A Comprehensive Model for Predicting Water Advance and Determining Infiltration Coefficients in Surface Irrigation Systems Using Beta Cumulative Distribution Function

Surface irrigation systems are among the most common yet often inefficient methods due to poor design and management. A key factor in optimizing their design is the accurate prediction of the water advance and infiltration relationships’ coefficients. This study introduces a novel model based on the Beta cumulative distribution function for predicting water advance and estimating infiltration coefficients in surface irrigation systems. Traditional methods, such as the two-point approach, rely on limited data from only the midpoint and endpoint of the field, often resulting in insufficient accuracy and non-physical outcomes under heterogeneous soil conditions. The proposed model enhances predictive flexibility by incorporating the entire advance dataset and integrating the midpoint as a constraint during optimization, thereby improving the accuracy of advance curve estimation and subsequent infiltration coefficient determination. Evaluation using field data from three distinct sites (FS, HF, WP) across 10 irrigation events demonstrated the superiority of the proposed model over the conventional power advance method. The new model achieved average RMSE, MAPE, and R2 values of 0.790, 0.109, and 0.997, respectively, for advance estimation. For infiltration prediction, it yielded an average error of 12.9% in total infiltrated volume—outperforming the two-point method—and also showed higher accuracy during the advance phase, with average RMSE, MAPE, and R2 values of 0.427, 0.075, and 0.990, respectively. These results confirm that the Beta-based model offers a more robust, precise, and reliable tool for optimizing the design and management of surface irrigation systems.