A New Semi-Analytical Lag-Time Equation for Applications in the Kansas City Metropolitan Area

Abstract

Hydrologic methods that relate peak discharge to storm rainfall require as inputs time parameters that describe how fast the watershed responds to rainfall events. Two of these parameters are lag time (TL) and time of concentration (TC). In this report we present new equations for the estimation of TL and TC that are applicable to both urban and rural watersheds. Physical reasoning was used to formulate a semi-analytical equation that accounts for the major relevant factors. The new equation for lag time was derived from the Manning equation for hydraulic friction, the rational equation for peak flow and a rainfall intensity-duration relationship. The relevant factors include length and slope of the main channel, the average width of the watershed, and two measures of urbanization: the fraction of impervious surface area and the fraction of the main-channel length that is enclosed or paved. Lag time depends mainly on the three channel characteristics. The two watershed characteristics are significant but less influential. The equation was calibrated with data from the analysis of rainfall and stage data for 30 gage sites from the ALERT flash-flood system in the Kansas City metropolitan area and the analysis of the physical characteristics of the watersheds. An approximate analysis lends some support to the approximated NRCS-recommended relationship T_C=5/3 T_L. This relationship was used to obtain the TC equation. Other equations developed by regression methods proved to be less satisfactory. Because the semi-analytical equations have a solid physical basis, they should give reasonable results for smaller watersheds and for more densely developed watersheds.