## 3 Results and Discussion
### Effectiveness of Forecasting the Changes of Depth in Convergence Areas
Taking the experiment on January 1 st as an example, the SOFAR axis depth of these two sound speed profiles was 700 m and 1250 m, respectively (Figure 7). When the  
Figure 13: Comparison of TL between the distance-independent environment, model, and actual ocean front (1 January f = 50 Hz): the TL of distance-independent environment, and the SD = (**a**) 100 m, (**b**) 300 m, and (**c**) 500 m; the TL of the model, and the SD = (**d**) 100 m, (**e**) 300 m, and (**f**) 500 m; the TL of actual ocean front, and the SD = (**g**) 100 m, (**h**) 300 m, and (**i**) 500 m. 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 above phenomenon can help us achieve the forecasting of the depth change of the acoustic convergence area under ocean front environments. SD is fixed, according to [PERSON]'s law, the depth of the convergence area formed by the sound rays emitted at a small glancing angle near the sound source should be basically the same as the SD (or slightly shallower than the SD) under a distance-independent environment. As shown in Figure 13, when the SD is 100 m, 300 m, and 500 m, the depth of the convergence area always stays near 0 m (Figure 13a), 200 m (Figure 13b), and 400 m (Figure 13c) under a distance-independent environment. In our model and actual ocean front environment, when the SD is located at 100 m, 300 m, and 500 m, the depth of the convergence area near the sound source is 0 m (Figure 13d,g), 200 m (Figure 13e,h), and 400 m (Figure 13f,i), respectively since the ocean environment not far away from the sound source is also a distance-independent environment. Based on the above analysis, we obtained a forecast curve of the depth change of the convergence area during the transmission process in the ocean front environment:  
\[D(z)=D_{1}(z)+m(r;a)[D_{2}(z)-D_{1}(z)] \tag{10}\]  
where \(D_{1}(z)\) is the depth of the convergence area near the sound source, \(D_{2}(z)\) is the depth of the convergence area at the farthest distance (200 km). \(m(r;a)\) is the melt function, and the expression is consistent with Equation (4). In the ocean front environment, it is believed that the depth change of the convergence area is related to the change of the sound speed. Therefore, the depth of the SOFAR axis was extracted as the feedback depth and to estimate \(D_{2}(z)\):  
\[D_{2}(z)-D_{1}(z)=SOFAR_{2}(z)-SOFAR_{1}(z) \tag{11}\]  
where \(SOFAR_{1}(z)\) and \(SOFAR_{2}(z)\) are the depths of the SOFAR axis of two sound speed profiles. Take the experiment on January 1 st as an example, the \(SOFAR_{1}(z)\) and \(SOFAR_{2}(z)\) are known to be 700 m and 1250 m. When the SD = 100 m, the depth of the convergence area near the sound source was about 0 m (\(D_{1}(z)\) =0 m), so \(D_{2}(z)\) should be 550 m. We completed the forecast of the depth of the convergence area at the SD of 100 m on 1 January and compared this result with the model calculated one (we selected two convergence areas passing through the frontal zone) and the actual results of the ocean front (corresponding to the two convergence areas of the model), to obtain the following results (Figure 14). We found that the depth distribution of the convergence area in the model and the actual condition were in good agreement with the forecasted curve with only a little difference, which proves that the melt function was applied to effectively achieve the depth forecast of the convergence area in the ocean front environment. By respectively analyzing the results of the depth of the convergence area during the four periods (Figures 14 and 15), it was concluded that since the two sound speed profiles  
Figure 14: The forecasting curve of the depth of the convergence area (the red dotted line) and the calculating results of the model (blue dots) and actual ocean front (black dots) on 1 January (SD = 100 m).