Time of Concentration and Lag Time in WMS

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Time of Concentration and Lag Time in WMS

• Ryan Murdock
• CE 394K.2

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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

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Hydrograph Properties
Taken from Wanielista, M., R. Kersten, and R.
Eaglin, Hydrology Water Quantity and Quality
Control, p. 184
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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

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WMS Examples
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WMS Models Requiring Travel Time Input

• TR-55 (tc)
• TR-20 (tlag)
• HEC-1 (depends on unit hydrograph method)
• Rational Method (tc)

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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 lt300 ft
• Shallow Concentrated Flow
• Tt (hr) L(ft)/3600V(fps)
• V determined from slope of flow path
• Open Channel Flow (Mannings equation)
• TtL/VLn/(1.49R0.67S 0.5)
• R obtained from WMS channel calculator
• tcSTt
• Other Equations - FHWA and Maricopa Co., AZ

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Rational Method
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Rational Method Hydrograph
QpCiA
Taken from Wanielista, M., R. Kersten, and R.
Eaglin, Hydrology Water Quantity and Quality
Control, p. 208
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Time of Concentration
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Time of Concentration Methods (1)

• Kirpich Equation (1940)
• For overland flow
• tc (hrs) m0.00013(L0.77/S0.385)
• L length of overland flow (ft)
• S avg overland slope
• m based on earth type
• bare earth1, grassy earth2, concrete
  asphalt0.4
• 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

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Time of Concentration Methods (2)

• Ramser Equation (1927)
• For well-defined channels
• tc (min) m0.0078(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) (0.67nLo)/S0.50.467
• Lo length of overland flow (ft)
• n Mannings roughness coefficient
• S avg overland slope

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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

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HEC-1 Unit Hydrographs
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SCS Hydrograph
qp484AQ/(0.5D0.6tc)
Taken from Handbook of Hydrology, p. 9.25
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Lag Time
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Lag Time Methods

• General form of equation
• TLAG Ct(LLca/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)

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Lag Time Methods- General Form (1)

• Denver Area Flood Control District (1975)
• m0.48, Ct based on impervious
• For small urban watersheds (lt5 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

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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, m0.3

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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 lt0.3, 1 lt (L/S0.5) lt9
• Colorado State University
• TLAG Ct(LLca)0.3
• Ct 7.81/Ia0.78
• For watersheds in Denver, CO area
• With some amount of developed land
• Not valid when Ialt10

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Lag Time- SCS method

• SCS (1972)
• TLAG L0.8(S1)0.7/(1900Y0.5)
• L hydraulic lengthof watershed (ft)
• S(1000/CN)-10 max retention (in)
• Y watershed slope ()
• TLAG 0.6 tc

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Time to Rise

• Espey (1966)
• For Snyders 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