Sampling

sample_srs

We have demonstrated a simple example of using the sample_srs() function in vignette("sgsR"). We will demonstrate additional examples below.

#--- perform simple random sampling ---#
sample_srs(
  raster = sraster, # input sraster
  nSamp = 200, # number of desired sample units
  plot = TRUE
) # plot

#> Simple feature collection with 200 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431170 ymin: 5337710 xmax: 438530 ymax: 5343210
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>                  geometry
#> 1  POINT (432830 5343190)
#> 2  POINT (435230 5342790)
#> 3  POINT (438030 5338250)
#> 4  POINT (437690 5341770)
#> 5  POINT (437970 5338970)
#> 6  POINT (434370 5341030)
#> 7  POINT (435570 5341310)
#> 8  POINT (435310 5340730)
#> 9  POINT (432850 5342730)
#> 10 POINT (438530 5341150)

sample_srs(
  raster = mraster, # input mraster
  nSamp = 200, # number of desired sample units
  access = access, # define access road network
  mindist = 200, # minimum distance sample units must be apart from one another
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot

#> Simple feature collection with 200 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431150 ymin: 5337730 xmax: 438550 ymax: 5343230
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>                  geometry
#> 1  POINT (434750 5343070)
#> 2  POINT (435490 5341950)
#> 3  POINT (437750 5338690)
#> 4  POINT (433710 5340370)
#> 5  POINT (438330 5341150)
#> 6  POINT (432470 5340850)
#> 7  POINT (433430 5342250)
#> 8  POINT (431850 5338610)
#> 9  POINT (437170 5338050)
#> 10 POINT (435890 5342570)

sample_systematic

The sample_systematic() function applies systematic sampling across an area with the cellsize parameter defining the resolution of the tessellation. The tessellation shape can be modified using the square parameter. Assigning TRUE (default) to the square parameter results in a regular grid and assigning FALSE results in a hexagonal grid.

The location of sample units can also be adjusted using the locations parameter, where centers takes the center, corners takes all corners, and random takes a random location within each tessellation. Random start points and translations are applied when the function is called.

#--- perform grid sampling ---#
sample_systematic(
  raster = sraster, # input sraster
  cellsize = 1000, # grid distance
  plot = TRUE
) # plot

#> Simple feature collection with 38 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431484.5 ymin: 5337778 xmax: 438510 ymax: 5343165
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>                    geometry
#> 1  POINT (432408.6 5338327)
#> 2  POINT (433376.2 5338074)
#> 3  POINT (434343.7 5337821)
#> 4  POINT (431693.8 5339547)
#> 5  POINT (432661.4 5339295)
#> 6  POINT (434596.4 5338789)
#> 7    POINT (435564 5338536)
#> 8  POINT (436531.5 5338284)
#> 9    POINT (437499 5338031)
#> 10 POINT (438466.6 5337778)

#--- perform grid sampling ---#
sample_systematic(
  raster = sraster, # input sraster
  cellsize = 500, # grid distance
  square = FALSE, # hexagonal tessellation
  location = "random", # randomly sample within tessellation
  plot = TRUE
) # plot

#> Simple feature collection with 174 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431213.7 ymin: 5337728 xmax: 438559.7 ymax: 5343238
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>                    geometry
#> 1  POINT (438549.8 5342372)
#> 2  POINT (438504.2 5342656)
#> 3    POINT (438478 5342049)
#> 4  POINT (438276.9 5341076)
#> 5  POINT (438373.2 5340040)
#> 6  POINT (438559.7 5339515)
#> 7  POINT (438450.5 5338404)
#> 8  POINT (438520.5 5337742)
#> 9  POINT (438094.3 5342299)
#> 10 POINT (438275.8 5341303)

sample_systematic(
  raster = sraster, # input sraster
  cellsize = 500, # grid distance
  access = access, # define access road network
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  square = FALSE, # hexagonal tessellation
  location = "corners", # take corners instead of centers
  plot = TRUE
)

#> Simple feature collection with 631 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431296.7 ymin: 5337762 xmax: 438559.5 ymax: 5343216
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>                    geometry
#> 1  POINT (431296.7 5340859)
#> 2  POINT (431388.7 5342589)
#> 3  POINT (431296.7 5340859)
#> 4  POINT (431538.7 5340702)
#> 5  POINT (431523.4 5340413)
#> 6  POINT (431388.7 5342589)
#> 7  POINT (431630.7 5342431)
#> 8  POINT (431673.3 5338526)
#> 9    POINT (431658 5338238)
#> 10 POINT (431523.4 5340413)

sample_strat

The sample_strat() contains two methods to perform sampling:

• "Queinnec" - Hierarchical sampling using a focal window to isolate contiguous groups of stratum pixels, which was originally developed by Martin Queinnec.

• "random" - Traditional stratified random sampling. This method ignores much of the functionality of the algorithm to allow users the capability to use standard stratified random sampling approaches without the use of a focal window to locate contiguous stratum cells.

#--- perform stratified sampling random sampling ---#
sample_strat(
  sraster = sraster, # input sraster
  nSamp = 200
) # desired sample size # plot
#> Simple feature collection with 200 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431170 ymin: 5337750 xmax: 438490 ymax: 5343210
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata type  rule               geometry
#> x       1  new rule1 POINT (434570 5342430)
#> x1      1  new rule1 POINT (438370 5339510)
#> x2      1  new rule1 POINT (433810 5341030)
#> x3      1  new rule1 POINT (438410 5338190)
#> x4      1  new rule1 POINT (435130 5342750)
#> x5      1  new rule1 POINT (437850 5343110)
#> x6      1  new rule1 POINT (433510 5341010)
#> x7      1  new rule1 POINT (435930 5342670)
#> x8      1  new rule1 POINT (435870 5342310)
#> x9      1  new rule1 POINT (434630 5341050)

#--- extract strata values to existing samples ---#
e.sr <- extract_strata(
  sraster = sraster, # input sraster
  existing = existing
) # existing samples to add strata value to

sample_strat(
  sraster = sraster, # input sraster
  nSamp = 200, # desired sample size
  access = access, # define access road network
  existing = e.sr, # existing sample with strata values
  mindist = 200, # minimum distance sample units must be apart from one another
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot

#> Simple feature collection with 400 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431190 ymin: 5337710 xmax: 438530 ymax: 5343230
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata     type     rule               geometry
#> 1       1 existing existing POINT (437830 5341110)
#> 2       1 existing existing POINT (437250 5338030)
#> 3       1 existing existing POINT (435410 5342590)
#> 4       1 existing existing POINT (436090 5342370)
#> 5       1 existing existing POINT (433410 5340870)
#> 6       1 existing existing POINT (433810 5340570)
#> 7       1 existing existing POINT (437870 5343090)
#> 8       1 existing existing POINT (436570 5337730)
#> 9       1 existing existing POINT (437610 5339250)
#> 10      1 existing existing POINT (437830 5338010)

sample_strat(
  sraster = sraster, # input
  nSamp = 200, # desired sample size
  access = access, # define access road network
  existing = e.sr, # existing samples with strata values
  include = TRUE, # include existing sample in nSamp total
  buff_outer = 200, # outer buffer - no samples further than this distance from road
  plot = TRUE
) # plot

#> Simple feature collection with 200 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431190 ymin: 5337730 xmax: 438470 ymax: 5343210
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata     type     rule               geometry
#> 1       1 existing existing POINT (437830 5341110)
#> 2       1 existing existing POINT (437250 5338030)
#> 3       1 existing existing POINT (435410 5342590)
#> 4       1 existing existing POINT (436090 5342370)
#> 5       1 existing existing POINT (433410 5340870)
#> 6       1 existing existing POINT (433810 5340570)
#> 7       1 existing existing POINT (437870 5343090)
#> 8       1 existing existing POINT (436570 5337730)
#> 9       1 existing existing POINT (437610 5339250)
#> 10      1 existing existing POINT (437830 5338010)

#--- perform stratified sampling random sampling ---#
sample_strat(
  sraster = sraster, # input sraster
  method = "random", # stratified random sampling
  nSamp = 200, # desired sample size
  plot = TRUE
) # plot

#> Simple feature collection with 200 features and 2 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431110 ymin: 5337750 xmax: 438490 ymax: 5343230
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata type               geometry
#> x       1  new POINT (434630 5342970)
#> x1      1  new POINT (437450 5339370)
#> x2      1  new POINT (432970 5343030)
#> x3      1  new POINT (434470 5341790)
#> x4      1  new POINT (436110 5342670)
#> x5      1  new POINT (435270 5342810)
#> x6      1  new POINT (435850 5342370)
#> x7      1  new POINT (437730 5342590)
#> x8      1  new POINT (433690 5341230)
#> x9      1  new POINT (434050 5341290)

sample_sys_strat

sample_sys_strat() function implements systematic stratified sampling on an sraster. This function uses the same functionality as sample_systematic() but takes an sraster as input and performs sampling on each stratum iteratively.

#--- perform grid sampling on each stratum separately ---#
sample_sys_strat(
  sraster = sraster, # input sraster with 4 strata
  cellsize = 1000, # grid size
  plot = TRUE # plot output
)
#> Warning: [readStart] source already open for reading
#> Processing strata : 1
#> Warning: [extract] source already open for reading
#> Processing strata : 2
#> Warning: [extract] source already open for reading
#> Processing strata : 3
#> Warning: [extract] source already open for reading
#> Processing strata : 4
#> Warning: [extract] source already open for reading

#> Simple feature collection with 39 features and 1 field
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431100.9 ymin: 5337717 xmax: 438491.4 ymax: 5343157
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata                 geometry
#> 1       1 POINT (432259.4 5338109)
#> 2       1 POINT (432120.8 5340934)
#> 3       1 POINT (434343.5 5338919)
#> 4       1 POINT (435084.4 5338247)
#> 5       1 POINT (433533.3 5341003)
#> 6       1 POINT (435015.1 5339660)
#> 7       1 POINT (436496.9 5338317)
#> 8       1 POINT (437909.4 5338386)
#> 9       1 POINT (434135.6 5343157)
#> 10      1 POINT (435617.4 5341813)

Just like with sample_systematic() we can specify where we want our samples to fall within our tessellations. We specify location = "corners" below. Note that the tesselations are all saved to a list file when details = TRUE should the user want to save them.

sample_sys_strat(
  sraster = sraster, # input sraster with 4 strata
  cellsize = 500, # grid size
  square = FALSE, # hexagon tessellation
  location = "corners", # samples on tessellation corners
  plot = TRUE # plot output
)
#> Processing strata : 1
#> Warning: [extract] source already open for reading
#> Processing strata : 2
#> Warning: [extract] source already open for reading
#> Processing strata : 3
#> Warning: [extract] source already open for reading
#> Processing strata : 4
#> Warning: [extract] source already open for reading

#> Simple feature collection with 1188 features and 1 field
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431135.3 ymin: 5337702 xmax: 438542.8 ymax: 5343205
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata                 geometry
#> 1       1 POINT (432943.4 5343041)
#> 2       1 POINT (432943.4 5343041)
#> 3       1 POINT (433705.9 5342998)
#> 4       1 POINT (434261.3 5343155)
#> 5       1 POINT (432943.4 5343041)
#> 6       1 POINT (433705.9 5342998)
#> 7       1 POINT (434261.3 5343155)
#> 8       1 POINT (433913.1 5342797)
#> 9       1 POINT (433705.9 5342998)
#> 10      1 POINT (433705.9 5342998)

This sampling approach could be especially useful incombination with strat_poly() to ensure consistency of sampling accross specific management units.

#--- read polygon coverage ---#
poly <- system.file("extdata", "inventory_polygons.shp", package = "sgsR")
fri <- sf::st_read(poly)
#> Reading layer `inventory_polygons' from data source 
#>   `/tmp/RtmpZ425gb/Rinst1396490a568e/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

#--- stratify polygon coverage ---#
#--- 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")

#--- get polygon stratification ---#
srasterpoly <- strat_poly(
  poly = fri,
  attribute = attribute,
  features = features,
  raster = sraster
)

#--- systematatic stratified sampling for each stratum ---#
sample_sys_strat(
  sraster = srasterpoly, # input sraster from strat_poly() with 3 strata
  cellsize = 500, # grid size
  square = FALSE, # hexagon tessellation
  location = "random", # randomize plot location
  plot = TRUE # plot output
)
#> Processing strata : 1
#> Warning: [extract] source already open for reading
#> Processing strata : 2
#> Warning: [extract] source already open for reading
#> Processing strata : 3
#> Warning: [extract] source already open for reading
#> Simple feature collection with 171 features and 1 field
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431115.5 ymin: 5337781 xmax: 438559.6 ymax: 5343189
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata                 geometry
#> 1       1 POINT (438094.4 5342855)
#> 2       1 POINT (437724.1 5342565)
#> 3       1 POINT (437737.4 5342087)
#> 4       1 POINT (437585.2 5342509)
#> 5       1 POINT (437423.2 5341565)
#> 6       1 POINT (437905.9 5340732)
#> 7       1 POINT (436055.4 5342987)
#> 8       1 POINT (437973.3 5340321)
#> 9       1 POINT (438151.1 5339630)
#> 10      1 POINT (435715.2 5342890)

sample_nc

sample_nc() function implements the Nearest Centroid sampling algorithm described in Melville & Stone (2016). The algorithm uses kmeans clustering where the number of clusters (centroids) is equal to the desired sample size (nSamp).

Cluster centers are located, which then prompts the nearest neighbour mraster pixel for each cluster to be selected (assuming default k parameter). These nearest neighbours are the output sample units.

#--- perform simple random sampling ---#
sample_nc(
  mraster = mraster, # input
  nSamp = 25, # desired sample size
  plot = TRUE
)
#> K-means being performed on 3 layers with 25 centers.

#> Simple feature collection with 25 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431550 ymin: 5337810 xmax: 438450 ymax: 5343170
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>        zq90 pzabove2  zsd kcenter               geometry
#> 12742 12.60     52.0 3.53       1 POINT (432290 5342550)
#> 13536 15.40     89.8 3.65       2 POINT (433250 5342510)
#> 24800  4.63     31.9 1.05       3 POINT (434730 5341910)
#> 30328  6.92     13.4 1.84       4 POINT (433390 5341610)
#> 79890 15.70     95.3 2.77       5 POINT (432450 5338950)
#> 26025 19.60     67.6 5.90       6 POINT (436850 5341850)
#> 65511 16.60     65.2 4.60       7 POINT (435810 5339730)
#> 3753  18.50     85.0 5.19       8 POINT (431550 5343030)
#> 90994 11.00     17.3 3.17       9 POINT (438190 5338370)
#> 87961  6.12     58.2 1.42      10 POINT (437210 5338530)

Altering the k parameter leads to a multiplicative increase in output sample units where total output samples = \(nSamp * k\).

#--- perform simple random sampling ---#
samples <- sample_nc(
  mraster = mraster, # input
  k = 2, # number of nearest neighbours to take for each kmeans center
  nSamp = 25, # desired sample size
  plot = TRUE
)
#> K-means being performed on 3 layers with 25 centers.

#--- total samples = nSamp * k (25 * 2) = 50 ---#
nrow(samples)
#> [1] 50

Visualizing what the kmeans centers and sample units looks like is possible when using details = TRUE. The $kplot output provides a quick visualization of where the centers are based on a scatter plot of the first 2 layers in mraster. Notice that the centers are well distributed in covariate space and chosen sample units are the closest pixels to each center (nearest neighbours).

#--- perform simple random sampling with details ---#
details <- sample_nc(
  mraster = mraster, # input
  nSamp = 25, # desired sample number
  details = TRUE
)
#> K-means being performed on 3 layers with 25 centers.

#--- plot ggplot output ---#

details$kplot

sample_clhs

sample_clhs() function implements conditioned Latin hypercube (clhs) sampling methodology from the clhs package.

The syntax for this function is similar to others shown above, although parameters like iter, which define the number of iterations within the Metropolis-Hastings process are important to consider. In these examples we use a low iter value for efficiency. Default values for iter within the clhs package are 10,000.

sample_clhs(
  mraster = mraster, # input
  nSamp = 200, # desired sample size
  plot = TRUE, # plot
  iter = 100
) # number of iterations

The cost parameter defines the mraster covariate, which is used to constrain the clhs sampling. An example could be the distance a pixel is from road access (e.g. from calculate_distance() see example below), terrain slope, the output from calculate_coobs(), or many others.

#--- cost constrained examples ---#
#--- calculate distance to access layer for each pixel in mr ---#
mr.c <- calculate_distance(
  raster = mraster, # input
  access = access, # define access road network
  plot = TRUE
) # plot

sample_clhs(
  mraster = mr.c, # input
  nSamp = 250, # desired sample size
  iter = 100, # number of iterations
  cost = "dist2access", # cost parameter - name defined in calculate_distance()
  plot = TRUE
) # plot

sample_balanced

The sample_balanced() algorithm performs a balanced sampling methodology from the stratifyR / SamplingBigData packages.

sample_balanced(
  mraster = mraster, # input
  nSamp = 200, # desired sample size
  plot = TRUE
) # plot

#> Simple feature collection with 200 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431110 ymin: 5337810 xmax: 438530 ymax: 5343210
#> Projected CRS: +proj=utm +zone=17 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#> First 10 features:
#>                  geometry
#> 1  POINT (435930 5343210)
#> 2  POINT (434770 5343190)
#> 3  POINT (431610 5343130)
#> 4  POINT (431550 5343110)
#> 5  POINT (431870 5343110)
#> 6  POINT (433650 5343110)
#> 7  POINT (431590 5343070)
#> 8  POINT (431790 5343050)
#> 9  POINT (438090 5343010)
#> 10 POINT (432210 5342970)

sample_balanced(
  mraster = mraster, # input
  nSamp = 100, # desired sample size
  algorithm = "lcube", # algorithm type
  access = access, # define access road network
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200
) # outer buffer - no sample units further than this distance from road
#> Simple feature collection with 100 features and 0 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431530 ymin: 5337710 xmax: 438430 ymax: 5343230
#> Projected CRS: +proj=utm +zone=17 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#> First 10 features:
#>                  geometry
#> 1  POINT (435310 5343230)
#> 2  POINT (431850 5343170)
#> 3  POINT (433090 5343050)
#> 4  POINT (435410 5343050)
#> 5  POINT (432410 5343030)
#> 6  POINT (434670 5342970)
#> 7  POINT (438010 5342970)
#> 8  POINT (435550 5342930)
#> 9  POINT (437910 5342910)
#> 10 POINT (432190 5342890)

sample_ahels

The sample_ahels() function performs the adapted Hypercube Evaluation of a Legacy Sample (ahels) algorithm usingexisting sample data and an mraster. New sample units are allocated based on quantile ratios between the existing sample and mraster covariate dataset.

This algorithm was adapted from that presented in the paper below, which we highly recommend.

Malone BP, Minansy B, Brungard C. 2019. Some methods to improve the utility of conditioned Latin hypercube sampling. PeerJ 7:e6451 DOI 10.7717/peerj.6451

This algorithm:

1. Determines the quantile distributions of existing sample units and mraster covariates.

2. Determines quantiles where there is a disparity between sample units and covariates.

3. Prioritizes sampling within those quantile to improve representation.

To use this function, user must first specify the number of quantiles (nQuant) followed by either the nSamp (total number of desired sample units to be added) or the threshold (sampling ratio vs. covariate coverage ratio for quantiles - default is 0.9) parameters.

#--- remove `type` variable from existing  - causes plotting issues ---#

existing <- existing %>% select(-type)

sample_ahels(
  mraster = mraster,
  existing = existing, # existing sample
  plot = TRUE
) # plot

#> Simple feature collection with 287 features and 7 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431110 ymin: 5337730 xmax: 438470 ymax: 5343230
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>      type.x zq90 pzabove2  zsd strata type.y  rule               geometry
#> 1  existing 5.77     54.1 1.31      1    new rule1 POINT (437830 5341110)
#> 2  existing 8.16     83.7 1.73      1    new rule1 POINT (437250 5338030)
#> 3  existing 3.64     43.7 0.68      1    new rule1 POINT (435410 5342590)
#> 4  existing 6.08     45.4 1.49      1    new rule1 POINT (436090 5342370)
#> 5  existing 3.28      7.4 0.61      1    new rule1 POINT (433410 5340870)
#> 6  existing 2.88      4.7 0.47      1    new rule1 POINT (433810 5340570)
#> 7  existing 2.31      0.4 0.32      1    new rule1 POINT (437870 5343090)
#> 8  existing 8.51     46.0 2.22      1    new rule1 POINT (436570 5337730)
#> 9  existing 3.51     10.4 0.66      1    new rule1 POINT (437610 5339250)
#> 10 existing 6.38      3.9 1.49      1    new rule1 POINT (437830 5338010)

The first matrix output shows the quantile ratios between the sample and the covariates. A value of 1.0 indicates that the sample is representative of quantile coverage. Values > 1.0 indicate over representation of sample units, while < 1.0 indicate under representation.

sample_ahels(
  mraster = mraster,
  existing = existing, # existing sample
  nQuant = 20, # define 20 quantiles
  nSamp = 300
) # desired sample size

#> Simple feature collection with 500 features and 7 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431130 ymin: 5337710 xmax: 438550 ymax: 5343230
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>      type.x zq90 pzabove2  zsd strata type.y  rule               geometry
#> 1  existing 5.77     54.1 1.31      1    new rule1 POINT (437830 5341110)
#> 2  existing 8.16     83.7 1.73      1    new rule1 POINT (437250 5338030)
#> 3  existing 3.64     43.7 0.68      1    new rule1 POINT (435410 5342590)
#> 4  existing 6.08     45.4 1.49      1    new rule1 POINT (436090 5342370)
#> 5  existing 3.28      7.4 0.61      1    new rule1 POINT (433410 5340870)
#> 6  existing 2.88      4.7 0.47      1    new rule1 POINT (433810 5340570)
#> 7  existing 2.31      0.4 0.32      1    new rule1 POINT (437870 5343090)
#> 8  existing 8.51     46.0 2.22      1    new rule1 POINT (436570 5337730)
#> 9  existing 3.51     10.4 0.66      1    new rule1 POINT (437610 5339250)
#> 10 existing 6.38      3.9 1.49      1    new rule1 POINT (437830 5338010)

Notice that the total number of samples is 500. This value is the sum of existing units (200) and number of sample units defined by nSamp = 300.

sample_existing

Acknowledging that existing sample networks are common is important. There is significant investment into these samples, and in order to keep inventories up-to-date, we often need to collect new data for sample units. The sample_existing algorithm provides the user with methods for sub-sampling an existing sample network should the financial / logistical resources not be available to collect data at all sample units. The functions allows users to choose between algorithm types using (type = "clhs" - default, type = "balanced", type = "srs", type = "strat"). Differences in type result in calling internal sample_existing_*() functions (sample_existing_clhs() (default), sample_existing_balanced(), sample_existing_srs(), sample_existing_strat()). These functions are not exported to be used stand-alone, however they employ the same functionality as their sample_clhs() etc counterparts.

While using sample_existing(), should the user wish to specify algorithm specific parameters (e.g. algorithm = "lcube" in sample_balanced() or allocation = "equal" in sample_strat()), they can specify within sample_existing() as if calling the function directly.

I give applied examples for all methods below that are based on the following scenario:

• We have a systematic sample where sample units are 200m apart.

• We know we only have resources to sample 300 of them.

• We have some ALS data available (mraster), which we can use to improve knowledge of the metric populations.

See our existing sample for the scenario below.

#--- generate existing samples and extract metrics ---#
existing <- sample_systematic(raster = mraster, cellsize = 200, plot = TRUE)

#--- sub sample using ---#
e <- existing %>%
  extract_metrics(mraster = mraster, existing = .)

#--- sub sample using ---#
sample_existing(existing = e, nSamp = 300, type = "clhs")
#> Simple feature collection with 300 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431124.3 ymin: 5337724 xmax: 438555.2 ymax: 5343191
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>      zq90 pzabove2  zsd                 geometry
#> 457 19.40     94.7 4.31 POINT (434436.9 5339880)
#> 790 21.60     89.7 5.84   POINT (438108 5341391)
#> 840 12.50     97.7 2.75 POINT (437026.9 5338353)
#> 526 13.10     81.8 3.68 POINT (435871.9 5341397)
#> 554 23.30     85.9 6.53 POINT (436140.4 5341486)
#> 656  9.27      6.6 2.40 POINT (435327.9 5338536)
#> 593 20.00     69.7 6.07 POINT (435420.1 5339609)
#> 187  3.13     15.6 0.58 POINT (434087.6 5343190)
#> 616 18.10     77.5 5.29 POINT (436048.3 5340413)
#> 321 17.30     66.1 5.05 POINT (433453.7 5340151)

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = mraster, # include mraster metrics to guide sampling of existing
  plot = TRUE
) # plot
#> Simple feature collection with 300 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431125.5 ymin: 5337726 xmax: 438554 ymax: 5343197
#> Projected CRS: +proj=utm +zone=17 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#> First 10 features:
#>        zq90  pzabove2  zsd                 geometry
#> 91350 11.50 70.800003 3.28   POINT (432202 5340333)
#> 91505  2.96  8.400001 0.53 POINT (434442.6 5342116)
#> 91631 24.40 92.900002 4.98 POINT (434258.3 5339970)
#> 91811 18.10 77.500000 5.29 POINT (436048.3 5340413)
#> 91890  2.63  3.500000 0.51 POINT (437752.9 5342465)
#> 91626 14.20 90.000000 3.23 POINT (435157.3 5341756)
#> 91876  8.81 43.400002 2.40 POINT (435956.1 5339339)
#> 91445 19.50 93.000000 2.92 POINT (433905.5 5341939)
#> 92068 11.80 81.300003 2.87 POINT (437384.2 5338173)
#> 91529 12.70 95.500000 2.96 POINT (435070.8 5342919)

#--- create distance from roads metric ---#
dist <- calculate_distance(raster = mraster, access = access)

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = dist, # include mraster metrics to guide sampling of existing
  cost = 4, # either provide the index (band number) or the name of the cost layer
  plot = TRUE
) # plot
#> Simple feature collection with 300 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431127.8 ymin: 5337728 xmax: 438554 ymax: 5343194
#> Projected CRS: +proj=utm +zone=17 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#> First 10 features:
#>        zq90 pzabove2  zsd dist2access                 geometry
#> 91709  4.17      7.7 0.90   58.393480 POINT (434434.6 5338986)
#> 91363 13.30     91.7 2.95   33.625379 POINT (433369.6 5342208)
#> 91399 16.00     59.3 5.32    5.079995 POINT (432559.3 5340153)
#> 91453 13.80     80.0 2.97  428.703683 POINT (433186.3 5340509)
#> 91791  2.18      0.4 0.28   19.278584 POINT (435150.4 5339073)
#> 91844 20.80     65.6 6.48  100.047996   POINT (436137 5340144)
#> 92082  9.66     87.0 2.31  142.899143 POINT (437562.8 5338083)
#> 91276 18.70     89.5 5.03  102.821643 POINT (432295.3 5341853)
#> 92020  9.00     75.5 2.11  202.311298 POINT (436488.6 5337728)
#> 91205  0.00      0.0 0.00  371.489332 POINT (431133.5 5342214)

#--- ensure access and existing are in the same CRS ---#

sf::st_crs(existing) <- sf::st_crs(access)

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = dist, # include mraster metrics to guide sampling of existing
  cost = 4, # either provide the index (band number) or the name of the cost layer
  access = access, # roads layer
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 300, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot
#> Simple feature collection with 300 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431130.1 ymin: 5337727 xmax: 438548.3 ymax: 5343193
#> Projected CRS: +proj=utm +zone=17 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
#> First 10 features:
#>        zq90 pzabove2  zsd dist2access                 geometry
#> 91551 16.40     88.0 3.15   118.73293 POINT (437034.9 5341483)
#> 91281  9.91     70.2 2.58    65.89128 POINT (433997.7 5343012)
#> 91642  2.71     17.4 0.44    61.56608 POINT (437922.4 5338798)
#> 91373  6.02     75.5 1.36    72.46007 POINT (434711.2 5342205)
#> 91394 13.20     49.5 3.76   125.46901 POINT (434350.5 5341043)
#> 91353 12.80     73.4 3.04    60.62854 POINT (434712.3 5342652)
#> 91293 19.50     94.8 3.18    56.90434 POINT (432649.2 5340332)
#> 91383 12.60     90.9 2.56   279.17631 POINT (433182.9 5339168)
#> 91523  7.22     21.8 2.28    74.83604 POINT (435239.2 5338805)
#> 91290 18.80     69.8 5.80   287.98527 POINT (433008.8 5341046)

sample_existing(existing = e, nSamp = 300, type = "balanced")
#> Simple feature collection with 300 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431130.1 ymin: 5337730 xmax: 438559.7 ymax: 5343197
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>     zq90 pzabove2  zsd                 geometry
#> 1  19.50     77.0 5.90 POINT (431135.8 5343108)
#> 2  17.40     92.3 2.30 POINT (431404.4 5343197)
#> 3  18.80     88.8 4.82 POINT (431314.5 5343019)
#> 13 21.20     80.6 6.03 POINT (431671.8 5342839)
#> 15 16.10     93.5 2.24 POINT (431402.1 5342303)
#> 22  8.55     59.3 2.28 POINT (431580.7 5342213)
#> 23 14.30     76.3 3.61 POINT (431490.8 5342034)
#> 24 13.60     82.8 3.86 POINT (431400.9 5341856)
#> 25 11.40     46.6 3.25   POINT (431311 5341677)
#> 28 16.20     79.6 3.78 POINT (432029.1 5342659)

sample_existing(existing = e, nSamp = 300, type = "balanced", algorithm = "lcube")
#> Simple feature collection with 300 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431124.3 ymin: 5337724 xmax: 438557.5 ymax: 5343193
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    zq90 pzabove2  zsd                 geometry
#> 1  19.5     77.0 5.90 POINT (431135.8 5343108)
#> 4  19.7     81.2 6.20 POINT (431224.6 5342840)
#> 6  16.9     85.1 4.02   POINT (431583 5343107)
#> 14 20.7     85.9 4.66 POINT (431581.9 5342660)
#> 19 19.2     88.5 4.18 POINT (431850.4 5342749)
#> 23 14.3     76.3 3.61 POINT (431490.8 5342034)
#> 24 13.6     82.8 3.86 POINT (431400.9 5341856)
#> 26 16.3     68.4 4.03 POINT (432208.9 5343016)
#> 27 13.1     66.1 3.13   POINT (432119 5342838)
#> 36 17.9     76.7 5.16 POINT (431309.9 5341230)

sample_existing(existing = e, nSamp = 300, type = "srs")
#> Simple feature collection with 300 features and 3 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431122.1 ymin: 5337724 xmax: 438550.6 ymax: 5343190
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>     zq90 pzabove2  zsd                 geometry
#> 1   5.11     22.6 1.19   POINT (433010 5341494)
#> 2  12.80     73.4 3.04 POINT (434712.3 5342652)
#> 3  14.80     87.0 3.41 POINT (438201.3 5342911)
#> 4  16.50     94.9 3.37 POINT (433902.1 5340597)
#> 5  10.70     46.1 3.11 POINT (435515.7 5342024)
#> 6  11.90     21.9 3.61 POINT (435243.7 5340594)
#> 7  14.00     94.2 3.24 POINT (433537.9 5338093)
#> 8  27.00     90.3 7.19 POINT (433269.4 5338005)
#> 9  14.20     71.1 3.78 POINT (438291.2 5343090)
#> 10 16.40     95.3 3.61 POINT (438464.1 5340764)

sraster <- strat_kmeans(mraster = mraster, nStrata = 4)

e_strata <- extract_strata(sraster = sraster, existing = e)

#--- proportional stratified sampling of existing ---#
sample_existing(existing = e_strata, nSamp = 300, type = "strat", allocation = "prop")
#> Simple feature collection with 301 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431123.2 ymin: 5337726 xmax: 438555.2 ymax: 5343194
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata zq90 pzabove2  zsd                 geometry
#> 1       3 24.9     92.8 6.17 POINT (432560.5 5340600)
#> 2       3 19.2     80.8 6.02 POINT (431403.2 5342750)
#> 3       3 22.1     88.3 4.78 POINT (432739.1 5340510)
#> 4       3 21.6     89.7 5.84   POINT (438108 5341391)
#> 5       3 22.2     89.2 5.92 POINT (438555.2 5341390)
#> 6       3 19.2     90.6 5.00 POINT (431669.5 5341944)
#> 7       3 17.0     57.1 5.70 POINT (434529.1 5340953)
#> 8       3 19.2     95.6 5.15 POINT (432914.3 5339079)
#> 9       3 20.3     89.1 5.43 POINT (431128.9 5340425)
#> 10      3 19.4     59.4 6.17 POINT (433819.1 5343102)

#--- equal stratified sampling of existing ---#
sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "equal")
#> Simple feature collection with 400 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431125.5 ymin: 5337726 xmax: 438559.7 ymax: 5343197
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata zq90 pzabove2  zsd                 geometry
#> 1       3 20.4     93.2 5.98 POINT (432016.5 5337740)
#> 2       3 27.3     92.2 8.30 POINT (433271.6 5338899)
#> 3       3 16.5     45.6 4.86 POINT (437394.5 5342198)
#> 4       3 22.0     91.7 6.23 POINT (433806.5 5338182)
#> 5       3 18.8     90.9 5.01 POINT (433632.4 5340061)
#> 6       3 21.9     94.7 7.45 POINT (437214.7 5341841)
#> 7       3 24.9     52.5 7.90 POINT (437396.8 5343092)
#> 8       3 17.9     76.7 5.16 POINT (431309.9 5341230)
#> 9       3 20.8     94.6 6.06 POINT (431664.9 5340155)
#> 10      3 19.2     80.8 6.02 POINT (431403.2 5342750)

#--- manual stratified sampling of existing with user defined weights ---#
s <- sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "manual", weights = c(0.2, 0.6, 0.1, 0.1))

#--- check proportions match weights ---#
table(s$strata) / 100
#> 
#>   1   2   3   4 
#> 0.2 0.6 0.1 0.1

#--- manual stratified sampling of existing with user defined weights ---#
sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "optim", raster = mraster, metric = "zq90")
#> Simple feature collection with 100 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 431127.8 ymin: 5337735 xmax: 438554 ymax: 5343191
#> Projected CRS: UTM Zone 17, Northern Hemisphere
#> First 10 features:
#>    strata zq90 pzabove2  zsd                 geometry
#> 1       3 20.0     92.8 4.64 POINT (435780.8 5340771)
#> 2       3 18.7     89.5 5.03 POINT (432295.3 5341853)
#> 3       3 20.9     80.8 6.66 POINT (435783.1 5341665)
#> 4       3 21.7     86.5 6.73 POINT (437478.6 5340141)
#> 5       3 21.7     86.3 4.52 POINT (436405.6 5340233)
#> 6       3 20.5     78.0 6.36 POINT (436765.2 5340947)
#> 7       3 17.1     66.4 5.73 POINT (437480.9 5341035)
#> 8       3 19.2     95.6 5.15 POINT (432914.3 5339079)
#> 9       3 20.4     91.9 4.69 POINT (435331.3 5339878)
#> 10      3 21.8     85.7 6.29 POINT (431844.7 5340513)