## 4 Conclusions  
In-depth research of ocean atmospheric turbulence is significant for discussion on laser beam propagating and astronomical observation. We investigated the strength of optical turbulence over the offshore and open ocean areas, the corresponding conclusions are as follows:  
1. The refractive index structure constant has a relatively typical'seesaw' feature near the ocean surface in the offshore area, which disappears farther than 160 km away from the coast. The optical turbulence strength from the ground up to 30 km is strongest at noon with a maximum value close to \(5\times 10^{-13}\) m\({}^{-2/3}\), and relatively weak at morning and dusk even near the magnitude of \(10^{-19}\) m\({}^{-2/3}\) over the open ocean. For turbulence strength profiles of the offshore area, the value of \(C_{n}^{2}\) in the morning is larger than that in the evening.
2. Over the offshore and open ocean areas, the variance trends of the \(C_{n}^{2}\) profiles are similar near the same height, and the outer scale has the biggest influence weight among influence factors. It is reasonable to use the HMNSP99 model to estimate \(C_{n}^{2}\) profiles, although there is still room for improvement. Furthermore, the value of the outer scale of the offshore area is smaller than that of the open ocean overall, which may be caused by the difference in the location and the release time of the balloons.
3. The mean \(r_{0}\) from the radiosonde measurement at the open ocean area is smaller than offshore, which agrees with the finding that the optical turbulence of the open ocean from the ground up to 30 km is stronger than offshore. Otherwise, the characteristics of the coherence time \(\tau_{0}\) present that the turbulence strength develops faster over the open ocean. The establishment of astronomical observation sites on the ocean has certain limitations. The results we have achieved provide potential supports for the application of adaptive optics systems and astronomical observation.  
Conceptualization, M.X. and S.S.; software, M.X.; validation, formal analysis, M.X., S.S. and N.W.; investigation, M.X.; resources, L.Z.; data curation, L.Z and Q.L.; writing original draft preparation, M.X.; writing-review and editing, M.X.; visualization, M.X.; supervision, S.S., Y.Z.  
Figure 8: Integrated parameters (\(r_{0}\), \(\varepsilon\), \(\theta\) and \(\tau_{0}\)) derived from \(C_{n}^{2}\) profiles from offshore and open ocean.  
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 by [PERSON] under Grant 2018 YFC0213102, the open project of Equipment Pre-research Fund by [PERSON] under Grant 6142404180302, the National Natural Science Foundation of China by [PERSON] under Grant 41475024, and the National Natural Science Foundation of China by [PERSON] under Grant 42027804. Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data are contained within the article. We thank [PERSON] from the Beijing Aviation Meteorological Institute 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.