Spatial sampling

This work addresses spatial sampling design through clustering-based approaches. Spatial Coverage Sampling using K-means (scsKM) follows the method implemented in the spcosa R package, applying k-means clustering to spatial grid cell centers to ensure uniform coverage. Building on this, we introduce two new methods: scsCLARA, which uses the CLARA algorithm for spatially balanced sampling, and cdCLARA, which extends this approach by incorporating environmental complexity via geomorphological variables such as depth and roughness. These developments offer flexible tools for efficient and adaptive spatial sampling.

1 Prerequisites

To begin, users are required to download and install the following R packages, which are essential for running the analysis. Additionally, the following functions must be sourced from the provided repository on Zenodo. These functions are available for download, and users can access them through the following link: https://doi.org/10.5281/ zenodo.8436795

After installation, ensure that the packages are loaded and the functions are sourced correctly in your R environment before proceeding with the analysis.

1.1 Required R Packages

library(raster)
library(sf)
library(sp)
library(ggplot2)
library(ggspatial)
library(ggnewscale)

1.2 Required functions

source("cd-clara.R")
source("sample-points-plot.R")
source("scs-clara.R")
source("scs-kmeans.R")

2 Data

The study utilized a high-resolution (50 m) raster dataset containing geographic coordinates (longitude and latitude) alongside a set of environmental predictors to describe the geomorphological characteristics of the study area (Roos et al. 2017; Faye et al. 2024). Geographic coordinates are used as covariates in the spatial coverage sampling while two key variables - Depth and surface roughness- were subsequently used as covariates in the complexity-dependent sampling approach (Wilson et al. 2007; Faye et al. 2024).

load("./sysdata.rda")
Terrain_Attr_50 = terra::rast("50m_rast_Attr2.tif")
Terrain_Attr_50_df = as.data.frame(Terrain_Attr_50, xy = TRUE)

names(Terrain_Attr_50_df) = append(c("Longitude", "Latitude"), all_predicteurs)

theme_cust = theme(
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    plot.background = element_rect(colour = "white", fill = NA, linewidth = 1),
    legend.key = element_blank(),
    legend.text = element_text(size = 12),
    legend.title = element_text(size = 15, face = "bold"),
    axis.line = element_line(colour = "black"),
    axis.text = element_text(face = "bold", size = 15),
    axis.text.x = element_text(face = "bold", size = 15),
    axis.text.y = element_text(face = "bold", size = 15),
    axis.title.x = element_text(face = "bold", size = 15),
    axis.title.y = element_text(face = "bold", size = 15)
  )

# Depth (m) Plot
Depth_plot <- ggplot(shp2) +
  geom_sf(fill = NA, color = NA) +
  geom_tile(data = Terrain_Attr_50_df, 
            aes(x = Longitude, y = Latitude, fill = Prof_Moyenne)) +
  scale_fill_gradientn(
    colours = terrain.colors(100),
    na.value = "white",
    name = "Depth"
  ) +
  annotation_scale(location = "bl", text_cex = 1) +
  annotation_north_arrow(
    location = "tr",
    which_north = "true",
    height = unit(1.5, "cm"),
    width = unit(1, "cm")
  ) +
  theme_cust

png("Geyser_depth.png", width = 1000, height = 800, res = 150)
print(Depth_plot)
invisible(dev.off())

# Roughness Plot

Roughness_plot <- ggplot(shp2) +
  geom_sf(fill = NA, color = NA) +
  geom_tile(data = Terrain_Attr_50_df, 
            aes(x = Longitude, y = Latitude, fill = rough)) +
  scale_fill_gradientn("Rough", colours = RColorBrewer::brewer.pal(n = 5, name = "Blues"), na.value = "gray")+
  annotation_scale(location = "bl", text_cex = 1) +
  annotation_north_arrow(
    location = "tr",
    which_north = "true",
    height = unit(1.5, "cm"),
    width = unit(1, "cm")
  ) +
  theme_cust

png("Geyser_rough.png", width = 1000, height = 800, res = 150)
print(Roughness_plot)
invisible(dev.off())

3 Sampling methods

3.1 Spatial Coverage Sampling using K-means

The scsKM function selects sampling locations uniformly across the study area by applying the k-means clustering algorithm to the cells of a regular spatial grid (Hartigan 1975). The clustering is performed using the spatial coordinates of the grid cell centers, aiming to minimize the Mean Squared Shortest Distance (MSSD) between these centers and the corresponding cluster centroids (Royle and Nychka 1998). This approach ensures an approximately equal-area partitioning of the study region (Brus 2019). For advanced customization and related functionality, users are referred to the spcosa R package.

# Spatial Coverage Sampling using K-means

pvtscskm = scsKM(shp = Geyser_bathy, var = c("Longitude", "Latitude"), iter = 12, sampsize=50, nT=10)

pvtscskm$Method= "SCS-KMEANS"


scskm_plot = plotPoints(pvtscskm, Terrain_Attr_50_df[,c("Longitude", "Latitude", "rough")], Geyser_bathy)

print(scskm_plot)

png("Geyser_scskm.png", width = 1000, height = 800, res = 150)
print(scskm_plot)
invisible(dev.off())

3.2 Spatial Coverage Sampling using CLARA

scsCLARA function computes a SCS using the CLARA algorithm instead the K-means algorithm (Kaufman and Rousseeuw 1975). Like in scsKM, spatial coordinates of cells centers of a raster grid are used as variables. DBM at any resolution can be used as individuals which are then grouped into \(k\) clusters. Clusters centroids are returned and correspond to sampling locations.

# Spatial Coverage Sampling using CLARA

pvtscscl = scsCLARA(data = Terrain_Attr_50_df, var=c("Longitude", "Latitude"), iter=1, sampsize=50, disT="euclidean")

pvtscscl$Method= "SCS-CLARA"


scscl_plot = plotPoints(pvtscscl, Terrain_Attr_50_df[,c("Longitude", "Latitude", "rough")], Geyser_bathy)

print(scscl_plot)

png("Geyser_scscl.png", width = 1000, height = 800, res = 150)
print(scscl_plot)
invisible(dev.off())

3.3 Complexity-dependent sampling using CLARA

cdCLARA uses the CLARA algorithm to group DBM’s cells. Unlike scsCLARA, the covariate space is spanned by geomorphologic features. Depth and Roughness are used in the example below. Clusters centroids are returned and correspond to sampling locations.

# Complexity-dependent sampling using CLARA

pvtcdcl = cdCLARA(data = Terrain_Attr_50_df, var1=c("Longitude", "Latitude"), var2 =c("Prof_Moyenne", "rough") , iter=12, sampsize=50, disT="manhattan")

pvtcdcl$Method= "CDS"

cds_plot = plotPoints(pvtcdcl, Terrain_Attr_50_df[,c("Longitude", "Latitude", "rough")], Geyser_bathy)

print(cds_plot)

png("Geyser_cds.png", width = 1000, height = 800, res = 150)
print(cds_plot)
invisible(dev.off())

References

Brus, D. J. 2019. “Sampling for Digital Soil Mapping: A Tutorial Supported by r Scripts.” Geoderma 338: 464–80. https://doi.org/10.1016/j.geoderma.2018.07.036.

Faye, Paul Aimé Latsouck, Elodie Brunel, Thomas Claverie, Solym Mawaki Manou-Abi, and Sophie Dabo-Niang. 2024. “Automatic Geomorphological Mapping Using Ground Truth Data with Coverage Sampling and Random Forest Algorithms.” Earth Science Informatics, 1–18.

Hartigan, J. A. 1975. “Clustering Algorithms.” John Wiley & Sons, Inc.

Kaufman, L., and P. J. Rousseeuw. 1975. “Partitioning Around Medoids (Program Pam).” Finding Groups in Data: An Introduction to Cluster Analysis 344: 68–125.

Roos, D., P. Dupont, M. Gaboriau, L. Bigot, P. Durville, T. Mulochau, M. Pinault, et al. 2017. “Projet EPICURE : Etude Des Peuplements Ichtyologiques Et Des Communautés Récifales à Partir d’indicateurs Spatiaux Et de l’approche Fonctionnelle, Des Bancs Du Geyser, de La Zélée Et de l’iris.” Programme Du Xème FED Régional Gestion Durable Du Patrimoine Naturel de Mayotte Et Des Îles Éparses. https://doi.org/10.13155/54549.

Royle, J. A., and D. Nychka. 1998. “An Algorithm for the Construction of Spatial Coverage Designs with Implementation in SPLUS.” Computers & Geosciences 24(5): 479–88.

Wilson, M. F. J., B. O’CONNELL, C. Brown, J. C. Guinan, and Grehan A. J. 2007. “Multiscale Terrain Analysis of Multibeam Bathymetry Data for Habitat Mapping on the Continental Slope.” Marine Geodesy 30: 3–35. https://doi.org/ 10.1080/01490410701295962.