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library (dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library (tidyr)
library (ggplot2)
library (leaflet)
library (gsw)
library (matrixStats)
## 
## Attaching package: 'matrixStats'
## The following object is masked from 'package:dplyr':
## 
##     count
#library (ggOceanMaps)
#library (ggOceanMapsData)

install.packages(“dplyr”) install.packages(“tidyr”) install.packages(“leaflet”) install.packages(“knitr”) install.packages(“rmarkdown”) install.packages(“gsw”) install.packages(“matrixStats”) intall.packages("ggspatial)

##shell("cd C:/Users/ingri/MAST467/Data/output.dat")
shell("C:/Users/ingri/MAST467/Data/NASA.cmd", translate=TRUE)
Omg<-read.csv("C:/Users/ingri/MAST467/Data/output.dat",sep=" ")

###Plotting Temp and Sal ###From Dr.Muenchow's code
ggplot(Omg,mapping=aes(x=sal,y=tem,group=cast,color=dep)) +
  geom_point() +
  xlim(c(25,35)) +
  ylim(c(-2,8)) +
  xlab("Salinity, psu") +
  ylab("Temperature, C") +
  scale_color_viridis_c(guide=guide_colorbar(barheight=15)) +
  facet_wrap(~cast)

###Depth and Temp ###From Dr.Muenchow's code
ggplot(Omg,aes(x=dep,y=tem,group=cast)) +
  geom_path() +
  ylim(c(-1.5,6.5)) +
  xlim(c(500,0)) +
  ylab("Temperature, C") +
  xlab("Depth, m") +
  coord_flip(expand=FALSE) + 
  facet_wrap(~cast)
## Warning: Removed 3735 row(s) containing missing values (geom_path).

###Depth and Sal ###From Dr.Muenchow's code
ggplot(Omg,mapping=aes(x=dep,y=sal,group=cast)) +
  geom_line() +
  ylim(c(30,35)) +
  xlim(c(500,0)) +
  ylab("Salinity, psu") +
  coord_flip(expand=FALSE) +
  facet_wrap(~cast)
## Warning: Removed 3097 row(s) containing missing values (geom_path).

###Making data fram for 1 cast
Omg.df = data.frame(Omg$lon, Omg$lat, Omg$dep, Omg$tem, Omg$sal, Omg$cast)
###rename columns
colnames(Omg.df) = c("lon", "lat", "dep", "tem", "sal", "cast")
###Specifying cast number
C106 = Omg.df[Omg.df$cast==106,]

###Using one cast (106) to convert in-situ temperature, salinity, and depth to pressure, absolute salinity, and potential temperature
#Pressure
p = gsw_p_from_z(-C106$dep, C106$lat)
#Absolute Salinity
SA = gsw_SA_from_SP(C106$sal, p, C106$lat, C106$lon)
#Potential Temperature
pt = gsw_pt_from_t(SA, C106$tem, p, 0)


####Using cast 106 to estimate potential denisty at both zero and 1000-dbar pressure as well as the freezing point
#Conservative Temperature
CT= gsw_CT_from_t(SA, C106$tem, p)
#Potential Density to Zero Pressure
r0 = gsw_sigma0(SA,CT)
#Potential Density to 1000-m Pressure
r1 = gsw_sigma1(SA,CT)
#Freezing Point
tf = gsw_CT_freezing(SA, p, saturation_fraction = 1)

dat= data.frame(p, SA, pt, CT, r0, r1, tf, C106$tem)


###Plotting profile to compare in-situ with potential temperature
ggplot(dat, aes(x=p)) + 
  geom_line(aes(y = C106$tem), color = "darkred") + 
  geom_line(aes(y = pt), color="steelblue", linetype="twodash")+
  coord_flip(expand=FALSE)+
  ylim(c(3,6.5)) +
  xlim(c(350,0)) +
  ylab("Temperature, C") +
  xlab("Pressure, p")

###Plotting profile to compare absolute salinity with pressure
ggplot(dat, aes(x=p)) + 
  geom_line(aes(y = SA), color = "darkred") + 
  #geom_line(aes(y = r1), color="steelblue", linetype="twodash")+
  coord_flip(expand=FALSE)+
  ylim(c(31.5,35.5)) +
  xlim(c(325,0)) +
  ylab("Absolute Salinity, SA") +
  xlab("Pressure, p")

###Plotting profile to compare potential density with pressure
ggplot(dat, aes(x=p)) + 
  #geom_line(aes(y = SA), color = "darkred") + 
  geom_line(aes(y = r1), color="steelblue", linetype="twodash")+
  coord_flip(expand=FALSE)+
  ylim(c(29,32.5)) +
  xlim(c(325,0)) +
  ylab("Potential density to 1000-m pressure") +
  xlab("Pressure, p")

###Plotting profile to compare potential density with absolute salinity
ggplot(dat, aes(x=r1)) + 
  geom_line(aes(y = SA), color = "darkred") + 
  #geom_line(aes(y = r1), color="steelblue", linetype="twodash")+
  coord_flip(expand=FALSE)+
  ylim(c(31.5,35.5)) +
  xlim(c(29,32.5)) +
  ylab("Absolute Salinity, SA") +
  xlab("Potential density to 1000-m pressure")

p_2 = gsw_p_from_z(-Omg$dep, Omg$lat)
SA_2 = gsw_SA_from_SP(Omg$sal, p_2, Omg$lat, Omg$lon)
pt_2 = gsw_pt_from_t(SA_2, Omg$tem, p_2, 0)
CT_2= gsw_CT_from_t(SA_2, Omg$tem, p_2)

dat1<-data.frame(Omg$cast, Omg$lon, Omg$lat, Omg$dep, Omg$sal, Omg$tem, p_2, SA_2, pt_2, CT_2)

colnames(dat1) = c("cast", "lon", "lat", "dep", "sal", "tem", "p_2", "SA_2", "pt_2", "CT_2")
###Many steps are this chunk is borrowed from Sam's code
###Defining empty vectors/variables/etc. BEFORE for loop begins...
Dmax = 0
fresh = 0
y= NULL #y is an empty dataframe that we will store the output of each iteration for

###Looping through each cast to define bin averaged variables
for (i in 106:147) #i refers to cast
{data<-dplyr::filter(dat1, cast==i)
  #print(i)
  last=length(data[,1])
  #print(last)
  
  Depth<-as.numeric(data[,4])
  Temp<-as.numeric(data[,6])
  Salt<-as.numeric(data[,5])
  Long<-as.numeric(data[,2])
  Lat<-as.numeric(data[,3])
  p_2<-as.numeric(data[,7])
  SA_2<-as.numeric(data[,8])
  pt_2<-as.numeric(data[,9])
  CT_2<-as.numeric(data[,10])
  
  
#tail function goes to last value above. integer means it has no decimals vs. numeric
  maxDepth<-as.integer(tail(Depth,1)) 
  #print(maxDepth)
  Dmax = maxDepth
  
#Beginning the conditional statement for loop
  if (last>=1)
  {
    
#Calculating and defining bin averages
  binDepth<-seq(2,maxDepth,1)#starts at 2m, goes to maxdepth, sorts by 1m
  
  binSalt<-binMeans(Salt, x=Depth, bx=binDepth, na.rm=TRUE)
  binTemp<-binMeans(Temp, x=Depth, bx=binDepth, na.rm=TRUE)
  binp_2<-binMeans(p_2, x=Depth, bx=binDepth, na.rm=TRUE)
  binSA_2<-binMeans(SA_2, x=Depth, bx=binDepth, na.rm=TRUE)
  binpt_2<-binMeans(pt_2, x=Depth, bx=binDepth, na.rm=TRUE)
  binCT_2<-binMeans(CT_2, x=Depth, bx=binDepth, na.rm=TRUE)
  
###makes binDepth equal length to binSalt, binTemp, etc. borrowed from      michael's code
  binDepth = head(binDepth,-1)
  
  
###calculating the amount of freshwater at the surface. borrowed from sam's code.
  s_ref = 34.8
  s_ref_vec = c(rep(s_ref, length(binDepth)))
  fresh<-as.integer(sum(((s_ref_vec-binSalt)/s_ref_vec),na.rm=TRUE),digits=4)
  #print(fresh)
  
###creating dataframe for binvalues, adjusting their lengths so they all match
  n=maxDepth-2
  
###calculating first stability max in terms of bin averages values
N2 = gsw_Nsquared(binSA_2, binCT_2, binp_2, Lat)
print(N2)

###creating new datafram with binned data and Nsquared
dat2<- data.frame(binDepth[1:n], binSalt[1:n], binTemp[1:n], Long[1:n], Lat[1:n], binp_2[1:n], binSA_2[1:n], binpt_2[1:n], binCT_2[1:n], N2$N2[1:n])

###some binDepths don't exist and produce NAs in date 2. returns dat2 without rows with NA
dat2 = na.omit(dat2)
  
###define last as the number of rows in dat2 
last = length(dat2[,1]) 

###use new letter for index (we already used "i"). we are ignoring the first 50m of the profile; we are looking for the (deep) atlantic layer
j=50 

###starting a new conditional within the previous one
###(dat2[,10]) is N2
while(dat2[j,10] >= dat2[j-1,10]) 
{
###sorts through each row (binDepth). looking for max N2 (below 50m)
  j=j+1 
  
}###end of "while" statement


###setting Tmax to an arbitrary low number
Tmax= -99

###beginning another for loop (still within the for loop and if-statement)
###need new index "k"
for(k in j:last)
{
  ###looking at everything below Tmax
  if(dat2[k,8] >= Tmax)
  {Tmax = dat2[k,8]
  D_Tmax = dat2[k,1]
  SA_Tmax = dat2[k,7]
  Lat_Tmax = dat2[k,5]
  Long_Tmax = dat2[k,4]
  
  ###creating a new dataframe for this output
  dat3 <- data.frame(Tmax, D_Tmax, SA_Tmax, Lat_Tmax, Long_Tmax, i)
  
  }###end if-statment
}###end (second) for-loop

###combining output for each for-loop iteration. makes dataframe with one row per cast
y<- rbind.data.frame(y,dat3)
  
  }###end if-statement
}###end (first) for-loop
## $N2
##   [1]  1.050313e-03  1.265165e-04  4.544462e-05  2.407373e-05  5.850170e-05
##   [6]  5.659663e-05  3.027574e-04  1.787079e-04  2.927501e-05  4.029799e-05
##  [11]  3.311016e-04  6.580798e-04  5.364462e-04  6.614056e-04  7.174908e-04
##  [16]  2.937156e-03  1.312093e-03  2.200476e-04  2.259878e-03  1.413743e-03
##  [21]  5.726767e-04  2.455539e-04  4.884196e-05  1.037534e-04  1.281349e-04
##  [26]  1.792261e-04  1.897733e-04  1.133419e-04  7.314414e-05  4.211281e-05
##  [31]  7.265430e-05  3.812395e-05  3.498945e-05  1.021670e-04  9.917396e-05
##  [36]  4.673324e-05  1.303395e-04  2.861990e-04  7.505511e-05  1.384386e-04
##  [41]  2.581660e-04  3.120009e-04  2.542992e-04  3.360786e-04  5.392472e-04
##  [46]  6.486608e-05  1.077829e-04 -2.109378e-06  4.757724e-05  6.616747e-05
##  [51] -3.250517e-05  5.791594e-05  3.543294e-05  1.040269e-04  6.667830e-05
##  [56]  6.422060e-05 -1.464992e-05  9.835467e-05 -1.685010e-05  3.532570e-05
##  [61]  8.594229e-05  1.721135e-04  4.090546e-05  1.463214e-04  7.553812e-05
##  [66]  3.099341e-05  1.273738e-04 -3.542414e-05  7.698896e-05  4.214045e-05
##  [71]  2.502679e-06  6.578865e-05  7.668770e-05  4.023524e-05  1.531465e-04
##  [76]  3.395960e-05 -6.172005e-05  8.447087e-05 -2.271160e-05  9.364475e-05
##  [81]  6.568732e-05  4.824192e-05 -6.904474e-06  7.347150e-06  7.137543e-07
##  [86]  4.647732e-06  3.836884e-05 -8.637637e-06 -3.540055e-05  8.107680e-05
##  [91]  1.678996e-05  1.862319e-05  2.995854e-05  1.391044e-05  1.259498e-04
##  [96] -5.815024e-05  5.015705e-05  9.836164e-05  5.536878e-07  5.450758e-06
## [101]  1.535086e-05  1.614606e-04  1.671998e-04 -5.622533e-05  5.842307e-05
## [106]  2.117994e-05  3.237723e-05  2.310838e-05  9.974043e-06  2.857985e-05
## [111]  8.001282e-05  9.404269e-05 -3.638600e-05  2.758775e-05  1.024120e-05
## [116] -1.051797e-05  9.522069e-05  4.112247e-05  5.378210e-05  3.552015e-05
## [121]  6.360164e-05 -6.531924e-05 -1.228559e-05  5.382862e-05  7.733894e-05
## [126]  6.533580e-05 -1.425810e-05 -2.343933e-05  4.197219e-05  1.189830e-05
## [131]  7.334340e-05 -1.357644e-06  1.142744e-05  5.796138e-05  1.956572e-05
## [136] -3.016981e-05  4.054656e-05 -3.341357e-06  1.462446e-04 -4.342276e-05
## [141]  4.724423e-05  4.046797e-05 -1.413800e-05  7.635029e-05 -9.206888e-05
## [146]  2.705138e-05  1.273728e-05  1.934697e-05  2.769845e-05  1.624699e-07
## [151]  6.921290e-05 -1.587986e-06  2.529908e-05 -4.821402e-05  1.015310e-04
## [156]  2.540679e-05  8.166597e-05 -3.349937e-05  3.262919e-06  2.570988e-05
## [161]  1.626836e-07  1.468583e-05  3.312667e-05  1.448356e-05  1.630743e-07
## [166]  4.606760e-06  7.038966e-05 -5.280871e-06  8.695855e-05 -8.584023e-06
## [171] -2.198987e-05  8.336732e-05  7.950116e-05 -3.165808e-05 -2.404121e-05
## [176]  5.538350e-05  7.549588e-05 -2.950285e-05 -3.939999e-05  1.238941e-04
## [181] -4.998387e-05  2.068339e-05  1.756540e-07  1.290395e-05  2.987703e-05
## [186] -3.831873e-05 -1.577068e-05  5.926887e-05  5.697262e-05  5.374303e-05
## [191]  7.939776e-05  1.007827e-05  1.338820e-04 -3.009369e-05  1.039079e-04
## [196] -3.595508e-05  2.583018e-05  8.020301e-06  1.414590e-04  3.566189e-06
## [201]  6.020458e-06  4.304796e-05  2.876013e-05  4.303835e-05  1.725659e-05
## [206]  1.934856e-07 -1.712461e-05  3.554093e-05  1.168793e-05  2.891781e-05
## [211]  3.632976e-06  2.422710e-05 -3.394197e-05  1.726345e-05 -2.247565e-05
## [216]  6.439741e-05  1.903717e-05 -4.146600e-05  7.117618e-05  1.013529e-05
## [221] -1.114934e-05 -5.914691e-06 -3.137075e-05  3.283555e-05  3.002678e-05
## [226]  1.487152e-06  1.599436e-06  1.083597e-05  1.770854e-05  1.455178e-04
## [231]  6.290752e-05  1.728022e-05 -6.530232e-05  5.131633e-06  9.689884e-05
## [236]  3.136325e-05  1.014800e-05  9.645318e-05 -2.578438e-05 -2.623915e-06
## [241]  7.719272e-05  1.164068e-05  2.921077e-05 -1.920500e-05  1.015999e-05
## [246]  1.969443e-07  2.442039e-05  2.367221e-05 -1.115926e-05  3.007470e-05
## [251]  1.716352e-07  1.716724e-07  8.765947e-05 -2.312668e-06  4.381229e-06
## [256] -3.403874e-05  5.286013e-05  8.070333e-05 -1.683495e-05  7.995968e-05
## [261]  1.014542e-05  4.006914e-05  7.316167e-06 -8.358556e-06  1.716077e-07
## [266]  5.151862e-05 -6.829152e-05  4.552984e-05  2.367446e-05 -8.387928e-06
## [271] -2.710124e-06  2.159350e-05  1.100169e-05 -3.223537e-05 -3.407376e-05
## [276]  6.297537e-05  4.572320e-05 -6.170485e-06  1.018046e-05 -9.545147e-05
## [281]  2.015332e-05  7.880824e-06  1.913735e-06  4.446954e-06  3.443284e-05
## [286] -3.551903e-05  1.796255e-06 -1.449735e-06  1.303608e-05 -1.258932e-06
## [291] -2.242248e-05  3.764685e-05 -2.409847e-05 -1.550129e-05  2.615248e-05
## [296] -4.199384e-06  4.732837e-05 -3.699131e-05  1.729713e-05 -1.880614e-05
## [301]  9.636489e-06  1.552836e-07  2.017426e-05  4.852013e-05  1.929170e-06
## [306]  2.448812e-05 -5.555881e-05
## 
## $p_mid
##   [1]   3.013411   4.017074   5.020679   6.024228   7.027720   8.031161
##   [7]   9.062406  10.121451  11.152579  12.155782  13.158917  14.162000
##  [13]  15.165027  16.167997  17.170905  18.173761  19.176560  20.179298
##  [19]  21.181967  22.184595  23.187168  24.189672  25.219972  26.278045
##  [25]  27.308225  28.310497  29.312706  30.314864  31.316965  32.319010
##  [31]  33.320997  34.322928  35.324801  36.326601  37.328344  38.330059
##  [37]  39.359531  40.416756  41.446094  42.447553  43.448956  44.450296
##  [43]  45.451590  46.452822  47.454003  48.455127  49.456188  50.457181
##  [49]  51.485904  52.542406  53.571048  54.571809  55.572524  56.573177
##  [55]  57.573773  58.574311  59.574788  60.575207  61.575570  62.575876
##  [61]  63.603908  64.659664  65.687585  66.687664  67.687664  68.687612
##  [67]  69.687509  70.687349  71.687137  72.686869  73.686538  74.713910
##  [73]  75.768988  76.796244  77.795681  78.795055  79.794361  80.793627
##  [79]  81.792836  82.791971  83.791061  84.817841  85.872308  86.898966
##  [85]  87.897823  88.896611  89.895343  90.894024  91.892642  92.891209
##  [91]  93.917440  94.971370  95.997483  96.995794  97.994077  98.992292
##  [97]  99.990444 100.988534 101.986578 103.012282 104.065641 105.091220
## [103] 106.089020 107.086769 108.084455 109.082095 110.079684 111.077183
## [109] 112.102330 113.155140 114.180182 115.177465 116.174690 117.171853
## [115] 118.168960 119.166009 120.190695 121.243007 122.267569 123.264375
## [121] 124.261106 125.257808 126.254476 127.251065 128.247580 129.271728
## [127] 130.323492 131.347508 132.343796 133.340027 134.336200 135.332317
## [133] 136.356042 137.407375 138.430965 139.426832 140.422670 141.418446
## [139] 142.414153 143.409804 144.433049 145.483885 146.507007 147.502419
## [145] 148.497779 149.493071 150.488307 151.511137 152.561538 153.584246
## [151] 154.579254 155.574188 156.569077 157.563908 158.586309 159.636285
## [157] 160.658561 161.653154 162.647701 163.642185 164.636602 165.658579
## [163] 166.708130 167.729990 168.724174 169.718300 170.712364 171.706376
## [169] 172.691129 173.740239 174.798495 175.709462 176.730775 177.807247
## [175] 178.800845 179.849581 180.870658 181.864091 182.857472 183.850767
## [181] 184.871591 185.864788 186.940682 187.988928 188.926761 189.919715
## [187] 190.912624 191.933040 192.958914 193.979209 194.993920 195.986539
## [193] 196.979094 197.999138 199.046703 199.956376 200.948676 202.051193
## [199] 203.043390 204.063084 205.110275 206.129850 207.121809 208.113705
## [205] 209.105549 210.124883 211.171684 212.190892 213.182521 214.174069
## [211] 215.193090 216.239602 217.258511 218.249821 219.241079 220.232275
## [217] 221.250942 222.297080 223.315627 224.306585 225.297485 226.315856
## [223] 227.361683 228.379918 229.370579 230.361183 231.351736 232.369750
## [229] 233.415209 234.433086 235.423388 236.413639 237.431345 238.476492
## [235] 239.494076 240.484094 241.474049 242.491446 243.536281 244.553561
## [241] 245.543283 246.532947 247.550041 248.594560 249.611535 250.600960
## [247] 251.590329 252.607132 253.651339 254.667986 255.657127 256.646217
## [253] 257.662702 258.706608 259.722977 260.711816 261.700598 262.716783
## [259] 263.760366 264.776423 265.764971 266.753469 267.769353 268.812631
## [265] 269.828402 270.816643 271.804828 272.820413 273.863379 274.878841
## [271] 275.866786 276.854675 277.869961 278.912621 279.927780 280.915440
## [277] 281.930467 282.972883 283.987808 284.975218 285.962571 286.977304
## [283] 288.019403 289.034013 290.021138 291.008206 292.022636 293.064417
## [289] 294.078723 295.065552 296.079735 297.121278 298.135343 299.121932
## [295] 300.135870 301.177153 302.190974 303.177330 304.163629 305.177264
## [301] 306.218241 307.231756 308.217816 309.231214 310.271935 311.285194
## [307] 312.271020
## 
## $N2
##   [1]  1.152413e-03  1.545996e-04  8.002106e-05  1.084164e-04  1.405810e-04
##   [6]  2.040281e-04  5.772884e-04  1.518519e-03  3.420417e-03  6.996098e-04
##  [11]  1.400733e-03  7.563427e-04  7.026192e-04  7.425275e-04  1.106449e-03
##  [16]  8.109130e-04  3.343095e-04  7.058369e-04  4.650545e-04  3.378007e-04
##  [21]  2.834266e-04  3.034771e-04  4.867961e-04  2.592112e-04  2.849709e-04
##  [26]  1.502628e-04  1.054258e-04  3.027892e-04  3.362076e-04  3.301313e-04
##  [31]  2.099276e-04  1.173023e-04  2.925009e-04  3.471848e-04  4.289311e-05
##  [36]  1.283683e-04  1.440935e-04  2.586799e-04  1.904492e-04  1.267772e-04
##  [41]  2.240154e-05  1.178814e-04  1.837408e-04  5.396653e-05  2.852461e-04
##  [46]  3.075450e-05  5.003468e-05  7.937587e-05  1.266602e-04 -4.017535e-05
##  [51]  3.378911e-04  1.137449e-04  4.017250e-05  3.801866e-05  2.650265e-05
##  [56]  1.338346e-04  6.086069e-05  3.427962e-05  1.459641e-04 -5.634960e-06
##  [61]  1.226617e-04  9.550229e-05 -2.119041e-05  4.731780e-05  6.457983e-05
##  [66]  6.847518e-05  4.678998e-05  1.734955e-04  7.056836e-05  3.804214e-05
##  [71]  5.137215e-05 -1.778087e-05  3.316781e-05  2.663931e-05  1.977589e-06
##  [76]  3.141766e-05  9.590101e-06  1.814667e-05  2.859317e-05  2.286606e-05
##  [81]  9.139886e-05  2.702626e-05  5.151791e-05  5.596463e-05  5.145222e-05
##  [86]  1.721234e-05  4.762062e-05  1.913869e-04  2.021489e-04  4.860241e-05
##  [91]  1.123934e-04  4.064339e-05  1.233602e-04 -3.107831e-05  1.197100e-04
##  [96]  6.361557e-05  3.045383e-05  2.623883e-04  1.349443e-04  3.128714e-04
## [101]  1.846701e-04  8.914369e-05  2.540991e-04  3.012905e-04  1.585901e-04
## [106]  3.591963e-05  1.150270e-04  2.322460e-04  9.762948e-05 -2.216894e-05
## [111]  6.377301e-05  5.170616e-05  5.685285e-05  1.023834e-04  7.574755e-05
## [116]  3.361654e-05  5.294994e-05  7.266359e-05  5.234276e-06  8.500221e-06
## [121]  1.194127e-04  8.770265e-08  2.072462e-05  6.529153e-05  7.394081e-05
## [126]  2.495482e-05  4.142314e-06  4.931423e-05  1.070793e-07  1.125083e-05
## [131]  3.015902e-05 -1.035876e-05  6.683418e-05 -2.889024e-05 -1.358835e-05
## [136]  1.354464e-04  2.604080e-04  1.604834e-04 -1.270659e-06  9.482132e-05
## [141]  1.880709e-04  1.654604e-04  7.579091e-05  5.954950e-05  6.558925e-05
## [146]  3.716286e-05  4.404088e-05 -1.748788e-05  6.887891e-05  3.558139e-06
## [151]  5.095847e-05  2.112078e-04  1.040656e-05  1.017777e-04  4.418894e-05
## [156]  2.867139e-05  4.152808e-05  3.631607e-05  6.304717e-05  4.581042e-05
## [161]  1.839024e-06  1.399309e-05  4.420915e-05  7.073966e-05  1.199448e-04
## [166]  1.019058e-07  1.019292e-07  1.019561e-07  1.331548e-05  9.912824e-06
## [171]  4.718795e-05 -5.515766e-05  4.570655e-05  1.213569e-04  2.724078e-05
## [176]  3.033991e-05 -1.055430e-06  1.513657e-04  1.637252e-04 -1.772039e-05
## [181]  6.647720e-05  3.573097e-05  6.441561e-05  6.717629e-05  4.343304e-06
## [186]  6.782423e-05  3.712817e-05  1.039569e-05  7.476946e-05  1.178417e-05
## [191]  8.872996e-05 -1.796060e-06 -2.286815e-05  6.105843e-05  3.701809e-05
## [196]  5.369048e-05  2.588709e-05  5.505122e-05  1.166814e-04  3.385015e-05
## [201]  3.037886e-05  5.596694e-05  1.559213e-05  9.382381e-05  6.311931e-05
## [206]  2.460747e-05  5.086222e-05  1.348904e-04 -5.935615e-05  5.600270e-05
## [211]  5.570682e-05  2.871702e-05  1.538683e-05  1.970205e-04  1.559891e-05
## [216]  4.246544e-05 -5.272936e-05 -1.451916e-05  1.735715e-05  4.629018e-05
## [221]  1.363805e-04 -4.786258e-05  2.445610e-05  8.615932e-05  3.455765e-05
## [226] -1.068034e-04  3.561538e-05  4.421160e-05  7.390285e-06  1.509860e-05
## [231] -6.629491e-06  8.391303e-05 -6.878782e-06 -5.466651e-06  5.299532e-05
## [236]  4.568435e-05  1.919234e-05  1.225764e-05 -1.406187e-05  2.023838e-05
## [241]  5.062118e-05 -2.109737e-05 -1.917528e-05  6.126431e-05  1.579654e-07
## [246]  1.724199e-05  5.188367e-05  2.316010e-05 -7.103988e-06 -7.731395e-06
## [251]  8.543743e-05 -1.115389e-05 -3.123606e-06  6.490252e-05 -6.406484e-05
## [256]  1.378482e-07  1.378813e-07  5.883716e-05  6.037991e-05 -2.922283e-05
## [261]  1.971341e-05  3.068371e-05 -6.510038e-05  1.381743e-07  5.178980e-05
## [266]  2.748013e-05  1.025422e-05  4.234075e-05 -1.251308e-05 -5.240988e-05
## [271] -3.282366e-05  5.684404e-05  5.390844e-06  3.906290e-05  1.736306e-05
## [276]  1.393680e-07 -8.574042e-06  1.670488e-06  2.022620e-05  5.105055e-05
## [281]  3.658880e-06 -3.944934e-06  1.117721e-05 -1.395411e-05  1.800860e-06
## [286] -4.934942e-06  1.089846e-05 -7.993438e-08 -1.461824e-05  5.061710e-06
## [291]  1.809105e-05  3.697454e-05 -3.433572e-05  3.947231e-05  3.304209e-05
## [296] -4.894571e-06 -5.401010e-05  7.874818e-05  7.412115e-06  3.458194e-05
## [301]  3.086230e-05 -4.543504e-05  1.497036e-05 -1.619583e-05  1.275642e-07
## [306]  1.275997e-07  6.554399e-06 -4.017360e-05  5.395757e-05  1.294546e-06
## [311]  8.205590e-08  1.849333e-05 -8.126931e-06  2.928631e-05  4.323313e-05
## [316] -3.435998e-05  2.330767e-05  5.445768e-05 -2.573724e-05 -7.886227e-05
## [321]  6.112410e-05  1.100685e-05  1.021629e-06 -6.274710e-05  1.810120e-05
## [326]  7.202129e-05 -1.711819e-05  1.737822e-05 -2.765109e-05  2.648571e-05
## [331]  1.523344e-06  2.026640e-05 -4.792026e-06  1.799089e-05  1.630369e-05
## [336] -1.838681e-05  9.768685e-06 -5.312574e-05  1.108560e-04  4.533291e-06
## [341] -2.360987e-05 -8.309439e-06 -1.966836e-05  1.303673e-07  1.888989e-05
## [346]  1.304149e-07  1.317440e-07  1.739987e-05 -1.622194e-05  1.350269e-07
## [351] -4.303556e-05 -3.440249e-05  1.350809e-07  1.351172e-07  1.351530e-07
## [356]  3.467912e-05 -3.137524e-06  6.886861e-05 -8.623871e-05  5.741893e-05
## [361]  1.343291e-06  1.354413e-07 -7.228504e-06  5.880454e-05  2.359226e-05
## [366] -3.442819e-05  1.354921e-07 -1.787574e-05  5.089737e-05 -8.506993e-06
## [371]  8.778633e-06 -7.902467e-05  2.225784e-05  2.690057e-06  1.355778e-07
## [376]  1.893743e-05  6.960386e-05 -4.309924e-05  5.095522e-05 -2.719844e-06
## [381]  7.165261e-06 -4.275605e-05 -2.527088e-05  1.366416e-07  1.366764e-07
## [386]  1.367124e-07  1.367489e-07  1.743639e-05  6.933913e-05  6.570020e-05
## [391] -4.694882e-05 -1.974460e-05 -1.870124e-05 -2.200804e-05 -3.447360e-05
## [396]  4.985761e-05  2.020487e-06  1.708504e-05  1.219848e-07  1.220210e-07
## [401]  1.220577e-07 -1.422189e-05  2.725008e-05 -1.722451e-05  2.738620e-05
## [406]  1.218920e-07  1.219282e-07  1.219649e-07  1.220010e-07  5.103802e-05
## [411] -1.516346e-05  1.219580e-07  3.476936e-05  1.653496e-05  1.220933e-07
## [416]  1.221295e-07  1.221657e-07  1.222024e-07  1.222386e-07 -9.820350e-07
## [421] -9.191355e-05  1.745392e-05  1.225152e-07  2.996527e-05 -1.330025e-05
## [426]  1.008834e-05  2.517000e-05  1.490459e-05 -1.244487e-05  2.385035e-05
## [431] -3.388518e-05  2.613220e-05  1.316594e-05  1.703005e-05 -2.766571e-05
## [436]  3.480672e-05  1.619470e-05 -1.718733e-05  4.870712e-06 -2.263441e-05
## [441] -9.928747e-07  1.241663e-07  1.242028e-07  9.584022e-06  1.011028e-05
## [446] -1.879838e-05  1.243495e-07  1.243860e-07  1.244224e-07  1.244594e-07
## [451]  6.954372e-05 -3.604830e-05  6.918548e-05 -1.986308e-05 -7.377974e-05
## [456]  1.148852e-05 -1.986826e-05 -8.222294e-07  1.054401e-05 -9.874111e-06
## [461] -9.874951e-06  1.250724e-07  1.657616e-05  1.251533e-07 -1.632759e-05
## [466]  1.252195e-07  6.960109e-05  8.353101e-06  4.126582e-05 -4.330322e-05
## [471] -4.254234e-05 -4.615792e-06  1.255931e-07  1.340329e-05 -2.263844e-05
## [476]  1.257228e-07 -4.979578e-06  4.262485e-05 -3.463270e-05  1.005633e-04
## [481]  1.494551e-05  1.260802e-07  1.261168e-07  1.261539e-07 -3.692968e-05
## [486] -3.693266e-05  1.262166e-07 -2.140753e-06 -1.911843e-05 -9.898508e-06
## [491]  6.253699e-05 -3.631247e-05  5.966571e-05 -1.983907e-05 -1.286293e-05
## [496]  5.230978e-05 -3.009856e-05  2.902785e-05 -1.108495e-05  3.426988e-05
## [501] -6.485126e-05 -3.140573e-05  1.885885e-05 -7.103534e-06  1.173790e-05
## [506] -8.436558e-06  1.229067e-07  1.229435e-07  1.229807e-07  1.230175e-07
## [511]  1.230543e-07  1.230916e-07  1.231283e-07  1.496815e-05 -1.472231e-05
## [516]  1.753558e-05 -1.637361e-05  3.311867e-05 -2.544870e-05  9.484029e-07
## [521]  6.351577e-05 -1.835217e-05 -7.042241e-05  1.086614e-04
## 
## $p_mid
##   [1]   2.902020   3.905726   5.020898   6.024491   6.916532   7.920017
##   [7]   9.007056  10.094025  11.236676  12.156313  13.159487  14.151475
##  [13]  15.098819  16.168702  17.171653  18.174553  19.177397  20.247036
##  [19]  21.249749  22.166996  23.225313  24.246428  25.221072  26.279191
##  [25]  27.309416  28.289453  29.208188  30.260505  31.457507  32.431758
##  [31]  33.322450  34.324424  35.326342  36.305924  37.307711  38.331730
##  [37]  39.361247  40.418519  41.447901  42.477221  43.478667  44.452234
##  [43]  45.453572  46.427039  47.511695  48.540672  49.458345  50.431578
##  [49]  51.488149  52.628109  53.628993  54.640904  55.641663  56.575644
##  [55]  57.509580  58.510163  59.577386  60.644541  61.644947  62.578605
##  [61]  63.606682  64.662484  65.690450  66.690573  67.690616  68.690607
##  [67]  69.668327  70.668210  71.690264  72.690039  73.689752  74.717169
##  [73]  75.772292  76.799593  77.799074  78.798491  79.797841  80.797151
##  [79]  81.796403  82.795582  83.794716  84.858541  85.857560  87.013749
##  [85]  88.068143  88.900489  89.899264  90.842509  91.896644  92.950734
##  [91]  93.921537  94.975512  95.979482  96.977838  97.998351  98.996610
##  [97]  99.994805 100.992938 101.991026 103.016772 104.070177 105.095804
## [103] 106.093647 107.091439 108.089169 109.086853 110.084486 111.082028
## [109] 112.107219 113.160075 114.185163 115.182489 116.113273 117.110479
## [115] 118.174114 119.171207 120.195937 121.248296 122.272903 123.380500
## [121] 124.377275 125.263272 126.259984 127.256616 128.253174 129.249687
## [127] 130.356852 131.408593 132.349569 133.345843 134.342060 135.338220
## [133] 136.361990 137.413369 138.437004 139.432914 140.428796 141.424615
## [139] 142.420366 143.416059 144.356386 145.434920 146.541050 147.508853
## [145] 148.504257 149.499593 150.494871 151.407174 152.457621 153.590946
## [151] 154.585997 155.580975 156.575907 157.570781 158.593227 159.643248
## [157] 160.665569 161.660205 162.654796 163.649324 164.643784 165.665805
## [163] 166.715402 167.737307 168.842000 169.836169 170.719811 171.713867
## [169] 172.735471 173.806714 174.828207 175.799943 176.793697 177.787401
## [175] 178.808645 179.857427 180.878549 181.872024 182.865449 183.858788
## [181] 184.879656 186.038430 187.059197 187.941954 188.935003 190.038318
## [187] 191.031270 191.941413 192.989391 194.031789 195.024486 195.995089
## [193] 196.987688 198.007776 199.055387 200.075366 201.067710 202.126163
## [199] 203.118404 204.071987 205.119224 206.138843 207.296171 208.266066
## [205] 209.092628 210.134050 211.180897 212.172602 213.219358 214.238498
## [211] 215.202479 216.193959 217.240447 218.305237 219.269005 220.241884
## [217] 221.260595 222.306779 223.325371 224.316371 225.307314 226.325730
## [223] 227.371602 228.389882 229.380587 230.371234 231.361830 232.379889
## [229] 233.425393 234.443314 235.433660 236.423954 237.441704 238.486897
## [235] 239.422023 240.439585 241.512085 242.502026 243.546907 244.564231
## [241] 245.553996 246.543704 247.560843 248.605406 249.622426 250.611895
## [247] 251.601307 252.618154 253.662406 254.679098 255.668282 256.657415
## [253] 257.673945 258.717896 259.734309 260.723192 261.712017 262.728246
## [259] 263.771875 264.787976 265.776568 266.765108 267.781037 268.824360
## [265] 269.840175 270.828460 271.816688 272.832317 273.875328 274.890835
## [271] 275.878824 276.866755 277.882086 278.924791 279.939994 280.927698
## [277] 281.942769 282.985230 284.000200 284.987653 285.975049 286.989826
## [283] 288.031971 289.019205 290.088631 291.103163 292.035379 293.077206
## [289] 294.091556 295.078428 296.092655 297.134244 298.148352 299.134985
## [295] 300.148967 301.190296 302.204161 303.190560 304.176902 305.190581
## [301] 306.231603 307.245163 308.231266 309.244708 310.285475 311.298778
## [307] 312.284647 313.270465 314.283598 315.324059 316.337068 317.322647
## [313] 318.335534 319.375723 320.388495 321.373840 322.386489 323.426445
## [319] 324.438967 325.424072 326.436465 327.476160 328.488455 329.473316
## [325] 330.485474 331.524925 332.536967 333.521588 334.533498 335.682085
## [331] 336.693879 337.568888 338.580558 339.619511 340.631045 341.615183
## [337] 342.626631 343.665345 344.676646 345.660561 346.671746 347.710194
## [343] 348.721258 349.704928 350.715864 351.754068 352.764881 353.748317
## [349] 354.759027 355.796987 356.807548 357.790734 358.801188 359.838888
## [355] 360.849209 361.832178 362.842395 363.879840 364.889921 365.899940
## [361] 366.937197 367.947102 368.929632 369.939389 370.976413 371.986091
## [367] 372.968398 373.977932 375.014684 376.024096 377.006175 378.015462
## [373] 379.051964 380.061134 381.070235 382.106556 383.115531 384.097160
## [379] 385.106032 386.142115 387.150851 388.159533 389.195411 390.203964
## [385] 391.185205 392.193637 393.229255 394.237567 395.218569 396.226759
## [391] 397.262127 398.270203 399.278207 400.313377 401.321264 402.301844
## [397] 403.309602 404.344533 405.352177 406.359753 407.394485 408.401942
## [403] 409.409330 410.443875 411.451150 412.431125 413.438263 414.472581
## [409] 415.479605 416.486560 417.520674 418.527512 419.507076 420.513794
## [415] 421.547658 422.554254 423.560788 424.594459 425.600865 426.607203
## [421] 427.640687 428.646918 429.625883 430.631986 431.665220 432.671197
## [427] 433.677109 434.710150 435.715948 436.721680 437.754534 438.760147
## [433] 439.765693 440.798337 441.803750 442.781957 443.787268 444.819679
## [439] 445.824865 446.829984 447.862202 448.867200 449.872127 450.904152
## [445] 451.908966 452.913712 453.945550 454.950191 455.954766 456.986400
## [451] 457.990826 458.995204 460.026667 461.030926 462.035122 463.066392
## [457] 464.070463 465.074466 466.105549 467.109442 468.086131 469.089897
## [463] 470.120735 471.124371 472.127943 473.158588 474.162042 475.165426
## [469] 476.195878 477.199155 478.202362 479.232615 480.235700 481.238729
## [475] 482.268795 483.271698 484.274549 485.304422 486.307122 487.309774
## [481] 488.339471 489.342000 490.344463 491.373955 492.403396 493.432774
## [487] 494.434993 495.437147 496.466327 497.468369 498.470339 499.499326
## [493] 500.501177 501.502956 502.531756 503.533427 504.462844 505.491444
## [499] 506.630055 507.550293 508.540827 509.623305 510.570413 511.733945
## [505] 512.789187 513.681980 514.682946 515.683871 516.711778 517.712578
## [511] 518.713319 519.741039 520.741653 521.742198 522.769725 523.770158
## [517] 524.770524 525.797863 526.825155 527.852358 528.825428 529.852507
## [523] 530.924571 531.897485
## 
## $N2
##   [1]  1.812136e-03  1.044914e-03  3.810467e-03  1.753316e-03  4.388039e-04
##   [6]  7.401951e-04  1.148707e-03  1.338073e-03  7.961124e-04  2.846668e-04
##  [11]  1.444173e-04  4.900892e-05  5.655009e-05  6.622236e-05  5.615047e-05
##  [16]  8.023895e-05  2.842324e-04  1.683347e-04  2.292443e-04  9.889881e-05
##  [21]  7.152568e-04  1.572842e-04  6.437814e-05  6.437908e-05  4.860501e-05
##  [26]  3.893889e-05  1.959140e-05  3.399953e-05  3.388987e-05  2.908956e-05
##  [31]  1.214734e-05  4.116366e-05 -1.447093e-05 -3.022032e-05  1.274933e-06
##  [36]  2.789684e-05  5.233195e-05  6.137729e-06 -1.600941e-08  2.053528e-05
##  [41]  2.781419e-05  6.772218e-05  1.427387e-04  2.515674e-04  2.420953e-04
##  [46]  7.739262e-05 -3.034728e-05  1.599202e-04  1.451854e-04  2.856749e-04
##  [51]  8.995939e-05  1.073657e-04  2.268023e-04  2.418079e-04  8.928625e-05
##  [56]  5.219995e-05  1.168654e-04  9.726885e-06  5.830149e-05 -9.574815e-06
##  [61] -6.323209e-06  7.818542e-05 -3.548178e-05  5.855722e-06  9.443276e-05
##  [66]  1.388246e-04  2.551931e-04  2.829684e-04  3.840357e-05  3.731057e-04
##  [71]  3.233026e-04  3.070798e-04  3.955714e-04  4.592518e-04  1.819118e-04
##  [76]  1.827696e-04  2.119137e-04  6.625060e-05 -4.251898e-05  3.419994e-05
##  [81] -7.364516e-06  6.417909e-06  6.393405e-05  8.218686e-05  5.247942e-06
##  [86]  2.402027e-07  8.344249e-05  7.082958e-05  3.029804e-04  6.328117e-05
##  [91]  2.238634e-04  7.103157e-05  8.067963e-05  2.877230e-05  7.707511e-05
##  [96] -1.499743e-05  1.092605e-04  1.489362e-04  1.112131e-04  3.471135e-07
## [101]  6.288639e-05  2.263769e-04  1.741243e-04  1.739371e-04  3.858773e-05
## [106]  7.013924e-05  3.253350e-04  4.568610e-04  1.814377e-04  3.356682e-04
## [111]  2.327041e-05  7.981420e-05  2.768488e-04  1.551538e-04  2.363287e-04
## [116]  3.556173e-05  6.290323e-05  5.347946e-05  1.242539e-04  1.725957e-04
## [121]  3.108978e-05 -5.150877e-05  9.570496e-06  4.571500e-05  3.024905e-05
## [126]  2.876147e-05 -2.684651e-05  4.918425e-05  1.904713e-05 -5.411393e-05
## [131]  1.086349e-07  1.086616e-07  1.086891e-07  1.641446e-05  1.732205e-05
## [136]  5.174859e-05 -1.016161e-05 -2.831819e-05  1.088083e-07  9.586062e-06
## [141]  2.704613e-05  1.088560e-07  1.906746e-05  2.854827e-05  9.589232e-06
## [146]  2.855250e-05 -9.373406e-06  9.087280e-06  1.032579e-07  1.032856e-07
## [151] -2.312609e-05  1.312782e-04  7.685874e-05 -8.494169e-06  5.766820e-05
## [156]  5.357302e-05 -1.713666e-05  1.823479e-06  5.526624e-05 -5.937085e-06
## [161] -1.198026e-05  7.538656e-05  1.216815e-05 -2.319444e-05  3.026304e-05
## [166]  3.197861e-05  3.803101e-05  2.855068e-05  2.435937e-05 -3.812808e-05
## [171]  3.026190e-05  1.113397e-04  1.556879e-05 -5.109644e-06  2.166859e-05
## [176]  3.245209e-05  1.044378e-05 -3.356766e-05 -8.527082e-06  2.078708e-05
## [181]  3.353088e-05  2.630920e-06 -3.614066e-05  2.686375e-05 -9.385141e-06
## [186]  1.908675e-05  9.596690e-06  5.500904e-06  1.269585e-05  3.807995e-05
## [191]  1.909349e-05 -1.888370e-05  1.053272e-07  6.740436e-06  6.881138e-05
## [196] -1.717423e-05 -8.371916e-05  3.210175e-05  9.629493e-06 -1.796056e-05
## [201]  2.803646e-05  4.764394e-05 -8.540980e-05  1.282931e-07  4.075739e-05
## [206]  7.661407e-05 -3.050056e-05 -1.111119e-05 -1.603115e-06  7.102533e-05
## [211]  1.421530e-05 -2.951903e-05  3.473474e-05  2.780698e-05
## 
## $p_mid
##   [1]   3.013749   4.017524   5.021243   6.024905   7.028509   8.032063
##   [7]   9.063423  10.122587  11.153831  12.157146  13.160394  14.163590
##  [13]  15.166729  16.169812  17.172832  18.175801  19.178713  20.181563
##  [19]  21.184344  22.187086  23.189770  24.192387  25.222803  26.280995
##  [25]  27.311291  28.313675  29.315997  30.318267  31.320481  32.322638
##  [31]  33.324737  34.326781  35.328767  36.330679  37.332535  38.334362
##  [37]  39.363949  40.421293  41.450746  42.452318  43.453833  44.455286
##  [43]  45.456693  46.458037  47.459330  48.460566  49.461740  50.462846
##  [49]  51.491684  52.548304  53.577062  54.577936  55.578763  56.579528
##  [55]  57.580236  58.580887  59.498100  60.609789  61.693640  62.582901
##  [61]  63.611049  64.666923  65.694960  66.695151  67.695263  68.695323
##  [67]  69.695332  70.695284  71.695185  72.695030  73.694811  74.722298
##  [73]  75.777494  76.804866  77.804415  78.803901  79.803319  80.802697
##  [79]  81.802019  82.801266  83.800468  84.827363  85.881949  86.908722
##  [85]  87.907691  88.906592  89.905436  90.904229  91.902959  92.901638
##  [91]  93.927985  94.982033  96.008261  97.006684  98.005079  99.003406
##  [97] 100.001670 100.999872 101.998028 103.023848 104.077325 105.103019
## [103] 106.100931 107.098792 108.096590 109.094342 110.092044 111.089654
## [109] 112.114916 113.167845 114.193002 115.190397 116.187734 117.185009
## [115] 118.182228 119.179389 120.204190 121.256620 122.281298 123.278215
## [121] 124.275058 125.271872 126.268652 127.265353 128.261980 129.286243
## [127] 130.338125 131.362256 132.358656 133.354998 134.351284 135.347513
## [133] 136.371352 137.422804 138.446509 139.442488 140.438438 141.434325
## [139] 142.430144 143.425907 144.449267 145.500221 146.523457 147.518981
## [145] 148.514453 149.509858 150.505205 151.528150 152.578669 153.601492
## [151] 154.596611 155.591657 156.586658 157.581601 158.604116 159.654210
## [157] 160.676601 161.671306 162.665965 163.660561 164.655089 165.677181
## [163] 166.726850 167.748825 168.743120 169.737358 170.731533 171.725658
## [169] 172.747332 173.796560 174.818123 175.812014 176.805837 177.799609
## [175] 178.820923 179.869777 180.890969 181.884513 182.878006 183.871413
## [181] 184.892351 185.940843 186.961680 187.954859 188.947977 189.941043
## [187] 190.934063 191.954594 193.002644 194.023053 195.015818 196.008548
## [193] 197.001215 198.021374 199.069056 200.089105 201.081517 202.073883
## [199] 203.066192 204.086001 205.133309 206.152999 207.145069 208.137076
## [205] 209.129032 210.148481 211.195399 212.214722 213.206462 214.198122
## [211] 215.217257 216.263886 217.282910 218.274331
## Warning in gsw_Nsquared(binSA_2, binCT_2, binp_2, Lat): gsw_Nsquared() has some NA inputs ... these are not handled well
## $N2
##   [1]  4.537300e-04  1.177423e-04  7.721338e-05  3.815460e-05  7.064797e-06
##   [6]  6.042236e-05 -3.607553e-06  1.686734e-04  2.209594e-04  4.586367e-04
##  [11]  3.611103e-04  3.617711e-04  1.384729e-04  1.188175e-04  2.299114e-04
##  [16]  4.073846e-04  8.445761e-04  8.929600e-04  4.676629e-04  6.464207e-04
##  [21]  1.046567e-03  5.306033e-04  6.817718e-04  1.245348e-04  3.657223e-04
##  [26]  3.727874e-04  5.926098e-04 -2.465539e-04           NaN           NaN
##  [31] -8.941410e-04  3.091719e-05  1.850229e-04 -7.375141e-05 -5.395584e-04
##  [36]  4.610580e-04  3.969787e-05  8.318590e-04 -1.568670e-04  3.131431e-04
##  [41] -1.707969e-05 -9.949932e-05  1.236732e-05 -1.868387e-04           NaN
##  [46]           NaN -2.744072e-03  8.884489e-03  9.908486e-05  1.023017e-04
##  [51]  5.060179e-04  1.957339e-05  1.526648e-05           NaN           NaN
##  [56]           NaN           NaN           NaN  2.807302e-04  5.743312e-05
##  [61] -1.555766e-04  5.035681e-05  1.442954e-04  1.772838e-04 -1.605137e-05
##  [66]  1.091469e-04 -7.365382e-05  1.421652e-03 -1.194342e-03  2.446532e-05
##  [71]  5.121555e-06  1.943020e-05 -6.093720e-05  3.403830e-05  1.496162e-04
##  [76] -6.837152e-06  1.753487e-05  1.282437e-04 -9.044170e-05  3.957323e-04
##  [81] -1.613903e-04 -1.221068e-04  7.553390e-05 -1.076604e-04  9.639565e-05
##  [86]  1.152604e-04  7.411662e-05 -1.207399e-05  6.116836e-05  1.008076e-05
##  [91] -9.096142e-06  7.781778e-05 -3.533972e-05  2.180130e-05  6.140430e-05
##  [96]  6.724401e-05 -3.645303e-05 -4.509563e-05 -2.749045e-05  1.709873e-04
## [101]  3.604688e-05 -3.562359e-06  5.626396e-05 -2.567316e-05  9.635963e-05
## [106]  3.631760e-05  6.076148e-05  1.573359e-05 -2.579937e-05 -7.000960e-06
## [111]  1.023844e-04  8.523030e-05 -3.070399e-05  6.847447e-05 -3.112967e-05
## [116]  6.252474e-05  1.976153e-05  4.482822e-05 -2.296637e-06  4.944410e-05
## [121]  3.476156e-05 -1.425408e-05  9.812682e-05  5.500909e-05 -2.937621e-05
## [126]  8.843376e-05 -2.540017e-05  1.836483e-04 -7.887430e-05  7.492110e-05
## [131] -1.615191e-05 -7.528317e-06  1.547259e-04  5.096542e-05  4.481267e-05
## [136] -1.939730e-05  5.497565e-06  3.637596e-06  1.036471e-05 -2.809395e-05
## [141]  5.127043e-05  7.256063e-05 -2.044296e-05  5.141390e-06  4.076365e-05
## [146]  1.467918e-05  4.127616e-05 -1.677285e-06 -4.381332e-06  2.594001e-05
## [151]  2.686805e-05  1.031694e-07 -1.134398e-05  3.454031e-05  1.696922e-05
## [156]  5.709268e-06  5.357269e-05 -1.502195e-05 -1.881734e-05  1.122141e-04
## [161] -5.545563e-06  3.765107e-06  2.006837e-05 -3.811859e-05  8.428941e-05
## [166]  2.577169e-05  6.385609e-05  2.869303e-05 -8.345879e-06  2.295457e-05
## [171]  3.643183e-05 -2.905977e-05 -3.827350e-05  6.135407e-05  4.368307e-06
## [176] -2.459843e-05  3.153509e-05 -6.359527e-06  1.936124e-05  2.850123e-05
## [181]  2.194180e-05 -3.516521e-05  1.201786e-04 -2.880085e-05  7.541736e-05
## [186] -4.960835e-05  5.751399e-05  4.177997e-05 -4.380085e-05  2.963620e-06
## [191]  2.691387e-06  1.522382e-05  9.060906e-05  2.650921e-05 -1.084030e-05
## [196]  3.880067e-05 -4.624313e-05  3.667909e-05 -3.824837e-05  1.029696e-04
## [201] -4.033172e-05 -1.919204e-05  4.525717e-05  8.987011e-05 -8.188097e-06
## [206]  3.646505e-05  2.475912e-05  4.332865e-05 -3.483450e-05  7.674753e-05
## [211] -1.879973e-05  5.539011e-06  1.374100e-05  3.422647e-05  5.298535e-05
## [216] -3.939066e-05  1.178791e-05  5.270294e-05  8.076211e-06 -3.979338e-05
## [221]  5.933780e-05  4.391678e-05  2.604293e-05 -1.929425e-05 -1.407835e-05
## [226]  2.145108e-05 -5.075500e-05 -2.479636e-07  3.959724e-05  2.188987e-05
## [231]  1.619382e-07  4.114294e-05  1.360926e-05 -1.357509e-05  6.525753e-05
## [236] -7.668132e-06  3.406596e-05 -2.206564e-05  2.320428e-05  1.539289e-05
## [241]  2.044561e-05 -1.009482e-05  3.220393e-07  7.961488e-06 -1.553836e-05
## [246]  2.536721e-05 -2.178856e-05 -4.670354e-06  3.102663e-05 -3.043106e-05
## [251]  1.256720e-05 -1.920866e-05  5.245028e-05 -4.053798e-05  8.563527e-05
## [256] -2.738963e-05  5.486532e-05 -5.064477e-05  2.553102e-05  2.225489e-05
## [261]  7.502187e-06  7.490636e-06 -4.132506e-05  4.033754e-05  1.103045e-05
## [266]  1.478276e-05 -1.962424e-05  6.498046e-05 -3.241961e-05  5.285645e-05
## [271] -4.845824e-06 -2.454488e-05  3.528633e-05  2.972891e-05 -6.766760e-05
## [276]  7.997675e-05  1.520967e-05 -3.091066e-05 -1.800639e-05  3.110990e-05
## [281]  2.439713e-06 -3.723192e-05  8.858891e-05 -1.477636e-05  2.721924e-05
## [286]  1.988282e-05 -1.495607e-05 -1.759738e-05 -3.747532e-05  3.985732e-05
## [291]  3.565717e-05  5.041878e-05 -3.936256e-05 -1.100378e-05  4.051314e-05
## [296]  4.841337e-06 -6.885927e-05  3.328612e-05  3.295569e-05 -1.384984e-05
## [301]  8.942480e-06  6.131471e-05 -3.850919e-05  1.525756e-05  1.761838e-05
## [306] -2.955183e-05  4.883434e-05 -3.213167e-05 -3.623220e-06 -5.498855e-06
## [311]  1.270821e-07  8.738546e-06 -2.772746e-05 -1.553890e-07  1.272778e-07
## [316]  5.913032e-05 -4.335539e-05  5.219459e-05 -5.043065e-06  2.273795e-06
## [321] -1.236403e-05 -1.677085e-05  1.690186e-05  1.429683e-05  7.870792e-05
## [326] -2.993282e-05 -1.369040e-05 -6.379557e-06 -2.813569e-06 -7.560494e-06
## [331] -1.971355e-05  5.183906e-05 -1.768047e-05  5.951449e-05 -1.972256e-05
## [336] -9.796821e-06  3.398559e-05 -6.095008e-05  6.230470e-05 -8.247132e-05
## [341]  2.034579e-05 -1.591759e-05  3.592865e-05 -9.798899e-06  5.630803e-05
## [346]  8.759514e-05 -1.025949e-04  1.946708e-05 -1.013514e-05  3.760898e-05
## [351]  1.213827e-05  2.942669e-06 -7.873188e-05  5.906219e-05  1.007581e-05
## [356]  1.475249e-05  6.404881e-05 -3.388163e-06  2.770031e-06 -5.096400e-05
## [361]  3.045019e-05  3.800510e-05 -8.679522e-05  4.467087e-05  3.616665e-05
## [366]  4.862523e-05 -1.247898e-05 -7.465565e-07 -5.875082e-05 -9.828146e-06
## [371] -2.975244e-05  1.159956e-04  2.383895e-05 -6.893657e-05 -8.045995e-06
## [376]  1.337446e-07  1.337815e-07  4.142979e-05 -2.974365e-05  3.261366e-05
## [381]  1.327509e-07  2.657274e-05  8.317625e-06  2.404268e-05 -9.194848e-06
## [386] -2.757646e-05  2.092221e-05  1.334175e-07  1.544493e-05  3.408343e-06
## [391]  1.323414e-05  1.741912e-05  1.335332e-07  1.335707e-07  1.336076e-07
## [396]  1.336433e-07  1.328991e-07  1.249455e-07  1.226462e-07  1.226832e-07
## [401]  5.746715e-05 -6.113381e-05  1.202896e-05 -1.007379e-05  1.473348e-05
## [406]  5.932226e-05 -3.268191e-05  1.792269e-06  1.124227e-05  2.854166e-05
## [411]  1.215321e-05 -3.560048e-05 -1.831953e-05  1.487806e-05 -1.463110e-05
## [416]  1.238599e-07  4.832413e-05  1.932153e-05  1.012743e-05 -3.636179e-06
## [421] -5.592871e-06  6.641011e-05 -5.804084e-05 -2.028711e-05  1.645139e-05
## [426]  3.716318e-05 -1.144204e-05 -1.707470e-05  5.399480e-05 -9.465736e-06
## [431] -1.948972e-05  6.705135e-07  1.944809e-05 -1.126241e-05  3.017535e-05
## [436]  4.019387e-05 -1.683803e-05  4.398426e-05 -8.055674e-05  1.252083e-07
## [441] -2.144003e-05  4.939059e-05  3.108605e-06  7.582369e-06 -7.176830e-06
## [446]  8.750667e-05 -1.032632e-05 -3.999650e-05  3.093517e-06 -1.842471e-05
## [451] -3.083970e-06  3.917012e-05  4.099721e-05 -5.374470e-05  7.873444e-06
## [456]  1.913720e-05  1.256909e-07 -2.938326e-06  3.946102e-05 -2.094487e-05
## [461] -1.364595e-05 -6.890564e-06  4.498340e-05  1.015969e-05  8.681319e-06
## [466] -1.358310e-05  2.395042e-05 -2.178817e-05 -9.422384e-06 -6.215783e-06
## [471]  3.178970e-05 -2.587251e-05  1.748324e-05 -8.254801e-07  1.405131e-05
## [476] -1.356423e-05  9.297360e-06  4.806028e-05  6.407435e-05 -1.105402e-05
## [481]  8.702793e-06 -6.064691e-05 -1.162958e-05  3.575529e-05  5.845028e-06
## [486]  2.228457e-06  1.662457e-05  1.053141e-05  3.044863e-05 -5.199317e-05
## [491]  4.726184e-05 -3.274415e-05 -5.475267e-05  3.659522e-05 -1.205299e-05
## [496]  2.301199e-05  2.972131e-05  1.176643e-05  1.199549e-05  1.313643e-05
## [501] -2.588329e-05  3.306385e-05  1.364856e-05 -9.576163e-06 -5.099077e-06
## [506] -3.112041e-05  1.233371e-07  2.042880e-05  1.799829e-05  1.295977e-05
## [511] -9.656078e-07 -5.424693e-05  2.027799e-05  2.138961e-05  3.875821e-05
## [516] -2.640072e-05  1.717783e-05 -5.849934e-05  1.857580e-05  4.980438e-05
## [521] -3.516064e-05  3.072155e-05 -2.873624e-05 -4.019411e-05  1.210258e-05
## [526] -7.519159e-06  8.443193e-05 -2.445740e-05 -2.567271e-05  1.228143e-07
## [531]  1.662197e-05  1.296711e-05  4.886248e-05  8.724370e-06 -1.178218e-05
## [536] -2.649762e-06  1.767855e-05 -4.361863e-05 -4.348311e-06  2.030627e-05
## [541] -1.725275e-05  1.447191e-05 -3.335364e-05  3.785638e-05 -1.084295e-06
## [546]  8.385023e-06  3.664608e-05 -1.545882e-05 -1.770314e-05  6.749459e-05
## [551] -3.660096e-05 -1.762574e-05  2.828723e-05  8.729579e-06  1.324719e-05
## [556] -9.078118e-06 -4.111930e-05  3.700539e-05 -2.815362e-05  4.317550e-05
## [561]  1.218252e-07  8.733140e-06  6.109756e-05 -3.191286e-05 -4.271075e-05
## [566]  3.042629e-05  1.216925e-07  1.926399e-05  4.128110e-05  3.553951e-05
## [571]  1.022666e-05 -1.668166e-05  1.692602e-05  1.022909e-05  5.867252e-06
## [576] -2.086782e-05 -5.335195e-05 -5.624865e-06  1.023294e-05 -1.233141e-05
## [581] -1.616459e-05  5.437351e-06 -5.193109e-06  2.268641e-05 -3.276629e-06
## [586]  3.507303e-05 -1.233855e-05  2.216933e-05 -2.192652e-05 -1.094583e-05
## [591]  1.223645e-07  5.590672e-05 -2.254013e-05 -1.447930e-05  2.431674e-05
## [596]  2.313646e-05 -3.135486e-05 -9.825722e-06 -4.856216e-06  3.822070e-05
## [601]  5.258304e-05 -5.160373e-05  6.473030e-06  3.945606e-06 -3.716684e-06
## [606]  3.222808e-05
## 
## $p_mid
##   [1]   3.013751   4.017527   5.021247   6.024909   7.028514   8.032069
##   [7]   9.063430  10.122594  11.153839  12.157155  13.160403  14.163600
##  [13]  15.166740  16.169824  17.172844  18.175814  19.178727  20.181577
##  [19]  21.184359  22.187102  23.189787  24.192404  25.222821  26.281014
##  [25]  27.311310  28.313695  29.121123  30.179075        NaN        NaN
##  [31]  33.547474  34.326805  35.328792  36.330705  37.332561  38.334389
##  [37]  39.363977  40.461066  41.490520  42.452349  43.453864  44.455318
##  [43]  45.456725  46.402445        NaN        NaN  49.628643  50.546326
##  [49]  51.463915  52.659565  53.577101  54.577975  55.551002        NaN
##  [55]        NaN        NaN        NaN        NaN  61.638105  62.582945
##  [61]  63.675926  64.731801  65.695007  66.695199  67.695311  68.695372
##  [67]  69.695382  70.695335  71.695237  72.695081  73.694864  74.722351
##  [73]  75.777548  76.777153  77.776703  78.803957  79.803376  80.802755
##  [79]  81.774318  82.801319  83.828281  84.827424  85.882010  86.908784
##  [85]  87.907754  88.906655  89.905500  90.904294  91.903025  92.901705
##  [91]  93.928052  94.982101  96.008329  97.006754  98.005149  99.003477
##  [97] 100.001742 100.999944 101.998101 103.023921 104.077399 105.103094
## [103] 106.101007 107.098868 108.096667 109.094420 110.092122 111.089733
## [109] 112.114996 113.167925 114.193084 115.190479 116.187817 117.185093
## [115] 118.182312 119.179474 120.204275 121.256707 122.281385 123.278303
## [121] 124.275147 125.271962 126.268743 127.265444 128.262071 129.286335
## [127] 130.338218 131.362350 132.358750 133.355094 134.351380 135.347609
## [133] 136.371450 137.422902 138.446608 139.442587 140.438538 141.434426
## [139] 142.430246 143.426009 144.449370 145.500325 146.523562 147.519086
## [145] 148.514560 149.509964 150.505312 151.528258 152.578778 153.601601
## [151] 154.596722 155.591769 156.586769 157.581713 158.604230 159.654324
## [157] 160.676716 161.671421 162.666081 163.660678 164.655207 165.677299
## [163] 166.726969 167.748945 168.743241 169.737479 170.731655 171.725780
## [169] 172.747456 173.796684 174.818248 175.812140 176.805964 177.799736
## [175] 178.821051 179.869906 180.891098 181.884643 182.878136 183.871544
## [181] 184.892483 185.940976 186.961813 187.954994 188.948112 189.941178
## [187] 190.934199 191.954731 193.002782 194.023192 195.015957 196.008688
## [193] 197.001356 198.021515 199.069198 200.089248 201.081661 202.074027
## [199] 203.066337 204.086146 205.133456 206.153146 207.145217 207.971898
## [205] 209.046510 210.231286 211.195550 212.214874 213.206614 214.198275
## [211] 215.217411 216.264041 217.283065 218.274487 219.265858 220.257166
## [217] 221.275948 222.322204 223.340867 224.331936 225.322948 226.341435
## [223] 227.387379 228.405730 229.396503 230.387219 231.377884 232.396013
## [229] 233.441590 234.459582 235.449997 236.440360 237.458181 238.503445
## [235] 239.521145 240.511274 241.501342 242.518853 243.563807 244.581202
## [241] 245.571035 246.560812 247.578021 248.622658 249.639748 250.629285
## [247] 251.618766 252.635684 253.680008 254.696771 255.686024 256.675225
## [253] 257.691826 258.735850 259.752333 260.741285 261.730179 262.746478
## [259] 263.790180 264.806351 265.795011 266.783620 267.799620 268.843015
## [265] 269.858901 270.847254 271.835551 272.851251 273.894334 274.909912
## [271] 275.897969 276.885969 277.901370 278.944148 279.931984 280.919756
## [277] 281.962335 282.977436 284.074771 285.089725 285.994895 287.009743
## [283] 288.051960 289.066685 290.053922 291.041101 292.055646 293.097545
## [289] 294.090036 295.076976 296.113204 297.154865 298.169044 299.155745
## [295] 300.114988 301.211198 302.279943 303.211602 304.198012 305.211762
## [301] 306.252856 307.266486 308.252658 309.266170 310.307009 311.320383
## [307] 312.306321 313.292207 314.305410 315.345943 316.359023 317.344670
## [313] 318.357628 319.397889 320.410731 321.396145 322.408864 323.448892
## [319] 324.461484 325.446658 326.459121 327.498889 328.511254 329.496184
## [325] 330.508411 331.547935 332.560047 333.544737 334.556717 335.595997
## [331] 336.607862 337.592318 338.604058 339.643083 340.654688 341.638893
## [337] 342.650412 343.689198 344.700569 345.684553 346.695808 347.734328
## [343] 348.745462 349.729200 350.740206 351.778483 352.789366 353.772870
## [349] 354.783650 355.821683 356.832314 357.815568 358.826093 359.863864
## [355] 360.874256 361.857293 362.867581 363.905097 364.915248 365.925337
## [361] 366.962666 367.972641 368.955240 369.965067 371.002164 372.011911
## [367] 372.994287 374.003890 375.040715 376.050197 377.032344 378.041701
## [373] 379.078275 380.087515 381.096687 382.133080 383.142124 384.123822
## [379] 385.132764 386.168919 387.177725 388.186477 389.222427 390.231050
## [385] 391.212359 392.220861 393.256551 394.264934 395.246003 396.254263
## [391] 397.289703 398.297850 399.305924 400.341165 401.349123 402.329770
## [397] 403.337598 404.372601 405.380315 406.387961 407.422766 408.430292
## [403] 409.437750 410.472367 411.479712 412.459756 413.466964 414.501353
## [409] 415.508447 416.515472 417.549658 418.556566 419.536198 420.542986
## [415] 421.576922 422.583588 423.590191 424.623934 425.630410 426.636819
## [421] 427.670375 428.676675 429.655708 430.661881 431.695187 432.701234
## [427] 433.707215 434.740328 435.746196 436.751998 437.784924 438.790607
## [433] 439.796223 440.828939 441.834422 442.812696 443.818078 444.850560
## [439] 445.855816 446.861005 447.893295 448.898362 449.903359 450.935456
## [445] 451.940339 452.945156 453.977065 454.981776 455.986421 457.018126
## [451] 458.022622 459.027070 460.058605 461.062933 462.067199 463.098541
## [457] 464.102682 465.106755 466.137909 467.141872 468.118629 469.122464
## [463] 470.153374 471.157080 472.160722 473.191438 474.194962 475.198416
## [469] 476.228940 477.232286 478.235563 479.265888 480.269042 481.272141
## [475] 482.302278 483.305252 484.308172 485.338117 486.340887 487.343608
## [481] 488.373376 489.375976 490.378508 491.408072 492.437584 493.467034
## [487] 494.469322 495.471546 496.500798 497.502909 498.504949 499.534008
## [493] 500.535928 501.537779 502.566649 503.568388 504.570055 505.598727
## [499] 506.600280 507.601779 508.630269 509.631625 510.632923 511.661232
## [505] 512.689487 513.717648 514.718683 515.719677 516.747656 517.748526
## [511] 518.749336 519.777127 520.777811 521.778426 522.806024 523.806527
## [517] 524.806962 525.834373 526.861736 527.889010 528.889177 529.889303
## [523] 530.916401 531.916407 532.916337 533.943231 534.943046 535.942807
## [529] 536.969524 537.996168 539.022743 540.022260 541.021711 542.048093
## [535] 543.047413 544.046668 545.072868 546.099004 547.125074 548.124078
## [541] 549.123027 550.148909 551.147734 552.146503 553.172192 554.197806
## [547] 555.223375 556.221896 557.220332 558.245702 559.244037 560.242304
## [553] 561.267481 562.292598 563.317656 564.315673 565.313621 566.338480
## [559] 567.363283 568.388005 569.385687 570.383344 571.407901 572.432379
## [565] 573.456795 574.454188 575.451518 576.475746 577.499910 578.524001
## [571] 579.521078 580.518092 581.542001 582.538897 583.535737 584.559453
## [577] 585.583089 586.606674 587.603260 588.599779 589.623176 590.646503
## [583] 591.669764 592.692969 593.716111 594.712255 595.708338 596.731292
## [589] 597.754172 598.776984 599.772828 600.768596 601.791215 602.813781
## [595] 603.836274 604.831801 605.827270 606.849575 607.871812 608.893986
## [601] 609.889202 610.884360 611.906358 612.928270 613.950115 614.971910
## 
## $N2
##   [1]  6.900909e-04  1.275806e-04 -1.667200e-05  1.431511e-05  1.293015e-07
##   [6]  6.617551e-05  4.107258e-05  5.137051e-05  1.403179e-05  2.559765e-05
##  [11]  1.416520e-04  6.723609e-04  9.213411e-04  7.504344e-04  6.632730e-04
##  [16]  4.755547e-04  2.050130e-04  4.096130e-04  6.870286e-04  8.685894e-04
##  [21]  2.512297e-03  1.083613e-03  9.859397e-04  4.866841e-04  1.575760e-04
##  [26]  2.259302e-04  1.347355e-04  5.516122e-05  1.514462e-04  8.712560e-05
##  [31]  3.342233e-04  1.929819e-04  7.452830e-05  9.368615e-05  2.190256e-06
##  [36]  5.325264e-05 -1.113857e-05  6.054577e-05  1.908357e-05  5.952802e-05
##  [41]  3.505188e-05  2.439443e-05  1.720460e-04  1.941846e-04  3.672522e-05
##  [46]  7.071743e-05  1.626845e-04  1.642571e-04  1.512709e-04  9.180148e-05
##  [51]  1.718196e-04  4.676988e-05  5.224744e-05  1.010183e-04  1.191359e-04
##  [56]  6.929104e-05  3.086059e-05 -1.311211e-05  2.666215e-05  5.327266e-05
##  [61]  4.606653e-05 -6.158166e-06  3.814994e-05 -2.825333e-05 -5.462967e-05
##  [66]  9.550940e-05  9.450732e-05  1.306159e-04  5.814306e-05 -1.704655e-05
##  [71] -5.980219e-05  5.422469e-08  6.763511e-08  9.670011e-08  9.749178e-08
##  [76]  3.819512e-05  8.582073e-05  2.741218e-07  7.645211e-05  9.257220e-05
##  [81]  1.553634e-05  8.720796e-05  6.481598e-05  5.725101e-05 -1.776647e-06
##  [86]  5.719966e-05  5.823133e-06  4.198108e-05  5.530335e-05  2.864640e-05
##  [91]  9.548330e-08  2.714620e-05  5.721144e-05 -3.036319e-05 -2.846581e-05
##  [96]  5.720910e-05  7.148060e-05  3.245312e-05 -2.465768e-05 -2.426061e-05
## [101]  1.092644e-05  9.624354e-06  2.866819e-05  1.914739e-05  3.819439e-05
## [106] -4.184873e-05  1.999660e-06  7.628800e-05  2.716907e-05  3.075973e-05
## [111]  2.766814e-05  1.655650e-04  1.006581e-04  7.811018e-05 -7.058652e-05
## [116]  6.671842e-05  6.682020e-05 -7.214535e-06  8.090045e-05  1.275420e-04
## [121] -1.149111e-05  4.188186e-05  8.575825e-05 -1.729418e-05  8.153758e-05
## [126]  1.005967e-04  4.067343e-05  9.633059e-06 -2.504465e-05  9.491671e-05
## [131]  8.629040e-05  1.233785e-04  5.744244e-05  6.734210e-05  1.806778e-04
## [136]  9.180826e-05  6.607198e-05  4.761031e-05  9.616857e-06  1.177970e-07
## [141]  1.432448e-05  1.916603e-05  1.253937e-04  1.066774e-04  3.749319e-05
## [146]  8.736360e-05 -6.940016e-05  7.208326e-05  1.125200e-07  3.810033e-05
## [151]  4.760117e-05  1.125237e-07  1.125507e-07  1.911184e-05  7.272099e-05
## [156]  7.150383e-05 -1.711952e-05  3.392047e-05 -5.158925e-05  2.265005e-05
## [161]  4.585426e-05 -1.520601e-06 -1.458505e-05  3.459105e-05 -3.436641e-05
## [166]  6.664964e-05  1.912335e-05  2.863089e-05  6.376167e-05  6.202818e-06
## [171] -1.957778e-05  8.743185e-05 -5.871360e-06  4.270844e-05  5.588859e-05
## [176]  2.551492e-05 -1.788708e-05  7.713147e-05  9.522892e-05  2.353421e-05
## [181]  2.574792e-05  2.605511e-05  1.081208e-07  2.348653e-05  9.166935e-05
## [186]  7.609669e-05  4.415329e-05 -3.165418e-06  3.611253e-05  6.921283e-05
## [191]  1.077955e-07  7.881618e-06 -9.396821e-06 -3.198719e-05  6.738416e-05
## [196]  5.195063e-05  1.082221e-07  1.221217e-07 -7.851107e-05 -5.265635e-07
## [201]  5.480763e-05  2.693085e-05 -1.286716e-05  8.576772e-05  8.576749e-05
## [206]  1.323260e-07 -1.624890e-05 -5.900453e-06  4.423453e-05  3.042894e-05
## [211] -4.082922e-05 -4.083061e-05  1.742906e-05  4.424751e-05 -1.367821e-05
## [216]  3.218222e-05  5.425454e-05  8.208957e-05  1.743541e-05  3.474032e-05
## [221] -1.717217e-05  3.292171e-05  1.325770e-07  5.729588e-05  2.871529e-05
## [226]  1.325876e-07 -6.045344e-05 -7.624501e-07  7.408212e-05 -8.524371e-06
## [231]  1.325974e-07  6.939419e-05  6.888474e-05  4.953395e-05  2.873583e-05
## [236] -9.402401e-06 -3.801155e-05  1.309418e-05 -1.449075e-05  8.674545e-05
## [241]  5.210342e-05 -3.803131e-05  5.382577e-05  2.737740e-05  9.680034e-06
## [246]  3.301739e-05  1.143271e-04  1.244241e-05 -2.148734e-05  1.808651e-05
## [251]  1.386683e-05  4.316176e-05 -4.926144e-06  1.816474e-05  5.628257e-05
## [256] -8.057513e-05 -1.812394e-05  1.055445e-07  9.167228e-06  9.671302e-06
## [261]  1.923800e-05  4.793932e-05  1.056024e-07  1.056310e-07  1.056591e-07
## [266]  1.056864e-07  2.104545e-05  5.371064e-05 -2.459483e-05  1.564995e-05
## [271] -2.861467e-05  1.058165e-07  3.422169e-05 -1.143156e-06  1.745425e-05
## [276] -2.501554e-05  7.097243e-05 -7.983701e-05  1.655415e-05  3.481233e-05
## [281] -9.475570e-06 -1.709453e-06  1.100083e-05 -9.477848e-06  5.036431e-05
## [286]  3.896204e-05  7.244728e-05 -5.877411e-05 -4.329116e-05  4.077200e-05
## [291]  2.110143e-05 -2.607834e-05  1.746926e-05  2.934318e-05  1.563930e-05
## [296]  3.994882e-05  3.483575e-05 -6.068735e-05  8.491920e-08 -8.102974e-06
## [301] -4.631719e-05 -9.520248e-06 -1.912672e-05  1.489532e-05  1.730837e-06
## [306]  1.745747e-05  3.482927e-05  1.745906e-05  5.111015e-05 -2.888002e-05
## [311] -1.230483e-05 -1.060236e-04  3.050870e-05 -3.033917e-05  3.484295e-05
## [316] -3.467398e-05  8.565896e-08  4.948589e-05 -1.729688e-05  5.223470e-05
## [321]  6.673787e-06  4.290705e-05  1.747193e-05  8.594449e-08  8.597349e-08
## [326]  8.600289e-08 -1.730334e-05  1.747676e-05 -2.957043e-05 -6.087767e-05
## [331]  8.782645e-06  8.783051e-06  8.616270e-08  8.619215e-08  8.622121e-08
## [336]  8.624936e-08  8.627843e-08  3.305330e-05  5.200720e-05  8.627351e-08
## [341] -1.634727e-05 -1.619501e-05  6.970096e-05 -1.731823e-05  5.033326e-06
## [346]  1.162971e-05  1.749543e-05 -6.083690e-05  9.098058e-08  9.101033e-08
## [351]  9.103945e-08  9.106766e-08 -1.475511e-05  5.149991e-05  2.903699e-05
## [356]  1.973674e-06 -1.310877e-05 -3.209076e-06 -1.732715e-05 -9.810436e-06
## [361] -6.510060e-06  3.493351e-05  9.128316e-08  1.824795e-05  1.494673e-05
## [366]  9.138500e-08 -8.537714e-07 -7.079689e-06 -1.641798e-05  9.162952e-08
## [371]  9.165311e-08  1.660396e-05  9.172306e-08  9.175233e-08  9.178161e-08
## [376]  9.181129e-08  9.184058e-08  1.752695e-05 -1.642530e-05  1.661087e-05
## [381] -1.734535e-05  2.982867e-05  1.991763e-05 -4.350833e-05  9.207980e-08
## [386]  6.618834e-05 -1.823999e-05  1.944434e-05 -1.926153e-05  1.925953e-06
## [391]  7.427732e-06 -9.586640e-06  1.926573e-06 -1.741881e-06 -2.895311e-05
## [396]  1.945814e-05 -1.366903e-05 -1.367861e-05  4.467181e-05 -2.096066e-05
## 
## $p_mid
##   [1]   3.013918   4.017749   5.021523   6.025241   7.028902   8.032512
##   [7]   9.063929  10.123152  11.154454  12.157825  13.161129  14.164381
##  [13]  15.167577  16.170715  17.173791  18.176816  19.179784  20.182690
##  [19]  21.185528  22.188325  23.191066  24.193738  25.224212  26.282463
##  [25]  27.312817  28.315257  29.317634  30.319961  31.322230  32.324443
##  [31]  33.326599  34.328698  35.330740  36.332709  37.334620  38.336503
##  [37]  39.366148  40.423551  41.453062  42.454690  43.456261  44.457769
##  [43]  45.459232  46.460632  47.461981  48.463273  49.464503  50.465665
##  [49]  51.494560  52.551240  53.580055  54.580984  55.581868  56.582689
##  [55]  57.583453  58.584160  59.584804  60.585392  61.585923  62.586397
##  [61]  63.614602  64.670536  65.698630  66.698877  67.699044  68.699161
##  [67]  69.699226  70.699234  71.699191  72.699091  73.698928  74.726472
##  [73]  75.781728  76.809156  77.808761  78.808303  79.807778  80.807212
##  [79]  81.806589  82.805892  83.805150  84.832102  85.886747  86.913577
##  [85]  87.912602  88.911559  89.910459  90.909307  91.908094  92.906828
##  [91]  93.933232  94.987339  96.013624  97.012104  98.010555  99.008937
##  [97] 100.007257 101.005515 102.003727 103.029604 104.083140 105.108891
## [103] 106.106859 107.104775 108.102629 109.100437 110.098194 111.095861
## [109] 112.121180 113.174167 114.199382 115.196832 116.194226 117.191557
## [115] 118.188830 119.186047 120.210905 121.263395 122.288130 123.285102
## [121] 124.282001 125.278872 126.275707 127.272463 128.269146 129.293466
## [127] 130.345407 131.369596 132.366051 133.362449 134.358791 135.355075
## [133] 136.378972 137.430482 138.454244 139.450279 140.446285 141.442228
## [139] 142.438102 143.433920 144.457338 145.508350 146.531644 147.527224
## [145] 148.522752 149.518211 150.513614 151.536617 152.587194 153.610074
## [151] 154.605250 155.600351 156.595407 157.590406 158.612979 159.663131
## [157] 160.685579 161.680339 162.675054 163.669706 164.664289 165.686438
## [163] 166.736166 167.758198 168.752549 169.746842 170.741073 171.735253
## [169] 172.756985 173.806271 174.827892 175.821838 176.815717 177.809544
## [175] 178.830915 179.879828 180.901077 181.894677 182.888225 183.881688
## [181] 184.902683 185.951233 186.972127 187.965362 188.958535 189.951657
## [187] 190.944732 191.965320 193.013429 194.033895 195.026715 196.019501
## [193] 197.012224 198.032439 199.080180 200.100287 201.092754 202.085175
## [199] 203.077540 204.097405 205.144772 206.164519 207.156645 208.148708
## [205] 209.140719 210.160224 211.207201 212.226581 213.218376 214.210092
## [211] 215.229284 216.275972 217.295052 218.286529 219.277955 220.269317
## [217] 221.288156 222.334469 223.353188 224.344312 225.335379 226.353922
## [223] 227.399924 228.418331 229.409159 230.399930 231.390649 232.408835
## [229] 233.454469 234.472518 235.462987 236.453405 237.471281 238.516604
## [235] 239.534359 240.524544 241.514666 242.532234 243.577245 244.594696
## [241] 245.584584 246.574416 247.591681 248.636375 249.653521 250.643113
## [247] 251.632649 252.649622 253.694005 254.710823 255.700131 256.689387
## [253] 257.706044 258.750126 259.766665 260.755671 261.744619 262.760975
## [259] 263.804734 264.820961 265.809677 266.798340 267.814396 268.857849
## [265] 269.873791 270.862199 271.850549 272.866305 273.909447 274.925080
## [271] 275.913192 276.901246 277.916704 278.959539 279.974869 280.962695
## [277] 281.977893 283.020484 284.035580 285.023157 286.010676 287.025580
## [283] 288.067854 289.082635 290.069926 291.057161 292.071761 293.113718
## [289] 294.128194 295.115189 296.129543 297.171262 298.185497 299.172252
## [295] 300.186361 301.227819 302.241811 303.228333 304.214798 305.228603
## [301] 306.269755 307.283441 308.269667 309.283235 310.324132 311.337562
## [307] 312.323554 313.309495 314.322754 315.363345 316.376480 317.362182
## [313] 318.375196 319.415514 320.428412 321.413880 322.426655 323.466741
## [319] 324.479389 325.464617 326.477136 327.516961 328.529383 329.514366
## [325] 330.526650 331.566231 332.578399 333.563143 334.575179 335.614516
## [331] 336.626437 337.610948 338.622743 339.661826 340.673486 341.657746
## [337] 342.669321 343.708165 344.719592 345.703629 346.714941 347.753518
## [343] 348.764708 349.748500 350.759562 351.797896 352.808835 353.792394
## [349] 354.803229 355.841319 356.852006 357.835314 358.845895 359.883724
## [355] 360.894172 361.877263 362.887606 363.925180 364.935387 365.945532
## [361] 366.982918 367.992949 368.975602 369.985485 371.022639 372.032442
## [367] 373.014872 374.024531 375.061413 376.070950 377.053152 378.062565
## [373] 379.099197 380.108492 381.117719 382.154170 383.163270 384.145021
## [379] 385.154020 386.190232 387.199094 388.207901 389.243909 390.252587
## [385] 391.233950 392.242508 393.278255 394.286693 395.267817 396.276133
## [391] 397.311630 398.319832 399.327962 400.363261 401.371274 402.351976
## [397] 403.359859 404.394920 405.402689 406.410391
## Warning in gsw_Nsquared(binSA_2, binCT_2, binp_2, Lat): gsw_Nsquared() has some NA inputs ... these are not handled well
## $N2
##   [1]  2.141482e-03  4.100821e-04  4.425345e-04  7.531391e-04  5.962768e-04
##   [6]  5.001567e-04  3.898596e-04  1.150947e-03  6.914712e-04  2.981317e-04
##  [11]  4.958619e-04  6.338610e-04  7.159984e-04  4.437821e-04  4.481088e-04
##  [16]  2.846700e-03  1.064819e-03  6.676778e-04  4.550656e-04  3.609823e-04
##  [21]  3.859934e-04  2.245415e-04  5.745807e-04  2.466259e-04  5.336560e-04
##  [26]  2.757071e-04  1.498338e-04  8.847692e-05  1.668414e-04  2.919148e-04
##  [31] -3.670561e-05  5.409163e-05 -1.458194e-05  3.879235e-05  1.052056e-04
##  [36]  2.239509e-04  1.051245e-04  4.630943e-05  5.309855e-05  1.707552e-04
##  [41]  4.023931e-05  1.983888e-04  2.029524e-04 -1.725537e-05  9.958338e-05
##  [46]  1.045812e-04  2.564859e-04  7.197801e-05  1.906734e-04  5.417634e-05
##  [51] -1.645316e-05  1.304805e-04  2.870181e-05 -3.792441e-05  3.364002e-05
##  [56]  8.097394e-05  1.717970e-04  7.765237e-05  3.541584e-05  7.225148e-05
##  [61]  1.396723e-04  7.334424e-05  7.719965e-05  1.426912e-04  2.657851e-04
##  [66]  1.774119e-05  1.090876e-04 -9.748010e-06  1.104699e-04 -4.172431e-06
##  [71]  4.212744e-05  6.634190e-05  1.440224e-04  4.107169e-04  6.053936e-05
##  [76]  9.912939e-06  4.989083e-05  5.059341e-05 -6.380113e-07  3.263928e-05
##  [81] -2.790113e-06  1.513631e-04  9.669825e-05  6.146469e-06  1.534590e-04
##  [86] -3.408784e-05  1.850586e-04  1.159224e-04  1.916542e-04 -1.549231e-06
##  [91]  1.647065e-05  4.369398e-04 -2.541500e-04  2.097806e-05  2.182489e-05
##  [96]  6.931735e-05  8.853917e-06  4.586061e-05  1.423722e-04 -5.315276e-05
## [101]  4.139026e-06  9.476243e-05 -6.056103e-05  6.584294e-05  1.905870e-04
## [106]  6.045421e-05  7.225179e-06 -2.249108e-05  7.930873e-05  5.678286e-05
## [111]  1.963471e-04  1.963774e-04  2.167284e-05 -1.604954e-04  1.171964e-04
## [116]  7.007910e-05 -2.693064e-05  5.456637e-05  7.136941e-05 -1.647706e-05
## [121] -6.268141e-06  3.051183e-05 -2.371386e-06  2.944206e-05  9.995778e-05
## [126] -6.496898e-05  2.568409e-05  4.244034e-05  3.587462e-05  9.608766e-05
## [131]  5.092602e-07 -6.678748e-05  6.656221e-05           NaN           NaN
## [136]  1.767409e-05  3.405081e-05  8.696834e-05  1.033026e-04  7.875452e-05
## [141]  1.177256e-05 -9.671381e-06  7.770182e-05  3.706971e-05  3.314821e-05
## [146]  6.343416e-05  1.871680e-05 -2.450990e-06  1.321864e-05  1.612653e-07
## [151] -3.012563e-05  7.384934e-05 -2.184632e-05  4.290030e-05  2.166082e-05
## [156]  6.855693e-05  6.727199e-07  3.913443e-05  2.186987e-05 -2.071475e-05
## [161]  1.382839e-04 -3.599416e-05  1.251583e-05  3.784927e-05 -2.809606e-05
## [166]  1.108148e-04  1.638596e-06  6.599534e-05 -1.072226e-05  8.680013e-06
## [171] -1.976777e-05  7.357964e-05 -2.716768e-05  3.706599e-05  4.879574e-05
## [176]  3.515519e-05  5.749466e-05  8.760780e-05  5.160693e-05  2.769633e-05
## [181]  8.556218e-06  4.435783e-05  3.682086e-05  1.319239e-05 -8.359161e-06
## [186]  8.702972e-05  7.351525e-06  3.227164e-05  1.273819e-04  1.515327e-05
## [191]  7.387549e-05 -2.544977e-05  4.233997e-05 -1.762368e-06  5.250929e-05
## [196] -1.304424e-05  1.116403e-04  1.520004e-07 -6.024217e-05 -7.690425e-07
## [201]  3.782312e-05  7.127733e-06  3.751796e-05 -6.676384e-08  6.031490e-05
## [206] -6.337381e-05  5.494766e-05  1.540705e-05  2.176735e-06  1.069818e-04
## [211] -1.862885e-05 -1.021738e-05  7.522669e-05 -8.449516e-06  1.728857e-05
## [216] -4.447464e-06  1.554877e-07  3.976754e-05  2.697349e-05  3.650560e-05
## [221]  4.458242e-05           NaN           NaN           NaN  4.630656e-05
## [226]  1.076283e-05  6.890889e-05  4.864394e-05 -8.162670e-05 -6.117878e-05
## [231]  5.173134e-05  7.400379e-05 -2.205376e-05 -3.316320e-05  1.735203e-05
## [236]  1.583553e-07  1.033321e-04  3.274133e-05  1.585688e-07 -1.314742e-05
## [241] -1.162182e-05  6.423658e-05 -2.524176e-05  1.629631e-05  2.881783e-05
## [246]  3.385606e-05  5.103432e-05 -5.336550e-05  1.398445e-05  1.273646e-07
## [251] -3.429033e-05  7.095285e-05  4.388059e-05  8.711255e-06 -5.558883e-05
## [256]  4.621121e-05  7.795901e-05  1.931566e-06  2.173220e-05  1.644866e-05
## [261]  2.570183e-06  1.330539e-06  3.041273e-05 -6.174513e-06 -3.633839e-05
## [266]  3.253662e-05  3.757396e-05 -4.201049e-06 -1.973128e-05 -8.190913e-06
## [271] -2.304469e-05  5.857517e-05 -2.104345e-05 -1.245698e-05  9.366538e-05
## [276] -5.394640e-05  4.161192e-05 -1.326386e-05 -7.922640e-06  8.148391e-05
## [281] -1.860130e-06 -2.124956e-05 -4.702396e-05  5.182562e-05  5.182858e-05
## [286]  7.541755e-06 -8.163742e-06  1.239248e-06  2.200391e-05  1.307025e-07
## [291]  2.399485e-05 -4.920409e-05  2.961103e-05  3.943955e-05  9.441417e-06
## [296]  2.806405e-05 -2.452970e-05  3.460615e-05 -2.696716e-05  2.203718e-05
## [301]  3.835288e-06  4.927383e-05  1.095099e-07 -8.800233e-05 -2.717039e-05
## [306]  2.477856e-05  8.637176e-05  1.098489e-07  1.287548e-05  2.387039e-05
## [311] -7.122242e-05  6.923991e-05  3.994445e-05 -2.071489e-06  2.625985e-06
## [316]  2.599682e-05  4.915982e-05 -1.143409e-04  3.579139e-05  9.856887e-05
## [321]  6.286972e-05 -2.538785e-05  2.552792e-06 -2.953911e-05  5.332429e-05
## [326]  5.430441e-05 -5.994397e-06  3.717648e-05  3.660516e-05  4.774845e-05
## [331]  1.241846e-05  3.710650e-05  3.187507e-05 -3.625827e-06  2.228531e-05
## [336]  1.738926e-05  1.113522e-07  1.113879e-07  1.464078e-05  6.607296e-05
## [341] -4.013905e-05  4.268468e-05  1.739638e-05 -8.631891e-05  8.299830e-06
## [346]  1.115012e-07  1.107377e-07  1.092988e-07  1.093061e-07  1.093418e-07
## [351]  1.093771e-07
## 
## $p_mid
##   [1]   3.014165   4.018079   5.021936   6.025737   7.029480   8.033172
##   [7]   9.064675  10.123985  11.155371  12.158825  13.162211  14.165546
##  [13]  15.168824  16.172045  17.161270  18.164377  19.181362  20.184350
##  [19]  21.187270  22.190150  23.192973  24.195728  25.226286  26.284624
##  [25]  27.315063  28.317585  29.320045  30.322454  31.324806  32.327101
##  [31]  33.329340  34.331521  35.333646  36.335697  37.337691  38.339656
##  [37]  39.369386  40.426876  41.456471  42.458181  43.459835  44.461425
##  [43]  45.462971  46.464453  47.465885  48.467259  49.468571  50.469815
##  [49]  51.498795  52.555562  53.584462  54.585473  55.586439  56.587342
##  [55]  57.588189  58.588978  59.589705  60.590375  61.590988  62.591544
##  [61]  63.619834  64.675855  65.704033  66.704363  67.704612  68.704811
##  [67]  69.704958  70.705049  71.705088  72.593973  73.649441  74.649301
##  [73]  75.815719  76.982099  77.815161  78.814785  79.814342  80.813858
##  [79]  81.813317  82.812703  83.756526  84.894591  86.004838  86.920726
##  [85]  87.892080  89.029868  90.056603  90.916785  91.915653  92.858978
##  [91]  94.079644  95.272554  96.104746  97.020083  98.018616  99.017081
##  [97] 100.015483 101.013823 102.012117 103.038078 104.091701 105.117537
## [103] 106.115587 107.113585 108.111521 109.109411 110.107250 111.104999
## [109] 112.130403 113.183476 114.208776 115.206308 116.203783 117.201196
## [115] 118.198552 119.195851 120.220794 121.273370 122.298189 123.295244
## [121] 124.292225 125.222713 126.219631 127.282933 128.279697 129.304102
## [127] 130.356129 131.380402 132.376939 133.373420 134.369843 135.366209
## [133] 136.390190        NaN        NaN 139.517090 140.457838 141.453863
## [139] 142.449820 143.445719 144.469221 145.520320 146.543698 147.539360
## [145] 148.534969 149.530511 150.525996 151.549083 152.599746 153.622711
## [151] 154.617968 155.613151 156.608289 157.603370 158.515472 159.593349
## [157] 160.726437 161.693640 162.688436 163.683170 164.677835 165.700068
## [163] 166.749883 167.771999 168.766431 169.760807 170.755120 171.749381
## [169] 172.771197 173.820570 174.842275 175.836303 176.830263 177.824172
## [175] 178.845627 179.894627 180.915960 181.909641 182.903271 183.896815
## [181] 184.917894 185.966531 186.987509 187.980826 188.974081 189.967284
## [187] 190.960441 191.981113 193.029308 194.049859 195.042760 196.035628
## [193] 197.028432 198.011976 199.059803 200.116749 201.109298 202.101801
## [199] 203.094247 204.114197 205.161650 206.181481 207.173688 208.165833
## [205] 209.157926 210.177515 211.202535 212.222000 213.235919 214.227716
## [211] 215.246992 216.293766 217.312930 218.304489 219.295996 220.287440
## [217] 221.306362 222.352762 223.371565 224.362770 225.298859        NaN
## [223]        NaN        NaN 229.455562 230.418887 231.409688 232.427957
## [229] 233.473677 234.491810 235.482360 236.472860 237.490820 238.536229
## [235] 239.554068 240.544334 241.534537 242.552189 243.597286 244.614821
## [241] 245.604791 246.594704 247.612053 248.656833 249.674063 250.663737
## [247] 251.653353 252.670411 253.714879 254.731782 255.721171 256.710508
## [253] 257.727248 258.688988 259.733088 260.804603 261.683744 262.727652
## [259] 263.853909 264.842752 265.831548 266.820294 267.836433 268.879972
## [265] 269.895997 270.884487 271.872919 272.888758 273.931986 274.947703
## [271] 275.935896 276.924032 277.939572 278.982493 279.997907 280.985815
## [277] 282.001096 283.043773 284.058953 285.046610 286.034211 287.049199
## [283] 288.091559 289.106423 290.093796 291.081111 292.095795 293.137838
## [289] 294.152398 295.139474 296.153911 297.195716 298.210034 299.196872
## [295] 300.211064 301.252607 302.266682 303.253286 304.239832 305.253721
## [301] 306.294959 307.308728 308.295036 309.308687 310.349670 311.363183
## [307] 312.349256 313.335278 314.348621 315.389297 316.402516 317.388299
## [313] 318.401396 319.441800 320.454781 321.440330 322.453189 323.493361
## [319] 324.506092 325.491402 326.504003 327.543914 328.556419 329.541484
## [325] 330.553851 331.593518 332.605769 333.590594 334.602713 335.642136
## [331] 336.654141 337.638732 338.650611 339.689779 340.701523 341.685864
## [337] 342.697522 343.736452 344.857310 345.841428 346.743475 347.782138
## [343] 348.793411 349.777285 350.788430 351.826849 352.837871 353.821511
## [349] 354.832430 355.870605 356.881376
## 
## $N2
##   [1]  4.180904e-04  1.276288e-04  4.214877e-05  8.546115e-06  9.246237e-05
##   [6]  9.199836e-05  1.086999e-04  9.746098e-05  1.224502e-04  1.215846e-04
##  [11]  4.950962e-05  1.537443e-04  8.354167e-05  1.278170e-04  1.416680e-04
##  [16]  7.433456e-05  1.799511e-04  8.617053e-05  7.749992e-05  9.028466e-05
##  [21]  7.929260e-05  8.531620e-06  8.650382e-05  1.276224e-04  8.712847e-05
##  [26]  5.640932e-04  7.141584e-04  5.843233e-04  4.091881e-04  7.238582e-04
##  [31]  4.238182e-04  8.624479e-04  1.813586e-04  7.097725e-04  4.099061e-05
##  [36]  6.067255e-04  4.556116e-04  1.668966e-05  1.442928e-05  4.675060e-04
##  [41]  6.025419e-04 -1.492109e-04  6.938835e-05  3.721227e-04  1.410011e-04
##  [46]  1.645815e-04  2.257449e-04  9.958808e-05 -1.777427e-04  7.336253e-04
##  [51] -3.342833e-05  8.863406e-05  9.961985e-05  2.736130e-05  6.303063e-05
##  [56]  3.671489e-05  1.920887e-04  6.445239e-06  4.186060e-05 -7.242673e-05
##  [61]  9.234146e-05 -2.440551e-05  3.013655e-05 -3.012103e-05  3.729943e-05
##  [66]  2.503907e-05  7.517606e-05  1.477817e-05  6.901859e-05  6.325613e-05
##  [71]  2.520170e-05  3.017047e-04 -2.177336e-04 -3.013146e-05  1.447844e-04
##  [76]  5.692447e-05  6.663013e-05 -1.481582e-05 -7.075783e-05  2.184094e-04
##  [81]  2.810865e-05 -3.582682e-05  1.559583e-04 -1.363789e-05  2.286514e-05
##  [86]  1.259766e-04 -9.022058e-05  8.532819e-05  2.514871e-06  1.766872e-05
##  [91]  4.494600e-05  3.112078e-05 -3.508138e-07  1.822741e-04  1.221572e-04
##  [96]  5.402893e-05 -2.529061e-05 -5.387252e-05  5.859128e-05  3.520784e-05
## [101]  2.860569e-05 -5.412184e-05  8.478770e-05  1.146421e-04  1.995809e-05
## [106]  1.701670e-04 -5.195308e-05  1.648762e-04 -5.136686e-05  2.844562e-06
## [111]  5.301510e-05  1.736740e-05 -4.614645e-05 -2.157939e-05  9.033034e-05
## [116] -5.822810e-05  3.902079e-05  3.490153e-05  1.020063e-05  6.566041e-05
## [121]  8.131602e-06  9.565264e-06 -1.732297e-06  1.194392e-04  1.278347e-04
## [126] -6.186180e-05 -3.917029e-05  1.366741e-04  1.106640e-04 -4.735125e-05
## [131]  5.304487e-05 -1.077910e-04  1.094070e-04  1.436849e-05  7.390646e-05
## [136] -2.758133e-05  6.784037e-05  2.714619e-05  1.441815e-04  1.235421e-04
## [141] -4.810817e-05  4.857313e-05 -4.284266e-05  5.619168e-05 -1.802515e-05
## [146]  1.008137e-04 -4.347605e-05  9.439912e-05 -2.396519e-05 -4.069009e-05
## [151] -3.794615e-05  1.323843e-04  4.227681e-05  7.563172e-05  2.114559e-05
## [156] -1.028678e-05  4.619672e-05  2.522239e-05  6.680541e-05  4.039674e-05
## [161] -1.313663e-05 -2.034672e-06  3.927822e-05 -3.435246e-06 -7.431297e-06
## [166]  3.937811e-05  4.584192e-05  4.082647e-05  5.623821e-05 -4.857001e-05
## [171]  8.916399e-06  8.494333e-05  1.419957e-05  6.225358e-05  6.234305e-06
## [176] -3.882832e-06 -2.411440e-05  2.692732e-05  1.004930e-04 -3.589320e-05
## [181]  4.879214e-05  7.576049e-06  9.104226e-05  7.391128e-06  1.381647e-05
## [186] -5.662091e-05 -1.913699e-05  5.450806e-05  4.251383e-06  6.113066e-05
## [191]  4.573385e-05 -1.962018e-06 -3.530527e-05 -3.745925e-06  6.745364e-05
## [196]  3.243183e-05  3.126826e-05  7.416455e-05 -3.425714e-05  5.810910e-05
## [201]  4.522679e-05  2.280817e-06 -5.147062e-05  3.572074e-05  1.408451e-05
## [206]  3.570479e-05 -6.992027e-06  5.604686e-05  2.694045e-05 -1.929278e-05
## [211]  2.042608e-05 -7.565079e-06  3.935350e-05  3.525809e-05 -1.108040e-06
## [216] -3.684298e-05  2.177781e-05 -6.446035e-07  1.295035e-05  6.072306e-05
## [221]  1.439199e-04 -8.203075e-05 -1.151725e-05  5.902995e-05  3.354644e-05
## [226]  1.177302e-04 -2.583808e-05 -7.212007e-05  7.183761e-05  6.718094e-06
## [231]  4.745415e-05  1.738145e-05 -3.366292e-05  7.708162e-05 -1.748230e-05
## [236] -2.767207e-05  3.637337e-05  1.266719e-05  5.582528e-05  2.549650e-06
## [241]  1.998462e-05 -2.986605e-05  2.233159e-05  2.519057e-05 -2.766133e-05
## [246]  2.617493e-06  9.274075e-05 -1.725470e-06 -1.463239e-04  2.023645e-04
## [251] -1.551205e-05  1.668312e-05  3.116525e-05  3.356509e-05 -3.068932e-05
## [256] -8.488697e-06  3.816799e-05  4.345472e-05  4.414697e-05 -6.591264e-06
## [261] -2.910085e-05  5.410229e-05 -1.694921e-05  1.646555e-05  4.962726e-05
## [266] -1.859963e-05 -1.524004e-05  2.357380e-05  1.267877e-07  2.562009e-05
## [271] -1.639179e-05  1.963556e-05  3.709239e-05  1.271604e-07 -7.777372e-06
## [276] -2.133083e-06  4.847307e-05  4.392246e-05 -3.213658e-05  1.270771e-07
## [281] -2.802191e-05  1.836462e-05  6.485785e-05 -4.350713e-05 -4.874074e-05
## [286]  5.129186e-05  4.867721e-05 -5.176921e-05  1.159366e-04 -3.401344e-05
## [291]  1.083724e-06  2.696183e-05  1.064696e-05 -2.453796e-07  2.739695e-05
## [296] -5.045042e-06  1.489830e-04 -9.815627e-05 -5.049709e-05  2.591774e-05
## [301]  1.167047e-04 -6.897019e-05  9.757437e-06 -7.061905e-06 -4.016362e-05
## [306]  2.873206e-05  3.689556e-05 -5.708855e-05  6.946638e-05  5.886037e-05
## [311] -6.876718e-05  1.244282e-07  3.602471e-05 -1.047814e-05 -2.097685e-05
## [316] -5.370868e-05  3.397893e-05  9.876025e-06 -2.918574e-05  1.477926e-05
## [321]  1.026668e-04 -1.162607e-04 -2.963222e-05  5.910542e-05 -2.070822e-05
## [326]  4.133599e-05  3.273308e-05  7.870260e-06  6.512025e-05 -3.967345e-05
## [331]  4.185809e-05 -4.904268e-06  1.016441e-05 -6.765373e-05 -4.371761e-06
## [336]  7.664640e-06 -1.515824e-06  1.326021e-04 -8.369144e-05 -9.125099e-06
## [341]  3.224746e-06  1.991818e-05  1.510642e-05  1.000432e-05  2.463915e-07
## [346]  2.255350e-06 -5.003830e-06  3.454219e-05  1.039937e-06  1.926267e-05
## [351] -3.714926e-05 -1.230700e-05  2.606905e-05 -2.822675e-05  1.037970e-04
## [356]  7.494608e-06 -3.073755e-06 -1.486636e-05 -1.035857e-04  2.959500e-05
## [361]  6.190758e-05 -9.997160e-06 -2.411860e-06  7.218438e-05 -3.918861e-05
## [366]  1.740948e-05 -1.106063e-05 -3.181324e-05  4.821472e-05 -1.247464e-07
## [371]  9.257013e-06  4.089174e-05 -5.173701e-05  3.917897e-05 -2.048990e-05
## [376]  3.071067e-05 -2.046289e-05  9.306143e-06  2.677425e-05 -3.926249e-06
## [381] -1.887327e-05 -2.972418e-05  7.132939e-05  5.024161e-05 -6.818156e-05
## [386]  3.154097e-05 -9.738642e-06  1.264482e-05 -5.429301e-06  4.169757e-05
## [391] -2.695350e-05  1.796153e-05  2.072444e-05  1.133174e-05  5.876397e-05
## [396]  1.203839e-06 -9.182183e-06 -1.667779e-05  6.941987e-05 -3.146637e-05
## [401] -1.505134e-05  1.079114e-07  2.802283e-05  4.039654e-05 -2.463604e-05
## [406] -3.191570e-05  8.914797e-05 -1.229496e-05  4.596904e-05 -3.716205e-05
## [411]  7.737348e-05 -3.823402e-05 -8.565118e-06  1.728529e-05  4.995792e-05
## [416]  1.003628e-05 -6.120224e-05 -2.195289e-05  1.003840e-05  1.908682e-05
## [421]  2.794771e-05 -5.182740e-05  2.637194e-05 -4.915101e-07  9.081857e-05
## [426] -6.588888e-05  3.378307e-05  2.040368e-05  3.565996e-05  9.057325e-05
## [431] -5.879061e-05 -3.445584e-05 -2.769151e-05  3.965470e-05 -2.220217e-05
## [436] -2.153230e-04  2.925065e-04  6.562363e-05 -5.471648e-05  7.598299e-06
## [441] -3.154688e-06  1.442653e-05  4.430638e-08  5.066569e-05 -2.247557e-05
## [446] -6.360326e-06  1.578179e-05 -6.189638e-05  1.833669e-05  3.068931e-05
## [451]  2.751807e-04 -1.108746e-04 -8.866040e-05 -3.164966e-06  9.189202e-05
## [456] -5.125597e-05 -3.425733e-05 -7.047815e-05  1.561210e-05  4.166859e-05
## [461]  5.212271e-06 -3.516727e-05  5.795894e-05  9.161776e-06  3.785534e-05
## [466]  5.424577e-07 -7.434466e-06  5.104985e-05 -8.124649e-05  1.920360e-04
## [471] -7.163365e-05  3.123288e-05  1.977520e-05 -5.565397e-05 -3.430682e-05
## [476]  5.475380e-05  4.909364e-05 -4.291041e-05 -2.208728e-05  4.786591e-05
## [481]  9.284309e-06 -1.890219e-04  1.377631e-04 -2.613643e-05 -6.065438e-05
## [486]  1.071824e-04  5.981266e-05 -3.817587e-05 -6.620539e-07 -9.705157e-06
## [491] -8.034768e-06  4.020349e-05  5.299268e-05 -3.473743e-05  1.929528e-06
## [496]  3.184458e-05  2.513057e-05 -3.369961e-05  1.720959e-05  1.140403e-05
## [501]  3.309153e-05 -5.823198e-05  6.984628e-06  2.587379e-05 -1.105997e-04
## [506]  8.380208e-05  3.798252e-05  1.166638e-05 -1.446776e-05  1.004995e-05
## [511] -3.395498e-06 -7.070117e-05  1.026460e-04 -1.760748e-05  3.183736e-05
## [516]  1.677767e-05  5.979079e-06 -1.322527e-05 -2.240680e-05 -3.209981e-05
## [521]  1.189822e-04 -1.491586e-05 -3.479929e-06  9.855379e-06 -3.237669e-05
## [526]  4.179172e-05 -9.386093e-06  2.104483e-05 -7.868031e-06 -5.668465e-05
## [531]  5.333803e-05 -1.950289e-05  4.898532e-05 -1.225084e-05  2.161517e-05
## [536]  4.296777e-05 -2.085477e-05  1.197218e-05  2.563465e-05  2.689240e-05
## [541] -1.735833e-05 -2.308246e-05 -2.465581e-05  1.642829e-05  1.009503e-05
## [546]  4.387779e-06  8.090882e-05 -3.310809e-05 -1.072403e-05  2.615266e-05
## [551] -3.110507e-05  1.224922e-04 -5.230060e-05 -1.759322e-06 -5.896724e-05
## [556]  2.185829e-05  1.853288e-06  3.262657e-05  7.268825e-05  6.114958e-06
## [561] -1.536322e-05  5.299903e-06  5.265080e-05 -4.337299e-05  1.750296e-05
## [566]  6.272218e-05  2.513232e-05 -5.841068e-05  5.186489e-05 -1.185677e-04
## [571]  3.924979e-05  2.642972e-05  2.010947e-05 -1.757381e-05  6.835600e-08
## [576]  6.838615e-08  1.677921e-05  1.487369e-05  2.019149e-06 -1.603740e-06
## [581]  1.846099e-05  8.410148e-06  8.409148e-06 -2.839503e-05  1.421266e-05
## [586]  5.885676e-05 -2.513899e-05 -3.070775e-06 -7.104008e-07  6.217359e-05
## [591]  5.537239e-05  1.203445e-05 -8.306816e-06 -1.012186e-05  2.671953e-05
## [596] -8.131494e-06 -1.236456e-05  6.628019e-05 -5.636708e-06  9.329676e-06
## [601]  3.696300e-05 -7.319684e-05  7.767147e-05 -1.533557e-06  2.507649e-05
## [606] -1.503117e-05 -7.087876e-05  1.962207e-05  2.586997e-05  2.402494e-05
## [611] -2.292032e-05  3.655253e-05 -1.189380e-05 -3.709825e-05  2.939013e-05
## [616]  2.877354e-05  8.394450e-06  5.637851e-08  9.322507e-06  9.837829e-06
## [621]  1.803248e-05 -3.405496e-06 -8.555740e-05  1.100399e-05  3.239440e-05
## [626]  2.508447e-05  5.637849e-08  5.640697e-08  5.643585e-08  5.646523e-08
## [631]  9.329998e-06  2.416891e-05  3.159106e-05  1.860710e-05 -1.674276e-05
## [636] -3.541068e-05 -2.435557e-05 -3.170611e-05  3.418916e-05 -1.464222e-05
## [641] -2.588080e-05  3.417768e-06 -3.542431e-05  2.511614e-05  3.068713e-05
## [646]  6.789762e-06  5.428287e-05 -1.008184e-04  7.116879e-05  2.774461e-05
## [651]  2.522771e-05 -2.749474e-05 -1.887119e-05  1.438438e-05  4.584665e-06
## [656]  8.298300e-06 -1.234857e-05  1.739682e-05  7.355567e-05 -2.763436e-05
## [661]  2.040820e-05 -1.509305e-05  5.547825e-08  5.550649e-08 -4.202992e-05
## [666] -3.361542e-05  5.556002e-08  8.414504e-06  1.782237e-05 -2.607254e-05
## [671]  5.567563e-08  8.417621e-06  6.428282e-05 -5.636876e-06 -1.802827e-06
## [676] -2.937459e-05  4.495912e-05 -1.185940e-07 -1.493274e-05  1.504467e-05
## [681] -1.493371e-05  3.364324e-05  2.870338e-05 -5.474359e-05  3.969288e-05
## [686]  1.185326e-05 -4.208259e-05 -4.208303e-05  4.219736e-05
## 
## $p_mid
##   [1]   3.014057   4.017935   5.021756   6.025520   7.029228   8.032884
##   [7]   9.064350  10.123622  11.154971  12.158389  13.161739  14.165038
##  [13]  15.168280  16.171465  17.174588  18.177659  19.180674  20.183626
##  [19]  21.186510  22.189354  23.192141  24.194860  25.225382  26.283682
##  [25]  27.314083  28.316570  29.318994  30.321367  31.323683  32.325942
##  [31]  33.328144  34.330290  35.332378  36.334393  37.336351  38.338281
##  [37]  39.367974  40.425426  41.454984  42.456658  43.458276  44.459831
##  [43]  45.461340  46.462787  47.464182  48.465521  49.466797  50.245537
##  [49]  51.274480  52.553677  53.582540  54.583515  55.584445  56.585313
##  [55]  57.586123  58.586876  59.587567  60.588202  61.588779  62.589299
##  [61]  63.617552  64.673535  65.701677  66.701970  67.702184  68.702347
##  [67]  69.702458  70.702512  71.702516  72.702462  73.702346  74.729938
##  [73]  75.785242  76.812718  77.812370  78.811958  79.811479  80.783197
##  [79]  81.782620  82.809732  83.809036  84.836037  85.890730  86.917608
##  [85]  87.916679  88.915682  89.914629  90.913523  91.912356  92.911137
##  [91]  93.937589  94.991745  96.018077  97.016603  98.015100  99.013529
##  [97] 100.011895 101.010199 102.008457 103.034382 104.087967 105.113766
## [103] 106.111780 107.109743 108.107643 109.105497 110.103301 111.101013
## [109] 112.126380 113.179416 114.204679 115.202175 116.199615 117.196992
## [115] 118.194312 119.191575 120.216481 121.269019 122.293801 123.290820
## [121] 124.287766 125.284682 126.281564 127.278366 128.275095 129.299463
## [127] 130.351452 131.375689 132.372190 133.368635 134.365022 135.361353
## [133] 136.385297 137.436857 138.460666 139.456747 140.452799 141.448788
## [139] 142.444709 143.440573 144.464038 145.515099 146.538441 147.534066
## [145] 148.529640 149.525146 150.520595 151.543646 152.594271 153.617199
## [151] 154.612421 155.607568 156.602670 157.597715 158.620336 159.670537
## [157] 160.693032 161.687839 162.682599 163.677297 164.671927 165.694123
## [163] 166.743900 167.765980 168.760376 169.754716 170.748993 171.743219
## [169] 172.764998 173.814333 174.836001 175.829994 176.823918 177.817792
## [175] 178.839210 179.888172 180.909468 181.903114 182.896708 183.890217
## [181] 184.911259 185.959859 186.980800 187.974081 188.967300 189.960468
## [187] 190.953590 191.974225 193.022382 194.042896 195.035762 196.028594
## [193] 197.021363 198.041625 199.089415 200.109569 201.102082 202.094550
## [199] 203.086960 204.106873 205.154289 206.174083 207.166254 208.158363
## [205] 209.150421 210.169973 211.216999 212.236426 213.228267 214.220029
## [211] 215.239268 216.286005 217.305133 218.296656 219.288127 220.279536
## [217] 221.298421 222.344784 223.363550 224.354720 225.345832 226.364423
## [223] 227.410474 228.428928 229.419802 230.410618 231.401384 232.419617
## [229] 233.465299 234.483395 235.473910 236.464374 237.482298 238.527669
## [235] 239.545472 240.535702 241.525870 242.543485 243.588545 244.606043
## [241] 245.595978 246.585855 247.603167 248.647910 249.665103 250.654741
## [247] 251.644323 252.661344 253.712645 254.729511 255.711994 256.701296
## [253] 257.718000 258.762130 259.778717 260.767768 261.756763 262.773166
## [259] 263.816973 264.833248 265.822009 266.810718 267.826821 268.870323
## [265] 269.886312 270.874765 271.863162 272.878965 273.922155 274.937836
## [271] 275.925993 276.914093 277.929598 278.972481 279.987859 280.975731
## [277] 281.990976 283.033616 284.048759 285.036381 286.023946 287.038897
## [283] 288.081219 289.096048 290.083385 291.070665 292.085312 293.127318
## [289] 294.141841 295.128882 296.143283 297.185050 298.199332 299.186134
## [295] 300.200289 301.241796 302.255834 303.242402 304.228913 305.242766
## [301] 306.283966 307.297699 308.283971 309.297586 310.338531 311.352008
## [307] 312.338046 313.324032 314.337339 315.377978 316.391160 317.376907
## [313] 318.389968 319.430335 320.443280 321.428794 322.441616 323.481750
## [319] 324.494445 325.479719 326.492285 327.532158 328.544627 329.529656
## [325] 330.541987 331.581616 332.593831 333.578621 334.590704 335.630089
## [331] 336.642057 337.626614 338.638456 339.677587 340.689295 341.673600
## [337] 342.685222 343.724114 344.735588 345.719671 346.731029 347.769655
## [343] 348.780892 349.764730 350.775839 351.814221 352.825207 353.808811
## [349] 354.819694 355.857832 356.868566 357.851920 358.862547 359.900424
## [355] 360.910919 361.894056 362.904446 363.942068 364.952322 365.962514
## [361] 366.999948 368.010026 368.992724 370.002654 371.039856 372.049706
## [367] 373.032182 374.041888 375.078818 376.088403 377.070650 378.080109
## [373] 379.116789 380.126132 381.135406 382.171904 383.181051 384.162848
## [379] 385.171894 386.208154 387.217063 388.225917 389.261973 390.270698
## [385] 391.252107 392.260712 393.296507 394.304992 395.286161 396.294524
## [391] 397.330069 398.338318 399.346494 400.381841 401.389901 402.370649
## [397] 403.378579 404.413687 405.421504 406.429252 407.464162 408.471791
## [403] 409.479351 410.514074 411.521521 412.501664 413.508975 414.543470
## [409] 415.550666 416.557793 417.592084 418.599094 419.578826 420.585717
## [415] 421.619758 422.626526 423.633232 424.667080 425.673658 426.680169
## [421] 427.713830 428.720233 429.699366 430.705641 431.739051 432.745201
## [427] 433.751285 434.784503 435.790473 436.796378 437.829408 438.835194
## [433] 439.840912 440.873733 441.879318 442.857692 443.863176 444.895763
## [439] 445.901122 446.906413 447.938808 448.943977 449.949076 450.981278
## [445] 451.986264 452.991182 454.023197 455.028010 456.032757 457.064567
## [451] 458.069165 459.073715 460.105355 461.109786 462.114154 463.145600
## [457] 464.149843 465.154019 466.185278 467.189343 468.166199 469.170136
## [463] 470.201151 471.204959 472.208703 473.239524 474.243150 475.246706
## [469] 476.277335 477.280783 478.284162 479.314592 480.317848 481.321049
## [475] 482.351291 483.354367 484.357389 485.387438 486.390311 487.393134
## [481] 488.423007 489.425708 490.428342 491.458011 492.487628 493.517183
## [487] 494.519573 495.521899 496.551255 497.553469 498.555611 499.584774
## [493] 500.586796 501.588748 502.617724 503.619565 504.621334 505.650110
## [499] 506.651765 507.653365 508.681960 509.683418 510.684819 511.713231
## [505] 512.741591 513.769857 514.770994 515.772090 516.800174 517.801145
## [511] 518.802057 519.829953 520.830738 521.831455 522.859158 523.859762
## [517] 524.860300 525.887815 526.915283 527.942662 528.942929 529.943157
## [523] 530.970360 531.970468 532.970500 533.997498 534.997415 535.997278
## [529] 537.024099 538.050847 539.077527 540.077145 541.076698 542.103185
## [535] 543.102606 544.101963 545.128267 546.154508 547.180682 548.179788
## [541] 549.178839 550.204825 551.203752 552.202623 553.228416 554.254134
## [547] 555.279808 556.278430 557.276968 558.302442 559.300879 560.299247
## [553] 561.324529 562.349750 563.374912 564.373031 565.371081 566.396044
## [559] 567.420951 568.445778 569.443561 570.441319 571.465981 572.490563
## [565] 573.515083 574.512577 575.510010 576.534341 577.558610 578.582805
## [571] 579.579983 580.577099 581.601113 582.598110 583.595051 584.618871
## [577] 585.642612 586.666301 587.662988 588.659608 589.683110 590.706541
## [583] 591.729906 592.753215 593.776461 594.772707 595.768891 596.791949
## [589] 597.814934 598.837850 599.833795 600.829665 601.852387 602.875057
## [595] 603.897655 604.893283 605.888853 606.911262 607.933603 608.955882
## [601] 609.951199 610.946458 611.968560 612.990576 614.012525 615.034423
## [607] 616.056253 617.051128 618.045942 619.067578 620.089152 621.110674
## [613] 622.132126 623.153501 624.147939 625.142333 626.163536 627.184648
## [619] 628.205693 629.199825 630.193899 631.214767 632.235579 633.256328
## [625] 634.276998 635.297610 636.291306 637.284933 638.305357 639.325708
## [631] 640.345990 641.366229 642.386397 643.406494 644.426532 645.419657
## [637] 646.412725 647.432575 648.452347 649.472054 650.491705 651.511287
## [643] 652.503981 653.496624 654.516029 655.535344 656.554597 657.573805
## [649] 658.592943 659.612015 660.631011 661.623130 662.615204 663.634023
## [655] 664.652775 665.671463 666.690083 667.708646 668.727144 669.745560
## [661] 670.763916 671.782217 672.773655 673.765030 674.783144 675.801184
## [667] 676.819150 677.837059 678.854911 679.872698 680.890419 681.908068
## [673] 682.925664 683.943187 684.960641 685.951268 686.941828 687.959099
## [679] 688.976292 689.993426 691.010512 692.027527 693.044466 694.061350
## [685] 695.078167 696.094931 697.111621 698.128227 699.144790
plot(binSalt, binDepth, ylim = rev(range(binDepth)), xlab = "Salinity (ppt)", ylab = "Depth (m)", type = "l")

###Plot the original profile with the bin average profile
plot(data$sal, data$dep, ylim = rev(range(data$dep)), xlab = "salinity (ppt)", ylab = "depth (m)", col="darkred", lwd = 2, type="l")
points(binSalt, binDepth, col="steelblue", lwd = 2, type = "l")
legend(x=33, y=400, legend=c("bin average", "original"), fill = c(4,2))

plot(data$tem, data$dep, ylim = rev(range(data$dep)), xlab = "temperature (C)", ylab = "depth (m)", col="darkred", lwd = 4, type="l")
points(binTemp, binDepth, col="steelblue", lwd = 2, type = "l")
legend(x=5, y=500, legend=c("bin average", "original"), fill = c(4,2))

###rearranging columns so cast is first
y <- y[,c(6, 1, 2, 3, 4, 5)]

###renaming columns
colnames(y)<-c("cast", "tmax", "d_tmax", "sa_tmax", "lat_tmax", "long_tmax")

###creating datafile of just "y"dataframe
write.csv(y, file = "C:/Users/ingri/MAST467/Data/dat3.csv")
###Using while loop to identify the surfame mixed layer (SML)
sst <-as.numeric(dat2[1,3])
print(sst)
## [1] 7.382222
  i = 2
  while(dat2[i,3]  <= (sst+.2) && dat2[i,3] >= (sst-.2))
{print(dat2[i,3])
    
   
    i = i+1
    
    
}###end loop
## [1] 7.371111
## [1] 7.37
## [1] 7.37
## [1] 7.37
## [1] 7.351111
## [1] 7.338889
## [1] 7.326
## [1] 7.314444
## [1] 7.285556
## [1] 7.27
## [1] 7.264444
## [1] 7.25
## [1] 7.237778
## [1] 7.211111
## [1] 7.186667
  print(i)
## [1] 17
  z_SML <- binDepth[12]
  print(z_SML)
## [1] 13
###calculate the mean value and standard deviation of potential temperature and absolute salinity 
  mean(pt_2[1:z_SML])
## [1] 7.378979
  sd(pt_2[1:z_SML])
## [1] 0.007628234
  mean(SA_2[1:z_SML])
## [1] 32.9982
  sd(SA_2[1:z_SML])
## [1] 0.04057656
plot(binpt_2, binDepth, ylim = rev(range(binDepth)), xlab = "potential temperature (C)", ylab = "depth (m)", col="black", lwd = 2, type="l")
points(binpt_2[z_SML], binDepth[z_SML], col = "red", lwd=2, pch = 20)

plot(binSA_2, binDepth, ylim = rev(range(binDepth)), xlab = "Absolute Salinity (ppt)", ylab = "depth (m)", col="black", lwd = 2, type="l")
points(binSA_2[z_SML], binDepth[z_SML], col = "red", lwd=2, pch = 20)

```