Geography Reference
In-Depth Information
24
100
L
= 3.0e
(0.825)
r
2
= 0.94
16
14
12
10
3
4.1
S
r
2
= 0.69
R
= 0.73e
(0.375)
r
2
= 0.61
m
= 2.2
+
20
80
2.5
60
Jiu (1.3)
Sacr. (1.4)
Prypyat (1.5)
Kabompo (1.6)
Mamoré (1.7)
Tana (1.8)
Manu (1.9)
Koyukuk (2.0)
Guaviare (2.1)
Purus 2 (2.3)
16
median
8
2
40
12
6
4
2
0
1.5
20
8
0
1
1
10
100
1.2
1.4
1.6
1.8
2
2.2
1.2
1.4
1.6
1.8
2
2.2
Lake length (channel widths)
S
S
(a)
(b)
(c)
Figure 11.3
Example of illustrations provided by Constantine and Dunne (2008) within their study of 30 meandering reaches
worldwide from Google Earth images : in (a) the cumulative size-frequency distributions of oxbow lake length, b) The geometric
mean lake length (
L
) and c) The geometric mean meander length (
m
) and the ratio (R) of the geometric mean lake length to m both
b) and c) versus the reach sinuosity (S). Reproduced from Constantine, J.A. & Dunne, T. (2008) Meander cutoff and the controls on
the production of oxbow lakes. Geology; 36(1):23-26, with permission from the Geological Society of America.
10
v: Vermillion R.
n: Neuse R.
m: Minnesota R.
b: Bogue chitto R.
p: Pearl R.
s: Sacramento R. (2 different time
periods)
st: Strickland R. (2 different time periods)
f: Fly R.
+Δ
t
Channel at t
st1
st2
f
s1
s2
Channel at t
V(s)
Δ
t
θ
(s)
p1
1
y = 5.70x
R
2
= 0.998
b1
p2
b2
m
p4
s(t)
p3
s(t)
+Δ
t
v
n
b3
0.1
0.010
0.100
1
.0
00
Rate of relative sinousity increase
ε
(1/yr)
∗
Width
B
(m)
(a)
(b)
Figure 11.4
a) Measured variables, b) Relationship between reach-average lateral migration and relative sinuosity increase. The
regression is for the best datasets only (represented here using filled symbols).
where corresponding points on the older and newer cen-
terline were identified using short Bezier curves oriented
normal to both axes (note that similar rates
ds/dt
could
also be determined simply by finding the nearest point
along the centerline arc at time
t
+Δ
t
to a given point at
coordinate
s
and time
t
). The cumulative rate of change
in channel coordinate,
ds/dt
, is then found by simple
difference:
of bend elongation vs. lateral translation in a given reach.
Dividing the reach elongation rate by reach length gives
a rate of relative sinuosity increase
ε
for the reach. The
variable
is used rather than the actual rate of sinuosity
increase (reach elongation rate/valley distance) because
ε
can be determined directly from channel centerlines,
without developing a separate centerline for the valley.
Developi
ng
a dimensionally homogenous relationship
between
|
V
|
and
ε
requires a second le
n
gth scale. We
assume that reach-average channel width
B
is appropriate
for this purpose and combine the variables into a single
dimensionless relative sinuosity change rate as follows:
ε
ds
s
(
t
+ Δ
t
)
−
s
(
t
)
dt
=
.
(11.2)
Δ
t
Note that
ds/dt
can also be approximated by accumulating
a set of local rates if multiple aerial images with different
dates are present for different portions of the reach.
However, the translation from an elongation rate or,
nearly equivalently, a sinuosity change rate to a reach-
average migration rate depends on the relative amount
|
V
|
B
E
∗
=
ε
.
(11.3)
In Figure 11.4b, cumulative up-channel elongation
rates are clearly correlated with lateral migration and are
Search WWH ::
Custom Search