New publication “Gradient-Boosted Mixture Regression Models for Postprocessing Ensemble Weather Forecasts” in Environmetrics!

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Traditional statistical postprocessing models for weather forecasts, such as the Ensemble Model Output Statistics (EMOS; Gneiting et al. (2005)), typically assume a single unimodal predictive distribution. This assumption may fail to adequately capture important features of the raw ensemble forecasts, such as skewness, or multimodality. Mixture regression models, such as the Bayesian model averaging (Raftery et al. 2005), have been proposed in this field to address these limitations. However, their estimation frameworks are generally not well suited to settings with a large number of covariates.

Key Contributions

In the novel publication “Gradient-Boosted Mixture Regression Models for Postprocessing Ensemble Weather Forecasts” (Jobst 2026), we propose a mixture regression model based on standardized anomalies of the response variable and summary statistics of the forecast ensemble. By expressing the variables as standardized anomalies, we first remove their temporal effects. We therefore refer to the resulting model as a mixture of standardized model output statistics (MIXSAMOS). When the model is estimated using gradient boosting, it benefits from data-driven variable selection and provides greater robustness to multicollinearity and overfitting, thereby facilitating the inclusion of a large number of potential predictors. We refer to this gradient-boosted version as MIXSAMOS-GB. We compare the performance of MIXSAMOS and MIXSAMOS-GB against two alternative postprocessing models: SAMOS-GB, which applies the EMOS framework to standardized anomalies within a gradient-boosting setting, and quantile regression forests (QRF). The models are evaluated at 280 observation stations for surface temperature in Germany.

Key Findings

• MIXSAMOS-GB provides the best forecasts in terms of the mean continuous ranked probability score, mean logarithmic score and mean absolute error.
• MIXSAMOS-GB provides the best calibrated forecasts, however also produces less sharp forecasts than SAMOS-GB.
• Adaptive mixture weights contribute to a more explainable modeling of sudden temperature changes.

Figure 1: 2m surface temperature predictive PDF of the raw ensemble (black line), SAMOS(-GB) (green line) and MIXSAMOS(-GB) (blue line) with corresponding CRPS in brackets. The red lines illustrate the observation, the gray dotted and dashed lines represent the deterministic ensemble mean and control forecast, respectively. The blue dotted and dashed lines represent the mixture component corresponding to the first and second group of MIXSAMOS(-GB), respectively. Figure reproduced from Jobst (2026), released under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

References

Gneiting, Tilmann, Adrian E. Raftery, Anton H. Westveld, and Tom Goldman. 2005. “Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation.” Monthly Weather Review 133 (5): 1098–118. https://doi.org/10.1175/mwr2904.1.

Jobst, David. 2026. “Gradient-Boosted Mixture Regression Models for Postprocessing Ensemble Weather Forecasts.” Environmetrics 37 (6): e70145. https://doi.org/10.1002/env.70145.

Raftery, Adrian E., Tilmann Gneiting, Fadoua Balabdaoui, and Michael Polakowski. 2005. “Using Bayesian Model Averaging to Calibrate Forecast Ensembles.” Monthly Weather Review 133 (5): 1155–74. https://doi.org/10.1175/mwr2906.1.