FLOOD05134

• County: Jefferson
• Community: Lakewood
• Stream Name: South Lakewood Gulch
• Basin: South Platte
• Title: Flood Hazard Area Delineation
• Date: 7/1/1977
• Prepared For: Lakewood
• Prepared By: UDFCD
• Contract/PO #: &&
• Floodplain - Doc Type: Floodplain Report/Masterplan

I

14

I

I

"The M.I.T. Catchment Model represents the physical movement of
water over the catchment surface and through the channel network
(Harley, 1970). The model recognizes that surface geometry is
extremely irregular and impossible (and unnecessary) to represent
in complete detail in either a physical or mathematical model. A
reductionist approach is used to replace the natural complexities
with a number of simple elements such as overland flow planes,
stream segments, pipe lengths, etc. A suitable combination of an
appropriate number of these simple elements is assumed sufficient
to model the behavior of an entire catchment."

"The kinematic wave equation for an overland flow segment is

I

2:t..+is.
at ax

(i - f) / 43200

(2)

I

q

=

CI YmC
c

(3)

I

I

"Streamflow'l

where y is the depth of flow (ft). q is the rate of flow (cfs/ft).
t is time (sec), x is distance along the segment (ft). is t:,e
rainfall intensity (in/hr) and f is the infiltration rate (in/hr).
In Eq. 2 both i and f may vary with x and t. The difference i -
f may be treated as an effective rainfall rate (which by convention
in hydrology is never negative), or the water remaining on the surface
when f exceeds i may be permitted to continue to percolate into the
soi 1. The fact that f may vary wi th x causes the model to simulate
runoff only from those locations where i exceeds f.

In the case of South Lakewood Gulch, only the streamflow routing elements
were used; this process is described below.

I

"For model ing of the stream segments many routing techniques are avaIl-
able. ranging from solutions of the full nonl inear continuity and momentum
equations through progressively simplified or linearized forms of these
equations to simple parametric storage models. It would be desirable to
use a form of these equations which is compatible with the overland flow
model requirements and which would represent those nonl inearities important
to the dynamic behavior of the catchment.

"The corresponding equation for the stream segments is

I

I
I

"Lighthill and Whitham (1955), in their comprehensive considerations of
the fluid mechanics of flood movement in rivers, have separated the effects
into dynamic and kinematic waves, both of which are initially present.
They show that for Froude numbers less than 2, the dynamic component decays
exponentially and the kinematic wave ultimately predominates. Wollhiser and
Liggett (1967), indicate that the rate of damping of the dynamic component
will be large enough to justify neglecting the dynamic effects provided
that

a,\
at

+

~
ax

=

q

(4)

I

I

Q

=

Ams
CIs

(5)

where A is the cross-sectional area of flow (ft2). Q is the discharge
rate (cfs) and q is the lateral inflow rate of overland flow (cfs/ft).

K =

SoL
yF2

> 10

(1)

"The above kinematic wave equations contain the parameters ClC' mc' CIS' and
ms which may be estimated from the Manning formula.

I

"Use of the kinematic form of the unsteady flow equations allows particu-
larly simple numerical solutions (since all disturbances propagate only in
the downstream direction), while retaining some of the nonlinear effects of
the full dynamic form. The successful appl ication by Wooding (1966) of
this approach to natural catchments ranging from 0.84 square miles to 3383
square miles has led to the adoption of the kinematic approach as the basic
routing element.

1.40 Y 5/3 S 1/2
q =
n c c
c
as
1. 49 S 1/2
ClC nc c
mc 5/3

(6)

I

where So is the slope of the stream; L, the length; Y. the depth of flow;
and F, the Froude number.

(7)

I

(8)

I

I

I