# Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer
## 3 Results and Discussion
### Setting Up of Contrast Experiments  
In this study, the training data started from 15 November 2017, and finished on 14 December 2017 (30 days). The predicted data started from 15 December 2017, and finished on 30 December 2017 (16 days). Using random indices, all the training data were divided into the three portions involved, training data (0.6), validation data (0.25), and testing data (0.15). Seven variables, including height, temperature, relative humidity, pressure, wind speed, potential temperature gradient, and wind shear, are inputs of the BPNN architecture. Following the normalization process of the original data, the network iterated until it reached the maximum iterations (1000), or the performance reached the preset goals. Moreover, the popular Levenberg-Marquardt backpropagation algorithm was employed as the training function, which updated the weight and bias values according to Levenberg-Marquardt optimization [52; 53]. The Levenberg-Marquardt backpropagation algorithm is often the fastest backpropagation algorithm and is highly recommended as a first-choice supervised algorithm, although it does require greater memory than other algorithms.  
To better evaluate the performance of the BPNN approach, the HMNSP99 model for outer scale and the HAP model for a single parameter were used here to estimate \(C_{n}^{2}\) profiles. The potential temperature gradient and wind shear, which may be the cause of atmospheric turbulence, were added to the HMNSP99 model, making its estimation of turbulence intensity more credible. The \(C_{n}^{2}\) profile obtained by the BPNN approach in Figure 4 was predicted by using the trained network and input of basic meteorological data. \(C_{n}^{2}\) profiles derived from the HMNSP99 and HAP models were evaluated using basic meteorological parameters. In addition, there are \(C_{n}^{2}\) profiles measured by the radiosonde in the figure. Each figure contains four \(C_{n}^{2}\) profiles. Each method could obtain 32 profiles, for a total of 32 figures. Due to this large number, only six consecutive comparisons of the \(C_{n}^{2}\) profile are shown in Figure 4; and as can be seen, the \(C_{n}^{2}\) vertical distribution decreases sharply in the surface layer, mostly below 100 m. In the boundary layer, the \(C_{n}^{2}\) is generally in the order of \(10^{-16}\) m\({}^{-2/3}\). Both the BPNN approach and HMNSP99 model respect the variability and complexity of atmospheric turbulence better than the HAP model, but comparing the BPNN approach with the HMNSP99 model, it is clearly observed that the BPNN approach outperforms the HMNSP99 model in capturing the spatial evolution of \(C_{n}^{2}\). The BPNN approach generally agrees with the measured values both in magnitude and trend. In contrast, the estimated values from the HMNSP99 model have relatively larger drift compared with radiosonde measurements at certain heights. The high variance may be attributed to a wider variety of atmospheric conditions, but overall, the estimated values of \(C_{n}^{2}\) profiles using the BPNN approach are more consistent with the measured values than the HMNSP99 model and HAP model.