This lesson covers the key spatial attributes that are needed to work with spatial data including: Coordinate Reference Systems (
CRS), extent and spatial resolution.
After completing this tutorial, you will be able to:
- Describe what a Coordinate Reference System (
- List the steps associated with plotting 2 datasets stored using different coordinate reference systems
What You Need
You will need a computer with internet access to complete this lesson and the data for week 4 of the course.
Intro to Coordinate Reference Systems
In summary - a coordinate reference system (
CRS) refers to the way in which spatial data that represent the earth’s surface (which is round / 3 dimensional) are flattened so that we can “Draw” them on a 2-dimensional surface. However each using a different (sometimes) mathematical approach to performing the flattening resulting in different coordinate system grids (discussed below). These approaches to flattening the data are specifically designed to optimize the accuracy of the data in terms of length and area (more on that later too).
In this lesson we will explore what a
CRS is. And how it can impact your data when you are working with it in a tool like
R (or any other tool).
The short video below highlights how map projections can make continents look proportionally larger or smaller than they actually are.
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
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
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).
# devtools::install_github("tidyverse/ggplot2") # load libraries library(rgdal) library(ggplot2) library(rgeos) library(raster) #install.packages('sf') # testing the sf package out for these lessons! library(sf) # set your working directory # setwd("~/Documents/earth-analytics/")
In the plot below, we will be using the following theme. You can copy and paste this code if you’d like to use the same theme!
# turn off axis elements in ggplot for better visual comparison newTheme <- list(theme(line = element_blank(), axis.text.x = element_blank(), axis.text.y = element_blank(), axis.ticks = element_blank(), # turn off ticks axis.title.x = element_blank(), # turn off titles axis.title.y = element_blank(), legend.position="none")) # turn off legend
# read shapefile worldBound <- readOGR(dsn="data/week_04/global/ne_110m_land/ne_110m_land.shp") # convert to dataframe worldBound_df <- fortify(worldBound)
# plot map using ggplot worldMap <- ggplot(worldBound_df, aes(long,lat, group=group)) + geom_polygon() + coord_equal() + labs(x="Longitude (Degrees)", y="Latitude (Degrees)", title="Global Map - Geographic Coordinate System ", subtitle = "WGS84 Datum, Units: Degrees - Latitude / Longitude") worldMap
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, Mallorca, Spain and Oslo, Norway # store coordinates in a data.frame loc_df <- data.frame(lon=c(-105.2519, 10.7500, 2.9833), lat=c(40.0274, 59.9500, 39.6167)) # add a point to the map mapLocations <- worldMap + geom_point(data=loc_df, aes(x=lon, y=lat, group=NULL), colour = "springgreen", size=5) mapLocations
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
CRS’s 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
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 data from longlat to robinson CRS worldBound_robin <- spTransform(worldBound, CRS("+proj=robin")) worldBound_df_robin <- fortify(worldBound_robin) # force R to plot x and y values without rounding digits # options(scipen=100) robMap <- ggplot(worldBound_df_robin, aes(long,lat, group=group)) + geom_polygon() + labs(title="World map (robinson)", x = "X Coordinates (meters)", y ="Y Coordinates (meters)") + coord_equal() robMap
Now what happens if you try to add the same Lat / Long coordinate locations that we used above, to our map, that is using the
CRS as it’s coordinate reference system?
# add a point to the map newMap <- robMap + geom_point(data=loc_df, aes(x=lon, y=lat, group=NULL), colour = "springgreen", size=5) newMap
Notice above that when we try to add lat/long coordinates in degrees to a map in a different
CRS the points are not in the correct location. We need to first convert the points to the new projection - a process called reprojection. We can reproject our data using the
spTransform() function in
Our points are stored in a data.frame which is not a spatial object. Thus, we will need to convert that
data.frame to a spatial
data.frame to use
# data.frame containing 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 dataframe to spatial points data frame loc_spdf<- SpatialPointsDataFrame(coords = loc_df, data=loc_df, proj4string=crs(worldBound)) loc_spdf ## class : SpatialPointsDataFrame ## features : 3 ## extent : -105.2519, 10.75, 39.6167, 59.95 (xmin, xmax, ymin, ymax) ## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 ## variables : 2 ## names : lon, lat ## min values : -105.2519, 39.6167 ## max values : 10.75, 59.95
Once we have converted our data frame into a spatial data frame, we can then reproject our data.
# reproject data to Robinson loc_spdf_rob <- spTransform(loc_spdf, CRSobj = CRS("+proj=robin"))
To make our data plot nicely with
ggplot, we need to once again convert to a dataframe. We can do that by extracting the
coordinates() and turning that into a
# convert the spatial object into a data frame loc_rob_df <- as.data.frame(coordinates(loc_spdf_rob)) # turn off scientific notation options(scipen=10000) # add a point to the map newMap <- robMap + geom_point(data=loc_rob_df, aes(x=lon, y=lat, group=NULL), colour = "springgreen", size=5) newMap
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.
To visually see the difference in these projections as they impact parts of the world, we will use a graticules layer which contains the meridian and parallel lines.
## import graticule shapefile data graticule <- readOGR("data/week_04/global/ne_110m_graticules_all", layer="ne_110m_graticules_15") # convert spatial sp object into a ggplot ready, data.frame graticule_df <- fortify(graticule)
Let’s check out our graticules. Notice they are just parallels and meridians.
# plot graticules ggplot() + geom_path(data=graticule_df, aes(long, lat, group=group), linetype="dashed", color="grey70")
Also we will import a bounding box to make our plot look nicer!
bbox <- readOGR("data/week_04/global/ne_110m_graticules_all/ne_110m_wgs84_bounding_box.shp") bbox_df <- fortify(bbox) latLongMap <- ggplot(bbox_df, aes(long,lat, group=group)) + geom_polygon(fill="white") + geom_polygon(data=worldBound_df, aes(long,lat, group=group, fill=hole)) + geom_path(data=graticule_df, aes(long, lat, group=group), linetype="dashed", color="grey70") + coord_equal() + labs(title="World Map - Geographic (long/lat degrees)") + newTheme + scale_fill_manual(values=c("black", "white"), guide="none") # change colors & remove legend # add our location points to the map latLongMap <- latLongMap + geom_point(data=loc_df, aes(x=lon, y=lat, group=NULL), colour="springgreen", size=5)
Below, we reproject our graticules and the bounding box to the Robinson projection.
# reproject grat into robinson graticule_robin <- spTransform(graticule, CRS("+proj=robin")) # reproject graticule grat_df_robin <- fortify(graticule_robin) bbox_robin <- spTransform(bbox, CRS("+proj=robin")) # reproject bounding box bbox_robin_df <- fortify(bbox_robin) # plot using robinson finalRobMap <- ggplot(bbox_robin_df, aes(long, lat, group=group)) + geom_polygon(fill="white") + geom_polygon(data=worldBound_df_robin, aes(long, lat, group=group, fill=hole)) + geom_path(data=grat_df_robin, aes(long, lat, group=group), linetype="dashed", color="grey70") + labs(title="World Map Projected - Robinson (Meters)") + coord_equal() + newTheme + scale_fill_manual(values=c("black", "white"), guide="none") # change colors & remove legend # add a location layer in robinson as points to the map finalRobMap <- finalRobMap + geom_point(data=loc_rob_df, aes(x=lon, y=lat, group=NULL), colour="springgreen", size=5)
Below we plot the two maps on top of each other to make them easier to compare. To do this, we use the
grid.arrange() function from the
require(gridExtra) # display side by side grid.arrange(latLongMap, finalRobMap)
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 the:
- shape and/or
- scale / distance and/or
of features in the data. And no one
CRS is great at optimizing all three elements: shape, distance AND area. Some
CRSs are optimized for shape, some are optimized for distance and some are optimized for 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.
We will discuss some of the differences between the projected
CRS and geographic
WGS84 in the next lesson.
Compare the maps of the globe above. What do you notice about the shape of the various countries. Are there any signs of distortion in certain areas on either map? Which one is better?
Look at the image below which depicts maps of the United States in 4 different
CRS’s. What visual differences do you notice in each map? Look up each projection online, what elements (shape,area or distance) does each projection used in the graphic below optimize?
Geographic vs. Projected CRS
The above maps provide examples of the two main types of coordinate systems:
- Geographic coordinate systems: coordinate systems that span the entire globe (e.g. latitude / longitude).
- Projected coordinate systems: coordinate systems that are localized to minimize visual distortion in a particular region (e.g. Robinson, UTM, State Plane)
We will discuss these two coordinate reference systems types in more detail in the next lesson.
- Read more on coordinate systems in the QGIS documentation
- The Relationship Between Raster Resolution, Spatial extent & Number of Pixels - in R - NEON
- For more on types of projections, visit ESRI’s ArcGIS reference on projection types.
- Read more about choosing a projection/datum