## 4 Model Implementation and Validation
### Statistical Interpolation in Sub-Regions  
The results of the feature importance analysis suggest that the SIC metrics of area, mean, variance and standard deviation are of significant relevance to the statistical interpolation, as depicted in Figure 4. Conversely, skewness and kurtosis do not seem to have any significant impact. Additionally, a close examination of Pearson's coefficients, as illustrated in Figure 5, highlights strong linear correlations between the SIC's area and mean, as well as between its standard deviation and variance. In this regard, the sea ice area, \(X_{t,si}\)  
Figure 3: The workflow for implementing the statistical interpolation and ARIMA model for evaluating the route availability. and standard deviation, \(X_{t,sdt}\), are selected out of the six statistics as features upon which to perform the interpolation. The results of the statistical regression are summarized in Table 1, and the SIC value can be expressed as  
\[\widehat{Y}_{t}=2.6803X_{t,sia}-0.2203X_{t,sdt}. \tag{13}\]  
In Table 1, the \(t\)-test suggests that the null hypothesis of \(\beta=0\) can be rejected since \(p\)-values of \(\beta_{1}\) and \(\beta_{2}\) are equal to zero. Additionally, the \(R^{2}\) value, which measures the proportion of variation in the dependent variables, is equal to 0.937 and also verifies that the statistical regression fits the reanalysis data well. Following the implementation of statistical interpolation across all sub-regions, the correlation between the interpolated and reanalysis SIC values is depicted in Figure 6. This illustrates that most of the points are situated in close proximity to the diagonal line, suggesting that the linear model effectively captures the SIC along the NSR. A diagnostic examination of the residual is depicted in Figure 7, which demonstrates, through the Q-Q plot and histogram, that the residual of the interpolation conforms to a normal distribution as intended. The scatter plots of \"residual vs. fitted values\" and \"residual vs. \(X\)\" evince \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Coeff.** & **Std. Err.** & **t-Statistic** & \(p\)**-Value** \\ \hline \(\hat{\beta}_{1}\) & 2.6803 & 0.056 & 47.970 & 0.000 \\ \(\hat{\beta}_{2}\) & \(-0.2203\) & 0.025 & \(-8.899\) & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical interpolation results. Figure 4: Feature ranking for statistical interpolation in sub-region No. 2. Figure 5: The Pearson’s coefficients of features in sub-region No. 2.  
randomness, thus affirming that the residual of the statistical interpolation constitutes white noise. As previously noted in Section 2, the precision of the nearest grid point interpolation is strongly contingent upon the resolution of the grid. To evaluate the sensitivity of the statistical interpolation to grid size, the nearest grid point interpolation and statistical interpolation were performed with grid sizes ranging from 0.5\({}^{\circ}\) by 0.5\({}^{\circ}\) to 3.5\({}^{\circ}\) by 3.5\({}^{\circ}\). The nearest grid point interpolation with a resolution of 0.25\({}^{\circ}\) by 0.25\({}^{\circ}\) served as the reference. As depicted in Figure 8, it is evident that as the grid size increases, the nearest grid point  
Figure 6: The correlation between interpolated and reanalysis SICs along the NSR. Figure 7: The residual diagnosis of the statistical interpolation in sub-region No. 2.  
interpolation progressively generates larger root-mean-squared errors (RMSEs, as indicated by Equation (14)). \[ \begin{array}{l}{e_{i}=\sqrt{\frac{\sum_{t=1}^{N}\left(\widehat{Y}_{t,\,m,\,i}- \widehat{Y}_{t,\,0.25,\,1}\right)^{2}}{N}},}\\ {\rm with}\ m\in\{0.5,1.0,1.5,2.0,2.5,3.0,3.5\},\\ {i=1,2,}\end{array}  \tag{14}\]  
where \(\widehat{Y}_{t}\) is the interpolated SIC defined in Equation (8). The nearest grid point interpolation and statistical interpolation are denoted as \(i=1\) and \(2\), respectively. The total number of timestamps is represented by \(N\), and \(m\) represents the grid sizes.