Q1：Below is the image of the geomorphologic evolution of an initial uplift:
In this simulation, we choose the parameters, and the total sediment transport includes two parts: one is soil creep and the other one is hydraulic erosion. This can be calculated as:. The former part soil creep is tending to make the hillside smoother and convex and the latter one: hydraulic erosion is tending to make the hillside concave. In this picture, we can see that when , there is no uplift and also there is no erosion. When , there is the initial uplift in the center of the x axis and the two kinds of sediment transport begins . After , there is no uplift and the sediment transport continues, when , the hillside was almost completely eroded. Select several time points: , at the given point, we can see that the curve is quite convex, so the dominant driving force for the geomorphologic evolution is the soil creep. The soil creep term is only related to and S, when the soil creep item is dominant, the shape of the hill side is convex, which means the further a point on the hillside to the peak, the more sediment transport can cross the section area, because the slope increases with the distance x from the peak of the hill.
Therefore, if the soil creep is performing the driving force, it will make the hill side smoother and convex. 3/3
Q2: Below is the image of the shape of the hillside when choosing different parameters.
Different heights when t=0.5 /
Different heights when x=0.5
We choose the two different group of parameters to do the simulation: and . The in the latter group has a much small value than in the former group. Therefore, there is much difference between the two processes.
When , the effect of soil creep declines. With the same , the total sediment transport will also decline from the equation . Therefore, less sediment is carried down slope from the hillside. From the images above, we can also get the same conclusion. When , the peak is about 0.07. When , the peak is about 0.05. The hillside height is also less than the former one at other time. Likewise, when , the shape curve is much more smoother than that of . Furthermore, the , the hillside height almost reaches 0 when , on the other hand, the hillside height is about 0.01 when . Therefore, the effect of soil creep increases when increases, and the total rate of sediment transport will increase and the hillside shape will be more convex and smoother.
Then, we choose another two groups of parameters: and. in the latter group is 5 times as much as in the former group. We can get different images of the hillside shape as below:
Good. But, to isolate the effects of each parameter, how about fixing a value of one parameter and then changing the other parameter?
Different heights when t=0.5 /
Different heights when x=0.5
When increases from 1.0 to 5.0, the effect of hydraulic erosion will increase. The hillside height decreases much faster when =5.0 compared with =1.0. The peak declines from 0.54 to 0.47 and after t > 0.5, the height almost reaches 0 when =5.0, but the height is about 0.01 when =1.0. So the rate of erosion is much faster when increases. Besides, at a given time t=0.5, when =1.0, the shape curve is convex, and when =5.0, the lower section of the shape curve is concave. Therefore, the value of can represent the effect of hydraulic erosion, when increases, the rate of hydraulic erosion will increase, when decreases, the rate of hydraulic erosion will increase, the total rate of sediment transport will also increase or decrease with the change of . And the hydraulic erosion is tending to make the hillside shape more concave. The larger , the more concave the hillside shape.
From the above discussion, if we increase and , the effect of soil creep and hydraulic erosion will also increase, and then the total rate of sediment transport will also increase. More sediment will be moved from the hillside. And the peak of hillside will decrease. The soil creep is tending to make the hillside more convex and smoother, and the hydraulic erosion is tending to make the hillside more concave. 2.5/3
Q3: Below are the image of hillside shape with different coefficients and mechanisms.
Different heights when t=0.5 /
Different heights when x=0.5
The latter simulation has a persistent uplift, which means the uplift is continuous after t > 0.1. Because of the persistent uplift, the total sediment transport and the uplift can get to a balanced situation or steady state. In this situation, after t > 0.6, the shape of hillside is fixed, and the total sediment transport is equal to the uplift. Meanwhile, because , the hydraulic erosion plays an important role, from the section profile image at t=0.5, we can see that the curve with the persistent uplift is concave. In contrast, the simulation with impulse uplift has a different hillside shape. The hillside shape gradually decreases with time and eventually will reach to the ground surface. 2/2
Q4: First, let keep constant and change the value of . We choose the following 4 sets of coefficients. ,,,. gradually increases, and the effect of hydraulic erosion increases. Below are the hillside shape images.
Different heights when t=0.5 /
Different heights when x=0.5
Nice graphs!
From the above image, we can clearly see that when increases, the height of hillside decreases quickly, and the hillside shape is more concave. Meanwhile, the time to reach steady state is shorter, from 0.9 to 0.3. This is because the effect of hydraulic erosion is increasing. For the sediment transport is equal to the uplift, and the uplift is fixed, if the effect of hydraulic erosion increases, it takes less time for the system to reach steady state and the two opposite force to reach the balanced situation.
Second, let keep constant and change the value of . We choose the following 4 sets of coefficients. ,,,. graduallyincreases and the effect of soil creep increases. Below are the hillside shape images.
Different heights when t=0.5 /
Different heights when x=0.5
I think Kh value is too high to overshadow the effect of Kg.
From the above image, we can clearly see that when increases, the height of hillside decreases quickly, and the hillside shape is more convex With lower Kh, you will have more convex shapes.. Meanwhile, the time to reach steady state is shorter, from 0.8 to 0.4. This is because the effect of soil creep is increasing. For the sediment transport is equal to the uplift, and the uplift is fixed, if the effect of sediment transport increases, it takes less time for the system to reach steady state.
Therefore, when increases or increases, the total effect of sediment transport increases, it takes less time for the system to reach steady state. And the height of hillside decreases. If or effect of hydraulic erosion plays a dominant role, the hillside shape is more concave, and if or soil creep plays a dominant role, the hillside shape is more convex. I cannot see an evidence for the last arguemnt clearly from your graphs.
3/3
Total: 10.5/11 = 9.5