FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

The effective precipitation rate, ie' (that which
occurs after interception is satisfied) is expressed by
the following equations:

ie = 0, for i ~icc
-PIS!
ie = i (1 - e ), for i > iee

. (3.4)

Most of the moislure accumulated in intercep-
tion storage is lost through evaporation; however,
little evaporalion occurs during short duration stonus.

Infiltration

Inf1ltration loss is represenled in the model as a
function of lime in accordance with the form proposed
by Horlon and used by Narayana et al. (1969).

_ -kf'
f - fe + (fo - fe) e (3.5)

in which

f
t

= instantaneous potential infiltralion rate
= time measured from Ihe beginning of
the infillration period
conslanl infiltration rale which f ap.
proaches asymlotically with time
= initial infiltration rale at t = 0
= positive coefficient depending upon
the soil characteristics

fe

fo
kf

The aclual rale of infillration, fa' is the smaller of
either I) the rate of water supply, ie' and 2) the po-
tential infillration rate given by Equation 3.5. Thus,

fa = it, for it ::s;;; f

and

. (3.6)

fa = f, fori) > f

The actual inf1ltration rate, fa' follows the effective
precipitation hyelograph, i), as long as precipitation
rates are less than Ihe potential infiltration rate curve.
When precipitation exceeds potential infiltration, ac-
tual infiltration rate is limiled to f. The initial infiltra-
tion rate (fo) depends on the prevailing soil moislure
status at I.he beginning of the storm event.

Surface Depression Storage

The capacily rate of inflow inlo depression slor-

age is expressed by the equation

. -(PI -Fl!Sd
ac=12e- . (3.7)

in which
i2 = (i1 - f) = net rate of precipilalion after sat-
isfying interception and inf1ltra-
tion

PI

F
Sd

= accumulaled rainfall having satis-
lied interception storage
accumulated infiltration loss
= lotal volume of available depres-
sion storage (expressed as mean
depth over the entire calchment
area)
= capacity rale of inflow into de-
pression storage

ac

The actual rate of inflow into depression storage, aa,
at any time is expressed in accordance with limiting
conditions as follows:

aa = i2, for i2 '" ac

. . (3.8)

and

ac = ac, for i2 >ac

Hydrograph of Rainfall Excess

The hyelograph of rainfall excess is compuled
by sequentially deducting the losses due to inlercep-
tion, infiltration, and depression storage from the
hydrograph of precipitation in compatible, finite, lime
incremenls (Figure 3.5).

Overland-Channel Routing

Narayana et al. (1969) adopled Ihe linear pro-
cedure of "storage routing" wherein the storage ef-
fects (overland and channel components) of Ihe catch.
ment area are accounted for by using the character-
istic time of the catchment area.

The general continuity equalion for any linear
slorage syslem is given as follows:

P _Q=dSt
e dt

in which
Pe
Q
St

. (3.9)

rainfall excess rate
= runoff rate
= catchmenl area storage (overland and
channel componenls)

Calchment area storage is considered as being
directly proportional to the outflow rate. Thus,

St=IRQ

(3.10)

in which
tR

a proportionality factor approximated
by the hydrograph rise time

The equation derived by Espey el aI. (1965), for 30-
minule unit hydrographs of urban walersheds, ex-
pressed Ihe time of rise as a function of the channel
length and Ihe mean slope oflhe catchment area.
Hence,

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