Identification of an appropriate low flow forecast model\ud for the Meuse River

This study investigates the selection of an appropriate low flow forecast model for the Meuse\ud River based on the comparison of output uncertainties of different models. For this purpose, three data\ud driven models have been developed for the Meuse River: a multivariate ARMAX model, a linear regression\ud model and an Artificial Neural Network (ANN) model. The uncertainty in these three models is assumed to\ud be represented by the difference between observed and simulated discharge. The results show that the ANN\ud low flow forecast model with one or two input variables(s) performed slightly better than the other statistical\ud models when forecasting low flows for a lead time of seven days. The approach for the selection of an\ud appropriate low flow forecast model adopted in this study can be used for other lead times and river basins\ud as well

Emulation of multivariate simulators using thin-plate splines with application to atmospheric dispersion

It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer simulator taking into account output structure in the responses. The utility of this approach is demonstrated by applying it to a chemical and biological hazard prediction model. Predicting the hazard area which results from an accidental or deliberate chemical or biological release is imperative in civil and military planning and also in emergency response. The hazard area resulting from such a release is highly structured in space and we therefore propose the use of a thin-plate spline to capture the spatial structure and fit a Gaussian process emulator to the coefficients of the resultant basis functions. We compare and contrast four different techniques for emulating multivariate output: dimension-reduction using (i) a fully Bayesian approach with a principal component basis, (ii) a fully Bayesian approach with a thin-plate spline basis, assuming that the basis coefficients are independent, and (iii) a “plug-in” Bayesian approach with a thin-plate spline basis and a separable covariance structure; and (iv) a functional data modeling approach using a tensor-product (separable) Gaussian process. We develop methodology for the two thin-plate spline emulators and demonstrate that these emulators significantly outperform the principal component emulator. Further, the separable thin-plate spline emulator, which accounts for the dependence between basis coefficients, provides substantially more realistic quantification of uncertainty, and is also computationally more tractable, allowing fast emulation. For high resolution output data, it also offers substantial predictive and computational ad- vantages over the tensor-product Gaussian process emulator