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. 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 applied Bayesian techniques to calibrate the VSD soil acidification model using data from 182 intensively monitored forest sites in Europe. Out of these 182 plots, 122 plots were used to calibrate VSD and the remaining 60 plots to validate the calibrated model. 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 approaches were applied. In the single-site calibration, the plots were calibrated separately to obtain plot-specific posterior distributions. In the multi-site approach priors were assumed constant in space for each soil group, and all plots were calibrated simultaneously yielding one posterior probability distribution for each soil group. Results from the single-site calibrations show that the model performed much 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 nitrogen modelling 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 decreased model error for most model output parameters, but model error was somewhat larger than the median model error from the single-site calibration except for nitrate. Because the large number of plots calibrated at the same time provided very many observations, the Markov Chain converged 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