National Institute for Water Resources, Water Resources Research Institute Program
3/1/2006 - 8/31/2008
The establishment of the rainfall-runoff relationship of a watershed is an important and difficult problem in applied hydrology. The rainfall-runoff relationships of Hawai‘i watersheds are even more difficult to establish than most because Hawai‘i watersheds tend to have steep slopes, small drainage areas, and a high infiltration rate. Currently, the simple rational formula is used for urban drainage design in Hawai‘i and the more sophisticated unit-hydrograph method is used for the design of large flood-control facilities.
The unit-hydrograph method is based on linear systems theory (Dooge 1973). The system impulse response function of a linear system describes the overall system characteristics which affect the input-output relationship. The determination of the system response function of a particular system is called system identification. By the unit-hydrograph method a watershed is taken as a linear system. Its input function is effective rainfall, its output function is direct runoff, and its system response function is called instantaneous unit hydrograph (IUH), which is the direct runoff generated by the watershed system when it receive an input of unit-pulse-effective rainfall. After the IUH of a watershed is identified, direct runoff generated by future rainstorms in the watershed can be calculated by a convolution integration of IUH and rainfall input.
Similarly for waste-loading simulation, the impulse-response function can be called the instantaneous pollutograph (IPG), which is the temporal variation of pollutant concentration at the watershed outlet generated by the watershed system when it receives an input of unitpulse- effective rainfall. The waste loading at the watershed outlet can then be readily calculated as a product of direct runoff and pollutant concentration.
The principal objectives of this research were to 1) demonstrate the applicability of a linearsystems approach for flood and water-quality analysis for Hawaiian watersheds and 2) develop techniques for deriving IUH and IPG.