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Alluvial vs. bedrock channelsAlluvial vs. bedrock channels
Hydraulic geometryHydraulic geometry
W, h, U, d W, h, U, d5050
Qbf (bankfull)Qbf (bankfull)
R.I. = 1.5 yrs R.I. = 1.5 yrs
W = QW = Q0.50.5
Hydraulic geometryHydraulic geometry
? ?
Qbf (bankfull)Qbf (bankfull)
R.I. = ? R.I. = ?
W = QW = Q??
alluvialalluvial
bedrockbedrock
22
(a) Rock-type and wetting-(a) Rock-type and wetting-drying cyclesdrying cycles (Stock et al., 1996)(Stock et al., 1996)
(b) Bedload tools(b) Bedload tools(Slingerland et al., 1997; Sklar and Dietrich, 1998)(Slingerland et al., 1997; Sklar and Dietrich, 1998)
1. Stable Q, increased q1. Stable Q, increased qss, , cool climatecool climate
2. Flashy Q, decrease q2. Flashy Q, decrease qssdry climatedry climate
(c) Climate (c) Climate Meyer et al., 1995Meyer et al., 1995
Climate, straths, valley widths, and incisionClimate, straths, valley widths, and incision
33
Tomkin et al., Figure 3Channel-Valley-Profile Interpolation.JNB
distance from coast (km)0 10 20 30 40 50 60 70 80
elev
atio
n (m
)
0
200
400
600
800
1000
1200
valleyprofile
channel profilefrom contour map
Long profilesLong profiles
Q, W, dQ, W, d5050
44
55
SL = (Z/X)(L)
66
= 0.55ks = -1.68 = 0.021
S = kS = kssAA
77
Modeling bedrockModeling bedrockincisionincision
abbkE
3/23/1
W
gSQC fwb
cqAkQ
bcbqw
bw AkkQkW
nmSKAE
(1)(1)
(2)(2)
(3)(3)
(4)(4)
(5)(5)
1 <1 < aa < 5/2< 5/2
CCff = dimensionless friction factor = dimensionless friction factor
cc ~ 1 for small, steep drainages; Next slide ~ 1 for small, steep drainages; Next slide
bb ~ 0.5; Second slide ~ 0.5; Second slideccombine with conservation of massombine with conservation of massand steady, uniform flow and steady, uniform flow Q=WhUQ=WhU
m/n = c(1-b)m/n = c(1-b)Calibration : Stock and Montgomery, 1999Calibration : Stock and Montgomery, 1999Snyder et al., 2000Snyder et al., 2000
Much has been said about this equation and we have not heard the final word. It hasMuch has been said about this equation and we have not heard the final word. It hasbeen an honest, exploratory attempt to reduce the complexities of a system we do notbeen an honest, exploratory attempt to reduce the complexities of a system we do notfully understand into a useful, simple expression that describes incision. Many of the fully understand into a useful, simple expression that describes incision. Many of the earlier calibration studies assumed uniform incision (uplift) and an equilibriumearlier calibration studies assumed uniform incision (uplift) and an equilibrium(graded) profile…..we are motivated to calibrate and extract useful tectonic information(graded) profile…..we are motivated to calibrate and extract useful tectonic informationwhere incision (uplift) is not uniform along the profile.where incision (uplift) is not uniform along the profile.
88
Drainage area, A (km2)10 100
Dis
char
ge,
Q (
m3 /s
)
1
10
100
1000
r2 = 0.99
r2 = 0.99bankfullQ = 0.2 A1.06
low flowQ = -0.33 A0.61
Discharge – Area relationshipsDischarge – Area relationships
c ~ 1 for wet climates, maybe best for bankfullc ~ 1 for wet climates, maybe best for bankfull
c ~ 0.5 for arid climatesc ~ 0.5 for arid climates
Clearwater RiverClearwater River
99
Drainage Area, A km2
1 10 100 1000 10000
Wid
th,
W (
m)
0.1
1
10
100
b = 0.47
b = 0.29
(Bedrock) channel widths
Tomkin et al., Tomkin et al., in pressin press (Clearwater R.) (Clearwater R.) b ~ 0.42 b ~ 0.42Snyder et al., 2000 Snyder et al., 2000 b ~0.6-0.7 b ~0.6-0.7
Mitchell
Discharge, Q (m3/s)0.1 1 10
Wid
th,
W (
m)
1
10
100
1000
10000
Rio Hondo
Jemez River
b=0.73 b=1.35
b=0.68
Discharge, Q (m3/s)0.01 0.1 1 10
Wid
th,
W (
m)
0.1
1
10
100
b = 0.59
b = 0.38
low flow
bankfullb for mixed bedrock-alluvial channels in N. NMb for mixed bedrock-alluvial channels in N. NM
~ 0.5 (bankfull width) wrt drainage area~ 0.5 (bankfull width) wrt drainage area~ 0.6 (bankfull width) wrt discharge~ 0.6 (bankfull width) wrt discharge
valley widthsWWbfbf
WWlflf
1010
The equilibrium (steady-state) profileThe equilibrium (steady-state) profile
nmSKAUt
z
nmn
e AK
US /
1
AkS s
(6)(6)
(7)(7)
(8)(8)
Rate of change of channel bed elevationRate of change of channel bed elevation= rate of uplift – incision rate= rate of uplift – incision rate
When When dz/dtdz/dt = 0, = 0, SeSe = equilibrium slope = equilibrium slope
kkss is the profile steepness is the profile steepness
~ stream gradient index of Hack (1973)~ stream gradient index of Hack (1973)
is the profile concavityis the profile concavity~ 0.3 – 0.6 (Hack, 1957)~ 0.3 – 0.6 (Hack, 1957)
……. Tested in the field by the rate of incision reconstructed from terraces. Tested in the field by the rate of incision reconstructed from terraces
Mean annualprecipitation
Precipitationintensity
Mean annualdischarge
Peak annualprecipitation
1515
Lab 4Lab 4Use EZ Profiler to extract a long profileUse EZ Profiler to extract a long profile
Use EZ profiler to extract the flow accumulation values from the flow accumulationUse EZ profiler to extract the flow accumulation values from the flow accumulationraster. Use the same polyline shape file that you used to extract the longraster. Use the same polyline shape file that you used to extract the longprofile. Note what your raster cell size is – you need to know this to computeprofile. Note what your raster cell size is – you need to know this to computethe drainage area. the drainage area.
Bring the long profile (X vs. Z) and flow accumulation profile (X vs. A) into ExcelBring the long profile (X vs. Z) and flow accumulation profile (X vs. A) into Excelor preferably SigmaPlot to or preferably SigmaPlot to
calculate correct areas in km2 based on the cell sizecalculate correct areas in km2 based on the cell size
smooth the long profile (use the Lowess filter in SigmaPlot) smooth the long profile (use the Lowess filter in SigmaPlot)
throw out the area data that are very small numbers – these were notthrow out the area data that are very small numbers – these were notclipped from the channel correctlyclipped from the channel correctly
calculate channel gradientcalculate channel gradient
DeliverablesDeliverables(1) your spreadsheet or SigmaPlot worksheet(1) your spreadsheet or SigmaPlot worksheet(2) a plot with the long profile, SL index, and slope-area inset(2) a plot with the long profile, SL index, and slope-area inset