FLOOD08849

• County: Statewide
• Basin: Statewide
• Title: Techniques of Water-Resources Investigations of the US Geological Survey Frequency Curves
• Date: 1/3/1997
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

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CONTENTS

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Preface__ __ ____ __ __ _ ______ ____ _ un _ _ _un __ _ III
Abstract_____ _ ___ _ ___ _ _ _ ____ _____ _ _____ _ ___ _ _ 1
Introductioll_ _ ____ _ __ __ ______ _ ___ _ ____ n ____ _ 1
Cumulative distributions_ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ _ _ _ _ _ 1
Distributions used in hydrology _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3
N armal rlistributioll__ _ _ __ n _ h h __ __ h _ n _ 3
Lognormal distributioll_____u___u___n___ 4
Type I extreme-value distribution (Gumbel) _ 4
Type III extreme-value distributioll____ ___ _ _ 4
Pearson Type III distribution_ _ _ _ _ _ _ _ _ _ _ _ _ _ 4
Graphically defined distributionSn__uuu__ 4

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Mathematical curve fitting______u_uu___un_ 4
Normal distributiollnhhu____uhu___n 4
Three-parameter distributions__ _ _ __ _ _ _____ _ 5
Type I extreme.value distribution (Gumbel) _ 6
Type III extreme-value distribution_n h _ h _ 7
Graphical fitting___nnuhu_________UUhh 7
Example of graphical fitting______uhhUh 8
Use of historical data______ _ _ __ __ ____ _ ___ __ 11
Comparison of mathematical and graphical fitting_ 11
Describing frequency curves____________________ 12
Interpretation of frequency curves______________ 12
Special cumulative frequency curves__________~__ 13
References citedu __ __ _ __ _ __ __ __ __ __ _ _ _ _ __ __ __ 15

FIGURES

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Graphs showing two normal distributions and their cumulative forms_ _ _ _ _ _ _ _ _ __
Graphs showing normal and skewed distributions and their cumulative forms on
a normal-probability plot____ ____ ____ _ _ _ ____ _____ _ _____ ____ _ _____ __ ____ __
Graphs showing relative positions of the mean, median, and mode for right-
skewed (upper) and left-skewed (lower) distributions_____ _____ _ ___ _ __ _ _ _ _ ___
Frequency curves showing effect of direction of skew and direction of cumulation
on position of the mean with respect to the median_________________________
Gumbel frequency curve of annual floods on Columbia River near The Dalles,
Oreg., showing agreement with the plotted points_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Frequency curve based on data from table 3, assuming that data are annual
rnaxirnurns____________________________________________~_______________
Frequency curve based on data from table 3, assuming that data are annual
minirnums__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
Design-probability curves (lower graphs) and the frequency curve on which
they are based (upper graph) _ _ _ __ _ ___ __ ___ _ ___ _ ___ _ _ ___ _ ___ _ ____ _ _ __ ____
Frequency curve of annual minimum flows and plot showing serial correlation,
South Fork Obion River near Greenfield, Tenn_____________________________

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TABLES

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1. Frequency factors for Pearson Type III distribution_ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ _ __
2. Means and standard deviations of reduced extremes__________________________
3. Computation of plotting position___________________________________________

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