# Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer
## 4 Conclusions  
Optical turbulence has a serious impact on laser beam propagation through the atmosphere and on astronomical observations. Effective predictions of optical turbulence strength are significant for discussing atmospheric motion and transmission characteristics. In this paper, we proposed a simple and efficient technique to predict \(C_{n}^{2}\) profiles in the offshore atmospheric boundary layer. The proposed BPNN approach was demonstrated to estimate profiles in the offshore atmospheric boundary layer without any prior formula. From the analysis and comparison of the results with the HMNSP99 model and the HAP model, the corresponding conclusions are as follows:  
(1) The BPNN approach identifies rules from big data without any assumptions, and so may be applied to a larger number of scenarios. Through continuous learning, the BPNN approach starts from basic meteorological parameters and obtains \(C_{n}^{2}\) profiles, avoiding the uncertainty and inaccuracy of model estimation.  
(2) The BPNN approach has the highest computing precision compared with the HMNSP99 and HAP models. Most bias values calculated from the BPNN approach were between \(-0.5\) and \(0.5\) in the offshore atmospheric boundary layer, and for the HMNSP99 model there existed a larger bias value from \(0\) to \(1500\) m, with the maximum value exceeding \(-1\). The RMSE and CRMSE of the BPNN approach and the HMNSP99 model were mainly smaller than \(1.25\) and \(1.75\) along the boundary layer, respectively, and as for the HAP model, it had a range from \(1\) to \(1.25\).  
(3) The profile modes of the offshore atmospheric boundary layer were induced using the BPNN approach. By calculating astroclimatic parameters, it was found that the BPNN approach provided more reasonable values, which are reliable when reconstructing integrated astroclimatic parameters.  
Furthermore, the total training data were insufficient, and so the accuracy of the approach must be further improved.  
Conceptualization, M.X. and S.S.; software, M.X.; validation, formal analysis, M.X., S.S. and N.W.; investigation, M.X.; resources, G.S.; data curation, G.S. and Q.L.; writing--original draft preparation, M.X.; writing--review and editing, M.X.; visualization, M.X.; supervision,  
Figure 7: Comparison of integrated astroclimatic parameters between measurement, the BPNN approach and the HMNSP99 model.  
S.S., Y.H. and N.W.; project administration, funding acquisition, S.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development program under Grant 2018 YFC0213102, the open project of Equipment Pre-research Fund under Grant 6142404180302, the National Natural Science Foundation of China under Grant 41475024, and the National Natural Science Foundation of China under Grant 42027804. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data are contained within the article. We thank [PERSON] from the Ocean University of China for comments and suggestions. In addition, the authors would like to thank [PERSON] and [PERSON] for their patient help and guidance. The authors declare no conflict of interest.