Global discret grids

Day 4 of 30DayMapChallenge. Hexagons
R
spatial
datavisualization
30DayMapChallenge
Author

Michaël

Published

2024-11-04

Modified

2024-12-25

Hexagons

Hexagonos – CC-BY-SA by Fernando Reyes Palencia

Day 4 of 30DayMapChallenge: « Hexagons » (previously).

Hexagonal grid?

We will do statistical binning on a hexagonal grid, but not just any grid. Geodesic Discrete Global Grid Systems (Kimerling et al. 1999; Sahr, White, and Kimerling 2003) allow to use hierarchical equal-area hexagon1 grids.

The {dggridR} package (Barnes 2017) will help us to generate these grids on France.

library(dggridR)
library(dplyr)
library(purrr)
library(sf)
library(units)
library(glue)
library(tibble)
library(ggplot2)
library(ggspatial)
library(rnaturalearth)
# devtools::install_github("ropensci/rnaturalearthhires")

First we are going to build these Discrete global grids for metropolitan France with cell size of 1, 5, 10, 20 and 100 km. We need a spatial footprint.

# get it from 
# https://static.data.gouv.fr/resources/admin-express-cog-simplifiee-2024-metropole-drom-saint-martin-saint-barthelemy/20240930-094021/adminexpress-cog-simpl-000-2024.gpkg
fx <- read_sf("~/data/adminexpress/adminexpress-cog-simpl-000-2024.gpkg",
              layer = "region") |> 
  filter(insee_reg > "06") |> 
  summarise()

We can chose which grid resolution we’ll make with the desired hexagon approximate “size” in km; the sampling allows us to have all the cells (if too large, some cells will be absent). It takes a few minutes…

res <- tribble(~distance, ~sampling,
                       1,     0.005,
                       5,     0.010,
                      10,     0.010,
                      20,     0.010,
                     100,     0.100)

#' Build a DGG
#'
#' Discrete Global Grid
#'
#' @param src (sf) : footprint
#' @param dest (char) : output filename
#' @param distance (num) : approximate cell size (km)
#' @param sampling (num) : points sampling to create the cells (°)
#' @param desc (char) : métadata (ex: layer description)
#'
#' @return (sf) : layer (+ file on disk with metadata)
build_dgg <- function(src, dest, distance = 100, sampling = 0.1, desc = "") {
  
  msg <- capture.output(
    dg <- dgconstruct(spacing = distance,
                      projection = "ISEA",
                      aperture = 3,
                      topology = "HEXAGON"))
  properties <- paste(glue_data(enframe(dg), "{name}: {value}"), 
                      collapse = "\n")
  
  hex <- dg |> 
    dgshptogrid(src, cellsize = sampling)
  
  hex |> 
    st_join(src, left = FALSE) |> 
    st_write(dest,
             layer = glue("dggrid_{distance}k"),
             layer_options = c(
               glue("IDENTIFIER=Discrete Global Grid - {distance} km"),
               glue("DESCRIPTION=ISEA3H
                    {desc}
                    
                    {msg}
                    
                    {properties}
                    
                    {Sys.Date()}")),
             delete_layer = TRUE)
}

# execute for all resolutions
res |> 
  pwalk(build_dgg, 
        src = fx,
        dest = "dggrid_fx.gpkg",
        desc = "France métropolitaine WGS84", .progress = TRUE)

Now we have a geopackage with all our grids:

st_layers("dggrid_fx.gpkg")
Driver: GPKG 
Available layers:
   layer_name geometry_type features fields crs_name
1   dggrid_1k       Polygon   466080      1   WGS 84
2   dggrid_5k       Polygon    17801      1   WGS 84
3  dggrid_10k       Polygon     6079      1   WGS 84
4  dggrid_20k       Polygon     2106      1   WGS 84
5 dggrid_100k       Polygon      102      1   WGS 84

And we can see the nice spatial scale nesting in Figure 1.

Map of grid samples
Figure 1: Samples at 100, 20 and 10 km

To demonstrate the binning we’ll use the commune population available in the GPKG downloaded earlier that we’ll use as a point layer.

First we need also some more data…

# output projection 
# we chose an equal-area projection
proj <- "EPSG:3035"

fx_laea <- fx |> 
  st_transform(proj)

# population data
pop <- read_sf("~/data/adminexpress/adminexpress-cog-simpl-000-2024.gpkg",
              layer = "commune") |> 
  filter(insee_reg > "06") |> 
   st_transform(proj) |> 
  st_point_on_surface()

# map zoom
fx_bb <- st_bbox(st_buffer(fx_laea, 0))

# projection name
lib_proj <- st_crs(fx_laea)$Name

# regional boundaries
reg_int <- read_sf("~/data/adminexpress/adminexpress-cog-simpl-000-2024.gpkg",
              layer = "region_int") |> 
  st_transform(proj)

# european base map
eu <- ne_countries(continent = "europe", scale = 10, returnclass = "sf") |> 
  st_transform(proj) |> 
  st_intersection(st_buffer(fx_laea, 500000))

Then we create a function to generate the maps with different grid resolutions.

#' Create a map of population for a grid resolution
#'
#' @param resolution (int) : the grid resolution (among those available in 
#'   dggrid_fx.gpkg)
#'
#' @return (ggplot) : population map
build_map <- function(resolution) {
  
  dggrid <- read_sf("dggrid_fx.gpkg",
                    layer = glue("dggrid_{resolution}k")) |> 
    st_transform(proj) |> 
    st_intersection(fx_laea)
  
  pop |>
    st_join(dggrid) |> 
    st_drop_geometry() |> 
    summarise(.by = seqnum,
              pop = sum(population, na.rm = TRUE)) |> 
    left_join(x = dggrid, y = _, 
              join_by(seqnum)) |> 
    mutate(dens = drop_units(pop / set_units(st_area(geom), km^2))) |> 
    ggplot() +
    geom_sf(data = eu, color = "#eeeeee", fill = "#eeeeee") +
    geom_sf(aes(fill = dens, color = dens)) +
    geom_sf(data = reg_int, color = "#ffffff", linewidth = 0.4, alpha = 0.5) +
    geom_sf(data = reg_int, color = "#555555", linewidth = .2) +
    scale_fill_fermenter(name = "inhabitants/km²",
                         palette = "Greens",
                         na.value = "white",
                         breaks = c(20, 50, 100, 500),
                         direction = 1) +
    scale_color_fermenter(name = "inhabitants/km²",
                          palette = "Greens",
                          na.value = "white",
                          breaks = c(20, 50, 100, 500),
                          direction = 1) +
    annotation_scale(location = "bl",
                     height = unit(.15, "cm"),
                     line_col = "#999999",text_col = "#999999",
                     bar_cols = c("#999999", "white")) +
    annotation_north_arrow(pad_x = unit(.25, "cm"), pad_y = unit(.8, "cm"),
                           style = north_arrow_fancy_orienteering(
                             text_col = "#999999", text_size = 8,
                             line_col = "#999999",
                             fill = "#999999"),
                           which_north = "true",
                           height = unit(.5, "cm"),
                           width = unit(.5, "cm")) +
    labs(title = "Population",
         subtitle = "Metropolitan France - 2022",
         caption = glue("https://r.iresmi.net/ - {Sys.Date()}
                        data: Discrete Global Grid ISEA3H ≈{resolution} km, 
                          Natural Earth and IGN Admin Express 2024
                        proj.: {lib_proj}")) +
    coord_sf(xlim = fx_bb[c(1, 3)], 
             ylim = fx_bb[c(2, 4)]) +
    theme_void() +
    theme(text = element_text(family = "Marianne"),
          plot.caption = element_text(size = 6, color = "darkgrey"),
          plot.caption.position = "plot",
          panel.background = element_rect(color = "#E0FFFF", 
                                          fill = "#E0FFFF55"))
}

Now we can demonstrate our different resolutions:

build_map(20)
Map of statistical binning on a hexagonal grid of french population
Figure 2: Population on grid size 20 km 
build_map(100)
Map of statistical binning on a hexagonal grid of french population
Figure 3: Population on grid size 100 km

References

Barnes, Richard. 2017. “dggridR: Discrete Global Grids for R.” https://CRAN.R-project.org/package=dggridR.
Kimerling, Jon A., Kevin Sahr, Denis White, and Lian Song. 1999. “Comparing Geometrical Properties of Global Grids.” Cartography and Geographic Information Science 26 (4): 271–88. https://doi.org/10.1559/152304099782294186.
Sahr, Kevin, Denis White, and A. Jon Kimerling. 2003. “Geodesic Discrete Global Grid Systems.” Cartography and Geographic Information Science 30 (2): 121–34. https://doi.org/10.1559/152304003100011090.

Footnotes

  1. mostly hexagons, in our case there are also five pentagons far away in the oceans.↩︎