Transcript Document
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?
Quiz #4 at end 45 min Do any 4 problems, 25% each
1.
2.
Name_____________
10. (10 points) This hydrograph, dated July 1996, is for the Selway River near Lowell,
Idaho (USGS site # 13336500), which drains the uninhabited, mountainous, BitterrootSelway wilderness. In four sentences or less, describe and explain the variations you see,
and determine anything you can about the character of this watershed.
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?
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
Need to know:
Water Level = “Stage”, S
Flow Rate = “Discharge”, Q
Units: ft or meters
Units ft3/s or m3/s
and Variations with time: “Hydrograph”
Meramec River, Missouri May 2000
S=27.8’ Q=56,000 cfs
Criss
Hydrograph
= plot of discharge vs. time, or
= plot of stage vs. time
Mean Flow
Qmean Area
Flood Hydrographs
Q Area
small watersheds
?
Q √(Area)
large watersheds
?
Storm & Annual Hydrographs can have rather similar forms
3788 mi2 = 9810 km2
Q, cfs
calculated
S, ft
measured
Ppt, in
measured
175 mi2 = 453 km2
Q, cfs
calculated
S, ft
measured
Ppt, in
measured
Stage Measurement: Staff Gage
Kanawah River, WVA NOAA
Stilling Well
Stage Measurement:
Recording Stilling Well
USGS Circ. 1123
Velocity
Measurement
Wading
Rod
<Current
Meter &
Weight ->
USGS
USGS Real-Time
USGS Stream Gaging program (USGS Circular 1123)
7292 stations, 4200 telemetered
GOES
DOMSAT
Geostationary Operations Environmental Satellite
Domestic Satellite
USES: Flood Forecasting
Reservoir Operations
Floodplain Engineering
Flow Regulation
Environmental & Pollution Regulation (Flow Minimums)
Highway & Bridge Design
Scientific Studies
USGS Real-Time Data Flow
USGS Circular 1123
Eureka Gauging Station
Since 1922
Criss
40.4 sq. mi.
downstream
781 sq mi
downstream
1475 sq mi
3788 sq mi
S, ft.
Q, cfs.
S, ft.
Q, cfs.
S, ft.
Q, cfs.
+
0 cfs.
-
259 sq. mi.
560 sq. mi.
781 sq. mi.
downstream
199 sq. mi.
3788 sq mi
downstream
1475 sq mi
Fetter, 2001
Freeze &
Cherry, 1978
Criss 2003
Hydrograph
= plot of discharge vs. time, or
= plot of stage vs. time
Mean Flow
Qmean 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
Qmean 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/2m)(a2-y2)
uavg = Ga2/3m
Q ~ g s W a3/3ncm3/sec
Pipe Flow
u = (G/4m)(a2-r2)
uavg = Ga2/8m
Q = g s p a4/8ncm3/sec
where G= “pressure gradient”, s=slope, 2a = slot depth or tube radius; W=width
m viscosity;
kinematic viscosity n=m/r cm2/sec
LAMINAR
SLOT FLOW
u =G(a2-y2)/2m
uavg = Ga2/3m
a
0
a
u = uavg @ a/√3 = 0.577 down
a
LAMINAR
PIPE FLOW
0
u =G(a2-r2)/4m
uavg = Ga2/8m
u = uavg @ a/√2 = 0.707 down
a
LINEAR RESERVOIR (Chow, 14-27)
Storage Outflow =>
S = Q/k
Also,
- dS/dt = Q
(material balance requirement)
Total flow = Base Flow:
Q = Qoe
-kt
where Qo is (peak) discharge @ t 0
For complete depletion, the "Total Potential GW Discharge" is,
Vol =
¥
ò Qdt = Q /k
o
0
Q = Qoe
-kt
Vol =
¥
ò Qdt = Q /k
o
0
Q = Qoe
-kt
1.5
Linear Reservoir
Qo=10
1
3.2
2.4
LogQ
1.6
0.5
0.8
0
0
-0.8
-0.5
Q = Qoe
-1
-kt
-1.6
-2.4
-3.2
-1.5
0
1
2
Time
3
4
5
LnQ
Note: not linear,
but Concave Up
Q =7.07*Exp{-1.25*(t-tpk)}
observed
Q =1.2*Exp{-0.2083*(t-tpk)}
QBGS = 7.07* Q (0.35, 56.167, 1)
observed
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 H2O 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 H2O 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 H2O sfc, dimensionless, e.g. ft/ft)
b. Manning (1889) Equn
Uavg = Q/A = (1/n) R2/3 S1/2 m/s
note: units!
where:
“n” = Manning roughness coeff. “n” , in units of sec/m1/3
n= 0.012 (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=3R1/6/2C where C=Chezy coeff. impossible unless n or C depends on scale!
3) WEIRS
Rectangular:
Qcfs = 3.333 ( L - H/5) H3/2
90° V-Notch:
Qcfs =
2.5 H5/2
where H, L in ft.
HH
Culvert:
See Chow 15-33; USGS Circ. 376)
Fetter p. 58
3) WEIRS
Rectangular:
Qm3/s = 1.84 ( L - H/5) H3/2
90° V-Notch:
Qm3/s = 1.379 H5/2
where H, L in m.
H
Culvert:
See Chow 15-33; USGS Circ. 376)
Fetter p. 58
3) WEIRS
Rectangular:
Qm3/s = 1.84 ( L - H/5) H3/2
90° V-Notch:
Qm3/s = 1.379 H5/2
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:
Qcfs = 3.333 ( L - H/5) H3/2
90° V-Notch:
Qcfs = 2.5 H5/2
V-Notch:
Culvert:
Qcfs =
æq ö
8
C d 2g tanç ÷H 5 /2
è2ø
15
See Chow 15-33; USGS Circ. 376)
Units!
Cd= “discharge coeff”;
Chow 7-46
http://www.hubbardbrook.org
V-Notch Weir
http://www.hubbardbrook.org
4) AREA-VELOCITY METHOD
Current Meter
Divide current into 15-30 segments
Measure velocity @ 0.6*depth of segment (60% down)
or, if channel is deep, take average v @ 0.8 and 0.2 times the depth.
Q = Vavg*A
Q = Sqi = S vi di wi
where:
vi = segment velocity
di = segment depth
wi = 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
Qcfs = Sa
or
Qcfs = (S - So)a
Make polynomial fit
where
USGS
So = stage @ zero flow
End L8
Stop
Is base flow
maximized or minimized
during peak streamflow?
Look at real systems.
Criss (2003)
after Fetter (2001)
& Freeze & Cherry (1979)
SMOW
dD
dD = 8 d18O + 10
d18O
Craig 1961
Criss (1999)
Criss
Isotopic Method of Hydrograph Separation
Total
Streamflow
=
Direct + Ground
Runoff
Water
Qsf
= Qof +
(
)
(
Qbf
)
(
)
d 18Osf Qsf = d 18Oof Qof + d 18Obf Qbf
Qbf
Qsf
æ d 18O - d 18O
sf
of
= ç 18
ç d Obf - d 18Oof
è
ö
÷
÷
ø
3a2001 Hydrograph Separation
Discharge
l/s
Winston & Criss 2004
Fetter, 2001
Freeze &
Cherry, 1978
Criss 2003