## 5 Conclusions  
This study introduces a systematic method for forecasting Sea Ice Concentrations along the Northern Sea Route for Arctic shipping and evaluating the transit navigation window. The Arctic region is divided into sub-regions that encompass the NSR segments, and the mean SIC of each NSR segment in each sub-region is obtained through the proposed statistical interpolation. This technique is found to be less sensitive to grid size variations than traditional nearest grid point interpolation, and yields stable results even with low grid resolution, as it incorporates all statistical information within the sub-region. Moreover, this proposed statistical interpolation has been demonstrated to exhibit comparable accuracy to the widely employed kriging interpolation method. The interpolated SICs are subsequently analyzed and modeled through the use of an Auto Regressive Integrated Moving Average model, which proves capable of producing  
Figure 23: Comparison of 80% ice-free transit navigation window utilizing SICs from statistical and kriging interpolations. Figure 22: Estimation of 80% ice-free transit navigation window for the selected NSR. accurate short-term SIC forecasts. This purely statistical model, which only relies on reanalysis (historical) data, has a forecast accuracy comparable to that of the more complex Climate Model Intercomparison Project 5 physical models, which require substantial meteorological and oceanographic data. Moreover, the ARIMA model is relatively simple to understand and implement, and is computationally efficient, making it an ideal candidate for real-time SIC estimation systems in onshore and offshore environments. The ARIMA model can be updated in real-time by re-training it with new SIC data, allowing for dynamic correction of forecasts, and continuous creation of new forecasts as the training set expands. Finally, the SIC forecasts are applied to evaluate the transit navigation window for the years to come, indicating that the selected NSR is poised to become readily accessible to shipping, with improved sea ice conditions in the years ahead. In this investigation, we selected a grid size of 0.25\({}^{\circ}\) by 0.25\({}^{\circ}\) in order to assess the transit navigation window and authenticate the proposed statistical models. Although this grid resolution is relatively large and may augment the uncertainty in estimating the transit navigation window, the utilization of high-resolution sea ice information through the proposed statistical technique can yield a more precise transit navigation window. The comparison of uncertainty between high and low resolution represents an intriguing topic and leaves further examination. The present study proposes a methodology that presents a reliable and efficient approach to forecasting sea ice conditions along the Northern Sea Route. The suggested technique is characterized by its explicitness and low computational requirements, which enable its successful implementation both onboard and onshore. The auto-regression model's inherent characteristics facilitate continual learning and updating, thereby providing a sound basis for weather forecast justifications. The proposed methodology has significant implications for shipping companies in terms of managing and scheduling their Arctic shipping itineraries. By providing a preliminary estimate of the navigation window, the methodology allows companies to optimize their shipping operations along the NSR, resulting in reduced risks of delay and financial loss. Conceptualization, D.W., W.T., X.L. and W.M. ; methodology, D.W.; software, D.W.; validation, D.W., X.L., W.T. and W.M. ; formal analysis, D.W.; investigation, D.W.; resources, D.W. and J.Z. ; data curation, D.W.; writing--original draft preparation, D.W.; writing--review and editing, X.L., W.T., W.M. and J.Z. ; visualization, D.W.; supervision, W.M. ; project administration, J.Z. ; funding acquisition, D.W. and J.Z. All authors have read and agreed to the published version of the manuscript.