Reconstructing historical daily weather fields using a deep-learning variational auto-encoder

To study historical weather extremes and their impacts, as well as the evolution of weather variability over time, gridded reconstructions of daily weather are of great importance. However, prior to the establishment of national meteorological services, starting in Europe in the second half of the 19^th century, observations from which to derive such reconstructions are greatly limited. As a result, traditional spatial-interpolation approaches such as inverse-distance weighting are unreliable in this context. Numerical weather prediction models that assimilate available observations are also unfavourable, because of their high computational demand. A promising alternative is the application of deep-learning models, which have already been shown to produce reliable reconstructions with relatively little cost. Given the wide range of possible deep-learning architectures, further studies into their application for historical weather reconstruction continue to be valuable.

 

In this study we present a deep-learning model based on a variational auto-encoder (VAE) architecture for reconstructing fields of mean daily air temperature and mean-sea-level pressure across Europe. While the use of VAEs for weather reconstruction has previously been proposed, to our knowledge no such studies have been published in the literature. Our model is trained using ERA5 data for the domain 36N-67N, 22W-41E, aggregated to a daily, 1° resolution. During training, the model’s encoder takes the complete fields of temperature and pressure for a given day and reduces them to a simplified representation within the model’s latent space. The model’s decoder then takes this as input and attempts to recreate the original fields. Once trained, the encoder is then discarded and the latent space is instead sampled iteratively such that the decoded set of output fields best matches any available observations from a given day of interest. This output then represents the reconstruction of that day.

 

To evaluate performance, we apply our model to reconstruct the year 1807 using 25 historical temperature records and 18 historical pressure records. The reconstruction is then compared to a separate set of hold-out records from the same year. We also apply our model to a test period of 1950-1954 using ERA5 pseudo-observations with the same availability as above. This is then compared to the corresponding complete fields of ERA5. Additionally, we examine the performance of the model relative to the daily re-analysis dataset 20CRv3 and to an existing deep-learning model WeRec3D inspired by video inpainting.

 

For 1807, our model performs relatively well in reconstructing the hold-out records, achieving correlations and root-mean-squared errors similar to or better than those of WeRec3D and 20CRv3 for each variable. On the other hand, when considering the entire study domain for the period 1950-1954, our model performs notably worse than WeRec3D with a greater reconstruction error, under-represented variance and overly smooth reconstructed fields. This is especially pronounced towards the edges of the domain where observations are particularly sparse. Thus, our model is ultimately not superior to an existing alternative. Nevertheless, this study successfully demonstrates the application of a VAE for the task of historical weather reconstruction and provides a foundation for further investigation.