Geology Reference
In-Depth Information
profile below which a stream can not degrade
and at which neither net erosion nor deposi-
tion occurs” (Bull, 1991). When a river is at
the base level of erosion, its equilibrium
longitudinal profile can be regarded as an
infinite succession of adjacent local base
levels that will be unchanging until the con-
trolling variables on the system change
(Gilbert, 1879). As the river adjusts to imposed
changes over time, it may re-establish an equi-
librium profile at several positions within the
landscape.
3
Channel versus Hillslope Relief
ridge profile
2
hillslope
relief
channel
relief
1
A
c
: critical area
0
0
5
10
15
20
25
Distance (km)
Fig. 8.1
Relief of rivers and hillslopes in nonglacial
landscapes.
River channels occupy most of the relief in many
landscapes. Their incision rates determine local base
level for all bounding slopes, and rivers are the most
geomorphically sensitive element to tectonic
perturbations at Holocene time scales. The critical area,
A
c
, comprises the catchment area above the head of the
fluvial channel. Modified after Whipple and Tucker
(1999).
Theoretical perspective on fluvial erosion
and river profiles
Lowering of a river's profile through time
requires incision of its bed. A river flowing in
alluvium can typically lower its bed much more
readily than one flowing on bedrock. In the
former case, incision depends on mobilizing
sediment on the river bed, whereas in the latter
case, the underlying bedrock has to be loosened
and then mobilized. Hence, these two classes of
rivers are typically defined as
transport-limited
or
detachment-limited
rivers. In Chapter 2, we
briefly examined the concept of stream power
(Box 2.2): a representation of the energy
expenditure that results from changes in potential
energy as water flows downstream. Stream
power can be estimated in the context of a river's
entire discharge at a point:
through 70-90% of the topographic relief of
non-glacial landscapes (Fig. 8.1) (Whipple, 2004),
and, although fluvial channels occupy only a
tiny fraction of any catchment area, their
behavior is a key control on adjacent slopes.
We will, therefore, examine some theoretical,
experimental, and natural responses of rivers to
deformation at the scale of a few meters to tens
of meters over periods of decades to thousands
of years.
Base level
W
=
r
w
gQ
w
S
(8.1)
John Wesley Powell (1875) introduced the
concept of
base level
: the lower limit of the
landscape below which rivers cannot erode. In
most cases, the ultimate base level is sea level,
although in closed tectonic depressions, such as
Death Valley or the Dead Sea, it can be lower.
Local base level
refers to the lowest topographic
point in any particular area. A lake, for example,
represents the lowest level to which upstream
rivers and hillsides can erode for the duration of
the lake's existence. The
base level of erosion
is
a concept that involves all reaches of a fluvial
system. It is the “equilibrium (graded) longitudinal
where
W
is stream power,
r
w
is the density of
water,
g
is gravitational acceleration, and
Q
w
and
S
are total discharge and average channel slope
at that point, respectively. Specific stream power,
or the power per unit area of the bed, is equal to
W
/
w
, where
w
is the bed width. Specific stream
power can also be expressed as the pr
o
duct
of bed shear stress,
t
, and mean velocity,
v
, as
follows:
Ω
/
wg S
=
r
δ
x
/
δ
t
=
t
v
(8.2)
w
where
d
is the water depth,
x
is bed length and
t
is time.
