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  • 1
    Publication Date: 2018-11-08
    Description: Natural hazards, such as European windstorms, have widespread effects that result in insured losses at multiple locations throughout a continent. Multivariate extreme-value statistical models for such environmental phenomena must therefore accommodate very high dimensional spatial data, as well as correctly representing dependence in the extremes to ensure accurate estimation of these losses. Ideally one would employ a flexible model, able to characterise all forms of extremal dependence. However, such models are restricted to a few dozen dimensions, hence an a priori diagnostic approach must be used to identify the dominant form of extremal dependence. Here, we present various approaches for exploring the dominant extremal dependence class in very high dimensional spatial hazard fields: tail dependency measures, copula fits, and conceptual loss distributions. These approaches are illustrated by application to a data set of high-dimensional historical European windstorm footprints (6103 spatial maps of 3-day maximum gust speeds at 14 872 locations). We find there is little evidence of asymptotic extremal dependency in windstorm footprints. Furthermore, empirical extremal properties and conceptual losses are shown to be well reproduced using Gaussian copulas but not by extremally dependent models such as Gumbel copulas. It is conjectured that the lack of asymptotic dependence is a generic property of turbulent flows. These results open up the possibility of using geostatistical Gaussian process models for fast simulation of windstorm hazard fields.
    Print ISSN: 1561-8633
    Electronic ISSN: 1684-9981
    Topics: Geography , Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 2
    Publication Date: 2018-10-24
    Description: This paper discusses how epistemic uncertainties are currently considered in the most widely occurring natural hazard areas, including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. Our aim is to provide an overview of the types of epistemic uncertainty in the analysis of these natural hazards and to discuss how they have been treated so far to bring out some commonalities and differences. The breadth of our study makes it difficult to go into great detail on each aspect covered here; hence the focus lies on providing an overview and on citing key literature. We find that in current probabilistic approaches to the problem, uncertainties are all too often treated as if, at some fundamental level, they are aleatory in nature. This can be a tempting choice when knowledge of more complex structures is difficult to determine but not acknowledging the epistemic nature of many sources of uncertainty will compromise any risk analysis. We do not imply that probabilistic uncertainty estimation necessarily ignores the epistemic nature of uncertainties in natural hazards; expert elicitation for example can be set within a probabilistic framework to do just that. However, we suggest that the use of simple aleatory distributional models, common in current practice, will underestimate the potential variability in assessing hazards, consequences, and risks. A commonality across all approaches is that every analysis is necessarily conditional on the assumptions made about the nature of the sources of epistemic uncertainty. It is therefore important to record the assumptions made and to evaluate their impact on the uncertainty estimate. Additional guidelines for good practice based on this review are suggested in the companion paper (Part 2).
    Print ISSN: 1561-8633
    Electronic ISSN: 1684-9981
    Topics: Geography , Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 3
    Publication Date: 2018-04-23
    Description: Natural hazard loss portfolios with exposure over a region are sensitive to the dependency between extreme values of the key hazard variable at different spatial locations. It is therefore important to correctly identify and quantify dependency to avoid poor quantification of risk. This study demonstrates how bivariate extreme value tail dependency methods can be used together in a novel way to explore and quantify extremal dependency in spatial hazard fields. A relationship between dependency and loss is obtained by deriving how the probability distribution of conceptual loss depends on the tail dependency coefficient. The approaches are illustrated by applying them to 6103 historical European windstorm footprints (spatial maps of 3-day maximum gust speeds). We find there is little evidence of asymptotic extremal dependency in windstorm footprints. Furthermore, empirical extremal properties and conceptual loss distributions between pairs of locations are shown to be well reproduced using Gaussian copulas but not by extremally-dependent models such as Gumbel copulas. It is conjectured that the lack of asymptotic dependence is a generic property of turbulent flows, which may extend to other spatially continuous hazards such as heat waves and air pollution. These results motivate the potential of using Gaussian process (geostatistical) models for efficient simulation of hazard fields.
    Electronic ISSN: 2195-9269
    Topics: Geography , Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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