Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

a b s t r a c tThe last decade has seen max-stable processes emerge as a powerful tool for the statistical modeling of spatial extremes and there are increasing works using them in a climate framework. One recent utilization of max-stable processes in this context is for conditional simulations that provide empirical distribution of a spatial field conditioned by observed values in some locations. In this work conditional simulations are investigated for the extremal t process taking benefits of its spectral construction.The methodology of conditional simulations proposed by Dombry et al. (2013) for Brown-Resnick and Schlather models is adapted for the extremal t process with some original improvements which enlarge the possible number of conditional points. A simulation study enables to highlight the role of the different parameters of the model and to emphasize the importance of the steps of the algorithm.An application is performed on precipitation data in the south of France where extreme precipitation events (Cevenol) may generate major floods. This shows that the model and the algorithm perform well provided the stationary assumptions are fulfilled.

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“…Nevertheless, when F denotes a GEV distribution, a closed-form expression exists (Friederichs and Thorarinsdottir, 2012).…”

Section: Comparison Criteriamentioning

confidence: 99%

Conditional simulations of the extremal t process: Application to fields of extreme precipitation

Bechler

Bel

Vrac³

2015

Spatial Statistics

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“…However, this method is widely used in the literature Friederichs and Thorarinsdottir, 2012;Wilks, 2011) to estimate confidence intervals as it does not require assumptions on the distribution.…”

Section: Estimating Uncertainty In the Skill Scoresmentioning

confidence: 99%

Hydrological drought forecasting and skill assessment for the Limpopo River basin, southern Africa

Trambauer

Werner

Winsemius

et al. 2015

Hydrol. Earth Syst. Sci.

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Abstract. Ensemble hydrological predictions are normally obtained by forcing hydrological models with ensembles of atmospheric forecasts produced by numerical weather prediction models. To be of practical value to water users, such forecasts should not only be sufficiently skilful, they should also provide information that is relevant to the decisions end users make. The semi-arid Limpopo Basin in southern Africa has experienced severe droughts in the past, resulting in crop failure, economic losses and the need for humanitarian aid. In this paper we address the seasonal prediction of hydrological drought in the Limpopo River basin by testing three proposed forecasting systems (FS) that can provide operational guidance to reservoir operators and water managers at the seasonal timescale. All three FS include a distributed hydrological model of the basin, which is forced with either (i) a global atmospheric model forecast (ECMWF seasonal forecast system -S4), (ii) the commonly applied ensemble streamflow prediction approach (ESP) using resampled historical data, or (iii) a conditional ESP approach (ESPcond) that is conditional on the ENSO (El Niño-Southern Oscillation) signal. We determine the skill of the three systems in predicting streamflow and commonly used drought indices. We also assess the skill in predicting indicators that are meaningful to local end users in the basin. FS_S4 shows moderate skill for all lead times (3, 4, and 5 months) and aggregation periods. FS_ESP also performs better than climatology for the shorter lead times, but with lower skill than FS_S4. FS_ESPcond shows intermediate skill compared to the other two FS, though its skill is shown to be more robust. The skill of FS_ESP and FS_ESPcond is found to decrease rapidly with increasing lead time when compared to FS_S4. The results show that both FS_S4 and FS_ESPcond have good potential for seasonal hydrological drought forecasting in the Limpopo River basin, which is encouraging in the context of providing better operational guidance to water users.

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“…with Grimit et al (2006) p i=1 ω i = 1, ω i=1,..., p > 0 Generalized extreme value: Y ∼ G E V (μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Generalized Pareto: Y ∼ G P D(μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Log-normal: ln(Y ) ∼ N (μ, σ ) Baran and Lerch (2015) Normal: Y ∼ N (μ, σ ) Gneiting et al (2005) Square-root truncated normal: √ Y ∼ N 0 (μ, σ ) Hemri et al (2014) Truncated normal: Y ∼ N 0 (μ, σ ) Thorarinsdottir and Gneiting (2010) The reference of the original article where to find the formula is also given. Taillardat et al (2016) gathers the closed form expression of the CRPS for these and other distributions in Appendix A, this score for an ensemble is minimized if all the members x i equal the median of F, which is obviously not the purpose of an ensemble.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Continuous Ranked Probability Score with Limited Information and Applications to Ensemble Weather Forecasts

Zamo

Naveau

2017

Math Geosci

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The continuous ranked probability score (CRPS) is a much used measure of performance for probabilistic forecasts of a scalar observation. It is a quadratic measure of the difference between the forecast cumulative distribution function (CDF) and the empirical CDF of the observation. Analytic formulations of the CRPS can be derived for most classical parametric distributions, and be used to assess the efficiency of different CRPS estimators. When the true forecast CDF is not fully known, but represented as an ensemble of values, the CRPS is estimated with some error. Thus, using the CRPS to compare parametric probabilistic forecasts with ensemble forecasts may be misleading due to the unknown error of the estimated CRPS for the ensemble. With simulated data, the impact of the type of the verified ensemble (a random sample or a set of quantiles) on the CRPS estimation is studied. Based on these simulations, recommendations are issued to choose the most accurate CRPS estimator according to the type of ensemble. The interest of these recommendations is illustrated with real ensemble weather forecasts. Also, relationships between several estimators of the CRPS are demonstrated and used to explain the differences of accuracy between the estimators.

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Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

Cited by 90 publications

References 47 publications

Conditional simulations of the extremal t process: Application to fields of extreme precipitation

Conditional simulations of the extremal t process: Application to fields of extreme precipitation

Hydrological drought forecasting and skill assessment for the Limpopo River basin, southern Africa

Estimation of the Continuous Ranked Probability Score with Limited Information and Applications to Ensemble Weather Forecasts

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