Abstract:An improved analytic solution is presented to estimate soil water infiltration by surface irrigation methods through a more rigorous determination of the subsurface shape factor, as applied in volume‐balance models. Based on the results of this analysis and by averaging the shape factor of previously published equations, a new relationship is presented, with a maximum error of 0.036%. Also, the effect of these relationships on the empirical parameters for the Kostiakov–Lewis equation and the water infiltration… Show more
“…Seyedzadeh, Panahi, et al (2022) and Kiefer (1965) presented relationships based on the values of r and a in the form of Equations () and (), respectively, to determine the value of the subsurface water storage shape factor: …”
Two exponential relationships ([1] from the beginning to the midpoint of the field, [2] from the beginning to the endpoint of the field) were considered for the advance curve of surface irrigation water along a field. The constant coefficients of these advance relationships were determined using the least squares optimization method. These relationships were compared with the advanced relationships obtained by the Elliott and Walker method (EW) using the advanced data related to 14 irrigation events and using root mean square error deviation (dRMS) and Nash–Sutcliffe (NSE) indices. The results of this evaluation showed that the advanced relationships obtained from the method presented in this research (TR) have better accuracy, with average values of 7.05 min and 0.984 for dRMS and NSE, respectively. Then, using the TR method for deriving the advance relationships and using the volume balance method, the coefficients of the Kostiakov–Lewis infiltration relationship were determined. The infiltration relationships derived from the TR method were compared with the infiltration relationships obtained from the two‐point method of EW. The results of this investigation showed that the TR method predicts the average infiltration depth with an average absolute relative error of 6%, which is more accurate than that of EW.
“…Seyedzadeh, Panahi, et al (2022) and Kiefer (1965) presented relationships based on the values of r and a in the form of Equations () and (), respectively, to determine the value of the subsurface water storage shape factor: …”
Two exponential relationships ([1] from the beginning to the midpoint of the field, [2] from the beginning to the endpoint of the field) were considered for the advance curve of surface irrigation water along a field. The constant coefficients of these advance relationships were determined using the least squares optimization method. These relationships were compared with the advanced relationships obtained by the Elliott and Walker method (EW) using the advanced data related to 14 irrigation events and using root mean square error deviation (dRMS) and Nash–Sutcliffe (NSE) indices. The results of this evaluation showed that the advanced relationships obtained from the method presented in this research (TR) have better accuracy, with average values of 7.05 min and 0.984 for dRMS and NSE, respectively. Then, using the TR method for deriving the advance relationships and using the volume balance method, the coefficients of the Kostiakov–Lewis infiltration relationship were determined. The infiltration relationships derived from the TR method were compared with the infiltration relationships obtained from the two‐point method of EW. The results of this investigation showed that the TR method predicts the average infiltration depth with an average absolute relative error of 6%, which is more accurate than that of EW.
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.
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