## 3 Methodology  
### GOCI Data Processing  
Supported by GOCI Data Processing System software (GDPS), the GOCI-L1B original data were preprocessed in terms of atmospheric correction and masking. Then, we used the built-in TSM inversion algorithm provided by GDPS processing software to process data into an L2-level TSM product [38]. Figure 3 shows the MCC method based on the image matching method. By performing this operation, hourly SSC can be obtained from two consecutive GOCI images on the same day. The former image used to estimate the present position is called the \"template window,\" and the latter is called the \"search window.\" The MCC method uses correlation relationship based on template matching technique to track change in the tracer structure. Template matching is a technique for finding the most similar part of an image to another template image [39]. The template is a small image, and template matching is a search for a target in a large image, where the target is known to be in the image and has the same size, orientation and image elements as the template, and a certain algorithm can find the target in the image and determine its coordinate position. Equation (1) is used to calculate the correlation coefficient between the \"template window\" and the \"matching window.\"  
\[\rho\left(S^{i}_{sub},T^{i+1}_{sub}\right)=\frac{\text{cov}(S^{i}_{sub}-T^{i+ 1}_{sub})}{\sqrt{\text{var}(S^{i}_{sub})\times\text{var}(T^{i+1}_{sub})}} \tag{1}\]  
where \(i\) is the time scale of GOCI observations, its value of 0 to 7 representing Beijing time from 8:30 to 15:30 (1-hr interval), and \(S^{i}_{sub}\) and \(T^{i+1}_{sub}\) are the two-dimensional matrix data of \"template window\" and the search sub-window with the same size in \"Search window,\" respectively,\(\rho\) is the cross-correlation coefficient, and its variation range is [-1,1]. The closer the correlation coefficient is to 1, the more accurate the matching of the two remote sensing images is, and the more accurate the retrieved current is. Using Equations (2) and (3), the speed and direction of the current can be calculated.  
\[\text{V}=\frac{\sqrt{\left(x_{i+1}-x_{i}\right)^{2}+\left(y_{i+1}-y_{i}\right) ^{2}}}{h} \tag{2}\]  
\[\text{D}=\text{arctan2}(y_{i+1}-y_{i},x_{i+1}-x_{i}) \tag{3}\]  
where \(x_{i}\) and \(y_{i}\) are the central coordinates of the template window, and \(x_{i+1}\) and \(y_{i+1}\) are the central coordinates of the matching window.\(h\) is the observation time interval between \(S^{i}_{sub}\) and \(T^{i+1}_{sub}\), which is 1 h.  
Figure 3: A schematic diagram of the MCC algorithm for estimating SSC field. Taking the first invertible current field as an example, the images on the left and right represent satellite remote sensing images observed in the same sea area and on the same day at 8:30 and 9:30, respectively. The solid box in the left panel is the template window, the solid box in the right panel is the matching window, and the dashed box is the same template window as that in the left panel.  
The template window size selected here is 20 \(\times\) 20 pixels, the search window size is 36 \(\times\) 36 pixels, and the fitting threshold is set to 0.9 to obtain more accurate vectors [9; 29]. The appropriate matching window is determined by calculating the correlation coefficient between the template window and the moving search window. If the calculated value is greater than the threshold value, the position that the template window moves to in unit time is considered as the matching window. Then, the above steps are repeated to obtain a relatively complete SSC field.