Estimation of watershed lag times and times of concentration for the Kansas City Area.
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2016-04-01
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Abstract:Lag time (TL) and time of concentration (TC) are two related measures of how quickly a stream responds to
runoff-producing rainfall over its watershed. In this report, a general relationship for lag time is derived from the
Manning equation for frictional resistance, the rational formula for bankfull discharge, and a generalized rainfall
intensity-duration relationship. This relationship accounts for the length, average slope, and average Manning n value
for the longest flow path and three watershed characteristics: average width, a rational runoff coefficient, and a
reference rainfall intensity. A simpler form of this relationship is derived for regional calibration. The regional form of
the lag-time equation accounts for the impacts of urbanization through two inputs: the fraction of the longest flow path
that is paved or enclosed, and the fraction of the drainage area covered by impervious surfaces. The relationships
indicate that lag time is strongly related to the length, slope, and roughness of the main channel and less strongly
related to other watershed characteristics that affect the bankfull discharge in the channel.
The regional lag-time equation was calibrated for the Kansas City area with observed lag times and channel
and watershed characteristics for 30 gage sites in the Automated Local Evaluation in Real Time (ALERT) flash-flood
warning system. Average lag times for the gaged watersheds were determined from archived rainfall and water-level
records for significant runoff events. The new lag-time equation for the Kansas City area performs better than the 2001
KU-KDOT equation for urban lag time, which was developed from a study of 14 gaged watersheds in Johnson County
(McEnroe & Zhao, 2001). The main advantage of the new lag-time equation is that it accounts directly for the higher
velocities in the paved and enclosed segments of the flow path. The new equation’s solid theoretical foundation is also
an advantage.
Because time of concentration cannot be determined from gaging data, direct calibration of an equation for TC
is not possible. However, time of concentration and lag time are closely related, so TC can be estimated from TL. The
Natural Resources Conservation System (NRCS, 2010) recommends the approximation TC = 5/3 TL. The
recommended time-of-concentration equation for the Kansas City area incorporates this approximation.
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