FLOOD06389

• County: Statewide
• Community: State of Colorado
• Basin: Statewide
• Title: Urban Storm Runoff Inlet Hydrograph Study - Volume 4
• Date: 5/1/1975
• Prepared By: Cheng-lung Chen
• Floodplain - Doc Type: Flood Mitigation/Flood Warning/Watershed Restoration

SUMMARY AND CONCLUSIONS

The formulation of a synthetic hyetograph of
desired frequency and duration for an urban highway
watershed is essential to the successful design of a
storm sewer system which drains storm water
collected at all drainage inlets. The derived synthetic
hyetograph equations that also contain storm
frequency and duration can readily be built into the
surface runoff model for computing the inlet
hydrographs of corresponding frequency and
duration. For general use in engineering practice, a
simple graphical method was developed to evaluate
the storm parameters that characterize the rainfall
intensity -duration-frequency relationships at any
location in the United States.

The principal conclusions drawn from this
study may be summarized as follows:

I. The rainfall intensity-duration.frequency
relationships and a unified time.coordinate system
have been utilized to develop the generalized
synthetic hyetograph equations for all types of
storms. Three parameters, a, b, and c. which describe
the intensity-duration.frequency curves also control
the time distribution of rainfall in heavy storms. In
general, the hyetograph equations so formulated were
classified according to whether they are positive or
negative b. A brief analysis of rainfall data obtained
from the Weather Bureau Technical Paper Nos. 25
and 40 has indicated that the equation for positive b
mainly applies to a large section of the
country -perhaps to the portion east of the Rocky
Mountains-while that for negative b generally applies
to the west of the Rocky Mountains.

2. The storm parameters, a, b, and c, can
be evaluated by using the method of least squares and
an optimization technique similar to the method of
steepest descent for optimizing an unconstrained
problem. The rainfall intensity.duration.frequency
data obtained from the 49 isopluvial maps in the
Weather Bureau Technical Paper No. 40 may be used
for this computation.

3. A simple graphical method was developed to
evaluate the a, b, and c values without using all of the
49 isop1uvial maps in the Weather Bureau Technical
Paper No. 40. The method has been described in

detail in the section under STANDARD
INTENSITY.DURATlON RELATIONSHIPS. The a,
b, and c values so determined were found to be
compatible with those computed directly from the 49
isopluvial maps.

4. Analysis of the Technical Paper No. 40
reveals that the standard storm parameters, 31' hI (=
b), and Cj (= c), vary only with the ratio of l.hour to
corresponding 24.hour rainfall depth which is unique
for each location in the United States and
independent of frequency. On the other hand, the
storm parameter, a, which can be expressed in terms
of 31, depends upon return period, as shown in Eq.
45. Therefore, given the ratio of I.hour to
corresponding 24.hour rainfall depth and frequency,
the values of the storm parameters, a, b, and care
already fixed, leaving only pattern skewness ( "'I value)
yet to be determined from other means.

5. Normalization of the derived hyetograph
equations reveals that three dimensionless parameters,
b/ld, c, and "'I , control the storm pattern. The
parameters, b and c, are more or less Hstandardized"
for each location in the United States, while the other
parameters, td and "f, remain to be evaluated from
actual rainfall records. For a storm of uniform
intensity, td may take the time of concentration, tc '
which in actual storms is, of course, trivial.

6. The hyetograph equations so formulated
were used to best fit actual hyetographs. The
best.fitted a, b, and c values for an actual hyetograph
were determined by first arranging the hyetograph in
the order of intensity in a way similar to the
formulation of Eq. 6 and then computing the a, b,
and c values by means of the least squares to
minimize the objective function as shown in Eq. 22.
The "'I value was finally determined by minimizing
the expression shown in Eq. 61 for positive b or Eq.
62 for negative b. An analysis of major storms for six
selected ARS experimental watersheds and two Salt
Lake City urban highway watersheds revealed that
the "'I value so determined varied almost randomly
for each station studied. The establishment of any
relationships between "'I and the other storm
parameters did not look very promising. The
statistical mean "f value for each station could be
calculated, but it would be meaningless unless more
actual hyetographs for each station are analyzed.

47