# Optimization of Data-Driven Soil Temperature Forecast--The First Model in Bangladesh
## 5 Results and Discussion
### Forecasting Soil Temperature at 10 cm Depth in Bangladesh
#### 5.1.1 One-Day Lead-Time Forecast
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Model** & **Time Window Size** & \multicolumn{2}{c}{**One**} & \multicolumn{2}{c}{**Two**} & \multicolumn{2}{c}{**Three**} & \multicolumn{2}{c}{**Four**} & \multicolumn{2}{c}{**Five**} \\ \hline \hline \multirow{10}{*}{Hybrid} & **Scenarios** & **RMSE** & **R** & **RMSE** & **R** & **RMSE** & **R** & **RMSE** & **R** & **RMSE** & **R** & **RMSE** & **R** \\ \cline{2-10}  & MEAN & 2.219 & 0.923 & 2.146 & 0.930 & 2.103 & 0.933 & 2.105 & 0.934 & 2.095 & 0.927 \\ \cline{2-10}  & MEAN-SUN & 2.175 & 0.927 & 2.111 & 0.933 & 2.060 & 0.935 & 2.071 & 0.937 & 2.060 & 0.933 \\ \cline{2-10}  & MEAN-MAX-MIN & 2.106 & 0.934 & 2.063 & 0.938 & 2.020 & 0.940 & 2.027 & 0.941 & 2.021 & 0.942 \\ \cline{2-10}  & MEAN-HUM-RAIN & 2.172 & 0.927 & 2.093 & 0.934 & 2.044 & 0.936 & 2.058 & 0.937 & 2.050 & 0.935 \\ \cline{2-10}  & MEAN-MAX-MIN-SUN & 2.098 & 0.934 & 2.052 & 0.938 & 2.008 & 0.940 & 2.020 & 0.941 & 2.013 & 0.942 \\ \cline{2-10}  & MEAN-MAX-MIN-SUN-RAIN & 2.091 & 0.935 & 2.048 & 0.939 & 2.001 & 0.941 & 2.017 & 0.942 & 2.009 & 0.943 \\ \cline{2-10}  & MEAN-MAX-MIN-SUN-HUM & 2.094 & 0.935 & 2.047 & 0.938 & 2.000 & 0.940 & 2.013 & 0.941 & 2.005 & 0.943 \\ \cline{2-10}  & MEAN-MAX-MIN-RUN-RUN-RAIN & 2.066 & 0.935 & 2.042 & 0.939 & 1.994 & 0.941 & 2.012 & 0.941 & 2.002 & 0.944 \\ \hline \multirow{10}{*}{Hybrid} & MEAN & 2.216 & 0.923 & 2.158 & 0.931 & 2.102 & 0.934 & 2.086 & 0.936 & 2.074 & 0.929 \\ \cline{2-10}  & MEAN-SUN-HUM & 2.165 & 0.928 & 2.097 & 0.935 & 2.058 & 0.938 & 2.045 & 0.939 & 2.032 & 0.935 \\ \cline{1-1} \cline{2-10}  & MEAN-MAX-MIN & 2.094 & 0.935 & 2.024 & 0.940 & 2.019 & 0.942 & 2.003 & 0.943 & 1.996 & 0.943 \\ \cline{1-1} \cline{2-10}  & MEAN-HUM-RAIN & 2.199 & 0.928 & 2.058 & 0.936 & 2.042 & 0.939 & 2.027 & 0.940 & 2.020 & 0.937 \\ \cline{1-1} \cline{2-10}  & MEAN-MAX-MIN-SUN & 2.083 & 0.935 & 2.015 & 0.940 & 2.007 & 0.942 & 1.993 & 0.943 & 1.987 & 0.944 \\ \cline{1-1} \cline{2-10}  & MEAN-MAX-MIN-SUN-RAIN & 2.075 & 0.936 & 2.007 & 0.941 & 1.999 & 0.943 & 1.990 & 0.944 & 1.983 & 0.944 \\ \cline{1-1} \cline{2-10}  & MEAN-MAX-MIN-SUN-HUM & 2.077 & 0.936 & 2.006 & 0.940 & 1.998 & 0.943 & 1.986 & 0.944 & 1.978 & 0.945 \\ \cline{1-1} \cline{2-10}  & MEAN-MAX-MIN-SUN-HUM-RAIN & 2.067 & 0.937 & 2.000 & 0.941 & 1.992 & 0.943 & 1.982 & 0.944 & 1.973 & 0.945 \\ \hline \end{tabular}
\end{table} 
Table 2: Conf. **Best combination for one-day lead-time forecast:** The combination of hybrid RF-GBT, eighth input scenario, and five-day time window achieved the best forecast performance with the lowest average RMSE (1.973 \({}^{\circ}\)C) and the highest average R (0.945). Figure 3 demonstrates strong agreement between the optimal predictions and actual observations at the four soil temperature observation stations. When the time window was reduced to four days, the best forecast was achieved by the combination of GBT and the eighth input scenario. Similarly, at three-day, two-day, and one-day time windows, the best predictions were obtained using GBT, hybrid RF-GBT, and GBT, respectively. This underscored the best forecasting capability of the hybrid RF-GBT and GBT for soil temperature at a 10 cm depth. Generally, the best combination of model, input scenario, and time window can properly capture the oscillation patterns of soil temperature at the 10 cm depth in the frame of a one-day lead-time forecast, but it cannot capture some extreme high/low soil temperatures. At the same time, some outliers in the observed soil temperature data (e.g., unusually high and low soil temperatures at the Barisal station) are likely caused by measurement errors.