Nonuniform and Unsteady Solute Transport in Furrow Irrigation. I: Model Development
This article has a reply.
VIEW THE REPLYPublication: Journal of Irrigation and Drainage Engineering
Volume 136, Issue 6
Abstract
A cross-section-averaged advection-dispersion equation (ADE) model was developed to simulate the transport of fertilizer in furrow irrigation. The advection and dispersion processes were solved separately at each time step by implementing a method of characteristics with cubic-spline interpolation and a time-weighted finite-difference scheme, respectively. The upstream boundary condition was a prescribed concentration. Downstream, a zero-flux boundary condition during advance and a concentration gradient following completion of advance were prescribed. Local pseudosteady state was assumed in order to apply Fischer’s longitudinal dispersion equation under nonuniform and unsteady furrow flow conditions. Statistical parameters were used to evaluate the ADE model performance.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research received support from USDA-CSREES-NRI Competitive Grant No. UNSPECIFIED2001-35102-10218. The writers would like to thank Dr. Dawit Zerihun, Dr. Peter Waller, Dr. William F. Ritter, and anonymous reviewers for helping to improve the manuscript. Also, we appreciate the support from Carl Arterberry, Don Powers, and Clint Jones of the U.S. Water Conservation Laboratory, Phoenix, in preparation and conduct of the field tracer experiment, and subsequent activities after that.
References
Abbasi, F., et al. (2003a). “Overland water flow and solute transport: Model development and field-data analysis.” J. Irrig. Drain. Eng., 129(2), 71–81.
Abbasi, F., Adamsen, F. J., Hunsaker, D. J., Feyen, J., Shouse, P., and van Genuchten, M. Th. (2003b). “Effects of flow depth on water flow and solute transport in furrow irrigation: Field data analysis.” J. Irrig. Drain. Eng., 129(4), 237–246.
Adamsen, F. J., Hunsaker, D. J., and Perea, H. (2005). “Border strip fertigation: Effect of injection strategies on the distribution of bromide.” Trans. ASAE, 48(2), 529–540.
Ahmad, Z., and Kothyari, U. C. (2001). “Time-line cubic spline interpolation scheme for solution of advection equation.” Comput. Fluids, 30, 737–752.
Boldt, A. L., Watts, D. G., Eisenhauer, D. E., and Schepers, J. S. (1994). “Simulation of water applied nitrogen distribution under surge irrigation.” Trans. ASAE, 37(4), 1157–1165.
Branski, J. M., and Holley, E. R. (1986). “Advection calculations using spline schemes” Proc., Water Forum '86, ASCE, Reston, Va.
Burden, R. L., and Faires, J. D. (2001). Numerical analysis, 7th Ed., Brooks/Cole, Australia.
Elder, J. W. (1959). “The dispersion of marked fluid in turbulent shear flow.” J. Fluid Mech., 5, 544–560.
Fischer, H. B. (1966). “Longitudinal dispersion in laboratory and natural streams.” Rep. No. KH-R-12, Div. of Engineering and Applied Science, California Institute of Technology. Pasadena, Calif.
Fischer, H. B. (1975). “Discussion of ’Simple method for predicting dispersion in streams’ by R. S. McQuivey and T. N. Keefer.” J. Envir. Engrg. Div., 101(3), 453–455.
Fischer, H. B., Imberger, J., List, J. E., Koh, R. C. Y., and Brooks, N. H. (1979). Mixing in inland and coastal waters, Academic, New York.
Fletcher, A. J. C. (2000). Computational techniques for fluid dynamics 1: Fundamentals and general techniques, Springer, Berlin.
García-Navarro, P., Playán, E., and Zapata, N. (2000). “Solute transport modeling in overland flow applied to fertigation.” J. Irrig. Drain. Eng., 126(1), 33–40.
Holly, F. M., Jr. (1975). “Two dimensional mass dispersion in rivers.” Hydrology Rep. No. 78, Colorado State Univ., Fort Collins, Colo.
Holly, F. M., Jr. (1985). “Dispersion in rivers and coastal waters—1. Physical principles and dispersion equations.” Developments in hydraulic engineering–3, P. Novak, ed., Chapter 1, Elsevier, London.
Holly, F. M., Jr., and Preismann, A. (1977). “Accurate calculation of transport in two dimensions.” J. Hydraul. Div., 103(11), 1259–1277.
Holly, F. M., Jr. and Usseglio-Polatera J. (1984). “Dispersion simulation in two-dimensional tidal flow.” J. Hydraul. Eng., 110(7), 905–926.
Karpik, S. R., and Crockett, S. R. (1997). “Semi-Lagrangian algorithm for two-dimensional advection-diffusion equation on curvilinear coordinates meshes.” J. Hydraul. Eng., 123(5), 389–401.
Khan, L. A., and Liu, L. -F. P. (1998). “An operator splitting algorithm for the three–dimensional advection-diffusion equation.” Int. J. Numer. Methods Fluids, 28, 461–476.
Knott, G. D. (2000). Interpolating cubic splines, Birkhäuser Boston, Boston.
Komatsu, T., Holly, F. M., Jr., Nakashiki, N., and Ohgushi, K. (1985). “Numerical calculation of pollutant transport in one and two dimensions.” J. Hydrosci. Hydr. Eng., 3(2), 15–30.
Komatsu, T., Ohgushi, K, and Asai, K. (1997). “Refined numerical scheme for advective transport in diffusion simulation.” J. Hydraul. Eng., 123(1), 41–50.
Kreyszig, E. (1993). Advanced engineering mathematics, Wiley, New York.
Kvasov, B. I. (2000). Methods of shape-preserving spline approximation, World Scientific, Singapore.
Neuman, S. P. (2001). Numerical methods in subsurface hydrology (class notes), Hydrology and Water Resources Dept., The Univ. of Arizona, Tucson, Ariz.
Perea, H. (2005). “Development, verification, and evaluation of a solute transport model in surface irrigation.” Ph.D. dissertation, Ag. and Biosystems Engineering, Dept., The Univ. of Arizona, Tucson, Ariz.
Playán, E., and Faci, J. M. (1997). “Border fertigation: Field experiments and a simple model.” Irrig. Sci., 17, 163–171.
Rutherford, J. C. (1994). River mixing, Wiley, New York.
Schohl, G. A., and Holly, F. M., Jr. (1991). “Cubic-spline interpolation in Lagrangian advection computations.” J. Hydraul. Eng., 117(2), 248–253.
Smith, G. D. (1985). Numerical solution of partial differential equation, Oxford University Press, N.Y.
Stefanovic, D. L., and Stefan, H. G. (2001). “Accurate two-dimensional simulation of advective-diffusive-reactive transport.” J. Hydraul. Eng., 127(9), 728–737.
Strelkoff, T. S., Clemmens, A. J., and Perea-Estrada, H. (2006). “Calculation of non-reactive chemical distribution in surface fertigation.” Agric. Water Manage., 86, 93–101.
Strelkoff, T. S., Clemmens, A. J., and Schmidt, B. V. (1998). SRFR, Version 3.31—A model for simulating surface irrigation in borders, basins and furrows, U.S. Arid-Lands Agricultural Research Center, USDA/ARS, Maricopa, Ariz.
Taylor, G. (1953). “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proc. R. Soc., London, Ser. A, 219, 186–203.
Taylor, G. (1954). “The dispersion of matter in turbulent flow through a pipe.” Proc. R. Soc., London, Ser. A, 223, 446–468.
Tsai, T., Yang, J., and Huang, L. (2002). “Hybrid finite difference scheme for solving the dispersion equation.” J. Hydraul. Eng., 128(1), 78–86.
Tsai, T., Yang, J., and Huang, L. (2004). “Characteristics method using cubic-spline interpolation for advection-diffusion equation.” J. Hydraul. Eng., 130(6), 580–585.
Varga, R. S. (1962). Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N.J.
Vreugdenhil, C. B., and Koren, B. (1993). “Numerical methods for advection-diffusion problems.” Notes on numerical fluid mechanics, Braunschweig, Vieweg, Vol. 45.
Warrick, A. W. (2003). Soil water dynamics, Oxford University Press, Oxford, N.Y.
Watts, D. G., Eisenhauer, D. E., Ostermeier, K. A., Norton, M. J., and Schepers, J. S. (1994) “Fertigation by surge irrigation on blocked-end furrows.” ASAE Meeting, Paper No. 94-2066/94-2090 Presented at the 1994 International Summer Meeting of ASAE, ASAE, Kansas City, Mo.
Yanenko, N. N. (1971). The method of the fractional steps, Springer, New York.
Zerihun, D., Furman, A., Warrick, A. W., and Sanchez, C. A. (2005). “Coupled surface—Subsurface solute transport model for irrigation borders and basins. I. Model development.” J. Irrig. Drain. Eng., 131(5), 396–406.
Zheng, C., and Bennett, G. D. (2002). Applied contaminant transport modeling, Wiley, New York.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 136 • Issue 6 • June 2010
Pages: 365 - 375
Copyright
© 2010 ASCE.
History
Received: Aug 8, 2008
Accepted: Apr 17, 2009
Published online: May 14, 2010
Published in print: Jun 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.