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Time of Concentration and Lag Time in WMS

Time of Concentration and Lag Time in WMS

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Time of Concentration and Lag Time in WMS

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  1. Time of Concentration and Lag Time in WMS Ryan Murdock CE 394K.2

  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

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

  4. 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

  5. WMS Examples

  6. WMS Models Requiring Travel Time Input • TR-55 (tc) • TR-20 (tlag) • HEC-1 (depends on unit hydrograph method) • Rational Method (tc)

  7. 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

  8. Rational Method

  9. Rational Method Hydrograph Qp=CiA Taken fromWanielista, M., R. Kersten, and R. Eaglin, Hydrology: Water Quantity and Quality Control, p. 208

  10. Time of Concentration

  11. 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

  12. 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

  13. 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

  14. HEC-1 Unit Hydrographs

  15. SCS Hydrograph qp=484AQ/(0.5D+0.6tc) Taken from Handbook of Hydrology, p. 9.25

  16. Lag Time

  17. 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)

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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