WMS:Fort Bend Tc Equation

The county of Fort Bend, Texas (Espey, Huston, & Associates, 1987) used the equation shown in the equation below to compute tc. In addition to defining an equation for time of concentration to be used in the Clark unit hydrograph method, they also defined a relationship for the Clark watershed storage coefficient that is given by the equation following the tc equation.

${\displaystyle t_{c}=48.64{\frac {\left({\frac {L}{\sqrt {S}}}\right)^{0.57}}{S_{o}{}^{0.11}10^{I}}}\log S_{o}}$
${\displaystyle R=128{\frac {\left({\frac {L}{\sqrt {S}}}\right)^{0.57}}{S_{o}{}^{0.11}10^{I}}}\log S_{o}-t_{c}}$

where:

tc = Clark time of concentration in hours.
R = Clark watershed storage coefficient.
L = length of longest flow path within the watershed in miles.
S = average slope along the longest flow path.
So = average basin slope.
I = percent impervious as a fraction (decimal).

Typical characteristics of the watersheds for which these equations were applied are:

• Area between 0.13 and 400 square miles.
• Length of longest flow path between 0.5 and 55 miles.
• Slope of longest flow path from 2 ft/mi. to 33 ft/mi.
• Slope of basin from 3 to 80 ft/mi.
• Impervious area from 0 to 100%.

Others have simply used the simple relationship defined by the equation below to compute the Clark watershed storage coefficient from the time of concentration.

${\displaystyle R=2t_{c}}$

Russell, Keening and Sunnell in their study of watersheds around Vancouver, British Columbia found the ${\displaystyle R=c*TC}$ , where the calibration parameter c for rural watersheds ranged from 1.5 to 2.8. ("Estimating Design Flows for Urban Drainage." Russell, S. Kenning, B. and Sunnell, G. ASCE Journal of the Hydraulics Division, Vol 105, No. HY1, pp 49, January 1979.)

For coastal watersheds in Southern California the USACE proposes that "the storage coefficient R equals 0.8 time the time of concentration, TC. ("Generalized Standard Project Rainflood Criteria, Southern California Coastal Streams." Hydrologic Engineering Center. Sacramento: U.S. Army Corps of Engineers, pp 6, 1967.)