Two-Dimensional Basin Flow with Irregular Bottom Configuration

Two-dimensional flow from a point or line source is simulated in an irrigated basin with a nonlevel soil surface; the goal is to predict the distribution uniformity of infiltrated depths. The zero-inertia approximation to the equations of motion allows computation in both wet and dry areas. A fully implicit, nonlinear finite-difference scheme is developed for the solution, but practical numerical considerations suggest local linearization instead. Both isotropic and anisotropic resistance to flow are considered. Results in basins with irregular bottom configurations and small inflows show stream advance confined to the lowest elevations in the basin.     

Field Properties in Surface Irrigation Management and Design

Field properties—topography, hydraulic resistance, and infiltration—play an important role in the performance of surface irrigation systems, and appropriate characterizations of these are required as data input to simulation or design software. The EWRI/ASCE Task Committee on Soil and Crop Hydraulic Properties has been charged with preparing a guide for practitioners faced with such data entry. The result is this special section of the Journal of Irrigation and Drainage Engineering in which this paper is the first in the series presented. It describes the characteristics of these field properties and notes a series of caveats to be considered when dealing with them in the course of analyses or designs of surface irrigation systems.     

Efficient Solution of the Coupled One-Dimensional Surface—Two-Dimensional Subsurface Flow during Furrow Irrigation Advance

Physically based modeling of the coupled one-dimensional surface and two-dimensional (2D) subsurface flow during furrow irrigation advance often causes numerical instabilities and nonconvergence problems. This is particularly the case for low irrigation advance rates when infiltration consumes a predominant part of the inflow volume. The proposed furrow advance phase model (FAPS) further develops the concepts of a previous study. An analytical zero-inertia surface flow model is iteratively coupled with the 2D subsurface water transport model HYDRUS-2. In contrast to the previous study, the flow domain is discretized using fixed space increments and the resulting set of nonlinear flow equations is solved using the Newton method. The complexity of the model was reduced by process adequate simplifications. FAPS exhibited better convergence, numerical stability, and less computational time than the original fixed time interval solution. The new solution converged rapidly for a number of model tests with various inflow rates including runs with very slow irrigation advance. Simulation model predictions agree very well with advance times measured in laboratory and field tests.     

Modeling Two-Dimensional Infiltration from Irrigation Furrows

Numerical simulation of the two-dimensional (2D) infiltration process during furrow irrigation requires considerable computational effort, which can be reduced by analytical modeling. This paper deals with the further development of the semianalytical infiltration model FURINF (furrow infiltration). Considering the varying impact of gravity and furrow geometry, the new approach models the impact of furrow geometry on infiltration progress using a transient geometric shape factor as a function of infiltration time and furrow geometry. FURINF portrays 2D infiltration from the wetted furrow perimeter by a series of one-dimensional (1D) infiltration computations that are performed in this paper on the basis of an analytical as well as a numerical solution of the 1D Richards equation. Comparing the FURINF results provided by the analytical and numerical 1D infiltration model confirmed the adequacy and reliability of the robust and simple analytical approach, which only requires soil parameters provided by rather simple measurements. The results and performances of the analytical FURINF model (FURINF-A) are compared within the frame of a sensitivity and error analysis with the outcome of the numerical subsurface flow model HYDRUS-2D considering three different soils.     

Finite Volume Model for Two-Dimensional Shallow Environmental Flow

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.     

Fertigation in Furrows and Level Furrow Systems. II: Field Experiments, Model Calibration, and Practical Applications

Furrow fertigation can be an interesting practice when compared to traditional overland fertilizer application. In the first paper of this series, a model for furrow fertigation was presented. The simulation model combined overland water flow (Saint-Venant equations), solute transport (advection-dispersion), and infiltration. Particular attention was paid to the treatment of junctions present in level furrow systems. In this paper, the proposed model is validated using five furrow fertigation evaluations differing in irrigation discharge, fertilizer application timing, and furrow geometry. Model parameters for infiltration and roughness were estimated using error minimization techniques. The error norm was based on observed and simulated values of advance time, flow depth, and fertilizer concentration. Model parameters could be adequately predicted from just one discharge experiment, although the use of more experiments resulted in decreased error. The validated model was applied to the simulation of a level furrow system from the literature. The model adequately reproduced irrigation advance and flow depth. Fertigation events differing in application timing were simulated to identify conditions leading to adequate fertilizer uniformity.     

Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids

A numerical model based upon a second-order upwind finite volume method on unstructured triangular grids is developed for solving shallow water equations. The HLL approximate Riemann solver is used for the computation of inviscid flux functions, which makes it possible to handle discontinuous solutions. A multidimensional slope-limiting technique is employed to achieve second-order spatial accuracy and to prevent spurious oscillations. To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary, the friction source terms are treated in a fully implicit way. A third-order total variation diminishing Runge–Kutta method is used for the time integration of semidiscrete equations. The developed numerical model has been applied to several test cases as well as to real flows. Numerical tests prove the robustness and accuracy of the model.     

Errors in Surface Irrigation Evaluation from Incorrect Model Assumptions

Some two-dozen methods have been proposed in the literature for estimating an infiltration function from field measurements. These methods vary in their data requirements and analytical rigor, however most assume some functional form of the infiltration equations. In this paper, if is shown that the form of infiltration and roughness equations can cause errors in the estimation of actual conditions. For example, assumptions regarding the influence of wetted perimeter on furrow infiltration can result in inappropriate infiltration equations and parameters. Also, the Manning n has been shown to vary with time during an irrigation event as the soil is smoothed by the flowing water. Thus estimates of Manning n based on the advance curve may vary substantially from those based on measured water depths. Inappropriate selection of equations or parameter values for infiltration or roughness can lead to unrealistic parameter values for the other. The estimated parameters from evaluation of a measured irrigation event usually give reasonable estimates of actual performance. However, extrapolation to future irrigation events, particularly with a different application depth or flow rate, can lead to inappropriate recommendations.     

Physically Based Modeling of Interacting Surface–Subsurface Flow During Furrow Irrigation Advance

Surface–subsurface flow during furrow irrigation is analyzed employing both a laboratory experiment and a surface–subsurface flow model. The proposed model overcomes the restrictions of traditional furrow irrigation models by rigorously describing the subsurface flow at computational nodes using the physically based two-dimensional (2D) model Hydrus-2D. Surface flow is portrayed by an analytical zero-inertia model. In order to couple both models efficiently, an iterative procedure was developed. Using a sensitivity analysis we investigated the space interval separating 2D infiltration computations. This variable showed little effect on model performance, thus permitting the selection of rather generous distances. Due to the similarity of the hydrographs at neighboring cross sections we investigated transferring the results of Hydrus-2D computations to the next downstream location. This was performed by interpolating cumulative infiltration using infiltration opportunity times. This procedure uncovered other dependencies, making the interpolation strategy unattractive. To validate the coupled surface–subsurface model, an irrigation furrow was set up in a 26.4 m long, 0.88 m wide, and 1.0 m deep tank, filled with 50 t of sandy loam soil and equipped with surface and subsurface measurement devices. Although the model results compared favorably with the observed data, the study also showed an important impact of surface cracking and preferential flow during the irrigation experiments.     

Investigation of the Importance of Spatial Resolution for Two-Dimensional Shallow-Water Model Accuracy

The importance of spatial resolution for two-dimensional shallow-water model accuracy has been investigated by testing the effect of mesh refinement on two test cases based on laboratory dam-break experiments. A balanced first-order accurate upwind Q-Scheme and a second-order accurate upwind Hancock Monotone Upstream-centered Scheme for Conservation Laws scheme were both first validated on an analytical test, and then applied to the experimental dam-break test cases on four meshes of different density. Simulation results were evaluated through comparison of experimental and computed water level values at several available gauge points. Model sensitivity analysis showed that (1) mesh density was not critical for results accuracy; (2) excessive mesh refinement somewhat deteriorated the results; and (3) optimal spatial resolution was relatively low. Response is shown to be highly complex and no simple relation between spatial resolution and model accuracy has been found.     

Fertigation in Furrows and Level Furrow Systems. I: Model Description and Numerical Tests

The simulation of fertigation in furrows and level furrow systems faces a number of problems resulting in relevant restrictions to its widespread application. In this paper, a simulation model is proposed that addresses some of these problems by: (1) implementing an infiltration model that adjusts to the variations in wetted perimeter; (2) using a friction model that adjusts to different flows and which uses an absolute roughness parameter; (3) adopting an equation for the estimation of the longitudinal diffusion coefficient; and (4) implementing a second-order TVD numerical scheme and specific treatments for the boundary conditions and the junctions. The properties of the proposed model were demonstrated using three numerical tests focusing on the numerical scheme and the treatments. The application of the model to the simulation of furrows and furrow systems is presented in a companion paper, in which the usefulness of the innovative aspects of the proposed model is demonstrated.     

Toward Physically Based Estimation of Surface Irrigation Infiltration

Irrigation practitioners use empirical infiltration equations. Theoretical infiltration equations are currently not capable of capturing surface irrigation infiltration behavior, particularly during initial wetting. For a coarse textured soil, an example is shown where the Green-Ampt equation can be adjusted to match field “average” infiltration conditions by altering the soil’s physical properties. For finer textured soils, a time offset is proposed for adjusting the Green-Ampt equation to account for cracking and soil consolidation upon wetting. This results in a nonzero infiltration amount at time 0, a phenomenon commonly observed for infiltration of cracking soils. Applying this concept to the Philip equation (same as Modified Kostiakov equation with a = 1/2) suggests the addition of an offset parameter. A modification to the two-point method is presented for this equation with the aim to better fit mathematical parameter functions to infiltration data.     

Physically Based Coupled Model for Simulating 1D Surface–2D Subsurface Flow and Plant Water Uptake in Irrigation Furrows. II: Model Test and Evaluation

A physically based seasonal Furrow Irrigation Model was developed, which comprises three modules: The one-dimensional surface flow, the two-dimensional subsurface flow, and a crop model. The modeling principles of these modules, their simultaneous coupling, and the solution strategies were described in a companion paper (W?hling and Schmitz 2007). In the current contribution, we present the model testing with experimental data from five real-scale laboratory experiments [Hubert-Engels Laboratory (HEL)], two field experiments in Kharagpur, Eastern India (KGP), one literature data set [Flowell-wheel (FW)], and data from three irrigations during a corn growing season in Montpellier, Southern France [Lavalette experiments (LAT)]. The simulated irrigation advance times match well with the observations of the HEL, FW, and KGP experiments, which is confirmed by coefficients of determination R2 ≥ 0.99 and coefficients of efficiency Ce ≥ 0.7. Predicted recession times also match with the observations of the HEL runs, however, the values of R2 ≥ 0.9 and Ce ≥ 0.6 are lower for predicted recession times as compared to predicted advance times. In contrast to the other experiments in the study, advance times are underpredicted for the experiments in France. The established soil hydraulic parameters for this site lead to an underestimation of the actual initial infiltration capability of the soil. In the long-term simulation, however, the overall change in soil moisture storage is correctly predicted by the model and the calculated yield of 12.8?t?ha?1 is in very good agreement with the observations (12.7?t?ha?1). We evaluated the sensitivity of the input parameters with regards to predicted advance time and runoff in both a 26.4?m long furrow and a long 360?m long furrow. The analysis revealed that calculated runoff is four to five times more sensitive to the inlet flow rate than to infiltration parameters. Furrow geometry parameters are most sensitive to calculated advance times in the short furrow with low infiltration opportunity time, whereas the inflow rate and infiltration parameters are more sensitive to calculated advance times in the long furrow with larger infiltration opportunity time.     

One-Dimensional Model of Shallow Water Surface Waves Generated by Landslides

A numerical model is presented as the basis for the study of surface waves generated by bank and bottom landslides in rivers. The flow is assumed to be properly modeled by the shallow water equations. The solid movement is introduced in the model as an external action, and assumed rigid and impervious. Two situations are identified in the flow subsequent to a solid movement: longitudinal and transversal sliding. A discussion on the modeling difficulties associated with the latter is included. The flow equations are solved by means of an upwind scheme specially adapted to advancing fronts over dry irregular beds.     

Estimating Soil Moisture Under Low Frequency Surface Irrigation Using Crop Water Stress Index

The present study investigated the relationship between the crop water stress index (CWSI) and soil moisture for surface irrigated cotton (Gossypium hirsutum, Delta Pine 90b) at Maricopa, Arizona during the 1998 season. The CWSI was linked to soil moisture through the water stress coefficient Ks that accounts for reduced crop evapotranspiration when there is a shortage of soil water. A stress recovery coefficient Krec was introduced to account for reduced crop evapotranspiration as the crop recovered from water stress after irrigation events. A soil water stress index (SWSI) was derived in terms of Ks and Krec. The SWSI compared reasonably well to the CWSI, but atmospheric stability correction for the CWSI did not improve comparisons. When the CWSI was substituted into the SWSI formulation, it gave good prediction of soil moisture depletion (fDEP; when to irrigate) and depth of root zone depletion (Dr; how much to irrigate). Disagreement was greatest for fDEP<0.6 because cotton is less sensitive to water stress in this range.     

Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. I. Model Development

Surface fertigation is widely practiced in irrigated crop production systems. Lack of design and management tools limits the effectiveness of surface fertigation practices. The availability of a process-based coupled surface–subsurface hydraulic and solute transport model can lead to improved surface fertigation management. This paper presents the development of a coupled surface–subsurface solute transport model. A hydraulic model described in a previous paper by the writers provided the hydrodynamic basis for the solute transport model presented here. A numerical solution of the area averaged advection–dispersion equation, based on the split-operator approach, forms the surface solute transport component of the coupled model. The subsurface transport process is simulated using HYDRUS-1D, which also solves the one-dimensional advection–dispersion equation. A driver program is used for the internal coupling of the surface and subsurface transport models. Solute fluxes calculated using the surface transport model are used as upper boundary conditions for the subsurface model. Evaluation of the model is presented in a companion paper.     

Extension of Preissmann Scheme to Two-Dimensional Flows

A numerical solution to the finite difference of two-dimensional (2D) depth-averaged equations on nonstaggered grid points is proposed in this technical note. Following a locally one-dimensional procedure, the basic equations are split into a pair of one-dimensional equations. Therefore, the solution of a 2D problem is reduced to the solution of a sequence of two one-dimensional problems. The discretization of the split one-dimensional equations is obtained with the use of the original Preissmann operator. Using Fourier’s classic linear analysis, stability, dissipation and dispersion with frictional resistance are investigated for the variations of the Courant number and weighting time factor.     

Coupled Surface–Subsurface Solute Transport Model for Irrigation Borders and Basins. II. Model Evaluation

The development of a coupled surface–subsurface solute transport model for surface fertigation management is presented in a companion paper (Part I). This paper discusses an evaluation of the coupled model. The numerical solution for pure advection of solute in the surface stream was evaluated using test problems with steep concentration gradients. The result shows that the model can simulate advection without numerical diffusion and oscillations, an important problem in the solution of the advection–dispersion equation in advection dominated solute transport. In addition, a close match was obtained between the numerical solution of the one-dimensional advection–dispersion equation and a simplified analytical solution. A comparison of field data and model output show that the overall mean relative residual between field observed and model predicted solute breakthrough curves in the surface stream is 16.0%. Excluding only two outlier (in the graded basin data) reduces the over all mean relative residual between field observed and model predicted breakthrough curves to 5.2%. Finally, potential applications of the model in surface fertigation and salinity management are highlighted.     

Two-Dimensional Fast-Response Flood Modeling: Desktop Parallel Computing and Domain Tracking

Emergency flood management is enhanced by using models that can estimate the timing and location of flooding. Typically, flood routing and inundation prediction is accomplished by using one-dimensional (1D) models. These have been the models of choice because they are computationally simple and quick. However, these models do not adequately represent the complex physical processes present for shallow flows located in the floodplain or in urban areas. Two-dimensional (2D) models developed on the basis of the full hydrodynamic equations can be used to represent the complex flow phenomena that exist in the floodplain and are, therefore, recommended by the National Research Council for increased use in flood analysis studies. The major limitation of these models is the increased computational cost. Two-dimensional flood models are prime candidates for parallel computing, but traditional methods/equipment (e.g., message passing paradigm) are more complex in terms of code refactoring and hardware setup. In addition, these hardware systems may not be available or accessible to modelers conducting flood analyses. This paper presents a 2D flood model that implements multithreading for use on now-prevalent multicore computers. This desktop parallel computing architecture has been shown to decrease computation time by 14 times on a 16-processor computer and, when coupled with a wet cell tracking algorithm, has been shown to decrease computation by as much as 310 times. These accomplishments make high-fidelity flood modeling more feasible for flood inundation studies using readily available desktop computers.     

Structured Application of the Two-Point Method for the Estimation of Infiltration Parameters in Surface Irrigation

The two-point method is one of the best known procedures for estimating empirical infiltration parameters from surface irrigation evaluation data and mass balance, mainly because of its limited data requirements and mathematical simplicity. However, past research have shown that the method can produce inaccurate results. This paper examines the limitations of the method, reviews alternatives for improving two-point method results based on data that are collected or can easily be collected as part of a two-point evaluation, and suggests strategies for estimation and validation of results for different levels of evaluation data. Results show the limitations of formulating the estimation problem with advance data only and the benefits of using instead an advance and a postadvance mass balance relationship in the analysis. Because different combinations of parameters can satisfy the mass balance equations, the estimated function cannot be extrapolated reliably beyond the times used in formulating those relationships. While results can be used with confidence to characterize the performance of the evaluated irrigation event, they need to be used carefully for operational analysis and design purposes.