Learning low-dimensional representations of ensemble forecast fields using autoencoder-based methods
Jieyu Chen, Kevin Höhlein, Sebastian Lerch
TL;DR
This paper tackles the challenge of processing high-dimensional ensemble forecast fields by learning probabilistic, low-dimensional representations that respect the ensemble's stochastic nature. It introduces two framework families: a two-step approach (PCA or autoencoder-based per-member reduction followed by Gaussian fusion in latent space) and an invariant variational autoencoder (iVAE) that enforces permutation invariance across ensemble members and learns a distributional latent representation. Evaluated on a decade of ECMWF European forecasts for 2-m temperature and 10-m wind components, all methods can reconstruct spatial structure, but the iVAE most accurately preserves ensemble variability, especially at lower latent dimensions; PCA catches variance better at high latent dimensions. The work highlights trade-offs between reconstruction quality, probabilistic fidelity, and computational cost, and points toward integrating these representations into downstream tasks like post-processing or hydrological/energy forecasting, with future extensions to multi-variable and spatio-temporal ensembles.
Abstract
Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using discrete gridded representations of the physical variables and dynamics. Uncertainties are assessed by running the simulations multiple times, yielding ensembles of simulated fields as a high-dimensional stochastic representation of the forecast distribution. The high-dimensionality and large volume of ensemble datasets poses major computing challenges for subsequent forecasting stages. Data-driven dimensionality reduction techniques could help to reduce the data volume before further processing by learning meaningful and compact representations. However, existing dimensionality reduction methods are typically designed for deterministic and single-valued inputs, and thus cannot handle ensemble data from multiple randomized simulations. In this study, we propose novel dimensionality reduction approaches specifically tailored to the format of ensemble forecast fields. We present two alternative frameworks, which yield low-dimensional representations of ensemble forecasts while respecting their probabilistic character. The first approach derives a distribution-based representation of an input ensemble by applying standard dimensionality reduction techniques in a member-by-member fashion and merging the member representations into a joint parametric distribution model. The second approach achieves a similar representation by encoding all members jointly using a tailored variational autoencoder. We evaluate and compare both approaches in a case study using 10 years of temperature and wind speed forecasts over Europe. The approaches preserve key spatial and statistical characteristics of the ensemble and enable probabilistic reconstructions of the forecast fields.