## 2 Materials and Methods
### Extraction of High-Resolution Sea Ice Concentration
#### 2.5.2 Calculation Method of Sea Ice Concentration  
In sea ice concentration calculation, the traditional method involves using a small sliding window and calculating the ratio of the number of sea ice pixels within it to the total number of pixels. This method is simple in principle, but time-consuming. Here, we propose a fast sea ice concentration calculation method based on convolution and array operations. The convolution operation quickly counts the number of sea ice and seawater points, and array operations can be used to directly obtain the sea ice concentration data at a 50 m resolution for the whole area. The algorithm proceeds as follows:  
Step 1: Segmentation maps of ice, water, and land are extracted based on the method outlined in Section 2.5.1, by identifying the land area followed by the land mask. Since sea ice concentration determination involves using the \(ks^{2}\) image elements in the surrounding rectangular area to calculate the sea ice concentration value at the center point, where \(ks\) indicates the size of the convolution kernel, the edge of the image needs to be filled symmetrically in advance before carrying out the rest of the process, and the length of the filled image elements on each side is calculated as \(\frac{ks}{2}\). Step 2: Preliminary processing of the triple classification map. Here, we set the pixel value of the sea ice point to 1 and the pixel value of seawater points to 0, while the land area is given the same pixel value as the sea ice point of 1. The first convolution operation is carried out with a convolution kernel value of 1 and convolution kernel size of \(k\)s to obtain the statistical map \(A_{II}\). Step 3: Similarly to Step 2, the land area is first given the same pixel value (0) as the seawater point, and the second convolution is carried out using a convolution kernel with a value of 1 and a size of \(k\)s to obtain the second statistical map \(A_{1w}\). Step 4: Matrix operations are carried out based on Equation (2) to obtain high-resolution sea ice concentration data. \[SIC=\frac{A_{1w}}{A_{k\textsuperscript{s}^{2}}-A_{1w}+A_{II}}\times 100\% \tag{1}\]  
where \(k\)s is the kernel size--the spatial resolution of the sea ice concentration data is \(50\,\text{m}\times k\textsuperscript{s}\); \(SIC\) denotes the point sea ice concentration matrix of the region; \(A_{k\textsuperscript{s}^{2}}\) is the matrix containing all values; \(A_{II}\) is the result obtained when setting all sea ice points to 1 and seawater points to 0, treating the land region as sea ice, and performing a single convolution using a rectangle of size \(k\)s with a fixed value of 1 for the convolution kernel; and \(A_{1w}\) is the result obtained when treating the land area as seawater and performing a single convolution using the same convolution kernel. A value of sea ice concentration between 0 and 1 is obtained by the formula, which greatly reduces the time of calculation of sea ice concentration. Any point within the result is the calculated sea ice concentration within the \(k\textsuperscript{s}^{2}\) pixel region adjacent to that point, and this approach thus preserves more of the details of the spatial distribution of sea ice (Figure 3c). All the convolution operations in this method use the fast Fourier transform (FFT) to optimize the computational speed [26]. This method has been shown to significantly improve computational speed, especially for convolution kernel sizes larger than \(8\times 8\). Through this calculation method, the overall time required for sea ice concentration computation is reduced to 11% that of the conventional method, although the memory required is increased. The reason for this is that the time complexity of the algorithm is reduced from \(\text{O}(n^{2})\), which is required for the sliding window calculation, to \(\text{O}(n\log_{2}n)\) due to optimization using a fast Fourier transform (FFT) in the convolution operation.