Although surface irrigation is perceived to have low irrigation efficiency, more or less 7% of the water resources in South Africa are still used to practise surface irrigation. The design of surface irrigation requires the combination of 7 to 10 interrelated variables on a given soil. Previous studies indicated that data from measured and simulated irrigation events could be analysed to reflect useful trends, which could be used to optimize surface irrigation design.
The aim of this study was to develop methods to generate boundary values for surface irrigation design in South Africa.
This was an analytical study, where multiple regression techniques were used to develop two new mathematical models which can predict boundary values for surface irrigation design.
From literature and previous unpublished research this study was planned to generate intersecting trend lines from simulated irrigation event data, in the following three categories:
■ Primary trends, analysed from the rate of recession of irrigation water (Yielding an optimized relationship between application and border length).
■ Secondary trends, from the analysis of the energy available for flow, during advance (Yielding maximum border length, application efficiency and cut off management detail).
■ Tertiary trends from criteria developed to set boundary conditions for nonviable-, undesirable - and invalid design solutions for surface irrigation (Yielding boundary values for design).
These trend lines were presented graphically or mathematically to form nodes where they intersect. These nodes define the position (or address) of data points, where data, simulated with hydrodynamic models to quantify irrigation events, are available. By fitting lines, curves and equations to the data at these nodes, mathematical models were developed and boundary values could be calculated.
The characteristics of irrigation bed behaviour during recession, the energy available for flow during advance and the sensitivity of the system to the management of the cut off of water supply, were investigated and documented in detail. Criteria were developed to define boundary conditions for nonviable-, undesirable - and invalid design solutions. Two new mathematical models were developed to calculate maximum length and predict the application efficiency.
Conclusions and recommendations
The strategy to generate irrigation event detail at nodes, by means of hydrodynamic simulation, gave good results. The development of criteria for boundary conditions and of new mathematical models to fit simulated values proved that the research was successful.
The development of analytical methods to calculate application efficiency and maximum field length are an international breakthrough. The concept is unique and allows the designer to visualize the effect of different design combinations. This result will pave the way to reconcile Empirical Design norms with the results from Hydrodynamic
Simulation models. Future research should validate these results statistically and incorporate it in a new version of the OPTIVLOED design programme.||