John Hammond

11/17/06

Matlab Ex 3

Q1:

The driving forces for the geomorphologic evolution illustrated in this graph are theuplift, erosion soil erosion is a general term. soil creep, and hydraulic transport processes along with the effects of gravity. Uplift affects the geomorphologic evolution by thrusting masses of land into the sky as a result of tectonic plates rubbing against one another and is apparent in the graph such that after a small, somewhat miniscule amount of activity between time t = 0 and time t = 0.1, there is a rapid rate of uplift starting at time t = 0.1. This rate of uplift peaks at time t = 0.2 where its height reaches past 0.05. Upon reaching this particular land mass’s maximum elevation, the other processes take effect and ultimately dictate the downward gradient of the hill’s slope. Gravity determines how much erosion and hydraulic transport occurs on the slope which culminates in the total sediment transport equation denoted by qt = (Kh)(qw^m)(S^n) + (Kg)(S). This equation allows an individual to measure how much sediment has entered and exited a particular system that has been previouslydetermined by its own set of boundaries. Gravity induces soil creep which plays into the downward gradient of the slope as well. The process of erosion also acts as a diffusivity diffusion term in that as erosion transports sediment down a hill’s slope, it smoothes things out and produces a more gentle hill face. Hydraulic transport processes produce concavities in the topography by transporting sediment from an area’s upper boundary towards its lower boundary as time passes. These processes are illustrated in the graphs above because starting at time t = 0.2, the slope begins to increase and rates of erosion and hydraulic transport increase as well. As time passes and the value of t increases, the slope increases until reaching the bottom of the hill where it gets smaller and smaller until the hill ultimately becomes nothing more than a flat area of topography. 3/3

Q2:

Graphs whose Kg values differ

You can just capture profiles of elevations like this.

From the graphs above, one can clearly see that the value of the process coefficient Kg greatly affects the geomorphologic evolution of the simulated slope forms. The effect of this erosion diffusivity coefficient is such that the higher the value of Kg, the faster the slope’s material is eroded down the hill. For example, in the first graph where Kg = 0.1, there is a moderate amount of sediment still remaining at the time t = 1. On the second graph where Kg = 0.4, there is still a small amount of material left at time t = 1. In fact, h = 0.01. Finally, on the graph where Kg = 0.7, material has been eroded by the time t = 0.9. Also, the maximum height of each simulated slope differs as a result of the different Kg values. This is a result of the effects of erosion that takes place both as the uplift occurs and after the uplift finishes. For the larger Kg value, in this case Kg = 0.7, erosion has a much larger effect on the material both during and after the uplift process because the maximum point of elevation is approximately equal to h = 0.045. Yet, on the other simulated graph with a lower Kg value, erosion plays a smaller role in the geomorphologic evolution of the uplifted material. The material has a higher point of peak elevation with its height being approximately equal to h = 0.071. Thus, the material has a higher elevation due to the weaker effect of erosion that has acted upon it thus far. Another interesting observation is that upon looking at each simulated hill straight forward where distance x is on the x-axis and h(x,t) is on the y-axis, the graph with the smallest Kg value of 0.1 has concave “tails” as distance x moves towards 0 and 1 whereas the graph with the largest Kg value of 0.7 does not possess the same concave “tails” as the distance x moves towards 0 and 1due to the fact that more sediment is being deposited in the concavities. Good observation.The slight concave tail here is the effect of hydraulic erosion (Kh is not zero but one). This process results in much straighter sides of the formation when compared to the other two graphs of lower Kg values.
Graphs whose Kh values differ

In terms of the hydraulic transport coefficient, Kh, the larger its value, the greater rate of sediment erosion due to water flow there exists. For example, in the first graph where Kh = 0.1, a smaller amount of sediment is being transported down the slope by water flow and does not completely erode until time approximately equals time t = 0.7. On the other hand, the graph that depicts the effects of the largest Kh value, Kh = 10, all sediment has been eroded by the time t = 0.55. Therefore, this also illustrates the notion that as the value of Kh increases, a greater rate of sediment erosion due to water flow exists. More evidence supporting this idea includes the fact that the maximum height of peak uplift differs between the two graphs as well. In the graph where Kh = 0.1, the maximum height is approximately equal to h = 0.0375 whereas in the graph where Kh = 10, the maximum height is approximately equal to h = 0.03. This difference shows that the larger the Kh value, the lower the maximum point of elevation is while the smaller the Kh value, the higher the maximum point of elevation is. Also, the higher the value of Kh, the steeper the slope is because a higher rate of sediment is being transported by water flow which ultimately leads to a much steeper slope gradient due to the increased amount of sediment leaving the boundary. Conversely, the smaller the Kh value, the more gradual the slope of the hillside will be when compared to the effect of higher Kh values. There is a much smoother transition from the higher elevations to the lower elevations upon inducing a lower Kh value and its effects on the simulated slopes. This is illustrated in the graphs because in the graph where Kh = 0.1, the drop in elevation only goes from approximately h = 0.0375 to h = 0.01 from time t = 0.2 to t = 0.3 whereas the graph where Kh = 10, the drop in elevation is much more dramatic in that it goes from approximately h = 0.03 to h = 0.0025 from time t = 0.2 to t = 0.3. Thus, the larger the Kh value, the greater rate of erosion due to water flow there exists. Also worth noting, the graphs who possess a larger Kh value also possess more concave “tails” as distance x moves to 0 and 1 while those graphs who possess a smaller Kh value possess straighter sides of the hill face. This contradicts the effects of the Kg value because while keeping the Kh value constant, the smaller Kg values possess more concave “tails” whereas in this case, it is the graphs illustrating the effects of the larger Kh values which show the concave “tails.” 3/3

Q3:2/2

Q4:

Uplift impulses and uplift steps whose Kg = 0.3 and Kh = 1.0

(Kg is the constant)

Uplift impulses and uplift steps whose Kg = 0.3 and Kh = 10

(Kg is the constant)

In the above set of graphs depicting different uplift impulses and steps, the Kg values were kept constant while the Kh values were varied. The impulses and steps are different in a variety of ways. First and foremost, the main difference between the two is that the impulse graphs depict a sudden rate of uplift which ultimately ceases at a given point whereas the step graphs depict a sudden and constant rate of uplift that continues as time passes. Second, the graphs show that a higher Kh value leads to a more rigidity characteristic of the slopes. There are hardly any smooth surfaces on the slope for those whose Kh value is high. On the other hand, for those slopes who have smaller Kh values, their slopes are generally smooth and gradually decline from the higher slope areas to the lower slope areas. The simulated slopes also show that for those slopes that have higher Kh values, the peak of the hill/uplift tends to be more pointed and sharper than those graphs that have smaller Kh values whose peak uplift is more curved and generally smoother. Third, those hills that have higher Kh values have much smaller maximum heights than those hills that have smaller Kh values. For example, the smaller Kh valued uplift impulse has a maximum height of approximately 0.06 and the uplift step has a maximum height of approximately 0.15. For those graphs that have a larger Kh value, the maximum height of the uplift impulse is approximately 0.047 while the uplift step has a maximum height of approximately 0.065. Therefore these numbers reiterate the idea that those land formations that consist of higher Kh valued soil have a much lower maximum elevation than those land formations that consist of lower Kh valued soils. The sides of each uplift impulse and step are also much more concave for those that have higher Kh values while those that have lower Kh values display much straighter sides.

As far as the time needed to achieve steady state is concerned, those landforms that possess higher Kh values tend to achieve time-independent status quicker than those landforms that possess lower Kh values. For instance, the uplift impulse graph with the higher Kh valueachieves time-independent status after approximately time t = 0.65 whereas the uplift impulse graph with the lower Kh value achieves time-independent status sometime after the range of the simulated time of the graph. Upon comparing the uplift steps, the uplift step with the higher Kh value achieves time-independent status after approximately time t = 0.7 while the uplift step with the lower Kh value achieves time-independent status sometime after the range of the simulated time of the graph. Using these numbers as a basis of comparison, one can clearly see that those landforms that possess higher Kh values achieve time-independent status much earlier than those that possess smaller Kh values.
Uplift impulses and uplift steps whose Kg = 1 and Kh = 0.5

(Kh is the constant)

Uplift impulses and uplift steps whose Kg = 2 and Kh = 0.5

(Kh is the constant)

In the above set of graphs which depict different uplift impulses and steps, the Kh values were kept constant while the Kg values were varied. The impulses and steps, much like those previously compared, are different in a variety of ways. First and foremost, the main difference between the two remains the same in that the impulse graphs depict a sudden rate of uplift which ultimately ceases at a given point of time whereas the step graphs depict a sudden and constant rate of uplift that continues as time passes. Second, the graphs show that a higher Kg value leads to increased slope rigidity. Smooth surfaces are more absent on the slope for those graphs whose Kg value is high. In contrast, those slopes that have smaller Kg values are generally much smoother and gradually decline at a slower rate from the hill’s higher boundary to itslower boundary. These graphs also show that for those slopes which have lower Kg values, the peak of the hill/uplift tends to be sharper than those graphs that have higher Kg values whose peak uplift is more curved and generally smoother. Third, those hills that have higher Kg values have much smaller maximum heights than those hills that have smaller Kg values. For example, the smaller Kg valued uplift impulse has a maximum height of approximately 0.0375 and the uplift step has a maximum height of approximately 0.055. For those graphs that have a larger Kg value, the maximum height of the uplift impulse is approximately 0.025 while the uplift step has a maximum height of approximately 0.03. So, as one can see, these numbers strengthen the notion that those land formations made of higher Kg valued material have a much lower maximum elevation than those land formations made of lower Kg valued material. The sides of each uplift impulse and step, however, do not exhibit much concavity or convexities in general under the simulated circumstances. Yet, it can still be said that the sides of those simulated uplift impulses and steps that have higher values of Kg are more immediate and linear when compared to those graphs of lower Kg values which have more gradually sloping sides.

When regarding the time needed to achieve steady state, it is clear that those landforms which possess higher Kg values tend to achieve time-independent status quicker than those landforms that possess lower Kg values. For example, the uplift impulse graph with the higher Kg value achieves time-independent status after approximately time t = 0.55 whereas the uplift impulse graph with the lower Kg value achieves time-independent status approximately after time t = 0.7. As far as the uplift steps are concerned, the uplift step with the higher Kg value achieves time-independent status after approximately time t = 0.5 while the uplift step with the lower Kg value achieves time-independent status approximately after time t = 0.7. So, thesenumbers clearly illustrate the idea that those landforms which possess higher Kg values achieve time-independent status much earlier than those which possess smaller Kg values.

Your arguments are correct, particularly concerning hillslop shapes. But, why don't you include temporal and spatial profiles to more stronly support your arguments? 2/3

e.g.

Total:

10/11= / 9.1