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https://github.com/isciences/exactextractr

R package for fast and accurate raster zonal statistics
https://github.com/isciences/exactextractr

gis r raster rcpp

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R package for fast and accurate raster zonal statistics

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README 

        
# exactextractr



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`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.



![Example Graphic](https://gitlab.com/isciences/exactextractr/-/raw/assets/readme/brazil_precip.png).



Calculations are performed using the C++

[`exactextract`](https://github.com/isciences/exactextract) tool. Additional

background and a description of the method is available

[here](https://github.com/isciences/exactextract#background).

Full package reference documentation is available

[here](https://isciences.gitlab.io/exactextractr/reference).



### Basic Usage



The package provides an

[`exact_extract`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

method that operates analogously to the

[`extract`](https://www.rdocumentation.org/packages/raster/topics/extract)

method in the

[`raster`](https://CRAN.R-project.org/package=raster) package.

The snippet below demonstrates the use of this function to compute monthly mean precipitation for each municipality in Brazil.



```r

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`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html).



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`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html):



| 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](#weighted-usage).



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`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

can accept an R function to summarize the cells covered by the polygon. Because

[`exact_extract`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

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`](https://www.rdocumentation.org/packages/raster/topics/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`](https://www.rdocumentation.org/packages/stats/topics/weighted.mean).

Some examples of custom summary functions are:



```r

# 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`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

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`](https://www.rdocumentation.org/packages/raster/topics/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`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

or

[`RasterStack`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

to the `weights` argument of

[`exact_extract`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html).



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



```r

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:



```r

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:



```r

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`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

be considered simultaneously.



Here, we compute an area-weighted average temperature by calling

[`exact_extract`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

with a

[`RasterStack`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

of minimum and maximum temperatures, and a

[`RasterLayer`](https://www.rdocumentation.org/packages/raster/topics/Raster-class),

of cell areas.



```r

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`](https://isciences.gitlab.io/exactextractr/reference/exact_extract.html)

is called with a 

[`RasterStack`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

of values or weights and `stack_apply = FALSE` (the default), the values or

weights from each layer of the 

[`RasterStack`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

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.



```r

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`](https://isciences.gitlab.io/exactextractr/reference/coverage_fraction.html)

function returns a

[`RasterLayer`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

with values from 0 to 1 indicating the fraction of each cell that is covered by

the polygon. Because this function generates a

[`RasterLayer`](https://www.rdocumentation.org/packages/raster/topics/Raster-class)

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:



```r

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](https://libgeos.org/) 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.)