# Soft Periodic Convolutional Recurrent Network for Spatiotemporal Climate Forecast
## 5 Results
### Results on ZH300
#### 5.1.3 Combination of PRD Types and Meta-Data  
To indicate the performance of the periodicity component on both nearby-time and periodic-depth representation, we mixed the proposals of SP-CRN-1 (1,1,0), SP-CRN-2 (0,4,0), and SP-CRN-3 (0,0,2) because they performed the best in their settings from the previous experiment (Table 1). The mixed proposals were combined with all the combinations that were SP-CRN-1+2 (1,4,0), SP-CRN-1+3 (1,0,2), SP-CRN-2+3 (0,4,2), and SP-CRN-1+2+3 (1,4,2). We also experimented with the idea of a metadata component from the original Periodic-CRN [27] to indicate the month of the year with one-hot encoding. The metadata component was added at the end of the fusion module in Figure 2f, and Section 3.6. The prediction output in Equation (12) was changed to combine the fusion module (\(h_{f}^{(t+N)}\)) and metadata component outputs (\(h_{meta}^{(t+N)}\)) as shown in Equation (15), where \(W_{f}\) and \(W_{meta}\) are weight the of \(h_{f}^{(t+N)}\) and \(h_{meta}^{(t+N)}\), respectively. The metadata component may help the model indicating the phase of periodicity better to increase prediction accuracy. Therefore, we selected SP-CRN-1+3 (1,0,2) as the mixed proposal to be added to the metadata component (SP-CRN-1+3-Meta (1,0,2)).  
\[\hat{X}^{(t+N)}=h_{f}^{(t+N)}*W_{f}+h_{meta}^{(t+N)}*W_{meta} \tag{15}\]  
Table 2 shows the experimental results of each model setting that had the best prediction accuracy. All the proposals on SP-CRN had better prediction accuracy than SP-CRN (LSTM) baseline, indicating that the periodicity utilization proposals helped improve prediction accuracy. The mixed proposal of SP-CRN-1+3 (1,0,2) was the best compared with the other mixed proposals, which improved SP-CRN-1 (1,1,0) and SP-CRN-3 (0,0,2) accuracy with an RMSE of 66.39 by considering the periodicity in both directions (nearby-time and periodic-depth). In contrast, the other mixed proposals with PRD-2 were worse than their baseline models. The metadata component in SP-CRN-1+3-Meta (1,0,2) was superior at indicating the phase of periodicity and had the lowest RMSE comparing to SP-CRN-1+3 (1,0,2) (base model).  
\begin{table}
\begin{tabular}{c c c} \hline
**Method** & **Avg. RMSE (m)** & **SD of RMSE (m)** \\ \hline SP-CRN-1 (0,1,0) & 76.89 & 13.43 \\ SP-CRN-1 (1,1,0) & 74.22 & 15.44 \\ SP-CRN-1 (2,1,0) & 81.64 & 13.89 \\ SP-CRN-1 (3,1,0) & 84.42 & 17.67 \\ \hline SP-CRN-2 (0,2,0) & 79.69 & 13.96 \\ SP-CRN-2 (0,3,0) & 94.85 & 14.05 \\ SP-CRN-2 (0,4,0) & 70.58 & 12.43 \\ SP-CRN-2 (0,5,0) & 103.93 & 12.62 \\ SP-CRN-2 (0,6,0) & 100.76 & 16.23 \\ \hline SP-CRN-3 (0,0,2) & 67.97 & 11.95 \\ SP-CRN-3 (0,0,3) & 70.05 & 12.23 \\ SP-CRN-3 (0,0,4) & 69.53 & 12.16 \\ SP-CRN-3 (0,0,5) & 68.12 & 12.13 \\ SP-CRN-3 (0,0,6) & 68.26 & 12.47 \\ \hline \end{tabular}
\end{table}
Table 1: Evaluation of different settings on the ZH300 prediction for SP-CRN with three proposals. The settings ((x, y, z) are the numbers of the nearby-time of PRD-1, periodic-depth of PRD-2, and periodic-depth of PRD-3, respectively. The SP-CRN-1, SP-CRN-2, and SP-CRN-3 indicate each proposal in SP-CRN which was a nearby-time representation, periodic-depth representation, and periodic-depth differencing representation, respectively. The highlighted result in blue is the best prediction accuracy for each proposal, while the gray highlight in the SP-CRN baseline result.