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Physically coherent probabilistic weather forecasts using multivariate discrete copula-based ensemble postprocessing methods

Schefzik, Roman

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Being able to provide accurate forecasts of future quantities has always been a great human desire and is essential in numerous situations in daily life. Meanwhile, it has become routine to work with probabilistic forecasts in the form of full predictive distributions rather than with single deterministic point forecasts in many disciplines, with weather prediction acting as a key example.

Nowadays, probabilistic weather forecasts are usually constructed from ensemble prediction systems, which consist of multiple runs of numerical weather prediction models differing in the initial conditions and/or the parameterized numerical representation of the atmosphere. The raw ensemble forecasts typically reveal biases and dispersion errors and thus call for statistical postprocessing to realize their full potential. Several ensemble postprocessing methods have been developed and are partly recapitulated in this thesis, yet many of them only apply to a single weather quantity at a single location and for a single prediction horizon. In many applications, however, there is a critical need to account for spatial, temporal and inter-variable dependencies.

To address this, a tool called ensemble copula coupling (ECC) is introduced and examined. Essentially, ECC uses the empirical copula induced by the raw ensemble to aggregate samples from predictive distributions for each location, variable and look-ahead time separately, which are obtained via existing univariate postprocessing methods. The ECC ensemble inherits the multivariate rank dependence pattern from the raw ensemble, thereby capturing the flow dependence.

Several variants and modifications of ECC are studied, and it is demonstrated that the ECC concept provides an overarching frame for existing techniques scattered in the literature.

From a mathematical point of view, it is shown that ECC can be considered a copula approach by pointing out relationships to multivariate discrete copulas, which are introduced in this thesis and for which relevant mathematical properties are derived.

A generalization of standard ECC is introduced, which aggregates samples from not necessarily univariate, but general predictive distributions obtained by low-dimensional postprocessing in an ECC-like manner.

Finally, the SimSchaake approach, which combines the notion of similarity-based ensemble methods with that of the so-called Schaake shuffle, is presented as an alternative to ECC. In this technique, the dependence patterns are based on verifying observations rather than on raw ensemble forecasts as in ECC.

The methods and concepts are illustrated and evaluated based on case studies, using real ensemble forecast data of the European Centre for Medium-Range Weather Forecasts. Essentially, the new multivariate approaches developed in this thesis reveal good predictive performances, thus contributing to improved probabilistic forecasts.

Document type: Dissertation
Supervisor: Gneiting, Prof. Dr. Tilmann
Date of thesis defense: 15 January 2015
Date Deposited: 30 Jan 2015 10:10
Date: 2015
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Dean's Office of The Faculty of Mathematics and Computer Science
The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
DDC-classification: 500 Natural sciences and mathematics
510 Mathematics
Controlled Keywords: Copulas <Mathematical statistics>, Wettervorhersage
Uncontrolled Keywords: probabilistic weather forecasting, ensemble postprocessing, dependence modeling, Schaake shuffle, ensemble copula coupling, discrete copula
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