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Hydrology Rainfall - Runoff Modeling (II) Synthetic unit hydrographs
Prof. Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

Synthetic unit hydrographs
For areas where rainfall and runoff data are not available, unit hydrograph can be developed based on physical basin characteristics. SCS unit hydrograph Clark’s IUH (time-area method) Linear reservoir model (Nash model)

SCS unit hydrograph

Misuse of SCS UH – an example

Clark’s IUH (time-area method)
The concept of isochrones Isochrones are lines of equal travel time. Any point on a given isochrone takes the same time to reach the basin outlet. Therefore, for the follwoing basin isochrone map and assuming constant and uniform effective rainfall, discharge at the basin outlet can be decomposed into individual contributing areas and rainfalls.

Contributing area and contributing rainfall

Using the basin isochrone map, the cumulative contributing area curve can be developed. The derivatives or differences of this curve constitute the instantaneous unit hydrograph IUH(t).

If the effect of watershed storage is to be considered, the unit hydrograph described above is routed through a hypothetical linear reservoir with a storage coefficient k located at the watershed outlet. For a linear reservoir with storage coefficient k, we have

Consider the continuity of the hypothetical reservoir during a time interval t.

Example. A watershed of 1000-acre drainage area has the following 15-minute time-area curve. The storage coefficient k of the watershed is 30 minutes. Determine the 15-minute unit hydrograph UH(15,t).

Area between isochrones t = 0 and t = 0. 25 hr is 100 acres
Area between isochrones t = 0 and t = 0.25 hr is 100 acres. Since we are interested in the unit hydrograph UH(15-min, t), the rainfall intensity in the time period (0.25 hr) should be 4 inch/hr. Therefore, the ordinate of UH(15-min, t) at time t = 0.25 hr is: 4 inch/hr  (1/12 ft/inch)  (1/3600 hr/sec)  100 acres  (43560 ft2/acre) = cfs

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