exactextractr

exactextractr is an R package that quickly and accurately summarizes raster values over polygonal areas, commonly referred to as zonal statistics. Unlike most zonal statistics implementations, it handles grid cells that are partially covered by a polygon. Despite this, it performs faster other packages for many real-world applications.

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Calculations are performed using the C++ exactextract tool. Additional background and a description of the method is available here. Full package reference documentation is available here.

Basic Usage

The package provides an exact_extract method that operates analogously to the extract method in the raster package. The snippet below demonstrates the use of this function to compute monthly mean precipitation for each municipality in Brazil.

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

# Pull municipal boundaries for Brazil
brazil <- st_as_sf(getData('GADM', country='BRA', level=2))

# Pull gridded precipitation data
prec <- getData('worldclim', var='prec', res=10)

# Calculate vector of mean December precipitation amount for each municipality
brazil$mean_dec_prec <- exact_extract(prec[[12]], brazil, 'mean')

# Calculate data frame of min and max precipitation for all months
brazil <- cbind(brazil, exact_extract(prec, brazil, c('min', 'max')))

Summary Operations

exactextractr can summarize raster values using several named operations as well as arbitrary R functions. Where applicable, a named operation will provide better performance and reduced memory usage relative to an equivalent R function. Named operations are specified by providing a character vector with one or more operation names to the fun parameter of exact_extract.

The following summary operations are supported:

Name	Description
count	Sum of all cell coverage fractions.
majority (or mode)	The raster value with the largest sum of coverage fractions.
max	Maximum value of cells that intersect the polygon, ignoring coverage fractions.
mean	Mean value of cells that intersect the polygon, weighted by the fraction of the cell that is covered.
median	Median value of cells that intersect the polygon, weighted by the fraction of the cell that is covered.
quantile	Arbitrary quantile value of cells that intersect the polygon, weighted by the fraction of the cell that is covered.
min	Minimum value of cells that intersect the polygon, ignoring coverage fractions.
minority	The raster value with the smallest sum of coverage fractions.
sum	Sum of values of raster cells that intersect the polygon, with each raster value weighted by its coverage fraction.
variety	The number of distinct raster values in cells wholly or partially covered by the polygon.
variance	The population variance of cell values, weighted by the fraction of each cell that is covered by the polygon.
stdev	The population standard deviation of cell values, weighted by the fraction of each cell that is covered by the polygon.
coefficient_of_variation	The population coefficient of variation of cell values, weighted by the fraction of each cell that is covered by the polygon.
frac	Fraction of covered cells that are occupied by each distinct raster value.

Three additional summary operations require the use of a second weighting raster, provided in the weights argument to exact_extract:

Name	Description
weighted_mean	Mean value of defined (non-NA) cells that intersect the polygon, weighted by the product of the coverage fraction and the value of a second weighting raster.
weighted_sum	Sum of defined (non-NA) values of raster cells that intersect the polygon, multiplied by the coverage fraction and the value of a second weighting raster.
weighted_variance	Population variance of defined (non-NA) values of cells that intersect the polygon, weighted by the product of the coverage fraction and the value of a second weighting raster.
weighted_stdev	Population standard deviation of defined (non-NA) values of raster cells that intersect the polygon, multiplied by the coverage fraction and the value of a second weighting raster.
weighted_frac	Fraction of covered cells that are occupied by each distinct raster value, with coverage fractions multiplied by the value of a second weighting raster.

Weighted usage is discussed in more detail below.

Undefined (NA) values are ignored in all of the named summary operations when they occur in the value raster. When they occur in the weighting raster, they cause the result of the summary operation to be NA.

Summary Functions

In addition to the summary operations described above, exact_extract can accept an R function to summarize the cells covered by the polygon. Because exact_extract takes into account the fraction of the cell that is covered by the polygon, the summary function must take two arguments: the value of the raster in each cell touched by the polygon, and the fraction of that cell area that is covered by the polygon. (This differs from raster::extract, where the summary function takes the vector of raster values as a single argument and effectively assumes that the coverage fraction is 1.0.)

An example of a built-in function with the appropriate signature is weighted.mean. Some examples of custom summary functions are:

# Number of cells covered by the polygon (raster values are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
                            sum(coverage_fraction))

# Sum of defined raster values within the polygon, accounting for coverage fraction
exact_extract(rast, poly, function(values, coverage_fraction)
                            sum(values * coverage_fraction, na.rm=TRUE))

# Number of distinct raster values within the polygon (coverage fractions are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
                            length(unique(values)))

# Number of distinct raster values in cells more than 10% covered by the polygon
exact_extract(rast, poly, function(values, coverage_fraction)
                            length(unique(values[coverage_fraction > 0.1])))

Weighted Usage

exact_extract allows for calculation of summary statistics based on multiple raster layers, such as a population-weighted temperature. The weighting raster must use the same coordinate system as the primary raster, and it must use a grid that is compatible with the primary raster. (The resolutions and extents of the rasters need not be the same, but the higher resolution must must be an integer multiple of the lower resolution, and the cell boundaries of both rasters must coincide with cell boundaries in the higher-resolution grid.)

One application of this feature is the calculation of zonal statistics on raster data in geographic coordinates. The previous calculation of mean precipitation amount across Brazilian municipalities assumed that each raster cell covered the same area, which is not correct for rasters in geographic coordinates (latitude/longitude).

We can correct for varying cell areas by creating a weighting raster with the area of each cell in the primary raster using the area function from the raster package.

Weighted Summary Operations

Performing a weighted summary with the weighted_mean and weighted_sum operations is as simple as providing a weighting RasterLayer or RasterStack to the weights argument of exact_extract.

The area-weighted mean precipitation calculation can be expressed as:

brazil$mean_dec_prec_weighted <- exact_extract(prec[[12]], brazil, 'weighted_mean', weights = area(prec))

With the relatively small polygons used in this example, the error introduced by assuming constant cell area is negligible. However, for large polygons that span a wide range of latitudes, this may not be the case.

Weighted Summary Functions

A weighting raster can also be provided when an R summary function is used. When a weighting raster is provided, the summary function must accept a third argument containing the values of the weighting raster.

An equivalent to the weighted_mean usage above could be written as:

brazil$mean_dec_prec_weighted <- 
  exact_extract(prec[[12]], brazil, function(values, coverage_frac, weights) {
    weighted.mean(values, coverage_frac * weights)
  }, weights = area(prec))

Or, to calculate the area-weighted mean precipitation for all months:

brazil <- cbind(brazil,
  exact_extract(prec, brazil, function(values, coverage_frac, weights) {
    weighted.mean(values, coverage_frac * weights)
  },
  weights = area(prec),
  stack_apply = TRUE))

In this example, the stack_apply argument is set to TRUE so that the summary function will be applied to each layer of prec independently. (If stack_apply = FALSE, the summary function will be called with all values of prec in a 12-column data frame.)

Additional Usages

Multi-Raster Summary Functions

A multi-raster summary function can also be written to implement complex behavior that requires that multiple layers in a RasterStack be considered simultaneously.

Here, we compute an area-weighted average temperature by calling exact_extract with a RasterStack of minimum and maximum temperatures, and a RasterLayer, of cell areas.

tmin <- getData('worldclim', var = 'tmin', res = 10)
tmax <- getData('worldclim', var = 'tmax', res = 10)

temp <- stack(tmin[[12]], tmax[[12]])

brazil$tavg_dec <- exact_extract(temp, brazil,
  function(values, coverage_fraction, weights) {
    tavg <- 0.5*(values$tmin12 + values$tmax12)
    weighted.mean(tavg, coverage_fraction * weights)
  }, weights = area(prec))

When exact_extract is called with a RasterStack of values or weights and stack_apply = FALSE (the default), the values or weights from each layer of the RasterStack will be provided to the summary function as a data frame.

In the example above, the summary function is provided with a data frame of values (containing the values for each layer in the temp stack), a vector of coverage fractions, and a vector of weights.

Multi-Valued Summary Functions

In some cases, it is desirable for a summary function to return multiple values for each input feature. A common application is to summarize the fraction of each polygon that is covered by a given class of a categorical raster. This can be accomplished by writing a summary function that returns a one-row data frame for each input feature. The data frames for each feature will be combined into a single data frame using using rbind or, if it is available, dplyr::bind_rows.

In this example, the mean temperature for each municipality is returned for each altitude category.

altitude <- getData('alt', country = 'BRA')

prec_for_altitude <- exact_extract(prec[[12]], brazil, function(prec, frac, alt) {
  # ignore cells with unknown altitude
  prec <- prec[!is.na(alt)]
  frac <- frac[!is.na(alt)]
  alt <- alt[!is.na(alt)]
  
  low <- !is.na(alt) & alt < 500
  high <- !is.na(alt) & alt >= 500

  data.frame(
    prec_low_alt = weighted.mean(prec[low], frac[low]),
    prec_high_alt = weighted.mean(prec[high], frac[high])
  )
}, weights = altitude)

Rasterization

exactextractr can rasterize polygons though computation of the coverage fraction in each cell. The coverage_fraction function returns a RasterLayer with values from 0 to 1 indicating the fraction of each cell that is covered by the polygon. Because this function generates a RasterLayer for each feature in the input dataset, it can quickly consume a large amount of memory. Depending on the analysis being performed, it may be advisable to manually loop over the features in the input dataset and combine the generated rasters during each iteration.

Performance

For typical applications, exactextractr is much faster than the raster package and somewhat faster than the terra package. An example benchmark is below:

brazil <- st_as_sf(getData('GADM', country='BRA', level=1))
brazil_spat <- as(brazil, 'SpatVector')

prec_rast <- getData('worldclim', var='prec', res=10)
prec_terra <- rast(prec_rast) 
prec12_rast <- prec_rast[[12]]
prec12_terra <- rast(prec_rast[[12]])

microbenchmark(
  extract(prec_rast, brazil, mean, na.rm = TRUE),
  extract(prec_terra, brazil_spat, mean, na.rm = TRUE),
  exact_extract(prec_rast, brazil, 'mean', progress = FALSE),
  exact_extract(prec_terra, brazil, 'mean', progress = FALSE),
  extract(prec12_rast, brazil, mean, na.rm = TRUE),
  extract(prec12_terra, brazil_spat, mean, na.rm = TRUE),
  exact_extract(prec12_rast, brazil, 'mean', progress = FALSE),
  exact_extract(prec12_terra, brazil, 'mean', progress = FALSE),
  times = 5)

Package	Raster Type	Layers	Expression	Time (ms)
raster	RasterLayer	1	extract(prec_rast, brazil, mean, na.rm = TRUE)	48708
terra	SpatRaster	1	extract(prec_terra, brazil_spat, mean, na.rm = TRUE)	436
exactextractr	RasterLayer	1	exact_extract(prec_rast, brazil, "mean", progress = FALSE)	1541
exactextractr	SpatRaster	1	exact_extract(prec_terra, brazil, "mean", progress = FALSE)	129
raster	RasterStack	12	extract(prec12_rast, brazil, mean, na.rm = TRUE)	10148
terra	SpatRaster	12	extract(prec12_terra, brazil_spat, mean, na.rm = TRUE)	266
exactextractr	RasterLayer	12	exact_extract(prec12_rast, brazil, "mean", progress = FALSE)	222
exactextractr	SpatRaster	12	exact_extract(prec12_terra, brazil, "mean", progress = FALSE)	112

Actual performance is a complex topic that can vary dramatically depending on factors such as:

• the number of layers in the input raster(s)
• the data type of input rasters (for best performance, use a terra::SpatRaster)
• the raster file format (GeoTIFF, netCDF, etc)
• the chunking strategy used by the raster file (striped, tiled, etc.)
• the relative size of the area to be read and the GDAL block cache

If exact_extract is called with progress = TRUE, messages will be emitted if the package detects a situation that could lead to poor performance, such as a raster chunk size that is too large to allow caching of blocks between vector features.

If performance is poor, it may be possible to improve performance by:

• increasing the max_cells_in_memory parameter
• increasing the size of the GDAL block cache
• rewriting the input rasters to use a different chunking scheme
• processing inputs as batches of nearby polygons

Accuracy

Results from exactextractr are more accurate than other common implementations because raster pixels that are partially covered by polygons are considered. The significance of partial coverage increases for polygons that are small or irregularly shaped. For the 5500 Brazilian municipalities used in the example, the error introduced by incorrectly handling partial coverage is less than 1% for 88% of municipalities and reaches a maximum of 9%.

Dependencies

Installation requires version 3.5 or greater of the GEOS geometry processing library. It is recommended to use the most recent released version for best performance. On Windows, GEOS will be downloaded automatically as part of package install. On MacOS, it can be installed using Homebrew (brew install geos). On Linux, it can be installed from system package repositories (apt-get install libgeos-dev on Debian/Ubuntu, or yum install libgeos-devel on CentOS/RedHat.)