2 Geographic data in R

Prerequisites

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

On Mac and Linux a few requirements must be met to install sf. These are described in the package’s README at github.com/r-spatial/sf.

Packages are ‘loaded’ (technically they are attached) with the library() function, which is used to load the two spatial data processing packages installed previously 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

Take care when using the word ‘vector’ as it can have two meanings in this book: geographic vector data and the vector class (note the monospace font) in R. The former is a data model, the latter is an R class just like data.frame and 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 vector objects.

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 c(-0.1, 51.5). 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.

Illustration of vector (point) data in which location of London (the red X) is represented with reference to an origin (the blue circle). The left plot represents a geographic CRS with an origin at 0° longitude and latitude. The right plot represents a projected CRS with an origin located in the sea west of the South West Peninsula.Illustration of vector (point) data in which location of London (the red X) is represented with reference to an origin (the blue circle). The left plot represents a geographic CRS with an origin at 0° longitude and latitude. The right plot represents a projected CRS with an origin located in the sea west of the South West Peninsula.

Figure 2.1: Illustration of vector (point) data in which location of London (the red X) is represented with reference to an origin (the blue circle). The left plot represents a geographic CRS with an origin at 0° longitude and latitude. The right plot represents a projected CRS with an origin located in the sea west of the South West Peninsula.

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) to represent a wide range of geographic information. It is a hierarchical data model that simplifies geographic data by condensing a complex range of geographic forms into a single geometry class. Only 7 out of 17 possible types of simple feature are currently used in the vast majority of GIS operations (Figure 2.2). The R package sf (E. Pebesma 2018) fully supports all of these (including plotting methods etc.).7

The subset of the Simple Features class hierarchy supported by sf.

Figure 2.2: The subset of the Simple Features class hierarchy supported by sf.

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 2017) 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.

A spatial plot of the world using the sf package, with a facet for each attribute.

Figure 2.3: A spatial plot of the world using the sf package, with a facet for each attribute.

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 world datasets. 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 world object.

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.

The word MULTIPOLYGON in the summary output above refers to the geometry type of features (countries) in the world object. 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 (geometry type, dimension, bbox and CRS information - epsg (SRID), proj4string), and the presence of final geometry column:

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.

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 st_)

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 st_as_sf():

2.1.3 Basic map making

Basic maps are created in sf with plot(). 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.

Plotting with sf, with multiple variables (left) and a single variable (right).Plotting with sf, with multiple variables (left) and a single variable (right).

Figure 2.4: Plotting with sf, with multiple variables (left) and a single variable (right).

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:

A plot of Asia added as a layer on top of countries worldwide.

Figure 2.5: A plot of Asia added as a layer on top of countries worldwide.

Adding layers in this way can be used to verify the geographic correspondence between layers: the 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

Since sf’s plot() function builds on base plotting methods, it has many optional arguments (see ?graphics::plot and ?par). This may not be the most concise way to generate maps for publication, as we will see in Chapter 8, but it is worth learning some base plotting arguments for future reference. A simple illustration of the flexibility of plot() is provided in Figure 2.6, which adds circles representing population size to a map of the world. A basic version of the map can be created with the following commands (see exercises in section 2.5 02-contplot.R in the book’s GitHub repo for details):

Country continents (represented by fill color) and 2015 populations (represented by points, with point area proportional to population) worldwide.

Figure 2.6: Country continents (represented by fill color) and 2015 populations (represented by points, with point area proportional to population) worldwide.

2.1.5 Simple feature classes

To understand new data formats in depth, it often helps to build them from the ground up. This section walks you through vector spatial classes step-by-step, from the elementary simple feature geometry to simple feature objects of class sf representing complex spatial data. Before describing each geometry type that the sf package supports, it is worth taking a step back to understand the building blocks of sf objects. As stated in section 2.1.1, simple features are simply data frames with at least one special column that makes it spatial. These spatial columns are often called geom or geometry and can be accessed like non-spatial columns: world$geom refers to the spatial element of the world object described above. These geometry columns are ‘list columns’ of class sfc. In turn, sfc objects are composed of one or more objects of class sfg: simple feature geometries.

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 sfg type in the next subsections before moving on to describe how these can be combined to form sfc and eventually full sf objects.

2.1.5.1 Simple feature 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: POINT, LINESTRING, POLYGON, MULTIPOINT, MULTILINESTRING, MULTIPOLYGON and GEOMETRYCOLLECTION. 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 2.7):

  • POINT (5 2)

A linestring is a sequence of points with a straight line connecting the points, for example (see middle panel in Figure 2.7):

  • LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)

A polygon is a sequence of points that form a closed, non-intersecting ring. Closed means that the first and the last point of a polygon have the same coordinates (see right panel in Figure 2.7).10

  • Polygon without a hole - POLYGON ((1 5, 2 2, 4 1, 4 4, 1 5))
Illustration of point, linestring and polygon geometries.

Figure 2.7: Illustration of point, linestring and polygon geometries.

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)))
Illustration of multipoint, mutlilinestring and multipolygon geometries.

Figure 2.8: Illustration of multipoint, mutlilinestring and multipolygon geometries.

Finally, a geometry collection might contain any combination of geometry types:

  • Geometry collection - GEOMETRYCOLLECTION (MULTIPOINT (5 2, 1 3, 3 4, 3 2), LINESTRING (1 5, 4 4, 4 1, 2 2, 3 2)))

2.1.5.2 Simple feature geometry (sfg) objects

The 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 - st_point()
  • A linestring - st_linestring()
  • A polygon - st_polygon()
  • A multipoint - st_multipoint()
  • A multilinestring - st_multilinestring()
  • A multipolygon - st_multipolygon()
  • A geometry collection - st_geometrycollection()

sfg objects can be created from three native data types:

  1. A numeric vector - a single point
  2. A matrix - a set of points, where each row contains a point - a multipoint or linestring
  3. 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 dim argument.

By contrast, use matrices in the case of multipoint (st_multipoint()) and linestring (st_linestring()) objects:

Finally, use lists for the creation of multilinestrings, (multi-)polygons and geometry collections:

2.1.5.3 Simple feature geometry column

One 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 st_sfc() function. 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. Equally, a geometry column of multilinestrings would result in an sfc object of type multilinestring:

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 sfc object. The default value of epsg (SRID) and proj4string is NA (Not Available):

All geometries in an sfc object must have the same CRS.

We can add coordinate reference system as a crs argument of st_sfc(). This argument accepts either an integer with the epsg code (for example, 4326) or a proj4string character string (for example, "+proj=longlat +datum=WGS84 +no_defs") (see section 2.3).

For example, we can set the UTM Zone 11N projection with epsg code 2955:

As you can see above, the proj4string definition was automatically added. Now we can try to set the CRS using proj4string:

However, the epsg string of our result remained empty. This is because there is no general method to convert from proj4string to epsg.

2.1.5.4 Simple feature objects

So far, we have only dealt with the pure geometries. Most of the time, however, these geometries come with a set of attributes describing them. These attributes could represent the name of the geometry, measured values, groups to which the geometry belongs, and many more. For example, we measured a temperature of 25°C on Trafalgar Square in London on June 21st 2017. Hence, we have a specific point in space (the coordinates), the name of the location (Trafalgar Square), a temperature value and the date of the measurement. Other attributes might include a urbanity category (city or village), or a remark if the measurement was made using an automatic station.

The simple feature class, sf, is a combination of an attribute table (data.frame) and a simple feature geometry column (sfc). Simple features are created using the st_sf() function:

The above example illustrates the components of sf objects. Firstly, coordinates define the geometry of the simple feature geometry (sfg). Secondly, we can combine the geometries in a simple feature geometry column (sfc) which also stores the CRS. Subsequently, we store the attribute information on the geometries in a data.frame. Finally, the st_sf() function combines the attribute table and the sfc object in an sf object.

The result shows that sf objects actually have two classes, sf and data.frame. 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 data.frame. 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).11 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 data: A - cell IDs; B - cell values; C - a colored raster map.

Figure 2.9: Raster data: A - cell IDs; B - cell values; C - a colored raster map.

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.

Examples of continuous (left) and categorical (right) raster.

Figure 2.10: Examples of continuous (left) and categorical (right) raster.

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). For example, srtm.tif is a digital elevation model of this area (for more details - see its documentation ?srtm) First of all, we would like to create a RasterLayer object named new_raster:

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):

To access individual header information, you can use following commands: dim(new_raster) (dimensions - number of rows, number of columns, number of raster layers), ncell(new_raster) (number of raster cells), res(new_raster) (spatial resolution), extent(new_raster) (spatial extent), and crs(new_raster) (coordinate reference system).

Note that in contrast to the sf package, raster only accepts the proj4string representation of the coordinate reference system.

Sometimes it is important to know if all values of a raster are currently in memory or on disk. Find out with the inMemory() function:

help(package = "raster", topic = "raster-package") returns a full list of all available raster functions.

The raster package is not yet fully compatible with objects from the sf package. Thus, we suggest to convert sf objects to Spatial^*^ class() when using a vector data inside a raster function, for example crop(raster_obj, as(sf_object, "Spatial").

2.2.2 Basic map making

Similar to the sf package, raster also provides plot() methods for its own classes.

There are several different approaches to plot raster data in R:

  • You can use spplot() to visualize several (such as spatiotemporal) layers at once. You can also do so with the rasterVis package which provides more advanced methods for plotting raster objects.
  • Packages such as tmap, mapview and leaflet facilitate especially interactive mapping of both raster and vector objects.

2.2.3 Raster classes

The 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 raster::writeFormats() and rgdal::gdalDrivers().

Rasters can also be created from scratch using the raster() function. This is illustrated in the subsequent code chunk, which results in a new RasterLayer object. The resulting raster consists of 36 cells (6 columns and 6 rows specified by nrow and ncol) centered around the Prime Meridian and the Equator (see xmn, xmx, ymn and ymx parameters). 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 (res). Values (vals) are assigned to each cell: 1 to cell 1, 2 to cell 2, and so on. Remember: 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 - ?raster.

Aside from RasterLayer, there are two additional classes: RasterBrick and RasterStack. Both can handle multiple layers, but differ regarding the number of supported file formats, type of internal representation and processing speed.

A RasterBrick consists of multiple layers, which typically correspond to a single multispectral satellite file or a single multilayer object in memory. The brick() function creates a RasterBrick object. Usually, you provide it with a filename to a multilayer raster file but might also use another raster object and other spatial objects (see its help page for all supported formats).

The nlayers function retrieves the number of layers stored in a Raster* object:

A RasterStack is similar to a RasterBrick in the sense that it consists also of multiple layers. However, in contrast to RasterBrick, 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 RasterStack objects.

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 RasterBrick, while RasterStack allows calculations based on many files, many Raster* objects, or both.

Operations on RasterBrick and RasterStack objects will typically return a RasterBrick.

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).12

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 proj4string definition. Both of these approaches have advantages and disadvantages. An 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.13 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 st_crs(). 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 (?zion).

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.

Examples of geographic (WGS 84; left) and projected (NAD83 / UTM zone 12N; right) and coordinate systems for a vector data type.

Figure 2.11: Examples of geographic (WGS 84; left) and projected (NAD83 / UTM zone 12N; right) and coordinate systems for a vector data type.

The projection() function can be used to access CRS information from a Raster* object:

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 proj4 definitions:

Examples of geographic (WGS 84; left) and projected (NAD83 / UTM zone 12N; right) and coordinate systems for a raster data type

Figure 2.12: Examples of geographic (WGS 84; left) and projected (NAD83 / UTM zone 12N; right) and coordinate systems for a raster data type

We will expand on CRSs and how to project from one CRS to another in much more detail in chapter 6.

2.4 Units

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 Nigeria:

The result is in units of square meters (m2), showing a) that the result represents two-dimensional space and b) and that Nigeria is a large country! This information, stored as an attribute (which interested readers can discover with attributes(st_area(nigeria))) is advantageous for many reasons, for example it could feed into subsequent calculations such as population density. Reporting units prevents confusion. To take the Nigeria example, if the units remained unspecified, one could incorrectly assume that the units were in km2. 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. The 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.

Again, the res() command gives back a numeric vector without any unit, forcing us to know that the unit of the WGS84 projection is decimal degrees.

2.5 Exercises

  1. What does the summary of the geometry column tell us about the world dataset, in terms of:
    • The geometry type?
    • How many countries there are?
    • The coordinate reference system (CRS)?
  2. Using sf’s plot() command, create a map of Nigeria in context, building on the code that creates and plots Asia above (see Figure 2.5 for an example of what this could look like).
    • Hint: this used the lwd, main and col arguments of plot().
    • Bonus: make the country boundaries a dotted gray line.
    • Hint: border is an additional argument of plot() for sf objects.
  3. What does the cex argument do in the plot() function that generates Figure 2.6?
    • Why was cex set to the sqrt(world$pop) / 10000 instead of just the population directly?
    • Bonus: what equivalent arguments to cex exist in the dedicated visualization package tmap?
  4. Re-run the code that ‘generated’ Figure 2.6 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.
    • What is similar?
    • What has changed?
    • Bonus: play around with and research base plotting arguments to make your version of Figure 2.6 more attractive. Which arguments were most useful?
    • Advanced: try to reproduce the map presented in Figure 2.1.4. Copy-and-pasting is prohibited!
  5. Read the raster/nlcd2011.tif file from the spDataLarge package. What kind of information can you get about the properties of this file?
  6. Create an empty RasterLayer object called my_raster with 10 columns and 10 rows and resolution of 10 units. Assign random values between 0 and 10 to the new raster and plot it.

References

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. 2017. 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.


  1. Note that spDataLarge is not on CRAN, meaning that the repos and type arguments must be set for it to install.

  2. 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.

  3. 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 (at the time of writing) all methods, such as plotting, are only supported for the 7 types described in this chapter.

  4. The development version, which may contain new features, can be installed with devtools::install_github("r-spatial/sf").

  5. 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.

  6. 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))

  7. 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.

  8. 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").

  9. A complete list of the proj4string parameters can be found at https://proj4.org/.