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

r. =~~ y

[(1 - c)(l - I.) + (b/ld)]
[(I . t.) + (b/td)] I + c

o S t. S I.,..........,...,...... (25)

(3) ForO< -y < 1

r.=~: )c

((I - c)(1 - I.h) + (b/ld)]
[(1 - I.h) + (b/ld)] 1 + e

o S t. S -y...........'....."'.. (26)

r jb)C
. \id

((1 - c)(t. - -y)/(1 - -y) + (b/td)]
[Ct. - -y)/(1 - -y) + (b/ld)] I +c

I..,.,..... _.....,....... (27)

"I:S t*S

The following normalized hyetograph equations
for -b are derived by normalizing Eqs, 14 through 20.

(1)For-y=O

r. = I t.S I ~ e (I: )........... (28)
L b \ C(l + ) e [(1 - c)t. - (b/td)]
r.=v/ 1 -~ [t.-(b/td)]l+C
t. 2: -2- (~) . . . . . . . . . . . . . . . . . . . (29)
1- c td
(2) For -y= 1

=~) c (l.!5.)C
r. ~d I - c

[(1 - c)(1 - t.) - (b/td)]
[(1 - t.) - (b/td)] 1 + c

Os t.S 1.2-(~) ............(30)
1 - c td

r.=1 1-r+(~djS t.S 1......(31)

(3) For 0 < -y < 1

Jb)C(I+ )c [(1-c)(1.t.h)-(b/ld)]
r. ~d 1 . ~ [(l _ t.h) _ b/ld)] I ... c

o S t. S -y - 12?c ( ~d ). . . . .. . . . . . . . . (32)

f* = 1

-y . I ~~ ( ~d) S t. S -y + ~ ( ;d)' (33)

j~)C (~) c
r. ~d 1 - c

[(1 - C)(I.. -y)/(1 - -y) - (bltd)J
1 +c
[Ct. - -y)/(1 - -y). (b/td)]

-y + 2(1 - 'Y) (~) S I. S I "...,.... (34)
--r:-c- I d

An inspection of Eqs, 24 through 34 reveals
that there are three dimensionless parameters which
control the storm pattern. They are b/td' c, and -y.
The -y value that indicates the position of the peak in
the hyetograph ranges from 0 to 1, but the ranges of
the other two values are unknown. There seems to be
no apparent physical meaning for b/td and ,c. For
illustration, Eqs. 26 and 27 for +b are plotted in Fig.
I for -y = 0.3 with various values ofb/td and c.lt can
be seen readily from Fig. I that the hyetograph is
uniform as c . 0 or b/td . 00. For given b and c
values, the storm pattern with b/td . 00 corresponds
to the one with td approaching zero. This implies that
as a first.order approximation a uniform design
hyetograph can be applied to a smaIl drainage area
which has a very short time of concentration, tc' In
this case, the -y value is no longer important.
However, when a drainage area and hence te under
consideration are larger and longer, respectively, the
position of the peak in the hyetograph (I.e., -y value)
becomes more important. In the limit as td .00 or
bit d. 0, r. becomes zero everywhere in the
hyetograph.

The fact that the parameter, a, is not one of the
controlling factors in the formulation of a storm
pattern, as manifested itself in the normalized
hyetograph equations, Eqs, 24 through 34, suggests
the possibility of "standardizing" for each location
the values of band c which do not seem to vary with
duration. This and other interesting aspects of de~
sign storms derived on the basis of the rainfall
intensity-duration-frequency relationships will be
further discussed in the following section,

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