Flow matching for in situ, spatially consistent weather forecast downscaling

Weather forecast downscaling, the problem of recovering accurate local predictions given a lower resolution forecast,  is commonly used in operational NWP pipelines. Its purpose is to recover some of the sub-grid processes that could not be represented by the underlying numerical model due to a limited resolution. This misrepresentation provokes statistical mismatches between the observation data gathered from stations and the nearest grid point in the numerical simulation.

Using a downscaling model typically requires making a compromise between spatial consistency and statistical calibration. Traditionally, these models are trained to target a traditional verification metric. Consequently, they suffer from the double penalty issue and fail to correctly model spatial correlation structures by becoming overly smooth. This is detrimental to downstream modeling tasks such as power grid management, which require a good assessment of spatially-correlated phenomena. 

Recently, the finer details of the atmospheric state have successfully been recovered using generative models such as denoising diffusion [2-4]. We propose a similar strategy for in situ downscaling by introducing a flow matching [1] model for that task. A cross-attention transformer [5] backbone allows us to build an internal representation for the gridded numerical forecast as well as the in situ downscaled forecast. 

Our model avoids the numerical instability and mode collapse issues related to Generative Adversarial Networks. It produces well-calibrated forecasts that better represent the spatial correlations between the stations when compared to non-generative alternatives. Our model makes no assumptions about the underlying forecast, and thus can be thought of in two ways. It can be considered a hybrid NWP/AI model, where we first run a numerical simulation and then downscale it. It can also be considered a supplementary forecasting product in a full machine learning pipeline.

Using our flow matching weather forecast downscaling model, we run experiments on the EUPPBench post-processing dataset to predict surface temperature and wind speed. Particular care is given to evaluating the model, where we assess both the marginal performance (via the CRPS, reliability histogram, and spread-error ratio) and the joint performance (via the Energy Score, local Variogram Score and forecast spatial frequency content). The accurate representation of extreme events is evaluated using Brier scores. Further experiments discuss the pitfalls of fitting the Energy Score directly without a generative model.

 

[1] Lipman, Y. et al. (2023) ‘Flow Matching for Generative Modeling’. arXiv. Available at: https://doi.org/10.48550/arXiv.2210.02747.

[2] Couairon, G. et al. (2024) ‘ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecasting’. arXiv. Available at: https://doi.org/10.48550/arXiv.2412.12971.

[3] Price, I. et al. (2023) ‘GenCast: Diffusion-based ensemble forecasting for medium-range weather’. arXiv. Available at: https://doi.org/10.48550/arXiv.2312.15796.

[4] Lang, S. and Chantry, M. (2024) ‘Enter the ensembles’, AIFS Blog, 21 June. Available at: https://www.ecmwf.int/en/about/media-centre/aifs-blog/2024/enter-ensembles (Accessed: 15 January 2025).

[5] Vaswani, A. et al. (2017) ‘Attention is All you Need’, in Advances in Neural Information Processing Systems. Curran Associates, Inc. Available at: https://proceedings.neurips.cc/paper/2017/hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html (Accessed: 17 May 2022).