# Lunar Calendar Usage to Improve Forecasting Accuracy Rainfall via Machine Learning Methods
## 3 Results
### Forecasting Result Comparison  
The comparison of forecasting based on two calendar systems is presented in Figure 2. As shown in Figure 2, the MAPE trend for all four methods across both calendar systems tends to increase as the forecast length extends. Forecasts based on the lunar calendar generally exhibited a lower MAPE than those based on the Gregorian calendar. Specifically, the MAPE for the lunar calendar was lower at forecast lengths of 3, 4, 6, and 12 months for the LSTM, 2-stacked LSTM, and 2-stacked BiLSTM methods, as illustrated in Figure 2a-d.  
For the BiLSTM method, at a forecast length of 12 months, the MAPE for both the lunar and Gregorian calendars was nearly identical. However, at forecast lengths of 16 and 18 months, the MAPE for the lunar calendar tended to be higher than that of the Gregorian calendar, particularly for the 2-stacked LSTM, BiLSTM, and 2-stacked BiLSTM methods. Interestingly, at a forecast length of 24 months, the lunar calendar exhibited a smaller MAPE. Figures 3 and 4 compare the MAPE for forecasts using two different calendars: (3) the lunar calendar and (4) the Gregorian calendar, across forecast lengths of 3, 4, 6, 12, 16, 18, and 24 months. Figure 3 shows that, for a forecast length of 4 months, the MAPE produced via all four methods was the smallest compared to other forecast lengths, while a forecast length of 24 months resulted in the highest MAPE. On the other hand, for forecasts based on the Gregorian calendar (Figure 4), the smallest MAPE was observed at a forecast length of 6 months for all methods, with the largest MAPE occurring at 24 months. When comparing the two calendars, the MAPE for the lunar calendar was smaller than that for the Gregorian calendar at forecast lengths of 4 and 6 months. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Month-Year** & **Monthly Rainfall** & **Month-Year** & **Monthly Rainfall** \\
**Gregorian** & **(mmHg)** & **Lunar** & **(mmHg)** \\ \hline April 2000 & 449 & Dhul Hijri 1420 & 84 \\ May 2000 & 339 & Muharram 1420 & 493 \\ Jun 2000 & 295 & Safar 1420 & 263 \\ Jully 2000 & 376 & Rabi Ul-Awal 1420 & 348 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ September 2022 & 250.7 & Safar 1444 & 444.7 \\ October 2022 & 505.3 & Rabi Ul-Awal 1444 & 334.1 \\ November 2022 & 299.2 & Rabi Al-Akbar 1444 & 303.4 \\ December 2022 & 428.7 & Jumadil Awal 1444 & 198.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calendar conversion results. Figure 5 compares the MAPE of different methods: GRU, 2-stacked GRU, BiGRU, and 2-stacked BiGRU. Overall, the MAPE for the lunar calendar approach was generally smaller than that for the Gregorian calendar. Specifically, for forecast lengths of 3, 4, and 6 months, all four methods produced a smaller MAPE with the lunar calendar compared to the Gregorian calendar. For the BiGRU and 2-stacked BiGRU methods, the MAPE at a forecast length of 12 months was similar, typically ranging between 25 and 30%. However,  
Figure 3: Comparison of MAPE for different forecast lengths for four different LSTM methods for forecasting based on the lunar calendar. Figure 2: Comparison of MAPE for lunar calendar-based forecasting and Gregorian calendar for the following: (**a**) LSTM; (**b**) 2-stacked LSTM; (**c**) BiLSTM; (**d**) 2-stacked BiLSTM methods. at forecast lengths of 16 and 18 months, the MAPE for the lunar calendar was larger than that for the Gregorian calendar. In contrast, at a forecast length of 24 months, the MAPE for the Gregorian calendar was greater than that for the lunar calendar. This comparison examines the MAPE for both the lunar and Gregorian calendars across four GRU method types: GRU, BiGRU, 2-stacked GRU, and 2-stacked BiGRU. As  
Figure 4: Comparison of MAPE for different forecast lengths for four different LSTM methods for forecasting based on the Gregorian calendar. Figure 5: Comparison of MAPE for lunar calendar-based forecasting and Gregorian calendar for the following: (**a**) GRU; (**b**) 2-stacked GRU; (**c**) BiGRU; (**d**) 2-stacked BiGRU methods.