# Modeling Hourly Soil Temperature Using Deep BiLSTM Neural Network
## 4 Results
### Model Comparisons  
The prediction performance of different models at each observation station are shown in Figures 6-8. As presented in Figure 6, the best performance is obtained by the integrated BiLSTM model, the root mean squared error (RMSE) of which at all 30 sites is lower than that of the benchmark algorithm, whereas the worst performance is obtained by the LR algorithm, the RMSE of which is the highest at all sites. According to the statistics, based on the RMSE index, the integrated BiLSTM is 4.8-18.7%, 8.8-23.6%, 20.9-25.7%, 12.8%-25.1%, 17.0-45.0%, and 42.0-65.1% more accurate than LSTM, BiLSTM, DNN, RF, SVR, and LR, respectively. The mean absolute error (MAE) of every model for each observation station is given in Figure 7. As can be seen, integrated BiLSTM performs better than the benchmark models at 27 observation sites (90% of the total number of stations), and based on the MAE index is 2.6-18.7%, 5.7-21.5%, 20.3-25.7%, 9.8-22.1%, 17.5-44.1%, and 42.2-65.1% more accurate than LSTM, BiLSTM, DNN, RF, SVR, and LR, respectively. At station 2215, the BiLSTM algorithm obtains the best MAE value of 1.06 \({}^{\circ}\)C, whereas the MAE value of the integrated BiLSTM algorithm is 1.07 \({}^{\circ}\)C, which is only 0.01 \({}^{\circ}\)C higher than that of the BiLSTM. By contrast, LSTM obtained the lowest MAE of 1.14 \({}^{\circ}\)C and 1.12 \({}^{\circ}\)C at the two stations 2031 and 2147, which are 0.06 \({}^{\circ}\)C and 0.02 \({}^{\circ}\)C lower than that of the integrated BiLSTM, respectively. In other words, the difference between the integrated BiLSTM and the best algorithm is not obvious at these three stations. Figure 8 shows the R\({}^{2}\) generated by every model at each observation, and as the figure indicates, the integrated BiLSTM was the best model with the highest R\({}^{2}\) value at each observation station. According to statistics, based on the R\({}^{2}\) index, the integrated BiLSTM is 1.3-4.8%, 2.4-8.0%, 5.1-8.3%, 3.2-9.3%, 4.4-45.0%, and 23-57.4% more accurate than LSTM, BiLSTM, DNN, RF, SVR, and LR, respectively. The performance of the LSTM model is slightly better than that of the BiLSTM, and the performance of the LR model is still not ideal. We also noted that the R\({}^{2}\) value of the LR is less than  
Figure 6: Performance comparison of forecasting models for 30 sites in terms of root mean squared error (RMSE). zero at the two sites labeled 2218 and 2147, which indicates that LR model is unsuitable for processing data with a nonlinear correlation. Although the RF model is not as good as the integrated BiLSTM, LSTM, and BiLSTM with respect to the three indicators, RMSE, MAE, and R\({}^{2}\), it can be clearly seen from Figures 6-8 that favorable agreements exist between the results of the RF model and these three deep learning models, and the prediction results at multiple sites are better than DNN, which confirms the potential of using the RF model for an estimation of the hourly ST. The best and worst statistical results for each model, and the identification number of the observation sites that produced these results, are given in Tables 3 and 4, respectively. The RMSE, MAE, and determination coefficient (R\({}^{2}\)) are used as the evaluation criteria. From Tables 3 and 4, we can clearly see that the performance of the integrated BiLSTM model developed in this study showed the best results. For the 30 observation stations involved in the experiment, the RMSE, MAE, and R\({}^{2}\) values obtained for the integrated BiLSTM are within the range of 0.95-2.53 \({}^{\circ}\)C, 0.76-1.99 \({}^{\circ}\)C, and 0.823-0.976, respectively. Figure 8: Performance comparison of forecasting models for 30 sites in terms of R\({}^{2}\). Figure 7: Performance comparison of forecasting models for 30 sites in terms of mean absolute error (MAE).