In tgoodbody/sgsR: Structurally Guided Sampling

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

```{css,echo=FALSE} .infobox { padding: 1em 1em 1em 4em; margin-bottom: 10px; border: 2px solid #43602d; border-radius: 10px; background: #738e41 5px center/3em no-repeat; }

.caution { background-image: url("https://tgoodbody.github.io/sgsR/logo.png"); }

```r
library(sgsR)
library(terra)

#--- Load mraster and access files ---#
r <- system.file("extdata", "mraster.tif", package = "sgsR")

#--- load the mraster using the terra package ---#
mraster <- terra::rast(r)

a <- system.file("extdata", "access.shp", package = "sgsR")

#--- load the access vector using the sf package ---#
access <- sf::st_read(a, quiet = TRUE)

#--- apply quantiles algorithm to metrics raster ---#
sraster <- strat_quantiles(
  mraster = mraster$zq90, # use mraster as input for sampling
  nStrata = 4
) # algorithm will produce 4 strata

#--- apply stratified sampling algorithm ---#
existing <- sample_strat(
  sraster = sraster, # use mraster as input for sampling
  nSamp = 200, # request 200 samples be taken
  mindist = 100
) # define that samples must be 100 m apart

#--- algorithm table ---#

a <- c("`calculate_representation()`", "`calculate_distance()`", "`calculate_pcomp()`", "`calculate_sampsize()`", "`calculate_allocation()`", "`calculate_coobs()`", "`calculate_pop()`", "`calculate_lhsOpt()`")

d <- c("Determine representation of strata in existing sample unit", "Per pixel distance to closest `access` vector", "Principal components of input `mraster`", "Estimated sample sizes based on relative standard error", "Proportional / optimal / equal / manual allocation", "Detail how `existing` sample units are distributed among `mraster`", "Population level information (PCA / quantile matrix / covariance matrix) of `mraster`", "Determine optimal Latin hypercube sampling parameters including sample size")

urls <- c("#rep", "#dist", "#pcomp", "#sampsize", "#allocation", "#coobs", "#lhspop", "#lhsopt")

df <- data.frame(Algorithm = a, Description = d)

df$Algorithm <- paste0("[", df$Algorithm, "](", urls, ")")

Currently, there are 8 functions associated with the calculate verb in the sgsR package:

knitr::kable(df, align = "c")

calculate_representation() {#rep .unnumbered}

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
)

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
)

::: {.infobox .caution data-latex="{caution}"} TIP!

Presence of very small (negligible) differences between srasterFreq and sampleFreq is common. In these situations, it is important for the user to determine whether to add or remove the samples.
:::

calculate_distance {#dist .unnumbered}

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

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

calculate_pcomp {#pcomp .unnumbered}

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

calculate_sampsize {#sampsize .unnumbered}

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
)

#--- 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
)

p

calculate_allocation {#allocation .unnumbered}

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).

Proportional allocation {#proportional .unnumbered}

Samples are allocated based on the spatial coverage area of the strata. This is the default allocation method.

#--- perform grid sampling ---#
calculate_allocation(
  sraster = sraster,
  nSamp = 200
)

In this case the sraster has equally sized strata, so the number of allocated sample units is always the same.

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

calculate_allocation(
  sraster = sraster,
  nSamp = 200,
  existing = e.sr
)

At times, values under total can be negative. Negative values indicate that existing sample units over represent those strata and that some sample units could removed to prevent over-representation. $total indicates the number of sample units that could be added or removed.

Optimal Allocation {#optimal .unnumbered}

Sample units are allocated based on within strata variance. The optimal allocation method uses the variation within the strata metric to allocate sample units. This means that in addition to providing an sraster, that a specific metric (mraster) must be provided to calculate variation to optimally allocate sample units.

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

Equal allocation {#equal .unnumbered}

There may be situations where the user wants an equal number of sample units allocated to each strata. In these situations use allocation = equal. In this case, nSamp refers to the total number of sample units per strata, instead of the overall total number.

calculate_allocation(
  sraster = sraster, # stratified raster
  nSamp = 20, # desired sample number
  allocation = "equal"
) # optimal allocation

The code in the demonstration above yields a total of 80 samples (20 nSamp for each of the 4 strata in sraster).

Manual allocation {#manual .unnumbered}

The user may wish to manually assign weights to strata. In this case, allocation = manual can be used and weights must be provided as a numeric vector (e.g. weights = c(0.2, 0.2, 0.2, 0.4) where sum(weights) == 1). In this case, nSamp will be allocated based on weights.

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

The code above yields a total of 20 sample units with plots being allocated based on the weights provided in ascending strata order.

Sample evaluation algorithms {#sampeval .unnumbered}

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 {#coobs .unnumbered}

calculate_coobs() function performs the COunt of OBServations (coobs) algorithm using an existing sample and mraster. This algorithm helps the user understand how an existing sample is distributed among the landscape in relation to mraster data.

::: {.infobox .caution data-latex="{caution}"} TIP!

The output coobs raster can be used to constrain clhs sampling using the sample_clhs() function to the areas that are under-represented. :::

The coobs raster determines how many observations are similar in terms of the covariate space at every pixel, and takes advantage of parallel processing routines.

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 {#lhseval .unnumbered}

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

calculate_pop {#lhspop .unnumbered}

calculate_pop() calculates population level statistics of an mraster, including calculating the principal components, quantile & covariate distributions, and Kullback-Leibler divergence testing.

The outputs produced from this functions are required to use the calculate_lhsOpt() function described in the following section.

::: {.infobox .caution data-latex="{caution}"} TIP!

This algorithm can be pre-emptively used to calculate matQ and MatCov, two values that are used for the sample_ahels() function. This will save processing time during sampling. :::

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

The output list contains the following:

• $values - Pixel values from mraster

• $pcaLoad - PCA loadings

• $matQ - Quantile matrix

• $matCov - Covariate matrix

#--- 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_lhsOpt {#lhsopt .unnumbered}

calculate_lhsOpt() function performs a bootstrapped latin hypercube sampling approach where population level analysis of mraster data is performed to determine the optimal latin hypercube sample size.

calculate_pop() and varying sample sizes defined by minSamp, maxSamp, step and rep. Sampling protocols are conducted and statistical effectiveness of those sampling outcomes are evaluated to determine where sample size is minimized and statistical representation is maximized.

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

calculate_lhsOpt(popLHS = poplhs)

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

tgoodbody/sgsR documentation built on March 7, 2024, 2:20 a.m.