## 3 Results and Discussion
### Effectiveness of Forecasting the Changes of Depth in Convergence Areas  
The convergence area is the area where the sound energy is concentrated near the sea surface during the sound propagation process [35]. The study of the convergence area is of practical significance for underwater acoustic detection [36; 37]. Due to the existence of the ocean front, the depth change of the convergence area has become a concern. Taking the experiment on January 1 st as an example, we set the sound source frequency to 50 Hz, and calculated the whole sea depth variation of the TL in the distance-independent environment (the environment without ocean fronts), model environment, and the actual ocean front environment at the SD of 100 m, 300 m, and 500 m (Figure 13). It was found that due to the existence of the ocean front, there was a significant downward shift in the distribution of TL after its passing through the frontal zone in the convergence area, which was a very obvious phenomenon is in both the model and the actual ocean front environments. The change in the depth of the convergence area is related to not only the SD but also the location of the frontal zone and the range of its influence. Since the effectiveness of the model from the perspective of TL is verified in the previous section, in this section the effectiveness of melt function in the rapid forecast of the convergence area depth in the ocean front environment is verified by combining the melt function with the depth of the convergence area calculated by the model and the actual ocean front. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Season**} & \multirow{2}{*}{**SD**} & **Unsmoothed Results** & **Smoothed Results** \\  & & **RMSE (dB)** & **RMSE (dB)** \\ \hline \multirow{3}{*}{Winter} & 100 m & 3.9682 & 3.3615 \\  & 300 m & 5.6548 & 4.6889 \\  & 500 m & 6.1374 & 4.9942 \\ \hline \multirow{3}{*}{Summer} & 100 m & 5.0845 & 4.7005 \\  & 300 m & 5.4907 & 4.2715 \\ \cline{1-1}  & 500 m & 5.2130 & 4.4184 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between the TL calculated through the model and the actual situation at different seasons and different sound source depths (the frequencies were 50 Hz and 400 Hz, respectively). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Season**} & \multirow{2}{*}{**Frequency**} & **Unsmoothed Results** & **Smoothed Results** \\  & & **RMSE (dB)** & **RMSE (dB)** \\ \hline \multirow{3}{*}{Winter} & 50 Hz & 5.2052 & 4.4518 \\  & 400 Hz & 5.3020 & 4.2448 \\ \hline \multirow{3}{*}{Summer} & 50 Hz & 5.3399 & 4.6469 \\  & 400 Hz & 5.1879 & 4.2224 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between the TL calculated through the model and the actual situation at different seasons and different frequencies (the sound source depths were 100 m, 300 m, and 500 m, respectively). The law of refraction followed by ray acoustics is [PERSON]'s law:  
\[\frac{\cos\alpha_{0}}{c_{0}}=\frac{\cos\alpha_{i}}{c_{i}}=const \tag{9}\]  
where \(\alpha_{0}\) is the angle between the incident direction and the horizontal direction of the sound rays, called grazing angle, \(c_{0}\) is the sound speed on the medium surface of the incident layer, \(\alpha_{i}\) and \(c_{i}\) is the grazing angle and sound speed of the sound rays on the surface of the outgoing layer respectively. According to [PERSON]'s law, when the sound speed changes with depth, the sound rays always bend to the place where the sound speed is lower. The convergence area is a manifestation of the concentrated area of sound ray turning, so the depth of the convergence area is not only related to the SD but also has a corresponding relationship with the distribution of sound speed. Since only the sound speed profiles of the water masses on both sides of the frontal zone were used in our model as input values, we only obtained the data of these two sound speed profiles.