Enhancing water use efficiency is essential in irrigated agriculture owing to declining water resources, increasing population, growing water needs, and greater competition among water users. If properly designed and managed, with good operation and maintenance, a center-pivot irrigation system can have high water-application efficiency. One of the design factors for a center-pivot irrigation system is the hydraulic loss in the lateral pipe. In this study, an analytical relationship is presented as a series for calculating the hydraulic loss in the lateral pipe of a center-pivot irrigation system. Given the difficulty and complexity of using a mathematical series, the equation presented in this study and the equation developed by Anwar turn out to be general and asymptotic relations. The final relationships have 0.6% and 0.4% errors, respectively, relative to the series relationships. Due to the high accuracy and ease of use of the asymptotic relationship presented to calculate the hydraulic loss in the lateral pipe, it is recommended for use in designing center-pivot irrigation systems.
Abstract 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.
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 depth were evaluated. Based on this evaluation, the relative error difference of the infiltration depth of the actual subsurface shape factor value and the new relationship was less than 0.01%. Given the high accuracy of the proposed methodology and the simplicity of its form, this relationship is recommended for use in practical work to predict surface irrigation hydraulic performance and irrigation application efficiency.
Abstract 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 ( d RMS ) 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 d RMS 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.
Radial gates are widely used for agricultural water management, flood controlling, etc. The existence of methods for the calculation of the discharge coefficient (Cd) of such gates are complex and they are based on some assumptions. The development of new usable and simple models is needed for the prediction of Cd. This study investigates the viability of a metaheuristic regression method, the Gaussian Process (GP), for the determination of the discharge coefficient of radial gates. For this purpose, a total of 2536 experimental data were compiled that cover a wide range of all the effective parameters. The results of GP were compared with the Group Method of Data Handling (GMDH), Multivariate Adaptive Regression Splines (MARS), and linear and nonlinear regression models for predicting Cd of radial gates in both free-flow and submerged-flow conditions. The results revealed that the radial basis function-based GP model performed the best in free-flow condition with a Correlation Coefficient (CC) of 0.9413 and Root Mean Square Error (RMSE) of 0.0190 while the best accuracy was obtained from the Pearson VII kernel function-based GP model for the submerged flow condition with a CC of 0.9961 and RMSE of 0.0132.
The movement of solutes in soil is crucial due to their potential to cause soil and groundwater pollution. In this study, a mathematical model based on the Advection Dispersion Equation (ADE) was developed to evaluate solutions for solute transport. This equation enabled us to attain a relationship for concentrations at different locations and times, also known as the breakthrough curve. Five columns (5 cm in diameter and 30 cm in height) of soil types were prepared to check the validity of the results. An evaluation of the calculated relations showed high accuracy in estimating the breakthrough curve and the saturated hydraulic conductivity of the soil.
Abstract In the quest to increase crop yields and production intensity to meet the demands of a growing global population, the responsible use of nitrogen ( N ) applications is paramount. Excessive application of these fertilizers results in economic losses, environmental pollution and reduced N ‐use efficiency. To address this challenge, precision agriculture techniques offer promising solutions. This study explored the relationships among applied N , maize crop parameters and the nitrogen nutrition index ( NNI ) to optimize N application usage and crop performance. The AquaCrop model was used to simulate water productivity and plant parameters accurately. The research establishes equations between the NNI and maize parameters, enabling the use of AquaCrop to simulate crop responses to varying N levels. The results demonstrate that AquaCrop effectively simulates more than 95% of the biomass changes. The findings suggest that applying N based on presented equations optimized the use of N applications, thereby mitigating economic losses and environmental impacts.