# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
## 6 Cn^2 Net Scintillometer Training with SIM Datasets: Machine Learning-Based Turbulence Profiling
the Kolmogorov turbulence model, or by the possible impact of turbulence inhomogeneities along the propagation path in Figure 1, or by both. First, we assumed that turbulence inhomogeneities rather than deviations from the Kolmogorov classical model were the reason for the Cn'2 Net poor performance. This notion was motivated by the visible comparison between the computer simulated scintillation patterns and those captured during the atmospheric trials, as shown in Figure 4. In this figure the spatial structures of scintillation speckles from the SIM-KO-U and ATM#2 datasets are quite similar under the weak-to-medium turbulence conditions typical for measurements during early morning hours, but noticeably different under the strong turbulence conditions observed for data collection during a sunny afternoon (see right row in Figure 4). This mismatch between simulations and measurements under strong turbulence could be explained by turbulence enhancement in the vicinity of the laser beacon that was located on the flat rooftop surface of the VAMC building (see Figure 1). The heated air flows generated on the roof surface are especially strong during sunny afternoon measurements (strong turbulence conditions), which may cause the turbulence enhancement for the propagation path region near the laser beacon and thus explain the observed mismatch in speckle structures. To verify this hypothesis, we introduced a simple modification into the uniform \(C_{n}^{2}\) profile that was originally used for SIM-KO-U dataset generation. In the wave-optics computer simulations of laser beacon beam propagation (see Section 3), we intentionally increased the strength of the two computer generated phase screens closest to the laser beacon by a factor of \(\kappa\geq 1\) (\(C_{n}^{2}\) profiling factor), while preserving the path-integrated \(C_{n}^{2}\) values through an equivalent decrease in \(C_{n}^{2}\) strength for the remaining eight phase screens. Note that the SIM-KO-U dataset corresponds to \(\kappa~{}=~{}\kappa_{0}~{}=~{}1\) (uniform profile). The initially uniform \(C_{n}^{2}\) profile was modified through a set of Cn'2 Net training-inference iterative steps. Each \(n\)th iteration of the \(C_{n}^{2}\) profile modification included: (a) generation of a SIM-KO-P dataset corresponding to a profiling factor \(\kappa_{n}~{}=~{}\kappa_{0}+n\Delta\kappa\), where \(\Delta\kappa~{}=~{}0.25\) is a selected profiling factor increment; (b) Cn'2 Net training using a SIM-KO-P dataset computed at the \(n\)th iteration; (c) evaluation of the trained DNN at ATM inference datasets; and (d) comparison of averaged prediction errors \(\overline{\varepsilon}_{\text{n}al}(\kappa_{n})\) with the corresponding errors obtained during the previous training-inference step. The steps (a)-(d) were repeated until the smallest prediction error \(\overline{\varepsilon}_{\text{n}al}(\kappa_{n})\) was obtained. The \(C_{n}^{2}\) profile tuning results are illustrated in Figure 10c,d. Both the measurement-vs.-prediction and prediction RMSE \(\varepsilon_{\text{n}al}(c_{n}^{2})\) plots indicate a significant improvement in \(C_{n}^{2}\) prediction accuracy, which was achieved with the Cn'2 Net training using the SIM-KO-P dataset obtained with the optimal profiling factor \(\kappa=2.5\). The averaged prediction errors \(\overline{\varepsilon}_{\text{n}al}\) and their standard deviations \(\sigma_{\varepsilon}\) obtained in the described cross-dataset machine learning experiments are summarized in Table 3. For both inference datasets examined, the smallest prediction errors (\(\overline{\varepsilon}_{\text{n}al}\) = 0.13 for ATM#1 and \(\overline{\varepsilon}_{\text{n}al}\) = 0.14 for ATM#2) were achieved with the profiling factor \(\kappa\) = 2.5. These errors (see Table 3) are comparable with the corresponding errors obtained when both training and validation of the Cn'2 Net were performed using subsets of the same dataset: either SIM-KO-U or ATM#1 or ATM#2 datasets.