Constrained speed and Johannesson-Parker tests

Summary

Now that I can run 100 year simulations in a reasonable amount of time (~1 hr), I am able to explore some of the paramater combinations for the Johannesson-Parker and other speed-based meandering methods (circumferential speed and variable-width). Here is a summary of the results so far:

• As with the curvature-only method, an enormous variation in river geometry can be produced, including many instances of 'big loops'. An important thing to do next is to pick one of these variations to use as the starting point for the population of simulations I will perform during the next several months. Please look at the examples below and tell me which ones you (a) like (b) think are representative of what the river actually does.
  
  
• I will use both the JP and one other meandering method to compare and contrast aggregate results. The circumferential speed method is essentially a simpler version of JP based on the same idea, while the variable-width method moves the inside bank based on the average upstream erosion of the outside bank (i.e. transports sediment downstream with the flow, rather than cross-stream at the same s coordinate).
  
  
• All aggregate simulations will be subject to the constraint that the initial erosion rate be close to 1.2 ha/yr/km, as reported in EJ2006. Most of the 'interesting' simulations have erosion rates far in excess of this value (up to 27x). Simulations limited to realistic erosion rates are considerably less dramatic, with far fewer cutoffs, but still consume planform area.
  
  
• The response of JP to increased flow is somewhat counter-intuitive. Although the feature size does increase, the erosion rate is reduced with increased flow. The migration rate must be turned up in order to maintain an initial erosion rate of 1.2 ha/yr/km, and the rate generally decreases over time (whereas with other methods the erosion rate increases with time as the river increases in length and sinuosity).
  
  
• The river has a tendency to 'stick' to the valley walls, and to increase the length of contiguous contact over time. I don't know if this is realistic behavior, or a problem inherent to the meandering math. I have tried various ways to alleviate this behavior, but I'm not convinced they should be used. Whether to pursue this issue or not will depend on what 'starting point' we select for the aggregate simulations, as it appears to occur more or less depending on the parameter combination used.

Still to do are:

• Accumulate erosion area and coverage statistics (e.g. 2d joint distribution) over time and plot river location with respect to grid, map, and satellite images.
  
  
• Automatically initialize migration rate to achieve desired initial erosion rate for all simulations.
  
  
• Formulate strategy and methodology for coordinating automated runs and handling results from multiple computers (well, at least 2). Full simulations yield from 1-5 Mb of data (depending on number of cutoffs), so that a full 'population' of 1000 runs might require several Gb of storage and management to easily view the final or intermediate results of any of the simulations for side-by-side comparison, and for generating illustrations for the final report and website.

River width

The digitized river has a minimum width of 186.79 m, maximum of 1647.97 m, mean of 747.84 m, and standard deviation of 337.62 m. I do not believe this to be an accurate representation of the active meandering width of the flow, and in general believe the bank-to-bank surface width to be a serious over-estimate of the submerged sediment-carrying conduit width, especially around islands and bars, and in shallow areas.

Here is a histogram of the distribution of the width (using 50 bins):

I am assuming that the tail of the distribution (everything over 1531 m wide) is spurious, due to islands, etc., included in the digitization. If these points are neglected, the adjusted histogram and cumulative distribution is:

The median width (i.e. at 50% cumulative distribution) is 693.15 m. I have used a constant 'effective' width of 400 m in some simulations, which is only as wide as about 18% of the measured values. In other examples, I allow a varied width limited to the median and below (i.e. from 186.79 to 693.15 m). The full width of the river can be used with the curvature, circumferential, and variable-width methods, but not with JP. I suggest that maximum width be one of the variable parameters in the aggregate runs performed next month, by choosing several values at different cumulative distributions from the adjusted histogram.

Simulation examples

Here are two 100 yr circumferential speed tests having medium size loops, but high erosion rates. Width is limited to 400 m:

file=test027.mnrr method=Circumferential speed avwidth=383.643 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=1000.000 mexp=1.000
pts=1909 time=100.000 len=191326.883 slope=9.596e-05 erate=12.172

file=test028.mnrr method=Circumferential speed avwidth=380.331 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=2500.000 mexp=0.500
pts=1770 time=100.000 len=177547.132 slope=1.034e-04 erate=14.198

Here are tests which run to 200 and 300 years (but only show the last 100 yr's cutoffs):

file=test029.mnrr method=Circumferential speed avwidth=375.840 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=1000.000 mexp=1.000
pts=1905 time=200.000 len=190887.791 slope=9.618e-05 erate=11.582

file=test032.mnrr method=Circumferential speed avwidth=372.926 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=1000.000 mexp=1.000
pts=1857 time=300.000 len=186234.589 slope=9.859e-05 erate=18.865

Here is a more realistic test (erosion-wise) which uses the full width of the river:

file=test034.mnrr method=Circumferential speed avwidth=709.620 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=400.000 mexp=1.000
pts=1658 time=100.000 len=166077.586 slope=1.106e-04 erate=2.525

Limited to the median width:

file=test036.mnrr method=Circumferential speed avwidth=562.342 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=750.000 mexp=0.500
pts=1587 time=100.000 len=159047.532 slope=1.154e-04 erate=2.786

Here's a JP test limited to 400 m:

file=test037.mnrr method=Johannesson-Parker avwidth=383.830 depth=3.500 flow=1000.000
diam=0.001 ldist=0.500 sdist=1.000 mrate=100.000 mexp=1.000
pts=1695 time=100.000 len=170413.807 slope=1.077e-04 erate=2.509

Limited to the median width:

file=test039.mnrr method=Johannesson-Parker avwidth=529.056 depth=3.500 flow=1000.000
diam=0.001 ldist=0.500 sdist=0.400 mrate=100.000 mexp=1.000
pts=1790 time=100.000 len=179940.451 slope=1.020e-04 erate=3.810

file=test040.mnrr method=Johannesson-Parker avwidth=513.915 depth=3.500 flow=1000.000
diam=0.001 ldist=0.500 sdist=0.400 mrate=125.000 mexp=0.500
pts=1748 time=100.000 len=175935.685 slope=1.044e-04 erate=5.437

file=test041.mnrr method=Johannesson-Parker avwidth=539.955 depth=3.500 flow=1000.000
diam=0.001 ldist=0.500 sdist=0.400 mrate=125.000 mexp=1.500
pts=1901 time=100.000 len=191199.598 slope=9.603e-05 erate=4.535

High flow and migration/erosion rates lead to more coverage, but also a kind of 'stylized' geometry (paisley?):

file=test042.mnrr method=Johannesson-Parker avwidth=504.953 depth=2.500 flow=1500.000
diam=0.001 ldist=0.500 sdist=2.000 mrate=500.000 mexp=1.000
pts=2308 time=100.000 len=232177.020 slope=7.908e-05 erate=27.315

Here is a more reasonable JP test:

file=test043.mnrr method=Johannesson-Parker avwidth=601.763 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=2.000 mrate=22.500 mexp=1.000
pts=1705 time=100.000 len=170766.447 slope=1.075e-04 erate=1.303

Decreasing the flow leads to smaller loops and more erosion:

file=test045.mnrr method=Johannesson-Parker avwidth=601.418 depth=3.429 flow=674.497
diam=0.001 ldist=0.500 sdist=2.000 mrate=22.500 mexp=1.000
pts=1609 time=100.000 len=161733.578 slope=1.135e-04 erate=2.533

Increasing the flow increases the loop size, but decreases the erosion rate:

file=test044.mnrr method=Johannesson-Parker avwidth=589.687 depth=3.429 flow=1348.995
diam=0.001 ldist=0.500 sdist=2.000 mrate=22.500 mexp=1.000
pts=1423 time=100.000 len=142431.316 slope=1.289e-04 erate=0.852

The migration rate can be increased to compensate for this:

file=test047.mnrr method=Johannesson-Parker avwidth=594.057 depth=3.429 flow=1348.995
diam=0.001 ldist=0.500 sdist=2.000 mrate=45.000 mexp=1.000
pts=1946 time=100.000 len=194907.709 slope=9.420e-05 erate=1.566

As the flow and migration rate are increased further, the geometry becomes stylized:

file=test048.mnrr method=Johannesson-Parker avwidth=558.223 depth=3.429 flow=1798.660
diam=0.001 ldist=0.500 sdist=2.000 mrate=55.000 mexp=1.000
pts=2045 time=200.000 len=204793.071 slope=8.965e-05 erate=1.956

The variable-width method produces results similar to JP, but can accept and produce a wider range of widths:

file=test049.mnrr method=Variable-width speed avwidth=604.807 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=2.000 mrate=290.000 mexp=1.000
pts=2054 time=100.000 len=206295.423 slope=8.900e-05 erate=3.641

file=test050.mnrr method=Variable-width speed avwidth=597.801 depth=3.429 flow=1348.995
diam=0.001 ldist=0.500 sdist=2.000 mrate=290.000 mexp=1.000
pts=1770 time=100.000 len=177526.019 slope=1.034e-04 erate=5.316

Here is a more reasonable variable-width simulation:

file=test051.mnrr method=Variable-width speed avwidth=602.643 depth=3.429 flow=899.330
diam=0.001 ldist=0.500 sdist=4.000 mrate=375.000 mexp=1.000
pts=1667 time=100.000 len=167079.050 slope=1.099e-04 erate=2.325

And at higher flow:

file=test052.mnrr method=Variable-width speed avwidth=656.815 depth=3.429 flow=1798.660
diam=0.001 ldist=0.500 sdist=4.000 mrate=375.000 mexp=1.000
pts=1642 time=100.000 len=164627.616 slope=1.115e-04 erate=4.596