## 2 Data and Methods
### Description of Ocean Front Characteristic Model  
For the study on the characteristic model of ocean front, we refer to the parameterized two-dimensional characteristic model of ocean front established by [PERSON] et al. [17]:  
\[T(r,z)=T_{0}(z)+m(r)[T_{i}(z)-T_{0}(z)] \tag{2}\]  
where \(r\) and \(z\) are the horizontal and vertical coordinates, \(T_{0}\) and \(T_{i}\) are the temperature profiles, and \(m\) is the melt function. The ocean front temperature model proposed by [PERSON] is relatively simple in form. The input value is only the temperature profile, and a better ocean front modeling effect can be obtained. Moreover, the strength of the ocean front and the position of the frontal zone can also be achieved by adjusting the melt function. We improved the above model by replacing the temperature profile with the SSP to represent the two-dimensional parameterized characteristic model of ocean front based on the SSP:  
\[C(r,z)=C_{1}(z)+m(r)[C_{2}(z)-C_{1}(z)] \tag{3}\]  
Figure 1: (**a**) The surface sound speed of parts of the Northwest Pacific and the location of the study area; (**b**) The sea surface sound speed distribution of the study area on 1 January 2019. The KEF divides the sea area into three water masses, namely, the low temperature and low salinity water mass in the north of the frontal zone, the high temperature and high salinity water mass in the south of the frontal zone, and the frontal transitional water mass between them. where \(C_{1}\) and \(C_{2}\) are the sound speed profiles and \(m\) is the melt function (which is consistent with Equation (2)). The expression is as follows:  
\[m(r;a)=\frac{1}{2}+\frac{1}{2}\text{tanh}\bigg{[}2\pi(\frac{r}{R})^{10^{\ast}}- \pi\bigg{]} \tag{4}\]  
where \(R\) is the distance between the two sound speed profiles, and the melt parameter \(a\) varies from \(-1.5\) to \(1.5\). In this paper, since the distance between the north and south of the study area extends across two latitudes, \(R\) is defined as 200 km. Figure 3 shows the function curve of melt function \(m\) with the melt parameter \(a\) in the range of \(-1.5\)-\(1.5\). Different melt parameters correspond to different frontal zone positions. Here, we define the initial position of the frontal zone as the position corresponding to when the value of the melt function \(m\) is \(0.1\), and the termination position of the frontal zone as the position corresponding to when the value of the melt function \(m\) is \(0.9\). Figure 2: Sound speed distribution of the 144\({}^{\circ}\) E section in different periods in the ocean front environment (the depth of influence of the ocean front is relatively shallow, we showed the sound speed distribution of 0–2000 m to better observe the ocean front): (**a**) 1 January 2019; (**b**) 1 February 2019; (**c**) 1 July 2019; (**d**) 1 August 2019. The sound speed distribution in the sea area was calculated through Equation (1). Due to the difference in time, the position and intensity of the KEF also vary greatly. According to Equation (3), in order to complete the establishment of the two-dimensional model of the sound speed field of the ocean front, we need to obtain the sound speed profiles of the water masses on both sides of the frontal zone and the melt function related to the distance between the two sound speed profiles. Since the KEF is relatively independent and the water masses on the north and south of the frontal zone are relatively stable, the sound speed profiles at (38\({}^{\circ}\) N, 144\({}^{\circ}\) E) and (36\({}^{\circ}\) N, 144\({}^{\circ}\) E) were selected to represent the sound speed profiles of the water masses on the north and south sides of the frontal zone (corresponding to \(R=200\) km mentioned above). Since different melt parameters \(a\) in the melt function correspond to different positions and widths of the frontal zone, the positions and widths of the frontal zone should be obtained first (clustering the surface sound speed of the study area with the fuzzy C-means (FCM) algorithm).