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Scientific Investigations Report 2012–5110
Prepared in cooperation with the
Department of Transportation Federal Highway Administration
Estimating Basin Lagtime and Hydrograph-Timing Indexes Used to Characterize Stormflows for Runoff-Quality Analysis
By Gregory E. Granato
Abstract
A nationwide study to better define triangular-hydrograph statistics
for use with runoff-quality and flood-flow studies was done by the U.S.
Geological Survey (USGS) in cooperation with the Federal Highway
Administration. Although the triangular hydrograph is a simple linear
approximation, the cumulative distribution of stormflow with a triangular
hydrograph is a curvilinear S-curve that closely approximates the
cumulative distribution of stormflows from measured data. The temporal
distribution of flow within a runoff event can be estimated using the
basin lagtime, (which is the time from the centroid of rainfall excess to
the centroid of the corresponding runoff hydrograph) and the hydrograph
recession ratio (which is the ratio of the duration of the falling limb to
the rising limb of the hydrograph). This report documents results of the
study, methods used to estimate the variables, and electronic files that
facilitate calculation of variables.
Ten viable multiple-linear regression equations were developed to
estimate basin lagtimes from readily determined drainage basin properties
using data published in 37 stormflow studies. Regression equations using
the basin lag factor (BLF, which is a variable calculated as the
main-channel length, in miles, divided by the square root of the
main-channel slope in feet per mile) and two variables describing
development in the drainage basin were selected as the best candidates,
because each equation explains about 70 percent of the variability in the
data. The variables describing development are the USGS basin development
factor (BDF, which is a function of the amount of channel
modifications, storm sewers, and curb-and-gutter streets in a basin) and
the total impervious area variable (IMPERV) in the basin. Two
datasets were used to develop regression equations. The primary dataset
included data from 493 sites that have values for the BLF,
BDF, and IMPERV variables. This dataset was used to
develop the best-fit regression equation using the BLF and
BDF variables. The secondary dataset included data from 896 sites
that have values for the BLF and IMPERV variables. This
dataset was used to develop the best-fit regression equation using the
BLF and IMPERV variables.
Analysis of hydrograph recession ratios and basin characteristics for
41 sites indicated that recession ratios are random variables. Thus,
recession ratios cannot be estimated quantitatively using multiple linear
regression equations developed using the data available for these sites.
The minimums of recession ratios for different streamgages are well
characterized by a value of one. The most probable values and maximum
values of recession ratios for different streamgages are, however, more
variable than the minimums. The most probable values of recession ratios
for the 41 streamgages analyzed ranged from 1.0 to 3.52 and had a median
of 1.85. The maximum values ranged from 2.66 to 11.3 and had a median of
4.36.
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First posted August 18, 2012
- Report PDF file (2.57 MB)
This report is available online with the asscociated electronic files that facilitate calculation of variables.
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Suggested citation:
Granato, G.E., 2012, Estimating basin lagtime and
hydrograph-timing indexes used to characterize stormflows for runoff-quality
analysis: U.S. Geological Survey Scientific Investigations Report 2012–5110, 47
p., with digital media at http://pubs.usgs.gov/sir/2012/5110/.
Contents
Abstract
Introduction
Purpose and Scope
Estimating Basin Lagtimes
Definition of Selected Basin Characteristics for Estimating Basin Lagtimes
Physiographic Basin Characteristics
Anthropogenic Basin Characteristics
Values of the Basin Lagtime and Explanatory Basin Characteristics
Analytical Procedures for Regression Analysis
Development of Basin Lagtime Regression Equations
Application of Basin Lagtime Regression Equations
Limitations of the Analysis
Estimating Hydrograph-Timing Indexes Using Recession-Ratio Statistics
Estimating Values of the Triangular-Hydrograph Recession Ratio from Published Curvilinear Hydrographs
Estimating Values of the Triangular-Hydrograph Recession Ratio from Instantaneous Streamflow Data
Methods
Values of the Triangular-Hydrograph Recession Ratios
Correlations to Potential Explanatory Basin Characteristics
Limitations of the Analysis
Summary
Acknowledgments
References Cited