FLOOD05499

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

where ~ is the correction factor for K(z). and
l)I(z)-distributions and

~~~L .. 1 ( 0 d~(Z.t)
uz. L J (lz
-L
w

h(t) - lJIo
dz U L

(43)

where the bar over the variables represents average
values over Lw times the ratio of Lw to L (Lw>L);
h(t) ~ ponding water depth; and 1)10 ~ initial soil
capillary potential, equal to I)I(-Lw ,t), negative in
value, Substituting Eqs, 41, 42, and 43 into Eq, 39
yields

( . a K
R

h - ~
_3_

+ ,
,

for t ~ t
P

,(44)

L

It is noted that Nielsen, Biggar, and Erb (1973)
treated spatial variation in soil properties over an
areal extent by expressing average hydraulic con-
ductivity as a function of average soil water content.

In particular, at the saturation front (z ~ -Lf),
where the saturated and unsaturated zones meet and
1)1 ~ 0, as shown in Figure 12b, one can derive Eq, 16
or

Water surface z = h

z

e
o

e
s

h

e

Lf
____J__

L

z~ -L

Wetting front
z ~ -L
-_..:!!_--------

(a)

fr.K~+K
S Lf S

, . , , , , . ' , ,(45)

A comparison of Eqs, 44 and 45 reveals that
the correction factor, (j , cannot become unity unless
L ~ L( and 1)10= O. Equating Eqs, 38 and 44 gives

(6 - 6 ) dL , a K
s 0 dt s

h - 1/10
L

+ K - K
8 0

for t ~ tp' (46)

If h and ~ are constant, Eq. 46 becomes a first-order,
nonlinear ordinary differential equation in L(t) and
has the solution

t = t
P

6 - 0
. 0
+ K - K
. 0

(L - L )
P

S K
8

(h - .oH68 -
(K _ K )2
8 0

00)

loge

[(K.
(K
.

K )L + K (h - · ) J
o so>
K)L + SK (h _.) for t -
o p s 0

t (47)
p

z

Soil surface, z = 0

-1\1

(b)

Figur'i 12. Defmition sketch of rain infiltration after ponding with (a) soil moisture profiles and (b) soil cap.
iIIary potential profiles.

33