Probabilistic Machine Learning for Short-Term Atmospheric Seeing Forecasting
Authors: Mary-Joe Medlej, Rahul Srinivasan, Simon Prunet, Aziz Ziad, Christophe Giordano
Organizations: Universit´e Cˆote d’Azur, Observatoire de la Cˆote d’Azur, J.L. Lagrange, Parc Valrose 06108 Nice Cedex 2, France · SISSA, Via Bonomea 265, 34136 Trieste, Italy · IFPU - Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
Accurate short-term forecasting of atmospheric seeing is of significant interest for astronomical observations and free-space optical communication systems, where rapid variations in optical turbulence can affect system performance and operational planning. In this work, we benchmark machine learning models for predicting atmospheric seeing up to two hours in advance, with a particular focus on probabilistic forecasting and uncertainty quantification. We compare two probabilistic approaches, Gaussian Processes (GPs) and a normalizing-flow- based model (FloTS), against deterministic recurrent neural network (RNN) and long short-term memory (LSTM) baselines. All models are trained and evaluated on seeing measurements from the Maunakea summit. We assess the models using both deterministic metrics, including the root mean square error and the Pearson correlation coefficient, and probabilistic metrics that evaluate the quality and calibration of predictive uncertainty estimates. The results show that deep learning approaches outperform standard recurrent networks for short-term forecasting, with LSTM and FloTS achieving the best overall predictive accuracy. While Gaussian Processes provide a useful probabilistic baseline, their predictive distributions are limited by the Gaussian assumption. FloTS combines competitive forecasting accuracy with flexible uncertainty quantification and produces the most informative probabilistic forecasts.
Figures & tables
Figure 1: Heatmap of combined forecast performance for each model over a 2-hour lookback window across forecast horizons. Each cell reports RMSE (top) and correlation (bottom, in parentheses). The background colour represents a composite performance score computed as the equally weighted average of min–max normalised RMSE (inverted) and correlation, where a score of 1 indicates the best performance and 0 the worst across all models and time steps. Red borders highlight the two best overall models, LSTM and FloTS, which consistently achieve the highest composite scores across all forecast horizons.
Figure 2: Comparison of the FloTS seeing prediction before and after calibration for the August case study. The top panel shows the uncalibrated prediction, while the bottom panel shows the calibrated prediction. In each panel, the left side shows the input sequence used for forecasting, and the right side displays the two-hour forecast horizon. The black curve indicates the observed target sequence, while the red, purple, and green dashed curves show the GP, RNN, and LSTM predictions, respectively. The heatmap represents the probability density predicted by FloTS . For visualization, the density is normalized independently at each forecast timestep. Calibration redistributes probability mass within the predictive density, modifying both the dispersion and the local non-Gaussian structure of the forecast distribution.
Probabilistic time series forecasting estimates distributions of future values or trajectories to quantify uncertainty and support risk-aware decisions.
Despite their high accuracy on point-wise metrics, machine learning weather forecasting models can exhibit different failure modes such as blurring, periodic irregularities, and other unphysical spatial artifacts. This has motivated a variety of metrics to detect known failure cases. Existing metrics fix a representation or transformation in advance, and that choice limits the artifacts they can detect. We propose to train a discriminator for separating reference data from the model's output, and using its output logit to obtain a divergence-like realism score. The discriminator learns whatever separates the model's fields from real weather, adapting to whichever failure mode that model exhibits. We compare our learned atmospheric critic to existing metrics using various synthetic corruptions applied to ERA5 reanalysis data. Our method successfully identifies the corruptions and ranks their severity, while existing metrics fail on at least one corruption. Additionally, we evaluate forecasts from real weather models, and find that the realism score degrades with longer lead times and the metric generally assigns higher realism to numerical models than to machine learning models.
Younes Elberkennou, Dmitri Demler, Thierry Meier +3
ETH Zürich, Switzerland · ETH AI Center, ETH Zürich, Switzerland
The bottleneck of Earth Observation processing chains is not the arrival of new imagery but whether the surface is actually visible when the image arrives. We study this as an observability forecasting problem on EarthNet2021. Given recent multispectral imagery and exogenous weather drivers, the goal is to predict whether the next acquisition will be usable and, if not, when a usable view is likely to return. To do this, we adapt LeWorldModel, a joint-embedding predictive architecture world model, to cloud-aware Earth Observation sequences. The final pipeline converts raw minicubes into episodic HDF5 sequences with five image channels (blue, green, red, near-infrared, cloud mask) and eight meteorological and calendar covariates. The resulting model has 18.0M trainable parameters and is trained from scratch on 23,904 training episodes. The trained leWorldModel is evaluated under a locked protocol: linear probes are fit on train only, calibration choices are set on an internal validation split, and the fitted heads are then frozen for valsplit, IID, OOD, and extreme evaluation. On the full frozen-bundle observability benchmark, LeWorldModel consistently outperforms persistence. For next-step usability, balanced accuracy ranges from 0.769 to 0.887, compared with 0.493 to 0.556 for persistence. For exact first-usable-horizon prediction, accuracy ranges from 0.602 to 0.806, compared with 0.120 to 0.369 for persistence. Against a frozen LightGBM baseline fit on the same training windows, LeWorldModel is better on continuous clear/cloud regression and on exact recovery timing on valsplit, IID, and extreme, while LightGBM is stronger on the simpler binary any-usable-within-six task and is more robust on OOD. In separate sampled diagnostic analyses, LeWM also produces strong ranking-based anomaly signals under synthetic temporal inconsistencies.
Mohanad Albughdadi
European Centre for Medium-Range Weather Forecasts
Numerical weather prediction has long been constrained by the computational bottlenecks inherent in data assimilation and numerical modeling. While machine learning has accelerated forecasting, existing models largely serve as "emulators of reanalysis products," thereby retaining their systematic biases and operational latencies. Here, we present FuXiWeather2, a unified end-to-end neural framework for assimilation and forecasting. We align training objectives directly with a combination of real-world observations and reanalysis data, enabling the framework to effectively rectify inherent errors within reanalysis products. To address the distribution shift between NWP-derived background inputs during training and self-generated backgrounds during deployment, we introduce a recursive unrolling training method to enhance the precision and stability of analysis generation. Furthermore, our model is trained on a hybrid dataset of raw and simulated observations to mitigate the impact of observational distribution inconsistency. FuXiWeather2 generates high-resolution (0.25∘) global analysis fields and 10-day forecasts within minutes. The analysis fields surpass the NCEP-GFS across most variables and demonstrate superior accuracy over both ERA5 and the ECMWF-HRES system in lower-tropospheric and surface variables. These high-quality analysis fields drive deterministic forecasts that exceed the skill of the HRES system in 91% of evaluated metrics. Additionally, its outstanding performance in typhoon track prediction underscores its practical value for rapid response to extreme weather events. The FuXiWeather2 analysis dataset is available at https://doi.org/10.5281/zenodo.18872728.
Xiaoze Xu, Xiuyu Sun, Songling Zhu +5
Shanghai Academy of Artificial Intelligence for Science, Shanghai, & 200232, China. · Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai & 200433, China. · FuXi Intelligent Computing Technology Co., Ltd., Shanghai & 200233, China.