Empirical formulas are indispensable tools in water engineering and hydraulic structure design. Derived from meticulous field observations, experiments, and diverse datasets, these formulas help to estimate water leakage in structures such as dams, tunnels, canals, and pipelines. By utilizing a few easily measurable parameters, engineers can employ these formulas to generate preliminary leakage rate estimates before proceeding with more detailed analyses. In this study, a physical model was developed, and a series of experiments were conducted, considering variables such as inflow rate, materials constituting the unsaturated medium, and variations in infiltration trench depth and width. As a result, a novel artificial recharge method was introduced, and an empirical equation, ${\text{Q}}_{\text{out}}$= 0.0066 × ${{\mathrm{D}}_{50}}^{0.64}$× L × ${\mathrm{P}}^{0.36}$, was proposed to estimate the infiltration capacity of the trench. This equation incorporates factors such as the wetted perimeter, mean soil particle diameter, trench length, and a coefficient. A comparative analysis between the observed data from nine Iranian earthen canals and the values calculated using the proposed equation revealed an average relative error of 15% between the two datasets. In addition, the Pearson correlation coefficient was determined to be 0.981 and the Root Mean Square Error (RMSE) was 0.381, demonstrating the strong predictive performance of the equation. The parameters considered in the proposed equation allow for its application across diverse regions. Given its accurate performance, this equation provides a reliable initial estimate of the leakage rate, thereby helping to reduce costs and save time.

Effective management of water resources, especially groundwater, is crucial and requires a precise understanding of aquifer characteristics, imposed stresses, and the groundwater balance. Simulation-optimization models plays a vital role in guiding planners toword sustainable long-term aquifer exploitation. This study simulated monthly water table variations in the Kashan Plain over a ten-year period from 2008 to 2019 across 125 stress periods using the GMS model. The model was calibrated for both steady-state and transient conditions for the 2008–2016 period and validated for the 2016–2019 period. Results indicated a 4.4 m decline in groundwater levels over the 10-year study period. Given the plain's location in a arid climatic zone with limited effective precipitation for aquifer recharge, the study focused on groundwater extraction management. A modified two-point hedging policy was employed as a solution to mitigate critical groundwater depletion, reducing the annual drawdown rate from 0.44 m to 0.31 m and conserving 255 million cubic meters (mcm) of water annually. Although this approach slightly decreased reliability (i.e. the number of months meeting full water demands), it effectively minimized the risk of severe droughts and irreparable damages. This policy offers managers a dynamical and intelligent tool for regulating groundwater extraction, balancing aquifer sustainability with agricultural and urban water requirements.