# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
## 5 DNN-Inspired Atmospheric Turbulence Characterization: Cn^2 Net Scintillometer
This difference would not explain the observed increase in the prediction error in DNN processing of the experimental data if the statistical properties of all of these (corresponding to each single measured \(C_{n}^{2}\) value) scintillation images are alike. On the contrary, we would expect a quite opposite effect: smaller prediction errors since more scintillation images were utilized for DNN training per a single \(C_{n}^{2}\) value. The observed prediction error increase with DNN processing of the ATM datasets could most likely be explained by the nonstationarity of atmospheric turbulence dynamics during the \(\Delta T=60\) s. time interval between sequential \(C_{n}^{2}\) measurements by the scintillator. During this time, the characteristic spatial features of turbulence-induced speckles in the scintillation images captured by the camera (e.g., characteristic size and contrast of speckles) could considerably evolve. Cn^2 Net, which is trained based on analysis of these spatial features, would respond to these changes by predicting \(C_{n}^{2}\) values that are different from those that were measured by the scintillator. Since \(C_{n}^{2}\) sensing with a conventional scintillator is based on time-averaging of data acquired during the time interval between sequential measurements, this instrument principally cannot detect changes in turbulence that may occur during the averaging time. On the other hand, the \(C_{n}^{2}\) sensing rate of the scintillometer cannot be increased to match the camera frame rate without sacrificing the accuracy required for obtaining statistical characteristics based on time-averaging. From this view point, the Cn^2 Net scintillometer could provide significantly higher temporal resolution in \(C_{n}^{2}\) sensing, which is highly desired for better understanding and prediction of atmospheric turbulence effects. As an illustration consider Figure 9, which shows an eight-minute long (\"time zoom\") extraction from the \"measurement-vs.-prediction\" plot in Figure 7, where the solid line and dots correspondingly show the measured by the scintillometer and predicted by the Cn^2 Net \(C_{n}^{2}\) values based on processing of the ATM#2 dataset. The dotted curve in this figure clearly displays changes in turbulence (in spatial features of turbulence-induced speckles) occurring between sequential \(C_{n}^{2}\) measurements by the scintillometer. These changes in spatial features of speckles can be easily seen in the exemplary \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DNN Training Dataset** & \(\overline{\varepsilon}_{val}\) & \(\sigma_{\varepsilon}\) & \# \(C_{n}^{2}\) **Values** & \# Frames \\ \hline SIM-KO-T & 0.072 & 0.06 & 10,000 & 10,000 \\ ATM\#1-T & 0.194 & 0.14 & 322 & 9668 \\ ATM\#2-T & 0.09 & 0.08 & 940 & 56,443 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averaged prediction error \(\overline{\varepsilon}_{val}\) and its standard deviation \(\sigma_{\varepsilon}\) for the Cn^2 Net trained using different datasets. short exposure scintillation images in Figure 9 which were recorded during \(\Delta t=20\) s. between two subsequent \(C_{n}^{2}\) measurements. This example outlines the principal difficulties with Cn^2 Net training by utilizing \(C_{n}^{2}\) data recorded with a conventional (\"trusted\") scintillometer as the \"ground truth\". Such training could be \"confusing\" for the DNN when turbulence strength and, hence, spatial features of the scintillation images used in such training are rapidly changing between sequential \(C_{n}^{2}\) measurements with conventional instruments having a relative low temporal resolution (from one to several minutes per single \(C_{n}^{2}\) data point). An indication of such \"misleading\" DNN training is the significant increase in prediction errors under strong turbulence conditions (\(C_{n}^{2}>C_{n,0}^{2}\)), as seen in Figure 8b,c.