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Dual Effects of Soil Creep and Hydraulic Erosion on Geomorphologic Evolution
Leah Edwards 11/17/06
Variables:
Kg= erosion diffusivity coefficient
Kh= hydraulic transport coefficient
Equations:
qc=KcS
qh=KhxmSn
Geomorphologic Evolution after Impulse Uplift
Q1: The driving force for this geomorphologic evolution is dominated by gravity and water, in addition to
tectonic activity, which provides the initial uplift. The gravity driven aspect is the erosion due to soil creep
and is represented by the term KgS (where Kg is the diffusivity coefficient and S is the slope). The water
driven aspect is the hydraulic erosion given by KhxmSn (where Kh is the hydraulic transport coefficient, xm is
the water discharge, and Sn is the slope). Hydraulic erosion causes more concave slopes. The flux of water
equals zero at the peak because it is a no flux boundary. Flux of water is high at the base of the slope
because the groundwater level is high, meaning that the soil is saturated and overland flow is high. Soil
creep causes more convex shaped slopes that round out the top of the mountain and prevents a knife edge
slope that would otherwise form if there were only hydraulic erosion. Soil creep helps to bring down the
height of the slope over time and flattens out the concavities. 3/3
2
Comparing Geomorphologic Evolution with Different Magnitudes of Transport Processes for Impulse Uplift
H(x,t)
Kg=.1
Kg=.01
H(x,t)
Kg=.01
Kg=.1
Kg=.4
Kg=.4
Kg=3
Kg=3
X
t
3
Q2: In the graphs above, Kh is held constant at a value of 1.0 and Kg is varied.
The spatial profile shows how the slope changes across its distance x when t=.5. When Kg is small, the
slope is shaped like a knife-edge, because there is mostly just hydraulic erosion which causes the very
concave shape. When Kg is medium, the top of the mountain becomes more rounded out and the slopes are
increasingly convex. When Kg is high, the mountain is completely flat. Therefore, as Kg increases, concave
slopes become more convex in a general flattening and smoothing process.
The temporal profile shows how the slope changes with time at the point where x=.5. For each of the
different Kg values, the height of the mountain is zero until time equals .1. The impulse uplift occurs from
t=.1 to t=.2, and the mountain height peaks at t=.2. The higher the Kg value, the lower the maximum peak.
Also, the higher the Kg, the faster the peak will come down due to sol creep because the limiting angle is
reached sooner. When Kg is small, the maximum height reached is about .045 by the time t=1 and is still
coming down. When Kg is medium, the slope has pretty much flattened to a height of zero by t=1. When
Kg is high, the slope flattened to a height of zero much sooner, at t=.3.
In the next set of graphs, Kg is held at a constant value of .4 while Kh is varied.
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Kh=.1
H(x,t)
H(x,t)
Kh=1
Kh=3
Kh=5
X
Kh=.1
Kh=1
Kh=3
Kh=5
t
5
Q2 Continued: The above graphs show the slopes when Kg is held constant at .4 and Kh is varied.
The spatial profile shows that when Kh is small, the shape is very convex because erosion is mostly due to
gravity driven soil creep. When Kh is medium, the shape begins to become more concave. There is a stream
located at x=0 and x=1. Water takes sediment out with it in greater quantities at the base of the slope where
it is saturated. Therefore, sediment transport is higher at the base, causing a concave shape. The flux of
water is zero at x=.5 because it is a no flux boundary at the top of the mountain, so sediment transport is
lower at the top of the slope and brings the height down less quickly than at the bottom.
The temporal profile shows that for all variations, height equals zero until t=.1, uplift occurs from t=.1 to .2,
the height peaks at t=/2 and begins to come down thereafter. Each of the slopes reach about the same
maximum height because hydraulic erosion does not bring this height down since there is very little water
flux at the boundary divide. Soil creep is responsible for rounding out the top of the mountain and in this
case, Kg is being held constant. The profile also shows that the higher the Kh value, the faster the slope will
come down, because more hydraulic erosion results from a higher Kh value.
The next set of graphs give different combinations in which both variables, Kh and Kg, are being changed.
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H(x,t)
H(x,t)
Kg=.1 Kh=.1
Kg=.4 Kh=.1
Kg=3 Kh=5
X
Kg=.1 Kh=.1
Kg=.4 Kh=.1
Kg=3 Kh=5
t
7
Q2 Continued: The above graphs show combinations of the two processes, soil creep and hydraulic erosion.
When Kg and Kh are both relatively low values, the spatial profile shows that the slope is mostly convex.
The temporal profile shows that it has the highest maximum peak height, and that height decreases with time
at a slower pace and does not reach zero by the time t=1.
When Kg and Kh are medium values, the spatial profile shows the shape as somewhat concave. The
temporal profile shows that its maximum height is lower, and that it flattens at a faster rate, reaching h=0 at
about t=1.
When Kg and Kh are both relatively high, the spatial profile shows that the slope is completely flat. From
the temporal profile, it has the lowest maximum height and flatten at the fastest rate, reaching h=0 at about
t=.3.
Therefore, the combination of the two processes can give way to varying shapes and temporal changes on the
slope. In general, it can be concluded that as Kg increases, the slope becomes more convex and smoothed
over until it is flat. As Kh increases, the slope becomes increasingly concave. Both processes help to bring
down the height of the slope at increasingly faster rates.
Very good. 3/3
8
Comparing Different Kinds of Tectonic Uplift: Impulse vs. Persistent
persistent
H(x,t)
H(x,t)
persistent
impulse
impulse
X
t
Q3: The graphs shown here compare the geomorphologic evolution of slopes caused by different uplifts:
impulse and persistent. In these graphs, Kh and Kg are held constant at 1.0 and .4 respectively. 2/2
The spatial profile shows that at t=.5, the impulse uplift has a much lower maximum peak (h=.01) and
persistent uplift has a height of .12. However, they both have a similar convex shape. The temporal profile
shows that at x=.5, both kinds of uplift give a height of zero until t=.1 and then uplift begins. In impulse
uplift, the height peaks at t=.2 and then begins to come down until it reaches zero. For persistent uplift, the
height continues to increase until it begins to level out at a maximum height of .14.
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Comparing Geomorphologic Evolution with Different Magnitudes of Transport Processes for Persistent
Uplift
Kg=.01
Kg=.1
H(x,t)
H(x,t)
Kg=.01
Kg=.1
Kg=.4
Kg=.4
Kg=3
Kg=3
t
X
10
Q4: In the above set of graphs, Kh is held constant at 1.0 and Kg is varied. Kh is too high compared to Kg.
So, you got quite concave slopes.
The spatial profile for persistent uplift, as was found for impulse uplift, shows that when Kg is small, a knifeedge slope results, characterized by its concave shape because the majority of the shape is due to the
hydraulic erosion. When Kg is medium, the shape is less concave and more convex, and the top begins to
become rounded out. When Kg is high, the slope is almost completely flattened out. Therefore, the effect of
the soil creep coefficient is, once again, that it contributes to a smoothing process that turns concavities into
convexities and rounds out the peak height.
The temporal profile shows that height is zero until uplift begins at t=.1. Because it is persistent uplift, the
height continues to rise as time goes on. When Kg is low, height continues to increase, even at t=1. When
Kg is medium, height is increasing but at a slower rate and begins to level out around t=1. When Kg is high,
the height increases slightly but uplift levels out completely much sooner, at about t=.2. Therefore, the
higher the Kg, the slope becomes time-independent, or reaches a steady state, sooner than when Kg is lower,
in addition to not being able to reach as high maximum heights as would other wise be possible.
Kh=.1
Kh=.1
Kh=1
Kh=1
Kh=3
Kh=5
Kh=3
H(x,t)
H(x,t)
11
Kh=5
X
t
12
Nice graphs.
Q4 Continued: In the above graphs, Kg is held constant at .4, while Kh is varied.
The spatial profile again shows, as we saw in the impulse uplift, that as Kh increases, the slope becomes
increasingly convex.
The temporal profile shows that persistent uplift begins at t=.1 and continues to cause the mountain height to
rise. When Kh is low, the height is still increasing by the time t=1. When Kh is medium, it reaches a steady
state around t=1. When Kh is high, it reaches a steady state much sooner, around t=.5. Therefore, as Kh
increases, the steady state is reached sooner and at a lower maximum height.
3/3
Total: 11/11 = 10.0 Excellent.
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Kg=.1 Kh=.1
Kg=.4 Kh=1
Kg=3 Kh=5
X
H(x,t)
H(x,t)
Kg=.1 Kh=.1
Kg=.4 Kh=1
Kg=3 Kh=5
t
14
Q4 Continued: In this final set of graphs, both variables Kh and Kg are changing.
When they are both relatively low, the spatial profile shows that the slope is somewhat concave. The
temporal profile shows that it has not reached steady state yet and height is still increasing when t=1 at a
height of .35. When they are both relatively medium values, The shape is more convex, beginning to round
out at the top, and reaches a lower maximum peak. It also reaches a steady state by the time t=1 at a height
of .1. When they are both very high values, the shape very flat and has reached a steady state very quickly at
time t=.2 at a height of .02.
These graphs show the effects of the combinations of the two variables on the shape and temporal changes of
the mountain. The same conclusions are drawn as those that came from the analysis of the impulse uplift.
As Kg increases, the slope becomes smoother and more convex. As Kh increases, the slopes become more
concave. The main difference in the impulse and persistent uplift models is that persistent uplift causes the
mountain to continually rise. These processes of erosion, driven by Kh and Kg, help to bring the slope to a
steady-state, time-independent height. In contrast, impulse uplift gives an initial rise which then stops. The
height of the mountain is then brought down and flattened by these processes until there is no slope because
height equals zero.