FLOOD00925

• County: Statewide
• Community: State of Colorado
• Title: Colorado Flood Hydrology Manual - Section 22 Program
• Date: 9/1/1993
• Prepared For: CWCB
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

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.i 3.2. DISPLAY AND USE OF ESTIMATED FREQUENCY CURVE. The
estimated frequency distribution is displayed on a grid with the magnitude of the event
as the ordinate and probability of exceedance (or percent chance exceedance) as the
abscissa. The plot thus provides a useful tool for estimating quantiles or exceedance
probabilities. Specialized plotting grids are available for the display. These grids are
constructed with the abscissa scaled so a selected frequency distribution plots as a
straight line. For example, a specialized grid was developed by Hazen for the
commonly-used normal frequency distribution.

The specialized normal-probability grid is a useful tool for judging the
appropriateness of the normal distribution as a model of the parent population. If data
drawn from a normally-distributed parent population are assigned plotting positions
using equation 1 and are plotted on Hazen's grid, the points will fall approximately on
a straight line. If the points do not, then either the sample was drawn from a
population with a different distribution, or sampling variation yielded a non-
representative sample.

A specialized plotting grid has been developed also for another commonly-used
frequency distribution, the log-normal distribution. If the data truly are drawn from a
log-normally-distributed parent population, the points will fall on a straight line.

4. ANALYTICAL TECHNIOUES.

Analytical techniques define the relationship between streamflow
magnitude and probability with analytical tools, instead of the graphical tools. With
numerical techniques, the following general steps are used to derive a frequency curve
to represent the population (McCuen and Snyder, 1986):

. Select a candidate frequency model of the parent population. Three
distributions are commonly used for frequency analysis of hydrometeorological
data: the normal distribution, the log-normal distribution, and the log-Pearson
type III distribution.

. Obtain a sample.

. Use the sample to estimate the parameters of the model identified in step 1.

. With the model and the parameters, estimate quantiles to construct the
frequency curve that represents the parent population.

4.1. NUMERICAL PARAMETER ESTIMATION. Parameters of a statistical
model commonly are estimated from a sample with method-of-moments estimators.
The method-of-moments parameter estimators are developed from the following

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