Correlation–based reliability index equipped with machine learning methods to complete the groundwater level gaps

Abstract

Completing gaps in groundwater level (GWL) data is critical for reliable hydrological analysis and modeling. The irregularities and missing values often present in GWL measurements necessitate robust methods for infilling. In this study, an innovative approach is proposed to reconstruct the GWL time series by addressing data gaps. Historical GWL data spanning 20 years from 40 observation wells in the Lenjanat aquifer, Isfahan Province, Iran, are used. Three clustering methods—K-means, Fuzzy C-means (FCM), and Self-Organizing Map (SOM)—are applied to group the wells, and a novel metric, the Correlation-based Reliability Index (CRI), is introduced to identify the most suitable clustering method for GWL prediction. The selected cluster is analyzed using four machine learning and hybrid models, including support vector regression (SVR) with linear, polynomial, and radial basis function (RBF) kernels, genetic programming (GP), artificial neural networks (ANN), and a hybrid model combining SVR with the whale optimization algorithm (WOA) (WOA-SVR). Results reveals that the SVR model with an RBF kernel outperformed its counterparts with linear and polynomial kernels, while the hybrid WOA-SVR model shows superior performance compared to other models. The hybrid approach significantly improves the accuracy of GWL gap completion. The WOA-SVR model leads to average R2, RMSE, MAPE, and NS values of 0.81 (0.74), 0.55 m (0.95 m), 0.02 % (0.04 %), and 0.80 (0.72) for the training (test and validation) data, respectively. The results demonstrates that the proposed approach, integrating clustering, CRI, and machine learning models, can effectively fill GWL gaps and provide clean data for further hydrological modeling and groundwater management. © 2025 The Authors