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Process-based forest models generally have many parameters, multiple outputs of interest and a small underlying empirical database. These characteristics hamper parameterization. Bayesian calibration offers a solution to the calibration problem because it applies to models of any type or size. It provides parameter estimates, with measures of uncertainty and correlation among the parameters. The procedure begins by quantifying the uncertainty about parameter values in the form of a prior probability distribution. Then data on the output variables are used to update the parameter distribution by means of Bayes' Theorem. This yields a posterior calibrated distribution for the parameters, which can be summarized in the form of a mean vector and variance matrix. The predictive uncertainty of the model can be quantified by running it with different parameter settings, sampled from the posterior distribution. In a further step, one may evaluate the posterior probability of the model itself (rather than that of the parameters) and compare that against the probability of other models, to aid in model selection or improvement. Bayesian calibration of process-based models cannot be performed analytically, so the posterior parameter distribution must be approximated in the form of a representative sample of parameter values. This can be achieved by means of Markov Chain Monte Carlo simulation, which is suitable for process-based models because of its simplicity and because it does not require advance knowledge of the shape of the posterior distribution. Despite the suitability of Bayesian calibration, the technique has rarely been used in forestry research. We introduce the method, using the example of a typical forest model. Further, we show that reductions in parameter uncertainty, and thus in output uncertainty, can be effected by increasing the variety of data, increasing the accuracy of measurements and increasing the length of time series.

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In a recent study, Magnani et al. report how atmospheric nitrogen deposition drives stand-lifetime net ecosystem productivity (NEP av ) for midlatitude forests, with an extremely high C to N response (725 kg C kg À1 wet-deposited N for their European sites). We present here a re-analysis of these data, which suggests a much smaller C : N response for total N inputs. Accounting for dry, as well as wet N deposition reduces the C : N response to 177 : 1. However, if covariance with intersite climatological differences is accounted for, the actual C : N response in this dataset may be o70 : 1. We then use a model analysis of 22 European forest stands to simulate the findings of Magnani et al. Multisite regression of simulated NEP av vs. total N deposition reproduces a high C : N response (149 : 1). However, once the effects of intersite climatological differences are accounted for, the value is again found to be much smaller, pointing to a real C : N response of about 50-75 : 1.

egetation dynamics involves processes operating at widely different spatial and temporal scales, from stomatal opening and closing (minutes to days, at the leaf level) to biome shifts (decades to centuries, across entire continents). Tremendous research efforts have been devoted to understanding and predicting how plant processes and functional traits of individuals combine to determine the structure, function and dynamics of vegetation on larger scales. To integrate process understanding from different disciplines, dynamic vegetation models (DVMs) have been developed that combine elements from plant biogeography, biogeochemistry, plant physiology, forest ecology and micrometeorology. The best-known DVMs, dynamic global vegetation models (DGVMs), have found a wide field of application, including assessments of land-atmosphere carbon, water and trace gas exchanges; water resources; impacts of environmental change on plants and ecosystems; land management; and feedbacks from vegetation changes to regional and global climates 1,2. DVMs have also been applied on local scales for testing of ecological hypotheses and to answer practical questions in forest management and agriculture. All DVMs are based on the assumption of universally valid processes, which, in principle, enable them to make predictions under conditions outside the range of observations used for model development.