# Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer
## 3 Results and Discussion
### Overall Approach to Performances  
To quantify the calculation error of the above BPNN approach, HMNSP99 model and HAP model, the statistical results from individual flights of lg\(C_{n}^{2}\) between measurements and estimations are demonstrated in Figure 5. As shown in Figure 5, we used the BPNN approach, HMNSP99 model and HAP model to predict 32 \(C_{n}^{2}\) profiles. Then, the error analysis of the \(C_{n}^{2}\) profile predicted by each method and the measured \(C_{n}^{2}\) profile was carried out according to Equations (18)-(20). For each method, 32 error profiles were obtained for each, including the Bias, RMSE, and CRMSE. Then, each error profile was averaged to the height, with an average value obtained. A total of 32 error average values for each method were obtained. It is noted that the bias of the BPNN approach and the HAP model have no similarities except in a few flights. Most bias values calculated from the BPNN approach were between \(-0.5\) and \(0.5\), but for the HMNSP99 model and HAP model, the maximum value exceeded \(-1\) and \(1\), respectively. Compared with the results obtained by the HMNSP99 model and HAP model, we can observe that the BPNN approach had the lowest RMSE and CRMSE for 32 individual meteorological balloon flights. Most RMSE and CRMSE values obtained from the BPNN approach were below \(1\). At the same time,most RMSE and CRMSE values from the HAP model were slightly larger than the BPNN approach, and for the HMNSP99 model, half of the values were more than 1. In general, the BPNN approach had the highest stability and showed more reliable \(C_{n}^{2}\) profiles with better statistical results than the HMNSP99 and HAP models. Figure 4: Vertical profiles of \(C_{n}^{2}\) from the radiosonde, BP neural network, HMNSP99 model and HAP model. Figure 5: Statistical analysis of lg\(C_{n}^{2}\) calculated by the BPNN approach, HMNSP99 model and HAP model for all samples of individual meteorological balloons. In addition, the overall statistics comparing the BNPP approach and the other models, derived from all 32 flights performed, are shown in Figure 6, with the vertical profiles of the bias, the RMSE and the CRMSE. According to Equations (18)-(20), \(N\) represents the amount of data in the horizontal direction for a couple \((X_{i},Y_{i})\) at each precise height. In this section, we use \(N=32\) at each precise height. In detail, the bias, RMSE and CRMSE were calculated based on the \(C_{n}^{2}\) profiles with 10 m vertical resolution; then, a five-point moving average was applied to the final profiles. It can be seen from Figure 6 that the absolute values of the bias from the BPNN approach were lower than that from the HMNSP99 model and HAP model at most heights. Most bias values calculated from the BPNN approach were between \(-0.5\) and \(0.5\) in the offshore atmospheric boundary layer. Note that for the HMNSP99 model there existed a larger bias value from 0 to 1500 m, and the maximum value exceeded \(-1\). The RMSE and CRMSE of the BPNN approach were similar in value, and mainly smaller than 1.25 along the boundary layer. It is notable that the RMSE and CRMSE of the HMNSP99 model were larger than the BPNN approach, more noticeable between 500 and 1000 m. Moreover, almost all the RMSE and CRMSE of the HAP model fell between the BPNN approach and the HMNSP99 model results, which had a range from 1 to 1.25. In conclusion, the BPNN approach was more reliable than the HMNSP99 model and HAP model in reconstructing the strength of optical turbulence through individual and overall statistical analyses. In this section, we focus attention on the ability of the BPNN approach to rebuild \(r_{0}\), \(\varepsilon\), and \(\tau_{0}\). The integrated astroclimatic parameters were obtained via \(C_{n}^{2}\) values measured by balloons and estimated by the BPNN approach and the HMNSP99 model. According to Equation (24), \(C_{n}^{2}\) is obtained through \(C_{T}^{2}\). This formula is applicable to visible and near-infrared wavelengths.