Climate and Social Stress Implications for Security Analysis (2013) / Chapter Skim
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Appendix D: Statistical Methods for Assessing Probabilities of Extreme Events
Appendix D: Statistical Methods for Assessing Probabilities of Extreme Events
Pages 193-202
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From page 193... ...
(2012) provided empirical analyses of temperature means from numerous parts of the world and noted the increasing frequency of extreme events, which they defined as events that are more than three standard deviations from the 1951–1980 mean.
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From page 194... ...
model with time-varying means, one could calculate future extreme event probabilities by simulating the time series many times and calculating the proportion of simulations for which the extreme event of interest occurs. The principal limitation of such methods lies not in the simulation itself, which is fast and accurate using modern computing techniques, but in the structure of the time series model; if this is misspecified, then the extreme value probabilities may be over- or under-estimated by orders of magnitude.
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From page 195... ...
annual temperature averages over a large area of western Europe and used climate models both with and without anthropogenic forcing to estimate the probability of an extreme event under either scenario. Their statistical methodology used a conventional detection and attribution approach to decompose the observational time series into components due to anthropogenic forcing, natural forcing, and internal variability, combined with the Generalized Pareto distribution, fitted to events beyond a high threshold, to estimate probabilities of extreme events.
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From page 196... ...
. Going beyond simple characterizations of extremal dependence, there are a number of formal statistical models that have been used to calculate joint probabilities of extreme events.
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From page 197... ...
This is empirical evidence that there is indeed dependence between the most extreme values in this example. To go further, we have fitted one of the standard extremal dependence models -- the logistic model, for which a detailed methodology based on
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A summary of all the estimates and confidence intervals is in Table D-1. TABLE D-1 Estimates of the Increase in Probability of a Joint Extreme Event in Both Variables, Relative to the Probability Under Independence, for the United States/Uruguay–Argentina Precipitation Data Logistic Model Ramos-Ledford Model Estimate 90% CI Estimate 90% CI 10-year 2.7 (1.2, 4.2)
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From page 199... ...
Using the same data source as for Example 1, we have constructed summer temperature means over Russia and precipitation means over Pakistan corresponding to the spatial areas used by Lau and Kim. Figure D-2 shows a scatterplot; the left-hand plot is of the raw data, and the right-hand plot is of the data after transformation to the unit Fréchet distribution (with the largest values on the original plot corresponding to the largest value on Fréchet scale, because the right-hand tail is of interest here)
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From page 200... ...
This should however be qualified by noting that the dataset used, consisting of monthly averages over half-degree grid cells, cannot be expected to reproduce extreme precipitation events over very short time and spatial scales, and it remains possible that an alternative data source, using finerscale data, would produce a different conclusion. FUTURE RESEARCH NEEDS There is a substantial body of statistical literature on univariate and bivariate extremes and more limited research on extremes in higher dimensions.
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From page 201... ...
For the bivariate case, the main question of interest is one of dependence: whether some underlying process creates a reliable association between the occurrence of an extreme event in one climate variable in one place and the probability of an extreme event in another variable or place. The relatively short length of most observational series limits the extent to which this question can be answered based on observational data.
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From page 202... ...
2011. An alternative point process framework for modeling multivariate extreme values.
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