A numerical kinematic wave model for border irrigation

Jain, Sharad K.; Singh, Vijay P.

doi:10.1007/bf00257491

Cited by 4 publications

(1 citation statement)

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“…Chen (1970), Smith (1972) and Cunge and Woolhiser (1975) were among the first to apply the kinematic wave theory to model some aspects of flow in irrigation borders. Singh (1978, 1982), Singh and Ram (1983) and Jain and Singh (1989) presented a complete mathematical treatment of the irrigation cycle based on the kinematic wave theory and showed that the theory was sufficiently accurate for irrigation modelling. In a study on errors in the kinematic wave solution by comparison with the full dynamic wave solution in irrigation borders and channels, Reddy and Singh (1994) and Singh (1994a, b, c) found the kinematic wave approximation to be reasonably accurate.…”

Section: Application In Irrigation Hydrologymentioning

confidence: 99%

Kinematic wave modelling in water resources: a historical perspective

Singh

2001

Hydrological Processes

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Abstract:The history of the kinematic wave theory and its applications in water resources are traced. It is shown that the theory has found its niche in water resources and its applications are so widespread that they may well constitute what may be termed 'kinematic wave hydrology'. Few theories have been applied in hydrology and water resources as extensively as the kinematic wave theory. This theory, however, is not without limitations and when it is applied they must be so recognized.

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Section: Application In Irrigation Hydrologymentioning

confidence: 99%

Kinematic wave modelling in water resources: a historical perspective

Singh

2001

Hydrological Processes

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Modeling and error analysis of kinematic-wave equations of furrow irrigation

Reddy

Singh

1994

Irrig Sci

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A moving control volume approach was used to model the advance phase of a furrow irrigation system whereas a fixed control volume was used to model the nearly stationary phase and the runoff rate. The resulting finite-difference equations of the kinematic-wave model were linearized and explicit algebraic expressions were obtained for computation of advance and runoff rate. The solutions for the advance increment and the runoff rate were compared with the nonlinear scheme, the zero-inertia model, and a set of field data. A close agreement was found between the models and the field data. Assuming a constant infiltration rate, a differential equation was derived to estimate the error between the kinematic-wave model and the zero-inertia model in predicting the flow cross-sectional area along the field length. The differential equation and two dimensionless terms were used to define the limits for use of the kinematic-wave model in furrow irrigation.The kinematic-wave model has become a useful tool for computing flow in surface irrigation (border and furrow irrigation) and has proved to be fast and accurate for sufficiently sloping conditions. An analytical solution for the wave equation can be obtained when the infiltration rate is constant. Since the infiltration rate changes very rapidly, at least during the advance phase, the solutions based upon constant infiltration rate are not appropriate for design and analysis of surface irrigation systems. Several numerical techniques are available to solve the kinematic-wave equations. Smith (1972) applied a finite-difference technique and the method of characteristics to solve the kinematicwave equations of border irrigation during the advance phase. Walker and Humpherys (1983) (1989) solved the kinematic wave equations of surface irrigation using a finite-difference method along with the Newton-Raphson iterative scheme. This technique might converge slowly under some circumstances. Here, a linearization scheme that Strelkoff and Katopodes (1977) used is applied to solve the nonlinear equation, both during the advance and the stationary phases, directly. Since the depletion and the recession phases are, in general, insignificant in furrow irrigation, they are not considered in this paper.The designer is often faced with the additional problem of choosing an appropriate model to use considering its limitations. Adequate data are not available on the range of applicability of the kinematic-wave equations in surface irrigation, and on the resulting error in using the model. Therefore, the objectives of this paper are to present the results of a comparative study of the linear and nonlinear schemes used to solve the kinematic-wave equations, to test the range of applicability of the KW equations in surface irrigation modeling and design, and to present an error equation that could be used to estimate the spatial variation in error in using the kinematic-wave model as compared to the zero-inertia model. Kinematic-wave equationsThe continuity equation for gradually varied, uns...

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