Development of Simplified Solutions for Modeling Recession in Basins
Publication: Journal of Irrigation and Drainage Engineering
Volume 134, Issue 3
Abstract
In irrigation basins the decrease in the gradient of the water-surface elevation following inflow cutoff often leads to reduced rate of convergence, increased computational time, and reduced robustness of the numerical solutions of the recession phase. As the water surface levels off, the underlying physical problem simplifies, thus allowing the use of highly accurate yet simple alternate solutions to the full-numerical solution of the zero-inertia equations. For level basins, the simplification involves treating the stream as a static pool, in which water level only falls in response to infiltration. Graded basins may require partitioning the stream into a flowing and static pool, before water-surface eventually levels off over the entire stream length. Implementation of these solutions enhances computational efficiency and robustness of surface irrigation models without a concomitant loss of accuracy. This paper discusses numerical problems related to the recession phase computation in basins and proposes simplified and robust, yet highly accurate solutions. A comparison of the recession trajectories and final infiltration profiles predicted by the full-numerical solution of the zero-inertia equations, obtained by using double-precision floating-point arithmetic, and the simplified alternate solutions, which is robust enough to be implemented over a range of hardware–software capabilities, show that the two approaches yield essentially identical results. Finally, the general validity of the proposed solutions is tested by comparing predictions of recession trajectories and infiltration profiles with those obtained using a surface irrigation hydraulic model, SRFR.
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References
Amein, M., and Chu, H. (1975). “Implicit numerical modeling of unsteady flows.” J. Hydr. Div., 101(6), 717–731.
Bazaraa, M., Sherali, H. D., and Shetty, C. M. (1993). Nonlinear programming: Theory and algorithms, Wiley, New York.
Bradford, S. F., and Katopodes, N. D. (2001). “Finite volume model nonlevel basin irrigation.” J. Irrig. Drain. Eng., 127(4), 216–223.
Clemmens, A. J., Strelkoff, T. S., and Playan, E. (2003). “Field verification of two-dimensional surface irrigation model.” J. Irrig. Drain. Eng., 129(6),402–411.
Cunge, J. A., Holly, F. M., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman, Marshfield, Mass.
Elliott, R. L., Walker, W. R., and Skogerboe, G. V. (1982). “Zero inertia modeling of furrow irrigation advance.” J. Irrig. and Drain. Div., 108(3), 179–195.
Katopodes, N. D., and Strelkoff, T. S. (1977). “Dimensionless solution of border irrigation advance.” J. Irrig. and Drain. Div., 103(4), 401–407.
Khana, M., Malano, H. M., Fenton, J. D., and Turral, H. (2003a). “Two-dimensional simulation model for contour basin layouts in southeast Australia. I: Rectangular basins.” J. Irrig. Drain. Eng., 129(5), 305–316.
Khana, M., Malano, H. M., Fenton, J. D., and Turral, H. (2003b). “Two-dimensional simulation model for contour basin layouts in southeast Australia. II: Irregular shape and multiple basins.” J. Irrig. Drain. Eng., 129(5), 317–325.
Liggett, J. A., and Cunge, J. A. (1975). “Numerical methods of solution of the unsteady flow equations.” Unsteady flow in open channels, K. Mahmood, and V. Yevejevich, eds., Vol. I, Water Resources Publication, Fort Collins, Colo.
Martin, J. L., and McCutcheon, S. T. (1999). Hydrodynamics and transport for water quality models, Lewis, Boca Raton, Fla.
The MathWorks Inc. (2002). Learning Math Lab 6.5. (Release 13), Natick, Mass.
The MathWorks Inc. (2006). Reliable computations, ⟨http://www.mathworks.com/access/helpdesk/help/toolbox/control/numerical/relcomp3.html⟩ (Mar. 1, 2007).
MathWorld. (1999). “Condition number.” ⟨http://mathworld.wolfram.com/ConditionNumber.html⟩ (Feb. 21, 2007).
Playan, E., Walker, W. R., and Merkley, G. P. (1994a). “Two-dimensional simulation of basin irrigation. I: Theory.” J. Irrig. Drain. Eng., 120(5), 837–856.
Playan, E., Walker, W. R., and Merkley, G. P. (1994b). “Two-dimensional simulation of basin irrigation. II: Applications.” J. Irrig. Drain. Eng., 120(5), 857–870.
Ponce, V. M., Indlekofer, H., and Simons, D. B. (1978). “Convergence of four-point implicit water wave models.” J. Hydr. Div., 104(7), 947–957.
Reklaitis, G. V., Ravindran, A., and Ragsdell, K. M. (1983). Engineering optimization: Methods and applications, Wiley, New York.
Singh, V., and Bhallamudi, S. M. (1997). “Hydrodynamic modeling of basin irrigation.” J. Irrig. Drain. Eng., 123(6), 407–414.
Strelkoff, T. (1985). BRDRFLW: A mathematical model of border irrigation, USDA-ARS, U.S. Water Conservation Laboratory, Phoenix.
Strelkoff, T., and Clemmens, A. J. (1994). “Dimensional analysis in surface irrigation.” Irrig. Sci., 15(2–3), 57–82.
Strelkoff, T., and Katopodes, N. D. (1977). “Border irrigation hydraulics with zero-inertia.” J. Irrig. and Drain. Div., 103(3), 325–342.
Strelkoff, T. S., Clemmens, A. J., and Schmidt, B. V. (1998). SRFR v.3.31. Computer program for simulating flow in surface irrigation: Furrows-basins-borders, U.S. Water Conservation Laboratory, USDA-ARS, Phoenix.
Strelkoff, T. S., Tamimi, A. H., and Clemmens, A. J. (2003). “Two-dimensional basin flow with irregular bottom configuration.” J. Irrig. Drain. Eng., 129(6), 391–401.
Walker, W. R., and Skogerboe, G. V. (1987). Surface irrigation: Theory and practice, Prentice-Hall, Englewood Cliffs, N.J.
Watkins, D. S. (1991). Fundamentals of matrix computations, Wiley, New York.
Utah State University Press. (1999). SIRMOD II: Surface irrigation simulation, evaluation and design, user’s guide and technical note, Logan, Utah.
Zerihun, D., Furman, A., Sanchez, C. A., and Warrick, A. W. (2003). “Calculation of recession in Basins and closed-end furrows: Problems and simplified solutions.” Proc., 2nd Int. Conf. on Irrigation and Drainage: Water for a Sustainable World Limited Supplies and Expanding Demand, U.S. Committee on Irrigation and Drainage.
Zerihun, D., Furman, A., Warrick, A. W., and Sanchez, C. A. (2005). “A coupled surface-subsurface flow model for improved basin irrigation management.” J. Irrig. Drain. Eng., 131(2), 111–128.
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© 2008 ASCE.
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Received: Nov 30, 2006
Accepted: Aug 16, 2007
Published online: Jun 1, 2008
Published in print: Jun 2008
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