A state-of-the-art Fuzzy Nonlinear Additive Regression (FNAR) model for groundwater level prediction

Abstract

Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems, necessitating endeavors to quantify Groundwater Levels (GWL) dynamics to inform policymakers and hydrogeologists. This study introduces a novel Fuzzy Nonlinear Additive Regression (FNAR) model to predict monthly GWL in an unconfined aquifer in eastern Iran, using a 19-year (1998–2017) dataset from 11 piezometric wells. Under three distinct scenarios with progressively increasing input complexity, the study utilized readily available climate data, including Precipitation (Prc), Temperature (Tave), Relative Humidity (RH), and Evapotranspiration (ETo). The dataset was split into training (70%) and validation (30%) subsets. Results showed that among three input scenarios, Scenario 3 (Sc3, incorporating all four variables) achieved the best predictive performance, with RMSE ranging from 0.305 m to 0.768 m, MAE from 0.203 m to 0.522 m, NSE from 0.661 to 0.980, and PBIAS from 0.771% to 0.981%, indicating low bias and high reliability. However, Sc2 (excluding ETo) with RMSE ranging from 0.4226 m to 0.9909 m, MAE from 0.3418 m to 0.8173 m, NSE from 0.2831 to 0.9674, and PBIAS from −0.598% to 0.968% across different months offers practical advantages in data-scarce settings. The FNAR model outperforms conventional Fuzzy Least Squares Regression (FLSR) and holds promise for GWL forecasting in data-scarce regions where physical or numerical models are impractical. Future research should focus on integrating FNAR with deep learning algorithms and real-time data assimilation expanding applications across diverse hydrogeological settings.