Development of Simplified Solutions for Modeling Recession in Basins

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.