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.