Analytical Solution for Normal Irrigation Distribution Parameters
Publication: Journal of Irrigation and Drainage Engineering
Volume 127, Issue 1
Abstract
The model most widely used to represent sprinkler irrigation distribution parameters is based on numerical solutions to the normal cumulative probability density function. For most practical irrigation design and management applications, numerical solutions are too laborious. One other study reported analytical approximations for several irrigation distribution parameters derived from the normal model. The estimation error resulting from those approximations were variable over the operational range of irrigation uniformity and irrigation adequacy and were quite high in some ranges. In this note, more accurate analytical approximations are presented for the distribution coefficient, the application efficiency, the water requirement efficiency, the deficiently irrigated volume, and the average deficit over the deficiently irrigated area. On average, over the entire operational range of irrigation uniformity and irrigation adequacy, the new approximations are about an order of magnitude more accurate than the previous approximations and introduce negligible error for most practical applications.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A., eds. ( 1968). Handbook of mathematical functions, Nat. Bureau of Standards Appl. Mathematics Ser. No. 55, U.S. Government Printing Office, Washington, D.C.
2.
Hart, W. E. ( 1961). “Overhead irrigation pattern parameters.” Agric. Engrg., 42(7), 354–355.
3.
Hart, W. E., and Reynolds, W. N. ( 1965). “Analytical design of sprinkler systems.” Trans. ASAE, 8(1), 83–85, 89.
4.
Heermann, D. F., Duke, H. R., Serafim, A. M., and Dawson, L. J. ( 1992). “Distribution functions to represent center-pivot water distribution.” Trans. ASAE, 35(5), 1465–1472.
5.
Ramberg, J. S., and Schmeiser, B. W. ( 1972). “An approximate method for generating symmetric random variables.” Communications of the Assn. for Computing Machinery, 15(11), 987–990.
6.
Walker, W. R. (1979). “Explicit sprinkler irrigation uniformity: Efficiency model.”J. Irrig. and Drain. Div., ASCE, 105(2), 129–136.
7.
Warrick, A. W. (1983). “Interrelationships of irrigation uniformity terms.”J. Irrig. and Drain. Engrg., ASCE, 109(3), 317–332.
Information & Authors
Information
Published In
History
Received: Dec 6, 1999
Published online: Feb 1, 2001
Published in print: Feb 2001
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.