Shape factors for elements of the infiltration profile in surface irrigation:Generic approach

Authors: Strelkoff, Theodor; Clemmens, Albert; Bautista, Eduardo

Submitted to: Journal of Irrigation and Drainage Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/24/2011
Publication Date: 4/1/2012
Citation: Strelkoff, T., Clemmens, A.J., Bautista, E. 2012. Shape factors for elements of the infiltration profile in surface irrigation: Generic approach. Journal of Irrigation and Drainage Engineering. 138(5):485-488.

Interpretive Summary: Experience has shown that poorly designed and/or operated surface-irrigation systems suffer from excessive deep percolation, wasting water and potentially degrading the ground water, as well as excessive runoff, with contaminants detrimental to the receiving water bodies. Simulation models of the surface irrigation process have been developed to help optimize the design and operation of poorly performing systems. Irrigation simulation models are based on mathematical expressions of the physical laws governing the process coupled with empirical relationships. The governing equations cannot be solved analytically, and thus the accuracy of the simulation models depends partly on the numerical techniques used to generate the solution. Numerical solutions of the irrigation equations present particular challenges because of the curvature of the infiltration profile. Techniques currently in use to integrate the governing equations have been noted to produce errors such that the applied volume does not match the sum of runoff, infiltrated, and surface volumes. This technical note presents an alternative method for describing the curvature of the infiltration profile in numerical calculations that can reduce the magnitude of the volume balance errors. This information should be of interest to hydraulic engineers and other researchers working in related surface-subsurface flow problems.

Technical Abstract: Advanced mathematical models of surface irrigation are based on the equations of motion applied to a series of cells comprising the surface stream and an infiltration profile. In the simulation, a mass balance must be preserved amongst the inflow, surface stream, infiltrated profile, and runoff volumes. The shapes of the profiles are not known a priori; yet the curvature of the element boundaries influences the calculation of the volume contained therein – especially near the front of the irrigation stream. This note focuses on the shape of the subsurface volume elements comprising the infiltration profile. Previous calculations of shape factors documenting departures from assumed first-order approximations (trapezoidal shapes) have been based on empirical equations selected to describe infiltration as a function of wetting time. Modern simulations are not always based on empirical formulas, but increasingly rely on solutions of physically based approaches like Green-Ampt or the Richards equation. These solutions provide tabulated values, only, of infiltration and infiltration rates along the profile. The proposed generic approach calculates shape factors for each cell of the profile based on the calculated change in infiltration rates on the two sides of the cell.