ALLUVIAL SYSTEMS What do we need to know? What are relevant hydrologic quantities? How are the data measured & calibrated? What is the relationship between Stage & Discharge? How does discharge relate to basin characteristics? What can be learned from Hydrographs? How can flood risk be determined?
1.10. (10 points) This hydrograph, dated July 1996, is for the Selway River near Lowell, Idaho (USGS site # ), which drains the uninhabited, mountainous, Bitterroot- Selway wilderness. In four sentences or less, describe and explain the variations you see, and determine anything you can about the character of this watershed. 2. a. What is the “hydraulic radius” of a 90° V-Notch weir with water depth H? b. Combine your result with the Chezy equation to determine a formula for the flow rate Q of a v-notch weir for various water depths. If the level of the water doubles, how much does the flow rate (discharge, Q) go up? Quiz #4 at end 45 min Do any 4 problems, 25% each Name _____________
Meramec River, Missouri Oct 2000 S=1.8’ Q=500 cfs Criss
Meramec River, Missouri May 2000 S=27.8’ Q=56,000 cfs Criss
Meramec River, Missouri May 2000 S=27.8’ Q=56,000 cfs Criss Need to know: Water Level = “Stage”, S Units: ft or meters Flow Rate = “Discharge”, Q Units ft 3 /s or m 3 /s and Variations with time: “Hydrograph”
Hydrograph = plot of discharge vs. time, or = plot of stage vs. time Mean Flow Q mean Area Flood Hydrographs Q Area small watersheds ? Q √(Area) large watersheds ? Storm & Annual Hydrographs can have rather similar forms
Q, cfs calculated S, ft measured Ppt, in measured 3788 mi 2 = 9810 km 2
Q, cfs calculated S, ft measured Ppt, in measured 175 mi 2 = 453 km 2
Stage Measurement: Staff Gage Kanawah River, WVA NOAA
USGS Circ Stilling Well Stage Measurement: Recording Stilling Well
Wading Rod <- Current Meter & Weight -> USGS Velocity Measurement
USGS Stream Gaging program (USGS Circular 1123) 7292 stations, 4200 telemetered GOES Geostationary Operations Environmental Satellite DOMSATDomestic Satellite USES: Flood Forecasting Reservoir Operations Floodplain Engineering Flow Regulation Environmental & Pollution Regulation (Flow Minimums) Highway & Bridge Design Scientific Studies USGS Real-Time
USGS Circular 1123 USGS Real-Time Data Flow
Eureka Gauging Station Since 1922 Criss
40.4 sq. mi.
3788 sq mi 1475 sq mi 781 sq mi downstream
S, ft. Q, cfs.
S, ft.
Q, cfs. S, ft. 0 cfs. + -
560 sq. mi. 259 sq. mi.
199 sq. mi. 781 sq. mi. downstream
1475 sq mi 3788 sq mi downstream
Fetter, 2001 Freeze & Cherry, 1978 Criss 2003
Hydrograph = plot of discharge vs. time, or = plot of stage vs. time Mean Flow Q mean Area Flood Hydrographs: dogma Q Area small watersheds ? Q √(Area) large watersheds ? Storm & Annual Hydrographs have rather similar forms
Hydrograph = plot of discharge vs. time, or = plot of stage vs. time Mean Flow Q mean Area Flood Hydrographs: dogma Q Area small watersheds normal flow & floods Q √(Area) large watersheds record floods Storm & Annual Hydrographs have rather similar forms
Criss 2003
STREAM GAGING: Establish link between Stage S & Discharge Q 1)THEORETICAL EQUATIONS 2) SEMI-QUANTITATIVE EQUATIONS 3) WEIRS 4)VELOCITY-AREA METHOD THEORY of STEADY LAMINAR FLOW of Newtonian Fluid Channel Flow (slot) u = (G/2 )(a 2 -y 2 ) u avg = Ga 2 /3 Q ~ g s W a 3 /3 cm 3 /sec Pipe Flow u = (G/4 )(a 2 -r 2 ) u avg = Ga 2 /8 Q = g s a 4 /8 cm 3 /sec where G= “pressure gradient”, s=slope, 2a = slot depth or tube radius; W=width viscosity; kinematic viscosity cm 2 /sec
LAMINAR SLOT FLOW a a 0 LAMINAR PIPE FLOW u =G(a 2 -y 2 )/2 u avg = Ga 2 /3 u = u a/√3 = down u =G(a 2 -r 2 )/4 u avg = Ga 2 /8 u = u a/√2 = down 0 a a
LINEAR RESERVOIR (Chow, 14-27) Storage Outflow => S = Q/k Also, - dS/dt = Q (material balance requirement) Total flow = Base Flow: where Q o is (peak) t 0 For complete depletion, the "Total Potential GW Discharge" is,
Q o =10 k=1
Note: not linear, but Concave Up
observed Q =7.07*Exp{-1.25*(t-t pk )} Q =1.2*Exp{ *(t-t pk )}
observed Q BGS = 7.07* Q (0.35, , 1) observed
2) SEMI-QUANTITATIVE EQUATIONS a. Chezy Equn (1769) U = C Sqrt [RS] where “C” = discharge coeff.; “R” = hydraulic radius = A/P = cross sectional area/wetted perimeter “S” = energy gradient (slope of H 2 O sfc.) Units ? U vs Q ?
2) SEMI-QUANTITATIVE EQUATIONS a. Chezy Equn (1769) U = C Sqrt [RS] where “C” = discharge coeff., in units of √g. “R” = hydraulic radius = A/P = cross sectional area/wetted perimeter (in ft) “S” = energy gradient (slope of H 2 O sfc, dimensionless, e.g. ft/ft)
2) SEMI-QUANTITATIVE EQUATIONS a. Chezy Equn (1769) U = C Sqrt [RS] where “C” = discharge coeff., in units of √g. “R” = hydraulic radius = A/P = cross sectional area/wetted perimeter (in ft) “S” = energy gradient (slope of H 2 O sfc, dimensionless, e.g. ft/ft) b. Manning (1889) Equn U avg = Q/A = (1/n) R 2/3 S 1/2 m/s note: units! where: “n” = Manning roughness coeff. “n”, in units of sec/m 1/3 n= (concrete) n= 0.05 (rocky mountain stream) Note: 1) 1/n => 1.49/n if use ft, cfs (English units) 2) Manning eq is not compatible w/ Poiseuille flow as these have different proportionalities! 3) Manning Eq. is asserted to be the “same” as Chezy Equn! with n=3R 1/6 /2C where C=Chezy coeff. impossible unless n or C depends on scale!
3) WEIRS Rectangular: Q cfs = ( L - H/5) H 3/2 90° V-Notch: Q cfs = 2.5 H 5/2 where H, L in ft. Fetter p. 58 Culvert: See Chow 15-33; USGS Circ. 376) H H
3) WEIRS Rectangular: Q m 3 /s = 1.84 ( L - H/5) H 3/2 90° V-Notch: Q m 3 /s = H 5/2 where H, L in m. Fetter p. 58 Culvert: See Chow 15-33; USGS Circ. 376) H
3) WEIRS Rectangular: Q m 3 /s = 1.84 ( L - H/5) H 3/2 90° V-Notch: Q m 3 /s = H 5/2 where H, L in m. Fetter p. 58 “Note that equations…. are empirical and not subject to dimensional analysis” Fetter p. 58 Culvert: See Chow 15-33; USGS Circ. 376)
3) WEIRS Rectangular: Q cfs = ( L - H/5) H 3/2 90° V-Notch: Q cfs = 2.5 H 5/2 Units! V-Notch: C d = “discharge coeff”; Chow 7-46 Culvert: See Chow 15-33; USGS Circ. 376)
V-Notch Weir
4) AREA-VELOCITY METHOD Current Meter Divide current into segments Measure 0.6*depth of segment (60% down) or, if channel is deep, take average 0.8 and 0.2 times the depth. Q = V avg *A Q = q i = v i d i w i where: v i = segment velocity d i = segment depth w i = segment width Rating Curve: Graph of Discharge (cfs) vs. Stage (ft) Use entire river channel as a weir Need to revise curve if channel changes Q cfs = S a or Q cfs = (S - S o ) a where S o = zero flow Make polynomial fit USGS
End L8 Stop
Criss (2003) after Fetter (2001) & Freeze & Cherry (1979) Is base flow maximized or minimized during peak streamflow? Look at real systems.
Craig 1961 SMOW 18 O DD MWL D = 8 18 O + 10
Criss (1999)
Criss
Isotopic Method of Hydrograph Separation Total = Direct + Ground Streamflow Runoff Water
3a2001 Hydrograph Separation Discharge l/s Winston & Criss 2004
Fetter, 2001 Freeze & Cherry, 1978 Criss 2003