## 3 Results and Discussion  
### \(C_{n}^{2}\) Evolution Trend  
The refractive index structure constant is the most important index indicating optical turbulence strength. To better investigate the surface turbulence strength, dual timelines are chosen here to characterize the variation of \(C_{n}^{2}\). The comparison of the variation of \(C_{n}^{2}\) between offshore and open ocean areas is depicted in Figure 2. In the figure, both the \(x\)-axis and the \(y\)-axis are time axes, respectively representing 24 h of a day and 30 days of a month. As shown in Figure 2, the refractive index structure constant has a relatively typical'seesaw' feature near the ocean surface in the offshore area. The turbulence strength is stronger between about 07:00 in the morning and 18:00 in the evening, and weaker at other times, which is basically in the range of \(10^{-17}\)-\(10^{-12}\) m\({}^{-2/3}\). The offshore experiment was mainly carried out in winter, and strong turbulence was measured during the daytime, which is consistent with the result of \(C_{n}^{2}\) statistics estimated by [PERSON] [27]. Compared with values in the offshore area, \(C_{n}^{2}\) over the open ocean in daytime, especially around noon, declines, in the nighttime increases, and is generally close to a constant value 2 \(\times\) 10\({}^{-14}\) m\({}^{-2/3}\). The typical'seesaw' feature disappears farther than 160 km from coast. According to the reference [27; 28], the optical turbulence over open ocean is mainly controlled by air temperature gradient. It may be the result that the open ocean has lower air temperature compared with offshore during the daytime, which inhibits the development of turbulence. At night, the ocean surface temperature is higher than offshore, resulting in a larger temperature gradient, so the turbulence strength is enhanced. When the scientific research vessel is approaching land, the variation characteristics of \(C_{n}^{2}\) are again consistent with the offshore area. In order to obtain the variation characteristics of refractive index structure constant profile, eight balloon-borne radiosondes were launched at different moments during the open ocean. The result is shown in Figure 3, where the whole trend is turbulence strength decreasing with height at different time, but there are inverse increases at height intervals. The profiles reveal that the value of \(C_{n}^{2}\) drops steeply with height near the ocean surface, then gradually increases from the boundary layer to the low stratosphere and again decreases with altitudes in the free atmosphere thereafter. The profile peaks correspond to the tropopause at around 15 km. Compared with \(C_{n}^{2}\) profiles of different moments, it is concluded that optical turbulence strength is strongest at noon and at its maximum is close to 5 \(\times\) 10\({}^{-13}\) m\({}^{-2/3}\). In contrast, optical turbulence strength is relatively weaker at about  
Figure 2: Distribution of diurnal curve of \(C_{n}^{2}\) over the offshore and open ocean surface. 09:00 and 19:00, the minimum reaches the magnitude of \(10^{-19}\) m\({}^{-2/3}\). Furthermore, the turbulence strength at 10:00 and 16:00 is also relatively strong, but slightly less than the turbulence strength value at noon. Similarly, the profiles of two moments, 7:40 in the morning and 19:40 in the evening, measured by the balloon-borne micro-thermometer over the offshore area are illustrated in Figure 4. In the figure, the \(x\)-axis and \(y\)-axis, respectively, represent the number of soundings and the height above ground level. Thirty profiles are displayed at every moment. Note that no matter whether morning or evening, the optical turbulence near the ground is strong, and there exists the strong turbulent layers from 10 to 18 km. With a comparison of the turbulence strength in the morning and evening, it is well visible that the value of \(C_{n}^{2}\) in the morning is larger.