Advances in statistical post-processing of weather forecasts, probabilistic forecasting, and modelling of extreme events

Accurate weather forecasts are crucial for a variety of applications. These forecasts are usually generated by ensembles of numerical weather prediction (NWP) models, which give a probabilistic estimate of future weather. However, these ensembles might have biases and errors in dispersion, thus necessitating the application of statistical corrections -- so-called statistical post-processing. In this thesis, I will make some methodological contributions to improved statistical post-processing of ensemble forecasts, with a particular focus on extreme events; together with contributions more generally for the probabilistic forecasting and modelling of extremes. I first address the problem of post-processing of forecasts across multiple lead times. Standard approaches fit separate models at each lead time, which is computationally expensive and limits both the usability of individual models and the amount of training data available. I demonstrate that there is regularity across models fitted for different lead times and propose lead-time-continuous post-processing models that operate across multiple lead times simultaneously. These models substantially reduce computational cost and show improved performance in small-data settings, both overall and for extremes. I then turn more concretely to the question of how to improve forecasts for extreme events. I propose to do so by adjusting model training. In particular, I propose to estimate the parameters of ensemble model output statistics (EMOS) -- a popular post-processing method -- using the threshold-weighted continuous ranked probability score (twCRPS), a proper scoring rule that puts special emphasis on extreme events. I show that this training approach improves forecasts for extreme wind speeds; however, it comes with a trade-off whereby improved tail performance leads to worse forecasts for the main body of the climatological distribution. I introduce strategies to mitigate this trade-off. Subsequently, I investigate the calibration of extreme event forecasts more closely. While probabilistic forecasts need to be sharp, they must also be calibrated to be useful for decision making. This also holds for forecasts of extremes. Using a notion of tail calibration I show that multiple state-of-the-art probabilistic post-processing methods fail to issue calibrated forecasts for high winds. To address this, I propose regularising tail calibration during training and contrast this with twCRPS-based penalisation. I show that this regularisation yields forecasts that are better tail calibrated, but trade-offs emerge between overall probabilistic calibration and tail calibration. Finally, one can also improve probabilistic forecasts for high-impact events using more flexible model structures, particularly suited to extremes. Thus, I propose a number of generative deep learning approaches for the modelling of the dependence structure of multivariate extremes. I showcase on simulated and real data the effectiveness of these methods and contrast them with a classical parametric approach. Whilst this considers unconditional modelling, it establishes a framework that can be extended to conditional modelling and forecasting in the future.<p></p>

Author dc:creator

• Jakob Wessel (21066059)

• weather forecasts
• numerical weather prediction (NWP) models

Statement dc:rights

• All rights reserved

Identifier

10779/exe.32805089.v1

OAI identifier oai:identifier

oai:figshare.com:article/32805089