## 4 Experiments
### Main Results and Discussion
#### 4.2.4 Impact of Strongly Correlated Variables  
One potential concern with the dataset used in our experiments is the presence of strongly correlated variables, particularly those related to humidity measurements (e.g., Tdew, rh, VPmax) and some temperature-related variables (e.g., T, Tlog). These variables describe similar physical properties but do so in different mathematical representations, which might introduce unwanted biases or redundancies in the model.  
To investigate this concern, we conduct additional experiments using a reduced variable set that excluded these potentially redundant features. Specifically, we removed the following variables: Tdew (dew point temperature), VPmax (saturation water vapor pressure), VPact (actual water vapor pressure), VPdef (water vapor pressure deficit), sh (specific humidity), H2 OC (water vapor concentration), Tpot (potential temperature), and Tlog (temperature in log).  
Table 4 presents a comparison of model performance with the full variable set and the reduced variable set. Contrary to what might be expected, the models trained on the full variable set consistently outperformed those trained on the reduced set regardless of whether PCC was applied. Moreover, PCC maintained its performance improvement ability even with the reduced variable set.  
These results suggest that while these particular variables are mathematically related or describe similar weather conditions, they also contribute unique and valuable information that is relevant to the forecasting task. The relationships between these variables appear to provide useful signals rather than misleading correlations. Furthermore, our PCC module effectively leverages these relationships rather than being hindered by them, as evidenced by its consistent performance improvement across both variable sets.  
These findings highlight the robustness and generalization capability of our approach even when processing highly correlated input features, which is a common characteristic in meteorological datasets.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Backbone**} & \multirow{2}{*}{**Design**} & \multicolumn{2}{c}{**Reduced Variable Set**} & \multicolumn{2}{c}{**Full Variable Set**} \\ \cline{3-6}  & & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline \multirow{2}{*}{SegRNN} & Original & 0.219 & 0.208 & 0.162 & 0.200 \\  & +PCC & 0.196 & 0.195 & **0.144** & **0.189** \\ \hline \multirow{2}{*}{DLinear} & Original & 0.284 & 0.253 & 0.207 & 0.233 \\  & +PCC & 0.207 & 0.207 & **0.152** & **0.197** \\ \hline \hline \end{tabular} Bold values indicate the best results.  
\end{table}
Table 4: Performance comparison (MSE) of models with the full variable set versus the reduced variable set. The forecasting and look-back length are both 96.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Air Temperature**} & \multicolumn{2}{c}{**Specific Humidity**} & \multicolumn{2}{c}{**Wind Velocity**} & \multicolumn{2}{c}{**Precipitation**} \\ \cline{2-9}  & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline Original & 0.099 & 0.223 & 0.097 & 0.212 & 0.001 & 0.021 & 0.067 & 0.055 \\ \hline +PCC & **0.082** & **0.218** & **0.062** & **0.173** & 0.001 & **0.018** & **0.052** & **0.035** \\ \hline \hline \end{tabular} Bold values indicate better results.  
\end{table}
Table 3: Prediction results of key variables using DLinear as the backbone. Results are reported as MSE and MAE, including predictions with and without PCC. The forecasting range and look-back length are both 96.