Zonal Statistics of Coastal Regions with exactextractr

Introduction

This vignette describes the use of exactextractr to summarize populationand elevation data from the Gridded Population of the World and EU-DEM datasets.

The exactextractr package includes samples of both of these datasets, cropped to the extent of São Miguel; the largest and most populous island of the Azores archipelago.

This vignette uses the following packages:

library(dplyr)
library(exactextractr)
library(raster)
library(sf)

Loading the sample data

To begin, we load the population count file from GPW. This raster provides the total population in each pixel for the calendar year 2020. Then we overlay the boundaries for the six municipalities, or concelhos, into which the island is divided on the GPW grid. The population is concentrated along the coastlines with smaller inland communities located in volcanic calderas.

pop_count <-
 raster::raster(system.file('sao_miguel/gpw_v411_2020_count_2020.tif',
 package = 'exactextractr'))
concelhos <- sf::st_read(system.file('sao_miguel/concelhos.gpkg',
 package = 'exactextractr'),
 quiet = TRUE)
concelhos_geom<-sf::st_geometry(concelhos)
sp::plot(pop_count, axes = FALSE)
sp::plot(concelhos_geom, add = TRUE)

Calculating total population

Because the population count raster is cropped and contains no land area outside of São Miguel, we can calculate the total population of the island using the cellStats function from the raster package.

raster::cellStats(pop_count, 'sum')

## [1] 145603

exactextractr::exact_extract(pop_count, concelhos, 'sum', progress = FALSE)

## [1] 14539.875 4149.851 66866.711 5293.968 31920.496 9093.449

concelho_pop <- exactextractr::exact_extract(pop_count, concelhos, 'sum', 
 append_cols = 'name', progress = FALSE) %>%
 dplyr::rename(pop = sum) %>%
 dplyr::arrange(dplyr::desc(pop)) %>%
 dplyr::bind_rows(dplyr::summarize(., name = 'Total', pop = sum(pop)))

pop_density <- raster::raster(system.file('sao_miguel/gpw_v411_2020_density_2020.tif',
 package = 'exactextractr'))

concelho_pop2 <- exactextractr::exact_extract(pop_density, concelhos, 
 function(density, frac, area) {
 sum(density * frac * area)
 }, 
 weights = raster::area(pop_density),
 append_cols = 'name',
 progress = FALSE)

exactextractr::exact_extract(pop_density, concelhos, 'weighted_sum', weights = 'area')

Population-weighted statistics

Suppose that we are interested in calculating the average elevation of a residence in each of the six concelhos. Loading the island’s EU-DEM elevation data, we can see that each concelho is, at least partly, occupied by interior mountains. This indicates that the results of a simple mean would be unrepresentative of the (primarily) coastal population.

elev <- raster::raster(system.file('sao_miguel/eu_dem_v11.tif', package = 'exactextractr'))

sp::plot(elev, axes = FALSE, box = FALSE)
sp::plot(concelhos_geom, add = TRUE)

As in the previous section, we avoid working with the population count raster to prevent population loss along the coastline. We can formulate the population-weighted average elevation in terms of population density and pixel areas as:

\[ \bar{x}_\mathrm{pop} = \frac{ \Sigma_{i=0}^n {x_ic_id_ia_i}}{\Sigma_{i=0}^n{c_id_ia_i}} \] where \(x_i\) is the population of pixel \(i\), \(c_i\) is the fraction of pixel \(i\) that is covered by a polygon, \(d_i\) is the population density of pixel \(i\), and \(a_i\) is the area of pixel \(i\).

If we are working with projected data, or geographic data over a small area like São Miguel, we can assume all pixel areas to be equivalent, in which case the \(a_i\) components cancel each other out and we are left with the direct usage of population density as a weighting raster:

exactextractr::exact_extract(elev, concelhos, 'weighted_mean', weights = pop_density)

What if pixel areas do vary across the region of our analysis?

One option is to create a scaled population count raster by multiplying the population density by the pixel area. For pixels that are partly covered by water, this inflates the pixel population such that we obtain the correct population when only the land area is covered by a polygon. This requires that we create and maintain a separate raster data set.

Another option is to create a RasterStack of pop_density and area(pop_density), and write a summary function to handle the necessary processing. We use the summarize_df = TRUE argument to combine the elevation, population density, pixel area, and pixel coverage fraction into a single data frame that is passed to the summary function.

exactextractr::exact_extract(elev, concelhos,
 function(df) {
 weighted.mean(
 x = df$value,
 w = df$coverage_fraction * df$pop_density * df$area,
 na.rm = TRUE
 )
 },
 weights = raster::stack(list(
 pop_density = pop_density,
 area = raster::area(pop_density)
 )),
 summarize_df = TRUE,
 progress = FALSE)

This solution shares the same limitations with the previous example using an R summary function with raster::area(): we must precompute an area raster and store it in memory, and load all raster values intersecting a given polygon into memory at once.

A better solution is to use the coverage_area argument to exact_extract, which specifies that all calculations use the area of each cell that is covered by the polygon instead of the fraction of each cell that is covered by the polygon.

concelho_mean_elev <- exactextractr::exact_extract(elev,
 concelhos,
 c('mean', 'weighted_mean'),
 weights = pop_density,
 coverage_area = TRUE,
 append_cols = 'name',
 progress = FALSE)

Here we also calculate the unweighted mean for comparison. We can see that the population-weighted mean elevation is substantially lower than the mean elevation in all concelhos.