A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction
Groundwater level (GLW) prediction is essential for monitoring water resources. Our study introduces a novel model called convolutional neural network (CNN)–long short-term memory neural network (LSTM)–Multiple linear regression (MLR) for groundwater level prediction. We combine two deep learning mo...
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/15/22/3940 |
| _version_ | 1797457476748050432 |
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| author | Mohammad Ehteram Fatemeh Barzegari Banadkooki |
| author_facet | Mohammad Ehteram Fatemeh Barzegari Banadkooki |
| author_sort | Mohammad Ehteram |
| collection | DOAJ |
| description | Groundwater level (GLW) prediction is essential for monitoring water resources. Our study introduces a novel model called convolutional neural network (CNN)–long short-term memory neural network (LSTM)–Multiple linear regression (MLR) for groundwater level prediction. We combine two deep learning models with the MLR model to predict GWL and overcome the limitations of the MLR model. The current paper has several innovations. Our study develops an advanced hybrid model for predicting groundwater levels (GWLs). The study also presents a novel feature selection method for selecting optimal input scenarios. Finally, an advanced method is developed to examine the impact of inputs and model parameters on output uncertainty. The current paper introduces the gannet optimization algorithm (GOA) for choosing the optimal input scenario. A CNN-LSTM-MLR model (CLM), CNN, LSTM, MLR model, CNN-MLR model (CNM), LSTM-MLR model (LSM), and CNN-LSTM model (CNL) were built to predict one-month-ahead GWLs using climate data and lagged GWL data. Output uncertainty was also decomposed into parameter uncertainty (PU) and input uncertainty (IU) using the analysis of variance (ANOVA) method. Based on our findings, the CLM model can successfully predict GWLs, reduce the uncertainty of CNN, LSTM, and MLR models, and extract spatial and temporal features. Based on the study’s findings, the combination of linear models and deep learning models can improve the performance of linear models in predicting outcomes. The GOA method can also contribute to feature selection and input selection. The study findings indicated that the CLM model improved the training Nash–Sutcliffe efficiency coefficient (NSE) of the CNL, LSM, CNM, LSTM, CNN, and MLR models by 6.12%, 9.12%, 12%, 18%, 22%, and 30%, respectively. The width intervals (WIs) of the CLM, CNL, LSM, and CNM models were 0.03, 0.04, 0.07, and, 0.12, respectively, based on IU. The WIs of the CLM, CNL, LSM, and CNM models were 0.05, 0.06, 0.09, and 0.14, respectively, based on PU. Our study proposes the CLM model as a reliable model for predicting GWLs in different basins. |
| first_indexed | 2024-03-09T16:22:42Z |
| format | Article |
| id | doaj.art-72416d16b6524b9da65c5b0a368022d3 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-09T16:22:42Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-72416d16b6524b9da65c5b0a368022d32023-11-24T15:11:22ZengMDPI AGWater2073-44412023-11-011522394010.3390/w15223940A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level PredictionMohammad Ehteram0Fatemeh Barzegari Banadkooki1Department of Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, Semnan University, Semnan 35131-19111, IranAgricultural Department, Payame Noor University, Tehran 19395-4697, IranGroundwater level (GLW) prediction is essential for monitoring water resources. Our study introduces a novel model called convolutional neural network (CNN)–long short-term memory neural network (LSTM)–Multiple linear regression (MLR) for groundwater level prediction. We combine two deep learning models with the MLR model to predict GWL and overcome the limitations of the MLR model. The current paper has several innovations. Our study develops an advanced hybrid model for predicting groundwater levels (GWLs). The study also presents a novel feature selection method for selecting optimal input scenarios. Finally, an advanced method is developed to examine the impact of inputs and model parameters on output uncertainty. The current paper introduces the gannet optimization algorithm (GOA) for choosing the optimal input scenario. A CNN-LSTM-MLR model (CLM), CNN, LSTM, MLR model, CNN-MLR model (CNM), LSTM-MLR model (LSM), and CNN-LSTM model (CNL) were built to predict one-month-ahead GWLs using climate data and lagged GWL data. Output uncertainty was also decomposed into parameter uncertainty (PU) and input uncertainty (IU) using the analysis of variance (ANOVA) method. Based on our findings, the CLM model can successfully predict GWLs, reduce the uncertainty of CNN, LSTM, and MLR models, and extract spatial and temporal features. Based on the study’s findings, the combination of linear models and deep learning models can improve the performance of linear models in predicting outcomes. The GOA method can also contribute to feature selection and input selection. The study findings indicated that the CLM model improved the training Nash–Sutcliffe efficiency coefficient (NSE) of the CNL, LSM, CNM, LSTM, CNN, and MLR models by 6.12%, 9.12%, 12%, 18%, 22%, and 30%, respectively. The width intervals (WIs) of the CLM, CNL, LSM, and CNM models were 0.03, 0.04, 0.07, and, 0.12, respectively, based on IU. The WIs of the CLM, CNL, LSM, and CNM models were 0.05, 0.06, 0.09, and 0.14, respectively, based on PU. Our study proposes the CLM model as a reliable model for predicting GWLs in different basins.https://www.mdpi.com/2073-4441/15/22/3940deep learning modelsfeature selection modelsgroundwater levelhybrid models |
| spellingShingle | Mohammad Ehteram Fatemeh Barzegari Banadkooki A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction Water deep learning models feature selection models groundwater level hybrid models |
| title | A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction |
| title_full | A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction |
| title_fullStr | A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction |
| title_full_unstemmed | A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction |
| title_short | A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction |
| title_sort | developed multiple linear regression mlr model for monthly groundwater level prediction |
| topic | deep learning models feature selection models groundwater level hybrid models |
| url | https://www.mdpi.com/2073-4441/15/22/3940 |
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