ترکیب مدل‌های فیزیکی و یادگیری ماشین برای پیش‌بینی کیفیت آب زیرزمینی: MODFLOW و SVM

Abstract
Groundwater depletion and salinity increase are among the most critical challenges affecting the Qom aquifer in arid regions of Iran. In this study, a hybrid modeling framework integrating physics-based and data-driven approaches was developed to simulate and predict groundwater quality. The MODFLOW model was employed to simulate groundwater flow, while MT3D was used to model chloride transport as an indicator of salinity. Subsequently, a Support Vector Machine (SVM) model was developed to predict chloride concentration. The MODFLOW model was calibrated using data from 16 piezometers and demonstrated satisfactory performance in reproducing groundwater levels, with RMSE values ranging from 0.10 to 0.18 m and a correlation coefficient of up to 0.96. MT3D simulations revealed significant spatial variability in chloride dispersion, highlighting the influence of hydrogeological heterogeneity on salinity distribution. The SVM model was trained using spatial coordinates, groundwater levels, previous-month chloride concentration, and surface recharge as input variables. The model showed strong predictive capability, achieving a correlation coefficient of 0.91 during the testing phase. Comparison between SVM predictions and numerical model outputs yielded an MSE of approximately 0.03 kg/m³ and a correlation coefficient of about 0.65, indicating acceptable agreement. The results demonstrate that the SVM model can effectively reproduce the behavior of the numerical model while requiring lower computational cost. Overall, the integration of physics-based and machine learning models provides an efficient and reliable framework for groundwater quality prediction and management under data-limited conditions.
 
Extended Abstract
Background and Objective
Groundwater resources in arid and semi-arid regions are increasingly threatened by overexploitation and salinity intrusion. The Qom aquifer in central Iran is a representative case, where declining groundwater levels and increasing salinity—primarily due to geological formations and saline water intrusion—have raised serious concerns for sustainable water management. Traditional numerical models such as MODFLOW are widely used for simulating groundwater flow; however, their application in water quality modeling is often limited by the availability of comprehensive spatial and temporal datasets.
To address this limitation, this study aims to develop a hybrid modeling framework by integrating a physically-based model (MODFLOW coupled with MT3D) and a data-driven approach (Support Vector Machine, SVM) to simulate and predict groundwater quality, with a particular focus on chloride concentration as a salinity indicator.
 
Methodology
The study area is located in the Qom plain, characterized by an arid climate and significant groundwater salinity issues. The MODFLOW model was developed to simulate groundwater flow and calibrated using observed data from 16 piezometers. The MT3D model was then applied to simulate chloride transport based on the advection–dispersion equation under transient conditions.
Due to limited water quality data, spatial interpolation techniques (kriging and polynomial approximation) were employed to generate continuous chloride concentration maps. The simulation period covered six months, with two months for calibration and four months for validation.
For predictive modeling, an SVM model with a radial basis function (RBF) kernel was developed. Input variables included piezometer coordinates, groundwater levels (from MODFLOW), previous-month chloride concentration, and surface recharge. The dataset was divided into training (70%) and testing (30%) subsets, and model performance was evaluated using RMSE, MSE, NMSE, and correlation coefficient (r). A 10-fold cross-validation approach was used to avoid overfitting and optimize model parameters.
 
Findings
The MODFLOW model exhibited reliable performance in simulating groundwater levels, with RMSE values ranging from 0.10 to 0.18 m and correlation coefficients reaching up to 0.96. The results indicated relatively stable groundwater conditions in the northwestern parts of the aquifer, whereas notable declines were observed in the southern regions.
The MT3D simulations highlighted considerable spatial variability in chloride transport, with horizontal dispersivity values ranging from 10 to 80 m, reflecting the heterogeneity of the hydrogeological system.
The SVM model demonstrated strong predictive performance, achieving a correlation coefficient of 0.91 during the testing phase. A comparison between SVM outputs and numerical model results yielded an MSE of approximately 0.03 kg/m³ and a correlation coefficient of about 0.65, indicating a reasonable level of agreement. Although the SVM model showed some limitations in capturing minor fluctuations, it effectively reproduced the overall spatial and temporal patterns of chloride concentration.
 
Conclusion
The results demonstrate that the integration of physically-based and data-driven models provides a robust framework for groundwater quality assessment under data-limited conditions. The SVM model, in particular, offers a computationally efficient alternative to complex numerical simulations while maintaining acceptable accuracy.
The proposed hybrid approach enhances predictive performance and can support sustainable groundwater management in arid and semi-arid regions. This framework is especially valuable for identifying critical regions prone to salinity and can be extended to similar hydrogeological settings facing data scarcity challenges.