Optimization of the furrow irrigation efficiency

Furrow irrigation is used for row crops. S.C.S., based on a great number of field experiments,
under different circumstances and soil families, has developed design equations for furrow
irrigation. These equations have been used for steady flow rate or for flow rate with one
reduction when the water reaches the end of the furrow. They can also be used for a small
period of time (time step) when the flow rate can assumed to be steady.
Many scientists, who dealt with furrow irrigation, try to improve the application efficiency by
investigation the importance of the parameters that influence the furrow irrigation. Slope,
furrow length, intake family have extensively been studied. Flow rate has been studied as
steady or with a cutback of flow when water has advanced to furrow end. This article studies
the influence of altering flow rate at furrow irrigation to application efficiency.
The steepest descent method is implemented for the optimisation at each time step flow rate.
Steepest descent method evaluates the derivative of the function, which has to be optimized
(application efficiency), to the parameter that is changing (flow rate). The derivative of the
application efficiency to flow rate is calculated analytically. The optimized application
efficiency is achieved when the derivative is zero, thus the value of flow rate is raised if the
derivative is positive or is decreased if the derivative is negative.
When the flow rate at each time step is optimised, the process begins again because the
optimisation for the flow rate of the initial steps didn’t take into account the optimized flow
rates of the later time steps. This process converges and estimates the optimised flow rate at
each time step.
The results of the optimisation for two samples are alike. The maximum application efficiency
is achieved by increasing the flow rate at the beginning of irrigation and before the water
reaches furrow end the flow rate must be decreased to the minimum value of flow rate that
fulfils instant infiltration.