A Developed Multiple Linear Regression (MLR) Model for Monthly Groundwater Level Prediction

Abstract

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.