The equations governing variations in water depth and cross-sectional area along a field are crucial for solving the Saint-Venant equations and determining surface water volume via the volume balance method to determine other hydraulic parameters of surface irrigation systems. Various researchers have proposed different formulations for this equation based on varying assumptions. In many investigations, the flow depth profile has been assumed to be parallel to the furrow bottom or modelled as an elliptical relationship. This study explored four different forms of equation to analyse changes in the water depth profile and to refine its mathematical representation. The coefficients of these equations were derived as functions of the surface storage coefficient. Using field data, the surface storage coefficient values and, consequently, the coefficients of the proposed relationships were determined. The calculated values of the flow cross-sectional area along the field and the water surface storage volume were compared with the measured values using the established relationships. The most accurate relationship for estimating the flow depth profile was identified through this analysis.
