Many methods for estimating the time of concentration and basin lag are given in var-ious private, federal, and local publications. Although each of these methods is differ-ent (in some cases only slightly), all are based on the type of ground cover, the slope of the land, and the distance along the flow path. In most localities, there is also a minimum tc (typically 5 to 10 minutes) recommended for small watersheds such as a section of a parking lot draining to a storm sewer. Some methods predict the response time directly, and others predict the velocity of flow. The predicted velocity coupled with estimates of the flow path length can then be used to estimate the response time.
With few exceptions, methods for the prediction of basin response time are empirical in nature. Consequently, large errors in response time estimates can be expected to occur if these methods are not carefully selected and applied. These errors can signif-icantly affect peak runoff estimates. The method selected for estimation of tc or tL should be one that was developed for basin conditions similar to those existing in the drainage basin for which an estimate is desired. McCuen, Wong, and Rawls (1984) compared a number of methods for estimating the time of concentration and
devel-oped measures of their reliability. As a general rule, methods that compute individual travel times for various types of flow segments (for example, overland flows and channelized flows), and then sum the individual travel times to estimate the total travel time, are thought to be the most reliable.
Physically, the response time of a drainage basin depends on, at a minimum, the length of the flow path, the slope of the basin, and the surface roughness. Additional factors included in some prediction methods are rainfall intensity and a measure of the basin shape. Because urbanization of a watershed tends to reduce surface rough-ness and often changes flow path lengths and slopes, a change in basin response time (nearly always a decrease) and corresponding increases in peak runoff rates should be expected as a consequence of urbanization. One way to help reduce the increase in peak runoff rate caused by urbanization is to increase the time of concentration and/or basin lag through practices such as terracing of land surfaces.
Table 5.9 lists several commonly used methods for estimating basin lag time.
Table 5.10 lists several commonly used methods for estimating the time of concentra-tion of a drainage basin. Figure 5.8 illustrates average overland flow velocities as a function of land use characteristics and surface slope. When flows are channelized in gutters, open channels, or storm sewers, Manning’s equation may be used to estimate the velocity of flow. For more information, see Section 6.2 (page 198), Section 7.2, and Section 10.1.
Table 5.9 Commonly used methods for estimation of basin lag time, in hours
Equation Source Remarks
Snyder (1938), Linsley (1943)
Ct = empirical coefficient [typical range between 1.8 (steeper basins) and 2.2 (flatter basins)], L = basin length (mi), and Lca = length along main channel to a point adja-cent to the basin adja-centroid (mi).
Taylor and Schwarz (1952)
D = drainage density, L = basin length (mi), Lca = length along main channel to a point adjacent to the basin centroid (mi), and S = average channel slope (ft/ft).
Soil Conservation Service (1986)
Lw = length of drainage basin (ft), CN = curve number of drainage basin, and S = average basin slope (percent).
Kent (1972) Lag is approximated as 0.6tc for use in SCS Unit Hydrograph computations.
Table 5.10 Commonly used methods for estimation of the time of concentration, in minutes
Equation Source Remarks
Williams (1922) L = basin length (mi), A = basin area (mi2), D = diameter (mi) of a circular basin of area A, and S = basin slope (per-cent). The basin area should be smaller than 50 mi2. Kirpich (1940) Developed for small drainage basins in Tennessee and
Pennsylvania, with basin areas from 1 to 112 ac. L = basin length (ft), S = basin slope (ft/ft), K = 0.0078 and n = 0.385 for Tennessee; K = 0.0013 and n = 0.5 for Pennsylvania.
The estimated tc should be multiplied by 0.4 if the overland flow path is concrete or asphalt, or by 0.2 if the channel is concrete-lined.
Hathaway (1945), Kerby (1959)
Drainage basins with areas of less than 10 ac and slopes of less than 0.01. This is an overland flow method. L = over-land flow length from basin divide to a defined channel (ft), S = overland flow path slope (ft/ft), and N is a flow retar-dance factor (N = 0.02 for smooth impervious surfaces;
0.10 for smooth, bare packed soil; 0.20 for poor grass, row crops, or moderately rough bare surfaces; 0.40 for pasture or average grass; 0.60 for deciduous timberland; and 0.80 for coniferous timberland, deciduous timberland with deep ground litter, or dense grass).
Johnstone and Cross (1949)
Developed for basins in the Scotie and Sandusky River watersheds (Ohio) with areas between 25 and 1,624 mi2. L = basin length (mi), and S = basin slope (ft/mi).
Izzard (1946) Hydraulically derived formula. I = effective rainfall inten-sity (in/hr), S = slope of overland flow path (ft/ft), L = length of overland flow path (ft), and c is a roughness coef-ficient (c = 0.007 for smooth asphalt, 0.012 for concrete pavement, 0.017 for tar and gravel pavement, and 0.060 for dense bluegrass turf).
Henderson and Wooding (1964)
Based on kinematic wave theory for flow on an overland flow plane. I = rainfall intensity (in/hr), L= length of over-land flow (ft), n = Manning’s roughness coefficient, S = overland flow plane slope (ft/ft).
Federal Aviation Agency (1970)
Developed based on airfield drainage data. C = rational method runoff coefficient, L = overland flow length (ft), and S = slope (percent).
Soil Conservation Service (1986)
Time of concentration is developed as a sum of individual travel times. L = length of an individual flow path (ft) and V
= velocity of flow over an individual flow path (ft/s). V may be estimated by using Figure 5.8 or by using Manning’s equation.
Figure 5.8
Average overland flow velocities as a function of land use characteristics and surface slope (Kent, 1972)
Example 5.7 – Estimating Time of Concentration Using NRCS (SCS) Methods.
An urbanized drainage basin is shown in Figure 5.7.1. Three types of flow conditions exist from the furthest point of the drainage basin to its outlet. Estimate the time of concentration based on the fol-lowing data:
Solution: For the reach from A to B, the average flow velocity is V = 0.7 ft/s (from Figure 5.8). The travel time for that reach is therefore
tAB = L/V = 500/0.7 = 700 s
Similarly, for the reach from B to C, the average flow velocity is V = 2.8 ft/s. The travel time for that reach is therefore
tBC = L/V = 900/2.8 = 320 s
To compute the travel time in the storm sewer from C to D, Manning’s equation is employed to com-pute the pipe-full velocity:
Reach Flow Description Slope (%) Length (ft)
A to B Overland (forest) 7 500
B to C Overland (shallow gutter) 2 900
C to D Storm sewer with manholes, inlets, etc.
(n = 0.015, diam. = 3 ft) 1.5 2,000
D to E Open channel, gunite-lined, trapezoidal
(B = 5 ft, y = 3 ft, z = 1:1, n = 0.019) 0.5 3,000
2 / 3 2 / 3
1/ 2 1/ 2
1.49 1.49 3
(0.015) 10 ft/s
4 0.015 4
V D S
n
§ · § ·
¨ ¸ ¨ ¸
© ¹ © ¹
Figure E5.7.1 Flow paths in a drainage basin for calculation of tc The travel time for that reach is therefore
tCD = L/V = 2000/10 = 200 s
Travel time in the open channel from D to E is computed using the bank-full velocity, again found via the Manning equation:
The travel time for that reach is therefore tDE = L/V = 3,000/8.2 = 370 s
The time of concentration is the sum of the four individual travel times and is tc = 1,590 s = 0.44 hr