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Jakob W. Messner and Georg J. Mayr

Abstract

Three methods to make probabilistic weather forecasts by using analogs are presented and tested. The basic idea of these methods is that finding similar NWP model forecasts to the current one in an archive of past forecasts and taking the corresponding analyses as prediction should remove all systematic errors of the model. Furthermore, this statistical postprocessing can convert NWP forecasts to forecasts for point locations and easily turn deterministic forecasts into probabilistic ones. These methods are tested in the idealized Lorenz96 system and compared to a benchmark bracket formed by ensemble relative frequencies from direct model output and logistic regression. The analog methods excel at longer lead times.

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Jakob W. Messner and Georg J. Mayr
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Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Raw ensemble forecasts of precipitation amounts and their forecast uncertainty have large errors, especially in mountainous regions where the modeled topography in the numerical weather prediction model and real topography differ most. Therefore, statistical postprocessing is typically applied to obtain automatically corrected weather forecasts. This study applies the nonhomogenous regression framework as a state-of-the-art ensemble postprocessing technique to predict a full forecast distribution and improves its forecast performance with three statistical refinements. First of all, a novel split-type approach effectively accounts for unanimous zero precipitation predictions of the global ensemble model of the ECMWF. Additionally, the statistical model uses a censored logistic distribution to deal with the heavy tails of precipitation amounts. Finally, it is investigated which are the most suitable link functions for the optimization of regression coefficients for the scale parameter. These three refinements are tested for 10 stations in a small area of the European Alps for lead times from +24 to +144 h and accumulation periods of 24 and 6 h. Together, they improve probabilistic forecasts for precipitation amounts as well as the probability of precipitation events over the default postprocessing method. The improvements are largest for the shorter accumulation periods and shorter lead times, where the information of unanimous ensemble predictions is more important.

Open access
Markus Dabernig, Georg J. Mayr, and Jakob W. Messner

Abstract

Energy traders and decision-makers need accurate wind power forecasts. For this purpose, numerical weather predictions (NWPs) are often statistically postprocessed to correct systematic errors. This requires a dataset of past forecasts and observations that is often limited by frequent NWP model enhancements that change the statistical model properties. Reforecasts that recompute past forecasts with a recent model provide considerably longer datasets but usually have weaker setups than operational models. This study tests the reforecasts from the National Oceanic and Atmospheric Administration (NOAA) and the European Centre for Medium-Range Weather Forecasts (ECMWF) for wind power predictions. The NOAA reforecast clearly performs worse than the ECMWF reforecast, the operational ECMWF deterministic and ensemble forecasts, and a limited-area model of the Austrian weather service [Zentralanstalt für Meteorologie und Geodynamik (ZAMG)]. On the contrary, the ECMWF reforecast has, of all tested models, the smallest squared errors and one of the highest financial values in an energy market.

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Markus Dabernig, Georg J. Mayr, Jakob W. Messner, and Achim Zeileis

Abstract

Separate statistical models are typically fit for each forecasting lead time to postprocess numerical weather prediction (NWP) ensemble forecasts. Using standardized anomalies of both NWP values and observations eliminates most of the lead-time-specific characteristics so that several lead times can be forecast simultaneously. Standardized anomalies are formed by subtracting a climatological mean and dividing by the climatological standard deviation. Simultaneously postprocessing forecasts between +12 and +120 h increases forecast coherence between lead times, yields a temporal resolution as high as the observation interval (e.g., up to 10 min), and speeds up computation times while achieving a forecast skill comparable to the conventional method.

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Susanne Drechsel, Georg J. Mayr, Jakob W. Messner, and Reto Stauffer

Abstract

Wind speed measurements from one year from meteorological towers and wind turbines at heights between 20 and 250 m for various European sites are analyzed and are compared with operational short-term forecasts of the global ECMWF model. The measurement sites encompass a variety of terrain: offshore, coastal, flat, hilly, and mountainous regions, with low and high vegetation and also urban influences. The strongly differing site characteristics modulate the relative contribution of synoptic-scale and smaller-scale forcing to local wind conditions and thus the performance of the NWP model. The goal of this study was to determine the best-verifying model wind among various standard wind outputs and interpolation methods as well as to reveal its skill relative to the different site characteristics. Highest skill is reached by wind from a neighboring model level, as well as by linearly interpolated wind from neighboring model levels, whereas the frequently applied 10-m wind logarithmically extrapolated to higher elevations yields the largest errors. The logarithmically extrapolated 100-m model wind reaches the best compromise between availability and low cost for data even when the vertical resolution of the model changes. It is a good choice as input for further statistical postprocessing. The amplitude of measured, height-dependent diurnal variations is underestimated by the model. At low levels, the model wind speed is smaller than observed during the day and is higher during the night. At higher elevations, the opposite is the case.

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Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Nonhomogeneous regression is often used to statistically postprocess ensemble forecasts. Usually only ensemble forecasts of the predictand variable are used as input, but other potentially useful information sources are ignored. Although it is straightforward to add further input variables, overfitting can easily deteriorate the forecast performance for increasing numbers of input variables. This paper proposes a boosting algorithm to estimate the regression coefficients, while automatically selecting the most relevant input variables by restricting the coefficients of less important variables to zero. A case study with ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) shows that this approach effectively selects important input variables to clearly improve minimum and maximum temperature predictions at five central European stations.

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Jakob W. Messner, Georg J. Mayr, Daniel S. Wilks, and Achim Zeileis

Abstract

Extended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete categories whereas full predictive distributions were better predicted by censored regression.

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Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, and Achim Zeileis

Abstract

Nonhomogeneous regression models are widely used to statistically postprocess numerical ensemble weather prediction models. Such regression models are capable of forecasting full probability distributions and correcting for ensemble errors in the mean and variance. To estimate the corresponding regression coefficients, minimization of the continuous ranked probability score (CRPS) has widely been used in meteorological postprocessing studies and has often been found to yield more calibrated forecasts compared to maximum likelihood estimation. From a theoretical perspective, both estimators are consistent and should lead to similar results, provided the correct distribution assumption about empirical data. Differences between the estimated values indicate a wrong specification of the regression model. This study compares the two estimators for probabilistic temperature forecasting with nonhomogeneous regression, where results show discrepancies for the classical Gaussian assumption. The heavy-tailed logistic and Student’s t distributions can improve forecast performance in terms of sharpness and calibration, and lead to only minor differences between the estimators employed. Finally, a simulation study confirms the importance of appropriate distribution assumptions and shows that for a correctly specified model the maximum likelihood estimator is slightly more efficient than the CRPS estimator.

Open access
Jakob W. Messner, Georg J. Mayr, Achim Zeileis, and Daniel S. Wilks

Abstract

To achieve well-calibrated probabilistic forecasts, ensemble forecasts are often statistically postprocessed. One recent ensemble-calibration method is extended logistic regression, which extends the popular logistic regression to yield full probability distribution forecasts. Although the purpose of this method is to postprocess ensemble forecasts, usually only the ensemble mean is used as the predictor variable, whereas the ensemble spread is neglected because it does not improve the forecasts. In this study it is shown that when simply used as an ordinary predictor variable in extended logistic regression, the ensemble spread affects the location but not the variance of the predictive distribution. Uncertainty information contained in the ensemble spread is therefore not utilized appropriately. To solve this drawback a new approach is proposed where the ensemble spread is directly used to predict the dispersion of the predictive distribution. With wind speed data and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) it is shown that by using this approach, the ensemble spread can be used effectively to improve forecasts from extended logistic regression.

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