Optical Turbulence

Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations ($C_n^2$) is highly relevant for the successful development and deployment of future free-space optical communication links. In this letter, we propose a physics-informed machine learning (ML) methodology, $\Pi$-ML, based on dimensional analysis and gradient boosting to estimate $C_n^2$. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting $C_n^2$. For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of $R^2=0.958\pm0.001$. ...

Free-space optical communication (FSOC) links are considered a key technology to support the increasing needs of our connected, data-heavy world, but they are prone to disturbance through atmospheric processes such as optical turbulence. Since turbulence is highly dependent on local topographic and meteorological conditions, modeling optical turbulence strength $C_n^2$ is challenging during the design phase of an optical link or network. Over the past 25 years, $C_n^2$ parameterizations of varying complexities have been combined with various numerical weather prediction models for the spatio-temporal estimation of $C_n^2$. However, the outputs of these models can exhibit substantial variability based on the user-defined configuration that determines how atmospheric processes are represented. To address this concern, we propose to run not a single model configuration but multiple diverse ones to generate an ensemble estimate of $C_n^2$. We employ the Weather Research and Forecasting model (WRF) with ten different planetary boundary layer (PBL) physics schemes forming a diverse ensemble yielding a probabilistic $C_n^2$ estimate. We demonstrate that this ensemble outperforms the individual runs when compared to scintillometer field measurements and show it to be robust against outliers. We believe that FSOC downstream tasks such as link budget estimations should also become more robust if based on a $C_n^2$ ensemble estimate compared to single model runs. ...

For free-space optical communication (FSOC) or ground-based optical astronomy, abundant data of optical turbulence strength ($C_n^2$) is imperative but typically scarce. Turbulence conditions are strongly site-dependent, so their accurate quantification requires in-situ measurements or numerical weather simulations. If $C_n^2$ is not measured directly, e.g., with a scintillometer, $C_n^2$ parameterizations must be utilized to estimate $C_n^2$ from meteorological observations or model output. Even though various such parameterizations exist in the literature, their relative performance is unknown. We fill this knowledge gap by performing a systematic three-way comparison of a flux-based, a gradient-based, and a variance-based parameterization. Each parameterization is applied to both observed and simulated meteorological variables, and the resulting $C_n^2$ estimates are compared against observed $C_n^2$ from two scintillometers. The variance-based parameterization yields the overall best performance, and unlike other approaches, its application is not limited to the lowest part of the atmospheric boundary layer, i.e., the surface layer. We also show that $C_n^2$ estimated from the output of the Weather Research and Forecasting (WRF) model aligns well with observations, highlighting the value of mesoscale models for optical turbulence modeling. ...

This study introduces OTCliM (Optical Turbulence Climatology using Machine learning), a novel approach for deriving comprehensive climatologies of atmospheric optical turbulence strength ($C_n^2$) using gradient boosting machines. OTCliM addresses the challenge of efficiently obtaining reliable site-specific $C_n^2$ climatologies, crucial for ground-based astronomy and free-space optical communication. Using gradient boosting machines and global reanalysis data, OTCliM extrapolates one year of measured $C_n^2$ into a multi-year time series. We assess OTCliM’s performance using $C_n^2$ data from 17 diverse stations in New York State, evaluating temporal extrapolation capabilities and geographical generalization. Our results demonstrate accurate predictions of four held-out years of $C_n^2$ across various sites, including complex urban environments, outperforming traditional analytical models. Non-urban models also show good geographical generalization compared to urban models, which capture non-general site-specific dependencies. A feature importance analysis confirms the physical consistency of the trained models. It also indicates the potential to uncover new insights into the physical processes governing $C_n^2$ from data. OTCliM’s ability to derive reliable $C_n^2$ climatologies from just one year of observations can potentially reduce resources required for future site surveys or enable studies for additional sites with the same resources. ...