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Optimization of water and N application efficiency for surface irrigated production systems
irrig.jpg (59204 bytes)

Dawit Zerihun, Charles A. Sanchez, A. Warrick, and K. Bali


Irrigated desert soils are commonly used for the production of high value horticultural crops. The low desert region of Arizona and California and environs represent more than 300,000 ha of irrigated cropland producing multiple crops each year. In 1990, irrigation of agricultural crops accounted for 81% (4.5 billon m3) of the over all water consumption in the state of Arizona (Arizona Department of Water Resources, 1991). Each year, over 3.4 billion m3 of water is withdrawn from the Colorado River to irrigate crops in the Imperial Valley of southern California (Imperial Valley Irrigation District, 1999). This amounts to 95% of the water consumed in the area (Imperial Valley Irrigation District, 1999).

While scarcity of water in the arid southwestern United States is a major impetus for improving water use efficiency in agriculture, inefficient irrigation practices are also of paramount importance in water quality related issues. The influence of irrigation practices on salt loading on the Colorado River has long been recognized and the negative impact of salt afflicted drainage water from the United States on farmland in Mexico is a source of contention between the two nations. Nitrate contamination and of surface and groundwater resources in the desert southwestern United States is often associated with inefficient irrigation practices (Adriano et al., 1977; Letey et al., 1978; Stark et al., 1983). Approximately 16.8% of the irrigation water delivered to the Imperial Valley ends up being tail-water runoff while 13% becomes subsurface drainage (Boyle Engineering Corporation ,1993) . Excessively high drainage water has been identified as an important factor affecting NO3--N loss through leaching below the root zone (Letey,et al., 1977; Sanchez et al., 1994). Surface runoff and subsurface drainage water from the Imperial Valley contribute significant amounts of N and other chemicals to the Salton Sea, causing major environmental problems. Consequently, agricultural interests in this region are being challenged to evolve into a more efficient and environmentally benign technology.

It has been reported by researchers in Arizona and California that pressurized irrigation systems can be used to manage water and N efficiently for irrigated vegetable and citrus crops (Feigin et al. 1982; Hartz 1993; Pier and Dorege, 1995a; 1995b; Thompson and Dorege 1995a; 1995b; 1996a; 1996b; Roth et al. 1995). Nevertheless, practical considerations such as initial cost, complications associated with agronomic practices, and salinity management makes it likely that surface irrigation will, for the foreseeable future, remain the principal irrigation method for horticultural production systems of the low desert region. The use of chemigation, including fertigation, is expanding in surface irrigated systems (Jaynes 1992). Threadgill (1995) reported that about 4.6 million ha of land are chemigated at least once in the United States. N fertilizer application via fertigation is widely practiced for furrow irrigated vegetable and flood irrigated citrus production systems in the low desert region. In such systems, the spatial distribution and fate of N are closely intertwined with irrigation design and management decisions. Irrigation uniformity, efficiency, and target depth of application have a direct bearing on the efficient and uniform application of nitrogen. Mode of application of nitrogen (pulse, continuous) in an irrigation event, the duration of the irrigation event, the concentration of N applied, and the fertigation schedule all have an influence on the efficiency and adequacy of N over the season. Nevertheless, traditional on-farm water application methods are designed and operated with the express objective of maximizing irrigation performance without regard to other affiliated operations such as fertigation.

Recently, there is a growing research interest, among engineers, in the efficient management of surface applied nitrogen fertigation systems. Jaynes et al. (1992) used two conservative tracers (Br- and o-TFMBA) to study the transport of solutes in the soil profile as affected by soil surface application and chemigation in a level basin. Jaynes et al. observed considerable spatial variation, in the concentration of Br-, over the chemigated basin. The observation suggests poor fertilizer distribution uniformity under fertigation. In addition, Jaynes et al. noted deeper transport of tracers under fertigation compared to soil surface applications. The results reported by Jaynes et al. are from a single irrigation and did not take into account the effects of such factors as different irrigation management scenarios as well as mode, and timing, of fertigation on fertilizer application efficiency. Nevertheless, the results underline the possible undesirable outcomes from fertigation operations. Izadi et al. (1996) reported tracer studies in soils under furrow irrigated conditions. Izadi et al. used the experimental data from the tracer study to evaluate and compare two vadose zone solute transport models RAO (Rao et al., 1976) and TETrans (Corwin et al. 1991). The surface irrigation hydraulic model, SRFR (Strelkoff 1990), was used by Izadi et al. to determine the infiltration depth along the experimental furrow and this information was in turn used by the solute transport models to predict the location of the solute plume as well as concentration within the soil.

Recent research has demonstrated that there is a potential for substantial improvement in surface irrigation performance through the application of proper system design and management practices (Clemmens et al., 1999, Strelkoff et al., 1999; Fangmeier et al., 1999). The use of surface hydraulic simulation-optimization models in system design and management can help improve system performance substantially (Singh, 1990; Alemi and Goldhammer, 1990; Zerihun et al., 1999a, 1999b). The flow phenomena in surface irrigation can hydraulically be described as gradually-varied-unsteady open channel flow over a porous bed with variable intake rate. Universal physical laws such as mass and momentum/energy conservation govern the flow process. Extensive research has been performed to model surface irrigation processes in irrigation furrows, borders and basins. Depending on the form of the momentum/energy equation used, surface irrigation models can broadly be classified into three major groups: the hydrodynamic, zero-inertia, and kinematic-wave models all of which are based on the numerical solution of the continuity and a variant of the momentum/energy conservation equation (Bassett and Ftzsimons, 1976; Sakkas and Strelkofff, 1974; Strelkoff and Katopodes, 1977; Katopodes and Strelkoff, 1977; Elliott and Walker,1982; Bautista and Wallender, 1992; Walker, 1993; Strelkoff et al., 1997). A fourth class of surface irrigation model is the volume-balance model, which is based on the analytical or numerical solution of the spatially and temporally lumped form of the continuity equation, while the dynamic equation is supplanted by gross assumptions (Lewis and Milne, 1938; Davis, 1961; Hall, 1956; Philip and Farrel, 1964; Christiansen et al., 1965; Walker and Skogerboe, 1987).

Although the literature in surface irrigation is voluminous, currently only two surface irrigation models, SRFR (Strelkoff et al., 1997) and SIRMOD (Walker, 1993) are commonly used by researchers in real-life applications. These models have been extensively validated, have well developed user-interface, and have capabilities to analyze the effects of various management scenarios. In addition, SIRMOD and SRFR have capabilities to simulate all the three primary surface irrigation systems at three levels of complexity and accuracy (the hydrodynamic, the zeroinertia, and the kinematic-wave models) in the framework of a single integrated model. We are currently using this approach to enhance irrigation performance in the low desert of the southwestern United States. However, the approach disregards the effects of irrigation design and management decisions on ancillary operations such as fertigation, particularly N application with irrigation water.

Modeling the movement and fate of irrigation water and chemicals both in the surface as well as the unsaturated zone require the use of coupled hydrodynamic and chemical transport models. Attempts to develop such models for surface irrigation applications is a recent phenomena. Strelkoff et al. (1997) have developed a quasi-steady erosion, sediment transport, and deposition model coupled with the surface irrigation simulation model, SURFR, for use in the simulation of irrigation induced erosion processes. Katopodes (1994) proposed a hydrodynamic model that accounts for vertical variations in flow velocity based on finite element solutions of the turbulent Naver-Stokes equations. The author suggests that the model provides an accurate description of the hydrodynamic basis for pollutant and fertilizer transport in surface irrigation streams. Playan and Faci (1997) reported an experimental and a (simplified) modeling study of the fertigation process in border irrigation. Playan and Faci=s simplified nitrogen transport model, which treats the irrigation border as a "plug flow reactor", was not coupled with the hydrodynamic model (Walker, 1993) used in the study. The authors showed that while the lower-half distribution uniformity for the conservative tracer,

Br-, calculated using their simplified model was in good agreement with field observations, the model performance was not as good for nitrogen. The authors attributed the less than satisfactory results vis--vis NO3- transport to the inadequacy of the "plug-flow-reactor" assumption. A numerical solution of the one dimensional dispersion (turbulent diffusion and differential convection) equation have been used successfully to model the transport of conservative chemicals in water courses and canals within stream reaches where the chemical is well mixed within a cross-section (Brebion et al., 1971, Krenkel and Novotney, 1980; Cunge et al., 1980). Provided fertigation systems are designed such that the fertilizer solution is well mixed with the irrigation stream at the upstream end of the turnout, a similar approach can be used to model the transport of NO3- in a surface irrigation stream.

Real-life data is required in order to calibrate and verify surface hydraulics as well as chemical transport models. Experimental work must be performed in order to build the necessary database. There are two sets of model parameters that are of interest in such a study: the hydraulic parameters and transport parameters. There are a variety of methods for the estimation of the hydraulic parameters, mainly: infiltration, roughness, and furrow geometry parameters. The methods range in complexity from the simplified approaches based on volume balance principles and uniform flow assumption (Strelkoff et al., 1999; Elliott and Walker, 1982 ) to the more complex approaches that rely on the inverse solution of the governing equations of surface irrigation phenomena and the matching of calculated and observed advance and recession or flow profile (Katopodes et al., 1990; Walker and Busman, 1992; Bautista and Wallender, 1994). Inverse solution techniques are too complex for routine practical applications. In addition, most of these methods are still under development. Currently, the approach proposed by Strelkoff et al. (1999) is the most convenient for real-life applications. Strelkoff et al. have developed an operational parameter estimation model called EVALUE, which is simple and has already been successfully used in a real-life irrigation setting in Egypt. The principal transport parameter of the one-dimensional dispersion model is the longitudinal dispersion coefficient. In most practical applications, the longitudinal dispersion coefficient is determined empirically based on crosssectional average concentrations measured at regular temporal and spatial intervals (Elder, 1959; Brebion, 1971).

The ultimate use of mathematical models in engineering applications is to help analyze, design, and manage systems for ‘‘optimal’’ performance. Evidently, quantitative performance indices are required to evaluate alternate design and management scenarios. While the definition, related assumptions, as well as methods of quantification of surface irrigation performance indices have been the subject of various past studies (Zerihun et al., 1997, Burt et al., 1997), evaluation of system performance from the perspective of system effectiveness vis--vis water and nitrogen application is a relatively new area of research. Existing surface irrigation performance indices are inadequate to characterize the performance of N-fertigation management systems. Consequently, there is a need to identify and define a new set of performance indices for the integrated water and fertilizer application operations. In this endeavor, the methodology used by Zerihun et al. (1997) and Burt et al. (1997) to identify and describe a self-contained set of irrigation performance indices can be used to advantage.

This project seeks to develop guidelines for the optimal management of irrigation water and water applied N for surface irrigated production systems of the low desert southwestern US. The specific objectives of the project are outlined as follows: (1) To identify and define a self-contained set of performance indices that can adequately characterize the effectiveness of N-fertigation management systems. (2) To develop a numerical one-dimensional dispersion model that is capable of simulating the surface transport of conservative chemicals and NO3- and to couple the transport model with an existing surface irrigation hydraulics model. (3) To conduct field experiments to develop a database that will be used in the calibration as well as verification of the coupled surface hydraulics and mass transport models. (4) To conduct N-fertigation management scenario analysis and to develop performance curves for improved management of N-fertigation operations.


Efficient water and N management remains a high priority in the southwestern United States. Disputes over water between states, municipalities, and agricultural and urban interests are commonplace. This situation is further confounded by a common international border with similarly arid northwestern Mexico. While the scarcity of water in the southwestern United States is a major impetus for improving water use efficiency in agriculture, inefficient irrigation practices are also a factor in water quality related issues. Abundant evidence indicates irrigation practices are a significant factor contributing to leaching and runoff losses of N from soils used for crop production. The negative impact of salt afflicted drainage water from the United States on farmland in Mexico remains a source of contention between our two nations. Because of their southern geographical location among the states of the Lower Colorado Basin, their 400 mile (640 km) border with Mexico, their proximity to large urban centers, and their productive but water demanding agricultural industries; the low desert region of Arizona and southern California is of major geopolitical importance with respect to water quantity and quality issues.

The Lower Colorado River Valley and Imperial Valleys of Arizona and California and environs represent more than 300,000 ha of irrigated cropland producing multiple crops each year. This area produces more than 90% of the nation's salad vegetables and a significant portion of the nations citrus shipped during the winter months. There is a tendency for vegetable and citrus growers to apply generous amounts of water and N because of anxiety about crop quality and the lack of sufficient information to do otherwise. For the foreseeable future, surface irrigation will remain the principal irrigation method for horticultural production systems of the low desert region. In addition, owing mainly to its cost effectiveness and flexibility, the application of N fertilizer via fertigation will continue to be widely practiced for furrow irrigated vegetable and flood irrigated citrus production systems in the low desert region.

This project seeks to evaluate and demonstrate efficient irrigation and N management practices for surface irrigated vegetables and citrus produced in the low desert region of Arizona and California. It is anticipated that the implementation of irrigation and N management practices developed and demonstrated in this project will result in more efficient water utilization, reduced nitrate-N leaching, and reduced salt loading to surface waters. Results from this research could have an immediate impact on water and N efficiency in the low desert where the need for water conservation and water quality protection are urgent. Results from this research may ultimately be applicable to irrigated areas throughout the western United States and northern Mexico. The long term outcome of these studies should result in an increase in the amount and quality of water available to other urban and rural users in the region. Overall, the long term results of these studies should serve to make agriculture more sustainable since they seek to reconcile stewardship of the environment with the economic realities of crop production.

Research Methods

The proposed research project aims at the development of best management practices for the integrated surface-irrigation/nitrogen management systems. A complete set of performance indicators for the integrated resource management system will be identified. A numerical model that solves the one-dimensional dispersion equation in the surface irrigation stream will be developed and verified. An existing surface irrigation model will provide the hydrodynamic basis for the chemical transport module. The subsurface solute transport process will be modelled as a series of elements resembling large rectangular cylinders spaced across the field in the direction of flow. Within each element, flow of both water and solute will be taken as one-dimensional (in the vertical direction) similar to that used for convective-tube models when describing more traditional spatially-varying systems. The surface boundary condition for each element will be matched to the surface irrigation stream. Existing subsurface flow models may be utilized for the vertical flow within the element. The surface hydraulics and solute transport model will be coupled with the subsurface water movement and mass transport model.

Field experiments will be performed to develop a database to be used in the calibration and validation of the coupled surface hydraulics and chemical transport models. The coupled nitrogen transport and surface irrigation simulation model will be used to develop improved management guidelines for the N-fertigation operations in the southwestern U.S.

Identification, description and quantification of a self-contained set of performance indices: A couple of indices are required to fully characterize the performance of a given N-fertigation event. In this study, a self-contained set of performance indices for the integrated resource management system will be identified and defined and methods to quantify them will be developed. An approach similar to that used by Zerihun et al. (1997) will be used.

Mathematical modelling of the combined resource management system: Mathematical models will be used to develop best management practices for the integrated irrigation-nitrogen-fertilizer management system for the Southwestern United States. A surface irrigation hydraulics model that simulates the complete cycle of a surface irrigation event forms the hydrodynamic basis for the chemical transport model. SRFR (Strelkoff et al., 1997), a surface irrigation hydraulics simulation model developed at the US Water Conservation Laboratory, in Phoenix, will be used in this study.

A one-dimensional dispersion (turbulent diffusion and differential convection) model will be used to describe the mass transport of chemicals in the surface irrigation stream. The governing partial differential equation will be solved using a finite difference scheme (Holly and Preismann, 1977; Cunge et al, 1980). The subsurface part will consist of multiple vertical cylinders. Within each cylinder, the one-dimensional Richards' equation and CDE (ADE) equation will be solved simultaneously. The old version of HYDRUS from the U. S. Salinity Lab (Kool, J.B., and M.Th. vanGenuchten. 1991) or succeeding versions is a candidate for adoption for the 1-D flow which can then be coupled together with the surface flow model. The time scales involved will be such that the nitrate can be considered as a conservative tracer and the use of transformations will not be necessary although this will be verified experimentally and numerically. Also, the validity of one-dimensional models will be verified and if necessary for furrowed-systems a 2-D model can be introduced, such as a version of SWMS 2D or later versions (Simunek, 1994). The mass transport models will be coupled with the surface irrigation simulation model. For each time line, mean cross-sectional velocity and flow depth (discharge and flow cross-sectional area) as well as infiltration calculated for each computational node using SRFR forms the input matrix for the chemical transport models.

Field experiment and the determination of surface hydraulic and transport parameters (Model Calibration): Field experiments will be performed at the University of Arizona Yuma Agricultural Center (YAC) in Yuma, at the University of California Desert Research and Extension Center (DREC) near Holtville. Initially, the objective of the field experimental study is to determine model parameters. Ultimately, a portion of this data base will be used for model validation.

The field experiments in YAC will focus on N-fertigation of basins and diked-end furrows while the experiment in DREC will focus on free-draining graded furrows. During each irrigation event a three level complete factorial experiment with respect to inlet flow rate and fertilizer concentration, will be performed. In addition, a two level complete factorial experiment will be conducted with respect to inlet flow rate and Br concentration, for the Br tracer study. A summary of anticipated treatments is shown in Table 1.

Table 1. Experimental design

N-fertigation experiment

Br- tracer experiment


Inlet flow rate


Inlet flow rate














1X ,0.5Qmax






2X ,Qmax

2X ,0.5Qmax








Qmax = maximum nonerosive flow rate, AP = application time-irrigation, and X=10 g m-2

In order to take into account the effect of time-to-the-initiation- of- fertigation on the performance of a fertigation event, the timing of the fertigation event will be varied throughout the irrigation season. Among the furrow irrigation system hydraulic parameters: hydraulic resistance, infiltration, and furrow geometry parameters are the most difficult to quantify. In this study, the method of Strelkoff et al. (1999) is to be used in the determination of all these parameters. To estimate the transport parameter, particularly the dispersion coefficient, advance and recession as well as concentrations of the nitrogen fertilizer and the bromide tracer will be measured at regular spatial and temporal intervals during each irrigation event. Concentrations of nitrate and Br in the irrigation water will be determined using ion chromotography. The longitudinal dispersion coefficient will be estimated empirically using the method proposed by Elder (1959) and Brebion (1971). Concurrently, tracer studies, using a Br- conservative tracer, will be performed to estimate the potential for nitrogen leaching by drainage water. For basins and borders, soil samples will be collected on a pre-determined grid (about 24 to 40 sample locations) to a depth of 1.5 m. These cores will be sectioned into six 0.25 m and saved for extraction. For the furrow irrigation system, soil samples locations will be spaced at pre-selected intervals along the furrow (approximately 10 per furrow). However, because infiltration in furrows is a function of wetted perimeter, we will collect three individual cores (center of bed, edge of bed, and bottom of furrow) at each sample location. Each of these will be sectioned into six samples as described above. Nitrate and Br will be extracted from the sieved sectioned cores and concentrations will be determined as described previously. The subsurface model will be checked for one versus two-dimensional effects for the furrowed system (i.e., to check adequacy of a one-dimensional analysis within a "cylindrical cell"). In addition, a database will be developed for the verification of the coupled surface irrigation and chemical transport model.

Model validation: Water advance and recession data will be used to evaluate the predictive quality of the surface irrigation hydraulics model. The transport model will be validated by comparing the field observed and calculated advance and recession of the chemical plume, the temporal and spatial evolution of the concentration of the chemical in the surface stream, and the potential for leaching of nitrate. Based on results of model validation, further changes could be made to the models. Models will also be evaluated for numerical consistency. For example, mass conservation of water and solutes will be checked and analytical solutions will be compared for simplified conditions. Additionally, discretization sizes will be checked for consistency.

N-fertigation management scenario analysis and development of performance curves for N-fertigation systems management: Once the coupled surface hydraulics and chemical transport models are validated, they will be used to study the effects of different management scenarios. The coupled model will be used to study the effects of (1) mode of application (pulse, continuous, intermittent), (2) timing of application in an irrigation event, (3) concentration of fertilizer solution, (4) inlet flow rate, and (5) cutoff length or cutoff time. In addition, the mathematical model will be used to evaluate the effects of variations in furrow length, infiltration, roughness parameters, and bed slope on uniformity, adequacy, and efficiency of nitrogen fertilization. The models will further be used to develop performance curves via simulation experiments for use in the optimal management of fertigation systems.

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