| Forecast calibration or post-processing has become a standard tool in atmospheric and
climatological science due to the presence of systematic initial condition and model errors.
For ensemble forecasts the most competitive methods derive from the assumption of a fixed
ensemble distribution. However, when independently applying such “statistical”
methods at different locations, lead times or for multiple variables the correlation
structure for individual ensemble members is destroyed. Instead of reastablishing the
correlation structure as in Schefzik et al. (2013) we instead propose a calibration
method that avoids such problem by correcting each ensemble member individually.
Moreover, we analyse the fundamental mechanisms by which the probabilistic
ensemble skill can be enhanced. In terms of continuous ranked probability score, our
member-by-member approach amounts to skill gain that extends for lead times
far beyond the error doubling time and which is as good as the one of the most
competitive statistical approach, non-homogeneous Gaussian regression (Gneiting et al.
2005). Besides the conservation of correlation structure, additional benefits arise
including the fact that higher-order ensemble moments like kurtosis and skewness are
inherited from the uncorrected forecasts. Our detailed analysis is performed in the
context of the Kuramoto-Sivashinsky equation and different simple models but
the results extent succesfully to the ensemble forecast of the European Centre for
Medium-Range Weather Forecasts (Van Schaeybroeck and Vannitsem, 2013, 2014)
.
References
[1]Gneiting, T., Raftery, A. E., Westveld, A., Goldman, T., 2005: Calibrated
probabilistic forecasting using ensemble model output statistics and minimum
CRPS estimation. Mon. Weather Rev. 133, 1098-1118.
[2]Schefzik, R., T.L. Thorarinsdottir, and T. Gneiting, 2013: Uncertainty
Quantification in Complex Simulation Models Using Ensemble Copula
Coupling. To appear in Statistical Science 28.
[3]Van Schaeybroeck, B., and S. Vannitsem, 2013: Reliable probabilities
through statistical post-processing of ensemble forecasts. Proceedings of the
European Conference on Complex Systems 2012, Springer proceedings on
complexity, XVI, p. 347-352.
[4]Van Schaeybroeck, B., and S. Vannitsem, 2014: Ensemble post-processing
using member-by-member approaches: theoretical aspects, under review. |