Workshop on
Climate Change and Extreme Value Theory
May 11-13, 2009, 2009
EURANDOM & KNMI, The Netherlands|
Anthony Davison, EPFL
Geostatistics of extremes
Statistical methods for the analysis of independent extremes are now well-developed and widely used. However methods for the analysis of extremes of spatial and spatio-temporal data are much less well-developed. One approach that has been proposed is based on the application of Bayesian computational tools to extremal models, but this seems unsatisfactory because the usual formulation involves independence assumptions that contradict obvious properties of spatial extremes. It seems more natural to attempt to fit max-stable processes, which extend the classical extreme-value distributions in a natural way, but progress on this approach has been blocked until recently because of a lack of flexible models for spatial max-stable processes and because of difficulties in fitting the available models. In this talk I shall describe several families of models and outline how they may be fitted, with applications to a dataset on temperature extremes in the Alps. The work is joint with Mehdi Gholamrezaee.
Doug Nychka, National Center for Atmospheric
Research, Boulder, Colorado
Joint work with Stephen Sain and Linda Mearns
The distribution of precipitation over space from radar and models
As attention on climate change shifts from a global scale to local effects it becomes more important to quantify the full distribution of meteorological variables. Changes in the tails of meteorological variables, rather than just characterizing shifts in the mean are often more relevant for assessing economic and societal impacts Although it useful to apply extreme value theory to estimate the probability of large events it is often difficult to estimate rare occurrences due to short data lengths both in the observational record and from regional climate model simulations. As an alternative we suggest a nonparametric estimate of the probability density that blends a logspline model for the central portion of the density with a parametric Pareto form for the tails. This approach can characterize extremes in the distribution and avoid some of the sensitivity to choosing thresholds for fitting a parametric model directly to the tail. The method is illustrated on a unique 12 year gridded daily precipitation data set assembled from Doppler radar observations for the US. This is compared to daily precipitation simulated by regional climate models that are part of the NARCCAP numerical experiments. One challenge in this project is the comparison of distributions across space and functional data techniques are used for dimension reduction.
Gabi Hegerl, School of Geosciences University of Edinburgh
Making Sense of Observed Trends in temperature extremes
Climate change is expected to change the probability of daily temperature extremes, such as that of unusually hot or cold days and nights. However, results from work attributing observed changes to causes to date have been confusing. Some aspects of the temperature distribution have shifted more than others, showing changes that are more unusual compared to internal variability and are easier to attribute to external forcing than other aspects of the temperature distribution. Also, there are strong regional variations in observed changes in temperature extremes. This talk discusses reasons for these differences, and reviews some recent results on attributing changes in temperature extremes.
Many factors can influence temperature variability. The projected changes in coupled climate models indicate that only in very few locations it is expected that the tail of the temperature distribution simply shifts with seasonal mean temperatures. Changes in circulation influence hot and cold tails of the distribution and also daily minimum and maximum temperatures differently. Circulation exerts a quite strong influence on daily temperature extremes worldwide. Secondly, the available moisture influences how temperature extremes change. An example is the pattern of change in Southeastern US temperatures, where the number of hot days has been decreasing over the recent few decades. This decrease appears to relate to climatological precipitation, with a clear and strong seasonal cycle to the strength of this relationship, peaking in late spring. In other regions, changes in extremes appear to coincide with changes in aerosols and other factors. These results suggest that for reliable predictions of changes in tails of the temperature distribution, climate models need to be driven by a complete set of all forcings influencing regional climate, including aerosols and land use change, and need to be able to correctly predict changes in circulation. Despite these caveats, it can be shown that at least some aspects of the extreme temperature distribution have already changed due to anthropogenic influences.
Albert Klein Tank, KNMI
Guidelines on extremes in a changing climate
Climate change makes it likely that there will be change in some extremes that lie outside the envelope of constant variability assumed under stationary climate conditions. It is possible to account for this "non-stationarity", but the best way to do this is still under debate. Nevertheless, adaptation strategies should begin to take into account the observed and projected changes in extremes. In this paper a new guidance document on this topic will be presented and discussed, which has been prepared for the World Meteorological Organization (WMO).
Rolf-Dieter Reiss and Ulf Cormann, Universität Siegen
Statistical Models for Exceedances under Covariate Information
Holger Rootzén, Chalmers and Gothenburg University
Joint work with Clive Anderson, Anne-Laure Fougéres, Sture Holm,
Jacques de Maré, John Nolan, Olivier Perrin, and Roger Taessler
Extreme Value Statistics for geosciences: The Block maxima vs the Peaks over Thresholds method; the multivariate Generalized Pareto distribution; and mixture models for spatial extremes
Extreme value theory is the statistical methodology of choice for extreme occurrences – large economic fluctuations, floods, hurricanes, extreme waves, small p-values in gene expression experiments, very long life spans … The one-dimensional theory is by now well developed, and available and carefully packaged in books and software. The first topic of the talk is use of the one-dimensional Block Maxima method for a Swedish wind storm data set, and a review of results comparing it with the Peaks over Thresholds method.
In contrast, research on multivariate methods for extremes is intense. The second topic is the definition, properties, estimation and use of a new family of distributions, the Multivariate Generalized Pareto distributions. These are the natural distributions for exceedances over high thresholds. They describe what happens to all of the components when one or more of them exceed their threshold(s). We also touch on recent results of Hall, Peng, and Tajvidi on prediction intervals for extreme values. Wind storm insurance is used as a motivating problem for this part.
The third topic is a report on ongoing research on a new class of “stable mixture models for spatial extremes”. Here the results are much less definitive, but, prospects are exciting, we believe.
Richard L Smith, University of North Carolina, USA
Extreme precipitation trends over the United States
We consider the problem of estimating trends in 25-year return values for an environmental variable measured on a large spatial network - specifically, the US daily precipitation network (approximately 5000 active stations). Extreme value distributions are fitted to data from individual stations using the "point process approach" to threshold exceedances, and then combined across stations using spatial statistics. The results confirm what has been derived by different methods in the climatological literature, that there have been increasing trends in the extreme values over the period 1970-1999, but also that there is a complex spatial structure. We also compare the observation-driven results with those computed from climate model data, and discuss future projections using climate models. This is joint work with Amy Grady and Gabi Hegerl.
David B. Stephenson, University of Exeter, UK
Joint work with Renato Vitolo, and Christopher A. T. Ferro
University of Exeter, UK
Clustering of extreme windstorms in Northern Europe
Windstorms are known to exhibit significant temporal clustering in large regions of the Northern Hemisphere. Previous work has shown that such clustering is related to the time-varying effect of large-scale atmospheric patterns (including the North Atlantic Oscillation and the Scandinavian pattern) and that this effect is present for various intensity thresholds (as measured by the maximum vorticity within the storm). The present aim is to perform an analysis of this phenomenon using suitable adaptations of tools from Extreme Value theory. The classical 2D Poisson process approach, also known as the Peak Over Threshold method, is here extended to allow for nonstationarity of the rate and interaction between the rate and the parameters of the Generalised Pareto Distribution for the excess vorticity. This is achieved by introducing suitable covariates in both the rate and the scale parameter of the GPD distribution.
Andreas Sterl, KNMI, NL
Hot temperatures and storm surges: Modelling the change of climate extremes
Due to the anthropogenic increase of greenhouse gases global-mean temperature will rise by 2-4 K during the 21st century, and this temperature rise will be accompanied by changes in other climate variables.
Weather-related threads come from extremes (storms, heat waves, heavy precipitation) rather than from the mean weather (“climate”). Therefore, the socio-economic impacts of a changing climate are not so much determined by the change of the means, but by the accompanying change of the extremes. The central question arising in this respect is whether the extremes change in proportion to the change in the mean, or whether they are larger (or smaller). Mathematically , the question is whether the probability density function (PDF) of the variable in question is just shifting or also changing its shape.
To address this question, KNMI, as part of the Dutch Center for Climate Research (CKO), has conducted a project called ESSENCE (http://www.knmi.nl/~sterl/Essence), in which a stat-of-the-art climate model has been integrated for the period 1950-2100. 17 integrations, starting from slightly different initial conditions, have been performed. This gives enough data to reliably asses (changes of) extreme events. Two examples are presented.
The first example is the 100-year-return value of temperature (T100). In some areas T100 rises up to three times faster than the mean temperature. The cause is an increase of the scale parameter of a GEV distribution fitted to the annual-maxima of temperature. In other words: Extreme temperatures become more extreme. Physically, this is caused by a drying of the soil, which in the future, warmer, climate occurs more often. Even after correcting for a possible model bias,expected values of T100 at the end of this century far exceed 40ºC in many densely-populated regions.
The second example is the hight of storm surges along the Dutch coast, which have been modelled by forcing a surge model with the winds from ESSENCE. The large model ensemble makes it possible to reliably assess the 10,000-year return surge height, which by law is relevant for the coastal defence system. Winds tend to increase slightly in the southern North Sea. However, this increase is due to southwesterly winds which do not lead to high surges along the Dutch coast. Within the model uncertainty, no changes of the 10,000-year return height are found.