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

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. Bayesianmethods 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 applied Bayesian techniques to calibrate the VSD soil acidification model using data from182 intensively monitored forest sites in Europe. Out of these 182 plots,122 plotswere used to calibrate VSD and the remaining 60 plots to validate the calibratedmodel. 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. 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 approacheswere applied. In the single-site calibration, the plotswere calibrated separately to obtain plot-specific posterior distributions. In themulti-site approach priorswere assumed constant in space for each soil group, and all plotswere calibrated simultaneously yielding one posterior probability distribution for each soil group. Results fromthe single-site calibrations showthat themodel performedmuch better after calibration compared to a run with standard input parameters when validated on the 60 validation plots. Posterior distributions for H-Al equilibrium constants narrowed down, thus decreasing parameter uncertainty. For base cation weathering of coarse textured soils the posterior distribution shifted to larger values, indicating an initial underestimation of the weathering rate for these soils. Results for the parameters related to nitrogenmodelling showed that the nitrogen processes model formulations in VSD may have to be reconsidered as the relationship between nitrogen immobilization and the C/N ratio of the soil, as assumed in VSD, was not substantiated by the validation. The multi-site calibration also strongly decreasedmodel error formostmodel output parameters, butmodel errorwas somewhat larger than themedianmodel error fromthe single-site calibration except for nitrate. Because the large number of plots calibrated at the same time provided very many observations, theMarkov Chain converged to a very narrowparameter 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 howthe results can be used on a European scale by looking at regional patterns in calibrated parameters fromthe site calibration or by calibrating for regions instead of all of Europe.