FLOOD09736

• County: Statewide
• Basin: Statewide
• Title: Estimating Flood Flows from Mixed Populations in Colorado
• Date: 1/1/1978
• Prepared For: State of Colorado
• Prepared By: CWCB
• Floodplain - Doc Type: Educational/Technical/Reference Information

logarithmetic transformations, A special case of the gamma function, the
log-Pearson type III distribution has been found to fit most annual flood
series best, The log-Pearson type III distribution has subsequently been
adopted by the U,S. Water Resources Council as the standard for flood fre-
quency analysis, .
Three statistical parameters, the mean logarithm (Xl, standard deviation
of logarithms (5), and skew coefficient of logarithms (G), define the
log-Pearson type III distribution. In a typical hydrological analysis, these
parameters are computed for the sample consisting of the common logarithms of
the annual flood series for a specific gauging station record. The magnitude
of flood flow, or peak discharge, at any exceedance probability or return
period is then computed by the equation:

;..
log Q = $\+ K S
T ..~.. G,T

X

(1)

where,

QT
X

= peak discharge at return period of T years, in cfs,

= mean logarithm of peak flows,

KG,T

= a factor known as the Pearson type III deviate, or percentage point,
that is a function of the skew coefficient of logarithms (G) and
selected return period (T),

S

= standard deviation of logarithms.

Values of K and equations for computing the three statistical parameters by
the method of moments are gi ven in "Gu i de 1 i nes for Determi ni ng Flood Flow
Frequency" (U.S. Water Resources Council, 1977), The return period (T) in
years, also known as recurrence interval, is equal to the inverse of the
exceedance probability,

MIXED POPULATIONS

:e.

When the annual series consists of the peak recorded flow for each year
regardless of the source of flooding, the data are said to have come from a
"mixed population." A frequency analysis based on a mixed population does not
distinguish among the several possible types of floods such as snowmelt or
rainfall events which comprise two distinct and generally independent popula-
tions. A flood flow frequency analysis using a mixed population will tend to
underestimate flood magnitudes for rare events,
A !eparate analysis of the identifiable principal flood types, such as
annual rainfall and snowmelt events, is important in making a reliable esti-
mate of flood flow frequencies. The procedure would be to segregate the flood
data by cause, analyze each annual series separately, and then combine the
results. For practical reasons only the two major flood types of rain and
melting snow are separated although the procedure would be applicable to as
. many independent populations as can be identified,

,