The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time-area curve of a watershed by the S-curve method. The time-area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time-area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km2 watershed, using 1 km x 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km x 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time-area curve.
The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.