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November 2013 Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling
Roman Schefzik, Thordis L. Thorarinsdottir, Tilmann Gneiting
Statist. Sci. 28(4): 616-640 (November 2013). DOI: 10.1214/13-STS443


Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples. There is a strongly increasing recognition of the need for uncertainty quantification in such settings, for which we propose and review a general multi-stage procedure called ensemble copula coupling (ECC), proceeding as follows:

1. Generate a raw ensemble, consisting of multiple runs of the computer model that differ in the inputs or model parameters in suitable ways.

2. Apply statistical postprocessing techniques, such as Bayesian model averaging or nonhomogeneous regression, to correct for systematic errors in the raw ensemble, to obtain calibrated and sharp predictive distributions for each univariate output variable individually.

3. Draw a sample from each postprocessed predictive distribution.

4. Rearrange the sampled values in the rank order structure of the raw ensemble to obtain the ECC postprocessed ensemble.

The use of ensembles and statistical postprocessing have become routine in weather forecasting over the past decade. We show that seemingly unrelated, recent advances can be interpreted, fused and consolidated within the framework of ECC, the common thread being the adoption of the empirical copula of the raw ensemble. Depending on the use of Quantiles, Random draws or Transformations at the sampling stage, we distinguish the ECC-Q, ECC-R and ECC-T variants, respectively. We also describe relations to the Schaake shuffle and extant copula-based techniques. In a case study, the ECC approach is applied to predictions of temperature, pressure, precipitation and wind over Germany, based on the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble.


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Roman Schefzik. Thordis L. Thorarinsdottir. Tilmann Gneiting. "Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling." Statist. Sci. 28 (4) 616 - 640, November 2013.


Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1331.62265
MathSciNet: MR3161590
Digital Object Identifier: 10.1214/13-STS443

Keywords: Bayesian model averaging , empirical copula , ensemble calibration , nonhomogeneous regression , numerical weather prediction , probabilistic forecast , Schaake shuffle , Sklar’s theorem

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.28 • No. 4 • November 2013
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