## 3 Results and Discussion
### Analysis of Influencing Factors  
Based on the previous equation, it is known that the surface optical turbulence strength is proportional to the variance of air temperature variation at a fixed distance. However, for the turbulence strength profile, there are many associated factors. Previous research has shown that turbulence can be brought out by a buoyancy heat bubble and wind shear. According to the currently widely used HMNSP99 model, the relationship is investigated between the two factors and turbulence strength profile. The HMNSP99 model was developed from the statistics of the connection between the outer scale to wind shear and temperature lapse rate at the Air Force Research Laboratory. The model contained more atmospheric parameters and might be better in line with the nature of the actual development of turbulence. The introduction of using this model to estimate the strength of optical turbulence is given in [29]. Figure 5 shows the \(C_{n}^{2}\) profiles of estimated and measured, as well as the profiles of temperature gradient, wind shear, outer scale, and potential refractive index gradient. These profiles came from different launched sites from the open ocean area and the corresponding launched time points of three balloon-borne radiosonde were 23 October, and 3 and 4 November 2020. As shown in Figure 5, although the magnitude of the four parameters is different, the profile fluctuation changes in similar degrees. At the same height, the variance trends of the four parameters are similar. Comparing the temperature lapse rate profiles and the wind shear profiles, the variations in the two parameters below 15 km are quite different and have good consistency above 15 km, which may cause the HMNSP99 model to use two equations when estimating \(L_{0}\). As for the profiles of outer scale and potential refractive index gradient, the \(L_{0}\) has a maximum value near the ground and around 15 km, while \(M\) shows an inverse increase above 15 km. Among the four parameters, the outer scale, whose variance trend is the closest to the turbulence strength, is obviously dominant since its value is higher than other parameters with the order of magnitude multiple. It can conclude that the profiles are related to several influence factors, but the outer scale has the biggest influence weight among them. The result shows that it is reasonable to use the HMNSP99 model to estimate \(C_{n}^{2}\) profiles, which adds more meteorological parameters to obtain a relatively accurate outer scale. The differences between the model and the measurement are relatively small from 3 to 15 km. Differences in fine structure may be attributed to the surroundings that have a mutual effect on atmospheric conditions and, hence, on optical turbulence. Figure 6 shows the profiles of the same characters with Figure 5 except that the experiment site is offshore and the corresponding releasing time points are 07:40 and 19:40, when the turbulence strength is in the weaker period. The variation characteristics of the turbulence strength profiles and four parameters' profiles with height is similar. However, there is little disagreement between the estimated results and the measurement results in the offshore area, where the \(C_{n}^{2}\) estimated by the HMNSP99 model is closer to the measured value over 15 km. In general, the profiles obtained by the model are in accordance with the profiles obtained by the radiosonde measurement. Certainly, there is still some room to improve the estimated model. From the previous discussion, we know that the outer scale contributes more than other parameters. Therefore, it is necessary to study the outer scale characteristics. Figure 7 shows the statistically averaged outer scale profiles of offshore and open ocean areas. Obviously, the outer scale profiles of two scenes are consistent in trend.