Multivariate Probabilistic Forecasting of Weather Using Joint Distributional Regression

The proposed research aims at developing new statistical methods for gaining multivariate probabilistic information through a numerical weather prediction system. The phrase multivariate probabilistic can be illustrated here by a brief example of its possible use: Multivariate means that a quantity of interest, e.g. temperature, is predicted for several simultaneous points in time or space. Probabilistic means that the degree of confidence is incorporated into the weather prediction. Thus not only the expected temperature is predicted, but also the spread of potential variations of the temperature. Traditionally multivariate post-processing methods sequentially calibrate the (probabilisitc) margins using univariate methods and restore the covariance (i.e. the multivariate information) by so called empirical copulas. The proposed research aims at developing a new framework for single-step multivariate post-processing, which simultaneously models the margins and correlations. The novelty of the approach is the synthesis of joint distributions and distributional regression towards joint distributional regression. In order to be able to develop these new methods, a considerable amount of interdisciplinary effort is required. Thus, the proposed research is centered around the intersection of meteorology and statistics. Knowledge from both fields is indispensable: Firstly, a physical understanding of the atmosphere is crucial and its use in numerical weather prediction. Secondly, statistical methods have to be described theoretically and transferred into computationally efficient software. The new methods will be evaluated for different forecasting problems, e.g. temperature, pressure and wind speed.

Researchers have made groundbreaking advances in weather forecasting, paving the way for more accurate and reliable predictions. By developing a new framework for multivariate post-processing in numerical weather prediction (NWP) ensemble systems, scientists can now model atmospheric parameters and their correlations more effectively. This innovative approach, based on distributional regression and regularisation techniques, ensures physically consistent forecasts and improves our understanding of complex weather patterns. In addition, the integration of machine learning methods with classical statistical modelling has led to weather-adaptive post-processing that improves forecast accuracy while requiring smaller training data sets. These breakthroughs have broader implications, including the estimation of lightning climatologies, enabling a deeper understanding of lightning occurrence and its response to changing climate. These advances are critical for disaster management, climate adaptation and risk assessment, and are driving progress in atmospheric and environmental sciences.