Learning Low‐Dimensional Representations of Ensemble Forecast Fields Using Autoencoder‐Based Methods

Abstract Large‐scale numerical simulations often produce high‐dimensional gridded data, which 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 data sets imposes 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 they 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 efficient generation of additional member forecast fields.