Initial MNRR test simulations

Since last week I have:

• Changed the input file to support all simulation parameters.
• Set default values for some MNRR parameters (see below).
• Added an 'info window' for displaying information about selected river points.
• Extracted a 200 point subset of the MNRR with which to test the meandering methods.
• Estimated the yearly erosion rate in ha/km.
• Run 100 year simulations using several meandering methods.
• Added a 'print' function to create new (text) input files from the current simulation state. (This is in addition to saving the entire simulation state and history in a binary file, which has been supported since April.)

An input file now looks like:

flow 899.33
depth 3.429
slope 1.918e-04
diam 0.000e+00
lambda 1.00
ldist 149.00
sdist 300.00
# rates per year
lerate 1.00
rerate 1.00
mrate 1.355e+04
mexp 1.00
# time in years
dt 1.000e-01
method Simple_curvature
rk4 True
idist 150.00
removeCutoffs True
keepCutoffs -1
showIO False
showDetails False

   42002.528659   -11148.542330     1453.870408
   42027.162631   -11245.387997     1480.893985
   42076.206003   -11332.086710     1476.524216
   42143.964734   -11405.547198     1441.182920
   42212.005134   -11478.795697     1367.589553
...

Some default values were initialized from the following sources:

• A constant flow was estimated by averaging the Gavins Point Dam discharge quotes from Table 2 of Elliott & Jacobson 2006. This value is consistent with the discharge plots in Figures 2 & 4.
  
  
• A constant depth was estimated from gauge height plots at Yankton and Sioux City, and corroborated by the MNRR National Park Service site. However, see discussion below.
  
  
• A constant water slope was estimated from USGS topographic maps which show a drop of 60-70 feet in just over 95 km.
  
  
• Initial transverse bed slope was set at zero to test the JP methods (diam = 0). (See JP discussion below.)
  
  
• The lag distance and sum distance (where used) were set to average curvature from 3 river points (at post- and pre-interpolation separations of 75-150 m).
  
  
• The migration rate was adjusted so that the initial total erosion rate estimate (using 'unmeandered' river geometry) was close to 1.2 ha/yr/km, as quoted in Table 1 of Elliott & Jacobson 2006.
  
  
• The time step was set at 0.1 yr, so that there would be 1000 steps in 100 years. Runge-Kutta 4th-order integration was used to achieve reasonable accuracy at this step size.

Here is a plot of the entire river, showing the 200 point subset of interest:

(Click for larger image)

Here is the subset loaded and ready to go, also showing width lines every 200 m:

(Click for larger image)

Here is the 100 year simulation, using curvature alone as the basis for meandering. Each image is 10 years apart. At the bottom are images showing just the centerlines for the final river and cutoffs, and the widths of the final configuration. This is currently an 'unconstrained' simulation, as neither the valley walls nor any artificial modifications to the banks are considered:

(Click for larger image)

During the simulation, the erosion rate increased from 1.19 to about 3.5 ha/yr/km, where it remained stable (actually it increased slightly with river sinuosity, and then decreased as cutoffs were removed). During 100 years, the average width changed from 804 to 671 m. Although the width did not affect the meandering in this case (it was not a parameter), and was not changed explicitly, it did change over time due to two factors: 1) as new points were added, their width was interpolated from the surrounding points, and new points tended to be added in regions of high curvature, which were already narrow, 2) as cutoffs were removed.

Note also that the cutoff removal process is currently not sensitive to width --cutoffs are determined by centerline intersections only, without regard to width at either location. In future versions of the simulation, cutoffs will need to be determined by centerline proximity wrt the widths of both river segments. Therefore, much of the high sinuosity currently found in wide segments of the river is spurious, and should not occur.

Here is the 100 year simulation using circumferential speed (i.e. the uncorrected 'sigma' of the JP method for circular arcs) as the basis for meandering (shown every 20 years):

(Click for larger image)

Again, the erosion rate increased from 1.2 to about 3.5 ha/yr/km, and the average width changed from 849 (maximum) to 681 m (minimum). In this case the width did affect meandering, as it altered the proportional speed excess at the outside bank of each bend, but the width was not changed by the meandering routine.

I'm currently working on the JP simulations, and will have more to show next week. However, I have done a preliminary run (using method 3: JP89 integral eqns with partial integration), but had to make the following changes to eliminate math errors and get even semi-reasonable output:

• Set dt = 0.05 years.
• Interpolate points to less than 50 m, with re-interpolation distance = 75 m.
• Increase the flow to 4000 m^3/s.
• Use a particle size of 1 mm.

Even so, the results are not very appealing (each image every 5 yrs):

(Click for larger image)

Improving the JP results --and other things-- will be topics for next week. In addition, I feel that we should do one of the following:

1. Invent a meandering method that a) moves each bank independently of the other, or b) increases or decreases the width as a result of meandering, or
2. Replace the variable river width with a constant average width.

I will give (1) some thought during the next week.