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.     

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.     

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.     

Estimation of Soil and Crop Hydraulic Properties

Some two dozen methods for estimating infiltration and roughness parameters from field measurements of test irrigations are reviewed in this paper. They differ in their assumptions, ease of analysis, quantity of field data required, and accuracy. They are divided into two broad categories, depending upon the basic approach to determine infiltration. One features direct application of mass conservation, expressed in terms of the infiltration parameters and then inverted in some way in order to extract those parameters. The other involves repeated simulation with a sequence of values of the infiltration parameters, coupled to some kind of search procedure—an optimization—to minimize differences between simulation and measurement. A new one-point technique is proposed, along with suggestions for extending existing methods.     

Optimal and Postirrigation Volume Balance Infiltration Parameter Estimates for Basin Irrigation

Engineering analysis of surface irrigation systems is predicated on reasonably accurate estimates of a field’s infiltration properties. Optimal estimation methods pose multiple volume balance equations at various stages of an irrigation event and are assumed to produce the most accurate results among volume balance based procedures. They have the disadvantage of requiring surface volume determinations, which may be difficult to obtain in practice under many field conditions. This study contrasts infiltration solutions from optimal and a simpler postirrigation volume balance method and examines the implications of those solutions on the performance of management strategies with zero-slope and low-gradient basins. With those types of systems, there is little benefit in using optimization over postirrigation volume balance due to the nonuniqueness of solutions and uncertainties of inputs required by the estimation procedures. In addition, system hydraulic characteristics mitigate the insensitivity of the distribution uniformity to reasonable variations in infiltration characteristics from those assumed in the analysis. For the type of systems considered here, management can be optimized based on time needed to infiltrate a target depth, even if the infiltration function parameters are uncertain.     

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.     

Multilevel Calibration of Furrow Infiltration and Roughness

A stepwise multilevel scheme is developed to sequentially calibrate infiltration and roughness parameters for free-draining furrow irrigation systems. The scheme is one dimensional at each level, thereby simplifying computations and providing more robust and unique solutions using field data which exhibit variation. The scheme is easily programmed and implemented within any kinematic wave, zero inertia, or hydrodynamic analysis and will provide straightforward initiation and convergence. Applications to two comprehensive data sets are made and shown to be substantially more accurate and extensive than traditional two-point fitting algorithms. In addition to the field length and slope, the flow cross section, and the duration of the irrigation, the multilevel model only requires measurements of the inflow and outflow hydrographs. Field data collection is therefore simpler than required for traditional methods which require spatial and temporal advance and recession measurements.     

Field Verification of Two-Dimensional Surface Irrigation Model

A two-dimensional (2D) model of unsteady shallow-water flow in surface irrigation was developed to evaluate the influence of field-grading precision on surface irrigation performance. This paper presents field data for verification of this 2D model. No attempt was made here to evaluate irrigation performance. Verification of such models relies on independent estimates of parameters for infiltration and roughness. To accomplish this, water surface elevations were measured at 26 points within a 3 ha level basin. A double-bubbler system was used to obtain relative water depths. Field surveys were used to convert these to water surface elevations and field water depths, from which surface water volumes over time were computed. The infiltration function was determined by matching inflow minus surface volume over time with computed subsurface volume. A value of Manning n (0.05) was found for which advance and water depth hydrographs were both well predicted with the 2D model. Differences in advance for a plane versus undulating field surface were minor, except near the end of advance.     

Physically Based Model for Simulating Flow in Furrow Irrigation. I: Model Development

Researchers developed several mathematical models for simulating furrow irrigation using the Saint-Venant equations. Most of these irrigation models use numerical techniques to solve these equations, which in general, require extensive programming and computational skills. Moreover, several of these models consider uniform soil and use empirical equations for modeling infiltration. In this article, a physically based furrow irrigation model was presented for simulating flow in irrigated furrows under both uniform and layered soils. The model consisted of an overland flow and an infiltration module that are modeled using analytical solution of the zero-inertia and the Green and Ampt [one-dimensional and two-dimensional infiltration equations) equations, respectively. Furthermore, the infiltration was also modeled using the Kostiakov-Lewis infiltration equation. The model considered all possible furrow shapes and included graphical user interface. The developed model was evaluated using the field data and the model performance was discussed in the second part of the article.     

Physically Based Model for Simulating Flow in Furrow Irrigation. II: Model Evaluation

In this study, the physically based furrow irrigation model presented in Part 1 was evaluated using the experimental data collected from a field plot consisting of three 40-m-long free-drained furrows of parabolic shape and having a top width of 0.30 m, a depth of 0.15 m, and a slope of 0.5%. The irrigation experiments were carried out with a constant inflow of 0.2–0.5ls?1 and 0.3–0.7ls?1 on bare and cropped fields, respectively. The field data pertaining to furrow cross section, advance and recession times, water depth and velocity, and runoff rate and volume were collected from the irrigation experiments. The model performance was studied for simulating advance, recession, infiltration, and runoff using two–dimensional (2D) Fok, one–dimensional (1D) Green-Ampt, and KL infiltration functions (Part 1) by estimating the root mean square error and index of agreement (Ia). For all the irrigations performed under bare and cropped furrow conditions, the model slightly overpredicted the advance time and runoff rate and slightly underpredicted the recession time and infiltration using the 2D Fok, 1D Green-Ampt, and KL infiltration functions. Furthermore, simulated results were closer to their observed counterparts for 2D Fok infiltration function than for 1D Green-Ampt and KL infiltration functions. Sensitivity analysis was carried out to study the effect of ±5 and ±10% change in 2D or 1D infiltration parameters (i.e., Ks and Sav) and KL infiltration parameters (i.e., Ak and Bk) on outputs. Ks is the most sensitive parameter for predicting advance time, infiltration, and runoff followed by Sav. In the KL infiltration parameter, Bk is the most sensitive parameter for estimating advance and recession times, infiltration, and runoff. The test results of the model suggested that the model can be used as a tool for designing and managing furrow irrigation.     

Infiltration under Variable Ponding Depths of Water

Cumulative infiltration was computed as a function of time-varying ponded water depths using a Green and Ampt analysis. The input water depths were field-measured values from two irrigation events on Superstition sand, one from a basin and one from a border. For both types of irrigation, the computed cumulative infiltration at a given measuring station was nearly the same whether using a variable head input or a constant (average) head during the time of opportunity. As an example, at the first measurement station for the basin event, the ponded depth went from a 0 to 9 cm depth over the 2–12 min. from the time water was introduced into the basin; this was followed by a decrease to a depth of 4 cm at 60 min. The computed infiltration using the depth hydrograph was 14.3 cm compared to 14.1 cm when using an average depth. A smaller value of 13.7 cm is found using the appropriate time of opportunity with a field averaged depth and a considerably smaller value of 12.4 cm was found when a zero-depth boundary is considered. Basin and border uniformities were also computed based on variable and different constant depths and the results were found to be reasonably robust whether infiltration is computed using a variable or an appropriate constant ponded depth.     

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.     

Green-Ampt One-Dimensional Infiltration from a Ponded Surface into a Heterogeneous Soil

Saturated hydraulic conductivity and wetting front pressure head (as soil properties) on an abrupt Green-Ampt front are assumed to increase and decrease with depth of a porous heterogeneous soil subject to a constant ponding or infiltration-evaporation depleted ponding on the surface. The corresponding Cauchy problem for a nonlinear ordinary differential equation describing the wetting front propagation in the soil profile is solved by computer algebra routines. Sensitivity of the cumulative infiltration to variation of hydraulic conductivity and capillarity is studied. A concave-convex infiltration graph is obtained for some values of parameters of the assumed exponential growth/decay of conductivity/capillarity. Texture of soil samples collected from a pedon is used for calculation of conductivity from a pedotransfer function. Synthesis of heterogeneity resulting in a specified front dynamics is discussed.     

Maintaining Equity in Surface Irrigation Network Affected by Silt Deposition

Planning maintenance activities in surface irrigation systems is essential for optimal use of the annual credits. In many countries, the equity of the water distribution is largely affected by sediment deposition but budgets do not allow the performance of all the necessary maintenance works and priorities must be defined by the irrigation agencies. A methodology based on numerical modeling is developed and illustrated on a secondary network in South Pakistan. Improvements on the current desilting procedure are proposed, but it is shown as well that the system could be designed differently in order to preserve the equity longer.     

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.     

Validation of a Predictive Form of Horton Infiltration for Simulating Furrow Irrigation

Due to spatially varying conditions the improvement of furrow irrigation efficiency should be sought not just for a limited number of furrows or for one specific irrigation event. A simplified predictive modeling approach of the averaged advance-infiltration process is proposed in this paper. Horton’s equation, derived from the asymptotic form of the Talsma-Parlange infiltration equation, allows us to use a predictive approach for the advance infiltration process by means of the exact solution of the Lewis and Milne water balance equation. The references to the works of White and Sully, for a surface point source, result in the use of parameters which characterize the hydraulic properties of the soil: Δθ (saturated water content minus initial water content); Ks (saturated conductivity); and λc (macroscopic capillary length). The physical meaning of parameters involved in the proposed modeling is attested using field experiments carried out in a loamy soil plot context. Assuming a same Δθ measured value before irrigation for the whole of a 30 furrow sample, the averaged values of λc and Ks obtained from calibration on the advance trajectory are comparable to those derived from local infiltration tests (disk permeameter and double ring methods). The applicability of the model is then extended to heavy clay soil where the parameters λc and Ks still agree with the values proposed in the literature. This paper can be considered as a contribution to the development of a tool for evaluating the impact of irrigation practices on the efficiency at the plot and cropping season scale.     

Estimation of Unsaturated Hydraulic Parameters from Infiltration and Internal Drainage Experiments

Inverse problem of determining unsaturated soil hydraulic properties from transient infiltration and internal drainage events are analyzed. Hydraulic properties are assumed to be described by van Genuchten’s relationships. The inverse problem is solved using Levenberg-Marquardt method while the forward problem is solved using a mass conservative finite difference numerical scheme. The bias induced by different objective functions on the parameter estimates with error free and noisy data are analyzed. Field experiments are conducted at two sites to compare the parameter estimates obtained from the infiltration and internal drainage tests. The results indicate that some objective functions induce undue bias in the estimated parameters in the presence of noise in the data and as such selecting a suitable objective function should be given due importance in the parameter estimation. The comparison of the parameter estimates from infiltration and internal drainage experiments at two sites indicates that the parameter estimates are close to each other. It is concluded that infiltration experiment, which is simpler and of short duration can be an alternative to internal drainage experiment for estimating the unsaturated soil parameters.     

Modified Kostiakov Infiltration Function: Accounting for Initial and Boundary Conditions

The effect of specific initial and boundary conditions is generally not considered when applying the Kostiakov infiltration functions. A methodology is developed to account for changes in water levels and initial soil moisture. First, Richards’ equation is solved numerically to generate a database of one-dimensional infiltration values, with varying initial (water content or pressure head) and boundary (ponding depth) conditions for three contrasting soils. These are then used to calibrate corresponding coefficients for modified Kostiakov models and, by considering linear regressions, to obtain simple correction factors. Results show that the correction factors are not universally valid, and only the correction to the Kostiakov k parameter shows statistically consistent applicability. However, examples demonstrate potentially significant improvement in the accuracy of irrigation models by correcting the Kostiakov equation to account for initial and boundary conditions.     

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.     

Spatial and Temporal Variation of Manning’s Roughness Coefficient in Furrow Irrigation

Manning’s roughness coefficient is one of the input parameters in many surface irrigation simulation models. It affects the velocity of flow and thereby its variation with time and distance along the field length influence water application. In this study, variation of Manning’s roughness coefficient was studied for a furrow plot consisting of three 40 m long free drained furrows of parabolic shape and having a top width of 0.30 m, a depth of 0.15 m and a slope of 0.5%. The irrigation experiments were carried out with the inflow rates of 0.2, 0.3, 0.4, and 0.5?L?s1; and 0.3, 0.4, 0.5, 0.6, and 0.7?L?s?1 under bare; and cropped field conditions, respectively. Furrow cross-section data were collected before each irrigation event at 0.5, 13, 26 and 39.5 m from the head end along the center furrow using a profilometer. During the irrigation event, water depth and velocity of flow were measured at these locations at an interval of 15 min using point gauge and color dye, respectively. The furrow cross-section data were fitted into a second-degree polynomial equation to determine the furrow shape parameters that were used along with the flow depth data for determining the wetted area and wetted perimeter. The wetted area, wetted perimeter, and the velocity data were used to estimate Manning’s roughness coefficient spatially and temporally. It is found that for both bare and cropped field conditions, Manning’s roughness coefficient was more at second and last quarter of the furrow due to soil erosion at these locations. Manning’s roughness coefficient at these locations varied from 0.019 to 0.022 and 0.015 to 0.018 for bare field whereas from 0.02 to 0.024, and 0.019 to 0.022 for cropped field, respectively. The temporal variation of Manning’s roughness coefficient for both bare and cropped furrow conditions decreased with the elapsed time. However, these decreasing trends were observed more for lower inflow rates. Further, the average Manning’s roughness coefficient for the subsequent irrigations was varied from 0.018 to 0.02 and from 0.019 to 0.0245 for bare and cropped conditions, respectively. Thus, the values of Manning’s roughness coefficients were more for cropped furrow conditions than for bare furrow.