# Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer
## 3 Results and Discussion  
### Principle of \(C_{n}^{2}\) and Measurement  
The values of \(C_{n}^{2}\) measured by the micro-thermometer are derived from a pair of horizontally separated micro-temperature probe wires [42]. The refractive index fluctuation mainly results from temperature fluctuation at visible and near-infrared wavelengths [35]. According to Equation (24), the \(C_{n}^{2}\) is related to the corresponding temperature structure constant (\(C_{T}^{2}\)):  
\[C_{n}^{2}=\left(79\times 10^{-6}\frac{P}{T^{2}}\right)^{2}C_{T}^{2} \tag{24}\]  
where \(T\) is the air temperature (K) and \(P\) is the air pressure (hPa). [PERSON] defined the \(C_{T}^{2}\) as the constant of proportionality in the inertial subrange of the temperature structure function \(D_{T}(r)\), and the \(C_{n}^{2}\) can be described as follows [43; 44]:  
\[D_{T}(r)=\langle[T(x)-T(x+r)]\rangle=C_{T}^{2}r^{2/3},l_{0}\ll r\ll L_{0} \tag{25}\]  
where \(x\) and \(r\) denote the position vector, \(\langle\dots\rangle\) represents the ensemble average, and \(l_{0}\) and \(L_{0}\) are the inner and outer scales of turbulence and have units of m.  
From November to December in 2017, a field campaign of balloon-borne radiosondes equipped with micro-thermometers and GPS was conducted by the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences in the offshore area. The balloon-borne radiosondes explored the atmosphere twice a day, and all the flights were released at local time 7:00 a.m. and 19:00 p.m. every day. The scene of the launching balloon is shown in Figure 2.  
The vertical profiles of \(C_{n}^{2}\), and the structure function parameters for temperature (\(C_{T}^{2}\)), air pressure, atmospheric temperature, relative humidity, wind speed, and wind direction were obtained by balloon-borne radiosondes. The ascent rate of the balloon was 6 m/s, with a vertical resolution of about 10 m. A micro-thermometer, which is a crucial piece of equipment for detecting the atmospheric temperature structure constant, was erected and whose equivalent noise of temperature fluctuation was about 0.002 \({}^{\circ}\)C [45; 46; 47]. Here, the frequency response range of the micro-thermometer was 0.1-30 Hz, and the corresponding statistical average time was 5 s.  
The monthly average profiles of \(C_{n}^{2}\), as well as the profiles of possible influencing factors, are depicted in Figure 3. In this figure we have added the Richardson number, which is used to characterize the influence of temperature stratification and wind speed shear on the development of turbulence [48]. The height reported is the vertical distance above ground level in all figures of this paper. Furthermore, many studies have proved that the height of the offshore atmospheric boundary layer is below 2 km [49; 50; 51], so the maximum height of all profiles was fixed at 2 km in all panels. From Figure 3, we can see that the Richardson number profile has peaks when the wind shear and potential temperature gradient profile has large fluctuations at many altitudes. At the same height, the turbulent outer scale profile and the potential refractive index gradient profile also have maximum values, which can cause the appearance of a strong, turbulent, thin layer.  
Figure 3: Average profiles of (**a**) wind shear, (**b**) potential temperature gradient, (**c**) Richardson number, (**d**) outer scale, (**e**) potential refractive index gradient and (**f**) \(C_{n}^{2}\) measured by all samples of balloon-borne radiosondes.  
Figure 2: Launching a balloon-borne radiosonde.