Modelling of a dimensionless synthetic unit hydrograph

When use of a synthetic unit hydrograph on ungauged and non-comparable catc hments is required, a further complication is how to choose a suitable time -step to use. The computed time-step is rarely an integral multiplier or di vider of the rainfall time-step thus necessitating reanalysing the rainfall chart, at the new time-step. It would be easier if the time-step of the un it hydrograph could be expressed as a continuous function. In February 1995 there was a flash flood in mid-Eastern Botswana which resu lted in all gauges being washed away. The only available data were from upl and recording rain gauges from which the reconstruction of the flood hydrog raph had to be done. Use of a dimensionless synthetic unit hydrograph (DSUH ) was indicated. This is the first part of a two-part paper which involves analyticising (transforming a numerical/graphical function into a continuou s one i.e. rendering it analytical) the dimensionless unit hydrograph i.e. developing a piecewise/zonal continuous function of time vs. the runoff. A DSUH was piecewise modelled using usual statistical methodology and speci al mathematics software. In spite of having had to use several and basicall y different functions from piece/zone to piece/zone. the final goodness of fit was exceptional. Demonstrating the application results is shown in the unit hydrograph-based mathematical model which was developed to solve for t he above flood. This will be presented in a follow-up paper, which with dwe ll more on the hydrology of the exercise.