Calculating

calculate_representation()

calculate_representation() function allows the users to verify how a stratification is spatially represented in an existing sample. Result in tabular and graphical (if plot = TRUE) outputs that compare strata coverage frequency and sampling frequency.

#--- quantile sraster ---#
quantiles <- strat_quantiles(
  mraster = mraster$zq90,
  nStrata = 8
)

#--- random samples ---#
srs <- sample_srs(
  raster = sraster,
  nSamp = 50
)

#--- calculate representation ---#
calculate_representation(
  sraster = quantiles,
  existing = srs,
  plot = TRUE
)

#> # A tibble: 8 × 6
#>   strata srasterFreq sampleFreq diffFreq nSamp  need
#>    <dbl>       <dbl>      <dbl>    <dbl> <int> <dbl>
#> 1      1        0.13       0.18   0.05       9    -2
#> 2      2        0.13       0.14   0.0100     7     0
#> 3      3        0.12       0.12   0          6     0
#> 4      4        0.13       0.04  -0.09       2     5
#> 5      5        0.13       0.14   0.0100     7     0
#> 6      6        0.12       0.16   0.04       8    -2
#> 7      7        0.13       0.12  -0.0100     6     1
#> 8      8        0.12       0.1   -0.0200     5     1

The tabular output presents the frequency of coverage for each strata (srasterFreq) (what % of the landscape does the strata cover) and the sampling frequency within each strata (sampleFreq) (what % of total existing samples are in the strata). The difference (diffFreq) between coverage frequency and sampling frequency determines whether the values are over-represented (positive numbers) or under-represented (negative numbers). This value translates to a discrete need attribute that defines whether there is a need to add or remove samples to meet the number of samples necessary to be considered representative of the spatial coverage of strata inputted in sraster.

Performing the algorithm on a sample set derived using sample_strat() exhibits proportional sampling to strata coverage given that samples were allocated proportionally to spatial coverage.

calculate_representation(
  sraster = sraster,
  existing = existing,
  plot = TRUE
)

#> # A tibble: 4 × 6
#>   strata srasterFreq sampleFreq diffFreq nSamp  need
#>    <dbl>       <dbl>      <dbl>    <dbl> <int> <dbl>
#> 1      1        0.25       0.26   0.0100    51    -1
#> 2      2        0.25       0.25   0         50     0
#> 3      3        0.25       0.24  -0.0100    49     1
#> 4      4        0.25       0.25   0         50     0

calculate_distance

calculate_distance() uses input raster and access data and outputs the per pixel distance to the nearest access point. This algorithm has a specific value for constraining sampling protocols, such as with sample_clhs(), where the output raster layer can be used as the cost for the constraint. The output raster consists of the input appended with the calculated distance layer (dist2access). The slope parameters also exists to calculate slope distance instead of geographic distance, which becomes very handy in the case of steep mountainous areas and is faster from a computational point of view. If slope == TRUE, the mraster provided should be a digital terrain model.

calculate_distance(
  raster = sraster, # input
  access = access, # define access road network
  plot = TRUE
) # plot
#> 
|---------|---------|---------|---------|
=========================================
                                          

#> class       : SpatRaster 
#> dimensions  : 277, 373, 2  (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 
#> names       : strata, dist2access 
#> min values  :      1,      0.3438 
#> max values  :      4,   1061.6599

This function performs considerably slower when access has many features. Consider mergeing features for improved efficiency.

calculate_pcomp

calculate_pcomp() uses mraster as the input and performs principal component analysis. The number of components defined by the nComp parameter specifies the number of components that will be rasterized.

calculate_pcomp(
  mraster = mraster, # input
  nComp = 3, # number of components to output
  plot = TRUE, # plot
  details = TRUE
) # details about the principal component analysis appended

#> $pca
#> Standard deviations (1, .., p=3):
#> [1] 1.5479878 0.7359109 0.2493371
#> 
#> Rotation (n x k) = (3 x 3):
#>                PC1        PC2        PC3
#> zq90     0.6286296 -0.1795433 -0.7566961
#> pzabove2 0.5104140  0.8293596  0.2272450
#> zsd      0.5867729 -0.5290812  0.6130014
#> 
#> $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       :       PC1,       PC2,       PC3 
#> min values  : -4.402269, -5.357801, -1.446156 
#> max values  :  5.282663,  2.155242,  1.510955

calculate_sampsize

calculate_sampsize() function allows the user to estimate an appropriate sample size using the relative standard error (rse) of input metrics. If the input mraster contains multiple layers, the sample sizes will be determined for all layers. If plot = TRUE and rse is defined, a sequence of rse values will be visualized with the indicators and the values for the matching sample size.

#--- determine sample size based on relative standard error (rse) of 1% ---#
calculate_sampsize(
  mraster = mraster,
  rse = 0.01
)
#>   nSamp  rse      var
#> 1  1394 0.01     zq90
#> 2  1341 0.01 pzabove2
#> 3  1859 0.01      zsd

#--- change default threshold sequence values ---#
#--- if increment and rse are not divisible the closest value will be taken ---#
p <- calculate_sampsize(
  mraster = mraster,
  rse = 0.025,
  start = 0.01,
  end = 0.08,
  increment = 0.01,
  plot = TRUE
)
#> 'rse' not perfectly divisible by 'increment'. Selecting closest sample size (rse = 0.03) based on values.

p
#> $nSamp
#> # A tibble: 3 × 3
#> # Groups:   var [3]
#>   nSamp   rse var     
#>   <dbl> <dbl> <chr>   
#> 1   157  0.03 zq90    
#> 2   151  0.03 pzabove2
#> 3   211  0.03 zsd     
#> 
#> $plot

calculate_allocation

calculate_allocation() determines how sample units are allocated based on the desired sample size (nSamp) and the input sraster. It is used internally in a number of algorithms, including sample_strat. Currently, there are four allocation methods: proportional (prop; default), optimal (optim), equal (equal), and manual (manual).

#--- perform grid sampling ---#
calculate_allocation(
  sraster = sraster,
  nSamp = 200
)
#>   strata total
#> 1      1    51
#> 2      2    50
#> 3      3    49
#> 4      4    50

#--- calculate existing samples to include ---#
e.sr <- extract_strata(
  sraster = sraster,
  existing = existing
)

calculate_allocation(
  sraster = sraster,
  nSamp = 200,
  existing = e.sr
)
#>   strata total need
#> 1      1     0   51
#> 2      2     0   50
#> 3      3     0   49
#> 4      4     0   50

calculate_allocation(
  sraster = sraster, # stratified raster
  nSamp = 200, # desired sample number
  existing = e.sr, # existing samples
  allocation = "optim", # optimal allocation
  mraster = mraster$zq90, # metric raster
  force = TRUE
) # force nSamp number
#> # A tibble: 4 × 3
#> # Rowwise: 
#>   strata total  need
#>    <dbl> <dbl> <dbl>
#> 1      1    27    78
#> 2      2   -14    36
#> 3      3   -25    24
#> 4      4    12    62

calculate_allocation(
  sraster = sraster, # stratified raster
  nSamp = 20, # desired sample number
  allocation = "equal"
) # optimal allocation
#> Implementing equal allocation of samples.
#> # A tibble: 4 × 2
#>   strata total
#>    <dbl> <dbl>
#> 1      1    20
#> 2      2    20
#> 3      3    20
#> 4      4    20

weights <- c(0.2, 0.2, 0.2, 0.4)

calculate_allocation(
  sraster = sraster, # stratified raster
  nSamp = 20, # desired sample number
  allocation = "manual", # manual allocation
  weights = weights
) # weights adding to 1
#> Implementing allocation of samples based on user-defined weights.
#>   strata total
#> 1      1     4
#> 2      2     4
#> 3      3     4
#> 4      4     8

Sample evaluation algorithms

The following algorithms were initially developed by Dr. Brendan Malone from the University of Sydney. Dr. Malone and his colleagues supplied an in depth description of the functionality of these algorithms, which were originally developed to improve soil sampling strategies. These functions were modified and implemented to be used for structurally guided sampling approaches. Many thanks to Dr. Malone for being a proponent of open source algorithms.

Please consult the original reference for these scripts and ideas as their publication holds helpful and valuable information to understand their rationale for sampling and algorithm development.

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

calculate_coobs(
  mraster = mraster, # input
  existing = existing, # existing samples
  cores = 4, # parallel cores to use
  details = TRUE, # provide details from algorithm output
  plot = TRUE
) # plot

Latin hypercube sampling evaluation algorithms

The following 2 algorithms present the means to maximize the effectiveness of the latin hypercube sampling protocols.

#--- by default all statistical data are calculated ---#
calculate_pop(mraster = mraster) # input

#--- statistical analyses can be chosen by setting their parameter to `FALSE` ---#
mat <- calculate_pop(
  mraster = mraster, # input
  nQuant = 10
) # desired number of quantiles

#--- use matrix output within sample ahels algorithm ---#
sample_ahels(
  mraster = mraster, # input
  existing = existing, # existing sample
  nQuant = 10, # number of desired quantiles
  nSamp = 50, # desired sample size
  matCov = mat
) # covariance matrix

#--- calculate lhsPop details ---#
poplhs <- calculate_pop(mraster = mr)

calculate_lhsOpt(popLHS = poplhs)

calculate_lhsOpt(
  popLHS = poplhs,
  PCA = FALSE,
  iter = 200
)