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. 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) = 403.33 cfs
坡地開發滯留池之水文設計
Hydrological Analysis for Detention
Pond Design in Hillslope
Development
坡地開發水文設計相關規範
現行設計規範之檢討
逕流量分析
(水土保持技術規範第 十七條 )

洪峰流量之估算，有實測資料時，得採用單位歷
線分析；面積在一千公頃以內者，無實測資料時，
得採用合理化公式(Rational Formula)計算。合理
化公式如下：
1
Qp 
CIA
360
式中，
Q ：洪峰流量
(立方公尺 / 秒),
p
C：逕流係數(無單位),
I：降雨強度(公釐 / 小時),
A：集水區面積(公頃。
)
滯洪設施規劃設計原則
(水土保持技術規範第 九十五 條 )
滯洪量之估算
(水土保持技術規範第 九十六 條 )