FLOOD07843

• County: Statewide
• Basin: Statewide
• Title: Nationwide Summary of US Geological Survey Regional Regression Equations for Estimating Magnitude and Frequency of Floods or Ungaged Ssites 1993
• Date: 1/1/1993
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

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TESTING AND VALIDATION OF TECHNIQUES

By J.B. Atkins

INTRODUCTION

Three to five sites from each hydrologic region in
each State were selected to use for the testing of
National Flood Frequency (NFF) Program, using
watershed and climatic data obtained from published
flood-frequency reports or provided by local USGS
District offices. The sites represented a range of the
independent variables required by the region's respec-
tive flood-frequency equations, Of particular interest
was the accuracy of the 500-year extrapolation proce-
dure described in an earlier section of this report. Pub-
lished 500-year peak prediction equations for eight
States (Arizona, Colorado, Florida, Illinois, Oklahoma,
Utah, West Virginia, and Wyoming) provided the basis
for evaluating the 500-year extrapolation procedure in
NFF. Since these tests were completed, regression
equations have been updated for six more States
(Mississippi, New York, South Carolina, Montana,
North Dakota and Tennessee) that have 500-year equa-
tions, These latter States were not used in the tests.

Testing and evaluation of NFF was performed by
comparing values from State 500-year equations with
extrapolated 500-year values for the eight States noted
above. Certain ratios were also computed such as the
ratios of the 500-year peak discharge to the lOO-year
peak discharge from NFF which was subtracted from I
so that extreme values would be easier to recognize.
The ratio of the 500-year peak discharge to the Crippen
and Bue maximum flood-envelope value was also com-
puted.

Evaluation of NFF also examined how well the
frequency curve from NFF at each site confonned to a
smooth log-Pearson Type III distribution frequency
curve, Confonnity to a smooth curve was measured by
computing the Root-Mean-Square (RMS) deviation of
log residuals of the T-year peak discharges of the esti-
mated State equation from a titted log-Pearson 1Ype ill
frequency curve through those T-year values. This sta-
tistic was used to examine how the frequency curve
computed by the regression equations compared to a
smooth titted log-Pearson type ill frequency curve.

Next, a site-specific skew coefficient computed
by NFF for the smooth fitted log-Pearson type III curve
was compared with a generalized skew coefficient from
Plate I of Bulletin 17B (Interagency Advisory Commit-
tee on Water Data, 1982). This comparison was made
in the fonn of a standardized skew residual statistic,
which was computed by subtracting the generalized
skew coefficient from the site-specific skew coefficient
and dividing the difference by 0.55 ((site skew - gener-
alized skew)/0.55), which is the nationwide standard
deviation of station values of skew coefficient about the
skew contour lines of Plate I in Bulletin 17B (Inter-
agency Advisory Committee on Water Data, 1982). In
addition to the fitted-curve skew, the fitted-curve stan-
dard deviation was computed (in 10glO units). This
standard deviation was used to evaluate the slope of the
smooth curve.

General Testing

The published 500-year peak discharge equa-
tions for the eight States noted earlier, were derived by
linear regression techniques except for Utah, in which
a 500-year peak discharge can be computed by multi-
plying the 1000year peak discharge by a factor. The
500-year peak discharge estimates computed from
these equations were evaluated using the above men-
tioned procedures.
The extrapolated 500-year peak discharges dif-
fered from the 500-year estimates from the equation
developed by regression analysis by as much as +35
percent and -68 percent with a mean difference of -0.83
percent. One minus the ratio of the 500-year peak dis-
charges from the computed State equations to the 100-
year peak discharges (1 - Q500/Q I (0) was 0,57, This
same statistic, using extrapolated values, had a mean
ratio of 0.58 indicating that extrapolated 500-year val-
ues are similar to those from the State equations devel-
oped by regression analysis,
The mean ratio of 500- year peak discharges from
the State equations to the Crippen and Bue maximum
envelope values was 0,22 while the same mean ratio
using extrapolated 500-year peak discharge values was

TESTING AND VAUDATION OF TECHNIQUES 17