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

The rainfall intensity-duration-frequency data
obtained from Weather Bureau Technical Paper Nos.
25 and 40 can be used for this computation,

Duration of rainfall, l,t

Although the rainfall duration, td, of an actual
storm can be almost any length of time, the design td
of a synthetic hyetograph may be assumed to be the
one that produces the maximum runoff from a given
highway drainage area which consists of a number of
elemental urban highway watersheds, as described
previously_ For a storm of uniform intensity. the
maximum runoff happens at the time of
concentration, t , at which all parts of the drainage
area may contrifiute to the flow concurrently at the
outlet of a storm sewer system. However, for a storm
having time- or space-varying intensities, the
preceding statement is no longer true. Even under a
uniform-intensity storm, the strict determination of
the te value is very difficult because te depends on
both the meteorological and physiographical factors
involved in the rainfaU-runoff process on the given
drainage area as well as the hydraulic characteristics
of a storm sewer system under study. Many methods
(see, e.g. Jens and McPherson, 1964) are available in
urban hydrology for evaluating the te that includes
the time of lot runoff; time of flow in gutters, open
swales, or channels to an inlet; and time of flow in
the storm drain. However, they are not further
discussed herein because it is beyond the scope of the
present study.

In an actual storm, td may be greater than,
equal to, or less than te. However, for design
purposes, it may be more appropriate to set

td <: tc ..............,.,......... (23)

since td < te yields a smaller peak discharge at the
inlet.

Pattern skewness, l'

Theoretically, the l' value of a design storm
pattern should be evaluated on the basis of the same
criterion as used in the determination of the td value.
In other words, the design l' value must be such that
the design storm pattern, if applied as an input to the
surface runoff computation, will produce the
maximum runoff from a given drainage area. The
most practical, if not the best, way to determine the
l' value is thus to maximize the computed runoff
discharge by using the surface runoff model subjected
to an excitation of the design hyetograph (Eqs. 12
and 13 for +b and Eqs. 18 through 20 for -b) with
various assumed values of 1'. It is conceivable that the
l' value so determined for geometrically different
drainage areas at the same meteorological locality
may be different even though the a, b, and c values

used in the hyetograph equations are exactly the
same. Conversely, if a drainage area (or te) is given
such as in the present case of an elemental urban
highway watershed, the l' value so determined
depends on the a, b, and c values and hence on the
frequency of a design storm. This unique feature of
the design l' value cannot reflect in the computation
based solely on rainfall records,

The determination of the l' value based on the
design criterion of the maximum runoff would give
the joint occurrence of a rainfall intensity of low
probability and a pattern of low probability (Pilgrim
and Cordery, 1975), From the engineering point of
view, it would be too conservative to use such "y
value. Because an actual storm pattern is a
meteorological phenomenon resulting from the
interaction of meteorological and physiographical
variables relevant to the study basin, the runoff
computation and hence drainage design based on the
'Y value determined from rainfall records alone may
be acceptable,

The "f value determined from the maximum
runoff criterion will be included in another phase of
this research project and it is not further treated
herein. Instead, the l' values will be computed
directly from actual rainfall records for both selected
ARS experimental watersheds (ARS Black Book
Series, 1933-1967) and two urban highway
watersheds in the Salt Lake City area (Fletcher and
Chen, 1975).

Normalized (Dimensionless)
Hyetograph Equations

For gaining an insight into the significant
parameters that control the design hyetograph, Eqs,
10 through 20 are further normalized, The
normalizing quantities selected in the case of +b are
ro = albe, the maximum intensity in the hyetograph,
and t = td and those in the case of -b are r 0 =
(afbe)1(1 - c)/(1 + c)] e, also the maximum intensity
in the hyetograph, and to = td. The normalized
hyetograph equations for +b are obtained as follows:

(1) For 1'= 0
r.~b),C [(1-c)t.+(b/ld)]

~dJ [I. + (b/ld)] 1 + c

O=" t. =" 1",. . ' . . . , . . . . . . . . . , . . . . (24)

in which r. = rlro Is the normalized rainfall intensity
and t. = tlto is the normalized time.

(2) For 1'= 1

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