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Estimating basin lagtime and hydrograph-timing indexes used to characterize stormflows for runoff-quality analysis

August 20, 2012

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.