More Tools from
Fluvial
Geomorphology
Brian Bledsoe
Department of
Civil and Environmental Engineering
Colorado State University
1
Tools we will focus on at present:
– previous presentation
 Hydraulic geometry
 Planform geometry
 Meandering / braiding ‘threshold’
 Qualitative response models
 Historical analysis
 Classifications
2
Hydraulic Geometry
An analog or regime approach
3
Regime Theory / Hydraulic Geometry
(e.g. Lacey 1929, Leopold and Maddock 1953)
Channel parameters may be sufficiently
described with power functions utilizing Q as
the sole independent variable
w  aQ
b
h  cQ
f
Q  whv  (a  c  k )Q
v  kQ
m
b f m
ack  b  f  m 1
4
Hydraulic Geometry - Exponents
At-a-Station
Downstream
b  0.1  0.2
b  0.5
f  0.4
f  0.33  0.40
m  0.4  0.5
m  0.10  0.17
b is width, f is depth, and m is velocity
5
Downstream hydraulic geometry
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7
The Basic Issue
Predicting channel width / depth in the
context of heterogeneous bed and bank
conditions
w, h, S, v
•
Continuity
Friction loss
Sediment transport or incipient motion
•
???
•
•
8
Hydraulic Geometry Approach
in Stable Channel Design
•
Rooted in regime theory of Anglo-Indian
engineers
• Canal design
• Low sediment loads
• Low variability in Q
•
•
•
Does not directly consider sediment load
(slope equations are dangerous for sand
bed channels)
Neglects energy principles and time scales
of different adjustment directions
Fluvial system is actually discontinuous,
e.g. tributaries, variability in coefficients 9
Downstream hydraulic geometry
equations for width provide an
important channel design and
analysis tool
Depth, velocity, and slope
equations are less reliable
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11
12
13
Some Factors Affecting a
w  aQ
0.5
•
Vegetation / soils / light interactions
• Root reinforcement and depth / bank height
• Woody debris inputs and bank roughness
• Bank cohesion / stratigraphy / drainage
• Freeze / thaw
• Sediment load
• Flow regime (e.g. elevation of veg. on banks)
• Return period of extremes vs. recovery time
• Lateral vs. vertical adjustability / time
• Historical context
14
Downstream Hydraulic Geometry
and Boundary Sediments
Schumm (1960)
w
1.08
 255M
h
Richards (1982)
w
0.15 1.20
 800Q B
h
15
16
Hey and Thorne (1986)
All Veg. Types
Bankfull Width (m)
100
y = 3.663x0.4468
10
1
1
10
100
1000
Bankfull Discharge (cms)
17
Hey and Thorne (1986)
Separate Vegetation Types
Bankfull Width (m)
100
10
Veg Type 1
y = 5.1864x0.4468
Veg Type 2
y = 3.2647x0.5015
Veg Type 3
y = 1.969x0.5702
Veg Type 4
y = 1.9209x0.5444
1
1
10
100
1000
Bankfull Discharge (cms)
18
Downstream Hydraulic Geometry
and Vegetation – Gravel Channels
w  aQ
0.5
Hey and Thorne (1986)
Grassy banks  a = 4.33
• 1-5% tree / shrub  a =
3.33
• 5-50% tree / shrub  a =
2.73
• > 50% tree / shrub  a =
2.34
Andrews
(1984)
•
Thin  a = 4.3
• Thick  a = 3.6
•
19
Downstream Hydraulic Geometry
and Vegetation – Sand Channels
Small rivers are not well represented in the data set, and extrapolation is
required if applied when discharge is less than 17 m3/s and 38 m3/s in type
T1 and T2 channels, respectively
Soar and Thorne (2001)
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22
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24
Width (m)
10
1
Davies-Colley forest
Davies-Colley pasture
Hession et al. forest
Hession et al. non-forest
1
Hey and
Thorne (1986)
and Charlton
et al. (1978)
data
10
Drainage Area (km 2)
100
25
26
100
Width (m)
Davies-Colley
(1997) and
Hession et al.
(2003) data
10
Hey and Thorne thick
Hey and Thorne thin
Charlton et al thick
Charlton et al thin
10
100
Qbf (m 3/s)
27
Grass
Log Channel Width
Forest
10 -100 km2
Log Watershed Area
28
% Silt and Clay
29
Root Density (ml l-1)
30
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Values of a in w =
0.5
aQ
Unit
System
Very
Wide
Average
Width
Very
Narrow
English
2.7
2.1
1.3
SI
4.9
3.8
2.3
Vegetation Density, Stiffness, Root Reinforcement
Bank Cohesion
?
Suspended Sediment Load
Bed Material Size / Braiding Risk
32
Summary
 Downstream
hydraulic geometry
relationships for width can provide a
useful, additional relationship in channel
design
 Selection of the coefficient a is
complicated and requires consideration of
many factors
 Vegetation effects tend to override
sedimentary effects
 Processes are scale-dependent?
33
Planform Geometry
Direction of response is much easier to
predict than direction of response
34
Meandering and Planform
Design
Photo by Frans Lanting
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From Leopold (1994)
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Photo by Frans Lanting
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40
From Leopold (1994)
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42
43
44
45
After Thorne (1997)
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47
48
ccc
49
50
Initial planform layout
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Meandering – Braiding
Threshold
52
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54
55
56
Uvas Creek
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Uvas Creek
58
Planform Predictors
Meandering-Braiding Threshold
59
(a)
0.01
LEO
PO
LD
SLOPE (m/m)
LANE
&W
OLM
AN
BRAIDED
0.001
LANE
TRANSITIONAL
S Q 0 .2 5
S Q 0 .4
0.0001
MEANDERING
4
S Q 0 .2 5
= 0.0
041
=0
.01
25
= 0.0
0070
0.00001
1
10
100
1000
10000
100000
MEAN ANNUAL DISCHARGE (m3/s)
(b)
60
61
62
The units for w and d50 in the equation
for the braiding threshold in the
previous slide are W/m2 and meters,
respectively. Be sure to use valley
slope in the van den Berg equation.
wv  2100 S v Qbf
wv  3300 S v Qbf
for sand channels
for gravel channels
63
1
Braided
Meandering
90%
SvQ0.5 (m1.5/s0.5)
0.1
70%
50%
30%
10%
0.01
0.001
10
100
D50 (mm)
64
A useful guideline:
In many contexts, as
width/depth at ~Q2
approaches 40-50, braiding
becomes likely
65
66
1
Braided
Incised
Meandering
SvQ0.5 (m1.5/s0.5)
0.1
0.01
90%
70%
50%
30%
10%
0.001
0.0001
0.1
1
D50 (mm)
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Qualitative Response
Models
Direction of response is much easier to
predict than magnitude of response
70
LANE’S BALANCE
QS ~ Q s D 50
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72
Construction Phase - Sediment Delivery 
Q+S ~ Qs+ds
Post-Construction - Sediment Delivery 
Q++S-- ~ Qs- ds+
Incision and Widening
73
Alteration
Schumm’s River
Metamorphosis
Q+
QQsb+
Qsb-
Response
Width
Depth
Ratio
Sinuosity
So
d50
Meander
Wavelength
w
d
w/d
l
P
+
+
-
+
+
+
-
+
+
+
+
-
+
+
-
+
Slope
Grain Size
+
74
Alteration
Schumm’s River Metamorphosis
– Part II
Slope
Grain Size
Width
Depth
Ratio
Meander
Wavelength
Sinuosity
So
d50
w
d
w/d
l
P
Q+ Qsb+
±
±
+
±
+
+
-
Q- Qsb-
±
±
-
±
-
-
+
Q+Qsb-
-
+
±
+
±
±
+
Q-Qsb+
+
-
±
-
±
±
75
Response
-
76
Downs (1995)
Rosgen in
NRCS (2007)
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Historical analysis
78
A few examples
 Aerial
photos
 Early surveys / maps
 Comparative surveys – x-sections,
thalweg
 Sediment budgets
 Specific gage analysis
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Historical surveys / maps
82
Repeat surveys
83
84
Sediment budgets
mass movements or
small fluvial events
colluvium, vertical accretion
+
-
flushing
20 - 100
years
High-energy instability, mountain and arid streams. (adapted from Trimble,
S.W.,1995. Changing River Channels. John Wiley & Sons, Chichester. pp. 212.)
85
Specific gage
86
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NRCS (2007) adapted from
Copeland et al. (2001)
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