M. Pierzyna
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Free-space optical communication (FSOC) is a key technology to meet the growing demand for high-bandwidth, secure, and energy-efficient data links.
However, the atmospheric channel introduces a major challenge: optical turbulence (OT). Turbulent fluctuations of the refractive index, driven by wind shear and buoyancy in the atmosphere, distort the propagating optical beam, degrading communication performance. This dissertation investigates the modelling of optical turbulence, quantified through the refractive index structure parameter Cn2, along two complementary avenues: traditional numerical weather prediction (NWP) using mesoscale models and machine learning (ML) techniques.
The first part establishes the state of the art in mesoscale Cn2 modelling for FSOC. Chapter 2 presents a systematic intercomparison of the three main classes of Cn2 parameterizations -- flux-based, gradient-based, and variance-based -- applied to both observed data and output from a numerical mesoscale model.
Evaluated against scintillometer observations, the variance-based parameterization yields the best overall performance and, unlike the other two, is not restricted to the atmospheric surface layer. Building on this foundation, chapter 3 proposes an end-to-end framework that translates Cn2 estimates into FSOC link performance metrics, specifically turbulence-induced losses and a theoretically achievable information rate (generalized mutual information, GMI).
Applied to an urban example link, the framework reveals that the sensitivity of the estimated FSOC performance to Cn2 errors strongly depends on the specific link. Reporting Cn2 model errors alone is therefore considered insufficient for FSOC, and end-to-end assessments of link performance are needed.
Running mesoscale models is computationally expensive, and the traditional parameterizations used to obtain Cn2 -- while physically motivated -- are often limited in their applicability or accuracy. Machine learning offers a promising alternative by learning complex relationships directly from data, as explored in the second part of this dissertation. Chapter 4 introduces OTCliM, a gradient boosting-based methodology that relates globally available ERA5 reanalysis data to observed near-surface Cn2. Across 17 diverse stations in New York State, OTCliM trained on just one year of observations accurately extrapolates Cn2 over four held-out years. However, the resulting models are limited to near-surface Cn2, which is sufficient for terrestrial links but not for satellite-to-ground applications that require vertical profiles. To extend modelling into the vertical, chapter 5 introduces Π-ML, a physics-inspired ML framework that combines automated dimensional analysis with gradient boosting. By expressing inputs and outputs as non-dimensional groups grounded in physical principles, Π-ML derives an interpretable, data-driven similarity theory for Cn2 in the atmospheric surface layer. The framework achieves high accuracy under both stable and unstable atmospheric conditions and identifies scalings that are physically consistent with established theories. Finally, chapter 6 addresses the full atmospheric column by developing OTProf. This deep-learning-based model estimates Cn2 profiles of high vertical resolution from low-resolution ERA5 pressure-level inputs. Trained on one year of mesoscale simulations, the model substantially outperforms the commonly used Hufnagel-Valley analytical model.
The estimated profiles exhibit a physically realistic vertical structure, although ML-typical smoothing leads to some underestimation of integrated turbulence parameters, such as the Fried parameter and the scintillation index.
Nevertheless, OTProf is regarded as a computationally efficient and considerably more accurate approach compared to traditional analytical models.
Taken together, this dissertation demonstrates that both numerical mesoscale modelling and machine learning deliver practical advances for optical turbulence estimation and FSOC applications. The overarching conclusion, however, is that the greatest potential lies in combining the two paradigms, which is viewed as a promising direction for future research. ...
However, the atmospheric channel introduces a major challenge: optical turbulence (OT). Turbulent fluctuations of the refractive index, driven by wind shear and buoyancy in the atmosphere, distort the propagating optical beam, degrading communication performance. This dissertation investigates the modelling of optical turbulence, quantified through the refractive index structure parameter Cn2, along two complementary avenues: traditional numerical weather prediction (NWP) using mesoscale models and machine learning (ML) techniques.
The first part establishes the state of the art in mesoscale Cn2 modelling for FSOC. Chapter 2 presents a systematic intercomparison of the three main classes of Cn2 parameterizations -- flux-based, gradient-based, and variance-based -- applied to both observed data and output from a numerical mesoscale model.
Evaluated against scintillometer observations, the variance-based parameterization yields the best overall performance and, unlike the other two, is not restricted to the atmospheric surface layer. Building on this foundation, chapter 3 proposes an end-to-end framework that translates Cn2 estimates into FSOC link performance metrics, specifically turbulence-induced losses and a theoretically achievable information rate (generalized mutual information, GMI).
Applied to an urban example link, the framework reveals that the sensitivity of the estimated FSOC performance to Cn2 errors strongly depends on the specific link. Reporting Cn2 model errors alone is therefore considered insufficient for FSOC, and end-to-end assessments of link performance are needed.
Running mesoscale models is computationally expensive, and the traditional parameterizations used to obtain Cn2 -- while physically motivated -- are often limited in their applicability or accuracy. Machine learning offers a promising alternative by learning complex relationships directly from data, as explored in the second part of this dissertation. Chapter 4 introduces OTCliM, a gradient boosting-based methodology that relates globally available ERA5 reanalysis data to observed near-surface Cn2. Across 17 diverse stations in New York State, OTCliM trained on just one year of observations accurately extrapolates Cn2 over four held-out years. However, the resulting models are limited to near-surface Cn2, which is sufficient for terrestrial links but not for satellite-to-ground applications that require vertical profiles. To extend modelling into the vertical, chapter 5 introduces Π-ML, a physics-inspired ML framework that combines automated dimensional analysis with gradient boosting. By expressing inputs and outputs as non-dimensional groups grounded in physical principles, Π-ML derives an interpretable, data-driven similarity theory for Cn2 in the atmospheric surface layer. The framework achieves high accuracy under both stable and unstable atmospheric conditions and identifies scalings that are physically consistent with established theories. Finally, chapter 6 addresses the full atmospheric column by developing OTProf. This deep-learning-based model estimates Cn2 profiles of high vertical resolution from low-resolution ERA5 pressure-level inputs. Trained on one year of mesoscale simulations, the model substantially outperforms the commonly used Hufnagel-Valley analytical model.
The estimated profiles exhibit a physically realistic vertical structure, although ML-typical smoothing leads to some underestimation of integrated turbulence parameters, such as the Fried parameter and the scintillation index.
Nevertheless, OTProf is regarded as a computationally efficient and considerably more accurate approach compared to traditional analytical models.
Taken together, this dissertation demonstrates that both numerical mesoscale modelling and machine learning deliver practical advances for optical turbulence estimation and FSOC applications. The overarching conclusion, however, is that the greatest potential lies in combining the two paradigms, which is viewed as a promising direction for future research. ...
Free-space optical communication (FSOC) is a key technology to meet the growing demand for high-bandwidth, secure, and energy-efficient data links.
However, the atmospheric channel introduces a major challenge: optical turbulence (OT). Turbulent fluctuations of the refractive index, driven by wind shear and buoyancy in the atmosphere, distort the propagating optical beam, degrading communication performance. This dissertation investigates the modelling of optical turbulence, quantified through the refractive index structure parameter Cn2, along two complementary avenues: traditional numerical weather prediction (NWP) using mesoscale models and machine learning (ML) techniques.
The first part establishes the state of the art in mesoscale Cn2 modelling for FSOC. Chapter 2 presents a systematic intercomparison of the three main classes of Cn2 parameterizations -- flux-based, gradient-based, and variance-based -- applied to both observed data and output from a numerical mesoscale model.
Evaluated against scintillometer observations, the variance-based parameterization yields the best overall performance and, unlike the other two, is not restricted to the atmospheric surface layer. Building on this foundation, chapter 3 proposes an end-to-end framework that translates Cn2 estimates into FSOC link performance metrics, specifically turbulence-induced losses and a theoretically achievable information rate (generalized mutual information, GMI).
Applied to an urban example link, the framework reveals that the sensitivity of the estimated FSOC performance to Cn2 errors strongly depends on the specific link. Reporting Cn2 model errors alone is therefore considered insufficient for FSOC, and end-to-end assessments of link performance are needed.
Running mesoscale models is computationally expensive, and the traditional parameterizations used to obtain Cn2 -- while physically motivated -- are often limited in their applicability or accuracy. Machine learning offers a promising alternative by learning complex relationships directly from data, as explored in the second part of this dissertation. Chapter 4 introduces OTCliM, a gradient boosting-based methodology that relates globally available ERA5 reanalysis data to observed near-surface Cn2. Across 17 diverse stations in New York State, OTCliM trained on just one year of observations accurately extrapolates Cn2 over four held-out years. However, the resulting models are limited to near-surface Cn2, which is sufficient for terrestrial links but not for satellite-to-ground applications that require vertical profiles. To extend modelling into the vertical, chapter 5 introduces Π-ML, a physics-inspired ML framework that combines automated dimensional analysis with gradient boosting. By expressing inputs and outputs as non-dimensional groups grounded in physical principles, Π-ML derives an interpretable, data-driven similarity theory for Cn2 in the atmospheric surface layer. The framework achieves high accuracy under both stable and unstable atmospheric conditions and identifies scalings that are physically consistent with established theories. Finally, chapter 6 addresses the full atmospheric column by developing OTProf. This deep-learning-based model estimates Cn2 profiles of high vertical resolution from low-resolution ERA5 pressure-level inputs. Trained on one year of mesoscale simulations, the model substantially outperforms the commonly used Hufnagel-Valley analytical model.
The estimated profiles exhibit a physically realistic vertical structure, although ML-typical smoothing leads to some underestimation of integrated turbulence parameters, such as the Fried parameter and the scintillation index.
Nevertheless, OTProf is regarded as a computationally efficient and considerably more accurate approach compared to traditional analytical models.
Taken together, this dissertation demonstrates that both numerical mesoscale modelling and machine learning deliver practical advances for optical turbulence estimation and FSOC applications. The overarching conclusion, however, is that the greatest potential lies in combining the two paradigms, which is viewed as a promising direction for future research.
However, the atmospheric channel introduces a major challenge: optical turbulence (OT). Turbulent fluctuations of the refractive index, driven by wind shear and buoyancy in the atmosphere, distort the propagating optical beam, degrading communication performance. This dissertation investigates the modelling of optical turbulence, quantified through the refractive index structure parameter Cn2, along two complementary avenues: traditional numerical weather prediction (NWP) using mesoscale models and machine learning (ML) techniques.
The first part establishes the state of the art in mesoscale Cn2 modelling for FSOC. Chapter 2 presents a systematic intercomparison of the three main classes of Cn2 parameterizations -- flux-based, gradient-based, and variance-based -- applied to both observed data and output from a numerical mesoscale model.
Evaluated against scintillometer observations, the variance-based parameterization yields the best overall performance and, unlike the other two, is not restricted to the atmospheric surface layer. Building on this foundation, chapter 3 proposes an end-to-end framework that translates Cn2 estimates into FSOC link performance metrics, specifically turbulence-induced losses and a theoretically achievable information rate (generalized mutual information, GMI).
Applied to an urban example link, the framework reveals that the sensitivity of the estimated FSOC performance to Cn2 errors strongly depends on the specific link. Reporting Cn2 model errors alone is therefore considered insufficient for FSOC, and end-to-end assessments of link performance are needed.
Running mesoscale models is computationally expensive, and the traditional parameterizations used to obtain Cn2 -- while physically motivated -- are often limited in their applicability or accuracy. Machine learning offers a promising alternative by learning complex relationships directly from data, as explored in the second part of this dissertation. Chapter 4 introduces OTCliM, a gradient boosting-based methodology that relates globally available ERA5 reanalysis data to observed near-surface Cn2. Across 17 diverse stations in New York State, OTCliM trained on just one year of observations accurately extrapolates Cn2 over four held-out years. However, the resulting models are limited to near-surface Cn2, which is sufficient for terrestrial links but not for satellite-to-ground applications that require vertical profiles. To extend modelling into the vertical, chapter 5 introduces Π-ML, a physics-inspired ML framework that combines automated dimensional analysis with gradient boosting. By expressing inputs and outputs as non-dimensional groups grounded in physical principles, Π-ML derives an interpretable, data-driven similarity theory for Cn2 in the atmospheric surface layer. The framework achieves high accuracy under both stable and unstable atmospheric conditions and identifies scalings that are physically consistent with established theories. Finally, chapter 6 addresses the full atmospheric column by developing OTProf. This deep-learning-based model estimates Cn2 profiles of high vertical resolution from low-resolution ERA5 pressure-level inputs. Trained on one year of mesoscale simulations, the model substantially outperforms the commonly used Hufnagel-Valley analytical model.
The estimated profiles exhibit a physically realistic vertical structure, although ML-typical smoothing leads to some underestimation of integrated turbulence parameters, such as the Fried parameter and the scintillation index.
Nevertheless, OTProf is regarded as a computationally efficient and considerably more accurate approach compared to traditional analytical models.
Taken together, this dissertation demonstrates that both numerical mesoscale modelling and machine learning deliver practical advances for optical turbulence estimation and FSOC applications. The overarching conclusion, however, is that the greatest potential lies in combining the two paradigms, which is viewed as a promising direction for future research.
For free-space optical communication or ground-based optical astronomy, ample data of optical turbulence strength (C 2 n) are imperative but typically scarce. Turbulence conditions are strongly site dependent, so their accurate quantification requires in situ measurements or numerical weather simulations. If C 2 n is not measured directly (e.g., with a scintillometer), C 2 n parameterizations must be utilized to estimate it from meteorological observations or model output. Even though various 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-, gradient-, and variance-based parameterization. Each parameterization is applied to both observed and simulated meteorological variables, and the resulting C 2 n estimates are compared against observed C 2 n 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 2 n estimated from the output of the Weather Research and Forecasting model aligns well with observations, highlighting the value of mesoscale models for optical turbulence modeling.
...
For free-space optical communication or ground-based optical astronomy, ample data of optical turbulence strength (C 2 n) are imperative but typically scarce. Turbulence conditions are strongly site dependent, so their accurate quantification requires in situ measurements or numerical weather simulations. If C 2 n is not measured directly (e.g., with a scintillometer), C 2 n parameterizations must be utilized to estimate it from meteorological observations or model output. Even though various 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-, gradient-, and variance-based parameterization. Each parameterization is applied to both observed and simulated meteorological variables, and the resulting C 2 n estimates are compared against observed C 2 n 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 2 n estimated from the output of the Weather Research and Forecasting model aligns well with observations, highlighting the value of mesoscale models for optical turbulence modeling.
We present a machine learning-based measure-correlate-predict approach that predicts a multi-year time-series of optical turbulence strength (Cn2) with high accuracy (r = 0.78 at 16 locations) based on a single year of in-situ Cn2 measurements and reanalysis data.
...
We present a machine learning-based measure-correlate-predict approach that predicts a multi-year time-series of optical turbulence strength (Cn2) with high accuracy (r = 0.78 at 16 locations) based on a single year of in-situ Cn2 measurements and reanalysis data.
Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations (𝐶2𝑛) 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, Π-ML, based on dimensional analysis and gradient boosting to estimate 𝐶2𝑛. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting 𝐶2𝑛. For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of R2 = 0.958 ± 0.001.
...
Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations (𝐶2𝑛) 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, Π-ML, based on dimensional analysis and gradient boosting to estimate 𝐶2𝑛. Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting 𝐶2𝑛. For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of R2 = 0.958 ± 0.001.
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 (Cn 2) is challenging during the design phase of an optical link or network. Over the past 25 years, (see manuscript PDF for symbol) parameterizations of varying complexities have been combined with various numerical weather prediction models for the spatio-temporal estimation of (Cn 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 (Cn 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 (Cn 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 (Cn 2) ensemble estimate compared to single model runs.
...
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 (Cn 2) is challenging during the design phase of an optical link or network. Over the past 25 years, (see manuscript PDF for symbol) parameterizations of varying complexities have been combined with various numerical weather prediction models for the spatio-temporal estimation of (Cn 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 (Cn 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 (Cn 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 (Cn 2) ensemble estimate compared to single model runs.