Stochasim Algorithm
stochasim.RdSend multiple annual event hydrograph(s) through a channel, with either
bank erosion or revegetation occurring.
Erosion is determined by the gbem::gbem() algorithm, and revegetation
occurs at a specified rate if no erosion occurs, using revegetate().
Usage
stochasim(x, cross_section, rv_rate = 0.1, niter = 300, progress = FALSE)
stochasim2(
x,
y,
cross_section,
rv_rate = c(0, 0.1),
niter = 300,
progress = FALSE
)Arguments
- x, y
Hydrographs, as a list or bare. Recycled to the same length.
- cross_section
A
"cross_section"object representing a stream's cross section.- rv_rate
Rate parameter for revegetation, passed to
revegetate(). Forstochasim2(), possibly a vector of length two corresponding to different revegetation rates for hydrographsxandy. Note: a rate of 0 means no revegetation happens.- niter
Number of iterations for
gbem::gbem()when running each hydrograph.- progress
Display a progress bar? Logical; defaults to
FALSE.
Details
For stochasim2(), x and y are paired and looped through, with
the x hydrograph occurring before y in each iteration.
The default interpretation of x and y are snowmelt-related
and rainfall-related event hydrographs (respectively), with each iteration
corresponding to a year. This is why the default revegetation rate is
c(0, 0.1), so that revegetation only occurs in the fall if no
rainfall-related erosion occurs.
Examples
# Start with a cross section
cs <- cross_section(40, grad = 0.01, d50 = 65, d84 = 100, roughness = 0.01)
# Make 500 rain hydrographs and run stochasim
library(distionary)
dst_rain <- hydist_rain(dst_gev(11, 3, 0.1), baseflow = 2)
set.seed(42)
rain <- realise(dst_rain, n = 500)
(ss <- stochasim(rain, cross_section = cs, progress = TRUE))
#> Iterating ■■■■■■■■■■ 30% | ETA: 2s
#> Iterating ■■■■■■■■■■■■■■■■■■■■■ 66% | ETA: 1s
#> Iterating ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 100% | ETA: 0s
#> Stochasim object with 500 runs.
# View evolution of channel width; view peak flows.
plot(ss)
plot(ss, what = "flows")
# Or, make your own plot by extracting the data
ss_widths(ss)
#> [1] 40.000000 36.424264 33.206102 30.309756 27.703044 25.357004 23.245567
#> [8] 21.345275 19.635011 18.095774 16.710461 15.463679 14.341575 13.331682
#> [15] 12.422778 11.604764 13.009501 15.509059 14.382418 13.368440 12.455860
#> [22] 11.634538 10.895348 16.926657 15.658255 14.516694 13.489289 12.564624
#> [29] 11.732426 10.983447 10.309366 9.702694 10.186833 9.592414 9.057437
#> [36] 8.575957 10.490709 9.865902 9.303576 11.910773 11.143960 10.453828
#> [43] 9.832709 9.273702 14.832107 13.773161 13.977468 13.003985 12.127851
#> [50] 14.754102 13.702956 12.756925 11.905496 11.139211 10.449554 9.828862
#> [57] 9.270240 8.767480 8.314996 7.907761 7.541249 8.835735 15.787098
#> [64] 14.632652 13.593651 12.658550 11.816959 11.059527 10.377839 9.764319
#> [71] 9.212151 8.715200 8.267944 7.865414 7.503136 7.177087 9.202812
#> [78] 8.706795 8.260380 7.858606 7.497009 8.171236 7.778376 7.424803
#> [85] 8.608435 9.763539 9.211449 8.714568 8.267375 7.864902 7.502676
#> [92] 8.771982 8.319048 7.911407 12.669087 11.826443 11.068062 10.385520
#> [99] 9.771232 9.218373 8.720800 8.272984 7.869950 7.507219 7.180761
#> [106] 12.997037 14.220409 13.222632 12.324633 11.516434 10.789054 10.134413
#> [113] 10.548868 9.918245 9.350685 8.839881 8.380157 7.966405 7.594029
#> [120] 8.372581 10.432617 9.813619 9.256521 8.755133 8.303884 9.205516
#> [127] 8.709228 12.249793 14.180998 13.187162 12.292710 11.487703 10.763197
#> [134] 10.111141 12.840424 11.980645 11.206845 10.510425 9.883646 9.319546
#> [141] 8.811855 8.354934 7.943704 7.573598 9.803079 9.247035 10.268963
#> [148] 9.666331 13.136580 12.247186 11.446731 10.726322 10.077954 9.494423
#> [155] 8.969245 8.496584 9.763557 9.211466 8.714583 8.267389 8.871852
#> [162] 12.738035 11.888495 11.123910 10.435783 9.816469 9.259086 8.757441
#> [169] 8.305961 7.899629 7.533930 9.297405 8.791929 8.337000 7.927564
#> [176] 7.559072 7.227428 10.371790 9.758875 9.977856 9.404335 12.214175
#> [183] 11.417022 10.699584 10.053889 9.472765 8.949752 12.209485 11.412801
#> [190] 10.695785 10.050470 9.469687 9.856935 9.295505 8.790219 8.335461
#> [197] 7.926179 7.557825 7.226307 9.425239 8.906979 11.419851 10.702130
#> [204] 10.789514 10.134826 9.545608 9.015311 14.359863 13.348141 12.437591
#> [211] 11.618096 10.880550 10.216759 9.619347 9.081677 8.597773 10.578638
#> [218] 9.945039 9.374799 8.861583 11.590854 10.856033 10.194693 9.599488
#> [225] 13.973603 13.000507 12.124720 11.336512 10.627125 9.988677 9.414073
#> [232] 8.896930 8.431501 8.012615 7.635618 19.645022 18.104784 16.718570
#> [239] 15.470977 14.348143 13.337593 12.428098 11.609552 10.872861 10.209839
#> [246] 9.613119 9.076071 8.592728 8.157719 7.766212 12.914428 12.047249
#> [253] 11.266788 10.564374 9.932200 9.363244 10.030938 9.452109 8.931162
#> [260] 8.462310 8.040343 9.162754 8.670742 8.227932 13.147657 12.257155
#> [267] 11.455704 10.734398 10.085222 12.439860 11.620138 10.882388 10.218414
#> [274] 9.620836 9.083017 11.422096 10.704151 10.058000 9.476464 8.953081
#> [281] 8.482037 8.058098 7.676552 7.333161 15.729217 14.580560 13.546768
#> [288] 12.616355 11.778984 11.025349 10.347079 11.059795 10.378080 9.764536
#> [295] 9.212346 8.715376 8.268102 9.563701 9.031595 8.552699 8.121693
#> [302] 7.733788 7.384673 7.070470 6.787687 11.278840 12.635947 11.796616
#> [309] 11.041219 10.361361 9.749489 9.198804 15.370435 14.257656 13.256154
#> [316] 12.354803 12.689511 11.844824 11.084605 11.794001 17.466442 16.144062
#> [323] 14.953920 13.882792 12.918777 12.051163 12.834657 11.975455 11.202174
#> [330] 10.506220 9.879862 12.404315 11.588148 10.853597 10.192502 9.597515
#> [337] 9.062028 8.580089 8.146344 10.235749 9.636438 9.097058 8.611617
#> [344] 10.028927 9.450298 8.929533 8.460843 13.536410 12.607033 11.770594
#> [351] 12.033805 11.254689 10.553484 9.922400 9.354424 9.393355 8.878284
#> [358] 8.914888 13.419053 12.501412 11.675535 10.932245 10.263285 9.661221
#> [365] 15.475596 14.352300 13.341334 12.431465 12.499493 11.673808 10.930691
#> [372] 10.261886 9.659962 9.118230 8.630671 9.122623 14.274324 13.271155
#> [379] 12.368304 11.555738 10.824428 10.166249 9.573888 9.040764 8.560951
#> [386] 8.129120 10.287137 9.682688 14.106512 13.120125 12.232377 11.433403
#> [393] 10.714327 10.067158 9.484707 8.960500 8.488714 14.179878 13.186154
#> [400] 12.291803 11.486887 10.762462 10.110480 9.523696 8.995590 11.296037
#> [407] 10.590697 15.560009 14.428272 13.409709 12.493002 11.667966 10.925433
#> [414] 10.257154 9.655703 9.114397 8.627221 8.188763 9.786475 9.232092
#> [421] 8.733146 8.284096 7.879950 15.337338 14.227869 13.229346 12.330675
#> [428] 11.521872 10.793949 10.138818 9.549200 9.018544 8.540954 8.111123
#> [435] 7.724274 12.561367 11.729495 10.980809 10.306992 9.700557 9.154765
#> [442] 8.663553 12.317218 11.509760 10.783048 10.129007 9.540371 9.010598
#> [449] 10.143564 9.553472 9.022389 8.544414 8.114237 9.008965 8.532332
#> [456] 8.103363 7.717291 7.369826 8.811890 11.630233 10.891474 10.226591
#> [463] 9.628196 10.425129 9.806880 9.250456 8.749675 8.298971 7.893338
#> [470] 7.528269 10.964446 10.292265 9.687303 12.024343 13.549268 12.618605
#> [477] 11.781009 11.027172 11.923896 11.155770 10.464457 9.842276 9.282312
#> [484] 10.611392 9.974517 11.666006 10.923670 11.624293 10.886128 10.221779
#> [491] 9.623865 15.466536 14.344146 13.333996 12.424860 11.606638 10.870239
#> [498] 10.207479 9.610995 9.074160 8.591008
ss_flows(ss)
#> [1] 19.208604 20.430800 10.334991 16.499229 13.540609 12.293414 14.774428
#> [8] 8.984067 13.718075 14.325818 11.749010 14.520029 20.278302 10.081311
#> [15] 11.788212 20.626005 24.939098 8.800396 11.898536 12.683749 18.734268
#> [22] 9.025698 28.023426 21.108644 8.378003 12.248649 11.182713 18.805546
#> [29] 11.656840 16.629232 14.789562 16.076770 11.165500 14.064494 6.282134
#> [36] 16.556444 6.583915 9.673448 18.842118 13.209137 11.095414 11.561884
#> [43] 7.635714 24.080538 11.527989 22.060363 18.114603 13.520453 23.676939
#> [50] 13.285324 10.719941 10.828077 11.250913 15.566603 7.667897 14.961588
#> [57] 13.964841 9.343790 10.128422 12.250487 13.944034 26.002437 15.133608
#> [64] 12.744142 16.969417 9.511422 10.212868 16.446914 14.168221 9.956387
#> [71] 7.750637 9.043740 9.749640 11.937082 9.582721 14.523473 6.621902
#> [78] 11.062131 12.250440 5.895606 12.895109 9.216538 10.927900 13.585237
#> [85] 15.408591 12.716188 9.898394 8.475948 8.419802 10.490772 13.843398
#> [92] 5.266512 9.681445 20.177748 19.754587 14.737186 10.717058 12.256434
#> [99] 14.886680 13.288815 13.366479 9.756340 9.751219 11.172373 20.796091
#> [106] 22.592833 14.823710 14.724591 12.448372 6.042823 13.178783 16.648249
#> [113] 15.004564 11.706035 12.448642 12.463583 5.846503 10.900548 13.212936
#> [120] 16.464744 10.909137 11.351475 12.813445 12.977405 14.527740 11.221958
#> [127] 19.420735 22.588559 9.896863 14.596833 18.717885 13.120894 13.424921
#> [134] 20.450952 16.990083 12.877095 16.296523 8.758420 15.215516 13.337497
#> [141] 9.123808 8.348869 11.803561 15.471005 14.728774 16.206414 9.333444
#> [148] 20.960942 10.396220 9.130014 14.523795 10.644125 15.461105 11.217576
#> [155] 13.981308 15.408620 9.496883 7.439397 8.994902 14.001046 20.287688
#> [162] 12.588445 13.102926 9.579008 12.443438 9.420873 11.698805 10.587015
#> [169] 8.785851 9.480828 14.672790 11.361751 11.379859 11.945087 11.492208
#> [176] 9.002912 16.368728 13.004431 15.746896 15.291629 19.364227 17.321412
#> [183] 10.586380 10.113230 14.860454 14.939161 19.356786 15.724048 8.970179
#> [190] 10.348179 9.558266 15.556018 8.923410 8.925705 8.237401 7.937674
#> [197] 12.411913 8.742535 14.874578 14.696071 18.023113 12.275188 17.028113
#> [204] 11.621354 9.216295 11.617351 23.221731 11.982755 10.056504 10.116802
#> [211] 12.507467 13.634439 10.744222 8.067058 11.693883 16.695242 12.825044
#> [218] 10.881720 12.559022 18.293045 12.030575 9.347239 12.517108 22.465632
#> [225] 10.559634 16.277145 10.505718 9.474922 7.852593 9.999620 10.863486
#> [232] 9.227338 10.481649 7.088738 33.880813 15.941537 8.432384 17.535416
#> [239] 12.627903 11.440980 8.169891 12.694548 8.215296 9.706153 12.580053
#> [246] 11.959783 9.231655 9.135036 12.113411 20.663695 10.726467 9.502009
#> [253] 10.199900 12.401347 7.221969 15.830687 8.720145 12.486453 12.791120
#> [260] 13.286556 14.460240 8.863883 10.538219 21.037487 12.120162 8.989906
#> [267] 17.515112 9.650482 19.722274 18.079605 9.000907 15.578551 11.710931
#> [274] 8.995197 18.026657 10.746612 10.605054 11.294679 11.934263 11.000182
#> [281] 11.817587 7.880644 9.492233 25.960961 10.678120 9.341277 12.015181
#> [288] 7.129673 10.769107 7.454138 17.454758 14.701849 10.572451 11.151920
#> [295] 10.711978 8.473378 15.093143 13.115569 9.093415 7.524231 11.975523
#> [302] 11.636418 8.058078 10.671886 17.800524 20.033365 11.198953 9.225642
#> [309] 10.610523 10.504995 8.691211 25.171646 12.092182 8.514823 9.709488
#> [316] 20.027296 10.422533 13.673541 18.613716 28.920571 11.516058 11.212108
#> [323] 9.058251 10.283031 12.727735 20.307479 10.922789 16.774767 14.566887
#> [330] 14.992124 19.665883 6.061504 9.240902 11.257412 13.940457 11.945631
#> [337] 12.430220 10.586177 16.153984 10.384744 11.338999 8.487806 15.827512
#> [344] 10.934060 7.700206 7.712460 21.761356 11.044575 15.982184 18.992252
#> [351] 11.598288 12.842055 8.257583 9.281074 14.824249 11.904776 14.068979
#> [358] 21.502862 12.097203 11.859333 12.682375 13.665230 10.281115 25.297381
#> [365] 13.564888 12.904978 13.253167 19.727350 11.181229 10.349570 8.485505
#> [372] 10.627465 15.112841 8.651705 14.396893 23.058052 9.619019 8.699010
#> [379] 7.976423 16.482604 12.891000 11.855783 10.976643 10.285643 13.081431
#> [386] 16.235102 8.573271 22.717416 9.320015 8.425935 17.281189 12.345970
#> [393] 13.715925 9.862724 14.550013 12.037323 22.905125 18.856666 12.595721
#> [400] 8.284777 7.260936 12.239772 13.416203 11.419207 17.827670 8.693238
#> [407] 25.380878 10.160603 8.402337 11.147433 8.881053 12.894605 9.953048
#> [414] 14.559444 9.098709 9.167163 10.112915 15.444796 11.483581 8.052685
#> [421] 8.770897 11.966611 25.137079 16.086315 12.515985 8.239035 11.824470
#> [428] 10.772520 14.125512 12.248152 12.255151 12.540757 11.660995 8.397169
#> [435] 20.005984 7.047322 11.380215 9.840963 8.595091 11.968082 13.637386
#> [442] 19.527703 10.956991 17.113614 10.455643 11.817343 9.066562 16.008469
#> [449] 13.823737 8.082715 11.521041 11.237467 14.217481 13.745745 11.324225
#> [456] 10.504626 10.078629 13.906395 18.355206 16.868017 11.204905 8.332401
#> [463] 16.452925 8.246541 8.770116 13.520516 10.615547 9.504865 11.212542
#> [470] 17.304247 10.837524 5.860774 19.046928 21.520762 12.038821 11.799949
#> [477] 13.047598 18.818758 9.360050 15.588251 9.891850 12.849195 16.746945
#> [484] 8.958434 18.411674 11.683857 18.345828 10.023732 8.394669 7.857978
#> [491] 25.277003 11.979047 16.859342 11.398544 12.024824 9.455145 15.127358
#> [498] 10.490161 9.291068 7.531154
# Make 500 snow hydrographs and run stochasim on both hydrographs.
dst_snow <- hydist_snow(dst_norm(13, 2^2), baseflow = 2)
set.seed(43)
snow <- realise(dst_snow, n = 500)
(ss2 <- stochasim2(snow, rain, cross_section = cs, progress = TRUE))
#> Iterating ■■■■■■■■■■ 28% | ETA: 5s
#> Iterating ■■■■■■■■■■■■■■■■■■■■■■■ 75% | ETA: 2s
#> Iterating ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 100% | ETA: 0s
#> Stochasim object with 500 runs.
# Plot again.
plot(ss2)
plot(ss2, what = "flows")
ss_widths(ss2)
#> [1] 40.000000 36.424264 33.206102 30.309756 27.703044 25.357004 23.245567
#> [8] 21.345275 19.635011 18.095774 16.710461 15.463679 14.341575 13.331682
#> [15] 12.422778 11.604764 13.009501 15.509059 14.382418 13.368440 12.455860
#> [22] 11.634538 10.895348 16.926657 15.658255 14.516694 13.489289 12.564624
#> [29] 11.732426 10.983447 10.309366 10.206578 9.610184 9.526922 8.998494
#> [36] 8.522909 10.490709 9.865902 9.303576 11.910773 11.143960 10.453828
#> [43] 9.832709 9.273702 14.832107 13.773161 13.977468 13.003985 12.127851
#> [50] 14.754102 13.702956 12.756925 11.905496 11.139211 10.449554 9.828862
#> [57] 9.270240 8.767480 8.314996 7.907761 8.282944 9.840981 15.863509
#> [64] 14.701422 13.655544 12.714253 11.867092 11.104647 10.418446 9.800866
#> [71] 9.245043 8.744803 8.294587 9.092459 9.358231 9.575873 9.042550
#> [78] 8.860333 8.398564 8.207992 7.811457 9.998753 9.441921 8.921993
#> [85] 8.454058 9.763539 9.211449 8.714568 8.267375 7.864902 7.502676
#> [92] 8.452619 8.220376 8.291980 12.669087 11.826443 11.068062 10.385520
#> [99] 9.771232 9.218373 8.720800 8.272984 8.176505 8.306221 7.949676
#> [106] 12.997037 14.220409 13.222632 12.324633 11.516434 10.789054 10.134413
#> [113] 10.548868 9.918245 9.350685 8.839881 10.718883 10.071258 9.488397
#> [120] 9.042993 10.432617 9.813619 9.256521 8.755133 8.303884 9.205516
#> [127] 10.065803 12.249793 14.180998 13.187162 12.292710 11.487703 10.763197
#> [134] 10.111141 12.840424 11.980645 11.206845 10.510425 9.883646 9.319546
#> [141] 8.811855 8.906224 8.439866 8.532509 9.803079 9.247035 10.268963
#> [148] 9.666331 13.146302 12.255936 11.454607 10.733410 10.882945 10.218914
#> [155] 9.621287 9.083422 9.960303 9.388537 8.873947 8.699022 8.871852
#> [162] 12.738035 11.888495 11.123910 10.435783 9.816469 9.758066 9.206523
#> [169] 8.909498 8.727546 8.279055 9.117408 9.023584 9.695908 9.150581
#> [176] 8.659787 9.317854 10.371790 9.758875 9.977856 9.404335 12.214175
#> [183] 11.417022 10.699584 10.224851 9.626630 9.088231 12.209485 11.412801
#> [190] 10.695785 10.050470 9.469687 9.856935 9.295505 8.880021 10.186865
#> [197] 9.592442 9.057462 8.575980 10.837819 10.178301 11.419851 10.702130
#> [204] 10.789514 10.134826 9.545608 9.015311 14.375410 13.362133 12.450184
#> [211] 11.629429 10.890750 10.225939 9.627610 9.089113 8.604466 10.578638
#> [218] 9.945039 9.374799 8.861583 11.590854 10.856033 10.194693 9.599488
#> [225] 13.973603 13.000507 12.124720 11.336512 10.627125 10.268750 9.666139
#> [232] 9.123789 8.635675 8.196371 7.800998 19.811009 18.254172 16.853019
#> [239] 15.591981 14.457047 13.435606 12.516310 11.688943 10.944313 10.274145
#> [246] 9.670995 9.128160 9.071606 8.588710 8.671933 12.937302 12.067836
#> [253] 11.285316 10.581049 9.947208 9.376751 10.030938 9.452109 10.939446
#> [260] 10.269766 9.667053 9.124612 8.636415 8.491457 13.147657 12.257155
#> [267] 11.455704 10.734398 10.085222 12.439860 11.620138 10.882388 10.218414
#> [274] 9.620836 9.083017 11.422096 10.704151 10.058000 9.476464 9.183067
#> [281] 8.689025 8.468227 8.045668 7.665366 15.838289 14.678724 13.635116
#> [288] 12.695868 11.850546 11.089755 10.405044 11.059795 10.378080 9.764536
#> [295] 9.212346 8.715376 8.268102 9.563701 9.031595 8.552699 8.516015
#> [302] 8.623114 9.568077 9.035533 8.556244 11.278840 12.635947 11.796616
#> [309] 11.041219 10.361361 9.749489 9.198804 15.370435 14.257656 13.256154
#> [316] 12.354803 12.689511 11.844824 11.084605 11.794001 17.466442 16.144062
#> [323] 14.953920 13.882792 12.918777 12.051163 12.834657 11.975455 11.202174
#> [330] 10.506220 9.879862 12.404315 11.588148 10.853597 10.192502 9.597515
#> [337] 9.062028 8.580089 8.146344 10.235749 9.636438 9.097058 8.611617
#> [344] 10.028927 9.450298 8.929533 8.460843 13.536410 12.607033 11.770594
#> [351] 12.033805 11.254689 10.553484 9.922400 9.354424 9.393355 8.878284
#> [358] 8.914888 13.419053 12.501412 11.675535 10.932245 10.263285 9.661221
#> [365] 15.475596 14.352300 13.341334 12.431465 12.499493 11.673808 10.930691
#> [372] 10.261886 9.659962 9.118230 8.630671 9.122623 14.274324 13.271155
#> [379] 12.368304 11.555738 10.824428 10.166249 9.573888 9.040764 8.560951
#> [386] 8.129120 10.287137 9.682688 14.106512 13.120125 12.232377 11.433403
#> [393] 10.714327 10.067158 9.484707 8.960500 8.488714 14.179878 13.186154
#> [400] 12.291803 11.486887 10.762462 10.110480 9.523696 8.995590 11.296037
#> [407] 10.590697 15.634441 14.495261 13.469999 12.547263 11.716801 10.969385
#> [414] 10.296710 9.691303 9.313194 10.515310 9.888043 9.323502 8.918550
#> [421] 8.450959 9.294417 8.789239 15.410994 14.294159 13.289007 12.384370
#> [428] 11.570197 10.837442 10.177961 9.584429 9.050251 8.569490 8.136805
#> [435] 7.747388 12.561367 11.729495 10.980809 10.306992 9.700557 9.321732
#> [442] 8.813823 12.317218 11.509760 10.783048 10.129007 9.540371 9.427893
#> [449] 10.143564 9.553472 9.022389 8.544414 9.377436 8.863956 8.401824
#> [456] 7.985906 8.122208 7.734251 8.811890 11.630233 10.891474 10.226591
#> [463] 9.628196 10.425129 9.806880 9.250456 8.749675 8.298971 9.854869
#> [470] 9.667619 10.964446 10.292265 9.687303 12.024343 13.549268 12.618605
#> [477] 11.781009 11.027172 11.923896 11.155770 10.464457 9.842276 9.282312
#> [484] 10.611392 9.974517 11.666006 10.923670 11.624293 10.886128 10.221779
#> [491] 9.623865 15.466536 14.344146 13.333996 12.424860 11.606638 10.870239
#> [498] 10.207479 9.610995 9.074160 8.591008
ss_flows(ss2)
#> $x
#> [1] 12.924973 15.690975 9.850791 14.079982 12.028065 13.216154 13.930372
#> [8] 13.033608 11.191804 15.274265 12.445134 11.001159 13.772869 11.732705
#> [15] 12.879192 13.874518 11.627641 11.391136 9.187727 10.590136 16.607519
#> [22] 15.295424 11.066254 8.350812 12.293764 10.982816 15.213875 13.360395
#> [29] 14.132649 12.552649 17.128618 10.993977 15.938556 9.403900 9.697000
#> [36] 13.881476 13.405273 12.502238 11.558040 11.387924 12.681916 16.155236
#> [43] 14.468497 10.461133 12.273394 10.509455 12.979812 9.571386 14.165592
#> [50] 10.752623 12.413423 14.109943 10.211235 15.032418 12.829837 12.367094
#> [57] 11.623809 13.374774 11.446956 13.760376 16.488465 13.284263 13.913111
#> [64] 13.203933 12.763648 12.458861 16.350824 13.851213 10.682076 13.534141
#> [71] 12.918781 13.484462 15.177819 15.643180 16.024267 9.888193 14.771373
#> [78] 10.251880 13.629138 12.122747 16.764721 15.789720 12.171039 14.058937
#> [85] 11.171875 10.968343 14.096978 11.594389 11.383227 11.477971 14.057474
#> [92] 13.650822 13.776199 12.388597 12.513199 9.161476 12.002131 10.354521
#> [99] 13.068123 10.973973 13.587582 13.574004 13.801135 13.176831 12.650966
#> [106] 10.895644 13.480199 15.517513 10.517895 12.884731 8.825290 12.936636
#> [113] 11.981932 12.478824 13.026420 18.025652 10.988737 13.442210 15.091206
#> [120] 12.398567 12.741925 10.451414 13.053963 10.749712 12.879395 16.882123
#> [127] 14.089057 12.183709 14.561874 9.744440 10.601467 11.456353 10.399223
#> [134] 11.900588 13.379442 12.219928 10.911442 13.964436 14.197787 9.896655
#> [141] 14.851727 11.824036 14.197359 14.613730 13.531027 14.599743 12.438701
#> [148] 15.360327 13.387095 17.271840 16.398222 18.312921 13.267391 15.440200
#> [155] 10.479664 16.697395 13.296646 12.595536 14.488921 11.756083 12.840229
#> [162] 14.551314 11.673563 7.842157 10.764837 16.343283 9.014248 14.857458
#> [169] 14.538865 12.554725 15.221505 15.057221 16.234446 13.941185 14.132616
#> [176] 15.572481 9.771686 11.835887 11.599667 13.009925 15.487260 12.415806
#> [183] 16.472945 17.160614 13.286208 8.700449 14.070521 11.995464 11.732883
#> [190] 13.803331 12.251154 11.715000 12.393477 14.805845 17.094101 14.334735
#> [197] 12.846202 13.219063 18.233906 10.064698 11.294748 13.379230 13.038824
#> [204] 13.158856 8.258320 13.473242 14.710085 11.877831 15.772041 8.418013
#> [211] 14.717761 13.862891 13.455678 12.891261 12.965338 15.011179 12.494215
#> [218] 15.663506 14.211314 15.784604 15.025601 15.633045 10.850028 14.834194
#> [225] 13.255322 10.825392 15.174671 11.647891 17.237480 12.435933 13.647591
#> [232] 12.364127 11.365783 12.782120 16.518314 14.125092 9.804807 15.199187
#> [239] 11.361331 15.224641 12.063783 17.101524 11.710154 10.377347 13.055621
#> [246] 11.518941 15.141307 10.564134 14.441488 10.676098 12.108308 11.437515
#> [253] 11.329999 9.163016 13.505452 14.130359 13.867632 18.411854 12.830525
#> [260] 15.314215 13.934317 10.551794 14.125478 14.432662 16.482463 14.351325
#> [267] 14.051017 16.221593 13.422501 12.292849 13.847161 17.111420 15.044947
#> [274] 10.201756 17.036594 14.020786 11.885854 12.729843 15.336473 12.273766
#> [281] 14.084803 11.220916 9.468119 16.292377 11.201277 14.409504 15.938402
#> [288] 12.542578 12.369236 9.251375 15.701933 10.099556 11.243657 12.345411
#> [295] 10.701014 10.998009 12.856291 14.276244 11.541850 14.168480 14.356007
#> [302] 16.010616 14.077495 13.572992 11.421225 15.378680 15.442534 14.222452
#> [309] 9.785674 13.274274 12.510682 13.158964 14.468718 10.419673 13.840066
#> [316] 13.705846 15.664235 12.446924 15.057679 16.579769 11.542647 12.108489
#> [323] 14.548014 16.858248 11.305515 11.588690 13.254076 13.439688 11.509358
#> [330] 13.977303 14.581085 13.231779 17.215708 11.455765 12.038508 13.316806
#> [337] 10.530008 12.378130 11.141373 12.542260 13.095514 14.258768 14.868730
#> [344] 11.865362 14.093917 12.782947 10.738942 15.939869 9.322041 12.318404
#> [351] 17.164407 14.367635 15.092984 12.728946 11.663175 11.316669 11.175282
#> [358] 13.952477 13.155320 14.882188 11.699046 14.148993 12.815404 10.142955
#> [365] 10.324859 13.958909 13.400057 11.939384 14.534814 13.054083 12.263515
#> [372] 15.774228 12.848527 10.516874 11.782153 13.769297 11.715286 13.211227
#> [379] 13.419179 8.356849 12.703059 15.356704 14.158272 9.489097 11.923620
#> [386] 12.784637 15.071688 13.659525 16.417789 14.170584 11.556358 11.974828
#> [393] 13.592714 11.729412 12.341966 12.268044 13.186442 12.136300 12.897230
#> [400] 15.433728 10.558357 8.615645 13.726477 8.995572 9.649418 14.400952
#> [407] 18.456498 14.312859 10.396378 10.669334 11.184896 14.873567 14.515568
#> [414] 10.620387 15.564322 17.669200 11.923131 11.109689 14.873310 11.866486
#> [421] 15.531444 11.600674 16.022089 11.879488 15.933976 12.337758 11.440317
#> [428] 9.924424 8.984967 11.633290 10.772592 12.728904 9.678215 12.586508
#> [435] 13.680881 11.412767 7.100549 13.195474 9.896904 15.579272 13.696317
#> [442] 14.580114 14.994549 10.662262 13.500198 13.752444 15.765157 12.101350
#> [449] 13.181292 13.368230 14.039802 15.676807 11.748447 13.887224 11.559125
#> [456] 13.478932 10.381020 12.622441 13.985733 15.379686 14.475777 8.934713
#> [463] 11.711898 14.918422 13.483077 11.016548 10.391197 16.512784 16.184913
#> [470] 14.402182 14.547017 12.593341 9.174339 12.314373 13.234686 9.040165
#> [477] 10.483477 11.632703 12.704223 12.535093 14.123329 9.966140 14.096951
#> [484] 10.522566 12.759651 11.326324 15.452074 12.841962 11.899588 13.896354
#> [491] 11.972652 13.958783 13.335911 13.780853 11.401763 12.399031 10.476297
#> [498] 14.526329 13.029287 12.658277
#>
#> $y
#> [1] 19.208604 20.430800 10.334991 16.499229 13.540609 12.293414 14.774428
#> [8] 8.984067 13.718075 14.325818 11.749010 14.520029 20.278302 10.081311
#> [15] 11.788212 20.626005 24.939098 8.800396 11.898536 12.683749 18.734268
#> [22] 9.025698 28.023426 21.108644 8.378003 12.248649 11.182713 18.805546
#> [29] 11.656840 16.629232 14.789562 16.076770 11.165500 14.064494 6.282134
#> [36] 16.556444 6.583915 9.673448 18.842118 13.209137 11.095414 11.561884
#> [43] 7.635714 24.080538 11.527989 22.060363 18.114603 13.520453 23.676939
#> [50] 13.285324 10.719941 10.828077 11.250913 15.566603 7.667897 14.961588
#> [57] 13.964841 9.343790 10.128422 12.250487 13.944034 26.002437 15.133608
#> [64] 12.744142 16.969417 9.511422 10.212868 16.446914 14.168221 9.956387
#> [71] 7.750637 9.043740 9.749640 11.937082 9.582721 14.523473 6.621902
#> [78] 11.062131 12.250440 5.895606 12.895109 9.216538 10.927900 13.585237
#> [85] 15.408591 12.716188 9.898394 8.475948 8.419802 10.490772 13.843398
#> [92] 5.266512 9.681445 20.177748 19.754587 14.737186 10.717058 12.256434
#> [99] 14.886680 13.288815 13.366479 9.756340 9.751219 11.172373 20.796091
#> [106] 22.592833 14.823710 14.724591 12.448372 6.042823 13.178783 16.648249
#> [113] 15.004564 11.706035 12.448642 12.463583 5.846503 10.900548 13.212936
#> [120] 16.464744 10.909137 11.351475 12.813445 12.977405 14.527740 11.221958
#> [127] 19.420735 22.588559 9.896863 14.596833 18.717885 13.120894 13.424921
#> [134] 20.450952 16.990083 12.877095 16.296523 8.758420 15.215516 13.337497
#> [141] 9.123808 8.348869 11.803561 15.471005 14.728774 16.206414 9.333444
#> [148] 20.960942 10.396220 9.130014 14.523795 10.644125 15.461105 11.217576
#> [155] 13.981308 15.408620 9.496883 7.439397 8.994902 14.001046 20.287688
#> [162] 12.588445 13.102926 9.579008 12.443438 9.420873 11.698805 10.587015
#> [169] 8.785851 9.480828 14.672790 11.361751 11.379859 11.945087 11.492208
#> [176] 9.002912 16.368728 13.004431 15.746896 15.291629 19.364227 17.321412
#> [183] 10.586380 10.113230 14.860454 14.939161 19.356786 15.724048 8.970179
#> [190] 10.348179 9.558266 15.556018 8.923410 8.925705 8.237401 7.937674
#> [197] 12.411913 8.742535 14.874578 14.696071 18.023113 12.275188 17.028113
#> [204] 11.621354 9.216295 11.617351 23.221731 11.982755 10.056504 10.116802
#> [211] 12.507467 13.634439 10.744222 8.067058 11.693883 16.695242 12.825044
#> [218] 10.881720 12.559022 18.293045 12.030575 9.347239 12.517108 22.465632
#> [225] 10.559634 16.277145 10.505718 9.474922 7.852593 9.999620 10.863486
#> [232] 9.227338 10.481649 7.088738 33.880813 15.941537 8.432384 17.535416
#> [239] 12.627903 11.440980 8.169891 12.694548 8.215296 9.706153 12.580053
#> [246] 11.959783 9.231655 9.135036 12.113411 20.663695 10.726467 9.502009
#> [253] 10.199900 12.401347 7.221969 15.830687 8.720145 12.486453 12.791120
#> [260] 13.286556 14.460240 8.863883 10.538219 21.037487 12.120162 8.989906
#> [267] 17.515112 9.650482 19.722274 18.079605 9.000907 15.578551 11.710931
#> [274] 8.995197 18.026657 10.746612 10.605054 11.294679 11.934263 11.000182
#> [281] 11.817587 7.880644 9.492233 25.960961 10.678120 9.341277 12.015181
#> [288] 7.129673 10.769107 7.454138 17.454758 14.701849 10.572451 11.151920
#> [295] 10.711978 8.473378 15.093143 13.115569 9.093415 7.524231 11.975523
#> [302] 11.636418 8.058078 10.671886 17.800524 20.033365 11.198953 9.225642
#> [309] 10.610523 10.504995 8.691211 25.171646 12.092182 8.514823 9.709488
#> [316] 20.027296 10.422533 13.673541 18.613716 28.920571 11.516058 11.212108
#> [323] 9.058251 10.283031 12.727735 20.307479 10.922789 16.774767 14.566887
#> [330] 14.992124 19.665883 6.061504 9.240902 11.257412 13.940457 11.945631
#> [337] 12.430220 10.586177 16.153984 10.384744 11.338999 8.487806 15.827512
#> [344] 10.934060 7.700206 7.712460 21.761356 11.044575 15.982184 18.992252
#> [351] 11.598288 12.842055 8.257583 9.281074 14.824249 11.904776 14.068979
#> [358] 21.502862 12.097203 11.859333 12.682375 13.665230 10.281115 25.297381
#> [365] 13.564888 12.904978 13.253167 19.727350 11.181229 10.349570 8.485505
#> [372] 10.627465 15.112841 8.651705 14.396893 23.058052 9.619019 8.699010
#> [379] 7.976423 16.482604 12.891000 11.855783 10.976643 10.285643 13.081431
#> [386] 16.235102 8.573271 22.717416 9.320015 8.425935 17.281189 12.345970
#> [393] 13.715925 9.862724 14.550013 12.037323 22.905125 18.856666 12.595721
#> [400] 8.284777 7.260936 12.239772 13.416203 11.419207 17.827670 8.693238
#> [407] 25.380878 10.160603 8.402337 11.147433 8.881053 12.894605 9.953048
#> [414] 14.559444 9.098709 9.167163 10.112915 15.444796 11.483581 8.052685
#> [421] 8.770897 11.966611 25.137079 16.086315 12.515985 8.239035 11.824470
#> [428] 10.772520 14.125512 12.248152 12.255151 12.540757 11.660995 8.397169
#> [435] 20.005984 7.047322 11.380215 9.840963 8.595091 11.968082 13.637386
#> [442] 19.527703 10.956991 17.113614 10.455643 11.817343 9.066562 16.008469
#> [449] 13.823737 8.082715 11.521041 11.237467 14.217481 13.745745 11.324225
#> [456] 10.504626 10.078629 13.906395 18.355206 16.868017 11.204905 8.332401
#> [463] 16.452925 8.246541 8.770116 13.520516 10.615547 9.504865 11.212542
#> [470] 17.304247 10.837524 5.860774 19.046928 21.520762 12.038821 11.799949
#> [477] 13.047598 18.818758 9.360050 15.588251 9.891850 12.849195 16.746945
#> [484] 8.958434 18.411674 11.683857 18.345828 10.023732 8.394669 7.857978
#> [491] 25.277003 11.979047 16.859342 11.398544 12.024824 9.455145 15.127358
#> [498] 10.490161 9.291068 7.531154
#>