D. Zerihun

ANALYSIS AND DESIGN OF BORDER IRRIGATION SYSTEMS

Application efficiency (Ea) is the primary criterion for border irrigation design and management. The objective of this study is to analyze the behavior of the application efficiency function of border irrigation with respect to border length (L) and unit inlet flow rate (qo), given a target minimum application depth. The results show that the application efficiency function is unimodal with respect to L and qo. Optimality conditions are derived for both the Ea(L) and Ea(qo) functions, based on which simple rules that reduce the design and management procedure into a series of one-dimensional optimization problems with respect to qo are developed. The proposed procedure has a variable bounding step in which the feasible ranges of L and qo are determined. This is then followed by a step wherein alternative approximate optimum values of Ea(qo) are calculated for each of the feasible values of L. Finally, the optimal Ea(qo) is selected from the available alternatives based on sensitivity analysis and other locally pertinent practical criteria. In addition, the advantages and limitations of advance-phase and post-advance-phase inflow cutoff options and their effects on system design and management are discussed. The distance-based (advance-phase) inflow cutoff option offers two main advantages over post-advance-phase cutoff: operational convenience, and a lower degree of sensitivity of design and management prescriptions to inaccuracies in inflow measurements and to non-uniformities in the distribution of inlet flow over the width of the border. However, the results of the study also show that, depending on the parameter set, there exist limiting conditions that preclude the applicability of the distance-based cutoff criterion in border irrigation management. Even when the distance-based inflow cutoff criterion is feasible, the corresponding design and management scenario can be sub-optimal, in which case a near-optimum operation scenario can be realized only with post-advance-phase inflow cutoff.

External Iterative Coupling Strategy for Surface-Subsurface Flow Calculations in Surface Irrigation

Coupling the unsteady open-channel flow equations of surface irrigation with the equation of variably saturated porous media flow is a computationally complex problem because of the dependence of infiltration on surface-flow depths. Several models of this coupled process have been developed, all of which solve the surface and subsurface flow iteratively at each time step of the surface-flow solution. This study presents an alternative strategy, in which stand-alone surface and subsurface-flow models are used to conduct the calculations sequentially and iteratively at the time level of the irrigation event. At each iteration, the subsurface-flow results are computed using the surface-flow depths generated by the surface-flow model at the current iteration. Infiltration results computed at selected computational nodes are fitted to an empirical infiltration function, and then fed back to the surface-flow model. The proposed strategy, labeled external iterative coupling, was prototyped for border and basin irrigation systems using the WinSRFR and HYDRUS-1D models. The proposed procedure produced irrigation performance results comparable to those generated with an internally coupled model, even when using a single representative location to calibrate the empirical infiltration equation used by the surface-flow model. In comparison with models that iterate at each time step, the proposed coupling strategy reduces the computational effort and improves convergence. The approach provides a practical alternative for coupling existing and future surface and subsurface flow models.

Field-Scale Sprinkler Irrigation System Hydraulic Model. I: Hydraulic Characterization

AbstractA mathematical model for a field-scale hydraulic characterization and simulation of solid set sprinkler systems with single-line and double-line lateral layout configurations is developed. This paper describes the hydraulic equations, numerical solution algorithms, and the hydraulic characterization functionality of the model for a system with single-line laterals. Numerical solutions of the lateral and mainline hydraulic equations are based on standard manifold hydraulics. A rigorous and flexible formulation of the sprinkler hydraulic problem is obtained by coupling the energy equation for each lateral and mainline segment with the continuity equation at a node. The resulting set of equations is then solved iteratively, starting from the distal end sprinkler or mainline outlet and moving sequentially upstream. The hydraulic characteristics of the sprinklers is defined based on manufacture’s pressure head and discharge data, and the hydraulic characteristics of each mainline outlet are computed by...

Modeling Flow and Solute Transport in Irrigation Furrows

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a numerical cross-section averaged advection-dispersion model. A procedure for integrating the furrow volumetric cumulative intake integral in the context of a hydraulic model is presented. Two hydraulic and solute transport data sets collected in sloping free-draining test furrows were used in model evaluation. Soil intake and hydraulic parameters were estimated with a simple approach that matches simulated and measured flow depth hydrographs. The field-scale Weighted Mean Relative Residual (WMRR) between measured and model predicted flow depth hydrographs are 22.0% and 29.0% for the two data set. Furthermore, it is shown that the WMRR of 29.0% reduces to 16.0%, when only the error associated with the downstream end computational node is excluded. This suggests that a significant fraction of the error is related to the form of the downstream boundary condition used. It also shows that the effect of the downstream boundary condition does not extend to a large segment of the flow upstream. The longitudinal dispersion coefficient is approximated with an explicit equation as a function of the hydraulic and geometric variables. Model evaluation is conducted in three steps: (1) cumulative intakes and intake rates computed with the numerical formulation presented here were compared with a subsurface flow model, HYDRUS-2D; (2) solute breakthrough curves computed with the coupled flow and transport model were compared with those from exact analytical solutions for applicable conditions; and (3) model predicted solute breakthrough curves were compared with those obtained from field measurements. Overall the results suggest that the coupled flow and transport model is a useful irrigation and fertigation system management and evaluation tool.

Development of Management Guidelines for Efficient Irrigation of Basins on Sandy Soils

Level and graded-basins are widely used to irrigate citrus (Citrus sp.) and alfalfa (Medicago sativa L.) crops grown on sandy soils of the Yuma Mesa Irrigation and Draniange Districts (YMIDDs) of southwestern Arizona. Historically, irrigation application efficiencies in the YMIDDs have been low (generally <40%). Owing to rising demands for water from urban and industrial interests and heightened water quality concerns, raising irrigation efficiencies have become a high priority in the Lower Colorado River Region. Thus, the objective of this study is to develop a management package (management tools and guidelines) for increased irrigation performance of basins in the YMIDDs. The study consists of field experimentation, modeling (model calibration, model verification, and the development of management tools by simulation), and outreach-educational components. Results show higher application efficiencies (Ea) and distribution uniformities (DU) can be obtained in level and graded-basins through the proper selection of unit inlet flow rate (qo) and cutoff length (Lco) or cutoff time (tco). In addition, for the relatively small net irrigation requirements and long basisn of the YMIDDs, higher application efficiencies are obtained with level basins compared to graded-basins. Since implementation of the proposed management tools does not require reconfiguration of the physical infrastructure, it has the potential to be smoothly adopted by growers. Finally, some aspects of an on-going outreach program are highlighted.

Modified two-point method for closed-end level-bed furrows

The two-point method is a simple, compact, and relatively accurate inverse solution technique widely used to estimate the parameters of the Kostiakov-Lewis infiltration function. However, the applicability of the method is limited to sloping free-draining furrows. In this paper, the two-point method is modified to extend its application to close-end level-bed furrows. The modifications deal with the calculation of the basic intake rate and the inlet flow cross-sectional area during the advance phase. With the modified method, basic intake rate is calculated as the quotient of the change in volumetric surface storage between two selected time lines during the steady state period and the product of the furrow length and related time interval. In addition, the inlet flow cross-sectional area can be calculated as a function of flow depth at the inlet or using the Manning equation and an assumed linear flow depth gradient. The proposed approach was tested by comparing advance trajectories computed by SRFR, on the basis of infiltration parameter estimates by the modified two-point method, with field observed advance. A satisfactory agreement was obtained between SRFR predicted and field observed advance.

Sprinkler irrigation droplet dynamics. I: Review and theoretical development

AbstractDroplet dynamics simulations are key to predicting sprinkler irrigation precipitation patterns. This paper includes derivations of equations describing droplet motion through a steady, uniform horizontal airflow (wind). The assumptions on which sprinkler irrigation droplet dynamics is based are stated, and the limitations they entail are highlighted. The motion of droplets is treated as an impulsively started accelerated motion of rigid spheres, originating at the sprinkler nozzle with known initial conditions, and involving no interactions between themselves. The following steps are used in the derivation of pertinent equations. First, the forces that the ambient air exerts on a water droplet undergoing a steady or accelerated rectilinear relative motion are defined, and their significance in the context of sprinkler irrigation droplet dynamics is discussed, based on which relevant equations are derived. This is followed by a discussion on the dynamics of accelerated motion of a water droplet thr...

Field-Scale Sprinkler Irrigation System Hydraulic Model. II: Hydraulic Simulation

AbstractThis paper describes a mathematical model for the hydraulic characterization of a field-scale solid set sprinkler irrigation system with a double-line lateral layout configuration. Formulation of the basic hydraulic equations along the mainline and laterals is based on manifold hydraulics. Lateral hydraulics remains the same as that described in a previously published paper, for systems with single-line laterals. A description of the mainline hydraulics of systems with a double-line lateral layout configuration, which requires the formulation and iterative solution of a system of nonlinear equations, is presented here. The hydraulic characterization functionality of the model, described in a previously published paper, serves as an interface for coupling the numerical solutions of the lateral and mainline hydraulic equations. In addition, this paper presents a description of the simulation functionality of the sprinkler hydraulic model and a related numerical algorithm, which is based on one-dimen...

Sprinkler Irrigation Droplet Dynamics. II: Numerical Solution and Model Evaluation

AbstractA system of equations, with strong physical basis, was derived for sprinkler irrigation droplet dynamics in the companion paper. Numerical solution of these equations and model evaluation is discussed in this paper. With the aim of enhancing computational efficiency and robustness, the droplet dynamics equations were scaled using four characteristic variables: characteristic time, length, velocity, and density. The characteristic time, length, and velocity are derived based on consideration of the motion of a droplet falling freely, starting from rest, through a quiescent ambient air, to an eventual steady-state condition. The characteristic density was set to the density of water at standard conditions. The dimensionless system of equations was then solved numerically with a fourth-fifth order pair Runge-Kutta method capable of local error estimation and time-step size control. The numerical model was first evaluated through successful comparisons with simplified solutions derived based on more l...

Irrigation lateral hydraulics with the gradient method

AbstractLaterals constitute the basic element of a field-scale pressurized irrigation hydraulic network. The availability of accurate and robust computational methods applicable to lateral hydrauli...