soilsampling

Soil Sampling Design Methods Including Spatial Coverage, Maxvol Optimal Design, Simple Random, and Stratified Sampling

Overview

The soilsampling package provides methods for designing soil sampling schemes. It implements:

• Simple Random Sampling: Uniform random selection of sampling locations
• Stratified Random Sampling: Random sampling within compact geographical strata
• Spatial Coverage Sampling: Purposive sampling at stratum centroids for optimal coverage
• Maxvol Optimal Design Sampling: Feature-based sampling using D-optimal experimental design
• Composite Sampling: Sampling from equal-area strata for combined samples
• Validation Metrics: Assess stratification quality through coverage efficiency and distance statistics
• KL Sample Size Optimization: Determine optimal cLHS sample size via Kullback-Leibler divergence
• cLHS + Random Forest Optimization: Refine a cLHS design with simulated annealing to minimize RF prediction error
• Alternative Site Selection: Find environmentally similar replacement sites for inaccessible sampling locations

Installation

Install from GitHub (Recommended)

# Using pak (fastest)
pak::pak("ccarbajal16/soilsampling")

# Or using devtools
devtools::install_github("ccarbajal16/soilsampling")

Install from Local Source

# Install from local directory
install.packages(".", repos = NULL, type = "source")

# Or using devtools
devtools::install_local("path/to/soilsampling")

Dependencies

• R (>= 4.1.0)
• sf (>= 1.0-12)
• ggplot2 (>= 3.3.0)
• terra
• clhs
• dplyr
• minpack.lm
• randomForest
• gridExtra

Quick Start

library(soilsampling)
library(sf)

# Create a study area
poly <- st_polygon(list(rbind(
  c(0, 0), c(100, 0), c(100, 50), c(0, 50), c(0, 0)
)))
study_area <- st_sf(geometry = st_sfc(poly))

# Set seed for reproducibility
set.seed(42)

# Spatial coverage sampling
samples <- ss_coverage(study_area, n_strata = 25, n_try = 5)
ss_plot(samples)

# Get coordinates
coords <- ss_to_data_frame(samples)
head(coords)

Sampling Methods

Simple Random Sampling

Select locations uniformly at random:

samples <- ss_random(study_area, n = 30)
ss_plot_samples(samples)

Stratified Random Sampling

Create strata first, then sample randomly within each:

# Create 25 compact strata
strata <- ss_stratify(study_area, n_strata = 25, n_try = 5)

# Take 1 random sample per stratum
samples <- ss_stratified(strata, n_per_stratum = 1)
ss_plot(strata, samples = samples)

Spatial Coverage Sampling

Place samples at stratum centroids for optimal spatial coverage:

# Direct approach
samples <- ss_coverage(study_area, n_strata = 25, n_try = 5)

# Or use pre-computed strata
strata <- ss_stratify(study_area, n_strata = 25, n_try = 5)
samples <- ss_coverage(strata)

ss_plot(samples)

Spatial Coverage with Prior Points

Incorporate existing sampling locations:

# Existing sample locations
prior_pts <- st_as_sf(
  data.frame(x = c(25, 75), y = c(25, 25)),
  coords = c("x", "y")
)

# Create stratification around prior points
strata <- ss_stratify(
  study_area, 
  n_strata = 20, 
  prior_points = prior_pts,
  n_try = 5
)

samples <- ss_coverage(strata)
ss_plot(samples)  # Prior points shown with different symbol

Equal-Area Stratification

Create strata of equal size:

samples <- ss_coverage_equal_area(study_area, n_strata = 25, n_try = 5)

Composite Sampling

For combining samples from multiple locations:

# Create 3 composite samples from 20 equal-area strata
samples <- ss_composite(study_area, n_strata = 20, n_composites = 3)
ss_plot(samples)  # Different symbols for each composite

Maxvol Optimal Design Sampling

Feature-based sampling using D-optimal experimental design to maximize diversity:

# Create a grid with terrain features
strata <- ss_stratify(study_area, n_strata = 100, n_try = 5)
cells_sf <- strata$cells

# Add terrain features (in practice, extract from DEM)
coords <- st_coordinates(cells_sf)
cells_sf$elevation <- coords[,2] + rnorm(nrow(coords), 0, 5)
cells_sf$slope <- abs(rnorm(nrow(coords), 5, 2))
cells_sf$twi <- rnorm(nrow(coords), 8, 1.5)

# Select 20 optimal samples based on features
samples <- ss_maxvol(
  cells_sf,
  n = 20,
  features = c("elevation", "slope", "twi"),
  min_dist = 5,        # Minimum distance between samples
  normalize = TRUE,    # Normalize features to equal scales
  add_coords = TRUE    # Include coordinates as features
)

ss_plot_samples(samples)

The maxvol algorithm selects locations that maximize the determinant (volume) of the feature submatrix, ensuring maximum diversity in feature space. This is particularly effective when:

• Features explain soil-forming factors
• You need deterministic (non-random) point selection
• You want optimal coverage with few samples

Sample Size Optimization (KL Divergence)

Determine the cLHS sample size that best represents the population distribution, based on Kullback-Leibler divergence (Malone et al. 2019):

library(terra)

predictors <- rast("data/predictors.tif")

result <- ss_kl_size(
  predictors,
  min_samples = 10,
  max_samples = 200,
  step_size = 10,
  n_replicates = 10,
  output_dir = "outputs"   # optional: writes CSVs and plots
)

result$optimal_sample_size
result$plot_cdf

ss_kl_size() accepts a raster path, an already-loaded SpatRaster, or a population data frame directly. Use ss_kl_optimize() for the underlying optimization without raster I/O, or ss_kl_divergence() to compute divergence between an arbitrary population and sample.

cLHS + Random Forest Optimization

Refine a cLHS baseline design using simulated annealing to minimize cross-validated Random Forest prediction error (Wadoux et al. 2019):

predictors <- rast("data/predictors.tif")

result <- ss_rf_size(
  predictors,
  n_samples = 100,
  n_iterations = 500,
  seed = 123,
  output_dir = "outputs"   # optional: writes CSVs and comparison plot
)

result$comparison_table
result$improvement   # % MSE reduction vs. the cLHS baseline

ss_clhs_sample() generates the cLHS baseline alone; ss_rf_optimize() runs the simulated-annealing refinement; ss_rf_mse() exposes the cross-validated MSE objective function directly.

Alternative Site Selection

Find environmentally similar alternative sites when original sampling locations become inaccessible:

predictors <- rast("data/predictors.tif")
inaccessible <- read.csv("data/inaccessible_sites.csv")  # needs x, y columns

result <- ss_alt_sites(
  predictors,
  inaccessible,
  method = "mahalanobis",       # or "euclidean", "gower"
  n_alternatives = 3,
  min_distance_buffer = 300,    # exclude candidates within 300m of any target
  seed = 123,
  output_dir = "outputs"        # optional: writes CSVs
)

result$alternatives   # top alternatives for every inaccessible site

Lower-level building blocks are also exported: ss_alt_candidates() (candidate pool generation), ss_alt_filter_buffer() (distance exclusion), ss_alt_similarity() (similarity scoring), ss_alt_rank() (top-N selection), and ss_alt_standardize_sites() (normalize raw CSV coordinates to the package's site layout).

Assessing Stratification Quality

The package provides validation metrics to assess the quality of your stratification:

Coverage Efficiency

Evaluate how uniformly cells are distributed across strata:

# Create stratification
strata <- ss_stratify(study_area, n_strata = 25, n_try = 5)

# Assess coverage efficiency
efficiency <- ss_coverage_efficiency(strata)
print(efficiency)

Output metrics:

• CV (Coefficient of Variation): Lower values indicate more uniform distribution
• Min/Max Ratio: Ratio of smallest to largest stratum (1.0 = perfect equality)
• Gini Coefficient: Standard inequality measure (0 = perfect equality)
• Efficiency Score: Qualitative assessment (Excellent/Good/Fair/Poor)

Comparing stratification methods:

# Regular stratification
strata_regular <- ss_stratify(study_area, n_strata = 20, n_try = 5)

# Equal-area stratification
strata_equal <- ss_stratify(study_area, n_strata = 20,
                             equal_area = TRUE, n_try = 5)

# Compare efficiency
eff_regular <- ss_coverage_efficiency(strata_regular)
eff_equal <- ss_coverage_efficiency(strata_equal)

cat("Regular CV:", eff_regular$cv, "\n")
cat("Equal-area CV:", eff_equal$cv, "\n")
# Equal-area should have much lower CV (< 0.05 vs 0.15-0.30)

Distance Statistics

Compute distance from cells or samples to stratum centroids:

# For stratification
dist_summary <- ss_distance_summary(strata)
print(dist_summary)

# For samples (works with coverage or stratified samples)
samples <- ss_coverage(strata)
dist_samples <- ss_distance_summary(samples, actual_distance = TRUE)
print(dist_samples)

Output (per stratum):

• Mean, SD, min, max, median distances to centroid
• Helps identify dispersed or compact strata
• Default: squared distances (consistent with MSSD metric)

Use cases:

• Compare different stratification runs (n_try values)
• Verify equal-area maintains compactness
• Identify strata with unusual geometry

Working with Shapefiles

# Read study area
study_area <- st_read("path/to/study_area.shp")

# Create sampling design
set.seed(42)
samples <- ss_coverage(study_area, n_strata = 50, n_try = 10)

# Export as CSV
coords <- ss_to_data_frame(samples)
write.csv(coords, "sampling_points.csv", row.names = FALSE)

# Export as GeoPackage
samples_sf <- ss_to_sf(samples)
st_write(samples_sf, "sampling_points.gpkg")

Function Reference

Stratification

Function	Description
ss_stratify()	Create compact geographical strata using k-means

Sampling

Function	Description
ss_random()	Simple random sampling
ss_stratified()	Stratified random sampling
ss_coverage()	Spatial coverage sampling (centroids)
ss_coverage_equal_area()	Coverage sampling with equal-area strata
ss_maxvol()	Maxvol optimal design sampling (feature-based)
ss_composite()	Composite sampling

Visualization

Function	Description
ss_plot()	Plot stratification and/or samples
ss_plot_samples()	Plot sampling points only

Validation

Function	Description
ss_coverage_efficiency()	Assess uniformity of cell distribution across strata
ss_distance_summary()	Compute distance statistics from cells/samples to centroids

Utilities

Function	Description
ss_to_sf()	Convert to sf object
ss_to_data_frame()	Convert to data frame with coordinates
ss_summary()	Get summary statistics
ss_get_samples()	Extract samples sf object
ss_n_strata()	Get number of strata
ss_n_samples()	Get number of samples
ss_area()	Get stratum areas
ss_relative_area()	Get relative stratum areas

KL Sample Size Optimization

Function	Description
ss_load_rasters()	Load a multi-layer raster or a directory of single-layer rasters
ss_kl_divergence()	KL divergence between population and sample distributions
ss_kl_optimize()	Optimize cLHS sample size via KL divergence
ss_kl_size()	End-to-end workflow from raster/data frame to optimal sample size
ss_kl_save_plots()	Save KL divergence and CDF plots independently

cLHS + Random Forest Optimization

Function	Description
ss_clhs_sample()	Conditioned Latin hypercube baseline sampling
ss_rf_mse()	Cross-validated Random Forest MSE objective function
ss_rf_optimize()	Simulated annealing refinement to minimize RF MSE
ss_rf_size()	End-to-end workflow with comparison plots

Alternative Site Selection

Function	Description
ss_alt_similarity()	Environmental similarity (Mahalanobis, Euclidean, or Gower distance)
ss_alt_candidates()	Generate a candidate site pool (random or systematic grid)
ss_alt_filter_buffer()	Exclude candidates within a minimum distance of target sites
ss_alt_rank()	Rank and select the top similar alternatives
ss_alt_standardize_sites()	Standardize site coordinate data to the package's layout
ss_alt_sites()	End-to-end alternative site selection workflow

When to Use Each Method

Method	Best For	Inference Type
ss_coverage()	Interpolation (kriging)	Model-based
ss_maxvol()	Feature diversity, D-optimal design	Model-based
ss_stratified()	Estimating means/totals	Design-based
ss_random()	Simple design-based analysis	Design-based
ss_composite()	Reducing laboratory costs	Design-based
ss_kl_size()	Choosing how many cLHS samples to collect	Model-based
ss_rf_size()	Maximizing predictive accuracy of a fixed-size design	Model-based
ss_alt_sites()	Replacing inaccessible sites with similar alternatives	Model-based

Algorithm Details

The package uses pure R implementations of k-means algorithms:

1. Transfer Algorithm (default): Standard k-means that iteratively transfers cells to nearer cluster centers. Creates compact but potentially unequal-sized strata.

2. Swop Algorithm (equal_area = TRUE): Modified k-means that swaps cells between clusters to maintain equal sizes while optimizing compactness.

Both algorithms minimize the Mean Squared Shortest Distance (MSSD) between cells and their assigned cluster centroids.

Tips for Best Results

1. Use multiple tries: Set n_try = 10 or higher to avoid local optima
2. Set a seed: Use set.seed() for reproducible results
3. Adjust resolution: Use n_cells parameter to control grid density
4. Check convergence: The output includes a converged flag
5. Validate your stratification: Use ss_coverage_efficiency() to ensure uniform strata
6. Compare alternatives: Test different n_strata values and assess efficiency

References

• de Gruijter, J.J., Brus, D.J., Bierkens, M.F.P., and Knotters, M. (2006). Sampling for Natural Resource Monitoring. Springer, Berlin.

• Walvoort, D.J.J., Brus, D.J., and de Gruijter, J.J. (2010). An R package for spatial coverage sampling and random sampling from compact geographical strata by k-means. Computers & Geosciences 36, 1261-1267. DOI: 10.1016/j.cageo.2010.04.005

• Petrovskaia, N., Korveh, K., and Maas, E. (2021). Optimal soil sampling design based on the maxvol algorithm. Geoderma 381, 114733. DOI: 10.1016/j.geoderma.2020.114733

• Malone, B.P., Minasny, B., and Brungard, C. (2019). Some methods to improve the utility of conditioned Latin hypercube sampling. PeerJ 7, e6451. DOI: 10.7717/peerj.6451

• Wadoux, A.M.J-C., Brus, D.J., and Heuvelink, G.B.M. (2019). Sampling design optimization for soil mapping with random forest. Geoderma 355, 113913. DOI: 10.1016/j.geoderma.2019.113913

License

GPL (>= 3)