## 4 Experiments
### Main Results and Discussion
#### 4.2.3 Key Variables Analysis  
We also conducted a key variables analysis to demonstrate the effectiveness of the PCC module with different crucial meteorological variables, including air temperature, specific humidity, wind velocity, precipitation, etc. These variables are widely utilized in weather forecasting tasks, have shown significant impacts on climate change, and correlate closely with real-world applications such as agriculture, transportation, etc. Importantly, they also exhibit significant correlation patterns between each other and have specific ranges of values. A Table 3 demonstrates, the PCC module can improve the performance of different backbone models with respect to these different key meteorological variables.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Design**} & \multicolumn{4}{c}{**96**} & \multicolumn{2}{c}{**192**} & \multicolumn{2}{c}{**336**} & \multicolumn{2}{c}{**720**} & \multicolumn{2}{c}{**Average**} \\ \cline{3-10}  & & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline \multirow{2}{*}{iTransformer} & Original & 0.175 & 0.215 & 0.225 & 0.258 & 0.281 & 0.299 & 0.358 & 0.350 & 0.260 & 0.281 \\  & +PCC & **0.159** & **0.204** & **0.208** & **0.248** & **0.267** & **0.291** & **0.347** & **0.344** & **0.245** & **0.272** \\ \hline \multirow{2}{*}{PatchTST} & Original & 0.175 & 0.216 & 0.221 & 0.257 & 0.280 & 0.298 & 0.352 & 0.347 & 0.257 & 0.280 \\  & +PCC & **0.157** & **0.205** & **0.207** & **0.249** & **0.270** & **0.293** & **0.345** & **0.344** & **0.245** & **0.273** \\ \hline \multirow{2}{*}{SegRNN} & Original & 0.162 & 0.200 & 0.208 & 0.243 & 0.264 & 0.285 & 0.347 & 0.340 & 0.245 & 0.267 \\  & +PCC & **0.144** & **0.189** & **0.189** & **0.233** & **0.238** & **0.273** & **0.299** & **0.317** & **0.218** & **0.253** \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Backbone**} & \multirow{2}{*}{**Design**} & \multicolumn{4}{c}{**Observation Length**} \\ \cline{3-6}  & & **48** & **96** & **192** & **336** & **720** \\ \hline \multirow{2}{*}{stackLSTM} & Original & 0.326 & 0.298 & 0.326 & 0.322 & 0.349 \\  & +PCC & **0.236** & **0.221** & **0.213** & **0.195** & **0.228** \\ \hline \multirow{2}{*}{DLinear} & Original & 0.230 & 0.207 & 0.190 & 0.177 & 0.168 \\  & +PCC & **0.188** & **0.152** & **0.145** & **0.143** & **0.142** \\ \hline \multirow{2}{*}{iTransformer} & Original & 0.202 & 0.175 & 0.170 & 0.162 & 0.175 \\  & +PCC & **0.181** & **0.159** & **0.154** & **0.151** & **0.159** \\ \hline \multirow{2}{*}{PatchTST} & Original & 0.211 & 0.175 & 0.159 & 0.150 & 0.147 \\  & +PCC & **0.188** & **0.157** & **0.150** & **0.146** & **0.145** \\ \hline \multirow{2}{*}{SegRNN} & Original & 0.203 & 0.162 & 0.150 & 0.146 & 0.142 \\  & +PCC & **0.169** & **0.144** & **0.139** & **0.138** & **0.138** \\ \hline \hline \end{tabular} Bold values indicate better results.  
\end{table}
Table 2: MSE of forecasting results for different backbones with and without PCC across different lengths of observed time series (\(\{48,96,192,336,720\}\)) with a consistent prediction horizon of 96.