Bayesian calibration of the VSD soil acidification model using European forest monitoring data

Abstract

Over the past years, Bayesian calibration methods have been successfully applied to calibrate ecosystem models. Bayesian methods combine prior probability distributions of model parameters, based on assumptions about their magnitude and uncertainty, with estimates of the likelihood of the simulation results by comparison with observed values. Bayesian methods also quantify the uncertainty in the updated posterior parameters, which can be used to perform an analysis of model output uncertainty. In this paper, we apply Bayesian techniques to calibrate the VSD soil acidification model for 182 intensively monitored forest sites in Europe. Prior distributions for the model parameters were based on available literature. Since the available literature shows a strong dependence of some VSD parameters on, for example, soil texture, prior distributions were allowed to depend on soil group (i.e. group of soils with similar texture or C/N ratio). The likelihood was computed by comparing modelled soil solution concentrations with observed concentrations for the period 1996-2001. Markov Chain Monte Carlo (MCMC) was used to sample the posterior parameter space. Two calibration approaches were applied. In the singe-site calibration, the plots are calibrated separately to obtain plot-specific posterior distributions. In the multi-site approach priors are assumed constant in space for each soil group, and all plots are calibrated simultaneously yielding one posterior probability distribution for each soil group.Results from the single-site calibrations show that the model performs much better after calibration compared to a run with standard input parameters. Posterior distributions for HAl equilibrium constants narrow down, thus decreasing parameter uncertainty. For base cation weathering of coarse texture soils the posterior distribution is shifted to larger values, indicating an initial underestimation of the weathering rate for these soils. Results for the 2 parameters related to nitrogen modelling show that the nitrogen processes model formulations in VSD may have to be reconsidered as no evidence is found for a relationship between nitrogen immobilization and the C/N ratio of the soil, as assumed in VSD. The multi-site calibration also strongly decreases model error for most model output parameters, but model error is larger than the median model error from the singe-site calibration.Because the large number of plots calibrated at the same time provides very many observations, the Markov chain converges to a very narrow parameter space, leaving little room for posterior parameter uncertainty. For an uncertainty analysis with VSD on the European scale, this study provides promising results, but more work is needed to investigate how the results can be used on a European scale by looking at regional patterns in calibrated parameters from the site calibration or by calibrating for regions instead of all of Europe.

Toward a Bayesian procedure for using process-based models in plant breeding, with application to ideotype design

“…PBMs are more commonly parameterised site-specifically, even when multiple sites are examined in the same study (e.g. Lehuger et al 2009, but see Reinds et al 2008 Fig. 4 Yields (g m -2 ) for each of the six within-rotation harvests, averaged over all three-year long rotations that were simulated (1995-1997, 1998-2000, ..., 2010-2012).…”

Application of the Bayesian calibration methodology for the parameter estimation in CoupModel

“…Further information about data acquisition can be derived from Conrad and Fohrer (2009b). Observed soil solution concentrations can vary considerably, and measurement uncertainty is affected most likely by the spatial variability within the plot (Reinds et al, 2008). De Vries et al (1999 reported a spatial variability of measured soil solution concentrations between 20-60% depending on depth and type of ion in forest soils from the Netherlands.…”

“…De Vries et al (1999 reported a spatial variability of measured soil solution concentrations between 20-60% depending on depth and type of ion in forest soils from the Netherlands. In Reinds et al (2008), an uncertainty of 30% was used for major ions at 40-60 cm depth for the Dutch forest plots. For low concentrations that are often measured for NO 3 or aluminium, the measurement uncertainty is probably higher than 30%.…”

“…Until recently, calibration of highly parameterized models was performed by an intensive sensitivity analysis and fitting modeling results to measurements by "trial and error" procedure until observed values were reproduced well. Several procedures such as single, multiple or sequential parameter calibration procedures to optimize process-based models were tested, but the uncertainty in model input parameters and observations were not taken into account (Reinds et al, 2008). Consequently, only that parameter setting resulting in the best agreement between model and observations was accepted.…”

“…The updated parameter uncertainty can be used to analyze model output uncertainty. Reinds et al (2008) defined the Bayesian calibration as a twofold extension of Maximum Likelihood estimation including prior information about input parameters and indentifying a single parameter vector with maximum probability and its uncertainty estimate. The Bayesian calibration technique was applied in this study to optimize the CoupModel (Jansson and Karlberg, 2004) on two different grassland systems in Northern Germany.…”