It is, of course, best to obtain Tp by calibration with measurements. If data is available, the following procedure may be utilized to estimate Tp.
DEFINITION OF TIME LAG
The first step involves determining the time lag which is defined as the time difference between the centroids of the rainfall excess hyetograph and the direct runoff hydrograph (after subtracting baseflow). is related to n and in the Nash conceptual model by
Once is determined and n is estimated by 3 for example, then can be obtained by equation 16.
Since measurements are usually available only at the outlet of a watershed, the values would still have to be determined for each subwatershed after discretization. The main parameters that affect are the slope and the area. Since in small watersheds the slope does not vary too much, an approximate relation can be utilized. With the calibrated at the outlet, constants m and n can be obtained by trial and error.
In the Seymaz and Etobicoke studies, the Williams and Hann equation for t_p was found adequate. For smaller watersheds, the values obtained can be checked by using the velocity charts in the SCS TR-55 tables (1975) for overland flow and swale flow.
Several relations for or can be found in the literature such as Chow (1962), Kibler et al (1982), Boyd (1978) and Nash (1960).