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This update shows differences in 100 year common coverage for subsets of runs having fixed values of the 6 different input parameters, arranged in increasing sequences of these values. Thus, it does not represent new information about the simulations, but is a filtering of the full output so as to look for trends in the data, in this case indicated by the 95% to 1% contour lines of the coverage. Shown are subsets of all runs for both the Johannesson-Parker (u1b) and the simpler Circumferential Speed (sigma) simulations for comparison. Comments are interspersed with the plots, discussion at bottom. Numerical values indicating cumulative and differential coverage area between contour lines are also shown, along with statistics about when subsets reach various targets (e.g. towns) in the valley.
The first plot shows differences in coverage (JP method) with respect to maximum river width. Note that the total coverage decreases with increasing river width, although the 95% area increases slightly with width. The 50% cumulative area is virtually the same for all widths:
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The next plots shows coverage with respect to river depth. In this case, the total coverage and the 95% to 50% areas are greatest for the shallowest rivers:
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The next plot shows coverage with respect to bed particle diameter. In this case, all areas increase with increasing particle size:
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The next plot shows coverage with respect to flow. As expected, the total coverage increases with increasing flow, but this is not necessarily the case for the fractional areas. The 95% to 50% areas appear to be greatest for a moderate flow, and then decrease with larger flows:
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The next plot shows coverage with respect to upstream summation distance (in local river widths). This clearly indicates that the coverage increases, and is somewhat sensitive to, the amount of upstream river geometry that affects the lateral migration at any point:
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Finally, as expected, the major contributing parameter to all coverage areas appears to be the initial (set by program to specific value) erosion rate:
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During the simulation, the erosion rate is not adjusted, and may end up either higher or lower than its initial value for specific rivers. However, since this seems to be the primary variable responsible for variations in coverage, it might be worthwhile to repeat the previous analyses for a single initial erosion rate (e.g. 1.8 ha/yr/km) to see if the observed trends remain.
Here is a sample of the numerical output of the coverage areas and target acquisition for the cases shown above. Click the links below for the full files:
*** maxwidth0=500.00 ***
Area at x percent common coverage:
1.00 - 0.95: 133.12 133.12 km^2
0.95 - 0.75: 95.14 228.27 km^2
0.75 - 0.50: 91.58 319.84 km^2
0.50 - 0.25: 111.27 431.11 km^2
0.25 - 0.05: 172.73 603.84 km^2
0.05 - 0.01: 107.41 711.25 km^2
0.01 - 0.00: 154.06 865.31 km^2
Total: 865.31 km^2
Total coverage: 865.31 km^2
...
Average fraction of target area occupied during simulation:
case coverEP coverG coverHDF coverJ coverMe coverMi coverPSP coverR coverVe coverVo coverW coverYE coverYS
-------------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
maxwidth0=500.00 0.279948 0.002604 0.695833 0.000868 0.000000 0.028971 0.710729 0.000000 0.308594 0.000000 0.000000 0.098586 0.124349
maxwidth0=600.00 0.372472 0.001953 0.712760 0.000000 0.000000 0.026693 0.755486 0.000000 0.394301 0.000000 0.000000 0.094215 0.077546
maxwidth0=700.00 0.518689 0.002604 0.653125 0.000000 0.000000 0.041016 0.782118 0.000000 0.394914 0.000000 0.000000 0.147972 0.027705
maxwidth0=800.00 0.684436 0.004557 0.779948 0.000000 0.000000 0.047852 0.798524 0.000000 0.434972 0.000000 0.000000 0.187779 0.011863
...
Here is the coverage (CS method) with respect to maximum river width. Unlike the JP results, the CS coverage is not as sensitive to width, and does not always respond in a monotonic fashion:
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Here is the coverage with respect to river depth. Unlike the JP results, in this case the coverage is relatively insensitive to depth, as depth is not a primary variable determining migration in this method:
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Here is the coverage with respect to flow. Again, coverage is relatively insensitive to flow, as flow is not a primary migration variable in this method:
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The CS method is based on water speed, which varies as the ratio of flow / depth, so that a similar range of values can be generated by holding one parameter constant while varying the other. The CS method does not use bed particle diameter as a parameter. The next input parameter is upstream summation distance. In this case, the CS coverage response is the same as for JP (in fact, the two methods share the same upstream summation code):
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The CS method also has a similar response to the JP method with respect to initial erosion rate, although this is an actual result of the two meandering methods, rather than because of similar code. (Note that the CS method was not run using an initial erosion rate of 3.6, as 1.2 - 2.4 ha/yr/km were deemed sufficient):
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Here is a sample of the numerical output of the coverage areas and target acquisition for the cases shown above. Click the links below for the full files:
*** maxwidth0=500.00 ***
Area at x percent common coverage:
1.00 - 0.95: 222.28 222.28 km^2
0.95 - 0.75: 115.78 338.06 km^2
0.75 - 0.50: 96.89 434.95 km^2
0.50 - 0.25: 85.89 520.84 km^2
0.25 - 0.05: 89.33 610.17 km^2
0.05 - 0.01: 38.30 648.47 km^2
0.01 - 0.00: 12.25 660.72 km^2
Total: 660.72 km^2
Total coverage: 660.72 km^2
...
Average fraction of target area occupied during simulation:
case coverEP coverG coverHDF coverJ coverMe coverMi coverPSP coverR coverVe coverVo coverW coverYE coverYS
-------------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
maxwidth0=500.00 0.056645 0.000000 0.508148 0.000000 0.000000 0.000000 0.860247 0.000000 0.261874 0.000000 0.000000 0.374603 0.729630
maxwidth0=600.00 0.000000 0.000000 0.894815 0.000000 0.000000 0.000000 0.888494 0.000000 0.487146 0.000000 0.000000 0.253968 0.617695
maxwidth0=700.00 0.117647 0.000000 0.522963 0.000000 0.000000 0.031481 0.887012 0.000000 0.416558 0.000000 0.000000 0.180952 0.374074
maxwidth0=800.00 0.298475 0.000000 0.577778 0.000000 0.000000 0.000000 0.873383 0.000000 0.334205 0.000000 0.000000 0.216402 0.350206
...
Some comparisons between the two meandering methods are noteworthy:
This suggests that most of the CS rivers tend to stay closer to the original river, even though total coverage area of all CS rivers is greater than for JP rivers at the same initial erosion rate. A possible explanation for this is suggested by plots showing the initial and final distributions of erosion rates for the JP runs (top) and the CS runs (bottom):
Although both sets of runs start with discrete erosion rates, the JP method seems to redistribute the erosion according to an exponential or Poisson process, yielding a final histogram which has a characteristic unimodal peak, and where some rivers have increased their erosion rates while others have decreased. The CS runs, however, all increase their rates, although it is unclear what redistribution mechanism is at work.
During the remaining 2 weeks of this month, I will try to work on one or more of the following, although it is not clear how much I can accomplish in such a short time:
There will be another update at the end of November.