Groundwater balance analysis for assessing the sustainability of the Izeh plain aquifer using IDW and Thiessen polygon methods

Abstract
This research, to quantitatively assess the groundwater sustainability of the Izeh Plain, adopted an integrated approach combining Inverse Distance Weighting (IDW) and Thiessen polygon methods with hydrogeological water balance calculations. Monthly groundwater level data from 10 wells were analyzed in a Geographic Information System (GIS) and a representative hydrograph was extracted. Although comparison of the two methods indicates a very high correlation (with a determination coefficient exceeding 99%) between them, the IDW method demonstrated superior operational accuracy in reconstructing the spatial variations of groundwater levels, with a Mean Absolute Error (MAE) of 2.8 cm. The results of the water balance calculations revealed a critical condition of the aquifer: annual effective recharge amounts to approximately 18.9 million cubic meters (MCM) against outflows of 20.2 MCM. This imbalance leads to a net annual deficit of approximately 1.3 MCM, a decrease in the average groundwater level, and the creation of a negative hydrodynamic balance. Finally, the findings suggest that current exploitation exceeds the natural recharge capacity of the aquifer, threatening its long-term sustainability. However, the integration of these simple analytical methods provides a practical tool for monitoring and sustainable management of groundwater resources. Achieving a sustainable balance in the Izeh Plain requires the immediate implementation of strategies to reduce abstraction, balancing measures, and a revision of cropping patterns. 
Extended Abstract
Background and Objective
Despite extensive research on groundwater resources in Iran and numerous studies on interpolation methods, no study has yet conducted an integrated evaluation of the Izeh plain aquifer's stability by combining simple, practical interpolation techniques (Thiessen and IDW) within a GIS framework alongside groundwater budget calculations. Previous research in this domain has either relied on complex numerical and artificial intelligence models or remained confined to separate analyses; consequently, the synergistic combination of these straightforward interpolation methods with balance calculations to simultaneously analyze spatio-temporal variations of water levels and derive an accurate representative hydrograph has been overlooked. This research addresses this gap by presenting a systematic integration of Thiessen and IDW methods in GIS with groundwater budgeting to comprehensively evaluate the stability of the Izeh plain aquifer.
 
Methodology
Local methods, such as inverse distance weighting (IDW) and radial basis functions (RBF), perform prediction based on a subset of adjacent points and are classified as accurate (Exact Interpolators) in terms of values, meaning that predicted values at the sample locations are equal to the observed values.
In the inverse distance weighting method (IDW), which is known as a deterministic approach in spatial interpolation, the weight of each sample point in determining the value of unknown points is calculated according to the inverse distance from that point to the expected position.
In the applied part of this study, which is focused on the Izeh plain, the IDW method was used for interpolation of groundwater and rainfall data.
For spatial analysis of point data and providing continuous maps of hydrogeological parameters (such as surface water level), deterministic spatial interpolation methods were used.
Spatial-temporal analysis of the hydrogeological variable in the Izeh plain using the IDW interpolation method based on monthly data was performed.
 
Findings
The infiltration rate was 714 mm at the Izeh station, and with an aquifer area of 313 square meters, the effective infiltration volume was calculated.
Applying an effective diffusivity of 20%, based on previous studies and the dominant lithology of the area (silty sandstone), this volume is estimated to be approximately 18.9 m³ per year.
Side currents were assessed to estimate lateral flow, initially by determining the hydro field potential using Surfer software.
Subsequently, the hydraulic gradient (i) was calculated based on the difference in water level at the boundaries of the aquifer.
The effective cross-sectional area of flow was obtained by multiplying the distance between streamlines by the effective thickness of the aquifer.
Using a hydraulic conductivity coefficient (k) of 0.22 m³/day, extracted from previous studies, the discharge of lateral inflow was estimated using Darcy’s equation and based on the dimensions of the entrance boundary (750 m), resulting in 69 m³/day and an approximate annual volume of 295 m³.
Similarly, the lateral outflow rate was calculated as 76 m³/day, and the annual volume is close to 824 m³, considering the dimensions of the output boundary (450 m).
In the remaining portion of the budget, the annual withdrawal from the aquifer, based on official statistics from the regional water organization for 10 wells, was estimated to be 200 m³.
 
Conclusion
The results of this research with an integrated and operational approach to assess the stability of the Izeh plain and comparison of simple interpolation methods in hydrogeological analysis.
The results clearly showed that integration of spatial - temporal variations analysis using deterministic methods such as inverse distance weighting and thiessen polygons, provides an effective and efficient tool for monitoring and understanding the dynamic situation of aquifers.
This approach allows the drawing of more accurate representation of hydrograph without requiring complex and expensive numerical modeling.
Quantitative evaluation of different components of the balance revealed the warning of the studied aquifer and showed a negative balance and a continuous drop in the water level.
These conditions confirm the hydrodynamic instability of the reservoir and the increased pressure induced by the operation beyond renewable capacity.
In general, the findings of this study emphasize the necessity of adopting immediate and sustainable management strategies to control the discharge and restoring the balance of this vital resource.
The proposed integrated approach, as an extensible analytical framework, can be used to monitor and evaluate the initial evaluation of other aquifers in the restricted area.