Calibration of short-range global radiation ensemble forecasts Zied Ben Bouallègue, Tobias Heppelmann 3rd International Conference Energy & Meteorology Boulder, Colorado USA June 2015
Outline EWeLiNE: improving weather forecasts for energy applications COSMO-DE-Ensemble Prediction System Calibration of ensemble forecasts Outlook and summary
EWeLiNE DWD Weatherforecast IWES TSOs Feedback Powerforecast
Ensemble Prediction System COSMO-DE-EPS based on COSMO-DE x = 2.8 km operational (since May 2012)
Ensemble Prediction System COSMO-DE-EPS based on COSMO-DE x = 2.8 km operational (since May 2012) 20 ensemble members forecast 27 hours 45 hours (3 UTC)
Ensemble Prediction System COSMO-DE-EPS based on COSMO-DE x = 2.8 km operational (since May 2012) 20 ensemble members forecast 27 hours 45 hours (3 UTC) Global radiation Observations: Pyranometers, 32 stations, hourly, quality controlled Verification period: spring 2013, 1 to 18h lead time
Raw forecasts Examples: Station Arkona, April 18 2013, 03UTC run (a) raw ensemble (b) quantile forecasts Red: observations
Raw forecasts Examples: Station Arkona, April 21 2013, 03UTC run (a) raw ensemble (b) quantile forecasts Red: observations
Raw forecasts Examples: Station Arkona, April 26 2013, 03UTC run (a) raw ensemble (b) quantile forecasts Red: observations
Raw forecasts Verification results: Rank Histogram: Spring 2013, 3UTC run, 8h lead time U shape : underdispersiveness and/or combination of biases Need for calibration
Calibration concept Correct statistical inconsistencies of a forecast based on past data Y: observation, predictand X: forecast, predictors Training dataset: rolling window
Calibration method Quantile regression (QR) [ Koenker and Basset 1978 ]
Standard calibration Quantile regression (QR) predictors : global radiation (GR), GR², radiation at the top of the atmosphere (TOA) training: 45 day rolling window before after Rank Histogram: spring 2013, 3UTC run, 8h lead time
Standard calibration Example: Station Arkona, April18 2013, 03UTC run (a) quantile forecasts (b) calibrated quantile forecasts Red: observations before after Reliable probabilistic forecasts
Weather dependent calibration Additional predictors Ensemble mean forecast at each station (grid point)
Weather dependent calibration Predictors in the probability space F(xi) : cumulative distribution from the training period for predictor xi Interaction terms as predictors F(x1) F(x2), F(x1) F(x3), Multiplicative model in order to better capture weather conditions
Weather dependent calibration Quantile regression (QR) [ Koenker and Basset 1978 ] Least absolute shrinkage and selection operator (lasso) [ Tibshirani 1996 ] Penalized quantile regression (PQR) Penalized quantile regression in probability space (PQRPS)
Weather dependent calibration (PQRPS) Regularization set-up Continuous ranked probability skill score (CRPSS): Reference: calibrated forecast with a 45-day training period and no regularization Training period: 45 days (black) 90 days (orange) Regularization allows to avoid over-fitting
Weather dependent calibration (PQRPS) Selection of predictors, diagnostic Regression coefficients as function of the quantile probability level Mean over spring 2013 Horizon: 1 to 18h
Weather dependent calibration (PQRPS) Examples: Station Arkona, April 18 2013, 03UTC run Calibrated quantile forecasts with (a) QR (b) PQRPS Red: observations
Weather dependent calibration (PQRPS) Examples: Station Arkona, April 21 2013, 03UTC run Calibrated quantile forecasts with (a) QR (b) PQRPS Red: observations
Weather dependent calibration (PQRPS) Examples: Station Arkona, April 26 2013, 03UTC run Calibrated quantile forecasts with (a) QR (b) PQRPS Red: observations
Verification results Quantile skill score (QSS) PQRPS (PQR) vs QR PQRPS vs raw ensemble QSS as a function of the probability, spring 2013, 3UTC run, 8h lead time
Verification results Discrimination ability Discrimination ability of quantile forecasts estimated with the area under the Relative User Characteristic (RUC) curve [ Ben Bouallègue et al. 2015] RUCSS: gain in discrimination with respect to a a reference forecast RUCSS as a function of the probability, spring 2013, 3UTC run, 8h lead time. PQRPS compared to QR PQRPS improves the forecast information content
Outlook Generation of scenarios based on calibrated forecasts Retrieval of spatial and temporal structures of the forecast uncertainty after calibration Example: Station Arkona, April18 2013, 03UTC run (a) raw ensemble (b) calibrated quantile forecasts Ensemble copula coupling, Schaake shuffle, autoregressive approaches
Summary EWeLiNE Aims at improving the weather forecasts to support the integration of renewable energy COSMO-DE-EPS High resolution ensemble prediction system operational at DWD Ensemble global radiation forecasts Useful information but statistical inconsistencies Calibration with quantile regression Provides reliable ensemble forecasts Penalized Quantile Regression in the Probability Space : Penalization for forecast diagnostic and predictor selection, in the probability space for an efficient weather dependent calibration Better than the standard approach (improves the forecast information content)
References 1. Ben Bouallègue, Z. (accepted). Assessing COSMO-DE-EPS global radiation forecasts towards energy applications. Mausam. 2. Ben Bouallègue, Z., Pinson P. and Friederichs P. (submitted). Quantile forecast discrimination ability and value. Q.J.R. Meteorol. Soc. 3. Gebhardt C., Theis S. E., Paulat M. and Ben Bouallègue Z. (2011). Uncertainties in COSMO-DE precipitation forecasts introduced by model perturbations and variation of lateral boundaries. Atmos. Res. 4. Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica. 5. Peralta, C., Ben Bouallègue Z., Theis S. E., and Gebhardt C. (2012). Accounting for initial condition uncertainties in COSMO-DE-EPS. Journal of Geophysical Research. 6. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B.