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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)

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travel time basic concepts
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
Hydrograph Properties

Taken fromWanielista, M., R. Kersten, and R. Eaglin, Hydrology: Water Quantity and Quality Control, p. 184

wms travel time methods
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 models requiring travel time input
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
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 hydrograph
Rational Method Hydrograph

Qp=CiA

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

time of concentration methods 1
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
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
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)
      • 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
scs hydrograph
SCS Hydrograph

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

Taken from Handbook of Hydrology, p. 9.25

lag time methods
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
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
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
slide20
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
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
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