# Soft Periodic Convolutional Recurrent Network for Spatiotemporal Climate Forecast
## 5 Results
### Results on ZH300
#### 5.1.5 Attention Weight Analysis  
We analyzed the weight in the attention module (Section 3.5), which indicated the importance of the periodic representation collected in the PRD. Figure 7 shows the attention weight of the SP-CRN-1 (1,1,0) model, which was the best setting in SP-CRN-1 of the ZH300 prediction. The phase of periodicity for one prior periodic cycle for one month ahead (plus-1) was more important than the for same (self) or previous month (minus-1), respectively. The attention weight of plus-1 was high in May and September but low in February, while the attention weight for self was the opposite. The minus-1 was smooth for all phases, indicating the same amount of importance for every month of the ZH300 prediction.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **Avg. RMSE (m)** & **SD of RMSE (m)** \\ \hline CNN & 141.79 & 16.54 \\ ConvGRU & 125.80 & 8.19 \\ ConvLSTM & 126.75 & 9.70 \\ SP-CRN (GRU) & 73.47 & 11.37 \\ SP-CRN (LSTM) & 76.89 & 13.43 \\ \hline SP-CRN-1 (1,1,0) & 74.22 & 15.44 \\ SP-CRN-2 (0,4,0) & 70.58 & 12.43 \\ SP-CRN-3 (0,0,2) & 67.97 & 11.95 \\ \hline SP-CRN-1+2 (1,4,0) & 82.89 & 13.85 \\ SP-CRN-1+3 (1,0,2) & 66.39 & 12.21 \\ SP-CRN-2+3 (0,4,2) & 88.44 & 10.56 \\ SP-CRN-1+2+3 (1,4,2) & 80.59 & 11.65 \\ SP-CRN-1+3-Meta (1,0,2) & 50.27 & 12.77 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation of different settings on the ZH300 prediction for SP-CRN and comparison methods.  
Figure 6: The prediction and error distribution of ZH300 on February 2017 (**a**) Ground truth and prediction results. (**b**) Error distribution (absolute error).  
Figure 8 shows the attention weight for the ZH300 prediction with the SP-CRN-2 (0,4,0) model. The periodic cycle of prior 1-4 years was considered together by the attention module. The overall weights were almost equal among the different depths between the weight of 0.1 to 0.4 excepts depth-4, which indicated the importance of the fourth prior year over the other years. However, depth-4 did not show the same periodic pattern in 2017 and 2018. The depth-3 showed a similar pattern with the phase shift which had the highest value in February 2017, but in 2018, the highest value was in March. The lowest value of depth-3 in 2017 was in September, but in 2018 the lowest value was in November. The attention weight dropped drastically from August to September in 2017 and 2018, but the difference in August was slightly different. In summary, depth-4 of the SP-CRN-2 (0,4,0) attention weights pattern had the highest impact while depth-3 had the steadiest.  
SP-CRN-3 (0,0,2) was the best setting for PRD-3 with a periodic-depth of two. The depth of 2 with a first-order derivative had only single weight to consider, so the attention weight analysis was not necessary.  
Figure 8: Attention weight on SP-CRN-2 (0,4,0) for ZH300 prediction from the average of five runs. The attention weight of depth-1 to depth-4 was the value of the prediction month for one to four prior periodic cycles. The scale is from 0.1 to 0.5.  
Figure 7: Attention weight on SP-CRN-1 (1,1,0) for ZH300 prediction from the average of five runs. The attention weight of minus-1, self, and plus-1 are the minus one month, the prediction month, and the plus one month of one prior periodic cycle, respectively. The scale is from 0 to 1.