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To efficiently manage the water supply for paddy rice and to reduce the inundation damage from floods, it is necessary to enhance our understanding of the characteristics of the surface water hydraulics in an irrigated paddy field. In this study, a two-dimensional numerical model is used, and the model's applicability for simulating surface irrigation and drainage is evaluated. The model's Manning roughness coefficient is estimated, taking into account the growth stage of the paddy rice; the simulation results are in good agreement with the observations. Model simulations reveal that the initial ponding depth affects the wave propagation and the increase in water depth during irrigation. There are few differences in piezometric heads among the positions except for those close to the outlets during drainage. Constructing drainage ditches in a paddy field reduces the drainage time to 24 h. Also, the study results reveal that it is preferable to determine the appropriate water management measures by considering the characteristics of the surface water hydraulics of paddy fields to reduce costs and labor input. DOI: 10.1061/(ASCE)IR. 1943-4774.0000016 CE Database subject headings: Surface water; Numerical models; Drainage; Soil consolidation; Water supply; Floods.

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. DOI: 10.1061/(ASCE)IR. 1943-4774.0000098 CE Database subject headings: Infiltration; Furrow irrigation; Surface irrigation; Shallow water; Flow simulation; Numerical models; Experimentation.

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 (Wohling 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 [R.sup.2] 0.99 and coefficients of efficiency [C.sub.e] [less than or equal to] 0.7. Predicted recession times also match with the observations of the HEL runs, however, the values of [R.sup.2] [less than or equal to] 0.9 and [C.sub.e] [less than or equal to] 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.sup.-I] is in very good agreement with the observations (12.7 t [ha.sup.-l]). 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. DOI: 10.106 l/(ASCE)0733-9437(2007)133:6(548) CE Database subject headings: Furrow irrigation; Vegetation; Infiltration; Two-dimensional models; Mathematical models; Coupling.

Physically based modeling of the interacting water flow during a furrow irrigation season can contribute to both a sustainable irrigation management and an improvement of the furrow irrigation efficiency. This paper presents a process based seasonal furrow irrigation model which describes the interacting one-dimensional surface-two-dimensional subsurface flow and crop growth during a whole growing period. The irrigation advance model presented in a previous study is extended to all hydraulic phases of an irrigation event. It is based on an analytical solution of the zero-inertia surface flow equations and is iteratively coupled with the two-dimensional subsurface flow model HYDRUS-2. A conceptual crop growth model calculates daily evaporation, transpiration and leaf area index. The crop model and HYDRUS-2 are coupled via its common boundaries, namely (1) by the flux across the soil-atmosphere interface; and (2) by the flux from the root zone, which is associated with the plant water uptake. We assume the water stress is the only environmental factor reducing crop development and hence final crop yield. The model performance is evaluated with field experimental data in the companion paper, Part II: Model Test and Evaluation (Wohling and Mailhol 2007). DOI: 10.1061/(ASCE)0733-9437(2007) 133:6(538) CE Database subject headings: Furrow Irrigation; Vegetation; Infiltration, Two-dimensional models; Mathematical models; Coupling.

In recent years, upwind techniques have been successfully applied in hydrology to simulate two-dimensional free surface flows. Basin irrigation is a surface irrigation system characterized by its potential to use water very efficiently. In basin irrigation, the field is leveled to zero slope and flooded from a point source. The quality of land leveling has been shown to influence irrigation performance drastically. Recently, two-dimensional numerical models have been developed as tools to design and manage basin irrigation systems. In this work, a finite volume-based upwind scheme is used to build a simulation model considering differences in bottom level. The discretization is made on triangular or quadrilateral unstructured grids and the source terms of the equations are given a special treatment. The model is applied to the simulation of two field experiments. Simulation results resulted in a clear improvement over previous simulation efforts and in a close agreement with experimental data. The proposed model has proved its ability to simulate overland flow in the presence of undulated bottom elevations, inflow hydrographs, and colliding fronts, CE Database keywords: Numerical models; Surface irrigation; Overland flow.

Level basins, when properly designed and managed, often attain very high irrigation efficiencies. Problems can arise when the infiltrated depth exceeds the soil water holding capacity or when the crops are sensitive to waterlogging. Both cases could benefit from allowing part of the applied water to run off the basin. This water can be reused for on-farm irrigation of the subsequent basin. Such a setup will be referred to as the 'runoff rescue' (RR) system. In this work, an RR system composed of five adjacent terraced basins is described and evaluated. The basins were connected by outflow points located at the upstream and downstream ends of the fields. To provide terms for comparison, the performance resulting from conventional irrigation (without RR) of each basin was estimated using a simulation model. The RR system showed reductions of 14, 16, and 24% in irrigation time, infiltrated depth, and recession time, respectively. The average increments for distribution uniformity and application efficiency were 2 and 9%, respectively.

A zero-inertia furrow irrigation model with specified space solution was used to investigate the effects of variability in furrow inflow rate and spatial variability in infiltration, geometry, and roughness on end-of-furrow advance, average infiltrated depth, and Christiansen's and distribution uniformities. Extensive field-gathered infiltration, geometry, and roughness data were used as input to the zero-inertia model. Simulations were performed on a single furrow as well as fieldwide. Variable furrow inflow was incorporated into the fieldwide analysis. Model simulations were evaluated to determine the importance to irrigation performance of variability in each input variable. Variability of furrow physical characteristics, in decreasing order of their relative impact on furrow irrigation performance, were furrow inflow rate, infiltration, geometry, and roughness for the conditions studied.

A nonhydrostatic model for overland flow is developed for the purpose of providing the framework for predicting the fate and transport of chemicals under surface irrigation. The technique is based on the turbulent Navier-Stokes equations for the surface wave and the Richards equation for the movement of moisture in the underlying porous medium. The model consists of a novel two-dimensional combination of the marker-and-cell and finite-element methods and utilizes a deforming computational grid that automatically adapts to moving wave fronts in the solution. Convergence and conservation tests are performed to demonstrate the robustness of the model. Results are presented for laminar and turbulent flow cases and compared to similar computations based on traditional depth-averaged models.

A numerical method is developed for the identification of bed resistance and infiltration parameters in surface irrigation based on global procedures. The method is characterized by global convergence - a unique solution from any feasible set of initial parameter estimates, which is not possible for standard variable metric methods. The algorithm is applied to border irrigation described by the zero-inertia model and is used to produce three-dimensional maps of the convergence history of some well-known field observations. Additional enhancements regarding parameter scaling, gradient modification, and combination with a Gauss-Newton method yield a robust and efficient algorithm that can be applied to a variety of practical problems.

In regions where irrigation water supply is less than the required amount, extensive but deficit irrigation becomes unavoidable, unless the irrigated area can be limited to ensure full supply. When reliable dated crop-water response (DCWR) functions are available, a scientific planning of deficit irrigation schedules can be undertaken. This paper presents the formulation of a nonlinear programming (NLP) problem for identifying optimal cropping pattern as well as optimal deficit irrigation schedule along with its application to a minor irrigation system. The model indicates, for the case studied, that an increase in the cropped area by approximately 50% is possible over that underintensive irrigation approach. In terms of the net monetary return from the system, it means an increase of approximately 20%. The adoption of extensive irrigation policy in such a setting is seen to be desirable.

In this study, a hydrodynamic model is presented for simulating basin irrigation. An explicit, second-order-accurate finite-volume technique is used for solving the two-dimensional governing equations of basin irrigation. The empirical Kostiakov-Lewis infiltration equation is used for the calculation of infiltration. The model is validated using field data and numerical results available in the literature. The proposed model was used for simulating a basin irrigation event in an irregular field with a high spot inside the computational domain. The resulting numerical error was smaller than that produced by previous models applied to the solution of this problem. The proposed model was also used for studying the effect of basin shape on the time of advance and to check the validity of one-dimensional flow assumption when the inflow to the field is provided only through a part of the edge. In the case of a rectangular field with a partial line inflow, the two-dimensionality effects become significant when the ratio of inflow width to the field width is less than a particular value. A simple subgrid technique was introduced to obtain a high grid resolution near the advancing front and maintain a low computational cost.

A seasonal furrow irrigation model was constructed from soil moisture, kinematic-wave hydraulic, and economic optimization models to study the effects of heterogeneity in water balance, soil water holding properties and rooting depth, and infiltration functions on furrow irrigation design (flow rate and cutoff time), bean yield, and net return to water. Irrigation designs achieving nearly 100% irrigation adequacies were unchanged by heterogeneity in water balance, soil water properties, and rooting depth, but both bean yield and net return to water decreased with increasing heterogeneity. Irrigation designs were sensitive to infiltration characteristics and to irrigation interval. At a given irrigation interval, bean yield was insensitive to infiltration characteristics but consistently decreased with increasing irrigation interval. Net return to water was less for spatially variable infiltration functions as compared to homogeneous infiltration conditions. Using mean evapotranspiration (ET) of a grass reference crop (ETo) resulted in slightly higher bean yield and net return to water as compared to observed ETo (1992 season values of grass reference crop ET). Spatial and temporal variability in infiltration gave the same optimal irrigation interval (10 d) under both ETo conditions for the chosen irrigation criteria (80% irrigation adequacy at cutoff time). Both ETo conditions led to essentially the same design inflow rates. Errors in inflow volume were less than 12 and 3.5%, respectively, for individual irrigations and on a seasonal basis. Irrigation scheduling and surface irrigation design can be forecast at the beginning of the growing season for the conditions studied using historical mean ETo if spatial and temporal variability of infiltration are considered.

Distributed, physically based watershed and irrigation advance models require robust infiltration estimation capabilities. The empirical Green and Ampt (GA) equation of infiltration is a popular method for estimating infiltration. The GA parameters have physical basis and considerable prior research has focused on relating these parameters to soil textural classification. However, the original GA method is limited in that it is applicable only for a single ponding period. An explicit Green and Ampt redistribution (GAR) technique is developed herein to estimate interstorm redistribution of soil water and allow multiple ponding simulations using the GA methodology. Soil water redistribution during interponding periods is estimated using the physical constructs of water retention curves without hysteresis. A GA wetting-front suction parameter scaling function is derived for use between arbitrary soil water contents. Simulations on 11 soil textural classifications comparing the GAR method with the numerical solution of Richards equation reveal that the GAR method is a viable technique for estimating infiltration for multiple pondings with acceptable error.

Previous research in the estimation of surface irrigation parameters from advance time or surface profile observations has focused on the development of solutions for parallel surface flow conditions. This study was conducted to assess the usefulness of a polar model simulating radial flow in the estimation of infiltration and roughness parameters of a point-inflow level-basin irrigation event. The two-step explicit McCormack scheme was applied to the solution of the governing equations. The method of characteristics was used at boundary nodes. Point-wise semiimplicit discretization of the friction and geometric source terms was used. Results of this model compared well with those obtained with a two-dimensional Cartesian model simulating radial flow. Gradient and nongradient minimization techniques were applied to determine pairs of infiltration and roughness parameters. The estimation of the parameters is as feasible for radial flow as it is for parallel flow.

Infiltration parameter estimation (IPE) is a simulation model of furrow irrigation that allows us to estimate infiltration parameters in real time. The model calculates infiltration parameters from measured advance times in the field using a kinematic wave model that includes spatial and temporal variability of infiltration due to variations of the wetted perimeter. The model then calculates cutback inflow rates to reduce runoff and the irrigation application time as a function of the required water depth. Thus, real-time irrigation control and management by the IPE model leads to better irrigation application efficiencies.

Microtopography has long been regarded as a key variable affecting basin irrigation performance. This paper reports on the extension of a flat bed two-dimensional basin irrigation model to the simulation of irrigation events in basins with microtopography. The model incorporates the local surface slopes in the x and y directions to the governing set of partial differential equations. Three field experiments were used to validate the extended model. Elevation was measured over irregular grids, and geostatistical techniques were applied to estimate the nodal elevation of the computational grids. Results indicate that inclusion of microtopography improves the estimation of the advance and recession processes and produces lower, more realistic estimates of irrigation performance. To further explore this phenomenon, two numerical experiments were devised consisting of a series of simulations on a level basin with gradually growing microtopography. The times of advance and recession and the irrigation performance indexes are significantly affected by field microtopography, even if laser leveling is used.

Subsurface drip irrigation has become a common method for the irrigation of field crops, trees, and landscaping. When the predetermined discharge of the emitter is larger than the soil infiltration capacity, water pressure at the dropper outlet increases and can become positive. This pressure buildup in the soil decreases the pressure difference across the dripper and, subsequently, decreases the trickle discharge in a manner that depends on the dripper characteristic curve. A device was developed to measure simultaneously the pressure difference at the inlet and outlet of a subsurface emitter and the emitter discharge. In a preliminary study, discharge rate declines of 10-50% were measured for unplugged subsurface emitters. The extent of the discharge decrease due to back pressure depends on: (1) the soil type (the lower the hydraulic properties the larger the decrease); (2) the dripper discharge (larger decreases occur for higher nominal discharge); (3) possible cavities near the dripper outlet (a larger cavity decreases the back pressure); and (4) the drip system hydraulic properties. The increase in back pressure is rapid at the beginning and then approaches a final value after several minutes, which allows the use of an analytical approximation that assumes steady-state conditions.

Soil variability can affect the flow rate of water from subsurface trickle emitters. This is because of a buildup of pressure in the soil when water cannot be easily transmitted away from the emitter. In this paper, an analysis was developed showing the relationship between discharge versus the design discharge as a function of emitter characteristics and the soil hydraulic properties. When the design flow volume increases or the hydraulic conductivity of the soil decreases, the pressure head of the soil next to the emitter increases, which reduces the flow rate (other factors remaining equal). The subsequent effect on irrigation uniformity was examined using soil data from a field in the Arava Valley, Israel. The average of the calculated ratio of the actual discharge to the designed discharge was 0.905, 0.825, and 0.704 for designed discharges of 1, 2, and 4 L/h, respectively. Corresponding coefficients of variability were 0.072, 0.124, and 0.193, respectively; likewise Christiansen's uniformities were 0.95, 0.91, and 0.85.

A seasonal furrow irrigation model consisting of submodels to predict irrigation schedule (water balance), irrigation design (surface irrigation hydraulics), and crop yield (yield function) under spatially and temporally variable conditions was developed and verified with the field data. The model was used to predict irrigation performance for each irrigation event during the season, soil moisture before each irrigation, seasonal evapotranspiration (ET), and bean yield along the furrow at 10-m intervals. In addition, measured inputs along the furrow, including heterogeneous infiltration, soil moisture, and yield were used in conjunction with the model to estimate mean (17.3%) and variation in available water-holding capacity (AWC) (15.4%-19.8%). Variation in crop yield represents an integrated effect of variability in infiltration, soil water characteristics, root depth, soil fertility, microclimate, fertilizer and pesticide applications, plants, and disease. Using the calibrated model, nearly 88% of the variance in ET estimated with the yield function was explained by simulated variation in infiltration characteristics, soil water-holding capacity, and root depth. By assuming homogeneous infiltration characteristics, soil water properties, and root depth, the average absolute error in seasonal ET increased by only 0.6 cm but the variance explained decreased to 30%. Although in absolute terms the impact of heterogeneity seems negligible, Raghuwanshi (1994) showed that heterogeneity strongly affected the optimal flow rate and irrigation time as well as net returns to water.

In this study, a hydrodynamic model is presented for simulating all the phases of border-strip irrigation. The explicit, second-order accurate MacCormack scheme is used for solving the governing equations of surface irrigation. In this method, the advance and recession fronts need not be considered explicitly and any infiltration equation can be coupled to the surface flow equations easily. The empirical Kostiakov equation (Model 1DKO) and the analytical Parlange equation (Model 1DPA) for infiltration are considered in this study. The implicit Parlange equation is solved using the Newton-Raphson technique. The models are validated using the experimental data available in literature. The present results are also compared with the earlier numerical results based on the characteristic method. A simple subgrid technique is introduced in order to obtain a high grid resolution near the advancing front and at the same time achieve a minimum computational cost. This is based on using two different grid sizes for computation. An equation for the optimum grid size ratio is presented and is validated using numerical experimentation.

The purpose of this study was to investigate the reliability of combining a surface irrigation model (SRFR) and two functional solute transport models (RAO and TETrans) in predicting the position of bromide ([Br.sup.-]) measured in a 0.81-ha field under furrow irrigation. The SRFR model was used to first predict the infiltrated depths and then RAO and TETrans models were used to predict the position of the solute. Solute was transported according to piston flow theory for the first irrigation and both models predicted the position of the solute with good accuracy. The solute was transported slightly faster than estimated by piston flow for the second irrigation, resulting in a reduction of correct predictions by both models. Both models predicted poorly for the third irrigation because deviations from piston flow were large. RAO model was more successful in predicting the peak solute position, while TETrans was more accurate in predicting mean solute depths. The latter was attributed to the differences between the two models and the sensitivity of TETrans to nodal spacing when predicting peak solute position.

Knowledge of the sensitivity of performance and other related dependent furrow-irrigation parameters, in quantitative terms, to variations in field, design, and management variables can help save a considerable amount of cost, time, and effort spent in field data collection. A univariate analysis, based on the concept of relative sensitivity, was used to quantify the sensitivity of seven dependent irrigation parameters ([E.sub.a], [E.sub.r], [R.sub.r], [D.sub.r], [U.sub.cc], [l.sub.r], and [t.sub.a]) to 13 variables ([t.sub.co], [S.sub.0], [[Delta].sub.1], [[Delta].sub.2], [[Rho].sub.1], [[Rho].sub.2], n, k, a, c, l, [q.sub.0], and [Z.sub.r]). Three d'lfferent data sets, representative of a wide range of irrigation conditions have been used in the analysis. The response of each dependent parameter to variations in a variable has been evaluated using a zero-inertia model. It was found that no general conclusion can be drawn regarding the relative significance of variables in terms of their effect on each of the dependent parameters, since the interaction between variables is significant enough to weaken or strengthen the effect of changes in a given variable on a dependent parameter. Nevertheless, based on observed relative sensitivity clues, a qualitative categorization of variables into five sensitivity classes, with respect to each dependent parameter, was made.

The irrigation land management model is praised because it simulates not only irrigation water requirements but also the response of a multi-field crop irrigation system under different schedules. The consumptive-use portion of the single-field module is discussed to show how to estimate evapotranspiration and determine its impact on irrigation water requirements. Certain points on crop yield predictions and distribution queue system are suggested for further studies.

The Colorado State University Irrigation and Drainage (CSUID) model is a simulation model, which can be used in the design and management of conjunctive irrigation and drainage systems. It is based on the numerical implementation of a quasi-three-dimensional finite-difference model, which solves the Richards equation and the advective-dispersive transport equation for one-dimensional vertical flow and salt transport in the variably saturated zone above the water table; and it also solves the depth-averaged Boussinesq equation and two-dimensional advective-dispersive transport equation for areal flow and transport in the fully saturated zone below the water table. In this paper, the model is validated and applied. Its performance is compared to known analytical solutions of simplified problems, the performance of other numerical models, and results of reported laboratory and field experiments. Its capabilities as a design and management tool are demonstrated by considering a hypothetical field problem. It is shown that the model can be used to evaluate design and management strategies to achieve the improved performance of conjunctive irrigation and drainage systems.

This paper introduces a model for the design and management of conjunctive irrigation and drainage systems. The mathematical model is based on the numerical implementation of a quasi-three-dimensional finite-difference model, which solves the Richards equation and the advective-dispersive transport equation for one-dimensional vertical flow and salt transport in the variably saturated zone above the water table; and it also solves the depth-averaged Boussinesq equation and two-dimensional advective-dispersive transport equation for areal flow and salt transport in the fully saturated zone below the water table. The model is fully interactive and is provided with a graphic user interface (GUI). It can be used to estimate the growth response of a crop to its soil-water-air-solute subsurface environment as influenced by drainage design and management practices such as irrigation scheduling, leaching, and cropping patterns. An illustrative example is included to demonstrate the capabilities of the model as a design and management tool in irrigation and drainage systems.

Values of reference evapotranspiration (E[T.sub.0]) are used with crop coefficients (KC) for many aspects of irrigation and water resources planning and management. More than a score of methods are used for estimating E[T.sub.0]. Estimated values vary widely due to the lack of standardization of the reference. Evaporation (ET) measured by lysimeters of various grasses and/or alfalfas has been used as the standard for developing estimating equations. Due to variation in the references used, some international organizations now wish to promote the use of a single equation or method to avoid the confusion caused by the current diversity. Different versions of the Penman combination equation have been proposed. The Research Center for the European Community and the ASCE Committee on Irrigation Requirements have evaluated various equations for estimating E[T.sub.0]. Due to its simplicity and the accuracy of estimates, the 1985 Hargreaves et al. equation is recommended for general use. E[T.sub.0] is used in irrigation planning, design, and scheduling and for other water adequacy studies.

The cumulative water demand (CWD) curve was used for validating and calibrating the unit command area (UCA) model, which predicts the aggregate water demands of individual command areas for the entire crop season. During the model calibration process, as presented in the companion paper, three important variables in the operation stage on the prediction of demand were found to be dominant in determining the CWD curve profile. The logistic function with three parameters, which is a particular form of the exponential-type function, was adopted for fitting the CWD curve. High correlations, were observed between the individual curve parameters and the field variables. Three parameters are management-allowable depletion (MAD), irrigation application uniformity (IAU), and initial soil moisture (ISM). Effectiveness of the equation developed for a particular UCA using the regression analysis was successfully demonstrated, and applicability for some other UCAs in the same water system was also recognized.

Simulation of aggregate water demands by areas commanded by canal and lateral turnouts is an important input to the operation and management of the irrigation delivery system. A computer simulation model to predict these command area water-demand functions was developed and reported by Keller in 1987. To test the validity of the model, data from an existing irrigation project in the Delta, Utah, area were used to simulate the aggregate irrigation demand of five turnouts operated on a demand basis. During the model calibration process, the influence of three important variables in the operation stage on the prediction of demand was identified using the cumulative water-demand curve. The key variables were: (1) Management-allowable depletion (MAD); (2) irrigation application uniformity (IAU); and (3) initial soil moisture (ISM).

The development of a two-dimensional hydrodynamic simulation model of basin irrigation is reported in a companion paper. This article presents four applications of the model. Two hypothetical case studies are used to illustrate the ability of the model to accommodate multiple inflows and irregular field shapes including internal high spots. The model is applied to study the effect of field shape on irrigation performance. The particular case of a rectangular basin irrigated from a corner is considered. Results show that one-dimensional models can underestimate the time of advance by up to 20%. Finally, the model i applied to explore the effects of spatially varied infiltration on irrigation performance. A series of infiltration observation points is used to estimate th infiltration rate in unmeasured locations. The model is used to simulate a hypothetical case study involving the design of a square level-basin irrigation field with spatially varied infiltration irrigated from a corner. Results show that irrigation performance changes dramatically with the location of the corne inflow.

Overland flow of water over a porous bed in two spatial dimensions is governed by three partial differential equations accounting for continuity of momentum i the x- and y-directions and continuity of mass. A leapfrog explicit finite-difference numerical scheme was applied to solve this system of equation for the initial and boundary conditions that characterize level-basin irrigation. The numerical procedure is stable and robust for different applications, and can accommodate three different inflow configurations: line, corner, and fan. These configurations simulate inflow from an overflowing canal on a field boundary and at point sources from a corner or in the middle of a straight boundary, respectively. A numerical test was performed to assess the effect of grid fineness on the results of the simulation and on central-processing-unit time requirement. Data from two field tests were used t validate the model in quasi-one-dimensional and two-dimensional conditions.

In the present paper the use of mathematical programming theory is proposed to define optimization criteria for the deficit irrigation of an area. A first application, which was carried out on a sample farm in the Upper Tiber Valley (Central Italy), gave significant results. By using a multiplicative Stewart's formula, it was possible to determine, for various crops, the relationships between crop yield and applied water, which depend on the deterministic component of the process of water exchange soil-crop-atmosphere. The stochastic component of the same process is defined by the hypothesis that the functions are variable from year to year. These relationships were introduced as a constraint in a mathematical programming framework, with the aim of optimizing, in economic terms, the application of available irrigation water taking into account the possibility of varying the crop pattern. Finally, since the optimal solution can be found only on an annual basis, due to the stochastic component of the process, an attempt was made to define a method for determining a single, constant and optimal solution.

A three-dimensional Green-Ampt analysis is developed, and the infiltration capacity curve for a three-dimensional infiltration model is presented. The infiltration-capacity curve represents the time distribution of wetting-pattern volume of a water source with unlimited inflow supply. A significant feature of the infiltration-capacity curve is that the infiltration-capacity rate increases with time during extended infiltration periods. This feature is different from the one-dimensional infiltration model where the infiltration-capacity rate decreases with time. The infiltration-capacity curve is applied to describe the wetting pattern of a surface emitter with a constant discharge by matching the emitter discharge with the average infiltration-capacity rate. Algebraic solutions of the wetted radius and the maximum wetting-pattern depth are derived. Graphical solutions of the infiltration-capacity curve are presented. A numerical example is prepared to illustrate the procedure for estimating time of application, wetting pattern volume, emitter discharge, and irrigation period of a surface emitter in a drip-irrigation system.

Sound irrigation management models require the information of root-depth development with time in order to determine the active zone of soil reservoir. Development indicates rate of change. Sigmoidal as well as exponential root-depth-development models as a function of time, soil, crop, and management practices are developed. The models require as input data the maximum rooting depth to be achieved under a particular set of soil, crop, and management practices as well as the days until the root depth attains a maximum value, A comparison was made between experimental observations of a wheat crop and the estimates derived from several previously developed root-growth models and the models developed in this study. The results clearly indicate that both of the developed models had a high degree of accuracy, which was comparable with or better than other reported empirical root-growth models.

Clay soils frequently develop large cracks after irrigation. Infiltration equations therefore need to be modified to take cracking soil properties into account when modeling and optimizing furrow irrigation, In this article, we propose an infiltration equation for cracked soils, based on two parameters, Other parameters of the global model are assumed to be known (furrow length, shape, slope, and estimated roughness). One parameter is linked to the type of soil and is calibrated separately for the entire irrigation process. The second parameter takes soils' cracks into account and is calibrated in real time during the advance phase (before the water front overruns the middle of the plot). This global furrow irrigation model for cracked soils is derived from a conceptual approach and can be used either to predict in real time, water-use efficiency during irrigation (infiltrated volume, runoff water losses, uniformity) or to optimize irrigation parameters (head flow, irrigation duration). The model was tested and validated on three irrigation applications on 60 furrows in a corn field in Tarascon in southeastern France. This conceptual model can be easily adapted to the statistical approach, which is based on the variability of water advance between the furrows.

The computation of wetted-perimeter-dependent intake in a furrow irrigation simulation model using an empirical infiltration formula was examined. Different formulations were applied under increasing and decreasing depth of flow (and wetted-perimeter) conditions. Four computational methods were compared for the former condition and only one was tested for the latter. The merit of the procedures was evaluated in relation to the performance of a finite difference unsteady surface flow model. The hydraulic model was developed using fixed spatial increments and variable time steps and solved with a shooting technique. Differences in advance trajectory resulted from application of each formulation, and numerical accuracy was also different with each computational method. Convergence of the shooting solution was obtained with all infiltration formulas during the advance phase, but there were noticeable differences in convergence rate. Only one of the formulas provided consistent results during storage and recession calculations. Numerical instability resulted as well from the application of the procedures with limited convergence.

The Irrigation Land Management (ILM) model was developed as a research tool to simulate the demand and response of a multiple-field multicrop irrigation system in a variety of environments in order to assist managers in exploring strategies that can be used to improve system performance. It addresses the two-fold problem of first determining the aggregate irrigation water requirement for a command area represented by multiple landowners, cropping patterns, and water-management schemes; then, once water is delivered, simulating the command area's response to the water supply. It includes field- and weather-generation components to assist in the exploration of alternative management strategies. The model was validated using field data from a large irrigation system in Utah and used to analyze its current management program.

Irrigation in a river basin generally implies that the drainage water from upstream schemes is reused in the downstream schemes. The processes of water and salt movement in the schemes (over the soil surface, through the soil profile, and through the substrate) are successfully modeled in other studies. In the model presented here (called RE-USE), these processes are linked for a series of irrigation schemes along a river. The model can be run for variable conditions (agricultural, soil, hydrological, and climatological) and variable regimes (irrigation and drainage), although these conditions and regimes have to be similar for all considered schemes. Time-dependent variables may be defined on a daily basis (e.g., for rainfall) or on a monthly basis (e.g., irrigation-water requirements). The model is used to explore relationships between annual rainfall, irrigation efficiency, and irrigation-induced soil salinization. The usefulness of the model in evaluating strategies for irrigation-water management in a basin has also been demonstrated.

This paper describes the formulation of a model for optimized crop and water planning decisions in an irrigation system in Thailand. It facilitates consultation in which representatives of stakeholders, officials, farmers, and researchers can contribute to the decision making. Linear programming and the analytical hierarchy process are the principal modeling tools to optimize the collective system objectives: productivity, equity, and security. The results of the model are compared with observed events of one dry season. The optimized policy generated by the model suggested a diversified cropping pattern, which would decrease the water requirement by 16.4% and enhance net benefit per cubic meter of water used by 39.9%. The erratic water availability from the reservoir and the operational procedures inside the system are reviewed, analyzing historical data in terms of reliability, resiliency, and vulnerability. These include lack of proper assessment of available water, effective farmer organization, and prompt data processing and communication. Furthermore, for the effective implementation of an optimized irrigation policy, a water release pattern of the storage reservoir has been suggested.

A theoretical analysis based on the energy principle for discharge over side weirs was presented, and its application was demonstrated using a numerical approach. The decrease in water surface elevation in lateral direction was considered. The inclination of the deflected flow over the weir was also taken into account. The side weir was divided into elementary strips to develop generalized equations for discharge and surface profile. Dimensionless parameters were used, and equations were solved using numerical methods and computer techniques. Discharges and water surface elevations that were computed were compared with the experimental results. Equations that were developed were also used to obtain hydraulic characteristics of storm water overflows as a practical application.

A finite volume model for unsteady, two-dimensional, shallow water flow is developed and applied to simulate the advance and infiltration of an irrigation wave in two-dimensional basins of complex topography. The fluxes are computed with Roe's approximate Riemann solver and the monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to eliminate spurious oscillations and the model incorporates an efficient and robust scheme to capture the wetting and drying of the soil. Model predictions are compared with experimental data for one- and two-dimensional problems involving rough, impermeable, and permeable beds, including a poorly leveled basin.

A particularly simple equation is developed to explicitly calculate the time of advance in surface irrigation. The proposed equation can be used for routine furrow irrigation design. The equation is derived as an extension of the small-time, large-time explicit solutions. Systematic comparisons of dimensionless solutions indicated that the prediction of the equation is in agreement with the accurate zero-inertia numerical solutions. The accuracy of the simple U.S. Soil Conservation Service explicit time of advance empirical equation was also evaluated. Comparisons have shown that the U.S. Soil Conservation Service equation generally performed poorly. The suggested equation is also compared with observed furrow data and with the accurate zero-inertia model. The provided predictions are in agreement with the numerical model and observed data.

The furrow irrigation system design problem (at minimum cost) is significantly simplified by analytically solving it. For a specified furrow length, a simple algebraic equation is derived to directly calculate the appropriate inflow rate (and cutoff time) so that the minimum cost of the furrow system is obtained. The proposed equation is independent of the water and labor cost coefficients. Comparison tests indicated that the optimum inflow rate values obtained analytically were in close agreement to the optimum values obtained using the outcome of the zero-inertia numerical model. The method is extended for furrow design considering the furrow length also as a design variable. The optimum number of distribution lines and widthwise furrow sets are easily determined by a simple calculation procedure.

A model and computer program were developed to calculate water application depth and uniformity coefficient for small spray nozzles mounted on a center-pivot irrigation system. The program requires two basic inputs. First, the experimental data for the static distribution pattern of the spray nozzle, including collection time, spacing between collection cups, cup opening radius, and volume of water collected in each cup at a specific pressure and height are required. Second, irrigation system inputs including spacing between spray nozzles, radius of distal end tower and moving velocity, distance of spray nozzle from the pivot, move stop cycle time, or cycle time, and percentage of moving time from the cycle time, or percentage of moving time are needed. The outputs are water application depth and uniformity coefficient. Experiments were conducted to validate the simulation for various moving velocities, spacing between spray nozzles, cycle times, and percentages of moving time. Results showed that the uniformity coefficient of water distribution was 98.4% of the predicted coefficient and that by changing cycle time, or percentage of moving time, the uniformity coefficient was improved by as much as 14.2%.

A mixed-integer program is presented for scheduling canal irrigation among a group of users where the duration of flow of each outlet and a target start time is specified by the users. Two models are developed. The first is a single-period model which uses as input a minimized demand at the head of the canal. This will allow the discharge at the head of the canal to be set once at the beginning of the irrigation period. Within this constraint, the single-period model minimizes the sum over all outlets of the difference between the scheduled start time of flow to each user and the requested target start times. The second model is a multiperiod model. This model favors those users who had been disadvantaged in the previous irrigation periods by giving them priority in scheduling their actual start times with target start times for the subsequent irrigation period. The proposed models can be used to support decisions in irrigation schemes operating on an arranged demand.

Vivekanand Singh and S. Murty Bhallamudi's work on the development of a hydrodynamic border-strip irrigation model is noted for two distinct achievements. First, the Kostiakov equation was correctly replaced with the modified Parlange quasi-analytic infiltration equation. Second, the MacCormack predictor corrector scheme offers ease of use compared with other implicit predictor schemes.

Equations (5) and (6) in the report by R. Singh and colleagues on the discharge coefficient of rectangular side weirs, contradict each other. Equation (5) can be expressed as Cd = 0.99 - (1.26 x Q1)/(by1 x square root of gy1). Cd increases if y1 increases with Q1, b and s constant. However, equation (6) shows Cd decreasing for the same conditions. Also, the limit of Cd in (6) should be at its smallest value as s/y1 approaches one.