calculate_representation()

calculate_representation() function allows the users toverify how a stratification is spatially represented in anexisting sample. Result in tabular and graphical (ifplot = TRUE) outputs that compare strata coverage frequencyand 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       0.12  -0.0100     6     1#> 2      2        0.13       0.08  -0.05       4     3#> 3      3        0.12       0.14   0.0200     7    -1#> 4      4        0.13       0.1   -0.03       5     2#> 5      5        0.13       0.16   0.03       8    -1#> 6      6        0.12       0.16   0.04       8    -2#> 7      7        0.13       0.16   0.03       8    -1#> 8      8        0.12       0.08  -0.04       4     2

The tabular output presents the frequency of coverage for each strata(srasterFreq) (what % of the landscape does the stratacover) and the sampling frequency within each strata(sampleFreq) (what % of totalexisting samplesare in the strata). The difference (diffFreq) betweencoverage frequency and sampling frequency determines whether the valuesare over-represented (positive numbers) or under-represented (negativenumbers). This value translates to a discreteneedattribute that defines whether there is a need to add or remove samplesto meet the number of samples necessary to be considered representativeof the spatial coverage of strata inputted insraster.

Performing the algorithm on a sample set derived usingsample_strat() exhibits proportional sampling to stratacoverage given that samples were allocated proportionally to spatialcoverage.

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 inputraster andaccess data and outputs the per pixel distance to thenearest access point. This algorithm has a specific value forconstraining sampling protocols, such as withsample_clhs(), where the output raster layer can be used asthecost for the constraint. The output raster consists ofthe input appended with the calculated distance layer(dist2access). Theslope parameters alsoexists to calculate slope distance instead of geographic distance, whichbecomes very handy in the case of steep mountainous areas and is fasterfrom a computational point of view. Ifslope == TRUE, themraster provided should be a digital terrain model.

calculate_distance(raster = sraster,# inputaccess = access,# define access road networkplot =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 whenaccess has many features. Consider mergeing features forimproved efficiency.

calculate_pcomp

calculate_pcomp() usesmraster as the inputand performs principal component analysis. The number of componentsdefined by thenComp parameter specifies the number ofcomponents that will be rasterized.

calculate_pcomp(mraster = mraster,# inputnComp =3,# number of components to outputplot =TRUE,# plotdetails =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, -2.155242, -1.510955 #> max values  :  5.282663,  5.357801,  1.446156

calculate_sampsize

calculate_sampsize() function allows the user toestimate an appropriate sample size using the relative standard error(rse) of input metrics. If the inputmrastercontains multiple layers, the sample sizes will be determined for alllayers. Ifplot = TRUE andrse is defined, asequence ofrse values will be visualized with theindicators 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 areallocated based on the desired sample size (nSamp) and theinputsraster. It is used internally in a number ofalgorithms, includingsample_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 rasternSamp =200,# desired sample numberexisting = e.sr,# existing samplesallocation ="optim",# optimal allocationmraster = mraster$zq90,# metric rasterforce =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 rasternSamp =20,# desired sample numberallocation ="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 rasternSamp =20,# desired sample numberallocation ="manual",# manual allocationweights = 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. BrendanMalone from the University of Sydney. Dr. Malone and his colleaguessupplied an in depth description of the functionality of thesealgorithms, which were originally developed to improve soil samplingstrategies. These functions were modified and implemented to be used forstructurally guided sampling approaches. Many thanks to Dr. Malone forbeing a proponent of open source algorithms.

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

Malone BP, Minansy B, Brungard C. 2019. Some methods to improvethe utility of conditioned Latin hypercube sampling. PeerJ 7:e6451 DOI10.7717/peerj.6451

calculate_coobs(mraster = mraster,# inputexisting = existing,# existing samplescores =4,# parallel cores to usedetails =TRUE,# provide details from algorithm outputplot =TRUE)# plot

Latin hypercube sampling evaluationalgorithms

The following 2 algorithms present the means to maximize theeffectiveness of thelatin hypercube samplingprotocols.

#--- 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,# inputnQuant =10)# desired number of quantiles#--- use matrix output within sample ahels algorithm ---#sample_ahels(mraster = mraster,# inputexisting = existing,# existing samplenQuant =10,# number of desired quantilesnSamp =50,# desired sample sizematCov = mat)# covariance matrix

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

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