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Abstract:The accurate estimation of soil hydraulic parameters (θ s , α, n, and K s ) of the van Genuchten-Mualem model has attracted considerable attention. In this study, we proposed a new two-step inversion method, which first estimated the hydraulic parameter θ s using objective function by the final water content, and subsequently estimated the soil hydraulic parameters α, n, and K s , using a vector-evaluated genetic algorithm and particle swarm optimization (VEGA-PSO) method based on objective functions by cumulative infiltration and infiltration rate. The parameters were inversely estimated for four types of soils (sand, loam, silt, and clay) under an in silico experiment simulating the tension disc infiltration at three initial water content levels. The results indicated that the method is excellent and robust. Because the objective function had multilocal minima in a tiny range near the true values, inverse estimation of the hydraulic parameters was difficult; however, the estimated soil water retention curves and hydraulic conductivity curves were nearly identical to the true curves. In addition, the proposed method was able to estimate the hydraulic parameters accurately despite substantial measurement errors in initial water content, final water content, and cumulative infiltration, proving that the method was feasible and practical for field application.

Abbreviations used: AAE (average absolute error); ARE (average relative error); DE (differential evolution); Du (distribution uniformity); Ea (application efficiency); Es (storage efficiency); KW (kinematic-wave); RE (relative error); ZI (zero-inertia).

Soil infiltration is characterized by scale dependence, so the accuracy and reliability of indirect methods used to estimate soil infiltration properties from available soil physical data are often below expectations. This study aimed to determine the scale‐dependent relationship between soil infiltration and soil physical properties and to establish pedotransfer functions (PTFs) for estimating normalization factors (FC). Field studies were conducted using double‐ring infiltrometers in the first (sandy loam) and third (clay loam) terraces in Yangling District. Multiple scale variability and relationships were studied by multifractal and joint multifractal techniques. Results indicated that the Kostiakov–Lewis model best described the relationship between cumulative infiltration and time in the study areas, and that the normalization equation for predicting cumulative infiltration was accurate. Joint multifractal analysis showed that the variability of FC in the first terrace was related largely to sand content, soil bulk density, and silt content. FC in the third terrace depended on the contents of sand, silt, initial soil water, and clay at multiple scales. The PTFs that were established based on the results of joint multifractal analysis reliably estimated FC values. Copyright © 2017 John Wiley & Sons, Ltd.

Closed-end border irrigation has been widely used in China; however, such irrigation is usually associated with poor performance. Therefore, the performance of closed-end border irrigation must be improved. The objectives of this study were to develop and verify a simplified method for estimating the optimal cut-off time (T cop ) for closed-end border irrigation. The simulated results revealed that the relationship between T cop and the time when water advanced to 75% of the length of the border (T 0.75L ) can be characterized by using a power function. The comprehensive irrigation performance indicator Y (which is the geometric mean of the application efficiency and Christiansen's uniformity) obtained using the proposed method was consistent with that obtained using existing methods. The mean absolute value of the relative error and the standard error of Y between the proposed method and existing methods was 3.35 and 0.69%, respectively. This result indicates that the proposed method has high reliability. Moreover, in the proposed method, only T 0.75L is required to determine T cop for closed-end border irrigation. Therefore, the proposed method has high practicality and can be used to improve the performance of closed-end border irrigation. K E Y W O R D Sirrigation en circuit fermé, temps limite, débit par unité de largeur, performances d'irrigation Abstract Résumé L'irrigation en circuit fermé a été largement utilisée en Chine; cependant, une telle irrigation est généralement associée à de mauvaises performances. Par conséquent, la performance de l'irrigation en circuit fermé doit être améliorée.Les objectifs de cette étude étaient de développer et de vérifier une méthode simplifiée pour estimer le temps de coupure optimal (T cop ) pour l'irrigation en circuit fermé. Les résultats simulés ont révélé que la relation entre T cop et le moment où l'eau a avancé jusqu'à 75% de la longueur du circuit (T 0.75L ) peut être caractérisée à l'aide d'une fonction de puissance. L'indicateur complet de performance d'irrigation Y (qui est la moyenne géométrique de l'efficacité de l'application et de l'uniformité de Christiansen) obtenu à l'aide de la méthode * Méthode simplifiée d'estimation de l'heure de coupure optimale de l'irrigation en circuit fermé.

A synchronous optimization method for self-pressure drip irrigation pipe network system is proposed. We have generalized the optimization design problem of the system and have established the mathematical models for the simultaneous optimization design of pipeline layout and pipe diameters. A genetic algorithm based on the infeasibility degree of the solution was used to solve the model. A typical example is used to validate the presented method. The method exhibits effective performance in the case studied. Designers can use the results of this study to efficiently design self-pressurized drip irrigation network systems.

Infiltration parameters and Manning's roughness are essential input parameters for surface irrigation simulation models. Multiple points of infiltration experiments require time-consuming, costly data collection and problematic calculations of field mean infiltration parameters. This study estimated the field mean infiltration parameters and Manning's roughness values on a regional scale, on the basis of closed-end furrow irrigation experiments conducted at 45 experimental sites on the Guanzhong plain, and evaluated the influence of Manning's roughness on advance trajectory and performance indicators of closed-end furrow irrigation. Then, we present a functional normalization of the Kostiakov equation and pedotransfer function (PTF) to estimate the normalization factors. The proposed method can be used to estimate the field mean infiltration parameters using PTF and the represented Manning's roughness to determine the optimal discharge of closed-end furrow irrigation. The results revealed that the advance trajectory and performance of closed-end furrow irrigation was not sensitive to variations of Manning's roughness, which can be adopted as a representative value (i.e., 0.075) of the maize field. The normalization method was proven to be feasible for the Kostiakov equation, and the PTF reliably estimated the normalization factors. Last, the optimized values of the inflow discharge were determined using the proposed method, with various combinations of furrow lengths and bottom slopes in the study area, and also compared with the inflow discharge determined based on infiltration parameters and Manning's roughness, which were inversed by SIPAR_ID. The results indicated that the inflow discharge values obtained through using the two methods were approximately equal, proving that the proposed method was reliable and easy to use in practice.

Core Ideas Proposed an explicit Green–Ampt model (EGA model) to estimate cumulative 1D vertical infiltration. The form of error term ε is determined as a power‐function through non‐dimensional numerical analysis. The EGA model is reliable for estimation the cumulative infiltration for a variety of soil textures. Accurately estimating soil moisture infiltration information contributes to scientific understanding of the one‐dimensional (1D) vertical infiltration process. Because of its simple form, the Green–Ampt (GA) model has been extensively employed to simulate soil infiltration processes. However, the GA model is an implicit solution that must be solved through iterative techniques, and thus is inconvenient. Therefore, based on the two‐parameter infiltration equation proposed by Valiantzas, by adding an error term and non‐dimensional numerical analysis, this study proposes an approximate explicit Green–Ampt model (EGA model) for estimating cumulative infiltration with a determined power function expression for the error term. A total of 12 typical soils were selected from the USDA soil textural classes, and the 1D vertical soil infiltration process was simulated using Hydrus‐1D. The reliability of the proposed EGA model was verified using measured and simulated values. The mean absolute percentage relative error (MAPRE) and percentage of bias (PB) were taken as evaluation indicators to compare the estimated cumulative infiltration with the measured and simulated values. The results revealed that all cumulative infiltration values estimated by the EGA model are in good agreement with those measured in laboratory experiments and simulated using Hydrus‐1D; the mean MAPRE and PB values of all treatments were 4.2 and 0.7%, respectively. In addition, the estimated errors of the EGA model were consistent with those of the GA model. Hence, the EGA model can estimate the cumulative infiltration in 1D vertical soil infiltration with high accuracy and is suitable for a variety of soil textures.