Applying emulators for improved flood risk analysis Sajni Malde

Testo completo

(1)E3S Web of Conferences 7, 04002 (2016) FLOODrisk 2016 - 3rd European Conference on Flood Risk Management. DOI: 10.1051/ e3sconf/2016 0704002. Applying emulators for improved flood risk analysis 1,a. 1. 2. 1. 1. Sajni Malde , David Wyncoll , Jeremy Oakley , Nigel Tozer and Ben Gouldby 1. HR Wallingford, Howbery Business Park, Wallingford, Oxfordshire OX10 8BA, UK The University of Sheffield, School of Mathematics and Statistics, Sheffield, South Yorkshire S10 2TN, UK. 2. Abstract. Flood risk analysis often involves the integration of multivariate probability distributions over a domain defined by a consequence function. Often, solutions of this risk integral involves Monte-Carlo sampling techniques, .

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(7) each sampled event. A significant computational time is required in running flood related physical process models, making it computationally impractical to evaluate flood risk using this approach. To overcome the computational challenges, this paper focusses on the Gaussian Process Emulator (GPE) meta-modelling approach. Traditionally, a -

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(11) are required. This approach typically involves simulating conditions defined across a regular matrix, and then linearly interpolating intermediate conditions. In this paper we compare a traditional -approach to the GPE and analyse their performance in approximating SWAN wave transformation model. In both cases, selecting an appropriate training design set is important and is taken into consideration in the analysis. The analysis shows that the GPE approach requires significantly fewer SWAN runs to obtain similar (or better) accuracies, enabling a substantial reduction in computation time, hence aiding the practicality of Monte-Carlo sampling techniques in advanced flood risk modelling.. 1 Introduction and background Flood risk is generally recognized as the product of probability and consequence where the probability relates to probabilities of flood hazards e.g. extreme rainfall, river flows, coastal waves and sea levels or multivariate combinations of these variables. The probability can also relate to the performance of flood defence infrastructure and likelihood of failure. By definition, flood risk analysis involves the integration of multivariate probability distributions over a domain defined by a consequence function. Often, solutions of this risk integral involve the use of Monte-Carlo sampling

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(14) events are generated through statistical sampling techniques. It is, in principal, necessary to evaluate the consequence of flooding for each of these sampled events. There is, however, typically a significant computational time involved in running physical process models that are capable of simulating the consequences of flooding. It can therefore become computationally impractical to evaluate flood risk using this approach. Coastal flood risk in the UK is recognized to relate to both extreme offshore waves, winds (local windgeneration) and sea levels. To evaluate coastal flood risk it is therefore necessary to extrapolate these variables to extreme values, whilst accounting for the dependency between the variables. There are various methods that have been employed to do this. A robust multivariate a. extreme value approach is described by [1], and this has been implemented in coastal flood risk analysis by [2,3,4]. The output of the method is a Monte-Carlo

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(18) potential to cause coastal flooding. For each event it is required to model the transformation of waves from offshore to nearshore, wave overtopping, flood inundation and impact. Various models exist for undertaking this analysis. It is however, computationally challenging and impractical to execute all the models for each event. To overcome the computational challenges in practice, a few representative training events are simulated and the rest of the events are evaluated using various approximation techniques. Traditionally, within

(19) ! #$%&' based on a number of training events selected from a regular grid is used. These training events conditions are simulated and used to approximate the SWAN model using linear interpolation to evaluate intermediate conditions. More recently, advances in research show that more efficient and accurate meta-modelling approaches can be applied. These approaches include: Piecewise Polynomials, Neural Networks, and Gaussian Process Emulators (GPE). This paper focusses on the GPE metamodelling approach which has been shown to have advantages over other approaches [5]. Suppose, there exists a large set of pre-selected events, , that a model needs to be evaluated at. Each. Corresponding author: S.Malde@hrwallingford.com. © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/)..

(20) E3S Web of Conferences 7, 04002 (2016) FLOODrisk 2016 - 3rd European Conference on Flood Risk Management. DOI: 10.1051/ e3sconf/2016 0704002. 2.2 The Proposed GPE Approach. model run is however, computationally intensive, and thus time consuming to evaluate. The objective of this analysis is to minimize the number of model runs, , required in order to estimate the model evaluations at all events in to an appropriate degree of approximation. The case study used in this paper uses data generated from the SWAN model. This model is a third generation spectral wave model for obtaining realistic estimates of wave parameters in coastal areas, lakes and estuaries from given wind, bottom and current conditions, [6]. The model can compute how waves transform across the model domain by taking into consideration different tidal, wave and wind boundary conditions. The output of SWAN includes several parameters describing the properties of the wave at a given near shore location. Each model run can take up to few hours to evaluate. This paper extends analysis undertaken by Camus et al [7-8] and presents an analysis of the benefits of using a GPE of the SWAN spectral wave transformation model - context of a coastal flood risk analysis modelling chain. Additionally, in both cases, selecting appropriate training events is important, hence the efficiency of selecting the training events and the span of the training events are taken into consideration in presenting the analysis..

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(905) #! . 4.. 5.. 6. 7.. 8.. 9.. 6. Heffernan, J.E., and Tawn, J.A. (2004). A conditional approach for multivariate extreme values. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 66(3), 497)546 Lamb, R. . Lamb, R., Keef, C., Tawn, J., Laeger, S., Meadowcroft, I., Surendran, S., Dunning, P. and Batstone, C, (2010). A new method to assess the risk of local and widespread flooding on rivers and coasts. Journal of Flood Risk Management, 3(4): 323)336 Wyncoll D. and Gouldby B. (2014). Integrating a multivariate extreme value method within a system flood risk model, Journal of Flood Risk Management, 8(2), 145)160 Gouldby, B., Mendez, F., Guanche, Y., Rueda, A. and Minguez, R. (2014) A methodology for deriving extreme nearshore sea conditions for structural design and flood risk analysis, Coastal Engineering, Vol. 88, June. Buhmann, M. D. (2004). Radial basis functions: theory and implementations.Cambridge monographs on applied and computational mathematics, 12, 147165. Booij, N et al. (2004). SWAN cycle III version 40.41 user manual. Delft University of Technology 115. Camus, P., Mendez, F.J. and Medina, R. (2011). A hybrid efficient method to downscale wave climate to coastal areas. Coastal Engineering, 58(9): 851862. Camus, P., Mendez, F.J., Medina, R. and Cofiño, A.S. (2011). Analysis of clustering and selection algorithms for the study of multivariate wave climate. Coastal Engineering, 58(6): 453-462. Kennedy, M. C., & O'Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal.

(906) E3S Web of Conferences 7, 04002 (2016) FLOODrisk 2016 - 3rd European Conference on Flood Risk Management. Statistical Society: Series B (Statistical Methodology), 63(3), 425-464. 10. Kennedy, M. C., Anderson, C. W., Conti, S., & * +! , #-. .' /

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