# 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  
Assume that wave-optics numerical simulations could provide accurate modelling of laser beam propagation over any selected turbulence characterization site and, thus, can be utilized for the generation of sufficiently large SIM datasets for DNN training. A DNN that is trained at this SIM dataset (SIM-trained DNN) can then be further used for real-time processing of scintillation images and \(C_{n}^{2}\) prediction at the selected site. In the case of Cn^2 Net training using such SIM dataset, a \"trusted\" scintillator for collection of the training data (ATM dataset) is not required. Furthermore, the SIM-trained Cn^2 Net scintillometer could be further utilized at different propagation sites by simply computing a new SIM dataset specific for this site with corresponding Cn^2 Net retraining. There are, nevertheless, several potential issues with such Cn^2 Net scintillometer training using SIM datasets. First, it is not always clear how accurately we can mimic laser beam propagation at any  
Figure 9: Eight minute segment of the \(C_{n}^{2}\) “measurement-vs.-prediction” plot in Figure 7c obtained with the Cn^2 Net processing of the ATM #2-V data subset (**top**), and exemplary scintillation images captured during \(\Delta t=20\) s time interval (**bottom**). given turbulence characterization site in our numerical simulations. In other words, could we trust SIM datasets more than ATM datasets obtained using side-by-side \(C_{n}^{2}\) measurements with a \"trusted\" scintillator? Second, since there are several well-known atmospheric turbulence models, it is unclear which model to use for SIM datasets generation. Third, there could be one more potential issue associated with frequently observed inhomogeneities of the refractive index structure parameter along the propagation path. This \(C_{n}^{2}\) inhomogeneity is commonly accounted for in numerical simulations by applying one or another model to describe refractive index structure parameter dependence on the propagation distance \(0\leq z\leq L\) (\(C_{n}^{2}\)-profile): \(C_{n}^{2}(z)\)[30; 31]. In the most known \(C_{n}^{2}\)-profile models (e.g., Hufnagel-Valley [32], SLC [33], Gurvich [34], etc.) the structure parameter is considered as a function dependent solely on propagation path elevation (\(C_{n}^{2}\) vertical profile). However, at propagation sites with complicated terrain features, the refractive index structure parameter could be inhomogeneous along all three geographical coordinates (elevation, longitude and altitude), which makes generation of SIM datasets a challenging problem. Some progress in the modeling of refraction index and \(C_{n}^{2}\) fields dependent on 3D geographical coordinates and time has recently been made using numerical weather prediction (NWP) simulations [35; 36; 37]. The NWP approach could potentially be applied for generation of more accurate SIM datasets for DNN training. In another approach considered here, the deep machine learning paradigm is applied to fine-tune a model-based \(C_{n}^{2}\)- profile to a selected turbulence characterization site by utilizing atmospheric sensing data acquired at this site (inference ATM dataset). In this case, DNN is initially trained on a SIM dataset corresponding to a specified \(C_{n}^{2}\) profile model (e.g., uniform, or HV-21 \(C_{n}^{2}\)-altitude profile). The SIM-trained DNN is further applied for prediction (inference) of the experimentally measured \(C_{n}^{2}\) values based on processing of scintillation images from the inference ATM dataset. The initial (model-based) \(C_{n}^{2}\)-profile is further modified to decrease prediction error obtained during the DNN inference phase. This modification can be performed by adjusting a few tunable parameters that could be selected based on various factors including availability of additional information about terrain features and/or specific propagation site characteristics, weather conditions, etc.