Geospatial data types

Most common spatial data types:

• raster: gridded data
• vector: geographical feautures
  • points
  • lines
  • polygons

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.

Types of common coordinate systems

There are two types of Coordinate Reference Systems:

• Geographic coordinate system (GCS): A global or spherical coordinate system such as latitude-longitude.
• Projected coordinate systems (PCS): A projected coordinate system provides various mechanisms to project maps of the earth’s spherical surface onto a two-dimensional Cartesian coordinate plane. Projected coordinate systems are referred to as map projections.

Geographic Coordinate System

Geographic Coordinate Systems are defined by a Datum

A Datum essentially defines the Globe Model of the coordinate system.

It has:

• angular units (eg. degrees)
• defines a starting point (i.e. where is (0,0) in particular which longitude is defined to be 0°?), so the angles reference a meaningful spot on the earth.
• defines the position of the spheroid relative to the center of the earth and therefore the origin and orientation of latitude and longitude lines.

A point is referenced by its longitude and latitude values. Longitude and latitude are angles measured from the earth’s center to a point on the earth’s surface.

Image source: https://datacarpentry.org/r-raster-vector-geospatial/images/map_usa_different_projections.jpg

The right datum for the right job

A particular datum can be selected for use in a specific geographic area, because it does a good job of modelling the surface of the earth in that part of the world.

Image source: http://desktop.arcgis.com/en/arcmap/10.3/guide-books/map-projections/GUID-E94B3A5F-D997-4E6F-B400-BC15C4B0DCDC-web.gif

Orange Peel Analogy: a datum is your choice of fruit to use in the orange peel analogy. Is the earth an orange, a lemon, a lime, a grapefruit?

Citrus fruit on display at the market

Image source: https://farm3.staticflickr.com/2260/2508805118_500f5bba28_n.jpg

Projected coordinate systems (PCS)

Projected coordinate systems include a projection

A Projection is a mathematical transformation of the angular measurements on a round earth to a flat surface (i.e. paper or a computer screen).

Units of measurement are linear, usually meters.

Orange Peel Analogy: a projection is how you peel your orange and then flatten the peel.

Image source: http://blogs.lincoln.ac.nz/gis/2017/03/29/where-on-earth-are-we/

Common projected coordinate systems:

-Mercator projection: a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course as straight segments that conserve the angles with the meridians.

• Universal Transverse Mercator (UTM) system: The UTM system is not a single map projection. The system instead divides the Earth into sixty zones, each being a six-degree band of longitude, and uses a secant transverse Mercator projection in each zone.

• Albers Equal Area: a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.

Image source: https://datacarpentry.org/r-raster-vector-geospatial/images/map_usa_different_projections.jpg

Q: Why is WGS 84 so different to other three projected maps?

Latitude lines are concentric circles that become smaller near the poles. They form a single point at the poles.

When a lat/lon CRS is flattened, the implicit flattening function used is the Plate Carree Function, one of the simplest functions that simply turns the globe into a cylinder and then unwraps it, resulting in increasing distortion of features as one approaches the poles.

Q: Why do the three projected maps differ from each other?

Going back to the orange peel analogy, different projections use a different starting point and method to peel the earth’s surface into a flat surface.

Map reprojections

To change between projected CRSs you need to reproject your data. This often involves unprojecting back to lat/lon, transforming the unprojected coordinates and then reprojecting.

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EPSG Code

An EPSG (European Petroleum Survey Group) Code is an ID that has been assigned to most common projections to make reference to a particular projection easy. An EPSG Code is also called an SRID (Spatial Reference Identifier). Technically, EPSG is the authority that assigns SRIDs, but you will hear these terms used interchangibly.

PROJ.4 String

PROJ.4 is an open source library for defining and converting between coordinate reference systems. It defines a standard way to write projection parameters.

For example, the proj.4 string: +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 encodes:

• proj=longlat: the data are in a geographic (latitude and longitude) coordinate system
• datum=WGS84: the datum WGS84 (the datum refers to the 0,0 reference for the coordinate system used in the projection)
• ellps=WGS84: the ellipsoid (how the earth’s roundness is calculated) is WGS84

Note that there are no specified units above. This is because this geographic coordinate reference system is in latitude and longitude which is most often recorded in decimal degrees.

A motivating example

(from Geocomputation in R, Section 2.1):

The city of London 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’) coordinate system (GCS).

The same point could also be approximated in a PCS 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 (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.

Session information

sessionInfo()

R version 3.4.4 (2018-03-15)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.3

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
 [1] workflowr_1.0.1   Rcpp_0.12.18      digest_0.6.15    
 [4] rprojroot_1.3-2   R.methodsS3_1.7.1 backports_1.1.2  
 [7] git2r_0.21.0      magrittr_1.5      evaluate_0.11    
[10] stringi_1.2.4     whisker_0.3-2     R.oo_1.21.0      
[13] R.utils_2.6.0     rmarkdown_1.10    tools_3.4.4      
[16] stringr_1.3.1     yaml_2.1.19       compiler_3.4.4   
[19] htmltools_0.3.6   knitr_1.20