Time of Concentration and
Lag Time in WMS
Ryan Murdock
CE 394K.2
Travel Time Basic Concepts
• Time of concentration
– Longest time of travel for a drop of water to reach
the watershed outlet (as used in rational method)
– Time from the end of rainfall excess to the
inflection point on the hydrograph recession curve
(as considered in SCS method)
• Lag time
– Time from the center of mass of rainfall excess to
hydrograph peak
Hydrograph Properties
Taken from Wanielista, M., R. Kersten, and R. Eaglin, Hydrology: Water Quantity and Quality Control, p. 184
WMS Travel Time Methods
• Empirical equations based on basin data
• Create a time computation coverage
– Define representative flow path(s) within each
basin using arcs
– Travel time equation assigned to each arc
WMS Examples
WMS Models
Requiring Travel Time Input
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TR-55 (tc)
TR-20 (tlag)
HEC-1 (depends on unit hydrograph method)
Rational Method (tc)
Computing Travel Times From
Map Data- TR-55 Equations
• Sheet Flow
– Tt (hr) =0.007(nL(ft))0.8/(P20.5S0.4)
• P2 = 2 yr , 24 hr rainfall (TR-55 manual, NOAA)
• Equation used for lengths <300 ft
• Shallow Concentrated Flow
– Tt (hr) =L(ft)/3600V(fps)
• V determined from slope of flow path
• Open Channel Flow (Manning’s equation)
– Tt=L/V=Ln/(1.49R0.67S 0.5)
• R obtained from WMS channel calculator
• tc=STt
• Other Equations - FHWA and Maricopa Co., AZ
Rational Method
Rational Method Hydrograph
Qp=CiA
Taken from Wanielista, M., R. Kersten, and R. Eaglin, Hydrology: Water Quantity and Quality Control, p. 208
Time of Concentration
Time of Concentration Methods (1)
• Kirpich Equation (1940)
– For overland flow
– tc (hrs) = m*0.00013*(L0.77/S0.385)
• L= length of overland flow (ft)
• S= avg overland slope
• m based on earth type
– bare earth=1, grassy earth=2, concrete & asphalt=0.4
• In mountains multiply computed tc by (1+(80-CN)*0.4)
– Based on data from small agricultural watersheds
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Steep slopes
Well-drained soils
Timber cover 0- 56%
Area 1.2- 112 acres
Time of Concentration Methods (2)
• Ramser Equation (1927)
– For well-defined channels
– tc (min) = m*0.0078*(Lc0.77/Sc0.385)
• m= 0.2 for concrete channels
• Lc= length of channel reach (ft)
• Sc= avg channel slope
• Kerby Equation (1959)
– For overland flow distances 300 - 500 ft
– tc (min)= [(0.67*n*Lo)/S0.5]0.467
• Lo= length of overland flow (ft)
• n= Manning’s roughness coefficient
• S= avg overland slope
Time of Concentration Methods (3)
• Fort Bend County, Texas (1987)
– For use with Clark unit hydrograph method
– tc (hrs)=48.64(L/S0.5)0.57logSo/(So0.1110I)
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L = length of longest flow path (mi)
S = avg slope along longest flow path
So = avg basin slope
I = % impervious area
– Applicable watershed conditions
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Area 0.13- 400 mi2
Longest flow path 0.5- 55 mi
Slope of longest flow path 2- 33 ft/mi
Basin slope 3- 80 ft/mi
HEC-1 Unit Hydrographs
SCS Hydrograph
qp=484AQ/(0.5D+0.6tc)
Taken from Handbook of Hydrology, p. 9.25
Lag Time
Lag Time Methods
• General form of equation
– TLAG= Ct*(L*Lca/S0.5)m
• Ct= coefficient accounting for differences in watershed slope
and storage
• L= max flow length along main channel from point of reference
to upstream watershed boundary (mi)
• Lca= distance along main channel from point of reference to a
point opposite the centroid (mi)
• S= slope of the maximum flow distance path (ft/mi)
• m= lag exponent
• WMS allows user to customize the parameters
(enter your own Ct & m)
Lag Time Methods- General Form (1)
• Denver Area Flood Control District (1975)
– m=0.48, Ct based on % impervious
– For small urban watersheds (<5 mi2) with mild slopes
• Tulsa District USACoE
– For use with Snyder unit hydrograph
– Parameters
• Ct= 1.42 (natural watersheds in rural areas of central & NE
Oklahoma), 0.92 (50% urbanized), 0.59 (100% urbanized)
• L= watershed max flow distance (mi)
• S= slope of max flow dist (ft/mi)
– Applicable conditions
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Area 0.5- 500 mi2
Slope 4- 90 ft/mi
Length 1- 80 mi
Length to centroid 1- 60 mi
Lag Time Methods- General Form (2)
• Riverside County Flood Control & WCD (1963)
– Ct= 1.2 mountainous, 0.72 foothills, 0.38 valleys
– m= 0.38
– Areas near Riverside Co., CA (2- 650 mi2)
• Eagleson (1962)
– Completely storm-sewered watersheds
– Ct= 0.32, m= 0.39
– Typical Characteristics
• Area: 0.22- 7.5 mi2, L: 1-7 mi, Lca: 0.3-3 mi, S: 6-20 ft/mi,
33-83% impervious
• Taylor & Schwartz (1952)
– For Snyder unit hydrograph
– Developed in northeastern region of US
– Ct= 0.6, m=0.3
Lag Time- Adaptations to General Form
• Putnam (1972)
– TLAG= 0.49(L/S0.5)0.5Ia-0.57
– Watersheds around Wichita, Kansas
– Typical conditions
• Area: 0.3-150 mi2, Ia <0.3, 1 < (L/S0.5) <9
• Colorado State University
– TLAG= Ct*(L*Lca)0.3
• Ct= 7.81/Ia0.78
– For watersheds in Denver, CO area
– With some amount of developed land
– Not valid when Ia<10%
Lag Time- SCS method
• SCS (1972)
– TLAG= L0.8(S+1)0.7/(1900Y0.5)
• L= hydraulic lengthof watershed (ft)
• S=(1000/CN)-10 = max retention (in)
• Y= watershed slope (%)
– TLAG =0.6 tc
Time to Rise
• Espey (1966)
– For Snyder’s time to rise (time from beginning of
effective rainfall to hydrograph peak)
– Developed for small watersheds in TX, OK, NM
– Rural areas Tr = 2.65Lf 0.12Sf-0.52
• Lf= stream length (ft)
• Sf= stream slope
• Typical Conditions
– Lf: 3250-25300 ft, Sf: 0.008-0.015, Tr: 30-150 min, Area: 0.1-7 mi2
– Urban Areas Tr = 20.8 ULf0.29Sf-0.11Ia-0.61
• Ia= percent impervious cover
• U= urbanization factor (0.6 extensive- 1 natural conditions)
• Typical Conditions
– Lf: 200-54,800 ft, Sf: 0.0064-0.104, Ia: 25-40%, Tr: 30-720 min,
Area: 0.0125-92 mi2