorporate as much information as possible from measured data into probability distribution functions of parameter values (prior). A likelihood function derived from a statistical model for the observed data is used (for alternative approaches, see Marjoram et al., 2003, Sisson et al., 2007; and Wegmann et al., 2009) to update the prior distributions using the data (Patenaude et al., 2008, Van Oijen et al., 2005) to obtain a new parameter distribution (posterior). Calibration outcomes are thus characterized by simulated output variables and distributions of a set of model parameters, which are updated from distributional assumptions (prior information) reflecting new information given by experimental data (observation-based constraints). Our purpose is to show that for non-linear, complex ecosystem models such as PaSim, the uncertainties of outputs can be reduced by using Bayesian techniques to calibrate model parameters under climate change-driven altered conditions. In Section 2, we describe PaSim and the Bayesian methods used, as well as metrics of model performance. Illustrative results are presented in Section 3, followed by discussion and conclusions in Section 4.
Section snippets
The grassland model
The deterministic, biogeochemical Pasture Simulation model (PaSim, https://www1.clermont.inra.fr/urep/modeles/pasim.htm) deals with vegetation and major soil processes on a plot-scale configuration. Microclimate, soil biology and physics, vegetation, herbivores, and management are interacting modules. A vegetation module is coupled to a soil biology module derived from CENTURY (Parton et al., 1987), and soil physics equations from Campbell (1985) calculate the water and energy balances. The
Data sets
The data used in this study (Table 1) are from three field experiments in Austria and Switzerland, in which drought was mimicked by intercepting precipitation with transparent sheer roof to study the responses of grassland systems (plant and soil variables) to precipitation exclusion. A control plot that received ambient precipitation was built next to the treatment plot. Harvested biomass is the amount of dry matter that is removed from the field at each cutting event. Leaf area index
Discussion and concluding remarks
We present a framework for proper interpretation of model performance obtained with Bayesian calibration, when applied to a complex model of grassland systems (PaSim) under conditions of altered climate (i.e. precipitation reduction). There are multiple potential foci when designing calibration of a complex ecosystem model depending on the overall question to be answered. We have not identified the most influential parameters, have not come up with a set of parameter values of general validity,
Acknowledgement
The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreements no. 226701 (CARBO-Extreme, http://www.carbo-extreme.eu), no. 266018 (ANIMALCHANGE, http://www.animalchange.eu), and no. 613817 (MODEXTREME, http://modextreme.org). The simulation exercise was run under the auspices of FACCE MACSUR knowledge hub (http://www.macsur.eu). Romain Lardy (French National Institute for Agricultural Research,
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