Fast Extraction from Raster Datasets using Polygons.
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.
.
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.)