11

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