Simulation of furrow irrigation using the Slow-change/slow-flow equation

A furrow irrigation model is developed based on the Slow-change/slow-flow routing equation, which is an approximate reduced form of the Saint-Venant equations to a single equation with a single variable, the upstream volume of water. For downstream-propagating disturbances it can be shown that the only approximation is that the rate of change of upstream inflow is small, with no limit on Froude number, so that it can be used for all slopes. It can also be used with all common end conditions. To calculate resistance to flow a composite model in terms of almost any boundary roughness is proposed. Infiltration is assumed to follow the Kostiakov formula. The equation was solved numerically using explicit Euler and implicit Crank–Nicolson schemes. Seven furrow-field data sets were used to verify the model simulation of advance and recession trajectories and runoff. In all cases examined, the model predictions were in good agreement with field data and results from existing software. The proposed model can provide a suitable and simple numerical simulation tool for design and evaluation of furrow irrigation for all bottom slopes and boundary conditions.

► Introducing the concept of upstream volume leads to a single routing equation and enables the incorporation of any common boundary condition.
► A resistance equation is proposed for arbitrary boundary roughness.
► Explicit and implicit computational schemes are developed.
► The model was applied to the simulation of furrow irrigation with infiltration.
► Results from the model were compared with several field studies and it performed well.