2 Geographic data in R
This is the first practical chapter of the book, and therefore it comes with some software requirements. We assume that you have an up-to-date version of R installed and that you are comfortable using software with a command-line interface such as the integrated development environment (IDE) RStudio.
If you are new to R, we recommend reading Chapter 2 of the free online book Efficient R Programming Gillespie and Lovelace (2016), particularly sections 2.3 and 2.5, for details on R installation and set-up.
It is also worth learning the basics of the language, using resources such as Gillespie and Lovelace (2016), Grolemund and Wickham (2016) or interactive guides such as DataCamp before proceeding.
We recommend organizing your work as you learn with RStudio projects and clearly named script files (such as
chapter-02.R for example) containing code you have typed (not copy-pasted!) as you learn.
After you’ve checked you R installation and brushed-up on your R skills where appropriate, the next step is to install and load the packages used in this chapter.
Packages are installed with the
install.packages() function which can be used to get the prerequisites on your computer:5
To install these packages and all other packages used in this book in one go, you can use the following command, which requires the devtools package:
After the necessary packages have been installed, they can be ‘loaded’ (technically they are attached) with
library() as follows:
The other packages that were installed contain data that will be used in the book:
This chapter will provide brief explanations of the fundamental geographic data models: vector and raster. We will introduce the theory behind each data model and the disciplines in which they predominate, before demonstrating their implementation in R.
The vector data model represents the world using points, lines and polygons. These have discrete, well-defined borders, meaning that vector datasets usually have a high level of precision (but not necessarily accuracy as we will see in 2.4). The raster data model divides the surface up into cells of constant size. Raster datasets are the basis of background images used in web-mapping and have been a vital source of geographic data since the origins of aerial photography and satellite-based remote sensing devices. Rasters aggregate spatially specific features to a given resolution, meaning that they are consistent over space and scalable (many worldwide raster datasets are available).
Which to use? The answer likely depends on your domain of application:
- Vector data tends to dominate the social sciences because human settlements tend to have discrete borders.
- Raster often dominates in environmental sciences because of the reliance on remote sensing data.
There is much overlap in some fields and raster and vector datasets can be used side-by-side: ecologists and demographers, for example, commonly use both vector and raster data. Whether your work involves more use of vector or raster datasets, it is worth understanding the underlying data model before using them, as discussed in subsequent chapters. This book uses sf and raster packages to work with vector data and raster datasets respectively.
2.1 Vector data
vectorclass (note the
monospacefont) in R. The former is a data model, the latter is an R class just like
matrix. Still, there is a link between the two: the spatial coordinates which are at the heart of the geographic vector data model can be represented in R using
The geographic vector model is based on points located within a coordinate reference system (CRS). Points can represent self-standing features (e.g. the location of a bus stop) or they can be linked together to form more complex geometries such as lines and polygons. Most point geometries contain only two dimensions (3 dimensional CRSs contain an additional \(z\) value, typically representing height above sea level).
In this system London, for example, can be represented by the coordinates
This means that its location is -0.1 degrees east and 51.5 degrees north of the origin.
The origin in this case is at 0 degrees longitude (the Prime Meridian) and 0 degree latitude (the Equator) in a geographic (‘lon/lat’) CRS (Figure 2.1, left panel).
The same point could also be approximated in a projected CRS with ‘Easting/Northing’ values of
c(530000, 180000) in the British National Grid (BNG), meaning that London is located 530 km East and 180 km North of the \(origin\) of the CRS.
This can be verified visually: slightly more than 5 ‘boxes’ — square areas bounded by the gray grid lines 100 km in width — separate the point representing London from the origin (Figure 2.1, right panel).
The location of BNG’s origin, in the sea beyond South West Peninsular, ensures that most locations in the UK have positive Easting and Northing values.6 There is more to CRSs, as described in sections 2.3 and 6 but, for the purposes of this section, it is sufficient to know that coordinates consist of two numbers representing distance from an origin, usually in \(x\) then \(y\) dimensions.
sf is a package providing a class system for geographic vector data. Not only does it supercede sp it also provides a consistent command-line interface to GEOS and GDAL, superceding rgeos and rgdal (described in section 1.5). This section introduces sf classes in preparation for subsequent chapters (Chapters 5 and 7 cover the GEOS and GDAL interface respectively).
2.1.1 An introduction to simple features
Simple features is an open standard developed and endorsed by the Open Geospatial Consortium (OGC), a not-for-profit organization whose activities we will revisit in a later chapter (in section 7.4). Simple Features is a hierarchical data model that represents a wide range of geometry types. Of 68 geometry types supported by the specification, only 7 are used in the vast majority of geographic research (see Figure 2.2); these core geometry types are fully supported by R package sf (E. Pebesma 2018).7
sf can represent all common vector geometry types (raster data classes are not supported by sf): points, lines, polygons and their respective ‘multi’ versions (which group together features of the same type into a single feature). sf also supports geometry collections, which can contain multiple geometry types in a single object. Given the breadth of geographic data forms, it may come as a surprise that a class system to support all of them is provided in a single package, which can be installed from CRAN:8 sf incorporates the functionality of the three main packages of the sp paradigm, sp (E. Pebesma and Bivand 2018) for the class system, rgdal (Bivand, Keitt, and Rowlingson 2018) for reading and writing data, rgeos (Bivand and Rundel 2018) for spatial operations undertaken by GEOS, in a single, cohesive whole. This is well-documented in sf’s vignettes.
As the first vignette explains, simple feature objects in R are stored in a data frame, with geographic data occupying a special column, a ‘list-column’. This column is usually named ‘geom’ or ‘geometry’.
We will use the
world dataset provided by the spData, loaded at the beginning of this chapter (see nowosad.github.io/spData for a list datasets loaded by the package).
world is a spatial object containing spatial and attribute columns, the names of which are returned by the function
names() (the last column contains the geographic information):
It is the contents of this modest-looking
geom column that gives
sf objects their spatial powers, a ‘list-column’ that contains all the coordinates.
The sf package provides a
plot() method for visualizing geographic data:
the follow command creates Figure 2.3.
Note that instead of creating a single map, as most GIS programs would, the
plot() command has created multiple maps, one for each variable in the
This behavior can be useful for exploring the spatial distribution of different variables and is discussed further in 2.1.3 below.
Being able to treat spatial objects as regular data frames with spatial powers has many advantages, especially if you are already used to working with data frames.
The commonly used
summary() function, for example, provides a useful overview of the variables within the
Although we have only selected one variable for the
summary command, it also outputs a report on the geometry.
This demonstrates the ‘sticky’ behavior of the geometry columns of sf objects, meaning the geometry is kept unless the user deliberately removes them, as we’ll see in section 3.2.
The result provides a quick summary of both the non-spatial and spatial data contained in
world: the mean average life expectancy is 71 years (ranging from less than 50 to more than 80 years with a median of 73 years) across all countries.
MULTIPOLYGONin the summary output above refers to the geometry type of features (countries) in the
worldobject. This representation is necessary for countries with islands such as Indonesia and Greece. Other geometry types are described in section 2.1.5.
It is worth taking a deeper look at the basic behavior and contents of this simple feature object, which can usefully be thought of as a ’Spatial dataFrame).
sf objects are easy to subset.
The code below shows its first two rows and three columns.
The output shows two major differences compared with a regular
data.frame: the inclusion of additional geographic data (
bbox and CRS information -
proj4string), and the presence of final
world[1:2, 1:3] #> Simple feature collection with 2 features and 3 fields #> geometry type: MULTIPOLYGON #> dimension: XY #> bbox: xmin: -180 ymin: -18.3 xmax: 180 ymax: -0.95 #> epsg (SRID): 4326 #> proj4string: +proj=longlat +datum=WGS84 +no_defs #> iso_a2 name_long continent geom #> 1 FJ Fiji Oceania MULTIPOLYGON (((180 -16.1, ... #> 2 TZ Tanzania Africa MULTIPOLYGON (((33.9 -0.95,...
All this may seem rather complex, especially for a class system that is supposed to be simple. However, there are good reasons for organizing things this way and using sf.
Before describing each geometry type that the sf package supports, it is worth taking a step back to understand the building blocks of
Section 2.1.8 shows how simple features objects are data frames, with special geometry columns.
These spatial columns are often called
world$geom refers to the spatial element of the
world object described above.
These geometry columns are ‘list columns’ of class
sfc (see section 2.1.7).
sfc objects are composed of one or more objects of class
sfg: simple feature geometries that we describe in section 2.1.6.
To understand how the spatial components of simple features work, it is vital to understand simple feature geometries.
For this reason we cover each currently supported simple features geometry types in the section 2.1.5 before moving on to describe how these can be represented in R using
sfg objects, combined to form
sfc and eventually full
2.1.2 Why simple features?
Simple features is a widely supported data model that underlies data structures in many GIS applications including QGIS and PostGIS. A major advantage of this is that using the data model ensures your work is cross-transferable to other set-ups, for example importing from and exporting to spatial databases.
A more specific question from an R perspective is “why use the sf package when sp is already tried and tested”? There are many reasons (linked to the advantages of the simple features model) including:
- Fast reading and writing of data
- Enhanced plotting performance
- sf objects can be treated as data frames in most operations
- sf functions can be combined using
%>%operator and works well with the tidyverse collection of R packages
- sf function names are relatively consistent and intuitive (all begin with
Due to such advantages some spatial packages (including tmap, mapview and tidycensus) have added support for sf.
However, it will take many years for most packages to transition and some will never switch.
Fortunately these can still be used in a workflow based on
sf objects, by converting them to the
Spatial class used in sp:
Spatial objects can be converted back to
sf in the same way or with
2.1.3 Basic map making
Basic maps are created in sf with
By default this creates a multi-panel plot (like sp’s
spplot()), one sub-plot for each variable of the object, as illustrated in the left-hand panel in Figure 2.4.
A legend or ‘key’ with a continuous color is produced if the object to be plotted has a single variable (see the right-hand panel).
Colors can also be set with
col =, although this will not create a continuous palette or a legend.
Plots are added as layers to existing images by setting
add = TRUE.9
To demonstrate this, and to provide a taster of content covered in chapters 3 and 4 on attribute and spatial data operations, the subsequent code chunk combines countries in Asia:
We can now plot the Asian continent over a map of the world.
Note that the first plot must only have one facet for
add = TRUE to work.
If the first plot has a key,
reset = FALSE must be used (result not shown):
Adding layers in this way can be used to verify the geographic correspondence between layers:
plot() function is fast to execute and requires few lines of code, but does not create interactive maps with a wide range of options.
For more advanced map making we recommend using dedicated visualization packages such as tmap (see Chapter 8).
2.1.4 Base plot arguments
Advanced map making is covered in detail in Chapter 8.
However, it is worth knowing how to modify plots using the sf package for quick and flexible visualization.
Because sf extends base R plotting methods
plot()’s arguments such as
main = — which specifies the title of the map — work with
sf objects (see
Figure 2.5 illustrates this flexibility by overlaying circles, whose diameters (set with
cex =) represent country populations, on a map of the world.
A basic version of the map can be created with the following commands (see exercises at the end of this chapter and the script
02-contplot.R to create Figure 2.5):
The code above uses the function
st_centroid() to convert one geometry type (polygon) to another (point).
Here is not the place to explain how the function works (this is covered in Chapter 5).
The point is that simple feature geometries can come in different forms, the topic of the next sections.
2.1.5 Geometry types
Geometries are the basic building blocks of simple features.
Simple features in R can take on one of the 17 geometry types supported by the sf package.
In this chapter we will focus on the seven most commonly used types:
Find the whole list of possible feature types in the PostGIS manual.
Generally, well-known binary (WKB) or well-known text (WKT) are the standard encoding for simple feature geometries. WKB representations are usually hexadecimal strings easily readable for computers. This is why GIS and spatial databases use WKB to transfer and store geometry objects. WKT, on the other hand, is a human-readable text markup description of simple features. Both formats are exchangeable, and if we present one, we will naturally choose the WKT representation.
The basis for each geometry type is the point.
A point is simply a coordinate in 2D, 3D or 4D space (see
vignette("sf1") for more information) such as (see left panel in Figure 2.6):
POINT (5 2)
A linestring is a sequence of points with a straight line connecting the points, for example (see middle panel in Figure 2.6):
LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)
- Polygon without a hole -
POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))
So far we have created geometries with only one geometric entity per feature. However, sf also allows multiple geometries to exist within a single feature (hence the term ‘geometry collection’) using “multi” version of each geometry type:
- Multipoint -
MULTIPOINT (5 2, 1 3, 3 4, 3 2)
- Multistring -
MULTILINESTRING ((1 5, 4 4, 4 1, 2 2, 3 2), (1 2, 2 4))
- Multipolygon -
MULTIPOLYGON (((1 5, 2 2, 4 1, 4 4, 1 5), (0 2, 1 2, 1 3, 0 3, 0 2)))
Finally, a geometrycollection might contain any combination of geometries including (multi)points and linestrings (see Figure 2.8):
- Geometry collection -
GEOMETRYCOLLECTION (MULTIPOINT (5 2, 1 3, 3 4, 3 2), LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2))
2.1.6 Simple feature geometries (sfg)
sfg class represents the different simple feature geometry types: point, linestring, polygon (and their ‘multi’ equivalents, such as multipoints) or geometry collection.
Usually you are spared the tedious task of creating geometries on your own since you can simply import an already existing spatial file.
However, there are a set of functions to create simple feature geometry objects (
sfg) from scratch if needed.
The names of these functions are simple and consistent, as they all start with the
st_ prefix and end with the name of the geometry type in lowercase letters:
- A point -
- A linestring -
- A polygon -
- A multipoint -
- A multilinestring -
- A multipolygon -
- A geometry collection -
sfg objects can be created from three native data types:
- A numeric vector - a single point
- A matrix - a set of points, where each row contains a point - a multipoint or linestring
- A list - any other set, e.g. a multilinestring or geometry collection
To create point objects, we use the
st_point() function in conjunction with a numeric vector:
XY, XYZ and XYZM types of points are automatically created based on the length of a numeric vector.
Only the XYM type needs to be specified using a
By contrast, use matrices in the case of multipoint (
st_multipoint()) and linestring (
# the rbind function simplifies the creation of matrices ## MULTIPOINT multipoint_matrix = rbind(c(5, 2), c(1, 3), c(3, 4), c(3, 2)) st_multipoint(multipoint_matrix) #> MULTIPOINT (5 2, 1 3, 3 4, 3 2) ## LINESTRING linestring_matrix = rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)) st_linestring(linestring_matrix) #> LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)
Finally, use lists for the creation of multilinestrings, (multi-)polygons and geometry collections:
## POLYGON with a hole polygon_border = rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5)) polygon_hole = rbind(c(2, 4), c(3, 4), c(3, 3), c(2, 3), c(2, 4)) polygon_with_hole_list = list(polygon_border, polygon_hole) st_polygon(polygon_with_hole_list) #> POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5), (2 4, 3 4, 3 3, 2 3, 2 4))
2.1.7 Simple feature columns (sfc)
sfg object contains only a single simple feature geometry.
A simple feature geometry column (
sfc) is a list of
sfg objects, which is additionally able to contain information about the coordinate reference system in use.
For instance, to combine two simple features into one object with two features, we can use the
This is important since
sfc represents the geometry column in sf data frames:
In most cases, an
sfc object contains objects of the same geometry type.
Therefore, when we convert
sfg objects of type polygon into a simple feature geometry column, we would also end up with an
sfc object of type polygon, which can be verified with
Equally, a geometry column of multilinestrings would result in an
sfc object of type multilinestring:
# sfc POLYGON polygon_list1 = list(rbind(c(1, 5), c(2, 2), c(4, 1), c(4, 4), c(1, 5))) polygon1 = st_polygon(polygon_list1) polygon_list2 = list(rbind(c(0, 2), c(1, 2), c(1, 3), c(0, 3), c(0, 2))) polygon2 = st_polygon(polygon_list2) polygon_sfc = st_sfc(polygon1, polygon2) st_geometry_type(polygon_sfc) #>  POLYGON POLYGON #> 18 Levels: GEOMETRY POINT LINESTRING POLYGON ... TRIANGLE
# sfc MULTILINESTRING multilinestring_list1 = list(rbind(c(1, 5), c(4, 4), c(4, 1), c(2, 2), c(3, 2)), rbind(c(1, 2), c(2, 4))) multilinestring1 = st_multilinestring((multilinestring_list1)) multilinestring_list2 = list(rbind(c(2, 9), c(7, 9), c(5, 6), c(4, 7), c(2, 7)), rbind(c(1, 7), c(3, 8))) multilinestring2 = st_multilinestring((multilinestring_list2)) multilinestring_sfc = st_sfc(multilinestring1, multilinestring2) st_geometry_type(multilinestring_sfc) #>  MULTILINESTRING MULTILINESTRING #> 18 Levels: GEOMETRY POINT LINESTRING POLYGON ... TRIANGLE
It is also possible to create an
sfc object from
sfg objects with different geometry types:
As mentioned before,
sfc objects can additionally store information on the coordinate reference systems (CRS).
To specify a certain CRS, we can use the
epsg (SRID) or
proj4string attributes of an
The default value of
epsg (SRID) and
NA (Not Available), as can be verified with
All geometries in an
sfc object must have the same CRS.
We can add coordinate reference system as a
crs argument of
This argument accepts an integer with the
epsg code such as
4326, which automatically adds the ‘proj4string’ (see section 2.3):
It also accepts a raw proj4string (result not shown):
st_crs()will return a
proj4stringbut not an
epsgcode. This is because there is no general method to convert from
epsg(see Chapter 6).
2.1.8 The sf class
Sections 2.1.5 to 2.1.7 deal with purely geometric objects, ‘sf geometry’ and ‘sf column’ objects respectively. These are geographic building blocks of geographic vector data represented as simple features. The final building block is non-geographic attributes, representing the name of the feature or other attributes such as measured values, groups, and other things.
To illustrate attributes, we will represent a temperature of 25°C in London on June 21st 2017.
This example contains a geometry (the coordinates), and three attributes with three different classes (place name, temperature and date).12
Objects of class
sf represent such data by combining the attributes (
data.frame) with the simple feature geometry column (
They are created with
st_sf() as illustrated below, which creates the London example described above:
What just happened? First, the coordinates were used to create the simple feature geometry (
Second, the geometry was converted into a simple feature geometry column (
sfc), with a CRS.
Third, attributes were stored in a
data.frame, which was combined with the
sfc object with
This results in an
sf object, as demonstrated below (some output ommited):
The result shows that
sf objects actually have two classes,
Simple features are simply data frames (square tables), but with spatial attributes (usually stored in a special
geom list-column in the data frame).
This duality is central to the concept of simple features:
most of the time a
sf can be treated as and behaves like a
Simple features are, in essence, data frames with a spatial extension.
2.2 Raster data
The geographic raster data model usually consists of a raster header and a matrix (with rows and columns) representing equally spaced cells (often also called pixels; Figure 2.9:A).13 The raster header defines the coordinate reference system, the extent and the origin. The origin (or starting point) is frequently the coordinate of the lower-left corner of the matrix (the raster package, however, uses the upper left corner, by default (Figure 2.9:B)). The header defines the extent via the number of columns, the number of rows and the cell size resolution. Hence, starting from the origin, we can easily access and modify each single cell by either using the ID of a cell (Figure 2.9:B) or by explicitly specifying the rows and columns. This matrix representation avoids storing explicitly the coordinates for the four corner points (in fact it only stores one coordinate, namely the origin) of each cell corner as would be the case for rectangular vector polygons. This and map algebra makes raster processing much more efficient and faster than vector data processing. However, in contrast to vector data, the cell of one raster layer can only hold a single value. The value might be numeric or categorical (Figure 2.9:C).
Raster maps usually represent continuous phenomena such as elevation, temperature, population density or spectral data (Figure 2.10). Of course, we can represent discrete features such as soil or land-cover classes also with the help of a raster data model (Figure 2.10). Consequently, the discrete borders of these features become blurred, and depending on the spatial task a vector representation might be more suitable.
2.2.1 An introduction to raster
The raster package supports raster objects in R.
It provides an extensive set of functions to create, read, export, manipulate and process raster datasets.
Aside from general raster data manipulation, raster provides many low level functions that can form the basis to develop more advanced raster functionality.
raster also lets you work on large raster datasets that are too large to fit into the main memory.
In this case, raster provides the possibility to divide the raster into smaller chunks (rows or blocks), and processes these iteratively instead of loading the whole raster file into RAM (for more information, please refer to
vignette("functions", package = "raster").
For the illustration of raster concepts, we will use datasets from the spDataLarge (note these packages were loaded at the beginning of the chapter).
It consists of a few raster and one vector datasets covering an area of the Zion National Park (Utah, USA).
srtm.tif is a digital elevation model of this area (for more details - see its documentation
First of all, we would like to create a
RasterLayer object named
Typing the name of the raster into the console, will print out the raster header (extent, dimensions, resolution, CRS) and some additional information (class, data source name, summary of the raster values):
new_raster #> class : RasterLayer #> dimensions : 457, 465, 212505 (nrow, ncol, ncell) #> resolution : 0.000833, 0.000833 (x, y) #> extent : -113, -113, 37.1, 37.5 (xmin, xmax, ymin, ymax) #> coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 #> data source : /home/robin/R/x86_64-pc-linux../3.5/spDataLarge/raster/srtm.tif #> names : srtm #> values : 1024, 2892 (min, max)
Dedicated functions report each component:
dim(new_raster) returns the number of rows, columns and layers; the
ncell() function the number cells (pixels);
res() the raster’s spatial resolution;
extent() its spatial extent; and
crs() its coordinate reference system (raster reprojection is covered in section 6.6).
inMemory() reports whether the the raster data is stored in memory (the default) or on disk.
help("raster-package") returns a full list of all available raster functions.
sfobjects. We therefore suggest converting
sfobjects to an intermediate
Spatialclass (from the sp package) for compatibility between raster and vector data, for example
crop(raster_obj, as(sf_object, "Spatial")(see section 5.4).
2.2.2 Basic map making
Similar to the sf package, raster also provides
plot() methods for its own classes.
There are several other approaches for plotting raster data in R that are outside the scope of this section, including:
- Functions such as
levelplot()(from the sp and rasterVis packages, respectively) to create facets, a common technique for visualizing change over time.
- Packages such as tmap, mapview and leaflet to create interactive maps of raster and vector objects (see Chapter 8).
2.2.3 Raster classes
RasterLayer class represents the simplest form of a raster object, and consists of only one layer.
The easiest way to create a raster object in R is to read-in a raster file from disk or from a server.
The raster package supports numerous drivers with the help of rgdal.
To find out which drivers are available on your system, run
Rasters can also be created from scratch using the
This is illustrated in the subsequent code chunk, which results in a new
The resulting raster consists of 36 cells (6 columns and 6 rows specified by
ncol) centered around the Prime Meridian and the Equator (see
The CRS is the default of raster objects: WGS84.
This means the unit of the resolution is in degrees which we set to 0.5 (
vals) are assigned to each cell: 1 to cell 1, 2 to cell 2, and so on.
raster() fills cells row-wise (unlike
matrix()) starting at the upper left corner, meaning the top row contains the values 1 to 6, the second 7 to 12 etc.
For still further ways of creating a raster object have a look at the help file -
RasterLayer, there are two additional classes:
Both can handle multiple layers, but differ regarding the number of supported file formats, type of internal representation and processing speed.
RasterBrick consists of multiple layers, which typically correspond to a single multispectral satellite file or a single multilayer object in memory.
brick() function creates a
Usually, you provide it with a filename to a multilayer raster file but might also use another raster object and other spatial objects (see
?brick for all supported formats).
nlayers() retrieves the number of layers stored in a
RasterStack is similar to a
RasterBrick in the sense that it consists also of multiple layers.
However, in contrast to
RasterStack allows you to connect several raster objects stored in different files or multiply objects in memory.
More specifically, a
RasterStack is a list of
RasterLayer objects with the same extent and resolution.
Hence, one way to create it is with the help of spatial objects already existing in R’s global environment.
And again, one can simply specify a path to a file stored on disk.
Another difference is that the processing time for
RasterBrick objects is usually shorter than for
Decision on which
Raster* class should be used depends mostly on a character of input data.
Processing of a single mulitilayer file or object is the most effective with
RasterStack allows calculations based on many files, many
Raster* objects, or both.
RasterStackobjects will typically return a
2.3 Coordinate Reference Systems
Vector and raster spatial data types share concepts intrinsic to spatial data. Perhaps the most fundamental of these is the Coordinate Reference System (CRS), which defines how the spatial elements of the data relate to the surface of the Earth (or other bodies). CRSs are either geographic or projected, as introduced at the beginning of this chapter (see Figure 2.1). This section will will explain each type, laying the foundations for section 6 on CRS transformations.
2.3.1 Geographic coordinate systems
Geographic coordinate systems identify any location on the Earth’s surface using two values — longitude and latitude. Longitude is location in the East-West direction in angular distance from the Prime Meridian plane. Latitude is angular distance North or South of the equatorial plane. Distance in geographic CRSs are therefore not measured in meters. This has important consequences, as demonstrated in section 6.
The surface of the Earth in geographic coordinate systems is represented by a spherical or ellipsoidal surface. Spherical models assume that the Earth is a perfect sphere of a given radius. Spherical models have the advantage of simplicity but are rarely used because they are inaccurate: the Earth is not a sphere! Ellipsoidal models are defined by two parameters: the equatorial radius and the polar radius. These are suitable because the Earth is compressed: the equatorial radius is around 11.5 km longer than the polar radius (Maling 1992).14
Ellipsoids are part of a wider component of CRSs: the datum.
This contains information on what ellipsoid to use (with the
ellps parameter in the proj4 CRS library) and the precise relationship between the Cartesian coordinates and location on the Earth’s surface.
These additional details are stored in the
towgs84 argument of proj4 notation (see proj4.org/parameters.html for details).
These allow local variations in Earth’s surface, e.g. due to large mountain ranges, to be accounted for in a local CRS.
There are two types of datum — local and geocentric.
In a local datum such as
NAD83 the ellipsoidal surface is shifted to align with the surface at a particular location.
In a geocentric datum such as
WGS84 the center is the Earth’s center of gravity and the accuracy of projections is not optimized for a specific location.
Available datum definitions can be seen by executing
st_proj_info(type = "datum").
2.3.2 Projected coordinate systems
Projected CRSs are based on Cartesian coordinates on an implicitly flat surface. They have an origin, x and y axes, and a linear unit of measurement such as meters. All projected CRSs are based on a geographic CRS, described in the previous section, and rely on map projections to convert the three-dimensional surface of the Earth into Easting and Northing (x and y) values in a projected CRS.
This transition cannot be done without adding some distortion. Therefore, some properties of the Earth’s surface are distorted in this process, such as area, direction, distance, and shape. A projected coordinate system can preserve only one or two of those properties. Projections are often named based on a property they preserve: equal-area preserves area, azimuthal preserve direction, equidistant preserve distance, and conformal preserve local shape.
There are three main groups of projection types - conic, cylindrical, and planar.
In a conic projection, the Earth’s surface is projected onto a cone along a single line of tangency or two lines of tangency.
Distortions are minimized along the tangency lines and rise with the distance from those lines in this projection.
Therefore, it is the best suited for maps of mid-latitude areas.
A cylindrical projection maps the surface onto a cylinder.
This projection could also be created by touching the Earth’s surface along a single line of tangency or two lines of tangency.
Cylindrical projections are used most often when mapping the entire world.
A planar projection projects data onto a flat surface touching the globe at a point or along a line of tangency.
It is typically used in mapping polar regions.
st_proj_info(type = "proj") gives a list of the available projections supported by the PROJ library.
2.3.3 CRSs in R
Two main ways to describe CRS in R are an
epsg code or a
Both of these approaches have advantages and disadvantages.
epsg code is usually shorter, and therefore easier to remember.
The code also refers to only one, well-defined coordinate reference system.
On the other hand, a
proj4string definition allows you more flexibility when it comes to specifying different parameters such as the projection type, the datum and the ellipsoid.15
This way you can specify many different projections, and modify existing ones.
This also makes the
proj4string approach more complicated.
epsg points to exactly one particular CRS.
Spatial R packages support a wide range of CRSs and they use the long-established proj4 library.
Other than searching for EPSG codes online, another quick way to find out about available CRSs is via the
rgdal::make_EPSG() function, which outputs a data frame of available projections.
Before going into more detail, it’s worth learning how to view and filter them inside R, as this could save time trawling the internet.
The following code will show available CRSs interactively, allowing you to filter ones of interest (try filtering for the OSGB CRSs for example):
In sf the CRS of an object can be retrieved using
For this, we need to read-in a vector dataset:
Our new object,
new_vector, is a polygon representing the borders of Zion National Park (
In cases when a coordinate reference system (CRS) is missing or the wrong CRS is set, the
st_set_crs() function can be used:
The warning message informs us that the
st_set_crs() function does not transform data from one CRS to another.
projection() function can be used to access CRS information from a
The same function,
projection(), is used to set a CRS for raster objects.
The main difference, compared to vector data, is that raster objects only accept
We will expand on CRSs and how to project from one CRS to another in much more detail in chapter 6.
An important feature of CRSs is that they contain information about spatial units. Clearly it is vital to know whether a house’s measurements are in feet or meters, and the same applies to maps. It is good cartographic practice to add a scale bar onto maps to demonstrate the relationship between distances on the page or screen and distances on the ground. Likewise, it is important to formally specify the units in which the geometry data or pixels are measured to provide context, and ensure that subsequent calculations are done in context.
A novel feature of geometry data in
sf objects is that they have native support for units.
This means that distance, area and other geometric calculations in sf return values that come with a
units attribute, defined by the units package (Pebesma, Mailund, and Hiebert 2016).
This is advantageous because it prevents confusion caused by the fact that different CRSs use different units (most use meters, some use feet).
Furthermore, it also provides information on dimensionality, as illustrated by the following calculation which reports the area of Luxembourg:
The result is in units of square meters (m2), showing that the result represents two-dimensional space.
This information, stored as an attribute (which interested readers can discover with
attributes(st_area(luxembourg))) is advantageous for many reasons, for example it could feed into subsequent calculations such as population density.
Reporting units prevents confusion.
To take the Luxembourg example, if the units remained unspecified, one could incorrectly assume that the units were in hectares.
To translate the huge number into a more digestible size, it is tempting to divide the results by a million (the number of square meters in a square kilometer):
However, the result is incorrectly given again as square meters. The solution is to set the correct units with the units package:
Units are of equal importance in the case of raster data.
However, so far sf is the only spatial package that supports units, meaning that people working on raster data should approach changes in the units of analysis (for example, converting pixel widths from imperial to decimal units) with care.
new_raster object (see above) uses a UTM projection with meters as units.
Consequently, its resolution is also given in meters but you have to know it, since the
res() function simply returns a numeric vector.
If we used the WGS84 projection, the units would change.
res() command gives back a numeric vector without any unit, forcing us to know that the unit of the WGS84 projection is decimal degrees.
- What does the summary of the
geometrycolumn tell us about the
worlddataset, in terms of:
- The geometry type?
- How many countries there are?
- The coordinate reference system (CRS)?
- Using sf’s
plot()command, create a map of Nigeria in context, building on the code that creates and plots Asia above (see section 2.1.3).
- Hint: this used the
- Bonus: make the country boundaries a dotted gray line.
borderis an additional argument of
plot()for sf objects.
- Hint: this used the
- What does the
cexargument do in the
plot()function that generates Figure 2.5?
- Why was
cexset to the
sqrt(world$pop) / 10000instead of just the population directly?
- Bonus: what equivalent arguments to
cexexist in the dedicated visualization package tmap?
- Why was
- Re-run the code that ‘generated’ Figure 2.5 at the end of 2.1.4 and find 3 similarities and 3 differences between the plot produced on your computer and that in the book.
- Read the
raster/nlcd2011.tiffile from the spDataLarge package. What kind of information can you get about the properties of this file?
- Create an empty
my_rasterwith 10 columns and 10 rows and resolution of 10 units. Assign random values between 0 and 10 to the new raster and plot it.
Gillespie, Colin, and Robin Lovelace. 2016. Efficient R Programming: A Practical Guide to Smarter Programming. O’Reilly Media.
Grolemund, Garrett, and Hadley Wickham. 2016. R for Data Science. 1 edition. O’Reilly Media.
Pebesma, Edzer. 2018. “Simple Features for R: Standardized Support for Spatial Vector Data.” The R Journal.
Pebesma, Edzer, and Roger Bivand. 2018. Sp: Classes and Methods for Spatial Data. https://CRAN.R-project.org/package=sp.
Bivand, Roger, Tim Keitt, and Barry Rowlingson. 2018. Rgdal: Bindings for the ’Geospatial’ Data Abstraction Library. https://CRAN.R-project.org/package=rgdal.
Bivand, Roger, and Colin Rundel. 2018. Rgeos: Interface to Geometry Engine - Open Source (’Geos’). https://CRAN.R-project.org/package=rgeos.
Maling, D. H. 1992. Coordinate Systems and Map Projections. 2nd ed. Oxford ; New York: Pergamon Press.
Pebesma, Edzer, Thomas Mailund, and James Hiebert. 2016. “Measurement Units in R.” The R Journal 8 (2): 486–94.
Note that spDataLarge is not on CRAN, meaning that the
typearguments must be set for it to install. ↩
The origin we are referring to, depicted in blue in Figure 2.1, is in fact the ‘false’ origin. The ‘true’ origin, the location at which distortions are at a minimum, is located at 2° W and 49° N. This was selected by the Ordnance Survey to be roughly in the center of the British landmass longitudinally. ↩
The full OGC standard includes rather exotic geometry types including ‘surface’ and ‘curve’ geometry types, which currently have limited application in real world applications. All 68 types can be represented with the sf package, although (as of summer 2018) plotting only works for the ‘core 7’.↩
The development version, which may contain new features, can be installed with
plot()ing of sf objects uses
sf:::plot.sf()behind the scenes.
plot()is a generic method that behaves differently depending on the class of object being plotted.↩
Note: many plot arguments are ignored in facet maps, when more than one
sfcolumn is plotted.↩
By definition, a polygon has one exterior boundary (outer ring) and can have zero or more interior boundaries (inner rings), also known as holes. A polygon with a hole would be, for example,
POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5), (2 4, 3 4, 3 3, 2 3, 2 4))↩
Other attributes might include a urbanity category (city or village), or a remark if the measurement was made using an automatic station.↩
Depending on the file format the header is part of the actual image data file, e.g., GeoTiff, or stored in an extra header or world file, e.g., ASCII grid formats. There is also the headerless (flat) binary raster format which should fascilitate the import into various software programs. ↩
The degree of compression is often referred to as flattening, defined in terms of the equitorial radius (\(a\)) and polar radius (\(b\)) as follows: \(f = (a - b) / a\). The terms ellipticity and compression can also be used (Maling 1992). Because \(f\) is a rather small value, digital ellipsoid models use the ‘inverse flattening’ (\(rf = 1/f\)) to define the Earth’s compression. Values of \(a\) and \(rf\) used in a variety of ellipsoidal models can be seen be executing
st_proj_info(type = "ellps").↩