# WMS:Espey Lag Time Equations

Espey’s equations for Snyder’s parameters were developed for a series of small watersheds in Texas, Oklahoma, and New Mexico. Rather than defining the lag time, Espey (1966) used the time to rise. The difference is that the lag time is the time from the centroid of rainfall to the peak of the hydrograph, whereas the time to rise is the time from the beginning of effective rainfall to the peak of the hydrograph. The lag time can be computed by subtracting one-half the computation time interval from the time rise. Equations to compute Tr and Cp are given below:

$T_r = 2.65 \, L_f^{0.12} S_f^{-0.52}$
Rural Areas
$T_r = 20.8 \, UL_f^{0.29} S_f^{-0.11} I_a^{-0.61}$
Urban Areas

where:

Tr = time from the beginning of effective rainfall to the peak of the unit hydrograph.
Lf = stream length in feet.
Sf = stream slope in feet per foot.
Ia = percent impervious cover.
U = urbanization factor equal to 0.6 for extensive urbanization, 0.8 for some storm sewers, and 1.0 for natural conditions.

Typical conditions for typical rural watersheds include:

• Lf from 3,250 feet to 25,300 feet.
• Sf from 0.008 ft/ft to 0.015 ft/ft.
• Tr from 30 to 150 minutes.
• Areas from 0.1 sq. miles to 7 sq. miles.

Typical conditions for typical urban watersheds include:

• Lf from 200 feet to 54,800 feet.
• Sf from 0.0064 ft/ft to 0.104 ft/ft.
• Ia from 25 to 40 percent.
• Tr from 30 to 720 minutes.
• Areas from 0.0125 sq. miles to 92 square miles.

Espey developed the following equations to compute Snyders peaking coefficient.

$q_p = 1700 A^{-0.12}T_r^{-0.30}$
Rural Areas
$q_p = 19300 A^{-0.09}T_r^{-0.94}$
Urban Areas

Once qp is computed, the peaking coefficient can be determined using the following relationships:

$T_{LAG} = T_r^{} - \Delta t / 2$
$C_p = \frac {q_p \ast T_{LAG}}{640}$

where Δt is the computational time interval as define in the HEC-1 Job Control dialog (by default it is 15 minutes).