Author Contributions
Conceptualization, Z.W. and C.W.; methodology, Z.W.; software, C.L.; validation, Q.S., W.L. and X.H.; investigation, Z.W., C.W. and T.Q.; resources, Q.S.; data curation, C.W.; writing—original draft preparation, Q.S. and Z.W.; writing—review and editing, C.W.; visualization, Q.S.; supervision, W.L.; project administration, L.Y.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Location and hydrogeological profile of the study area in the Hebei Plain.
Figure 1.
Location and hydrogeological profile of the study area in the Hebei Plain.
Figure 2.
Three types of GWL data samples: (a) dynamic fluctuations; (b) dynamic increase; (c) dynamic decrease.
Figure 2.
Three types of GWL data samples: (a) dynamic fluctuations; (b) dynamic increase; (c) dynamic decrease.
Figure 3.
Structure of the LSTM cell.
Figure 3.
Structure of the LSTM cell.
Figure 4.
Structure of the GRU cell.
Figure 4.
Structure of the GRU cell.
Figure 5.
Structure of MLP model.
Figure 5.
Structure of MLP model.
Figure 6.
Running process of the SVM, LSTM, GRU, and MLP models.
Figure 6.
Running process of the SVM, LSTM, GRU, and MLP models.
Figure 7.
Results of hourly GWL simulation (m) in six stations using the SVM model during 2018–2020 in the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 7.
Results of hourly GWL simulation (m) in six stations using the SVM model during 2018–2020 in the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 8.
Results of the hourly GWL simulation (m) in six stations using the LSTM model during 2018–2020 in the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 8.
Results of the hourly GWL simulation (m) in six stations using the LSTM model during 2018–2020 in the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 9.
Results of hourly GWL simulation (m) in six stations using the MLP model during 2018–2020 during the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 9.
Results of hourly GWL simulation (m) in six stations using the MLP model during 2018–2020 during the training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 10.
Results of hourly GWL simulation (m) in six stations using the GRU model during 2018–2020 training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 10.
Results of hourly GWL simulation (m) in six stations using the GRU model during 2018–2020 training and testing periods: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 11.
Scatter diagrams of GWL simulations for each site by SVM, LSTM, MLP and GRU models: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d)Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 11.
Scatter diagrams of GWL simulations for each site by SVM, LSTM, MLP and GRU models: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d)Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 12.
Taylor diagrams of GWL simulations for each site by SVM, LSTM, MLP and GRU models: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Figure 12.
Taylor diagrams of GWL simulations for each site by SVM, LSTM, MLP and GRU models: (a) Huimazhai station, (b) Hongmiao station, (c) Xiliangdian station, (d) Yanmeidong station, (e) Wangduxiancheng station, and (f) XincunIIIzu station.
Table 1.
Data samples in the study area.
Table 1.
Data samples in the study area.
Number | Type | Station | City | GWL | Sequence Length (Day) |
---|
1 | dynamic fluctuations | Huimazhai | Qinhuangdao | 33.83 | 5480 |
2 | Hongmiao | Xingtai | 17.74 | 5480 |
3 | dynamic increase | Xiliangdian | Baoding | −20.23 | 5480 |
4 | Yanmeidong | Baoding | 1236.14 | 5480 |
5 | dynamic decrease | Wangduxiancheng | Baoding | −42.33 | 5480 |
6 | XincunIIIzu | Huanghua | −44.21 | 5480 |
Table 2.
Results of different performance indicators of the SVM model during the training and testing periods at each site.
Table 2.
Results of different performance indicators of the SVM model during the training and testing periods at each site.
Station | Training | Testing |
---|
RMSE | R2 | NSE | RMSE | R2 | NSE |
---|
Huimazhai | 0.253 | 0.953 | 0.921 | 0.396 | 0.757 | 0.691 |
Hongmiao | 2.299 | 0.98 | 0.967 | 3.823 | 0.867 | 0.804 |
Xiliangdian | 0.298 | 0.995 | 0.994 | 0.511 | 0.915 | 0.908 |
Yanmeidong | 0.204 | 0.998 | 0.909 | 0.193 | 0.998 | 0.984 |
Wangduxiancheng | 0.076 | 0.992 | 0.985 | 0.071 | 0.929 | 0.808 |
XincunIIIzu | 0.052 | 0.999 | 0.998 | 0.045 | 0.990 | 0.940 |
Table 3.
Results of the different performance indicators of LSTM model during training and testing periods at each monitoring station.
Table 3.
Results of the different performance indicators of LSTM model during training and testing periods at each monitoring station.
Station | Training | Testing |
---|
RMSE | R2 | NSE | RMSE | R2 | NSE |
---|
Huimazhai | 0.192 | 0.955 | 0.955 | 0.263 | 0.868 | 0.864 |
Hongmiao | 1.581 | 0.985 | 0.984 | 1.771 | 0.958 | 0.958 |
Xiliangdian | 0.244 | 0.996 | 0.996 | 0.338 | 0.961 | 0.96 |
Yanmeidong | 0.053 | 0.994 | 0.994 | 0.116 | 0.996 | 0.994 |
Wangduxiancheng | 0.049 | 0.994 | 0.994 | 0.036 | 0.953 | 0.95 |
XincunIIIzu | 0.037 | 0.999 | 0.999 | 0.028 | 0.987 | 0.976 |
Table 4.
Results of different performance indicators of the MLP model during the training and testing periods at each station.
Table 4.
Results of different performance indicators of the MLP model during the training and testing periods at each station.
Station | Training | Testing |
---|
RMSE | R2 | NSE | RMSE | R2 | NSE |
---|
Huimazhai | 0.201 | 0.959 | 0.95 | 0.128 | 0.979 | 0.968 |
Hongmiao | 1.419 | 0.988 | 0.987 | 0.514 | 0.997 | 0.996 |
Xiliangdian | 0.347 | 0.999 | 0.991 | 0.295 | 0.987 | 0.969 |
Yanmeidong | 0.033 | 0.998 | 0.998 | 0.08 | 0.998 | 0.997 |
Wangduxiancheng | 0.041 | 0.997 | 0.996 | 0.028 | 0.969 | 0.97 |
XincunIIIzu | 0.051 | 0.999 | 0.998 | 0.014 | 0.995 | 0.994 |
Table 5.
Results of different performance indicators of the GRU model during the training and testing periods at each station.
Table 5.
Results of different performance indicators of the GRU model during the training and testing periods at each station.
Station | Training | Testing |
---|
RMSE | R2 | NSE | RMSE | R2 | NSE |
---|
Huimazhai | 0.182 | 0.959 | 0.959 | 0.08 | 0.988 | 0.987 |
Hongmiao | 1.449 | 0.987 | 0.987 | 0.518 | 0.996 | 0.996 |
Xiliangdian | 0.229 | 0.996 | 0.996 | 0.123 | 0.995 | 0.995 |
Yanmeidong | 0.04 | 0.998 | 0.996 | 0.098 | 0.998 | 0.996 |
Wangduxiancheng | 0.041 | 0.996 | 0.996 | 0.033 | 0.961 | 0.96 |
XincunIIIzu | 0.081 | 0.999 | 0.996 | 0.027 | 0.995 | 0.978 |
Table 6.
Training time comparison of four models with 500 epochs.
Table 6.
Training time comparison of four models with 500 epochs.
Model | SVM | LSTM | GRU | MLP |
---|
Time (min) | 1081 | 1660 | 1251 | 2694 |