As of this morning, I have completed 2615 out of 3072 simulations (85%). I have also added new features to the database and plots, and have performed some new analyses of the results. Highlights of these are presented below. If all continues to go well, all simulations should be completed well before the end of October. So far there are no indications that any runs will need to be performed again, but I am keeping some time available at the end of the month in case it is needed. The project schedule calls for all additional analyses to be performed during November (as well as any other experiments such as variable-width or multiple-thread simulations if time permits), and for December to be used only for writing the final report and completing the website.
As before, the database can show the longest and shortest rivers:
Loading from runs.rsq
2615 entries read
Sorting by length...
Top 5 entries:
i file length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test0143.mnrr 245477.926265 433.661987 2.750000 0.001250 1400.000000 1.250000 3.599963
2 iMac/test0281.mnrr 242306.678435 433.661987 3.000000 0.001250 1400.000000 0.750000 3.600000
3 iMac/test0404.mnrr 236444.152114 433.661987 3.250000 0.001250 800.000000 1.250000 3.600008
4 iMac/test0413.mnrr 235817.205567 433.661987 3.250000 0.001250 1000.000000 1.250000 3.599998
5 iMac/test0245.mnrr 234978.637504 433.661987 3.000000 0.001000 1400.000000 0.750000 3.599993
Bottom 5 entries:
i file length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 MacBook/test2177.mnrr 126289.913940 596.127845 3.500000 0.000500 1000.000000 1.250000 3.599996
2 MacBook/test2160.mnrr 126171.706677 596.127845 3.500000 0.000500 800.000000 0.750000 1.200000
3 MacBook/test1739.mnrr 124709.513316 596.127845 2.750000 0.000500 1000.000000 0.750000 3.600000
4 MacBook/test1913.mnrr 123554.555611 596.127845 3.000000 0.000750 800.000000 1.000000 3.599996
5 iMac/test0509.mnrr 122863.106785 433.661987 3.500000 0.001000 800.000000 1.000000 3.600003
In addition, rivers can be sorted by total length = current length plus lengths of all cutoffs:
Sorting by totalLength...
Top 5 entries:
i file totalLength length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test0143.mnrr 776135.792425 245477.926265 433.661987 2.750000 0.001250 1400.000000 1.250000 3.599963
2 iMac/test0404.mnrr 662674.920443 236444.152114 433.661987 3.250000 0.001250 800.000000 1.250000 3.600008
3 iMac/test0116.mnrr 649278.177699 194657.363285 433.661987 2.750000 0.001250 800.000000 1.250000 3.600012
4 iMac/test0260.mnrr 637204.392931 224838.845225 433.661987 3.000000 0.001250 800.000000 1.250000 3.599987
5 iMac/test0269.mnrr 575770.123505 223716.055261 433.661987 3.000000 0.001250 1000.000000 1.250000 3.600025
Bottom 5 entries:
i file totalLength length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test0603.mnrr 133528.724745 133528.724745 494.557565 2.750000 0.000500 1400.000000 0.750000 1.200001
2 MacBook/test2016.mnrr 133139.111685 133139.111685 596.127845 3.250000 0.000500 800.000000 0.750000 1.200000
3 MacBook/test1755.mnrr 132885.307239 132885.307239 596.127845 2.750000 0.000500 1400.000000 0.750000 1.200002
4 MacBook/test2196.mnrr 127935.465352 127935.465352 596.127845 3.500000 0.000750 800.000000 0.750000 1.200000
5 MacBook/test2160.mnrr 126171.706677 126171.706677 596.127845 3.500000 0.000500 800.000000 0.750000 1.200000
And by erosion rate:
Sorting by erate...
Top 5 entries:
i file erate length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test0143.mnrr 10.922526 245477.926265 433.661987 2.750000 0.001250 1400.000000 1.250000 3.599963
2 iMac/test0134.mnrr 8.472486 191130.990917 433.661987 2.750000 0.001250 1200.000000 1.250000 3.600004
3 iMac/test0137.mnrr 7.848543 215845.829969 433.661987 2.750000 0.001250 1400.000000 0.750000 3.599998
4 iMac/test0287.mnrr 7.526362 191231.410205 433.661987 3.000000 0.001250 1400.000000 1.250000 3.599978
5 iMac/test0719.mnrr 7.511476 199541.975442 494.557565 2.750000 0.001250 1400.000000 1.250000 3.599955
Bottom 5 entries:
i file erate length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test1008.mnrr 0.679174 143251.750894 494.557565 3.500000 0.000500 800.000000 0.750000 1.200000
2 MacBook/test1584.mnrr 0.666959 134477.599026 548.391695 3.500000 0.000500 800.000000 0.750000 1.200000
3 MacBook/test2196.mnrr 0.657151 127935.465352 596.127845 3.500000 0.000750 800.000000 0.750000 1.200000
4 MacBook/test2160.mnrr 0.619784 126171.706677 596.127845 3.500000 0.000500 800.000000 0.750000 1.200000
5 MacBook/test2163.mnrr 0.609788 135282.403095 596.127845 3.500000 0.000500 800.000000 1.000000 1.200000
Here are some more nominal rivers which are within 0.05 standard deviations of the mean length and erosion rate:
length: min=122863.106785, max=245477.926265, mean=165040.107776, std=19339.154595
erate: min=0.609788, max=10.922526, mean=2.108859, std=1.150302
6 entries within 0.050000 stds of mean length and erate:
i file length erate avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac2/test5093.mnrr 164232.258206 2.072935 433.661987 3.000000 0.001250 1400.000000 0.750000 1.799998
2 iMac2/test5277.mnrr 165578.722902 2.085901 494.557565 3.000000 0.001250 800.000000 1.000000 1.799998
3 iMac/test1120.mnrr 165286.179166 2.088894 494.557565 3.500000 0.001250 800.000000 1.000000 2.399995
4 MacBook/test1640.mnrr 165358.440019 2.147791 548.391695 3.500000 0.000750 1200.000000 0.750000 3.600000
5 MacBook/test1658.mnrr 164236.967117 2.052708 548.391695 3.500000 0.001000 800.000000 0.750000 3.599997
6 MacBook/test1751.mnrr 164116.967355 2.109599 596.127845 2.750000 0.000500 1200.000000 1.000000 3.599999
Here are some histograms of a few variables across all runs. Note the differences between initial and final erosion rates, and between river length and total length (including cutoffs):
Here are plots of pairs of output variables showing best-fit lines and r values (Pearson product-moment correlation coefficients of Y x X):
r = -0.409079, r = -0.125027, r = -0.033386, r = -0.136603
r = 0.334147, r = 0.485051, r = 0.453311
r = 0.919896, r = 0.970732, r = 0.966282
Plots can now be colored to show the different locations of points with respect to a third variable (in this case the average river width). Note the differences in erosion rate, length, coverage area, and eroded area with respect to narrow vs. wide rivers:
If length is replaced by total length, the distributions and fits shown above become much better. Thus, the scattered 'cloud' in the previous plots is due to cutoffs reducing the length of the river. Here the third axis is flow:
r = 0.921904, r = 0.922270, r = 0.963438
Rivers can be sorted according to whether they reach certain points in the valley. In this case, specific points (0.5 km x 0.5 km areas) near the Vermillion shore:
The runs can then be divided into sets which (for example) either reach or do not reach the Vermillion shore. Here are the shortest (total length) river which crosses the valley, and the longest river which does not:
5 shortest total lengths which cross valley:
i file crossesValley totalLength length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac2/test5339.mnrr 1.000000 170654.565517 160768.034771 494.557565 3.500000 0.000500 1000.000000 0.750000 1.800001
2 iMac2/test5336.mnrr 1.000000 170306.295504 168369.613158 494.557565 3.500000 0.000500 800.000000 0.750000 1.800001
3 iMac2/test5417.mnrr 1.000000 167947.691347 158400.047473 548.391695 2.750000 0.001000 1400.000000 0.750000 1.800003
4 MacBook/test2130.mnrr 1.000000 167027.239227 146201.708347 596.127845 3.250000 0.001250 800.000000 1.250000 1.200000
5 MacBook/test2161.mnrr 1.000000 165564.747279 137208.941239 596.127845 3.500000 0.000500 800.000000 0.750000 2.400001
5 longest total lengths which do not cross valley:
i file crossesValley totalLength length avwidth0 depth diam flow sdist erate0
----- ------------------------------ ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 iMac/test0548.mnrr 0.000000 537046.222635 183716.166324 433.661987 3.500000 0.001250 800.000000 1.250000 3.600011
2 iMac/test0401.mnrr 0.000000 473804.300627 165519.621715 433.661987 3.250000 0.001250 800.000000 1.000000 3.600016
3 iMac/test0545.mnrr 0.000000 422096.988082 149274.006560 433.661987 3.500000 0.001250 800.000000 1.000000 3.600001
4 iMac/test0398.mnrr 0.000000 415260.614697 174804.835361 433.661987 3.250000 0.001250 800.000000 0.750000 3.600025
5 iMac/test0365.mnrr 0.000000 413195.087710 153678.680391 433.661987 3.250000 0.001000 800.000000 1.000000 3.599984
You may have noticed that some river plots show instabilities (a short sequence of oscillations), usually in the beginning of the river near Yankton. I don't know the exact reason for these, but they appear to be a product of the JP method possibly resonating with the local width and/or discretization and smoothing distances. Instabilities occur only for a small subset of parameter combinations, and usually only in the beginning of the river (I have noted previously that the JP method needs to 'get up to speed' with increasing s distance). Rather than try to debug this situation (if possible), I have elected to leave the instabilites as they are for 2 reasons:
Here are the rivers with the longest instabilities:
Top 10 instabilities:
i file instability erate avwidth0 depth diam flow sdist erate0
----- ------------------------------ ----------- ---------------- ---------------- ---------------- ---------------- ---------------- ---------------- ----------------
1 MacBook/test1929.mnrr 15 1.158797 596.127845 3.000000 0.000750 1200.000000 1.000000 1.199999
2 MacBook/test1365.mnrr 14 1.310471 548.391695 3.000000 0.000750 1400.000000 1.250000 1.199999
3 MacBook/test1500.mnrr 14 1.163723 548.391695 3.250000 0.000750 1200.000000 1.250000 1.200001
4 MacBook/test1941.mnrr 13 1.305311 596.127845 3.000000 0.000750 1400.000000 1.250000 1.200000
5 iMac2/test5435.mnrr 12 1.070309 548.391695 3.000000 0.000500 1000.000000 0.750000 1.799998
6 MacBook/test1441.mnrr 12 1.403860 548.391695 3.250000 0.000500 800.000000 0.750000 2.400000
7 MacBook/test1473.mnrr 12 1.115818 548.391695 3.250000 0.000500 1400.000000 1.250000 1.200001
8 MacBook/test1638.mnrr 12 0.907808 548.391695 3.500000 0.000750 1200.000000 0.750000 1.200002
9 MacBook/test2082.mnrr 12 1.149113 596.127845 3.250000 0.000750 1400.000000 1.000000 1.200002
10 MacBook/test2182.mnrr 12 1.242565 596.127845 3.500000 0.000500 1200.000000 1.000000 2.400002
Here are the fraction of all runs with instabilities up to a given length. Note that there are no rivers with zero instabilities. Two rivers having instabilities of length 4 (which are virtually invisible) are plotted. Since these account for more than 90% of all runs, I'm not going to worry about it too much:
Instabilities <= 15: 2615 (100.00 %) Instabilities <= 14: 2614 (99.96 %) Instabilities <= 13: 2612 (99.89 %) Instabilities <= 12: 2611 (99.85 %) Instabilities <= 11: 2605 (99.62 %) Instabilities <= 10: 2592 (99.12 %) Instabilities <= 9: 2580 (98.66 %) Instabilities <= 8: 2556 (97.74 %) Instabilities <= 7: 2526 (96.60 %) Instabilities <= 6: 2504 (95.76 %) Instabilities <= 5: 2467 (94.34 %) Instabilities <= 4: 2406 (92.01 %) Instabilities <= 3: 2299 (87.92 %) Instabilities <= 2: 2100 (80.31 %) Instabilities <= 1: 1502 (57.44 %) Instabilities <= 0: 0 (0.00 %)
Finally, here is the common coverage plot (to within 500 m x 500 m) for all 2615 runs:
By interpolating and smoothing this array by 4x, I can plot the coverage to within a 125 m x 125 m grid. This does not really contain any additional information, but is more visually appealing:
Since the coverage for all runs contains fairly active river examples, it might be useful to accumulate and plot coverage for specific subsets of these runs. For example, all runs having less than or equal to the mean length and erosion rate (n=971):
All runs which do not cross the valley to Vermillion (n=989):
All runs which do not have any cutoffs (n=212):
By providing coverage examples for different subsets of rivers, it might be possible to better define the '100 year migration corridor' under different conditions and assumptions. However, while different plots show differences in coverage values somewhat less than 1.0, they do not significantly change the shape of the 'core' set of points reached by all rivers (shown in red).
I will post another update and set of analyses when the entire set of runs is complete at the end of this month.