Estimating the full distribution of climate variables is essential for statistical climate modeling. However, existing approaches struggle with high-dimensional climate fields: classical distributional regression, such as quantile regression, cannot handle multivariate response variables, while modern generative models such as diffusion models are computationally demanding in high dimensions. We introduce engression, a simple yet powerful method for distributional learning. As an unsupervised extension, we present Distributional Principal Autoencoders, a dimension reduction approach that preserves the original data distribution in its reconstructions and captures meaningful structures in its embeddings, such as the seasonal cycle for precipitations. Building on these techniques, we develop a generative framework, EnScale, for statistical downscaling, i.e., emulation of regional climate models. EnScale jointly emulates multiple variables—temperature, precipitation, solar radiation, and wind—maintaining spatial consistency across Central Europe. It accurately estimates full distributions while remaining significantly more computationally efficient than both physical climate models and diffusion-based models.
This is joint work with Nicolai Meinshausen, Maybritt Schillinger, Maxim Samarin, and Reto Knutti.
Xinwei Shen is an assistant professor in the Department of Statistics at the University of Washington. Her research interests include distributional learning, causality, robustness, and applications in climate science.
