Forecasting Atmospheric Clarity: A Machine Learning Approach

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Author: Denis Avetisyan

New research demonstrates the power of machine learning to predict short-term atmospheric turbulence, improving conditions for astronomical observation and optical communication.

The study demonstrates how forecasting models, trained on a two-hour data window, exhibit performance-measured by both Root Mean Squared Error <span class="katex-eq" data-katex-display="false"> RMSE </span> and Pearson correlation-that degrades predictably as the forecast lead time increases, highlighting the inherent limitations in predicting atmospheric seeing conditions beyond short timescales.
The study demonstrates how forecasting models, trained on a two-hour data window, exhibit performance-measured by both Root Mean Squared Error RMSE and Pearson correlation-that degrades predictably as the forecast lead time increases, highlighting the inherent limitations in predicting atmospheric seeing conditions beyond short timescales.

This review explores the application of Gaussian Processes and Normalizing Flows for probabilistic forecasting of atmospheric seeing based on time series analysis of optical turbulence.

Atmospheric turbulence fundamentally limits the performance of ground-based optical systems, yet reliably forecasting its evolution remains a significant challenge. This is addressed in ‘Short-Term Turbulence Prediction for Seeing Using Machine Learning’, which investigates machine learning approaches to predict atmospheric seeing – a key metric of image clarity – up to two hours in advance. The study demonstrates that probabilistic deep learning models, specifically normalizing flows, outperform both statistical and deterministic baselines in balancing predictive accuracy with well-calibrated uncertainty estimates. Could these advancements pave the way for more robust adaptive optics control and improved data quality in both astronomical observation and free-space optical communication?

The Shimmering Illusion: Why Seeing Matters

The shimmering distortion observed when viewing distant objects through the atmosphere-commonly known as astronomical seeing-is a direct consequence of atmospheric turbulence. This turbulence, created by pockets of air at varying temperatures and densities mixing, bends and scatters light before it reaches a telescope. Consequently, even the largest ground-based telescopes are limited in their ability to achieve their theoretical resolution; a crisp, pinpoint image of a star is instead blurred into a fuzzy disk. This effect isn’t simply a matter of visual clarity; it directly impacts the ability to discern fine details in celestial objects, hindering studies ranging from exoplanet characterization to the observation of distant galaxies. The severity of this blurring varies significantly with atmospheric conditions, making precise characterization and prediction of turbulence essential for maximizing the scientific output of astronomical observatories.

Historically, characterizing atmospheric turbulence for astronomical observation relied on methods yielding only limited, often delayed, information about seeing conditions. These techniques, such as differential image motion monitoring and atmospheric profiling with balloons, frequently provided snapshots rather than the probabilistic forecasts necessary for efficient telescope scheduling. The challenge lies in turbulence’s inherent variability; traditional approaches struggle to anticipate how quickly and dramatically seeing will change, hindering the ability to proactively select the best times for observing faint or extended objects. Consequently, valuable observing time is sometimes lost to poor seeing, or telescopes are forced to observe under suboptimal conditions, limiting the quality of collected data and the potential for groundbreaking discoveries. A shift towards predictive modeling, capable of quantifying the likelihood of specific seeing conditions, is therefore critical for maximizing the scientific output of modern observatories.

The atmosphere, while seemingly stable, operates as a quintessential chaotic system – profoundly sensitive to initial conditions. This inherent characteristic means even the most minute uncertainties in current atmospheric states can rapidly propagate, leading to drastically different outcomes in predictive models. Unlike deterministic systems where future states are precisely determined by present ones, atmospheric turbulence evolves through nonlinear interactions, rendering long-term forecasting exceptionally difficult. Consequently, even with advanced computational power and increasingly detailed observational data, predicting turbulence with complete accuracy remains elusive; models can capture general trends, but precise, localized forecasts are hampered by the system’s fundamental unpredictability. This chaotic behavior necessitates probabilistic approaches to turbulence prediction, acknowledging a range of possible future states rather than a single definitive one, and fundamentally limits the achievable precision in astronomical seeing forecasts.

The potential for groundbreaking discovery at world-class observatories, such as those atop Maunakea, is directly tied to the clarity of the atmosphere; however, atmospheric turbulence routinely blurs astronomical images. Consequently, precise forecasting of this turbulence is not merely a technical refinement, but a fundamental necessity for maximizing scientific yield. By accurately predicting atmospheric conditions, astronomers can strategically schedule observations to coincide with periods of minimal distortion, enabling sharper images and more reliable data. This predictive capability allows telescopes to operate at their full potential, increasing the likelihood of detecting faint, distant objects and unraveling the mysteries of the universe. Investment in advanced turbulence modeling and forecasting techniques, therefore, represents a critical pathway towards unlocking the full scientific return from these invaluable astronomical resources.

Following calibration, the FloTS model (heatmap) accurately predicts seeing conditions (black) over the forecast horizon, outperforming both Gaussian Process (GP, red) and recurrent neural network (RNN & LSTM, purple/green) models, as demonstrated by an example observation from July 6, 2015.
Following calibration, the FloTS model (heatmap) accurately predicts seeing conditions (black) over the forecast horizon, outperforming both Gaussian Process (GP, red) and recurrent neural network (RNN & LSTM, purple/green) models, as demonstrated by an example observation from July 6, 2015.

Gathering the Threads: Data for Prediction

The Maunakea Weather Center (MKWC) serves as the primary source of atmospheric data utilized for turbulence analysis at the Maunakea Observatories. Data is collected via a suite of dedicated sensors, notably the Differential Image Motion Monitor (DIMM) and the Multi-Aperture Scintillation Transport (Mass) instrument. The DIMM measures atmospheric turbulence by analyzing the blurring of a star image, while Mass assesses turbulence strength and profiles using multiple apertures. These instruments continuously monitor key atmospheric parameters, providing the raw data necessary for quantifying seeing conditions and forecasting turbulence levels relevant to astronomical observations. Data collected is time-stamped and includes parameters like scintillation, isodromy, and atmospheric profiles.

Turbulence prediction models require data preprocessing techniques to address inconsistencies and gaps in atmospheric measurements. Temporal interpolation methods are employed to estimate data values at consistent time intervals, filling in missing observations from sensors like DIMM and Mass. Resampling adjusts the data’s frequency, ensuring compatibility with the input requirements of machine learning algorithms and enabling efficient processing. These techniques standardize the data’s temporal resolution, mitigating potential errors and improving the accuracy of subsequent turbulence analyses and forecasts. Without these preprocessing steps, data irregularities can lead to biased model training and unreliable predictions.

Preprocessing of atmospheric data from sources like the Maunakea Weather Center is essential for machine learning model input. This process addresses inconsistencies in data formats, missing values, and differing temporal resolutions. Techniques such as normalization, outlier removal, and data type conversion are applied to standardize the input features. Furthermore, resampling and interpolation methods ensure all datasets align on a common time grid, which is a requirement for most supervised learning algorithms. Properly preprocessed data minimizes bias, improves model convergence, and ultimately enhances the predictive performance of turbulence forecasting models.

The accuracy of turbulence forecasts is fundamentally constrained by the quality of the input data; errors, inconsistencies, or gaps in the initial atmospheric measurements from sources like the Maunakea Weather Center will propagate through the prediction process, directly reducing the reliability of the output. Specifically, inaccuracies in measured parameters such as seeing, wind speed, and temperature will translate into corresponding errors in turbulence estimations. Data affected by sensor malfunctions, calibration issues, or inadequate sampling rates will necessitate careful quality control and potentially introduce biases into the predictive models. Consequently, rigorous data validation, cleaning, and preprocessing steps are essential to minimize these effects and ensure the production of dependable turbulence forecasts.

Unveiling the Chaos: Machine Learning Approaches

Probabilistic turbulence prediction utilizes both Gaussian Processes (GP) and normalizing flow models to quantify forecast uncertainty. Gaussian Processes represent probability distributions over functions, enabling prediction with associated confidence intervals. Normalizing flows, such as FloTS, transform a simple probability distribution-typically Gaussian-into a complex one capable of representing the intricate dynamics of turbulence. These models differ in their ability to directly generate well-calibrated probabilistic forecasts; while GPs often require post-processing calibration to correct for biases in their uncertainty estimates, normalizing flows like FloTS are designed to produce inherently calibrated predictions without the need for external correction techniques. Both approaches aim to move beyond deterministic forecasts by providing a distribution of possible turbulence states, allowing for risk assessment and improved decision-making in applications like aviation safety and wind energy production.

Long Short-Term Memory Networks (LSTM) are a specific type of Recurrent Neural Network (RNN) designed to process sequential data, making them suitable for analyzing the temporal dependencies inherent in atmospheric data. Unlike traditional RNNs which struggle with vanishing gradients over long sequences, LSTMs utilize memory cells and gating mechanisms – input, forget, and output gates – to effectively learn and retain information over extended periods. These gates regulate the flow of information, allowing the network to selectively remember or discard past data relevant to predicting future atmospheric states. The architecture enables LSTMs to model complex, non-linear relationships within time series data, capturing how past atmospheric conditions influence present and future turbulence characteristics.

Probabilistic forecasts generated by machine learning models, such as Gaussian Processes and normalizing flows, often require calibration to ensure their reliability and trustworthiness. Calibration addresses the discrepancy between predicted probabilities and observed frequencies; an uncalibrated model may consistently overestimate or underestimate the likelihood of events. Techniques including Platt scaling and isotonic regression are employed to map model outputs to more accurate probability estimates. Properly calibrated forecasts are essential for informed decision-making, as they provide realistic assessments of uncertainty and allow for more effective risk management in applications like weather prediction and climate modeling. The need for calibration varies between models; FloTS, for example, naturally produces well-calibrated probabilistic forecasts, while Gaussian Processes typically require post-hoc calibration to correct for systematic miscalibration.

At a 2-hour forecast horizon, both Long Short-Term Memory Networks (LSTM) and normalizing flow models, specifically FloTS, demonstrate equivalent forecasting accuracy, each achieving a Root Mean Squared Error (RMSE) of 0.20″. However, a key distinction lies in probabilistic forecast calibration. FloTS inherently produces well-calibrated probabilistic forecasts, meaning the predicted probabilities align with observed frequencies. In contrast, Gaussian Processes, while achieving the same RMSE, require post-hoc calibration techniques to correct for systematic over- or under-confidence in their probabilistic predictions. This difference impacts the reliability and trustworthiness of the forecasts without additional processing steps.

On two example nights, probabilistic forecasts of atmospheric seeing, generated by FloTS (represented as a heatmap) and compared against ground truth (black) and models like GP (red, with 95% confidence intervals shown as dotted lines), RNN (purple), and LSTM (green), demonstrate the system's ability to predict future seeing conditions based on historical input sequences (blue).
On two example nights, probabilistic forecasts of atmospheric seeing, generated by FloTS (represented as a heatmap) and compared against ground truth (black) and models like GP (red, with 95% confidence intervals shown as dotted lines), RNN (purple), and LSTM (green), demonstrate the system’s ability to predict future seeing conditions based on historical input sequences (blue).

The Unblurred Future: Impact and Prospects

Precise, short-term prediction of atmospheric turbulence is now fundamentally linked to the performance of adaptive optics systems, which actively correct for distortions that blur astronomical images. By forecasting these rapid fluctuations in air density – often measured in milliseconds – telescopes can proactively adjust deformable mirrors, effectively ‘undoing’ the blurring effect and delivering sharper, more detailed observations. This optimization isn’t merely about achieving aesthetically pleasing images; it directly translates to increased sensitivity, allowing astronomers to detect fainter objects and measure their properties with greater precision. Consequently, improved turbulence prediction unlocks the full potential of ground-based telescopes, rivaling – and in some cases exceeding – the capabilities of space-based observatories by mitigating the limitations imposed by the Earth’s atmosphere.

Predicting atmospheric turbulence not just in the immediate future, but days or even weeks in advance, offers a transformative capability for astronomical observatories. This proactive approach allows for strategic scheduling of observations, prioritizing telescope time for periods expected to have the most stable atmospheric conditions. By anticipating optimal seeing, observatories can maximize the efficiency of valuable telescope resources, focusing on high-priority targets when the likelihood of obtaining high-quality data is greatest. This foresight minimizes wasted observing time due to poor atmospheric conditions, ultimately increasing scientific output and enabling the collection of more impactful astronomical data. The ability to effectively allocate telescope time based on long-term turbulence forecasts represents a significant step towards optimizing astronomical research and fully leveraging the potential of ground-based telescopes.

The seamless incorporation of probabilistic turbulence forecasts into observatory operations represents a significant advancement in astronomical observation. By anticipating atmospheric conditions, astronomers can dynamically adjust telescope settings and prioritize observations likely to yield the clearest data, thereby maximizing scientific return from limited telescope time. This proactive approach extends beyond immediate adjustments; long-term forecasts enable strategic scheduling, allowing astronomers to plan observations during periods of optimal atmospheric stability and efficiently allocate resources. The resulting improvements in data quality, coupled with increased observational throughput, directly translate to a higher volume of reliable scientific results and accelerate the pace of discovery across a wide range of astronomical disciplines.

The forecasting model, FloTS, presented in this study demonstrates a compelling level of performance in predicting atmospheric turbulence, achieving a Pearson correlation coefficient on par with established methods like Long Short-Term Memory networks (LSTM) and Gaussian Processes (GP). This suggests FloTS is a viable alternative for real-time and scheduled observations. Current research isn’t stopping there, however; future investigations will concentrate on broadening the data inputs used by the model – potentially including meteorological data and high-resolution atmospheric imaging – and on exploring more sophisticated model architectures. These advancements aim to not only refine the precision of turbulence predictions but also to bolster their overall reliability, ultimately maximizing the scientific return from ground-based astronomical observations.

Root mean squared error (RMSE) consistently decreases with increased training duration-up to 6 hours-across all models (RNN, LSTM, GP, and FloTS) when evaluated over a 2-hour prediction window.
Root mean squared error (RMSE) consistently decreases with increased training duration-up to 6 hours-across all models (RNN, LSTM, GP, and FloTS) when evaluated over a 2-hour prediction window.

The pursuit of predictive accuracy, as demonstrated by this study’s application of machine learning to atmospheric seeing, reveals a humbling truth about knowledge itself. The models, while capable of forecasting short-term turbulence with quantified uncertainty, are still bound by the inherent chaos of the atmosphere. As Pyotr Kapitsa observed, “It is better to be skeptical than to be certain.” This resonates deeply with the article’s core idea; the probabilistic forecasting isn’t about eliminating uncertainty, but about acknowledging and quantifying it. The cosmos generously shows its secrets to those willing to accept that not everything is explainable, and black holes are nature’s commentary on our hubris. The forecasting models, much like our theories, exist within a boundary, beyond which lies the unknown.

What’s Next?

The demonstrated efficacy of machine learning for short-term seeing prediction, while promising, merely pushes the fundamental limitations further into the unknown. Current methodologies treat atmospheric turbulence as a complex, but ultimately knowable, system. Yet, the very act of prediction implies a completeness of information that the atmosphere, by its chaotic nature, fundamentally resists. The models offer probabilistic forecasts, quantifying uncertainty, but this quantification itself rests on assumptions about the underlying distribution – assumptions that, beyond a certain horizon, become as fragile as the wavefronts they seek to correct.

Future work will undoubtedly explore more complex architectures and larger datasets. However, a more profound challenge lies in acknowledging the inherent epistemic limits. Gravitational collapse forms event horizons with well-defined curvature metrics; similarly, predictive models encounter horizons beyond which reliable forecasting is impossible, not due to computational constraints, but due to the fundamental nature of the system. Singularity is not a physical object in the conventional sense; it marks the limit of classical theory applicability. Predictive power, therefore, is not about achieving perfect foresight, but about intelligently navigating the inevitable uncertainty.

The true next step may not be a better algorithm, but a more honest appraisal of what can, and cannot, be known. Efforts should be directed towards developing robust observation strategies that accept uncertainty, rather than striving to eliminate it. Perhaps the most valuable prediction is not of the atmosphere itself, but of the limits of predictability.

Original article: https://arxiv.org/pdf/2603.24466.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-03-26 14:24