Regionalisation of the Environment
Markus Diesing
- Packages
- Loading the layerstack
- Normalise raster layers prior to PCA. Performs normalisation (scaling) and centering, i.e. divide by standard deviation
- kmeans classification (https://www.rdocumentation.org/packages/RStoolbox/versions/0.2.3/topics/unsuperclass)
- Export Geotiff
- Boxplots
- Figure for publication
Packages
library("raster") ## Loading required package: splibrary("RStoolbox")## Warning: package 'RStoolbox' was built under R version 3.6.3library("ggplot2")
library("gridExtra")## Warning: package 'gridExtra' was built under R version 3.6.3library("ggpubr")## Warning: package 'ggpubr' was built under R version 3.6.3## Loading required package: magrittr##
## Attaching package: 'magrittr'## The following object is masked from 'package:raster':
##
## extract##
## Attaching package: 'ggpubr'## The following object is masked from 'package:raster':
##
## rotatelibrary("rgdal")## rgdal: version: 1.4-7, (SVN revision 845)
## Geospatial Data Abstraction Library extensions to R successfully loaded
## Loaded GDAL runtime: GDAL 2.2.3, released 2017/11/20
## Path to GDAL shared files: C:/Users/diesing_markus/Documents/R/R-3.6.1/library/rgdal/gdal
## GDAL binary built with GEOS: TRUE
## Loaded PROJ.4 runtime: Rel. 4.9.3, 15 August 2016, [PJ_VERSION: 493]
## Path to PROJ.4 shared files: C:/Users/diesing_markus/Documents/R/R-3.6.1/library/rgdal/proj
## Linking to sp version: 1.3-2Loading the layerstack
vars <- stack(list.files(path="../input", pattern='.tif$', full.names=T),RAT=F)
names(vars) <- c("Bathymetry", "Current speed", "OCAR", "OC density", "OPD", "Orb Velocity")
vars## class : RasterStack
## dimensions : 2686, 2559, 6873474, 6 (nrow, ncol, ncell, nlayers)
## resolution : 500, 500 (x, y)
## extent : 3230952, 4510452, 3023466, 4366466 (xmin, xmax, ymin, ymax)
## crs : +proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## names : Bathymetry, Current.speed, OCAR, OC.density, OPD, Orb.Velocity
## min values : -857.74938965, 0.00000000, 0.01553161, 1.15797031, 0.93182999, 0.00000000
## max values : 50.689999, 2.025045, 66.181312, 13.595368, 2.928485, 2.764714plot(vars)
Normalise raster layers prior to PCA. Performs normalisation (scaling) and centering, i.e. divide by standard deviation
vars.norm <- normImage(vars, norm = TRUE)
vars.norm## class : RasterBrick
## dimensions : 2686, 2559, 6873474, 6 (nrow, ncol, ncell, nlayers)
## resolution : 500, 500 (x, y)
## extent : 3230952, 4510452, 3023466, 4366466 (xmin, xmax, ymin, ymax)
## crs : +proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : Bathymetry, Current.speed, OCAR, OC.density, OPD, Orb.Velocity
## min values : -8.8266827, -1.2770513, -0.3782746, -1.3081598, -1.2606624, -1.3171126
## max values : 1.581071, 11.282040, 9.006722, 3.706218, 1.590953, 8.828313hist(vars.norm)
Run PCA (https://www.rdocumentation.org/packages/RStoolbox/versions/0.2.3/topics/rasterPCA)
set.seed(25)
rpc <- rasterPCA(vars.norm, nSamples = NULL, nComp = nlayers(vars.norm), spca = TRUE, maskCheck = TRUE)
rpc## $call
## rasterPCA(img = vars.norm, nSamples = NULL, nComp = nlayers(vars.norm),
## spca = TRUE, maskCheck = TRUE)
##
## $model
## Call:
## princomp(cor = spca, covmat = covMat[[1]])
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## 1.9554992 0.8714080 0.8033553 0.7099885 0.4073997 0.3181713
##
## 6 variables and 6873474 observations.
##
## $map
## class : RasterBrick
## dimensions : 2686, 2559, 6873474, 6 (nrow, ncol, ncell, nlayers)
## resolution : 500, 500 (x, y)
## extent : 3230952, 4510452, 3023466, 4366466 (xmin, xmax, ymin, ymax)
## crs : +proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : PC1, PC2, PC3, PC4, PC5, PC6
## min values : -8.756754, -9.738404, -5.617817, -2.021233, -4.226620, -2.395745
## max values : 5.620377, 3.758767, 1.541429, 4.243877, 4.101794, 2.037000
##
##
## attr(,"class")
## [1] "rasterPCA" "RStoolbox"summary(rpc$model)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.9554992 0.8714080 0.8033553 0.70998845 0.40739969
## Proportion of Variance 0.6373295 0.1265587 0.1075633 0.08401393 0.02766242
## Cumulative Proportion 0.6373295 0.7638882 0.8714515 0.95546542 0.98312784
## Comp.6
## Standard deviation 0.31817128
## Proportion of Variance 0.01687216
## Cumulative Proportion 1.00000000hist(rpc$map)
plot(rpc$map)
ggRGB(rpc$map,1,2,3, stretch="lin", q=0)
Specify number of PCs to be used
n.pc <- 4kmeans classification (https://www.rdocumentation.org/packages/RStoolbox/versions/0.2.3/topics/unsuperclass)
Specify the maximum number of clusters to be analysed
max_cl <- 20How many clusters?
df_total <- data.frame()
for (i in 1:max_cl) {
set.seed(25)
unC <- unsuperClass(rpc$map[[1:n.pc]], nSamples = 4000, nClasses = i, nStarts = 100,
norm = FALSE, clusterMap = TRUE, algorithm = "Hartigan-Wong")
stat <- 100*(unC[["model"]][["betweenss"]]/unC[["model"]][["totss"]])
df <- data.frame(i,stat)
df_total <- rbind(df_total,df)
}Plot graph
ggplot(df_total,aes(i,stat)) + geom_bar(stat = "identity") +
xlab("Number of clusters") + ylab("between sum of squares/total sum of squares ") +
scale_x_continuous(breaks = c(1:max_cl))
Specify the number of clusters to be used (based on graph above)
n.cl <- 3Run k-means clustering
set.seed(25)
unC <- unsuperClass(rpc$map[[1:n.pc]], nSamples = 10000, nClasses = n.cl, nStarts = 100,
norm = FALSE, clusterMap = TRUE, algorithm = "Hartigan-Wong")
unC## unsuperClass results
##
## *************** Map ******************
## $map
## class : RasterLayer
## dimensions : 2686, 2559, 6873474 (nrow, ncol, ncell)
## resolution : 500, 500 (x, y)
## extent : 3230952, 4510452, 3023466, 4366466 (xmin, xmax, ymin, ymax)
## crs : +proj=laea +lat_0=52 +lon_0=10 +x_0=4321000 +y_0=3210000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : layer
## values : 1, 3 (min, max)unC$model## K-means clustering with 3 clusters of sizes 4401, 4543, 1056
##
## Cluster means:
## PC1 PC2 PC3 PC4
## 1 -0.4722387 0.1900850 0.6077706 -0.031614993
## 2 1.5152840 -0.1132621 -0.3727417 -0.008600807
## 3 -4.4595705 -0.3890747 -0.9077637 0.155511737
##
## Clustering vector:
## [1] 1 1 1 2 1 1 1 3 1 3 1 1 2 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 2 1 2 1 1 3 1 3
## [37] 2 1 1 2 1 3 1 1 1 1 2 2 1 2 1 2 2 2 2 1 1 2 1 2 1 3 1 2 1 1 2 2 1 3 2 1
## [73] 1 2 3 2 2 1 1 3 1 3 1 1 2 1 1 2 1 2 2 1 1 1 3 2 1 2 1 1 2 1 2 2 3 1 1 2
## [109] 2 1 2 2 1 1 1 2 2 2 1 3 1 1 2 3 2 2 1 2 2 2 1 2 1 2 2 1 2 2 1 2 2 2 3 1
## [145] 2 2 1 1 2 2 1 2 2 1 1 2 1 1 1 2 2 1 1 2 1 2 1 3 1 2 1 1 2 2 2 2 1 2 1 1
## [181] 2 3 2 1 1 2 2 2 1 2 2 1 1 2 1 2 2 1 1 1 1 2 3 1 1 2 1 3 2 3 3 2 1 2 1 2
## [217] 3 2 3 2 1 1 1 2 2 2 2 1 2 1 3 1 2 1 2 1 1 2 1 3 1 1 1 2 1 3 2 3 2 3 1 2
## [253] 2 1 1 1 2 2 2 1 1 2 1 1 3 2 3 2 1 2 1 1 2 2 1 2 3 2 2 2 1 2 2 2 2 2 1 2
## [289] 1 1 3 3 1 1 1 1 2 2 3 2 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 2 3 1 3 1 1 2 1 2
## [325] 1 1 1 2 1 3 3 1 1 2 1 1 1 2 2 1 2 3 2 2 3 1 2 2 1 2 1 1 1 2 2 1 2 1 1 1
## [361] 2 1 2 2 3 2 2 1 2 2 2 2 2 2 3 1 2 1 1 1 2 2 2 2 1 2 1 2 2 1 1 1 2 1 1 1
## [397] 3 1 3 1 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 1 3 2 1 1 1 2 1 1 2 2 2 1 2 2
## [433] 1 1 2 1 2 2 2 2 2 1 1 1 3 1 3 1 1 1 1 1 1 1 2 2 2 2 2 1 1 3 1 1 2 2 1 1
## [469] 3 1 1 2 2 1 2 1 1 2 2 1 2 2 2 1 1 2 2 2 2 2 1 2 3 1 2 2 2 3 3 1 3 2 1 2
## [505] 1 2 3 2 1 2 1 1 1 1 1 1 2 2 2 2 1 2 1 2 2 1 3 1 3 2 1 1 1 2 2 2 3 3 2 3
## [541] 1 1 2 1 1 1 1 2 1 3 1 1 1 1 2 2 2 1 3 2 1 2 1 1 1 2 1 1 1 2 3 2 2 2 2 1
## [577] 2 1 2 1 2 2 1 2 1 1 2 1 2 2 2 2 2 1 1 2 2 3 2 1 3 1 2 1 2 2 1 1 3 1 3 2
## [613] 1 1 1 1 1 2 1 2 1 3 1 1 2 2 1 2 2 3 2 1 1 2 2 1 1 2 1 3 2 2 2 3 2 1 1 1
## [649] 1 1 2 2 2 2 1 2 1 1 1 1 1 1 1 2 2 2 1 2 2 2 2 2 2 3 1 1 1 1 3 1 2 1 1 1
## [685] 1 2 2 2 2 2 1 2 2 2 1 1 1 1 1 1 2 1 1 2 2 3 3 1 1 1 1 2 1 2 2 2 2 1 1 1
## [721] 1 2 2 3 1 2 2 1 2 2 3 1 2 1 1 1 3 2 2 2 2 1 2 3 2 2 2 1 2 1 1 1 2 2 2 1
## [757] 1 1 1 1 1 1 1 1 1 2 1 2 3 1 1 2 2 2 2 3 2 1 2 2 1 1 1 2 3 1 1 2 1 2 3 1
## [793] 2 3 1 1 2 2 2 1 2 1 1 2 1 2 2 1 1 2 1 2 3 1 2 1 1 1 2 1 1 1 2 1 1 1 2 2
## [829] 3 1 1 1 2 2 1 3 1 3 1 1 1 2 2 2 1 1 3 2 2 1 1 1 2 2 1 1 2 2 2 1 1 1 1 1
## [865] 1 1 2 2 1 1 1 2 1 2 1 2 2 2 1 3 2 1 1 1 2 2 1 1 2 1 2 2 2 1 3 2 2 1 2 1
## [901] 2 2 3 1 1 2 3 1 1 2 2 2 2 1 1 1 3 1 2 1 1 3 3 1 2 3 2 2 1 1 1 1 1 1 1 1
## [937] 2 2 1 3 1 2 2 3 2 2 2 2 2 1 1 2 1 1 2 2 3 1 1 1 3 2 1 2 2 2 2 2 1 1 2 2
## [973] 2 2 2 1 2 2 2 1 1 1 1 2 1 3 1 1 1 1 1 1 3 2 2 1 2 2 1 1 2 1 2 1 3 2 1 3
## [1009] 2 2 3 2 2 2 1 1 1 1 2 2 1 2 3 2 1 3 1 3 1 1 1 2 1 2 1 2 1 3 2 2 2 1 2 1
## [1045] 1 2 1 2 1 2 3 2 1 2 1 2 1 1 2 2 2 2 1 2 2 3 1 1 2 3 1 2 2 2 3 1 2 1 2 2
## [1081] 2 2 3 1 2 2 2 1 1 1 3 3 2 1 1 3 2 2 3 2 1 1 1 2 1 2 1 3 1 2 1 1 2 1 2 2
## [1117] 1 1 1 1 1 1 1 1 2 3 2 1 2 1 3 2 1 2 2 2 2 2 1 2 1 1 1 3 1 2 2 3 1 2 2 1
## [1153] 1 1 2 2 1 1 2 2 3 1 2 2 2 1 1 1 2 1 1 2 1 1 2 2 2 2 2 1 2 1 1 2 2 1 3 1
## [1189] 2 2 3 3 1 2 2 2 2 1 2 1 2 2 2 2 2 3 2 2 1 1 2 2 2 2 1 2 1 2 1 2 1 2 3 3
## [1225] 2 1 1 2 1 3 1 1 2 1 2 1 3 2 2 2 1 1 2 2 2 2 1 2 1 2 2 2 1 2 2 2 2 1 1 2
## [1261] 2 2 2 2 2 2 1 1 2 1 1 2 2 1 2 1 3 2 3 1 1 1 2 2 2 1 1 3 1 2 1 2 2 1 2 2
## [1297] 2 3 2 2 1 2 1 2 1 1 2 2 1 2 3 1 2 1 2 2 2 1 3 2 2 2 2 3 1 2 2 1 2 3 1 1
## [1333] 3 2 1 2 1 1 2 2 2 1 1 1 1 2 2 2 2 2 1 1 1 2 2 1 1 3 2 2 2 3 2 1 2 3 3 1
## [1369] 1 1 2 2 2 1 1 1 2 2 2 2 2 3 1 2 2 1 2 1 1 2 2 2 2 2 1 2 2 1 2 2 2 3 3 1
## [1405] 1 1 2 2 1 2 1 2 1 2 2 1 2 2 1 2 2 1 1 2 2 1 2 1 1 2 1 1 1 1 2 2 1 1 1 1
## [1441] 2 2 1 1 2 1 2 2 3 2 1 1 1 2 1 2 1 2 3 2 2 2 1 1 1 1 1 3 1 2 3 2 1 2 2 1
## [1477] 1 2 3 2 3 1 2 2 2 1 2 2 2 1 2 1 2 2 1 2 2 2 2 2 1 3 2 1 2 2 2 1 2 1 1 3
## [1513] 3 2 2 2 2 1 1 2 1 2 2 1 1 1 2 1 3 2 1 1 1 2 2 2 1 1 1 3 2 1 1 2 2 2 1 2
## [1549] 1 1 2 1 2 1 2 2 2 2 2 2 1 1 1 1 2 3 1 2 2 3 2 3 2 2 2 2 1 2 2 1 1 3 1 3
## [1585] 1 1 2 2 2 2 2 1 1 1 1 2 1 1 2 1 3 1 3 1 2 1 1 2 2 1 2 1 1 1 2 2 1 3 2 2
## [1621] 2 1 1 2 1 1 2 1 1 2 2 1 2 2 2 1 3 1 3 1 2 2 1 2 2 2 2 2 3 2 1 2 3 2 1 2
## [1657] 2 2 1 1 1 1 2 1 2 1 2 2 2 1 2 2 3 2 1 1 2 2 3 2 2 3 2 2 1 1 1 1 1 1 2 1
## [1693] 2 1 2 1 2 2 1 1 1 1 2 3 1 2 3 1 1 1 2 3 3 2 2 1 3 2 2 1 2 2 2 2 2 2 1 2
## [1729] 1 1 2 1 1 2 2 1 2 1 2 1 2 1 1 3 2 1 1 1 1 2 2 1 1 2 2 1 3 1 2 1 1 1 2 2
## [1765] 1 2 1 2 2 1 1 1 1 2 2 2 1 2 1 3 2 2 1 1 1 1 1 2 2 2 2 1 2 2 2 1 2 2 1 3
## [1801] 2 1 2 1 2 2 1 2 1 2 2 1 2 1 1 1 2 1 2 1 1 2 2 2 1 2 2 2 1 1 2 1 1 2 1 2
## [1837] 1 1 3 1 2 2 1 3 1 1 2 1 1 1 2 1 2 1 1 1 2 2 1 1 1 1 2 1 1 1 2 2 1 1 1 3
## [1873] 1 2 1 2 1 2 2 2 2 3 2 1 1 2 1 3 2 3 2 2 1 3 1 1 2 1 1 1 1 1 1 3 3 1 2 1
## [1909] 1 2 2 2 2 1 1 1 1 2 1 2 2 2 1 1 2 2 2 3 2 2 2 1 2 2 2 2 3 1 1 2 1 2 3 1
## [1945] 2 2 2 3 2 2 1 1 2 3 3 1 1 2 1 2 1 1 1 1 2 2 2 1 2 1 2 2 2 2 3 2 2 3 3 2
## [1981] 1 2 1 2 2 2 2 2 2 2 3 1 3 1 1 2 1 1 1 1 2 1 2 2 2 1 1 1 3 1 2 2 2 3 1 1
## [2017] 2 2 1 1 1 1 2 1 2 3 2 2 2 2 1 3 1 1 3 2 1 1 3 2 1 3 2 2 2 1 1 2 2 1 3 2
## [2053] 1 3 1 1 1 1 2 1 1 3 1 1 2 1 3 2 2 2 2 2 2 1 2 2 3 1 2 2 2 1 2 2 2 2 2 2
## [2089] 1 2 3 2 2 1 3 2 2 1 1 1 1 1 1 3 1 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2
## [2125] 1 1 2 1 1 1 2 2 1 2 3 1 1 2 3 1 1 3 3 3 1 2 1 2 3 2 1 1 1 1 2 3 1 2 3 2
## [2161] 2 2 2 2 1 2 1 3 2 3 2 1 3 2 1 1 1 1 2 2 1 3 3 1 1 1 1 3 1 1 1 2 1 1 3 2
## [2197] 1 2 1 2 1 1 1 3 1 1 2 1 1 3 1 3 2 1 3 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 1 2
## [2233] 2 1 2 1 2 1 1 1 2 2 1 2 1 2 2 1 2 1 1 3 3 2 2 3 1 2 2 3 2 2 3 2 1 1 1 2
## [2269] 1 2 2 1 2 1 1 2 1 3 1 2 1 1 2 3 2 1 1 3 1 1 1 3 3 3 1 1 1 2 3 1 1 1 2 2
## [2305] 1 1 1 2 2 2 1 3 1 2 2 2 2 2 1 1 1 2 2 1 1 3 1 2 2 1 2 2 3 1 1 2 3 1 1 2
## [2341] 2 1 1 1 2 1 1 1 1 2 2 1 2 2 1 2 1 3 3 2 1 2 1 2 1 3 2 1 1 3 3 2 1 1 3 1
## [2377] 3 1 2 1 2 1 1 1 1 2 1 2 2 3 2 1 1 2 1 2 1 1 2 1 2 1 1 2 3 1 1 2 1 2 1 2
## [2413] 2 2 1 3 2 2 1 2 1 2 2 2 2 2 3 2 1 3 1 1 2 1 2 2 1 2 1 1 1 2 2 1 2 1 1 2
## [2449] 1 2 1 2 1 2 1 1 2 2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 1 2
## [2485] 2 3 2 1 1 2 2 2 1 2 2 1 1 1 1 2 1 2 3 1 2 2 2 2 2 2 1 1 2 1 1 2 1 1 2 1
## [2521] 2 1 1 1 1 2 3 1 2 3 2 2 2 1 3 1 1 2 1 2 1 1 2 2 2 2 2 2 1 2 1 2 2 1 3 2
## [2557] 3 2 2 3 1 2 2 1 2 3 2 1 2 2 1 1 2 1 2 2 2 2 1 2 1 3 1 1 1 1 2 1 2 3 1 1
## [2593] 3 2 2 2 2 1 2 1 3 3 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 3 1 2 3
## [2629] 2 2 3 2 1 2 2 1 1 2 2 2 2 3 2 1 2 1 2 1 2 1 2 2 2 3 3 1 1 2 1 1 1 2 1 1
## [2665] 1 1 2 2 2 1 1 3 1 2 3 2 2 2 2 2 2 1 2 3 2 3 2 3 1 3 2 1 2 1 3 1 2 1 2 2
## [2701] 2 1 2 2 2 2 2 1 2 1 2 2 1 2 3 1 3 3 2 1 1 2 1 1 1 2 1 3 1 1 1 3 1 3 2 1
## [2737] 1 1 1 1 2 3 3 1 1 2 2 1 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 1 1 2 2 3 2 1 2 3
## [2773] 2 1 1 2 2 1 2 2 1 1 1 1 2 2 1 1 2 1 2 2 2 1 3 1 2 2 2 2 2 2 2 1 1 2 2 3
## [2809] 2 1 2 2 1 2 1 2 2 2 2 3 1 2 2 1 2 3 1 2 2 3 2 1 2 2 1 1 2 1 1 3 2 1 2 2
## [2845] 1 1 1 1 1 2 2 1 2 2 3 1 2 2 2 1 1 1 2 2 1 2 1 2 1 1 2 1 2 2 1 2 1 1 2 1
## [2881] 1 1 2 2 1 2 1 2 1 2 1 2 1 1 3 1 2 2 1 2 1 2 2 1 1 2 1 3 3 1 3 3 1 1 3 2
## [2917] 1 3 2 3 2 2 1 2 1 1 2 1 2 1 1 1 2 2 1 1 2 2 2 2 1 1 1 1 1 2 1 1 2 1 1 1
## [2953] 1 3 1 2 1 1 3 1 3 2 1 2 1 1 2 2 1 1 2 1 2 1 2 3 2 3 3 2 2 2 2 2 2 2 2 2
## [2989] 1 1 1 1 1 3 1 2 2 1 2 1 2 1 2 3 1 2 2 2 2 1 1 2 3 1 1 1 2 2 2 2 2 1 2 2
## [3025] 1 2 1 2 2 2 1 2 1 1 1 1 1 2 2 1 2 1 2 1 1 2 1 3 2 1 1 1 1 1 3 2 3 1 3 2
## [3061] 1 2 1 3 1 3 2 1 1 2 3 1 2 1 2 2 2 1 1 1 1 2 2 2 1 3 1 1 2 1 3 1 2 1 2 2
## [3097] 3 2 3 3 1 1 1 1 3 2 1 1 1 1 1 2 1 2 2 2 3 1 2 2 2 3 1 2 1 2 2 1 1 2 2 2
## [3133] 1 3 1 1 3 2 1 2 2 1 1 1 2 2 3 2 2 1 1 1 2 1 3 1 2 1 3 1 2 2 2 2 2 1 1 1
## [3169] 2 3 1 3 1 2 1 3 1 1 1 2 3 2 2 1 1 2 1 1 3 1 1 2 2 3 1 2 1 1 1 2 1 3 1 1
## [3205] 1 1 2 2 2 1 2 1 1 2 2 2 1 1 2 2 2 1 2 2 1 1 1 2 1 3 1 1 2 2 2 1 1 2 2 3
## [3241] 2 1 1 1 2 1 3 3 2 3 2 1 1 2 1 2 1 1 2 2 2 1 1 2 2 3 1 1 2 2 2 1 1 2 1 2
## [3277] 2 1 1 1 1 1 1 3 1 2 2 2 2 1 1 1 1 2 2 1 2 1 3 1 2 2 2 2 2 1 2 3 2 1 1 3
## [3313] 3 2 1 2 1 1 1 1 3 2 1 2 2 1 1 3 2 1 1 1 1 2 2 3 1 1 2 1 1 3 1 3 2 2 2 2
## [3349] 2 1 2 2 2 1 1 1 2 2 1 3 3 1 2 2 2 2 2 1 2 2 1 2 3 1 1 1 1 2 2 2 2 2 2 2
## [3385] 2 2 2 2 1 2 2 1 2 2 2 2 1 1 2 2 2 2 1 2 2 2 1 3 2 1 1 1 1 1 1 3 2 2 3 1
## [3421] 1 1 3 1 3 3 2 2 2 2 2 1 1 1 1 2 2 2 1 1 2 3 1 3 1 2 2 1 2 1 2 1 2 2 1 2
## [3457] 2 1 1 1 1 1 2 3 3 2 1 3 2 2 2 1 2 1 1 1 3 2 2 1 2 2 1 2 1 2 2 1 2 1 2 1
## [3493] 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 1 3 2 2 2 1 2 1 2 2 1 3 1 2 1 2 3 1 1 2
## [3529] 1 1 2 2 2 1 2 1 1 2 1 1 2 2 1 1 2 2 1 1 3 1 1 1 2 1 3 1 1 1 2 2 2 1 1 2
## [3565] 2 1 1 2 2 2 1 1 3 1 1 2 1 2 2 2 1 1 2 2 2 1 2 1 2 2 2 3 1 2 1 2 1 1 1 1
## [3601] 2 3 2 1 2 2 1 2 2 1 2 2 1 2 2 3 2 1 1 1 2 2 1 2 1 2 1 1 2 1 1 2 2 3 1 1
## [3637] 2 3 2 2 2 1 2 3 2 1 1 2 1 2 2 2 2 1 1 2 1 1 3 2 2 3 2 2 1 1 1 2 1 2 2 2
## [3673] 1 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 1 1 3 2 2 2 2 2 3 1 2 2 2 2 1 2
## [3709] 1 2 1 3 1 2 2 1 2 1 2 2 2 2 2 3 1 1 1 1 3 1 1 1 3 2 2 2 1 1 1 1 2 1 1 1
## [3745] 2 1 1 1 2 1 2 1 1 2 2 2 2 1 1 1 2 2 2 1 2 3 2 1 1 3 2 3 1 1 2 2 2 1 1 1
## [3781] 1 1 1 1 2 3 1 2 1 3 2 3 1 2 1 2 3 2 2 2 1 2 2 3 2 1 1 1 1 1 2 3 2 1 3 2
## [3817] 3 1 2 1 2 1 2 2 2 1 2 1 2 1 1 2 3 2 1 1 1 1 2 2 1 2 1 1 1 2 1 1 1 2 2 2
## [3853] 1 3 3 1 2 2 1 1 2 3 2 2 1 2 2 3 1 1 2 2 1 1 1 1 1 2 2 2 1 3 1 2 3 1 2 2
## [3889] 1 1 2 2 1 1 2 3 3 3 2 1 2 2 1 1 1 2 3 2 2 3 1 3 1 2 1 1 1 2 2 2 1 2 2 3
## [3925] 2 1 2 2 2 2 1 1 1 2 1 2 1 2 1 2 2 2 1 2 1 2 1 1 3 1 1 2 1 1 1 1 1 1 1 1
## [3961] 3 2 2 2 2 1 2 3 2 2 2 1 1 1 2 3 2 2 2 2 2 1 1 1 2 1 2 2 2 1 1 2 1 1 2 1
## [3997] 2 2 2 2 3 2 2 1 1 1 2 1 1 2 3 1 2 2 1 1 2 1 2 2 2 2 1 2 2 1 1 3 2 1 2 1
## [4033] 2 1 2 2 3 1 2 2 1 2 1 1 2 1 2 1 1 1 3 2 1 2 2 1 2 2 1 1 1 1 1 2 2 1 1 2
## [4069] 1 1 2 2 1 2 2 2 1 3 2 1 3 2 2 2 1 2 2 3 1 2 2 2 1 2 2 1 1 2 1 2 3 2 2 1
## [4105] 2 2 2 1 2 2 1 2 2 1 1 1 1 2 1 2 2 2 3 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 2 1
## [4141] 2 1 3 1 2 1 1 3 2 1 1 1 1 2 2 2 2 2 2 3 1 3 3 1 2 2 3 1 2 1 1 1 2 1 2 1
## [4177] 2 1 1 2 2 3 2 2 2 3 1 1 2 2 2 1 1 2 2 1 2 2 3 1 1 2 2 1 2 2 1 1 2 2 2 3
## [4213] 1 2 2 3 2 1 2 2 1 2 1 1 1 2 2 1 1 1 1 2 1 1 2 1 2 1 1 1 2 2 1 3 2 2 2 1
## [4249] 2 1 3 2 1 1 1 3 2 2 2 1 2 1 1 2 2 1 1 1 1 1 1 1 2 3 1 2 1 3 2 1 2 2 1 1
## [4285] 2 1 2 2 2 1 1 1 2 2 2 1 2 2 1 2 1 2 3 2 1 1 2 1 2 1 1 1 2 2 3 2 2 1 2 2
## [4321] 1 2 2 3 2 2 1 1 2 2 1 1 2 1 2 1 1 1 2 2 1 2 1 2 1 2 1 1 2 3 2 1 2 2 2 1
## [4357] 2 3 2 1 2 1 3 1 3 2 2 1 1 2 1 1 1 2 1 2 2 1 1 1 1 1 1 2 2 2 1 1 2 1 2 2
## [4393] 2 1 2 2 3 2 2 1 2 1 3 1 1 1 2 2 2 3 1 2 2 1 2 1 1 2 2 2 1 2 2 1 3 2 2 3
## [4429] 2 1 2 1 1 1 2 2 2 2 1 1 2 2 2 2 1 3 2 2 1 2 1 2 3 1 2 1 1 3 3 2 2 2 1 3
## [4465] 2 2 1 2 1 2 2 1 2 1 2 1 1 1 3 2 1 1 2 1 1 1 1 2 2 1 2 2 1 1 3 2 2 1 1 2
## [4501] 2 2 2 2 1 2 1 2 2 1 1 1 2 2 1 3 1 3 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 1 3 1
## [4537] 1 2 1 2 2 1 2 1 2 3 3 2 2 1 1 1 3 2 2 2 3 1 1 2 1 2 2 1 2 2 1 2 1 1 2 1
## [4573] 1 2 2 2 3 1 2 1 2 3 2 1 1 2 2 2 1 1 2 2 1 1 3 1 2 2 1 1 2 2 2 2 1 1 1 1
## [4609] 1 2 1 2 2 1 3 1 2 1 2 1 2 1 3 2 1 1 2 1 3 1 1 2 3 2 3 2 2 2 1 2 1 2 1 2
## [4645] 1 1 2 2 2 1 1 2 2 2 1 3 1 1 2 2 2 1 1 1 1 1 3 3 3 1 2 1 2 1 1 1 1 3 2 2
## [4681] 2 2 1 1 1 2 1 3 1 1 1 1 2 3 1 1 1 2 3 1 3 2 2 1 1 2 3 1 1 2 1 1 2 1 2 2
## [4717] 2 2 1 1 2 2 3 1 1 1 2 2 2 1 3 2 2 2 3 1 1 1 1 1 1 2 3 2 2 1 1 1 1 2 1 1
## [4753] 1 2 2 2 2 3 3 2 3 1 2 2 1 2 2 3 1 2 2 1 2 2 1 1 2 2 3 2 2 2 2 2 2 2 2 1
## [4789] 3 1 1 1 1 2 1 3 2 1 1 1 3 2 2 1 3 1 1 2 2 1 1 2 1 2 3 2 2 3 2 3 1 2 3 1
## [4825] 1 1 2 1 2 3 2 3 3 1 2 2 1 1 3 2 2 3 2 1 2 3 2 1 2 2 2 3 2 3 2 2 1 1 3 1
## [4861] 2 1 2 1 1 1 2 2 3 3 2 1 1 1 3 1 1 2 1 1 2 2 2 1 1 2 2 2 2 2 2 1 2 2 2 1
## [4897] 1 1 2 1 2 1 2 2 1 1 2 2 1 2 1 2 2 2 1 1 2 1 3 3 1 2 2 1 1 1 2 3 1 1 1 1
## [4933] 1 1 2 2 1 2 2 2 1 1 2 1 2 3 3 1 2 2 1 2 1 3 1 1 1 2 3 2 1 1 1 2 2 2 2 2
## [4969] 1 1 1 2 2 1 2 2 2 2 1 1 2 1 3 3 2 2 3 1 2 1 1 2 1 2 1 1 1 2 2 2 1 1 2 2
## [5005] 1 2 1 3 2 2 2 1 1 1 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 1 1 2 1 1 2 2 3 2 2
## [5041] 2 2 2 2 2 1 2 1 1 1 1 2 1 1 1 1 3 1 1 1 2 2 1 1 1 1 2 1 1 1 2 1 2 2 2 1
## [5077] 3 3 1 2 2 1 1 3 1 1 1 2 2 1 2 1 2 1 1 2 2 2 3 2 2 1 2 2 1 2 1 1 2 2 2 2
## [5113] 1 2 3 3 1 3 1 2 2 2 2 1 2 2 1 2 2 2 1 1 1 1 1 2 2 3 1 2 2 2 2 1 1 3 1 1
## [5149] 1 1 1 3 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 3 3 2 2 1 2 2 1 2 2 1 1 1 2
## [5185] 1 3 2 1 1 1 1 1 1 1 2 2 2 2 1 2 1 1 3 1 1 2 1 2 1 3 2 2 2 3 2 1 2 1 2 1
## [5221] 3 3 2 3 1 1 3 1 1 2 2 3 3 1 1 3 1 1 3 2 1 1 2 2 3 2 2 2 2 2 3 2 1 2 2 3
## [5257] 1 2 1 1 1 2 2 2 2 2 3 1 2 2 2 1 1 2 3 3 2 2 2 1 2 2 2 2 2 2 2 1 2 1 3 1
## [5293] 2 2 3 1 2 1 2 2 1 2 2 1 2 2 1 3 1 1 1 2 1 2 1 1 2 1 2 2 2 1 1 1 2 3 2 1
## [5329] 1 2 2 1 2 1 1 2 1 1 1 2 3 2 1 3 1 2 2 2 2 2 1 2 2 1 2 3 1 1 1 2 1 2 1 1
## [5365] 2 3 3 1 1 1 2 2 1 1 1 1 1 1 1 3 2 3 2 1 3 2 3 1 1 1 2 1 3 1 1 1 2 1 2 2
## [5401] 2 3 2 1 1 2 2 3 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2 3 1 1 1 1 2 2 3 2 1 2 1 2
## [5437] 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 1 2 2 3 1 1 2 2 2 2 2 2 1 1 1 1 3 2 1
## [5473] 2 1 1 2 1 2 1 1 2 1 2 2 1 3 2 2 2 1 2 2 1 2 2 1 2 2 1 1 2 1 2 2 1 2 1 1
## [5509] 2 1 1 1 1 1 1 2 1 1 2 1 1 3 2 2 3 3 3 1 2 1 1 2 3 1 1 2 1 1 2 2 2 3 2 1
## [5545] 1 2 1 1 1 2 3 1 2 2 2 3 1 1 1 1 2 2 2 1 2 2 2 2 2 3 1 1 1 3 2 1 1 2 1 2
## [5581] 3 1 1 2 2 2 1 2 2 1 2 2 2 1 1 1 1 1 1 1 1 1 3 1 1 2 1 1 3 1 2 2 2 2 1 1
## [5617] 2 1 2 1 1 2 1 1 2 2 2 1 2 1 1 1 2 3 3 2 2 2 1 2 2 2 2 1 2 1 2 1 2 1 2 1
## [5653] 3 2 2 1 1 1 1 2 1 1 2 1 1 2 2 2 1 2 1 2 2 1 2 1 1 3 3 1 1 1 2 1 1 2 1 1
## [5689] 2 1 3 2 1 2 3 1 1 2 3 1 2 1 2 1 2 3 1 1 1 2 2 3 2 1 2 2 2 2 2 2 1 2 3 1
## [5725] 3 2 2 1 2 1 2 2 3 1 1 2 2 2 2 3 1 1 1 2 2 1 1 1 2 2 2 2 3 2 2 1 1 2 2 2
## [5761] 2 3 1 2 1 3 1 3 1 1 3 1 2 2 1 1 1 1 1 3 2 2 1 2 1 1 1 2 1 2 2 2 2 1 2 2
## [5797] 2 2 2 1 2 1 2 2 1 2 2 1 2 2 1 1 2 2 1 1 1 1 3 1 1 2 2 1 1 1 3 1 2 1 1 2
## [5833] 3 1 2 2 1 2 1 1 2 3 2 2 1 2 2 1 3 2 1 1 2 2 1 1 1 2 2 2 3 1 2 2 1 2 2 1
## [5869] 1 2 1 3 1 2 1 1 2 1 3 1 1 2 2 2 2 2 2 1 3 3 1 1 1 2 1 1 3 3 2 2 1 2 1 1
## [5905] 2 1 1 2 1 2 2 2 2 1 1 2 1 1 3 1 2 2 2 2 3 2 1 1 2 2 1 1 2 2 1 2 2 1 3 2
## [5941] 3 3 2 1 3 2 1 1 1 2 1 2 3 2 1 2 2 2 3 1 1 2 3 2 2 1 2 2 2 2 2 2 2 2 2 2
## [5977] 3 2 2 3 2 1 1 2 2 1 2 2 2 1 1 2 1 3 3 1 1 2 2 2 1 2 2 2 2 3 1 2 1 1 2 1
## [6013] 2 2 2 1 1 2 1 2 2 2 2 2 2 1 1 2 3 1 1 1 2 2 2 1 1 2 2 2 2 1 3 2 2 2 3 1
## [6049] 1 3 2 2 1 2 1 1 1 2 2 2 2 2 2 1 2 1 1 2 1 3 1 1 1 1 1 1 2 2 3 2 1 2 1 1
## [6085] 2 1 2 2 1 2 1 1 2 2 2 1 1 2 1 3 1 2 1 2 1 2 1 1 2 1 2 1 1 2 2 2 1 1 1 3
## [6121] 2 1 2 1 1 2 3 1 2 2 1 2 3 2 2 1 1 1 1 2 3 1 2 3 2 1 1 2 2 2 1 1 2 2 2 2
## [6157] 3 1 1 3 2 2 1 1 3 2 2 2 1 2 2 2 2 1 2 1 1 1 1 3 2 2 1 2 1 1 3 1 1 2 1 2
## [6193] 2 1 2 2 1 1 2 1 1 1 2 2 1 3 2 2 2 2 2 3 2 1 2 2 1 3 2 2 2 1 3 2 3 2 3 2
## [6229] 1 1 1 1 1 1 2 1 2 3 2 1 2 2 1 3 2 1 3 1 1 1 1 1 2 3 2 1 1 2 2 3 1 2 1 3
## [6265] 2 2 1 1 2 1 2 1 1 1 2 2 1 3 2 2 3 1 3 2 1 2 1 2 1 1 1 1 1 1 1 1 2 2 2 2
## [6301] 2 2 2 1 2 3 2 2 1 2 1 2 2 2 2 1 3 2 1 2 2 1 1 1 1 2 1 2 1 2 2 2 2 1 1 1
## [6337] 1 2 2 3 2 1 1 1 1 2 1 1 1 2 1 2 1 1 2 1 3 1 1 2 1 2 2 2 1 1 1 2 1 3 1 3
## [6373] 1 2 2 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 1 2 2 2 1 1 2 3 1
## [6409] 2 2 2 1 1 2 1 1 1 2 2 1 2 1 2 1 1 1 1 2 1 2 1 2 2 1 3 3 1 1 1 2 1 2 1 1
## [6445] 1 2 2 2 3 1 3 1 2 3 2 3 1 1 2 1 3 2 2 2 1 2 2 2 2 1 1 1 2 1 1 1 1 2 1 1
## [6481] 3 1 3 1 1 3 1 1 1 1 1 1 1 2 1 1 2 2 2 2 2 1 1 2 1 2 2 1 3 2 2 1 2 2 1 1
## [6517] 2 2 3 2 1 2 1 1 1 1 1 2 1 1 2 2 2 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 2 2 2 1
## [6553] 2 3 1 1 1 1 1 3 1 2 3 2 1 1 2 2 2 1 1 2 1 1 2 1 1 2 3 1 2 1 2 1 2 1 1 1
## [6589] 2 2 1 2 1 1 2 1 1 3 2 1 1 2 2 1 1 2 2 3 2 3 2 2 1 2 2 1 1 3 2 3 3 1 1 1
## [6625] 2 1 1 2 2 2 2 2 2 2 3 1 2 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 3 3 2 2 2 2 3 3
## [6661] 2 3 2 1 1 2 2 2 2 2 1 1 2 1 1 1 1 1 2 2 1 2 3 2 3 2 1 1 1 1 1 1 3 2 2 1
## [6697] 1 1 2 2 1 1 2 1 1 2 2 2 1 3 2 1 1 1 1 3 1 2 1 1 1 1 1 2 1 1 2 2 1 2 1 2
## [6733] 2 2 2 3 2 3 2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1 1 1 2 2 2 2 1 1 1 1 2 3 2
## [6769] 1 2 2 1 2 1 1 2 2 1 1 1 1 2 2 1 2 1 2 1 2 2 2 2 1 3 2 3 1 2 2 1 2 1 1 1
## [6805] 1 1 2 3 2 1 1 1 1 1 2 2 1 3 3 2 2 1 2 1 1 1 1 1 2 3 1 1 2 2 2 3 3 1 2 1
## [6841] 1 1 3 2 1 1 1 2 2 1 2 1 1 2 1 1 1 3 2 1 2 1 1 1 1 2 3 1 1 3 1 2 1 1 1 2
## [6877] 2 2 2 2 2 2 2 1 2 2 1 1 3 1 1 1 2 3 1 1 2 1 1 1 3 3 3 1 1 1 3 1 1 2 1 1
## [6913] 1 2 1 2 2 2 1 2 2 2 1 2 3 1 2 1 2 2 1 2 2 1 3 2 3 1 2 2 1 2 2 1 1 2 1 2
## [6949] 2 2 1 2 2 1 1 2 2 2 1 2 3 1 3 2 1 2 1 2 3 2 1 2 2 1 1 1 1 3 1 2 1 1 2 1
## [6985] 1 1 1 2 1 2 1 1 1 1 1 2 2 2 1 2 1 1 1 2 2 2 1 2 1 1 3 2 1 1 1 2 2 2 2 2
## [7021] 1 1 2 1 1 1 2 2 1 3 1 1 2 1 1 1 1 1 2 3 1 1 2 1 1 1 1 1 2 2 1 2 1 2 1 2
## [7057] 1 2 2 1 1 2 3 2 1 1 2 3 2 2 2 2 3 1 1 1 1 1 2 1 1 1 2 1 1 2 2 2 2 1 2 2
## [7093] 2 2 1 1 2 1 2 2 1 2 1 1 2 1 1 1 2 1 2 2 2 2 1 2 1 2 1 2 2 1 1 1 2 1 3 1
## [7129] 1 2 1 2 2 2 1 2 3 2 1 1 2 2 1 1 2 1 1 3 1 1 2 2 2 2 2 2 1 2 1 2 1 1 1 1
## [7165] 2 3 1 1 2 1 2 1 1 1 1 1 1 1 1 2 3 1 2 2 2 1 2 1 2 2 2 1 3 2 2 1 2 1 2 1
## [7201] 1 3 1 1 2 1 1 1 1 1 1 3 2 1 2 1 2 2 2 2 1 1 1 2 2 1 2 2 2 2 2 3 2 2 3 2
## [7237] 2 2 2 1 2 1 3 1 3 2 2 2 1 2 2 3 2 3 2 2 2 1 1 1 2 3 2 3 3 1 1 1 2 1 2 1
## [7273] 2 2 1 2 2 3 2 2 3 2 1 3 2 2 2 2 1 2 1 1 2 2 1 2 2 1 1 1 3 1 1 1 2 2 1 1
## [7309] 2 1 2 1 2 2 2 1 1 2 1 2 1 2 2 3 2 2 2 3 2 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1
## [7345] 2 3 2 1 2 1 3 2 1 1 2 1 2 1 1 2 1 1 2 1 2 3 2 2 2 1 1 2 3 1 1 2 1 2 2 2
## [7381] 1 1 2 1 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 2 1 1 2 1 1 3 2 1 1 2 1 2 1 1 2 1
## [7417] 1 2 1 3 2 1 1 3 1 2 2 1 1 1 2 1 2 1 2 1 1 3 1 2 2 2 2 3 2 1 1 1 2 2 1 2
## [7453] 2 1 1 3 1 2 2 1 2 3 2 1 2 1 2 1 1 2 3 2 1 2 1 2 1 1 1 2 1 1 1 2 2 1 1 1
## [7489] 1 1 2 2 2 1 2 1 2 2 1 3 2 1 1 1 1 2 1 3 1 2 1 2 1 1 1 2 2 1 1 2 1 1 3 1
## [7525] 1 2 2 3 3 1 1 1 2 2 3 2 2 1 2 3 2 1 2 2 2 2 1 1 1 1 2 1 1 1 2 2 2 3 1 2
## [7561] 2 1 1 2 1 1 1 2 2 1 2 2 3 3 1 3 2 2 1 2 2 1 2 1 1 2 1 2 2 2 2 3 2 2 2 2
## [7597] 2 1 1 2 2 2 2 2 1 2 2 1 1 1 1 3 2 1 2 1 1 1 1 3 2 2 2 2 2 1 1 2 1 2 1 2
## [7633] 1 2 1 1 3 2 2 2 3 2 2 3 2 1 1 2 1 2 2 2 2 3 2 1 1 2 2 1 2 3 3 2 1 1 1 2
## [7669] 2 1 1 2 1 2 3 2 1 1 1 1 1 1 1 2 1 2 1 2 1 3 2 3 2 2 2 3 1 3 3 2 2 3 1 2
## [7705] 1 1 2 3 2 2 2 1 1 2 3 1 2 1 2 2 2 1 1 2 2 2 1 1 2 2 2 3 1 1 3 1 3 1 2 2
## [7741] 1 2 2 2 1 1 3 2 1 1 2 2 2 1 1 2 2 1 1 1 2 1 2 3 1 3 2 2 2 3 2 1 1 1 1 3
## [7777] 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 2 1 2 2 1 3 1 1 3 2 2 2 1 2 3 2 2 1 1 2 1
## [7813] 2 2 1 2 1 1 3 1 1 1 2 1 2 2 3 1 2 1 3 2 1 2 2 2 1 2 2 2 3 2 2 2 2 3 1 1
## [7849] 2 2 1 1 2 1 1 1 2 1 1 1 2 3 1 2 2 2 1 2 1 2 2 2 2 1 1 2 1 1 2 1 2 3 1 3
## [7885] 2 1 2 2 1 2 1 2 1 2 3 1 3 2 1 3 1 2 1 3 1 2 2 1 1 2 1 1 2 1 1 2 2 2 2 1
## [7921] 1 2 2 3 1 2 2 1 1 1 2 2 2 1 3 2 2 1 1 3 2 2 2 1 1 3 2 1 3 2 2 1 1 2 2 3
## [7957] 2 2 2 2 2 1 1 1 2 1 1 2 1 2 1 1 2 2 2 2 1 1 2 1 2 2 2 1 2 2 2 2 1 1 1 1
## [7993] 1 1 1 1 1 3 1 2 3 1 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1
## [8029] 1 2 2 3 1 1 2 2 1 3 1 2 2 2 2 2 3 2 2 1 2 2 1 3 2 1 1 2 2 2 3 2 1 2 2 1
## [8065] 2 3 3 1 2 3 1 3 3 2 1 2 1 1 3 2 2 1 2 1 2 2 2 1 2 2 1 2 2 2 1 1 3 1 3 3
## [8101] 2 1 2 1 2 1 1 1 2 1 2 2 2 2 1 1 2 2 3 2 1 1 3 2 1 1 2 2 2 1 2 1 3 2 1 3
## [8137] 2 2 1 2 1 2 2 1 1 2 2 1 1 1 1 2 2 2 1 2 1 1 2 1 2 3 2 3 1 2 1 1 2 1 1 2
## [8173] 1 2 1 1 2 2 2 2 1 2 1 1 1 2 2 2 2 2 2 3 2 2 1 2 1 2 2 2 2 3 3 1 2 1 2 2
## [8209] 1 1 2 2 2 2 2 1 2 1 3 1 3 1 1 1 3 1 2 1 3 1 1 1 2 2 1 1 2 3 1 2 2 1 2 2
## [8245] 1 1 1 3 3 1 1 1 2 2 2 3 1 1 1 3 1 2 3 2 2 2 2 2 2 2 1 2 2 1 3 3 2 1 2 1
## [8281] 2 2 1 2 2 1 3 1 2 1 1 1 3 2 3 1 1 1 2 3 2 1 2 3 1 2 1 2 1 2 2 1 2 2 2 1
## [8317] 2 3 3 1 2 1 2 1 2 2 2 1 1 2 2 3 1 2 1 2 2 1 2 1 2 3 2 1 2 1 1 3 1 1 1 1
## [8353] 2 2 3 1 2 2 1 1 3 2 2 2 1 2 2 2 1 1 1 1 1 2 1 2 3 1 3 2 1 3 1 2 2 2 1 2
## [8389] 3 3 2 1 2 2 2 2 1 1 2 1 1 1 1 2 1 2 1 1 1 2 2 2 1 2 1 2 1 1 2 2 1 1 1 2
## [8425] 2 1 1 1 1 2 2 3 2 2 2 1 2 2 2 2 1 1 2 1 1 1 1 2 2 3 2 2 2 2 1 1 2 1 2 2
## [8461] 2 2 2 2 3 2 1 1 3 1 2 1 2 2 1 2 1 1 3 1 2 2 1 1 1 1 3 1 2 2 2 1 3 1 2 2
## [8497] 2 1 3 2 1 1 2 2 1 2 2 2 1 3 1 2 2 1 1 2 2 2 2 2 1 1 2 2 1 1 3 1 1 2 3 1
## [8533] 1 2 2 1 1 2 3 1 2 1 2 1 1 1 1 2 3 1 2 1 2 2 1 2 1 1 1 2 1 1 1 2 2 2 1 1
## [8569] 2 1 3 1 1 1 1 3 2 1 2 2 1 2 3 2 2 2 1 1 3 1 1 1 2 3 2 2 1 3 1 2 2 3 2 1
## [8605] 2 1 1 3 2 1 1 1 2 2 1 1 2 3 2 1 1 2 2 3 1 1 1 2 1 1 2 2 3 1 2 2 2 1 1 1
## [8641] 1 2 1 2 2 1 1 2 2 1 1 1 2 1 2 1 2 2 1 1 2 3 1 2 2 3 2 1 2 3 1 1 2 1 2 1
## [8677] 2 1 2 2 1 1 2 2 2 2 2 2 2 1 2 3 2 1 2 3 1 2 2 2 1 1 1 2 1 1 1 1 1 2 1 2
## [8713] 1 1 3 1 2 2 2 1 2 2 1 3 1 3 1 2 1 1 1 1 2 2 1 3 1 2 2 2 3 2 2 1 2 1 1 2
## [8749] 1 3 1 1 1 1 2 2 1 1 1 3 1 2 2 1 1 1 1 2 1 2 1 3 2 3 2 2 1 2 1 1 1 3 3 3
## [8785] 2 1 1 1 2 2 2 2 1 1 2 2 2 1 3 1 2 2 2 2 2 2 2 2 2 1 1 1 3 1 2 2 1 2 2 1
## [8821] 2 2 1 2 1 3 2 1 1 2 2 1 1 1 2 2 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 1 1 2 1
## [8857] 3 1 3 2 2 2 1 2 2 1 1 1 2 2 2 2 1 2 2 1 2 1 1 2 2 2 3 1 1 3 2 2 2 1 1 1
## [8893] 1 1 1 1 3 2 1 2 3 1 1 1 1 1 2 1 2 1 1 1 2 2 2 1 3 2 1 1 1 2 2 2 2 2 1 1
## [8929] 2 3 1 2 1 2 2 1 1 2 2 2 2 1 1 1 1 1 2 3 1 2 2 2 1 1 3 2 1 1 1 2 2 2 2 2
## [8965] 2 2 2 2 2 1 2 2 2 2 1 3 2 1 1 1 1 2 2 1 1 2 2 2 2 2 1 3 2 1 1 1 1 3 2 1
## [9001] 3 2 1 2 1 2 2 1 2 2 1 1 1 1 1 2 2 1 2 2 1 1 1 2 2 2 1 2 1 1 2 1 3 1 1 1
## [9037] 1 2 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 3 1 2 2 1 1 1 2 1 1
## [9073] 2 1 1 2 2 2 1 2 1 2 1 1 1 3 1 1 1 1 2 2 1 1 2 1 1 1 3 2 1 3 2 2 1 3 1 1
## [9109] 1 2 3 2 1 1 2 1 3 1 3 1 2 3 1 2 2 1 2 2 1 2 3 2 1 1 2 2 1 3 1 2 1 1 3 2
## [9145] 2 1 1 2 2 2 2 2 1 2 2 2 1 1 2 2 2 1 1 1 2 1 2 2 2 2 2 1 1 1 2 1 1 2 2 1
## [9181] 3 2 3 1 1 2 2 2 1 1 2 3 1 2 1 1 3 1 2 2 1 3 1 2 1 2 2 2 2 1 3 2 1 2 2 2
## [9217] 1 1 1 2 2 2 3 2 1 1 2 3 2 2 1 1 1 2 3 2 1 2 2 2 2 2 2 3 2 2 1 1 2 1 2 2
## [9253] 1 1 2 2 3 1 3 2 3 2 1 1 2 2 2 1 2 2 1 1 1 2 2 1 2 2 2 1 2 1 3 3 2 1 2 3
## [9289] 1 2 1 2 1 2 1 2 2 3 1 1 1 1 2 2 1 2 2 2 2 1 2 1 3 2 1 1 2 1 1 2 1 1 2 2
## [9325] 1 2 2 1 1 2 1 1 1 2 2 2 2 1 2 2 1 1 3 3 1 1 2 2 2 2 3 2 1 1 1 1 1 2 1 1
## [9361] 1 2 2 1 1 2 1 2 1 1 3 2 2 1 2 2 3 2 2 2 2 2 2 2 2 1 1 1 2 1 1 1 1 2 1 1
## [9397] 1 2 2 2 1 2 2 2 1 2 2 2 1 1 3 1 1 3 2 2 2 2 1 2 2 2 2 3 2 2 2 1 1 1 1 2
## [9433] 1 2 1 2 2 2 1 1 1 1 1 1 1 1 2 2 2 3 2 2 1 3 2 1 2 2 1 2 3 1 2 2 2 1 1 1
## [9469] 1 1 1 2 1 3 1 1 2 1 2 2 1 1 2 3 3 2 2 2 3 2 1 2 1 2 1 2 1 2 1 1 2 2 3 2
## [9505] 2 2 2 1 1 2 1 2 2 1 2 3 1 2 2 2 2 1 3 2 1 2 2 1 1 2 1 2 2 2 2 1 1 1 3 2
## [9541] 1 2 2 1 2 2 1 2 1 1 2 3 2 2 1 2 2 1 1 2 3 1 2 2 2 3 1 2 1 2 2 2 1 2 2 2
## [9577] 1 2 2 2 2 2 1 1 3 1 2 2 1 1 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2 2 2 1 2 2
## [9613] 2 2 2 1 1 2 2 1 1 1 2 2 3 1 3 2 2 1 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 3
## [9649] 1 3 3 2 1 2 1 3 2 2 2 2 2 2 1 1 2 2 2 1 2 1 2 1 1 2 2 2 1 1 2 3 2 2 3 2
## [9685] 1 2 2 2 2 1 1 2 2 2 2 1 2 2 1 1 2 1 1 2 1 2 2 3 1 2 1 1 2 2 1 2 1 2 2 2
## [9721] 2 1 2 1 2 2 1 2 2 1 2 1 1 2 2 2 1 1 2 1 2 2 2 2 1 1 2 1 2 2 1 1 2 1 2 2
## [9757] 2 2 3 2 2 2 2 2 2 1 2 1 2 3 2 1 1 1 2 2 2 2 1 2 3 1 2 1 2 2 1 2 3 2 1 1
## [9793] 2 1 2 2 1 2 1 2 2 2 2 2 1 1 1 2 3 2 1 2 1 1 1 2 1 2 1 2 2 2 1 3 3 2 2 1
## [9829] 1 1 3 1 2 1 2 2 1 1 3 2 2 2 2 1 1 1 2 1 1 1 2 1 1 2 3 2 1 2 2 2 2 2 1 2
## [9865] 2 2 2 3 2 2 1 1 1 2 1 2 1 1 2 2 2 2 1 2 2 1 1 1 2 1 1 1 2 2 1 2 2 2 1 1
## [9901] 1 2 2 1 2 1 3 1 1 2 1 1 2 1 2 1 1 1 2 3 2 2 2 1 2 1 3 2 1 1 1 1 1 1 2 2
## [9937] 1 1 2 2 2 2 2 2 1 1 3 1 1 1 1 2 1 3 2 2 1 3 1 2 1 3 2 2 2 2 1 1 3 2 1 1
## [9973] 1 2 1 3 1 1 2 1 2 2 2 1 1 2 1 1 1 1 3 2 1 2 1 1 3 2 1 1
##
## Within cluster sum of squares by cluster:
## [1] 6103.296 12369.985 2895.329
## (between_SS / total_SS = 62.7 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"plot(unC$map)
Smoothing the output (majority filter)
unC_sm3 <- focal(unC$map, w=matrix(1,3,3), fun=modal)
unC_sm5 <- focal(unC$map, w=matrix(1,5,5), fun=modal)
unC_sm7 <- focal(unC$map, w=matrix(1,7,7), fun=modal)Export Geotiff
writeRaster(unC$map,paste("../output/kmeans_", n.cl, "cl.tif", sep = ""), format="GTiff", overwrite = TRUE)
writeRaster(unC_sm3,paste("../output/kmeans_", n.cl, "cl_sm3.tif", sep = ""), format="GTiff", overwrite = TRUE)
writeRaster(unC_sm5,paste("../output/kmeans_", n.cl, "cl_sm5.tif", sep = ""), format="GTiff", overwrite = TRUE)
writeRaster(unC_sm7,paste("../output/kmeans_", n.cl, "cl_sm7.tif", sep = ""), format="GTiff", overwrite = TRUE)Boxplots
r <- stack(unC$map, vars)
smp <- as.data.frame(sampleRandom(x = r, size = 10000))
smp[,1] <- as.factor(smp[,1])
names(smp)[names(smp)=="layer"] <- "Cluster"
for (i in 2:ncol(smp)) {
print(ggplot(smp, aes(x = Cluster, y = smp[,i],fill = Cluster)) +
geom_boxplot() +
scale_y_continuous(name = names(smp[i])) +
theme(axis.text.x = element_blank(),
axis.title.x = element_blank(),
axis.ticks.x = element_blank()))
}
Figure for publication
col.pal <- c('#a6cee3','#b2df8a','#1f78b4')
AoI <- extent(3450000,4450000,3100000,4300000)
land <- readOGR(dsn = "N:/Prosjekter/311700_MAREANO/311720_Havbunnskart/c_Metodeprosjekter/xxx_Karbonlagring/GIS", layer = "Europe_coastline_poly")## OGR data source with driver: ESRI Shapefile
## Source: "N:\Prosjekter\311700_MAREANO\311720_Havbunnskart\c_Metodeprosjekter\xxx_Karbonlagring\GIS", layer: "Europe_coastline_poly"
## with 1 features
## It has 1 fieldsclmap <- crop(unC$map, AoI)
land <- crop(land, AoI)
p <- ggR(clmap, geom_raster = TRUE, forceCat = TRUE) +
geom_polygon(data = land, aes(x = long, y = lat, group = group)) +
scale_fill_manual(values = col.pal) +
theme(axis.title = element_blank()) +
theme(legend.position = "none" ) +
ggpubr::rotate_y_text()## Regions defined for each Polygonsp1 <- ggplot(smp, aes(x = Cluster, y = Bathymetry, fill = Cluster)) +
geom_boxplot() +
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = "Bathymetry (m)") +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
p2 <- ggplot(smp, aes(x = Cluster, y = Current.speed, fill = Cluster)) +
geom_boxplot()+
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = expression(M2~current~speed~(m~s^{-1}))) +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
p3 <- ggplot(smp, aes(x = Cluster, y = OCAR, fill = Cluster)) +
geom_boxplot()+
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = expression(OCAR~(g~m^{-2}~yr^{-1}))) +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
p4 <- ggplot(smp, aes(x = Cluster, y = OC.density, fill = Cluster)) +
geom_boxplot()+
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = expression(OC~density~(kg~m^{-3}))) +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
p5 <- ggplot(smp, aes(x = Cluster, y = OPD, fill = Cluster)) +
geom_boxplot() +
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = "OPD (cm)") +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
p6 <- ggplot(smp, aes(x = Cluster, y = Orb.Velocity, fill = Cluster)) +
geom_boxplot()+
scale_fill_manual(values = col.pal) +
scale_y_continuous(name = expression(Orbital~velocity~(m~s^{-1}))) +
theme(axis.title.x = element_blank()) +
theme(legend.position = "none")
lay <- rbind(c(1,1,1,2,3,4),
c(1,1,1,5,6,7))
tiff("../figs/OC_processing_regions.tif", width = 30, height = 15, units = "cm", res = 500, compression = "lzw")
grid.arrange(p, p1, p2, p3, p5, p6, p4, nrow=2, layout_matrix=lay)## Warning: Removed 278171 rows containing missing values (geom_raster).dev.off()## png
## 2