Modeling and error analysis of kinematic-wave equations of furrow irrigation

A moving control volume approach was used to model the advance phase of a furrow irrigation system whereas a fixed control volume was used to model the nearly stationary phase and the runoff rate. The resulting finite-difference equations of the kinematic-wave model were linearized and explicit algebraic expressions were obtained for computation of advance and runoff rate. The solutions for the advance increment and the runoff rate were compared with the nonlinear scheme, the zero-inertia model, and a set of field data. A close agreement was found between the models and the field data. Assuming a constant infiltration rate, a differential equation was derived to estimate the error between the kinematic-wave model and the zero-inertia model in predicting the flow cross-sectional area along the field length. The differential equation and two dimensionless terms were used to define the limits for use of the kinematic-wave model in furrow irrigation.     

Zero-inertia model for surge flow furrow irrigation

Summary A surge flow furrow irrigation model was developed based on the zero-inertia concept originally developed by Strelkoff and Kastapodes, (1977) for border irrigation and later modified for continuous furrow irrigation by Elliot et al. (1982). The model simulates all phases of continuous and surge flow irrigation including simultaneous advance and recession and can also be applied to basin and border irrigation with various field slopes. The surge model was verified for a wide range of actual field conditions and management alternatives. A sensitivity analysis was performed for the size of time step and the physical input parameters.     

Simulation of border irrigation system using explicit MacCormack finite difference method

The hydrodynamic, zero-inertia and kinematic wave models for simulating all phases of the border irrigation event are presented. The explicit second-order accurate MacCormack method is used for solving the governing equations. A technique for implementing the boundary conditions that are consistent with the numerical scheme is discussed. All the three models do not require a special treatment such as moving grid, deformable grid, subgrid technique, etc., to accurately simulate the advancing and receding fronts. The results of all the three models namely hydrodynamic finite difference model (HDFD), zero-inertia finite difference model (ZIFD) and kinematic wave finite difference model (KWFD) are compared with observed advance and recession times for four border irrigation events available in literature. A very good comparison of results is observed. The relative merits and demerits of the models are discussed. The HDFD model is found to be more suitable for simulation of all the four phases of border irrigation events.     

Best management of pesticide — furrow irrigation systems

Summary Effects of furrow irrigation designs, water management practices (irrigation scheduling, etc.), soil types and pesticide parameters on pesticide leaching were simulated. A hydraulic kinematic-wave irrigation model was used to estimate water infiltration for alternative furrow lengths and inflow rates. A one-dimensional simulation model then simulated the movement of pesticides through soils following furrow irrigation. Potential ground-water contamination by pesticides can be reduced by an integrated use of the best management practices (BMPs) such as careful selection and use of pesticides, efficient furrow irrigation designs and improved water management techniques (irrigation scheduling, etc.). Procedures for designing an appropriate furrow irrigation system for a particular site and pesticide, and selecting pesticides for a particular site, crop and furrow irrigation system are illustrated. These procedures are being used to develop decision support computer models for developing different BMPs for pesticide-agricultural management decisions.     

A spreadsheet model to evaluate sloping furrow irrigation accounting for infiltration variability

A spreadsheet model was developed to evaluate the performance of furrow irrigation that accounts for soil variability and requires few field measurements. The model adjusts an advance trajectory to three (advance distance, advance time) points and, similarly, it adjusts a recession trajectory to three (recession distance, recession time) points. The head of the furrow (distance = 0) is one of the points used to adjust both trajectories. It then calculates the parameters of the infiltration equation using the two-point method (based on the volume balance equation with assumed surface shape parameters). The model gives the option to enter an estimate of the soil infiltration variability in order to account for this variation when calculating irrigation performance indicators. The combination of variance technique was used for this purpose. A set of irrigation performance indicators (distribution uniformity, application efficiency, tail water ratio, deep percolation ratio and deficit coefficient) is calculated, assuming that the infiltrated water follows a normal frequency distribution. To illustrate the evaluation method, it was applied to three irrigation events conducted on a sunflower field, with 234 m long furrows spaced 0.75 m apart. The evaluations were performed in two 3-furrow sets. The application efficiency was satisfactory in the first irrigation, but low in the other two. Uniformity was high in all three irrigations. The performance indicator that was most affected by soil variability was distribution uniformity. Considering soil spatial variability was important for more realistic determination of the infiltrated water distribution, and therefore of the deep percolation, but it had less importance for the determination of the application efficiency, due to the relevance of runoff in our field application.     

Evaluation of infiltration measurements for border irrigation

A number of methods are discussed for obtaining a reasonable estimate of the infiltration function for irrigation borders. Data from ring infiltrometers are fit to power functions for infiltration rate and cumulative infiltration rate versus time and to a branch function where the infiltration rate is not allowed to go below some value (called the final infiltration rate). A volume balance within the border is used to adjust the data to give a better indication of the “average” infiltration conditions over the border. The results of Bouwer's method, which uses a series of borders as infiltrometers, were compared to the results of ring data for actual field data. Bower's method was also analyzed by developing advance and recession curves with the zero-inertia border-irrigation model with a known infiltration rate. The zero-inertia model was also used to examine the effect of different infiltration functions for specific examples (resulting from different irrigations or different estimation methods) on the application of water by surface irrigation.     

Infiltration parameters from optimisation on furrow irrigation advance data

Knowledge of the soil infiltration parameters is necessary for efficient furrow irrigation. A method is proposed for the determination of the parameters in the Kostiakov-Lewis infiltration equation from measurements of the furrow irrigation advance and inflow. The method employs a volume balance model using optimisation to minimise the error between the predicted and measured advance and differs from existing approaches in that only advance data and inflow rates are required. The average cross sectional area of the furrow and the final infiltration rate are treated as fitted parameters and need not be measured. A simple but effective optimisation algorithm is developed which allows for the solution of the four parameters without user input. The speed and simplicity of the optimisation may lead to application in real-time control of furrow irrigation. Received: 16 August 1995     

Evaluation of surface irrigation as a function of water infiltration in cultivated soils in the Nile Delta

As sources of irrigation water are decreasing, efficient use of surface irrigation is essential. The purpose of this study is to determine if partially-wetted furrow irrigation has more efficient water storage and infiltration than traditional border irrigation in an alluvial clay soil under cultivated grape production. The two irrigation components considered were wet (WT) and dry (DT) treatments, at which water was applied when available soil water reached 65 % and 50 %, and the traditional border irrigation control. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. Coefficient of variation (CV) was 5.2 and 9.5 % for WT and DT under furrow irrigation system comparing with 7.8 % in border, respectively. Water was deeply percolated as 11.9 and 19.2 % for wet and dry furrow treatments respectively, compared with 12.8 % for control, with no deficit in the irrigated area. Partially-wetted furrow irrigation had greater water-efficiency and grape yield than dry furrow and traditional border irrigation, where application efficiency achieved as 88.1 % for wet furrow irrigation that achieved high grape fruit yield (30.71 Mg /ha). The infiltration (cumulative depth, Z and rate, I) was functioned to opportunity time (t ₀ ) in minute for WT and DT treatments as: Z _WT ?=?0.528?t ₀ ^0.6, Z _DT ?=?1.2?t ₀ ^0.501, I _WT ?=?19?t ₀ ^?0.4, I _DT ?=?36?t ₀ ^?0.498. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. The irrigation parameters and coefficients, and soil water distribution have been also evaluated.     

Solution of the kinematic-wave equations for border irrigation

A method is developed to obtain solutions to the kinematic-wave equations for border irrigation. The accuracy of this method is assessed by comparing the results with the kinematic-wave train (KWT) method previously reported to be accurate. Experimental data on freely draining borders were utilized for comparison and evaluation of these methods. The prediction error for advance time resulting from the two methods was comparable: it was below 25% for three sets of data but as high as 50% for one set of data. The prediction error for recession time was also comparable: below 6% for the same three sets of data but 14.0% for one set.     

Simulation of furrow irrigation practices (SOFIP): a field-scale modelling of water management and crop yield for furrow irrigation

Because of the spatial and temporal variabilities of the advance infiltration process, furrow irrigation investigations should not be limited to a single furrow irrigation event when using a modelling approach. The paper deals with the development and application of simulation of furrow irrigation practices (SOFIP), a model used to analyse furrow irrigation practices that take into account spatial and temporal variabilities of the advance infiltration process. SOFIP can be used to compare alternative furrow irrigation management strategies and find options that mitigate local deep-percolation risks while ensuring a crop yield level that is acceptable to the farmer. The model is comprised of three distinct modelling elements. The first element is RAIEOPT, a hydraulic model that predicts the advance infiltration process. Infiltration prediction in RAIEOPT depends on a soil moisture deficit parameter. PILOTE, a crop model, which is designed to simulate soil water balance and predict yield values, updates the soil moisture parameter. This parameter is an input of a parameter generator (PG), the third model component, which in turn provides RAIEOPT with the data required to simulate irrigation at the scale of an N-furrow set. The study of sources of variability and their impact on irrigation advance, based on field observations, allowed us to build a robust PG. Model applications show that irrigation practices must account for inter-furrow advance variability when optimising furrow irrigation systems. The impact of advance variability on deep percolation and crop yield losses depends on both climatic conditions and irrigation practices.     

Two-dimensional zero-inertia model of surface water flow for basin irrigation based on the standard scalar parabolic type

The two-dimensional zero-inertia equations for basin irrigation were formulated as a standard scalar diffusion equation subject to Neumann boundary conditions. The formulation can handle anisotropic variations in hydraulic resistance. A numerical solution was developed using finite-volume method on unstructured triangular cells. The simulation performance of the constructed model was validated based on typical experimental data. The complete hydrodynamic model of basin irrigation was selected as the comparative model. The validated results show that the constructed model can successfully simulate the basin surface water flow when the basin surface microtopography condition is relatively smooth. Similar results were found in terms of both the water quantity conservation and convergence rate. Moreover, the computational efficiency of the constructed zero-inertia model is approximately 17 times of the complete hydrodynamic model of basin irrigation. Therefore, the constructed zero-inertia model has good simulation performance.     

垄膜沟种涌泉灌溉技术要素的试验研究

在垄膜沟种农田进行了涌泉灌灌水试验，通过对水流推进过程观测，分析了田面水流运动特性，研究了沟宽对田间灌水均匀度的影响，并对垄膜沟种涌泉灌溉技术要素进行了探讨。结果表明，涌泉灌田面水流推进曲线可用幂函数表示。随着沟宽的增大，灌水均匀度呈下降趋势。从灌水质量和管网成本两方面综合考虑，试验条件下灌水技术要素的入沟流量、沟宽和灌水器间距分别以80～100L/h、20-30cm和4～5m为宜。     

The comparison of advance and erosion of meandering furrow irrigation with standard furrow irrigation under varying furrow inflow rates

Meandering furrow irrigation (Gholam-gardeshi irrigation) is a modified form of furrow irrigation, which has being used in Iran, but to date, there is no study about the erosion of this method of irrigation. To measure the erosion of meandering furrow irrigation and to compare the results with standard furrow irrigation, two experimental fields with different soil textures and furrow inflow rates were used. The experiment utilized a randomized factorial design with three replications for each treatment. In both methods, the developed second order polynomial equation for the erosion, and advance equation were able to predict the field data with coefficients of determination of more than 0.94. The results showed that the velocity of advance, tail water runoff and erosion are significantly lower for meandering furrow irrigation as compared to standard furrow irrigation. As the furrow inflow rates increased, erosion and runoff in both irrigation methods increased significantly.     

Estimation of advance and infiltration equations in furrow irrigation for untested discharges

The exponents of the advance and infiltration power laws have been shown to remain practically constant for different furrow irrigation discharges. Under this hypothesis, a procedure to estimate the advance and infiltration equations corresponding to untested discharges was developed. The proposed procedure was validated with different field experiments, obtaining satisfactory results for non-erosive discharges. However, significant deviations were obtained when erosive discharges were used. This behavior corroborates the hypothesis presented by some authors that the erosion and sedimentation processes occurring in furrow irrigation as a consequence of high surface velocities can reduce—and even suppress—the effect of the wetted perimeter on the infiltration rate. Finally, an equation was derived to predict the effect of the wetted perimeter on the infiltration parameters.     

Surface water storage independent equation for predicting furrow irrigation advance

 A simple equation is developed to predict the advance rate of flow in furrows. The proposed equation does not use as inputs the data required for estimating the surface storage. In previous surface storage independent models it is generally assumed that the surface storage volume is negligible (compared with infiltrated volume). The proposed equation is derived by eliminating the surface storage term from the original volume balance equation and its derivative. The suggested equation thus needs no assumption about the magnitude of the value of surface storage volume. Infiltration is described by the extended Kostiakov-Lewis formula. The suggested equation is compared with observed furrow data, with the numerical kinematic-wave model and with a recently developed numerical model that ignores surface storage. For furrows in which the surface storage is not significant (compared with infiltration) all models predict advance reasonably well. For furrows in which the surface storage is relatively important, the proposed equation predicts advance with good accuracy, whereas previous models ignoring the surface storage greatly overpredict the advance rate. Received: 20 October 1998     

Empirical functions for dependent variables in cutback furrow irrigation

Water scarcity and the high consumption of water resources in agriculture have strengthened the need to manage and optimize irrigation systems. Among surface irrigation systems, furrow irrigation with cutback is commonly used because of its potentially higher irrigation efficiency, lower costs and relative simplicity. The performance of this system is affected by various management and design variables, and hence different management scenarios should be evaluated before it is applied in practice. For this purpose, empirical functions for the performance evaluation indices are useful. This paper employs sensitivity, dimensional and regression analyses in the development of empirical functions for application efficiency, deep percolation, runoff and distribution uniformity. The proposed functions were evaluated using a numerical zero-inertia model and field measured data. Coefficients of determination for E _a, D _r, R _r and U _cc were calculated to be 0.90, 0.91, 0.90 and 0.84, respectively. These values indicate that the proposed functions enable the performance indices to be predicted satisfactorily. Values for the indices calculated using the developed dimensionless functions showed a very good agreement with both the outputs of the zero-inertia model and values calculated from measured field data. As the functions were general (not site and irrigation specific) and explicit, they could prove to be of practical significance in both conventional and optimal design and management of free-draining, graded furrow irrigation systems with cutback flows.

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不同灌水方式下基于水面蒸发量的夏玉米灌溉试验研究

为了探索依据水面蒸发量确定灌溉定额的可行性,在防雨棚下测坑中进行了夏玉米灌溉试验。结果表明,从总耗水量看,畦灌略高于沟灌,而沟灌又略高于滴灌,但差别不是很大。畦灌条件下植株发育快,滴灌次之,沟灌最慢。畦灌和滴灌下产量均以中等灌溉定额处理最高,而沟灌下产量以最大灌溉定额处理最高。总体上,滴灌条件下水分利用效率高于其他2种灌溉方式。干旱条件下,畦灌下以E601蒸发皿蒸发量(PE)作为夏玉米灌溉定额,每次灌水60mm;滴灌下以2/3PE作为灌溉定额为宜,灌水定额为20mm。     

Effects of water infiltration and storage in cultivated soil on surface irrigation

Surface irrigation analysis and design require the knowledge of the variation of the cumulative infiltration water Z (L) (per unit area) into the soil as a function of the infiltration time t (T). The purpose of this study is to evaluate water infiltration and storage under surface irrigation in an alluvial clay soil cultivated with grape yield, and to determine if partially wetted furrow irrigation has more efficient water storage and infiltration than traditional border irrigation. The two irrigation components considered were wet (WT) and dry (DT) treatments, at which water applied when available soil water reached 65% and 50%, and the traditional border irrigation control. Empirical power form equations were obtained for measured advance and recession times along the furrow length during the irrigation stages of advance, storage, depletion and recession. The infiltration (cumulative depth, Z and rate, I) was functioned to opportunity time (t_o) in minute for WT and DT treatments as: Z_WT = 0.528 t_o^0.6, Z_DT = 1.2 t_o^0.501, I_WT = 19 t_o^−0.4, and I_DT = 36 t_o^−0.498. The irrigation efficiency and soil water distribution have been evaluated using linear distribution and relative schedule depth. Coefficient of variation (CV) was 5.2 and 9.5% for WT and DT under furrow irrigation system comparing with 7.8% in border, respectively. Water was deeply percolated as 11.88 and 19.2% for wet and dry furrow treatments, respectively, compared with 12.8% for control, with no deficit in the irrigated area. Partially wetted furrow irrigation had greater water-efficiency and grape yield than both dry furrow and traditional border irrigations, where application efficiency achieved as 88.1% for wet furrow irrigation that achieved high grape fruit yield (30.71 Mg/ha) and water use efficiency 11.9 kg/m³.     

土壤入渗特性和田面糙率的变异性对沟灌性能的影响

以杨凌区粘壤土和砂壤土区域进行的大田沟灌试验为基础,在假定各灌水沟内部土壤入渗特性和糙率均一的条件下,重点分析各灌水沟之间土壤入渗参数和田面糙率的不同组合对沟灌水流运动过程和灌水质量的影响,结果表明土壤入渗特性的变异性对沟灌水流推进过程和灌水质量指标影响较大,在模拟时必须充分考虑;而田面糙率的变异性对沟灌水流推进过程和灌水质量指标影响较小,可采用田块糙率均值代替各灌水沟的糙率。经实例验证,水流推进过程相对误差为7.28%,灌水效率、灌水均匀度和储水效率模拟值与实测值误差分别为5.74%、6.18%和4.07%,结果表明其模拟效果较好。     

基于非恒定渐变流-急变流方程的变流量畦灌数值模型

传统畦灌模型多是基于非恒定渐变流方程建立的,在模拟变流量畦灌水流运动时的精度难以保障。本文综合分析了变流量畦灌过程中田面水流的运动状况,将其按照边界条件的不同划分为恒定流量进水阶段、变流量进水阶段、畦首消退阶段、田面消退第1阶段、田面消退第2阶段等5个阶段,基于非恒定渐变流方程和非恒定急变流方程构建了适用于变流量畦灌系统的渐变流-急变流数值模型,通过2组恒定流量畦灌、4组变流量畦灌的田间试验以及2组文献资料中的畦灌试验数据对模型进行了验证。结果表明,渐变流-急变流畦灌模型模拟值与现场实测结果吻合较好,模拟推进时间决定系数R2均大于0.96、模拟消退时间R2大于0.90。与目前常用的WinSRFR模型相比,渐变流-急变流畦灌数值模型在模拟恒定流量畦灌方面具有相似的精度,且在模拟变流量畦灌方面精度更高。渐变流-急变流畦灌模型可以较精准地模拟变流量畦灌的水流运动状况,可为分析变流量畦灌系统、优化变流量畦灌方案提供支撑。