A statistical approach to estimating runoff in center pivot irrigation with crust conditions

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Abstract

There have been several proposals to evaluate potential runoff in center pivot irrigation, through the integration of time varying infiltration–precipitation rate curves, involving complex iterative procedures. Some methods use empirical infiltration functions, such as the Kostiakov equation. Others use physically based infiltration functions, such as the Green–Ampt equation. Another option is to use the Richards equation, describing the one-dimensional vertical infiltration of water into the soil for a specified irrigation event. This equation is generally accepted to provide a basis for comparison between other runoff estimation methods.

[P.B. Luz, J.C. Martins, M.C. Gonçalves, Reliable estimate of runoff in center pivot irrigation: statistical approach, in: Proceedings of the 16 Congress Mondial de Science du Sol, Poster 2-658, ISSS, Montpellier, France, August 19–25, 1998, pp. 577–593], developed a conceptual method of statistical nature, to estimate potential runoff in center pivot irrigation, comprising regression equations built with runoff results from a simulation computer model using the Richards equation. The procedure to simulate runoff involved a wide set of data related to water retention parameters and soil texture [W.J. Rawls, D.L. Brakensiek, Estimation of soil water retention and hydraulic properties, in: H.J. Morel-Seytoux (Ed.), Unsaturated Flow in Hydrologic Modeling, Theory and Practice, Kluwer Academic Publishers, Dordrecht, 1989, pp. 275–300], and water application. Such regression equations present a dependent variable, defined as an index of four parameters, related to the center pivot irrigation and to the soil-water system evaluation. The method had unacceptable results when a crust developed on the soil surface. Therefore, the objective of this study was to redefine the index, establishing new parameter coefficients with a trial and error approach. The model efficiency (similar to the coefficient of determination, r2) ranged from 90 to 98%, showing the results are in good agreement to those computed by Richards equation, exhibiting a strong predictive value.

Introduction

Runoff control is an important factor in the successful design and operation of a center pivot irrigation system. Runoff is most likely to occur with high application rates, typical of popular developed low pressure systems, and where soils have a low intake rate.

Estimation of potential runoff generally demands an iterative numerical calculation relating an infiltration function to a center pivot precipitation pattern. Some authors base their runoff models on the empirical Kostiakov infiltration equation (Kincaid et al., 1969), or on physically based infiltration functions such as the Green–Ampt equation (Slack, 1980, von Bernuth, 1982). In current runoff approaches, mainly when integrated in irrigation conceptual models (Wilmes et al., 1993, Kincaid, 2001), many authors still utilize the referenced equations. As far as those equations and the Richards equation are in agreement, they assume that the infiltration capacity can be approximated as a simple function of cumulative infiltration regardless of the application rate versus time history (Skaggs et al., 1983). The Richards equation, for describing the one-dimensional vertical infiltration of water into soil, is a useful tool to provide a data-base for comparisons between runoff simulation models. Therefore, soil samples, many times presenting a large degree of spatial and temporal variability, are not needed.

Luz et al. (1998) developed a simple statistical method to estimate potential runoff based on the theoretical results derived by numerical solution of the Richards equation, for vertical water infiltration into soil. Soil hydraulic properties used as input data to the Richards equation were estimated using equations from Rawls and Brakensiek (1989). Initial procedures to build regression equations comprised a selection of the main parameters with impact on runoff. The objective was to avoid very large and complex equations, thus parameters with small impact on infiltration were not included. The evaluations from several studies, reported by Risse et al. (1994), pointed to precipitation (amount and rate) and hydraulic conductivity as the parameters with major impact on infiltration and runoff. The final statistical solution includes three linear regression equations, each for a defined soil-sand percent class. The parameters, within the independent variable, are related to the center pivot design, the irrigation management, the soil hydraulic characterization, and the initial soil water. This procedure provides a fast and reasonably accurate result using basic functions with a small hand held calculator.

Field tests data for validating the runoff statistical model clearly showed that soil crusts were present. This factor may cause a determinant reduction on the infiltration rate by up to 80% (Moore, 1981). Summer and Stewart (1992) present a detailed examination of the chemical and physical processes of soil crusting. Rawls and Brakensiek (1983), reporting relationships of crust saturated hydraulic conductivity, state that, in most cases, soil crusting is characterized with a modified infiltration equation and parameters related to the hydraulic properties of the soil crust and subcrust. In center pivot irrigation, Luz et al. (1997), observed runoff from 0 to 25% of the water application where minimum tillage was the selected soil conservation practice and no crust was formed. In ploughed silt loamy soils runoff increased up to 80% and a soil crust of 0.3 cm was observed. Dixon and Peterson (1971) developed a channel system concept of infiltration that described the profound influence of large soil pores on the movement on soil water and air. This would partially explain the differences in tillage and soil texture on infiltration. The design peak application rate and initial soil water content have a reduced affect on runoff. From field observations, Luz et al. (1998) suggested some changes in the statistical model, in order to decrease the weight of such parameters when a surface crust is formed. The objective of this study is to reformulate the linear regressions to estimate runoff with soil crust conditions. A sensitivity analysis on alternative values of the parameters in the independent variable was performed to modify the statistical model for crust conditions.

Section snippets

Procedures

The development of the statistical runoff model for crust conditions, involve several models, methodologies and assumptions presented here.

Results and discussion

According to charts and Table 1 proposed by Rawls and Brakensiek (1989), Brooks–Corey water retention parameters were taken from Table 2 as soil input parameters to solve the numerical solution of the Richards equation (GNFLUX program). A total of 21 soils were for simulated, comprising 17 (5 R1, 6 R2 and 6 R3 soils) for assumed theoretical soil conditions, plus 4 for data collected from field research plots (R1-4, R2-4, R3-4, R3-5). These were selected (Table 2) to redefine the index, X, to

Conclusions

A conceptual statistical model (runoff statistical model (RSM)), developed to estimate potential runoff under center pivot irrigation was adapted to soil crusting conditions. This initial potential runoff model was based on a runoff data-base obtained with a numerical solution of the Richards equation. The procedures in the development of RSM, involved a sensitivity analysis and a trial and error method to change exponents for the proposed model parameters. A set of tests (slope, average and

Acknowledgements

To M.L. Fernandes and V.M. Martins, from EAN-INIA for statistical modeling support.

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