# Lunar Calendar Usage to Improve Forecasting Accuracy Rainfall via Machine Learning Methods
## 3 Results
### Forecasting Result Comparison
shown in Figure 6, the forecast length of 4 months yields the smallest MAPE, around 15%, while the forecast length of 24 months produces the highest MAPE, around 35%. In contrast, for the Gregorian calendar (Figure 7), the smallest MAPE occurs at forecast lengths of 3 and 6 months, approximately 25%, with the largest MAPE at 24 months, exceeding 40%. Overall, the MAPE for the lunar calendar was smaller than that of the Gregorian calendar at forecast lengths of 3, 4, 6, 12, and 24 months. However, at forecast lengths of 16 and 18 months, the MAPE values were relatively similar for both calendars. In comparison (according to Table 2) to the lunar calendar, the forecasted values for the Gregorian calendar are typically larger in magnitude (more negative) for each n, which represents a particular data point. For example, when n = 3, the Gregorian forecasts range from \(-201.38\) to \(-134.68\), while the lunar predictions range from \(-37.06\) to \(-17.53\). This indicates that, compared to the lunar forecasts, the Gregorian predictions generally involve greater errors or discrepancies. When comparing the GRU (gated recurrent unit) and its variants (stacked GRU and BiGRU) to LSTM (long short-term memory) and its variants (stacked LSTM, BiLSTM, and stacked BiLSTM), LSTM models typically produce lower error values. For instance, LSTM yields an error of \(-37.06\) for the lunar column when n = 3, while GRU produces a slightly smaller error of \(-19.46\). In both the lunar and Gregorian calendars, stacked models (stacked LSTM, stacked BiLSTM, and stacked GRU) generally  
Figure 6: Comparison of MAPE for different forecast lengths for four different GRU methods for forecasting based on the lunar calendar. Figure 7: Comparison of MAPE for different forecast lengths for four different GRU methods for forecasting based on the Gregorian calendar. perform better (i.e., result in smaller errors) than their non-stacked counterparts. This suggests that increasing the number of layers in the model can reduce errors and improve accuracy. Although bidirectional models (BiLSTM and BiGRU) do not always outperform conventional LSTM or GRU models in terms of error size, they often provide reasonably acceptable results. However, BiLSTM or BiGRU might perform better than the conventional models at specific data points. For example, while the regular LSTM produces an error of \(-38.34\) at n = 16 in the lunar calendar, BiLSTM and stacked BiLSTM show errors of \(-24.31\) and \(-31.09\), respectively. As the value of n increases, the forecasted values for all models generally show a trend of decreasing errors, indicating better performance at longer forecast horizons. This suggests that the model becomes more accurate when predicting data points farther from the training set. The discrepancies across the models (Table 2) are particularly noticeable for the Gregorian calendar, where LSTM and BiLSTM show relatively consistent results, while some models, such as GRU and BiGRU, tend to forecast lower values. A comparison of these two metrics (Table 3) revealed that the lunar calendar showed a slight overestimation in predictions (positive MBE) but performed with higher accuracy (lower MAPE). However, the Gregorian calendar showed a slight underestimation in prediction (negative MBE) and yielded larger prediction errors (higher MAPE). The lunar calendar model was more accurate in its predictions, with smaller errors, while the Gregorian calendar model had slightly larger errors and showed a tendency to underestimate the values. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Calendar**} & \multirow{2}{*}{**Forecast**} & \multicolumn{8}{c}{**Methods**} \\ \cline{3-10}  & & & **LSTM** & **2-Stacked LSTM** & **BiLSTM** & **2-Stacked BiLSTM** & **GRU** & **2-Stacked GRU** & **BiGRU** & **2-Stacked BiGRU** \\ \hline \multirow{4}{*}{Lunar} & 3 & \(-37.06\) & \(-29.76\) & \(-21.18\) & \(-27.96\) & \(-19.46\) & \(-18.52\) &