About

This lesson covers the key spatial attributes that are needed to work with spatial data including: Coordinate Reference Systems (CRS), Extent and spatial resolution.

R Skill Level: Beginner - you’ve got the basics of R down.

Getting Started with CRS

Check out this short video highlighting how map projections can make continents look proportionally larger or smaller than they actually are!

• For more on types of projections, visit ESRI’s ArcGIS reference on projection types..
• Read more about choosing a projection/datum.

What is a Coordinate Reference System

To define the location of something we often use a coordinate system. This system consists of an X and a Y value, located within a 2 (or more) -dimensional space.

While the above coordinate system is 2-dimensional, we live on a 3-dimensional earth that happens to be “round”. To define the location of objects on the earth, which is round, we need a coordinate system that adapts to the Earth’s shape. When we make maps on paper or on a flat computer screen, we move from a 3-Dimensional space (the globe) to a 2-Dimensional space (our computer screens or a piece of paper). The components of the CRS define how the “flattening” of data that exists in a 3-D globe space. The CRS also defines the the coordinate system itself.

A coordinate reference system (CRS) is a coordinate-based local, regional or global system used to locate geographical entities. – Wikipedia

The Components of a CRS

The coordinate reference system is made up of several key components:

• Coordinate System: the X, Y grid upon which our data is overlayed and how we define where a point is located in space.
• Horizontal and vertical units: The units used to define the grid along the x, y (and z) axis.
• Datum: A modeled version of the shape of the earth which defines the origin used to place the coordinate system in space. We will explain this further, below.
• Projection Information: the mathematical equation used to flatten objects that are on a round surface (e.g. the earth) so we can view them on a flat surface (e.g. our computer screens or a paper map).

Why CRS is Important

It is important to understand the coordinate system that your data uses - particularly if you are working with different data stored in different coordinate systems. If you have data from the same location that are stored in different coordinate reference systems, they will not line up in any GIS or other program unless you have a program like ArcGIS or QGIS that supports projection on the fly. Even if you work in a tool that supports projection on the fly, you will want to all of your data in the same projection for performing analysis and processing tasks.

Data Tip: Spatialreference.org provides an excellent online library of CRS information.

Coordinate System & Units

We can define a spatial location, such as a plot location, using an x- and a y-value - similar to our cartesian coordinate system displayed in the figure, above.

For example, the map below, generated in R with ggplot2 shows all of the continents in the world, in a Geographic Coordinate Reference System. The units are Degrees and the coordinate system itself is latitude and longitude with the origin being the location where the equator meets the central meridian on the globe (0,0).

library(rgdal)
library(ggplot2)

## 
## Attaching package: 'ggplot2'

## The following object is masked from 'package:raster':
## 
##     calc

library(rgeos)

## rgeos version: 0.3-26, (SVN revision 560)
##  GEOS runtime version: 3.5.1-CAPI-1.9.1 r4246 
##  Linking to sp version: 1.2-5 
##  Polygon checking: TRUE

library(raster)

# be sure to set your working directory
# setwd("~/Documents/data")

# read shapefile
worldBound <- readOGR(dsn="Global/Boundaries/ne_110m_land",
                      layer="ne_110m_land")

## Error in ogrInfo(dsn = dsn, layer = layer, encoding = encoding, use_iconv = use_iconv, : Cannot open data source

# convert to dataframe
worldBound_df <- fortify(worldBound)  

## Error in fortify(worldBound): object 'worldBound' not found

# plot map
worldMap <- ggplot(worldBound_df, aes(long,lat, group=group)) +
  geom_polygon() +
  xlab("Longitude (Degrees)") + ylab("Latitude (Degrees)") +
  coord_equal() +
  ggtitle("Global Map - Geographic Coordinate System - WGS84 Datum\n Units: Degrees - Latitude / Longitude")

## Error in ggplot(worldBound_df, aes(long, lat, group = group)): object 'worldBound_df' not found

worldMap

## Error in eval(expr, envir, enclos): object 'worldMap' not found

We can add three coordinate locations to our map. Note that the UNITS are in decimal degrees (latitude, longitude):

• Boulder, Colorado: 40.0274, -105.2519
• Oslo, Norway: 59.9500, 10.7500
• Mallorca, Spain: 39.6167, 2.9833

Let’s create a second map with the locations overlayed on top of the continental boundary layer.

# define locations of Boulder, CO and Oslo, Norway
# store them in a data.frame format
loc.df <- data.frame(lon=c(-105.2519, 10.7500, 2.9833),
                lat=c(40.0274, 59.9500, 39.6167))

# only needed if the above is a spatial points object
# loc.df <- fortify(loc)  

# add a point to the map
mapLocations <- worldMap + geom_point(data=loc.df,
                        aes(x=lon, y=lat, group=NULL),
                      colour = "springgreen",
                      size=5)

## Error in eval(expr, envir, enclos): object 'worldMap' not found

mapLocations + theme(legend.position="none")

## Error in eval(expr, envir, enclos): object 'mapLocations' not found

Geographic CRS - The Good & The Less Good

Geographic coordinate systems in decimal degrees are helpful when we need to locate places on the Earth. However, latitude and longitude locations are not located using uniform measurement units. Thus, geographic CRSs are not ideal for measuring distance. This is why other projected CRS have been developed.

Projected CRS - Robinson

We can view the same data above, in another CRS - Robinson. Robinson is a projected CRS. Notice that the country boundaries on the map - have a different shape compared to the map that we created above in the CRS:
Geographic lat/long WGS84.

# reproject from longlat to robinson
worldBound_robin <- spTransform(worldBound,
                                CRS("+proj=robin"))

## Error in spTransform(worldBound, CRS("+proj=robin")): object 'worldBound' not found

worldBound_df_robin <- fortify(worldBound_robin)

## Error in fortify(worldBound_robin): object 'worldBound_robin' not found

# force R to plot x and y values without abbrev
options(scipen=100)

robMap <- ggplot(worldBound_df_robin, aes(long,lat, group=group)) +
  geom_polygon() +
  labs(title="World map (robinson)") +
  xlab("X Coordinates (meters)") + ylab("Y Coordinates (meters)") +
  coord_equal()

## Error in ggplot(worldBound_df_robin, aes(long, lat, group = group)): object 'worldBound_df_robin' not found

robMap

## Error in eval(expr, envir, enclos): object 'robMap' not found

Now what happens if you try to add the same Lat / Long coordinate locations that we used above, to our map, with the CRS of Robinsons?

# add a point to the map
newMap <- robMap + geom_point(data=loc.df,
                      aes(x=lon, y=lat, group=NULL),
                      colour = "springgreen",
                      size=5)

## Error in eval(expr, envir, enclos): object 'robMap' not found

newMap + theme(legend.position="none")

## Error in eval(expr, envir, enclos): object 'newMap' not found

Notice above that when we try to add lat/long coordinates in degrees, to a map in a different CRS, that the points are not in the correct location. We need to first convert the points to the new projection - a process often referred to as reprojection but performed by the spTransform() function in R.

# define locations of Boulder, CO and Oslo, Norway
loc.df

##         lon     lat
## 1 -105.2519 40.0274
## 2   10.7500 59.9500
## 3    2.9833 39.6167

# convert to spatial Points data frame
loc.spdf <- SpatialPointsDataFrame(coords = loc.df, data=loc.df,
                            proj4string=crs(worldBound))  

## Error in crs(worldBound): object 'worldBound' not found

loc.spdf

## Error in eval(expr, envir, enclos): object 'loc.spdf' not found

# reproject data to Robinson
loc.spdf.rob <- spTransform(loc.spdf, CRSobj = CRS("+proj=robin"))

## Error in spTransform(loc.spdf, CRSobj = CRS("+proj=robin")): object 'loc.spdf' not found

loc.rob.df <- as.data.frame(cbind(loc.spdf.rob$lon, loc.spdf.rob$lat))

## Error in cbind(loc.spdf.rob$lon, loc.spdf.rob$lat): object 'loc.spdf.rob' not found

# rename each column
names(loc.rob.df ) <- c("X","Y")

## Error in names(loc.rob.df) <- c("X", "Y"): object 'loc.rob.df' not found

# convert spatial object to a data.frame for ggplot
loc.rob <- fortify(loc.rob.df)

## Error in fortify(loc.rob.df): object 'loc.rob.df' not found

# notice the coordinate system in the Robinson projection (CRS) is DIFFERENT
# from the coordinate values for the same locations in a geographic CRS.
loc.rob

## Error in eval(expr, envir, enclos): object 'loc.rob' not found

# add a point to the map
newMap <- robMap + geom_point(data=loc.rob,
                      aes(x=X, y=Y, group=NULL),
                      colour = "springgreen",
                      size=5)

## Error in eval(expr, envir, enclos): object 'robMap' not found

newMap + theme(legend.position="none")

## Error in eval(expr, envir, enclos): object 'newMap' not found

Compare Maps

Both of the plots above look visually different and also use a different coordinate system. Let’s look at both, side by side, with the actual graticules or latitude and longitude lines rendered on the map.

NOTE: The code for this map can be found in the .R document that is available for download at the bottom of this page!

## Error in theme(line = element_blank(), line = element_blank(), axis.text.x = element_blank(), : formal argument "line" matched by multiple actual arguments

## Error in ogrInfo(dsn = dsn, layer = layer, encoding = encoding, use_iconv = use_iconv, : Cannot open data source

## Error in fortify(graticule): object 'graticule' not found

## Error in ogrInfo(dsn = dsn, layer = layer, encoding = encoding, use_iconv = use_iconv, : Cannot open data source

## Error in fortify(data): object 'worldBound_df' not found

## Error in eval(expr, envir, enclos): object 'latLongMap' not found

## Error in spTransform(graticule, CRS("+proj=robin")): object 'graticule' not found

## Error in fortify(graticule_robin): object 'graticule_robin' not found

## Error in (function (classes, fdef, mtable) : unable to find an inherited method for function 'spTransform' for signature '"standardGeneric", "CRS"'

## Error in fortify(bbox_robin): object 'bbox_robin' not found

## Error in ggplot(bbox_robin_df, aes(long, lat, group = group)): object 'bbox_robin_df' not found

## Error in eval(expr, envir, enclos): object 'finalRobMap' not found

## Error in arrangeGrob(...): object 'latLongMap' not found

Why Multiple CRS?

You may be wondering, why bother with different CRSs if it makes our analysis more complicated? Well, each CRS is optimized to best represent:

• Shape and/or
• Scale / distance and/or
• Area

of features in the data. And no one CRS is great at optimizing shape, distance AND area. Some CRSs are optimized for shape, some distance, some area. Some CRSs are also optimized for particular regions - for instance the United States, or Europe. Discussing CRS as it optimizes shape, distance and area is beyond the scope of this tutorial, but it’s important to understand that the CRS that you chose for your data, will impact working with the data!

Geographic vs Projected CRS

The above maps provide examples of the two main types of coordinate systems:

1. Geographic coordinate systems: coordinate systems that span the entire globe (e.g. latitude / longitude).
2. Projected coordinate Systems: coordinate systems that are localized to minimize visual distortion in a particular region (e.g. Robinson, UTM, State Plane)

In the next tutorial, we will discuss the differences between these CRSs in more detail. Feel free to skip over this section and come back to it with fresh eyes if the concept of a CRS is becoming too complex. It’s easisest to take on in bite sized pieces!