## 4 Experiment and Results
### Performance with a Five-Month Lead Time  
Current Arctic sea ice prediction models primarily operate on subseasonal to seasonal timescales, with a lead time of approximately three months for forecasts. Achieving predictions over longer timescales remains a significant challenge. To test the performance of our model proposed for long-term timescale predictions, we set the lead time to five months. Figure 9 displays the trends of RMSE and MAE for different lead times from 2018 to 2020. The RMSE and MAE values for a five-month lead time are lower than those for a one-month lead time. The average RMSE value for a five-month lead time is 0.121, showing a reduction of 0.044 compared to the one-month lead time average RMSE. As can be seen from the PCC and NSE results in Table 5, setting a lead time of five months decreases the correlation between the predicted results and the actual values. This decrease is attributed to the lengthening of the prediction sequence, which weakens the model's performance. Nonetheless, the performance of our proposed model with a five-month lead time is still comparable to that of the one-month ConvLSTM model. This is because the encoder in the PDED-ConvLSTM model considers all historical sea ice concentration information when processing the input sequence, thereby avoiding the phenomenon of information loss. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **FLOPs** \\ \hline ConvLSTM & 21.6 \\ Multi-Stacking ConvLSTM & 53.8 \\ PDED-ConvLSTM & 44.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of the three models on the FLOP indicator. \begin{table}
\begin{tabular}{c l c c c} \hline \hline
**Metrics** &
\begin{tabular}{c} **Length of Input** \\ **SIC Sequence** \\ \end{tabular} & **2018** & **2019** & **2020** \\ \hline \multirow{2}{*}{NSE} & 1-Month Lead & 0.948 & 0.934 & 0.939 \\  & 5-Month Lead & 0.929 & 0.917 & 0.914 \\ \hline \multirow{2}{*}{PCC} & 1-Month Lead & 0.975 & 0.968 & 0.971 \\  & 5-Month Lead & 0.961 & 0.944 & 0.958 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: NSE And PCC predicted by different lead months. Figure 6: Spatial distribution of residuals in different models in 2018 (Ground truth–Prediction). (**a**) Climatology. (**b**) ConvLSTM. (**c**) Muti-Stacking ConvLSTM. (**d**) PDED-Convlstm. Figure 7: Spatial distribution of residuals in different models in 2019 (Ground truth–Prediction). (**a**) Climatology. (**b**) ConvLSTM. (**c**) Muti-Stacking ConvLSTM. (**d**) PDED-Convlstm. Figure 8: Spatial distribution of residuals in different models in 2020 (Ground truth–Prediction). (**a**) Climatology. (**b**) ConvLSTM. (**c**) Muti-Stacking ConvLSTM. (**d**) PDED-Convlstm. Figure 10 illustrates the spatial distribution of the predicted values and the ground truth for the melt seasons of 2018-2020, with a lead time of five months. Although the accuracy of these predictions, in terms of their alignment with the ground-truth data, is reduced compared to the one-month lead time forecasts, the predictions still accurately capture the dynamic changes in sea ice. Therefore, these forecasts continue to provide reliable information for shipping navigation and Arctic scientific research. Figure 11 represents the spatial distribution of residuals for the melt seasons from 2018 to 2019. It is evident that the errors are larger with a five-month lead time compared to a one-month lead time. In the first two months of the five-month lead time, most errors fall within the range of (\(-10\%\), \(10\%\)). In the subsequent three months, the errors gradually increase but are mostly kept within the range of (\(-25\%\), \(25\%\)). Additionally, compared to the one-month lead time, the five-month lead time consistently underestimates the one-year ice area in the Arctic, while the one-month lead time consistently overestimates it.