# Stratification

Fundamental to many structurally guided sampling approaches is the use of stratification methods that allow for more effective and representative sampling protocols. It is important to note that the data sets being used as inputs are considered to be populations.

Currently, there are 5 functions associated with the strat verb in the sgsR package:

Algorithm Description Approach
strat_kmeans() kmeans Unsupervised
strat_quantiles() Quantiles Either
strat_breaks() User-defined breaks Supervised
strat_poly() Polygons Supervised
strat_map() Maps (combines) srasters Unsupervised

## strat_kmeans

strat_kmeans() uses kmeans clustering to produce an sraster output.

#--- perform stratification using k-means ---#
strat_kmeans(
mraster = mraster, # input
nStrata = 5
) # algorithm will produce 4 strata
#> class       : SpatRaster
#> dimensions  : 277, 373, 1  (nrow, ncol, nlyr)
#> resolution  : 20, 20  (x, y)
#> extent      : 431100, 438560, 5337700, 5343240  (xmin, xmax, ymin, ymax)
#> coord. ref. : UTM Zone 17, Northern Hemisphere
#> source(s)   : memory
#> varname     : mraster
#> name        : strata
#> min value   :      1
#> max value   :      5

TIP!

plot = FALSE is the default for all functions. plot = TRUE will visualize raster and vector ouputs.

strat_kmeans(
mraster = mraster, # input
nStrata = 10, # algorithm will produce 10 strata
iter = 1000, # set minimum number of iterations to determine kmeans centers
algorithm = "MacQueen", # use MacQueen algorithm
plot = TRUE
) # plot output

#> class       : SpatRaster
#> dimensions  : 277, 373, 1  (nrow, ncol, nlyr)
#> resolution  : 20, 20  (x, y)
#> extent      : 431100, 438560, 5337700, 5343240  (xmin, xmax, ymin, ymax)
#> coord. ref. : UTM Zone 17, Northern Hemisphere
#> source(s)   : memory
#> varname     : mraster
#> name        : strata
#> min value   :      1
#> max value   :     10

## strat_quantiles

The strat_quantiles() algorithm divides data into equally sized strata (nStrata). Similar to strat_breaks(), this function is vectorized to allow users to input any number of metrics to stratify (mraster) so long as nStrata is a list containing a matching number of numeric objects. nStrata can be either nStrata can be either a scalar integer representing the number of desired output strata, or a numeric vector of probabilities between 0-1 demarcating quantile break points. The nStrata list can be a mix of these (e.g. nStrata = list(c(0.1,0.8,1), 4, 9) where mraster would have 3 layers) to allow users to define both explicit quantile breaks or a desired strata number that is converted to quantiles breaks internally. Specifying map = TRUE will combine (map) stratifications of all input mraster layers to produce a combined stratified output.

#--- perform quantiles stratification ---#
strat_quantiles(
mraster = mraster$zq90, nStrata = 6, plot = TRUE ) #> class : SpatRaster #> dimensions : 277, 373, 1 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> source(s) : memory #> varname : mraster #> name : strata #> min value : 1 #> max value : 6 #--- vectorized ---# strat_quantiles( mraster = mraster[[1:2]], # two metric layers nStrata = list(c(0.2, 0.4, 0.8), 3), # list with two objects - 1 probability breaks, 1 scalar integer plot = TRUE, # plot output srasters map = TRUE ) # combine stratifications to a mapped output #> class : SpatRaster #> dimensions : 277, 373, 3 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> source(s) : memory #> varnames : mraster #> mraster #> mraster #> names : strata_zq90, strata_pzabove2, strata #> min values : 1, 1, 1 #> max values : 4, 3, 12 ## strat_breaks strat_breaks() stratifies data based on user-defined breaks in mraster. This algorithm is vectorized. The user can provide an mraster with as many layers as they wish as long as the breaks parameters is a list of equal length comprised of numeric vectors. Like strat_quantiles() this function has the map parameter to combine input stratifications to generate a mapped output. #--- perform stratification using user-defined breaks ---# #--- define breaks for metric ---# br.pz2 <- c(20, 40, 60, 80) br.pz2 #> [1] 20 40 60 80 #--- perform stratification using user-defined breaks ---# #--- define breaks for metric ---# br.zq90 <- c(3, 5, 11, 18) br.zq90 #> [1] 3 5 11 18 Once the breaks are created, we can use them as input into the strat_breaks() function using the breaks parameter. #--- stratify on 1 metric only ---# strat_breaks( mraster = mraster$pzabove2, # single raster
breaks = br.pz2, # single set of breaks
plot = TRUE
) # plot output

#> class       : SpatRaster
#> dimensions  : 277, 373, 1  (nrow, ncol, nlyr)
#> resolution  : 20, 20  (x, y)
#> extent      : 431100, 438560, 5337700, 5343240  (xmin, xmax, ymin, ymax)
#> coord. ref. : UTM Zone 17, Northern Hemisphere
#> source(s)   : memory
#> varname     : mraster
#> name        : strata
#> min value   :      1
#> max value   :      5
#--- vectorized ---#
strat_breaks(
mraster = mraster[[1:2]], # two metrics
breaks = list(br.zq90, br.pz2), # list of two breaks vectors
map = TRUE, # map final output
plot = TRUE
) # plot outputs

#> class       : SpatRaster
#> dimensions  : 277, 373, 3  (nrow, ncol, nlyr)
#> resolution  : 20, 20  (x, y)
#> extent      : 431100, 438560, 5337700, 5343240  (xmin, xmax, ymin, ymax)
#> coord. ref. : UTM Zone 17, Northern Hemisphere
#> source(s)   : memory
#> varnames    : mraster
#>               mraster
#>               mraster
#> names       : strata_zq90, strata_pzabove2, strata
#> min values  :           1,               1,      1
#> max values  :           5,               5,     22

## strat_poly

Forest inventories with polygon coverages summarizing forest attributes such as species, management type, or photo-interpreted estimates of volume can be stratified using strat_poly().

TIP!

Users may wish to stratify based on categorical or empirical variables that are not available through raster data (e.g. species from forest inventory polygons).

Users define the input poly and its associated attribute. A raster layer must be defined to guide the spatial extent and resolution for the output stratification polygon. Based on the vector or list of features, stratification is applied and the polygon is rasterized into its appropriate strata.

#--- load in polygon coverage ---#
poly <- system.file("extdata", "inventory_polygons.shp", package = "sgsR")

#> Reading layer inventory_polygons' from data source
#>   C:\Users\goodb\AppData\Local\Temp\Rtmp8iA5Id\Rinst214c547c7592\sgsR\extdata\inventory_polygons.shp'
#>   using driver ESRI Shapefile'
#> Simple feature collection with 632 features and 3 fields
#> Geometry type: MULTIPOLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 431100 ymin: 5337700 xmax: 438560 ymax: 5343240
#> Projected CRS: UTM_Zone_17_Northern_Hemisphere

#--- specify polygon attribute to stratify ---#

attribute <- "NUTRIENTS"

#--- specify features within attribute & how they should be grouped ---#
#--- as a single vector ---#

features <- c("poor", "rich", "medium")

In our example, attribute = "NUTRIENTS" and features within, c("poor", "rich", "medium"), define the 3 desired strata.

#--- stratify polygon coverage ---#

srasterpoly <- strat_poly(
poly = fri, # input polygon
attribute = attribute, # attribute to stratify by
features = features, # features within attribute
raster = sraster, # raster to define extent and resolution for output
plot = TRUE
) # plot output

features can be grouped. In our example below, rich and medium features are combined into a single strata, while low is left in isolation. The 2 vectors are specified into a list, which will result in the output of 2 strata (low & rich/medium).

#--- or as multiple lists ---#
g1 <- "poor"
g2 <- c("rich", "medium")

features <- list(g1, g2)

strat_poly(
poly = fri,
attribute = attribute,
features = features,
raster = sraster,
plot = TRUE,
details = TRUE
)

#> $raster #> class : SpatRaster #> dimensions : 277, 373, 1 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> source(s) : memory #> varname : mraster #> name : strata #> min value : 1 #> max value : 2 #> #>$lookUp
#>   strata features
#> 1      1     poor
#> 2      2     rich
#> 3      2   medium
#>
#> $poly #> class : SpatVector #> geometry : polygons #> dimensions : 524, 2 (geometries, attributes) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM_Zone_17_Northern_Hemisphere #> names : features strata #> type : <chr> <int> #> values : poor 1 #> poor 1 #> poor 1 details details returns the output outRaster, the stratification $lookUp table, and the polygon ($poly) used to drive the stratification based on attributes and features specified by the users. ## strat_map Users may wish to pair stratifications. strat_map() facilitates vectorized mapping of sraster layers to generate a unique mapped strata output based on stratum pairings. The stack parameter will output a multilayer sraster with the inputs (strata_1, strata_2 ...) and mapped output (strata). This facilitates the user to generate stratifications detailing quantitative and qualitative measures such as structure by species, or multiple qualitative measures such as species by management type. #--- stack srasters together ---# srasters <- c(srasterpoly, sraster) plot(srasters) #--- map srasters ---# strat_map( sraster = srasters, # two layer sraster plot = TRUE ) #> class : SpatRaster #> dimensions : 277, 373, 1 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> source(s) : memory #> varname : mraster #> name : strata #> min value : 11 #> max value : 34 The convention for the numeric value of the output strata is the concatenation (merging) of sraster layers. Check $lookUP for a clear depiction of this step.

strat_map(
sraster = srasters, # input with 2 sraster layers
stack = TRUE, # output stacked input (strata_1, strata_2) and output (strata) layers
details = TRUE, # provide additional details
plot = TRUE
) # plot output
#> Stacking srasters and their combination (strata).

#> $raster #> class : SpatRaster #> dimensions : 277, 373, 3 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> source(s) : memory #> varnames : mraster #> mraster #> mraster #> names : strata_1, strata_2, strata #> min values : 1, 1, 11 #> max values : 3, 4, 34 #> #>$lookUp
#>    strata_1 strata_2 strata
#> 1         1        1     11
#> 2         1        2     12
#> 3         1        3     13
#> 4         1        4     14
#> 5         2        1     21
#> 6         2        2     22
#> 7         2        3     23
#> 8         2        4     24
#> 9         3        1     31
#> 10        3        2     32
#> 11        3        3     33
#> 12        3        4     34`