Short-Term Turbulence Prediction for Seeing Using Machine Learning

Abstract

Optical turbulence, driven by fluctuations of the atmospheric refractive index, poses a significant challenge to ground-based optical systems, as it distorts the propagation of light. This degradation affects both astronomical observations and free-space optical communications. While adaptive optics systems correct turbulence effects in real-time, their reactive nature limits their effectiveness under rapidly changing conditions, underscoring the need for predictive solutions. In this study, we address the problem of short-term turbulence forecasting by leveraging machine learning models to predict the atmospheric seeing parameter up to two hours in advance. We compare statistical and deep learning approaches, with a particular focus on probabilistic models that not only produce accurate forecasts but also quantify predictive uncertainty, crucial for robust decision-making in dynamic environments. Our evaluation includes Gaussian processes (GP) for statistical modeling, recurrent neural networks (RNNs) and long short-term memory networks (LSTMs) as deterministic baselines, and our novel implementation of a normalizing flow for time series (FloTS) as a flexible probabilistic deep learning method. All models are trained exclusively on historical seeing data, allowing for a fair performance comparison. We show that FloTS achieves the best overall balance between predictive accuracy and well-calibrated uncertainty.

Figures (10)

• Figure 1: RMSE for each training duration: 2 hours (blue), 3 hours (orange), 4 hours (green), 5 hours (red), and 6 hours (purple), evaluated over a fixed 2-hour prediction window. Results are shown for all models: RNN, LSTM, GP, and FloTS (FLOW).
• Figure 2: Illustration of the calculation and calibration of the coverage for an example: predictions for +10 and $\pm20$ minutes. Left: examples of different observations (green star) and the corresponding predicted probability distribution shown by two contours of nominal coverage 0.2 (inner, red) and 0.80 (outer, blue). Right: the corresponding uncalibrated PP-plot of the empirical vs nominal coverage. The dashed black diagonal line is the ideal coverage, and the red (blue) curve represents under-(over) confident regions. The two figures together illustrate that the contours of nominal coverage 0.2 (0.80) have an empirical coverage of 0.32 (0.68), indicating under-(over) confidence. The ideal calibration temperature vector, a function of the nominal coverage, contracts (expands) the probability density of under-(over) confident regions in the parameter space.
• Figure 3: Comparison of the PP plots from the uncalibrated (purple) and calibrated (blue) FloTS predictions. The 45$^\circ$ black dashed line represents the ideal coverage. The green dot-dashed line, which corresponds to the secondary y-axis, shows the optimal temperature as a function of nominal coverage. The calibration temperature is parameterized according to Equation \ref{['eq:calib_temp_polynomial']}.
• Figure 4: Same as Figure \ref{['fig:coverage_flow']} for GP predictions. An alternative calibration is presented in Appendix \ref{['sec:appendix_piecewiselinear']}.
• Figure 5: Forecasting performance of all models trained using a 2-hour input window. Left: RMSE, and Right: Pearson correlation coefficient, both computed between the predicted and observed seeing values and plotted as a function of forecast lead time.