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

• 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/(P2

0.5S0.4)• 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=Tt

• Other Equations - FHWA and Maricopa Co., AZ

Rational Method

Rational Method Hydrograph

Taken from Wanielista, M., R. Kersten, and R. Eaglin, Hydrology: Water Quantity and Quality Control, p. 208

Qp=CiA

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 • 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/Sc

0.385)• 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/(So

0.1110I)• L = length of longest flow path (mi)• S = avg slope along longest flow path • So = avg basin slope• I = % impervious area

– Applicable watershed conditions• 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

Taken from Handbook of Hydrology, p. 9.25

qp=484AQ/(0.5D+0.6tc)

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• 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

• 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- Adaptations to General Form

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