Transcript modeling_long_profiles

Alluvial vs. bedrock channels
alluvial
Hydraulic geometry
W, h, U, d50
Qbf (bankfull)
R.I. = 1.5 yrs
W = Q0.5
bedrock
Hydraulic geometry
?
Qbf (bankfull)
R.I. = ?
W = Q?
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Climate, straths, valley widths, and incision
(b) Bedload tools
(Slingerland et al., 1997; Sklar and Dietrich, 1998)
(a) Rock-type and wettingdrying cycles
(Stock et al., 1996)
(c) Climate 
Meyer et al., 1995
1. Stable Q, increased qs,
cool climate
2. Flashy Q, decrease qs
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dry climate
Long profiles
1200
channel profile
from contour map
elevation (m)
1000
Q, W, d50
800
valley
profile
600
400
200
0
0
10
20
30
40
50
60
distance from coast (km)
70 3
80
160
60
150
50
140
40
130
30
120
20
110
10
100
0
2000
4000
6000
8000
10000
12000
0
14000
10000
12000
14000
area (km2)
70
elevation (m)
170
distance (m)
0.1
slope
0.01
0.001
0.0001
0
2000
4000
6000
8000
distance
4
170
70
SL = (DZ/DX)(L)
160
50
60
40
40
130
30
120
20
30
20
10
110
10
100
0
14000
0
2000
4000
6000
8000
10000
12000
0
distance (m)
5
SL index
140
area (km2)
50
elevation (m)
150
-
S = ksA
160
150
70
0.01
60
40
50
0.001
1
elevation (m)
50
10
100
area (km2)
140
40
130
30
120
20
30
20
10
110
10
100
0
14000
0
2000
4000
6000
8000
10000
12000
0
distance (m)
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SL index
170
 = 0.55
ks = -1.68 = 0.021
area (km2)
channel gradient (m/m)
0.1
(1)
Ek
a
b b
1 < a < 5/2
(2)    C 1/ 3  gSQ 
b
w f 

W


(3)
(5)
2/3
Q  kq A
c
(4) W
Cf = dimensionless friction factor
c
~ 1 for small, steep drainages; Next slide
 kwQ  k k A
b
E  KA S
m
Snyder et al., 2000
b
w q
n
Modeling bedrock
incision
bc
b ~ 0.5; Second slide
combine with conservation of mass
and steady, uniform flow Q=WhU
m/n = c(1-b)
Calibration : Stock and Montgomery, 1999
Much has been said about this equation and we have not heard the final word. It has
been an honest, exploratory attempt to reduce the complexities of a system we do not
fully understand into a useful, simple expression that describes incision. Many of the
earlier calibration studies assumed uniform incision (uplift) and an equilibrium
(graded) profile…..we are motivated to calibrate and extract useful tectonic information
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where incision (uplift) is not uniform along the profile.
Discharge – Area relationships
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Discharge, Q (m /s)
1000
bankfull
Q = 0.2 A1.06
100
10
1
10
r2 = 0.99
Clearwater River
low flow
0.61
Q = -0.33 A
r2 = 0.99
100
2
Drainage area, A (km )
c ~ 1 for wet climates, maybe best for bankfull
c ~ 0.5 for arid climates
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(Bedrock) channel widths
100
10000
Rio Hondo
b = 0.47
10
valley widths
1000
Width, W (m)
Width, W (m)
Wbf
b = 0.29
Wlf
1
Jemez River
100
Mitchell
b=0.68
10
b=1.35
b=0.73
1
0.1
0.1
1
10
100
1000
Drainage Area, A km
1
2
100
b for mixed bedrock-alluvial channels in N. NM
Tomkin et al., in press (Clearwater R.)  b ~ 0.42
Snyder et al., 2000  b ~0.6-0.7
bankfull
Width, W (m)
~ 0.5 (bankfull width) wrt drainage area
~ 0.6 (bankfull width) wrt discharge
10
Discharge, Q (m3/s)
10000
b = 0.38
10
low flow
b = 0.59
1
0.1
0.01
0.1
1
3
10
Discharge, Q (m /s)
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The equilibrium (steady-state) profile
(6)
z
 U - KAm S n
t
Rate of change of channel bed elevation
= rate of uplift – incision rate
1
n
U


(7) S    A- m / n
e
K
(8)
S  ks A
-
When dz/dt = 0, Se = equilibrium slope
ks is the profile steepness
~ stream gradient index of Hack (1973)
 is the profile concavity
~ 0.3 – 0.6 (Hack, 1957)
…. Tested in the field by the rate of incision reconstructed from terraces
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Mean annual
precipitation
Precipitation
intensity
Mean annual
discharge
Peak annual
precipitation
Lab 4
Use EZ Profiler to extract a long profile
Use EZ profiler to extract the flow accumulation values from the flow accumulation
raster. Use the same polyline shape file that you used to extract the long
profile. Note what your raster cell size is – you need to know this to compute
the drainage area.
Bring the long profile (X vs. Z) and flow accumulation profile (X vs. A) into Excel
or preferably SigmaPlot to
calculate correct areas in km2 based on the cell size
smooth the long profile (use the Lowess filter in SigmaPlot)
throw out the area data that are very small numbers – these were not
clipped from the channel correctly
calculate channel gradient
Deliverables
(1) your spreadsheet or SigmaPlot worksheet
(2) a plot with the long profile, SL index, and slope-area inset
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