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a b s t r a c tSensitivity Analysis (SA) investigates how the variation in the output of a numerical model can be attributed to variations of its input factors. SA is increasingly being used in environmental modelling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decision-making. In this paper we review the SA literature with the goal of providing: (i) a comprehensive view of SA approaches also in relation to other methodologies for model identification and application; (ii) a systematic classification of the most commonly used SA methods; (iii) practical guidelines for the application of SA. The paper aims at delivering an introduction to SA for non-specialist readers, as well as practical advice with best practice examples from the literature; and at stimulating the discussion within the community of SA developers and users regarding the setting of good practices and on defining priorities for future research.

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.

This paper describes an approach to computing probabilistic assessments of future climate, using a climate model. It clarifies the nature of probability in this context, and illustrates the kinds of judgements that must be made in order for such a prediction to be consistent with the probability calculus. The climate model is seen as a tool for making probabilistic statements about climate itself, necessarily involving an assessment of the model's imperfections. A climate event, such as a 2 • C increase in global mean temperature, is identified with a region of 'climate-space', and the ensemble of model evaluations is used within a numerical integration designed to estimate the probability assigned to that region.

Although computer models are often used for forecasting future outcomes of complex systems, the uncertainties in such forecasts are not usually treated formally. We describe a general Bayesian approach for using a computer model or simulator of a complex system to forecast system outcomes. The approach is based on constructing beliefs derived from a combination of expert judgments and experiments on the computer model. These beliefs, which are systematically updated as we make runs of the computer model, are used for either Bayesian or Bayes linear forecasting for the system. Issues of design and diagnostics are described in the context of forecasting. The methodology is applied to forecasting for an active hydrocarbon reservoir.