# Deep Learning-Based Predictive Framework for Groundwater Level Forecast in Arid Irrigated Areas

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Methodological Framework

#### 2.2. Data Decomposition Algorithm (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise)

#### 2.3. Deep Learning Forecast Algorithm (Deep Belief Network)

#### 2.4. Uncertainty Evaluation (Quantile Regression)

#### 2.5. Materials

#### 2.5.1. Study Area

#### 2.5.2. Dataset

_{norm}is the normalized data; and X

_{min}and X

_{max}are the minimum and maximum values of the data, respectively.

#### 2.5.3. Model Structure

_{t−2}, GWL

_{t−1}, GWL

_{t}, Pre

_{t−2}, Pre

_{t−1}, Pre

_{t}, Tem

_{t−2}, Tem

_{t−1}and Tem

_{t}were the model’s input variables.

#### 2.5.4. Model Performance Evaluation

## 3. Results and Discussion

#### 3.1. Performance of the Hybrid CEEMDAN-GA-DBN Model

#### 3.2. Comparison of the CEEMDAN-GA-DBN Model, the CEEMDAN-DBN Model and the DBN Model

#### 3.3. Uncertainty Analysis

#### 3.4. Model Interpretation

## 4. Conclusions

^{8}m

^{3}, whether the same high accuracy can be derived using the model remains uncertain and needs to be further studied. Secondly, a comprehensive assessment should be implemented to analyze the possible uncertainties that had influences on the performance of the models. For example, the spatial variation of the hydrogeological parameters should be considered in a future study to improve the model’s accuracy. Thirdly, certain anthropic or natural factors in the specific area, such as the excessive groundwater extraction, the change of water users as well as the irrigated areas in this groundwater-supported agricultural region, the intricate and intense interaction between river and groundwater in this inland river basin, may affect the accuracy of the GWL forecast. Therefore, there stands a chance that the model’s accuracy will be improved remarkably if these universal interfering factors and the controlling factors of different wells are taken into consideration. Finally, the performance of the CEEMDAN-GA-DBN model for 1-, 2- and 3-month ahead GWL forecasting was mainly discussed in this study; however, as a designed simulation model, further investigation of its potentiality in both short- and long-term forecasting would be an interesting exploration.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Barua, S.; Cartwright, I.; Dresel, E.P.; Daly, E. Using multiple methods to investigate the effects of land-use changes on groundwater recharge in a semi-arid area. Hydrol. Earth Syst. Sci.
**2021**, 25, 89–104. [Google Scholar] [CrossRef] - Khalil, M.M.; Tokunaga, T.; Heggy, E.; Abotalib, A.Z. Groundwater mixing in shallow aquifers stressed by land cover/land use changes under hyper-arid conditions. J. Hydrol.
**2021**, 598, 126245. [Google Scholar] [CrossRef] - Herrera, C.; Godfrey, L.; Urrutia, J.; Custodio, E.; Jordan, T.; Jódar, J.; Delgado, K.; Barreneche, F. Recharge and residence times of groundwater in hyper arid areas: The confined aquifer of Calama, Loa River Basin, Atacama Desert, Chile. Sci. Total. Environ.
**2021**, 752, 141847. [Google Scholar] [CrossRef] - Li, H.; Lu, Y.; Zheng, C.; Zhang, X.; Zhou, B.; Wu, J. Seasonal and inter-annual variability of groundwater and their responses to climate change and human activities in arid and desert areas: A case study in Yaoba Oasis, northwest China. Water
**2020**, 12, 303. [Google Scholar] [CrossRef][Green Version] - De Graaf, I.E.M.; Gleeson, T.; Rens van Beek, L.P.H.; Sutanudjaja, E.H.; Bierkens, M.F.P. Environmental flow limits to global groundwater pumping. Nature
**2019**, 574, 90–94. [Google Scholar] [CrossRef] - Abu-Bakr, H.A.e.-A. Groundwater vulnerability assessment in different types of aquifers. Agric. Water Manag.
**2020**, 240, 106275. [Google Scholar] [CrossRef] - Amaranto, A.; Munoz-Arriola, F.; Solomatine, D.P.; Corzo, G. A spatially enhanced data-driven multimodel to improve semiseasonal groundwater forecasts in the high plains aquifer, USA. Water Resour. Res.
**2019**, 55, 5941–5961. [Google Scholar] [CrossRef][Green Version] - Ghiglieri, G.; Buttau, C.; Arras, C.; Funedda, A.; Soler, A.; Barbieri, M.; Carrey, R.; Domènech, C.; Torrentó, C.; Otero, N.; et al. Using a multi-disciplinary approach to characterize groundwater systems in arid and semi-arid environments: The case of Biskra and Batna regions (NE Algeria). Sci. Total Environ.
**2021**, 757, 143797. [Google Scholar] [CrossRef] - Fang, C.; Sun, S.; Jia, S.; Li, Y. Groundwater level analysis using regional Kendall Test for trend with spatial autocorrelation. Groundwater
**2019**, 57, 320–328. [Google Scholar] [CrossRef] [PubMed] - Wang, S.; Liu, H.; Yu, Y.; Zhao, W.; Yang, Q.; Liu, J. Evaluation of groundwater sustainability in the arid Hexi Corridor of northwestern China, using GRACE, GLDAS and measured groundwater data products. Sci. Total Environ.
**2020**, 705, 135829. [Google Scholar] [CrossRef] [PubMed] - Hellwig, J.; de Graaf, I.E.M.; Weiler, M.; Stahl, K. Large-scale assessment of delayed groundwater responses to drought. Water Resour. Res.
**2020**, 56, e2019WR025441. [Google Scholar] [CrossRef][Green Version] - De Graaf, I.; Condon, L.; Maxwell, R. Hyper-resolution continental-scale 3-D aquifer parameterization for groundwater modeling. Water Resour. Res.
**2020**, 56, 1–14. [Google Scholar] [CrossRef][Green Version] - Deng, C.; Bailey, R.T. Assessing causes and identifying solutions for high groundwater levels in a highly managed irrigated region. Agric. Water Manag.
**2020**, 240, 106329. [Google Scholar] [CrossRef] - Chang, F.J.; Chang, L.C.; Huang, C.W.; Kao, I.F. Prediction of monthly regional groundwater levels through hybrid soft-computing techniques. J. Hydrol.
**2016**, 541, 965–976. [Google Scholar] [CrossRef] - Marçais, J.; de Dreuzy, J.R. Prospective interest of deep learning for hydrological inference. Groundwater
**2017**, 55, 688–692. [Google Scholar] [CrossRef] [PubMed] - Rahman, A.T.M.S.; Hosono, T.; Quilty, J.M.; Das, J.; Basak, A. Multiscale groundwater level forecasting: Coupling new machine learning approaches with wavelet transforms. Adv. Water Resour.
**2020**, 141, 103595. [Google Scholar] [CrossRef] - Wei, Z.L.; Wang, D.F.; Sun, H.Y.; Yan, X. Comparison of a physical model and phenomenological model to forecast groundwater levels in a rainfall-induced deep-seated landslide. J. Hydrol.
**2020**, 586, 124894. [Google Scholar] [CrossRef] - Rajaee, T.; Ebrahimi, H.; Nourani, V. A review of the artificial intelligence methods in groundwater level modeling. J. Hydrol.
**2019**, 572, 336–351. [Google Scholar] [CrossRef] - Mo, S.; Zabaras, N.; Shi, X.; Wu, J. Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification. Water Resour. Res.
**2019**, 55, 3856–3881. [Google Scholar] [CrossRef][Green Version] - Shahabi, H.; Shirzadi, A.; Ronoud, S.; Asadi, S.; Pham, B.T.; Mansouripour, F.; Geertsema, M.; Clague, J.J.; Bui, D.T. Flash flood susceptibility mapping using a novel deep learning model based on deep belief network, back propagation and genetic algorithm. Geosci. Front.
**2021**, 12, 101100. [Google Scholar] [CrossRef] - Zhong, Z.; Sun, A.Y.; Yang, Q.; Ouyang, Q. A deep learning approach to anomaly detection in geological carbon sequestration sites using pressure measurements. J. Hydrol.
**2019**, 573, 885–894. [Google Scholar] [CrossRef][Green Version] - Zhang, J.; Zhu, Y.; Zhang, X.; Ye, M.; Yang, J. Developing a Long Short-Term Memory (LSTM) based model for predicting water table depth in agricultural areas. J. Hydrol.
**2018**, 561, 918–929. [Google Scholar] [CrossRef] - Gochoo, M.; Akhter, I.; Jalal, A.; Kim, K. Stochastic remote sensing event classification over adaptive posture estimation via multifused data and deep belief network. Remote Sens.
**2021**, 13, 912. [Google Scholar] [CrossRef] - Niu, G.Q.; Yi, X.H.; Chen, C.; Li, X.Y.; Han, D.H.; Yan, B.; Huang, M.Z.; Ying, G.G. A novel effluent quality predicting model based on genetic-deep belief network algorithm for cleaner production in a full-scale paper-making wastewater treatment. J. Clean. Prod.
**2020**, 265, 121787. [Google Scholar] [CrossRef] - Rizk, Y.; Hajj, N.; Mitri, N.; Awad, M. Deep belief networks and cortical algorithms: A comparative study for supervised classification. Appl. Comput. Inform.
**2019**, 15, 81–93. [Google Scholar] [CrossRef] - Wen, X.; Feng, Q.; Yu, H.; Wu, J.; Si, J.; Chang, Z.; Xi, H. Wavelet and adaptive neuro-fuzzy inference system conjunction model for groundwater level predicting in a coastal aquifer. Neural Comput. Appl.
**2015**, 26, 1203–1215. [Google Scholar] [CrossRef] - Wu, C.C.; Zhang, X.Q.; Wang, W.J.; Lu, C.P.; Zhang, Y.; Qin, W.; Tick, G.R.; Liu, B.; Shu, L.C. Groundwater level modeling framework by combining the wavelet transform with a long short-term memory data-driven model. Sci. Total. Environ.
**2021**, 783, 146948. [Google Scholar] [CrossRef] - Yu, H.; Wen, X.; Feng, Q.; Deo, R.C.; Si, J.; Wu, M. Comparative study of hybrid-wavelet artificial intelligence models for monthly groundwater depth forecasting in extreme arid regions, northwest China. Water Resour. Manag.
**2018**, 32, 301–323. [Google Scholar] [CrossRef] - Zhang, J.; Zhang, X.; Niu, J.; Hu, B.X.; Soltanian, M.R.; Qiu, H.; Yang, L. Prediction of groundwater level in seashore reclaimed land using wavelet and artificial neural network-based hybrid model. J. Hydrol.
**2019**, 577, 123948. [Google Scholar] [CrossRef] - Meng, E.; Huang, S.; Huang, Q.; Fang, W.; Wu, L.; Wang, L. A robust method for non-stationary streamflow prediction based on improved EMD-SVM model. J. Hydrol.
**2019**, 568, 462–478. [Google Scholar] [CrossRef] - Qu, Z.; Mao, W.; Zhang, K.; Zhang, W.; Li, Z. Multi-step wind speed forecasting based on a hybrid decomposition technique and an improved back-propagation neural network. Renew. Energy
**2019**, 133, 919–929. [Google Scholar] [CrossRef] - Rezaie-Balf, M.; Kim, S.; Fallah, H.; Alaghmand, S. Daily river flow forecasting using ensemble empirical mode decomposition based heuristic regression models: Application on the perennial rivers in Iran and South Korea. J. Hydrol.
**2019**, 572, 470–485. [Google Scholar] [CrossRef] - Huang, G.; Li, X.; Zhang, B.; Ren, J. PM 2.5 concentration forecasting at surface monitoring sites using GRU neural network based on empirical mode decomposition. Sci. Total Environ.
**2021**, 768, 144516. [Google Scholar] [CrossRef] - Liu, H.; Cao, L.; Jia, J.; Gong, H.; Qi, X.; Xu, X. Effects of land use changes on the nonlinear trends of net primary productivity in arid and semiarid areas, China. Land Degrad. Dev.
**2021**, 32, 2183–2196. [Google Scholar] [CrossRef] - Huang, S.; Chang, J.; Huang, Q.; Chen, Y. Monthly streamflow prediction using modified EMD-based support vector machine. J. Hydrol.
**2014**, 511, 764–775. [Google Scholar] [CrossRef] - Zhang, Z.J.; Zhang, Y.M.; Lu, J.W.; Gao, F.; Xiao, G. A novel complex manufacturing business process decomposition approach in cloud manufacturing. Comput. Ind. Eng.
**2020**, 144, 106442. [Google Scholar] [CrossRef] - Fijani, E.; Barzegar, R.; Deo, R.; Tziritis, E.; Konstantinos, S. Design and implementation of a hybrid model based on two-layer decomposition method coupled with extreme learning machines to support real-time environmental monitoring of water quality parameters. Sci. Total Environ.
**2019**, 648, 839–853. [Google Scholar] [CrossRef] - Prasad, R.; Deo, R.C.; Li, Y.; Maraseni, T. Weekly soil moisture forecasting with multivariate sequential, ensemble empirical mode decomposition and Boruta-random forest hybridizer algorithm approach. Catena
**2019**, 177, 149–166. [Google Scholar] [CrossRef] - Wen, X.; Feng, Q.; Deo, R.C.; Wu, M.; Yin, Z.; Yang, L.; Singh, V.P. Two-phase extreme learning machines integrated with the complete ensemble empirical mode decomposition with adaptive noise algorithm for multi-scale runoff prediction problems. J. Hydrol.
**2019**, 570, 167–184. [Google Scholar] [CrossRef] - Yang, Y.; Wang, J. Forecasting wavelet neural hybrid network with financial ensemble empirical mode decomposition and MCID evaluation. Expert Syst. Appl.
**2021**, 166, 114097. [Google Scholar] [CrossRef] - Ali, M.; Deo, R.C.; Maraseni, T.; Downs, N.J. Improving SPI-derived drought forecasts incorporating synoptic-scale climate indices in multi-phase multivariate empirical mode decomposition model hybridized with simulated annealing and kernel ridge regression algorithms. J. Hydrol.
**2019**, 576, 164–184. [Google Scholar] [CrossRef] - Das, A.K.; Das, S.; Ghosh, A. Ensemble feature selection using bi-objective genetic algorithm. Knowl.-Based Syst.
**2017**, 123, 116–127. [Google Scholar] [CrossRef] - Rahmati, O.; Choubin, B.; Fathabadi, A.; Coulon, F.; Soltani, E.; Shahabi, H.; Mollaefar, E.; Tiefenbacher, J.; Cipullo, S.; Ahmad, B.B.; et al. Predicting uncertainty of machine learning models for modelling nitrate pollution of groundwater using quantile regression and UNEEC methods. Sci. Total Environ.
**2019**, 688, 855–866. [Google Scholar] [CrossRef] - Mohapatra, J.B.; Jha, P.; Jha, M.K.; Biswal, S. Efficacy of machine learning techniques in predicting groundwater fluctuations in agro-ecological zones of India. Sci. Total Environ.
**2021**, 785, 147319. [Google Scholar] [CrossRef] - Band, S.S.; Heggy, E.; Bateni, S.M.; Karami, H.; Rabiee, M.; Samadianfard, S.; Chau, K.W.; Mosavi, A. Groundwater level prediction in arid areas using wavelet analysis and Gaussian process regression. Eng. Appl. Comp. Fluid.
**2021**, 15, 1147–1158. [Google Scholar] [CrossRef] - Namous, M.; Hssaisoune, M.; Pradhan, B.; Lee, C.W.; Alamri, A.; Elaloui, A.; Edahbi, M.; Krimissa, S.; Eloudi, H.; Ouayah, M.; et al. Spatial prediction of groundwater potentiality in large semi-arid and karstic mountainous region using machine learning models. Water
**2021**, 13, 2273. [Google Scholar] [CrossRef] - Chen, C.; He, W.; Zhou, H.; Xue, Y.R.; Zhu, M.D. A comparative study among machine learning and numerical models for simulating groundwater dynamics in the Heihe River Basin, northwestern China. Sci. Rep.
**2021**, 10, 3904. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ao, C.; Zeng, W.Z.; Wu, L.F.; Qian, L.; Srivastava, A.K.; Gaiser, T. Time-delayed machine learning models for estimating groundwater depth in the Hetao Irrigation District, China. Agric. Water Manag.
**2021**, 255, 107032. [Google Scholar] [CrossRef] - Lykkegaard, M.B.; Dodwell, T.J.; Moxey, D. Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy. Comput. Methods Appl. Mech. Eng.
**2021**, 383, 113895. [Google Scholar] [CrossRef] - Wu, M.; Feng, Q.; Wen, X.H.; Yin, Z.L.; Yang, L.S.; Sheng, D.R. Deterministic analysis and uncertainty analysis of ensemble forecasting model based on variational mode decomposition for estimation of monthly groundwater level. Water
**2021**, 13, 139. [Google Scholar] [CrossRef] - Zuo, G.; Luo, J.; Wang, N.; Lian, Y.; He, X. Decomposition ensemble model based on variational mode decomposition and long short-term memory for streamflow forecasting. J. Hydrol.
**2020**, 585, 124776. [Google Scholar] [CrossRef] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Snin, H.H.; Zheng, Q.; Yen, N.C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A Math. Phys. Eng. Sci.
**1998**, 454, 903–995. [Google Scholar] [CrossRef] - Huang, C.L.; Wang, C.J. A GA-based feature selection and parameters optimization for support vector machines. Expert Syst. Appl.
**2006**, 31, 231–240. [Google Scholar] [CrossRef] - Ahn, G.; Hur, S. Efficient genetic algorithm for feature selection for early time series classification. Comput. Ind. Eng.
**2020**, 142, 106345. [Google Scholar] [CrossRef] - Divya, R.; Shantha Selva Kumari, R. Genetic algorithm with logistic regression feature selection for Alzheimer’s disease classification. Neural Comput. Appl.
**2021**, 33, 8435–8444. [Google Scholar] [CrossRef] - Yang, J.; Honavar, V. Subset selection using a genetic algorithm. In Feature Extraction, Construction and Selection; Liu, H., Motoda, H., Eds.; Longman: Boston, UK, 1998; Chapter 8; p. 117. [Google Scholar]
- Hinton, G.E.; Osindero, S.; Teh, Y.W. A fast learning algorithm for deep belief nets. Neural Comput.
**2006**, 18, 1527–1554. [Google Scholar] [CrossRef] - Koenker, R.; Bassett, G. Regression Quantiles. Econometrica
**1978**, 46, 33–50. [Google Scholar] [CrossRef] - Koenker, R.; Hallock, K.F. Quantile regression. J. Econ. Perspect.
**2001**, 15, 143–156. [Google Scholar] [CrossRef] - Kasraei, B.; Heung, B.; Saurette, D.D.; Schmidt, M.G.; Bulmer, C.E.; Bethel, W. Quantile regression as a generic approach for estimating uncertainty of digital soil maps produced from machine-learning. Environ. Modell. Softw.
**2021**, 144, 105139. [Google Scholar] [CrossRef] - Weerts, A.H.; Winsemius, H.C.; Verkade, J.S. Estimation of predictive hydrological uncertainty using quantile regression: Examples from the national flood forecasting system (England and Wales). Hydrol. Earth Syst. Sci.
**2011**, 15, 255–265. [Google Scholar] [CrossRef][Green Version] - The second hydrogeological brigade for the bureau of Gansu geology and mineral resources. In Manual of Comprehensive Hydrogeological Map of the People’s Republic of China-Jiuquan Sheet; SinoMaps Press: Beijing, China, 1981; p. 6.
- Wei, G.; Wang, G.; Xu, T.; Zhu, F. The evaluation of groundwater system in Jiuquan Basin. J. Arid Land Res. Environ.
**2008**, 22, 38–44. [Google Scholar] - Wan, L.; Dong, Y.; Xu, Z. A synthesis of hydrochemistry with an integrated conceptual model for groundwater in the Hexi Corridor, northwestern China. J. Asian Earth Sci.
**2017**, 146, 20–29. [Google Scholar] [CrossRef] - Ren, X.; Gao, Z.; An, Y.; Liu, J.; Wu, X.; He, M.; Feng, J. Hydrochemical and isotopic characteristics of groundwater in the Jiuquan East Basin, China. Arab. J. Geosci.
**2020**, 13. [Google Scholar] [CrossRef] - He, J.; Ma, J.; Zhang, P.; Tian, L.; Zhu, G.; Edmunds, M.W.; Zhang, Q. Groundwater recharge environments and hydrogeochemical evolution in the Jiuquan Basin, Northwest China. Appl. Geochem.
**2012**, 27, 866–878. [Google Scholar] [CrossRef] - Legates, D.R.; McCabe, G.J. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Shrestha, D.L.; Solomatine, D.P. Machine learning approaches for estimation of prediction interval for the model output. Neural Netw.
**2006**, 19, 225–235. [Google Scholar] [CrossRef] - Muthusamy, M.; Godiksen, P.N.; Madsen, H. Comparison of different configurations of quantile regression in estimating predictive hydrological uncertainty. Proc. Eng.
**2016**, 154, 513–520. [Google Scholar] [CrossRef] - Feng, Q.; Wen, X.; Li, J. Wavelet analysis-support vector machine coupled models for monthly rainfall forecasting in arid regions. Water Resour. Manag.
**2015**, 29, 1049–1065. [Google Scholar] [CrossRef] - Zeynoddin, M.; Bonakdari, H.; Ebtehaj, I.; Esmaeilbeiki, F.; Gharabaghi, B.; Haghi, D.Z. A reliable linear stochastic daily soil temperature forecast model. Soil Till. Res.
**2019**, 189, 73–87. [Google Scholar] [CrossRef] - Yin, Z.; Feng, Q.; Wen, X.; Deo, R.C.; Yang, L.; Si, J.; He, Z. Design and evaluation of SVR, MARS and M5 Tree models for 1, 2 and 3-day lead time forecasting of river flow data in a semiarid mountainous catchment. Stoch. Environ. Res. Risk Assess.
**2018**, 32, 2457–2476. [Google Scholar] [CrossRef] - Wen, X.; Feng, Q.; Deo, R.C.; Wu, M.; Si, J. Wavelet analysis-artificial neural network conjunction models for multi-scale monthly groundwater level predicting in an arid inland river basin, northwestern China. Hydrol. Res.
**2017**, 48, 1710–1729. [Google Scholar] [CrossRef] - Bahmani, R.; Ouarda, T.B.M.J. Groundwater level modeling with hybrid artificial intelligence techniques. J. Hydrol.
**2021**, 595, 125659. [Google Scholar] [CrossRef] - Barzegar, R.; Aalami, M.T.; Adamowski, J. Coupling a hybrid CNN-LSTM deep learning model with a Boundary Corrected Maximal Overlap Discrete Wavelet Transform for multiscale Lake water level forecasting. J. Hydrol.
**2021**, 598, 126196. [Google Scholar] [CrossRef] - Sui, G.S. Research on groundwater dynamic characteristics and influencing factors in Jiuquan west basin. Groundwater
**2019**, 41, 41–42; 57. [Google Scholar] [CrossRef]

**Figure 2.**Location of the Jiuquan basin, the study area, the groundwater level observation wells and the meteorological station.

**Figure 3.**Observed vs. predicted groundwater level for Well I generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 4.**Scatter plot of the observed and predicted groundwater level for Well I generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 5.**Observed vs. predicted groundwater level for Well II generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 6.**Scatter plot of the observed and predicted groundwater level for Well II generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 7.**Observed vs. predicted groundwater level of Well III generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 8.**Observed vs. predicted groundwater level of Well III generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models for 1-, 2- and 3-month ahead forecast in the testing period.

**Figure 9.**Boxplots of the predicted error for the 1-, 2- and 3-month ahead groundwater level forecast generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models in the testing period.

**Figure 10.**Boxplots of the distribution for the observed and simulated groundwater level forecast for the 1-, 2- and 3-month ahead groundwater level generated by the CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models in the testing period.

**Figure 11.**The Legates and McCabe’s Index in testing phase of the hybrid CEEMDAN-GA-DBN vs. CEEMDAN-DBN and DBN models for (

**a**) Well I, (

**b**) Well II and (

**c**) Well III.

**Table 1.**Summary of machine learning methods in groundwater level modeling for arid and semi-arid regions in the latest years.

Data Pre-Processing | Feature Selection | Machine Learning/Deep Learning Method | Uncertainty Analysis | Hybrid Model | Reference |
---|---|---|---|---|---|

WT | SVM; Random Forest (RF); Linear Boosting of XGB; Tree Boosting of XGB | WT-SVR; WT-RF; WT-XGBL; WT-XGBT | Rahman et al. (2020) [16] | ||

WT | Pearson correlation analysis | LSTM | WT-multivariate LSTM | Wu et al. (2021) [27] | |

Deep Neural Network (DNN); SVM; ANFIS | Mohapatra et al. (2021) [44] | ||||

WT | Support Vector Regression (SVR); Gaussian Process Regression (GPR) | W-SVR; W-GPR | Band et al. (2021) [45] | ||

Information Gain (IG);Variance Inflation Factor (VIF) | RF; Logistic Regression; Decision Tree; ANN | Namous et al. (2021) [46] | |||

Multi-layer Perceptron; Radial Basis Function Network; SVM; DNN | Chen et al. (2021) [47] | ||||

ANFIS; SVM; Kernel-based Nonlinear Arps decline; LSTM; Gated Recurrent Unit | Ao et al. (2021) [48] | ||||

DNN | Modified delayed acceptance Markov Chain Monte Carlo (MCMC) | Lykkegaard et al. (2021) [49] | |||

VMD | Boruta | ELM | Bootstrap | VBELM | Wu et al. (2021) [50] |

CEEMDAN | GA | DBN | QR | CEEMDAN-GA-DBN | This study |

**Table 2.**The statistical parameters of groundwater level (GWL) and related climatic data for three GWL observation wells in the whole dataset (January 2000 to December 2015), the training dataset (January 2000 to December 2010) and the testing dataset (January 2011 to December 2015).

Total Precipitation Per Month | Mean Monthly Temperature | Monthly GWL | ||||
---|---|---|---|---|---|---|

Pre (mm) | Tem (°C) | Well I (m) | Well II (m) | Well III (m) | ||

Minimum | All | 0 | −14.11 | 1440.03 | 1436.22 | 1328.63 |

Training | 0 | −14.11 | 1440.12 | 1436.39 | 1328.63 | |

Testing | 0 | −13.91 | 1440.03 | 1436.22 | 1328.78 | |

Maximum | All | 79.50 | 24.38 | 1442.63 | 1441.28 | 1329.93 |

Training | 52.40 | 24.38 | 1442.36 | 1441.28 | 1329.93 | |

Testing | 79.50 | 23.10 | 1442.63 | 1440.78 | 1329.82 | |

Mean | All | 7.75 | 8.20 | 1441.36 | 1438.74 | 1329.33 |

Training | 7.77 | 8.19 | 1441.30 | 1438.79 | 1329.30 | |

Testing | 7.70 | 8.21 | 1441.50 | 1438.64 | 1329.38 | |

Standard Deviation | All | 11.05 | 11.18 | 0.54 | 1.08 | 0.30 |

Training | 10.01 | 11.21 | 0.46 | 1.07 | 0.31 | |

Testing | 13.15 | 11.21 | 0.66 | 1.10 | 0.28 | |

Skewness | All | 2.83 | −0.24 | −0.13 | −0.08 | −0.22 |

Training | 2.19 | −0.23 | −0.38 | −0.04 | −0.08 | |

Testing | 3.39 | −0.27 | −0.28 | −0.15 | −0.55 |

**Table 3.**Performance metrics of the hybridized CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models in the training and testing phases for 1-, 2- and 3-month ahead GWL forecasting of Well I.

Training Phase | Testing Phase | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

R | MAE (m) | RMSE (m) | NSE | RSR | R | MAE (m) | RMSE (m) | NSE | RSR | |

CEEMDAN-GA-DBN | ||||||||||

1-month ahead | 0.967 | 0.095 | 0.117 | 0.935 | 0.254 | 0.930 | 0.210 | 0.277 | 0.819 | 0.421 |

2-month ahead | 0.940 | 0.123 | 0.157 | 0.883 | 0.341 | 0.904 | 0.225 | 0.315 | 0.759 | 0.486 |

3-month ahead | 0.883 | 0.204 | 0.253 | 0.700 | 0.545 | 0.865 | 0.247 | 0.333 | 0.732 | 0.513 |

CEEMDAN-DBN | ||||||||||

1-month ahead | 0.966 | 0.096 | 0.119 | 0.932 | 0.259 | 0.923 | 0.241 | 0.313 | 0.770 | 0.476 |

2-month ahead | 0.941 | 0.118 | 0.155 | 0.886 | 0.337 | 0.891 | 0.248 | 0.333 | 0.732 | 0.513 |

3-month ahead | 0.917 | 0.131 | 0.169 | 0.867 | 0.364 | 0.853 | 0.261 | 0.363 | 0.680 | 0.560 |

DBN | ||||||||||

1-month ahead | 0.920 | 0.147 | 0.180 | 0.845 | 0.392 | 0.881 | 0.259 | 0.341 | 0.727 | 0.518 |

2-month ahead | 0.897 | 0.163 | 0.203 | 0.804 | 0.441 | 0.815 | 0.290 | 0.394 | 0.624 | 0.607 |

3-month ahead | 0.874 | 0.180 | 0.225 | 0.764 | 0.484 | 0.839 | 0.304 | 0.396 | 0.621 | 0.610 |

**Table 4.**Performance metrics of the hybridized CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models in the training and testing phases for 1-, 2- and 3-month ahead GWL forecasting of Well II.

Training Phase | Testing Phase | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

R | MAE (m) | RMSE (m) | NSE | RSR | R | MAE (m) | RMSE (m) | NSE | RSR | |

CEEMDAN-GA-DBN | ||||||||||

1-month ahead | 0.951 | 0.238 | 0.291 | 0.920 | 0.283 | 0.968 | 0.254 | 0.291 | 0.929 | 0.264 |

2-month ahead | 0.942 | 0.268 | 0.338 | 0.887 | 0.334 | 0.941 | 0.375 | 0.443 | 0.840 | 0.397 |

3-month ahead | 0.942 | 0.269 | 0.337 | 0.887 | 0.334 | 0.906 | 0.412 | 0.495 | 0.801 | 0.442 |

CEEMDAN-DBN | ||||||||||

1-month ahead | 0.957 | 0.240 | 0.299 | 0.915 | 0.291 | 0.954 | 0.295 | 0.365 | 0.889 | 0.330 |

2-month ahead | 0.941 | 0.267 | 0.343 | 0.884 | 0.339 | 0.942 | 0.413 | 0.509 | 0.789 | 0.456 |

3-month ahead | 0.944 | 0.258 | 0.331 | 0.891 | 0.328 | 0.895 | 0.428 | 0.515 | 0.786 | 0.459 |

DBN | ||||||||||

1-month ahead | 0.915 | 0.336 | 0.415 | 0.836 | 0.404 | 0.932 | 0.345 | 0.414 | 0.857 | 0.375 |

2-month ahead | 0.856 | 0.416 | 0.521 | 0.733 | 0.515 | 0.876 | 0.458 | 0.575 | 0.730 | 0.515 |

3-month ahead | 0.833 | 0.458 | 0.556 | 0.694 | 0.551 | 0.835 | 0.518 | 0.656 | 0.652 | 0.585 |

**Table 5.**Performance metrics of the hybridized CEEMDAN-GA-DBN, CEEMDAN-DBN and DBN models in the training and testing phases for 1-, 2- and 3-month ahead GWL forecasting of Well III.

Training Phase | Testing Phase | |||||||||

R | MAE (m) | RMSE (m) | NSE | RSR | R | MAE (m) | RMSE (m) | NSE | RSR | |

CEEMDAN-GA-DBN | ||||||||||

1-month ahead | 0.909 | 0.098 | 0.131 | 0.827 | 0.415 | 0.843 | 0.110 | 0.157 | 0.688 | 0.554 |

2-month ahead | 0.904 | 0.105 | 0.135 | 0.816 | 0.428 | 0.810 | 0.129 | 0.169 | 0.630 | 0.602 |

3-month ahead | 0.872 | 0.122 | 0.153 | 0.757 | 0.491 | 0.760 | 0.134 | 0.178 | 0.570 | 0.650 |

CEEMDAN-DBN | ||||||||||

1-month ahead | 0.911 | 0.096 | 0.130 | 0.831 | 0.410 | 0.808 | 0.123 | 0.175 | 0.614 | 0.616 |

2-month ahead | 0.910 | 0.101 | 0.130 | 0.828 | 0.414 | 0.798 | 0.138 | 0.180 | 0.583 | 0.640 |

3-month ahead | 0.897 | 0.107 | 0.139 | 0.799 | 0.447 | 0.749 | 0.149 | 0.185 | 0.534 | 0.677 |

DBN | ||||||||||

1-month ahead | 0.880 | 0.111 | 0.150 | 0.772 | 0.475 | 0.778 | 0.133 | 0.180 | 0.588 | 0.636 |

2-month ahead | 0.908 | 0.096 | 0.132 | 0.823 | 0.419 | 0.808 | 0.144 | 0.182 | 0.573 | 0.648 |

3-month ahead | 0.893 | 0.104 | 0.139 | 0.798 | 0.448 | 0.820 | 0.152 | 0.191 | 0.507 | 0.696 |

**Table 6.**AIC values of the CEEMDAN-GA-DBN, CEEMDAN- DBN and DBN models for the 1-, 2- and 3-month ahead GWL forecasts at Well I, Well II, Well III.

CEEMDAN-GA-DBN | CEEMDAN-DBN | DBN | |
---|---|---|---|

Well I | |||

1-month ahead | −136.917 | −123.559 | −114.275 |

2-month ahead | −122.73 | −116.889 | −98.281 |

3-month ahead | −116.793 | −107.13 | −97.732 |

Well II | |||

1-month ahead | −131.507 | −106.671 | −92.663 |

2-month ahead | −85.33 | −70.112 | −56.719 |

3-month ahead | −73.025 | −68.82 | −42.152 |

Well III | |||

1-month ahead | −199.541 | −187.797 | −184.252 |

2-month ahead | −191.245 | −184.587 | −183.257 |

3-month ahead | −185.635 | −181.233 | −178.13 |

**Table 7.**Uncertainty analysis for the 1-, 2- and 3-month ahead GWL forecasts of the CEEMDAN-GA-DBN, CEEMDAN- DBN and DBN models at 90% confidence level.

Observation Well | Lead Time | CEEMDAN-GA-DBN | CEEMDAN-DBN | DBN | |||
---|---|---|---|---|---|---|---|

MPI (m) | PICP (%) | MPI (m) | PICP (%) | MPI (m) | PICP (%) | ||

Well I | 1 | 0.38 | 56.36 | 0.37 | 47.27 | 0.59 | 65.45 |

2 | 0.51 | 69.09 | 0.53 | 63.64 | 0.65 | 63.64 | |

3 | 0.74 | 76.36 | 0.51 | 62.82 | 0.68 | 56.36 | |

Well II | 1 | 0.98 | 92.73 | 0.97 | 85.45 | 1.41 | 92.73 |

2 | 1.14 | 80.00 | 1.07 | 70.91 | 1.69 | 81.82 | |

3 | 1.08 | 70.90 | 1.19 | 69.09 | 1.81 | 76.36 | |

Well III | 1 | 0.37 | 81.82 | 0.37 | 78.18 | 0.46 | 85.45 |

2 | 0.45 | 89.09 | 0.37 | 78.18 | 0.44 | 81.82 | |

3 | 0.47 | 83.64 | 0.47 | 80.00 | 0.44 | 80.00 |

**Table 8.**Uncertainty analysis for the 1-, 2- and 3-month ahead GWL forecasts of the CEEMDAN-GA-DBN, CEEMDAN- DBN and DBN models at 95% confidence level.

Observation Well | Lead Time | CEEMDAN-GA-DBN | CEEMDAN-DBN | DBN | |||
---|---|---|---|---|---|---|---|

MPI (m) | PICP (%) | MPI (m) | PICP (%) | MPI (m) | PICP (%) | ||

Well I | 1 | 0.41 | 56.36 | 0.43 | 58.18 | 0.71 | 70.91 |

2 | 0.62 | 72.73 | 0.67 | 83.64 | 0.84 | 78.20 | |

3 | 0.81 | 81.82 | 0.69 | 72.73 | 1.00 | 81.82 | |

Well II | 1 | 1.10 | 96.36 | 1.17 | 92.72 | 1.67 | 94.55 |

2 | 1.30 | 83.64 | 1.46 | 89.09 | 1.96 | 83.64 | |

3 | 1.24 | 74.55 | 1.31 | 76.36 | 2.07 | 83.64 | |

Well III | 1 | 0.48 | 90.91 | 0.46 | 89.01 | 0.57 | 90.91 |

2 | 0.47 | 89.09 | 0.52 | 89.09 | 0.53 | 87.27 | |

3 | 0.61 | 90.91 | 0.56 | 89.27 | 0.61 | 90.91 |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Yu, H.; Yang, L.; Yin, Z.; Zhu, M.; Wen, X. Deep Learning-Based Predictive Framework for Groundwater Level Forecast in Arid Irrigated Areas. *Water* **2021**, *13*, 2558.
https://doi.org/10.3390/w13182558

**AMA Style**

Liu W, Yu H, Yang L, Yin Z, Zhu M, Wen X. Deep Learning-Based Predictive Framework for Groundwater Level Forecast in Arid Irrigated Areas. *Water*. 2021; 13(18):2558.
https://doi.org/10.3390/w13182558

**Chicago/Turabian Style**

Liu, Wei, Haijiao Yu, Linshan Yang, Zhenliang Yin, Meng Zhu, and Xiaohu Wen. 2021. "Deep Learning-Based Predictive Framework for Groundwater Level Forecast in Arid Irrigated Areas" *Water* 13, no. 18: 2558.
https://doi.org/10.3390/w13182558