## 3 Methodology
### Multi-Candidate Multi-Correlation Coefficient Optimization Algorithm  
The prevailing tidal current is one of the important hydrodynamic processes in the Chinese seas. The precision of SSC field inversion using the remote sensing technique largely determines the accuracy of the SSC field, so it is necessary to improve the inversion precision. The OSU model current field is consistent with the in situ SSC field in terms of the current direction and can well reflect the vector rotation direction in a tidal current elliptic period. Therefore, combining the GOCI inversion SSC field and OSU model current field, we propose a multi-correlation coefficient optimization algorithm for the remote sensing inversion SSC vector based on the OSU tidal model (Figure 5). The goal is to identify and substitute the spurious vector in the GOCI inversion current field and improve the SSC precision. The main step is to obtain the three largest candidate SSC vectors under the first three correlation coefficients for seven consecutive periods of the GOCI  
Figure 4: (a) A vector diagram formed by calculating the buoy points (A, B, and C represent the three points on the projection surface of the sphere, and the angle of the ”arc” on the sphere at that point, respectively; a, b, and c represent the arc of the ABC three-point pair, O is the center of the sphere). (b) A right triangle composed of three points A, B, and C and the coordinates of each point. day by the MCC method. Figure 6a shows a schematic diagram for estimating the SSC field by the multi-correlation coefficient inversion algorithm. Based on template matching technique, this algorithm takes into account the mismatch phenomenon of this technique in high-turbidity sea areas; that is, the highest correlation coefficient does not necessarily correspond to the optimal matching and obtains the SSC vectors under the first three correlation coefficients to improve the optional rate. Then, the OSU tidal model is used to obtain corresponding tidal current vectors, and the two current field vectors are sorted according to the time order. For the sorted tidal current vectors, the rotation angle of the adjacent tidal current vectors is calculated, and the direction of the rotation angle is taken as the rotation direction. As shown in Figure 6b, the angle \(a_{n-1}\) is the rotation for vectors \(V_{n}\) and \(V_{n-1}\), and the angle \(a_{n}\) is the rotation for vectors \(V_{n}\) and \(V_{n+1}\). The direction from vector \(V_{n-1}\) to \(V_{n}\) is clockwise, and that from vector \(V_{n-1}\) to \(V_{n}\) is counterclockwise. Then, the rotation direction of the GOCI SSC vector obtained by the 1 st correlation coefficient is taken as the main rotation direction, the rotation direction and rotation angle of the two adjacent vectors are calculated, and the spurious vector is determined by comparing with the tidal current vector. As shown in Figure 6c(I), \(V_{n-1}\), \(V_{n}\) and \(V_{n+1}\) are the SSC vectors of three adjacent time periods in the main rotation direction, and \(v_{n-1}\), \(v_{n}\) and \(v_{n+1}\) are the corresponding tidal current vectors. To facilitate the calculation of rotation angle and direction, the starting points of all vectors are placed at the same point. As illustrated in Figure 6c(II), \(a\) is the rotation angle of \(V_{n}\) and \(V_{n+1}\), and \(a^{\prime}\) is the rotation angle of \(v_{n}\) and \(v_{n+1}\). The corresponding rotation directions of the two are opposite. It can be determined that vector \(V_{n+1}\) is the spurious vector. Finally, the spurious vectors are substituted by the candidate vectors of the 2 nd and 3 rd correlation coefficients of the corresponding time period; and the rotation angle between the substituted vector and its adjacent vector is calculated. The vector closest to the rotation angle of the tidal current vector in the corresponding time period is selected as the optimal substituted vector to obtain the final SSC vector in the main rotation direction and improve the precision of the inversion SSC field.