Abstract. Following the disruption to European airspace caused by the eruption of Eyjafjallajökull in 2010 there has been a move towards producing quantitative predictions of volcanic ash concentration using volcanic ash transport and dispersion simulators. However, there is no formal framework for determining the uncertainties of these predictions and performing many simulations using these complex models is computationally expensive. In this paper a Bayesian linear emulation approach is applied to the Numerical Atmospheric-dispersion Modelling Environment (NAME) to better understand the influence of source and internal model parameters on the simulator output. Emulation is a statistical method for predicting the output of a computer simulator at new parameter choices without actually running the simulator. A multi-level emulation approach is applied using two configurations of NAME with different numbers of model particles. Information from many evaluations of the computationally faster configuration is combined with results from relatively few evaluations of the slower, more accurate, configuration. This approach is effective when it is not possible to run the accurate simulator many times and when there is also little prior knowledge about the influence of parameters. The approach is applied to the mean ash column loading in 75 geographical regions on 14 May 2010. Through this analysis it has been found that the parameters that contribute the most to the output uncertainty are initial plume rise height, mass eruption rate, free tropospheric turbulence levels and precipitation threshold for wet deposition. This information can be used to inform future model development and observational campaigns and routine monitoring. The analysis presented here suggests the need for further observational and theoretical research into parameterisation of atmospheric turbulence. Furthermore it can also be used to inform the most important parameter perturbations for a small operational ensemble of simulations. The use of an emulator also identifies the input and internal parameters that do not contribute significantly to simulator uncertainty. Finally, the analysis highlights that the faster, less accurate, configuration of NAME can, on its own, provide useful information for the problem of predicting average column load over large areas.

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Further information on publisher's website:http://dx.doi.org/10.1007/s10479-011-0968-2Publisher's copyright statement:The original publication is available at www.springerlink.com Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended backward induction to arbitrary choice functions, yielding far more efficient solutions, and we identified simple necessary and sufficient conditions for this to work. In this paper, we show that backward induction works for maximality and E-admissibility, but not for interval dominance and Γ-maximin. We also show that, in some situations, a computationally cheap approximation of a choice function can be used, even if the approximation violates the conditions for backward induction; for instance, interval dominance with backward induction will yield at least all maximal normal form solutions.

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possibility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncertainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.

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