# Application of Artificial Intelligence to Forecast Drought Index for the Mekong Delta
## 3 Results
### Results of Evaluating Machine Learning Models
This table outlines the performance of the machine learning (Gradient Boosting and XGBoost models) and deep learning (RNN and LSTM) trained to predict the Standardized Precipitation Evapotranspiration Index (SPEI) over different time scales: 1, 3, 6, and 12 months (for six prediction steps). The input parameters for each model vary slightly but generally include measures of rainfall, temperature (maximum and minimum averages), humidity, potential evapotranspiration (PET), Southern Oscillation Index (SOI) Anomaly, and sea surface temperature in the NINO4 region (SST_NINO4). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Input Parameters**} & \multirow{2}{*}{**Output**} & \multicolumn{5}{c}{**Evaluation Criteria**} \\  & & & **MAE** & **MSE** & **RMSE** & **R\({}^{2}\)** & **MAPE** \\ \hline \multirow{8}{*}{ARIMA} & Rainfall, Avg\_Tmax, Avg\_Tmin, & \multirow{2}{*}{SPEI-1} & 0.34–0.40 & 0.22–0.28 & 0.46–0.50 & 0.73–0.75 & 23.9–28.6 \\  & Avg\_Hum, PET, SOI\_Anomaly, & & & & & & \\ SST\_NINO4 & & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & & \\ SST\_NINO4 & & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SOI\_Anomaly, SST\_NINO4 & & & & & & \\ \hline \multirow{8}{*}{Gradient Boosting} & Rainfall, Avg\_Tmax, Avg\_Tmin, & \multirow{2}{*}{SPEI-1} & 0.28–0.33 & 0.14–0.17 & 0.39–0.43 & 0.82–0.84 & 14.4–17.4 \\  & SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SOI\_Anomaly, SST\_NINO4 & & & & & & \\ \hline \multirow{8}{*}{XGBoost} & Rainfall, Avg\_Tmax, Avg\_Tmin, & \multirow{2}{*}{SPEI-1} & 0.28–0.32 & 0.13–0.16 & 0.36–0.40 & 0.84–0.87 & 13.2–16.3 \\  & SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SOI\_Anomaly, SST\_NINO4 & & & & & & \\ \hline \multirow{8}{*}{RNN} & Rainfall, Avg\_Tmax, Avg\_Tmin, & \multirow{2}{*}{SPEI-1} & 0.24–0.27 & 0.10–0.12 & 0.31–0.35 & 0.87–0.89 & 10.7–13.0 \\  & SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ SOI\_Anomaly, SST\_NINO4 & & & & & & \\ \hline \multirow{8}{*}{LSTM} & Rainfall, Avg\_Tmax, Avg\_Tmin, & \multirow{2}{*}{SPEI-1} & 0.18–0.19 & 0.05–0.06 & 0.23–0.25 & 0.93–0.94 & 5.80–6.70 \\  & SST\_NINO4 & & & & & & \\ Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} \cline{1-1} \cline{1-1}  & SST\_NINO4 & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_Hum, & & & & & & \\ \cline{1-1} Rainfall, Avg\_Tmin, Avg\_  
As the prediction step grows from 1 to 6, there is a consistent decline in model performance across all metrics. The Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) generally exhibit an upward trend, whereas the R2 Score shows a decline. The ARIMA model exhibits the most prominent manifestation of this tendency, while the machine learning models, including XGBoost and Gradient Boosting, display a less severe impact. In the XGBoost model for SPEI3, the MAE increases from 0.18 at Step 1 to 0.24 at Step 6. Simultaneously, the R2 Score declines from 0.938 to 0.91. This trend indicates that as the forecast horizon increases, all models face greater difficulty in making precise forecasts. This behavior is commonly observed in time series forecasting. When comparing model performance, there is a noticeable pattern of improvement as the SPEI scale grows from 1 month to 12 months. This is clearly apparent in all measurements and frameworks.