# Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network
## 4 Results
### Model Performance at Different Depths  
Figure 9 shows the performance of each model in estimating the hourly ST at different soil depths. With respect to RMSE, MAE, and R\({}^{2}\), the integrated BiLSTM models generally show the best performance at all soil depths, and the LSTM model is the second-best prediction algorithm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**R\({}^{2}\)**} \\ \cline{2-7}  & **Worst** & **Site id** & **Worst** & **Site id** & **Worst** & **Site id** \\ \hline Integrated BiLSTM & 2.53 \({}^{\circ}\)C & 2183 & 1.99 \({}^{\circ}\)C & 2183 & 0.823 & 2014 \\ LSTM & 3.03 \({}^{\circ}\)C & 2183 & 2.44 \({}^{\circ}\)C & 2183 & 0.701 & 2014 \\ BiLSTM & 3.22 \({}^{\circ}\)C & 2183 & 2.55 \({}^{\circ}\)C & 2183 & 0.658 & 2218 \\ DNN & 3.21 \({}^{\circ}\)C & 2028 & 2.80 \({}^{\circ}\)C & 2028 & 0.613 & 2014 \\ RF & 2.90 \({}^{\circ}\)C & 2218 & 2.26 \({}^{\circ}\)C & 2218 & 0.656 & 2014 \\ SVR & 3.33 \({}^{\circ}\)C & 2218 & 2.66 \({}^{\circ}\)C & 2218 & 0.388 & 2218 \\ LR & 4.87 \({}^{\circ}\)C & 2186 & 4.03 \({}^{\circ}\)C & 2186 & \(-\)0.311 & 2218 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Worst statistical results of each model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**R\({}^{2}\)**} \\ \cline{2-5}  & **Best** & **Site id** & **Best** & **Site id** & **Best** & **Site id** \\ \hline Integrated BiLSTM & 0.95 \({}^{\circ}\)C & 2042 & 0.76 \({}^{\circ}\)C & 2042 & 0.976 & 2171 \\ LSTM & 1.22 \({}^{\circ}\)C & 2042 & 0.93 \({}^{\circ}\)C & 2042 & 0.964 & 2171 \\ BiLSTM & 1.29 \({}^{\circ}\)C & 2083 & 0.95 \({}^{\circ}\)C & 2083 & 0.965 & 2171 \\ DNN & 1.22 \({}^{\circ}\)C & 2042 & 0.97 \({}^{\circ}\)C & 2042 & 0.961 & 2171 \\ RF & 1.42 \({}^{\circ}\)C & 2042 & 1.07 \({}^{\circ}\)C & 2083 & 0.954 & 2171 \\ SVR & 1.56 \({}^{\circ}\)C & 2013 & 1.24 \({}^{\circ}\)C & 2013 & 0.953 & 2183 \\ LR & 2.33 \({}^{\circ}\)C & 2083 & 1.86 \({}^{\circ}\)C & 2083 & 0.906 & 2183 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Best statistical results of each model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **RMSE(\({}^{\circ}\)C)** & **MAE(\({}^{\circ}\)C)** & **R\({}^{2}\)** \\ \hline Integrated BiLSTM & 1.53 & 1.22 & 0.923 \\ LSTM & 1.76 & 1.39 & 0.896 \\ BiLSTM & 1.85 & 1.44 & 0.882 \\ DNN & 1.99 & 1.58 & 0.865 \\ RF & 1.92 & 1.49 & 0.874 \\ SVR & 2.18 & 1.75 & 0.808 \\ LR & 3.43 & 2.76 & 0.518 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistic performance of each model for estimation of hourly soil temperature. Except for RF, the accuracy (based on the RMSE and MAE) of the other models increases with an increase in depth. Taking the integrated BiLSTM model as an example, the highest RMSE and MAE values (the worst results) are obtained at 5 cm, whereas the lowest values (the best results) are obtained at 100 cm. With respect to R\({}^{2}\), the accuracy of the integrated BiLSTM model increases from 5 to 20 cm, and decreases from 50 to 100 cm, whereas the R\({}^{2}\) values of the other models decrease with an increase in depth. This result differs from the conclusions in [21] and [53], the experimental results of which show that the accuracy of the machine learning algorithm will gradually decrease at a soil depth of 10 to 100 cm. This may be related to the different models used and the different climatic conditions. We noticed that the lowest RMSE value obtained by the integrated BiLSTM is 2.04 \({}^{\circ}\)C at 5 cm, which is 0.1 \({}^{\circ}\)C lower than that obtained by the second-best model. The difference gradually increases to 0.31 \({}^{\circ}\)C at 50 cm, and then decreases to 0.23 \({}^{\circ}\)C at 100 cm. In other words, from 5 to 50 cm, the difference between the integrated BiLSTM model and the second-best model widens, indicating that the integrated BiLSTM has potential for deeper ST prediction tasks.