Lesson 4. GIS With R: Projected vs Geographic Coordinate Reference Systems


This lesson briefly discusses the key differences between projected vs. geographic coordinate reference systems.

Learning Objectives

After completing this tutorial, you will be able to:

  • List 2-3 fundamental differences between a geographic and a projected CRS
  • Describe the elements of each zone within a Universal Trans Mercator (UTM) CRS and a Geographic (WGS84) CRS

What You Need

You will need a computer with internet access to complete this lesson and the data for week 4 of the course.

Download Week 4 Data (~500 MB)

Geographic vs Projected CRS

In the previous tutorial, we explored the basic concept of a coordinate reference system. During the lesson we looked at two different types of Coordinate Reference 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 this tutorial, we will discuss the differences between these CRS’s in more detail.

As we discussed in the previous lesson, each CRS is optimized to best represent the:

  • shape and/or
  • scale / distance and/or
  • area

of features in a dataset. There is not a single CRS that does a great job 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 CRS’s are also optimized for particular regions, for instance the United States, or Europe.

Intro to Geographic Coordinate Reference Systems

Geographic coordinate systems (which are often but not always in decimal degree units) are often optimal when we need to locate places on the Earth. Or when we need to create global maps. 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.

Graphic showing lat long as it's placed over the globe by ESRI.
A geographic coordinate system locates latitude and longitude location using angles. Thus the spacing of each line of latitude moving north and south is not uniform. Source: ESRI

The Structure of a Geographic CRS

A geographic CRS uses a grid that wraps around the entire globe. This means that each point on the globe is defined using the SAME coordinate system and the same units as defined within that particular geographic CRS. Geographic coordinate reference systems are best for global analysis however it is important to remember that distance is distorted using a geographic lat / long CRS.

The geographic WGS84 lat/long CRS has an origin - (0,0) - located at the intersection of the Equator (0° latitude) and Prime Meridian (0° longitude) on the globe.

Let’s remind ourselves what data projects in a geographic CRS look like.

library(ggplot2)
library(rgdal)
library(raster)

wgs 84 plot

Data Note: The distance between the 2 degrees of longitude at the equator (0°) is ~ 69 miles. The distance between 2 degrees of longitude at 40°N (or S) is only 53 miles. This difference in actual distance relative to “distance” between the actual parallels and meridians demonstrates how distance calculations will be less accurate when using geographic CRS’s

Projected Coordinate Reference Systems

As we learned above, geographic coordinate systems are ideal for creating global maps. However, they are prone to error when quantifying distance. In contrast, various spatial projections have evolved that can be used to more accurately capture distance, shape and/or area.

What is a Spatial Projection

Spatial projection refers to the mathematical calculations performed to flatten the 3D data onto a 2D plane (our computer screen or a paper map). Projecting data from a round surface onto a flat surface results in visual modifications to the data when plotted on a map. Some areas are stretched and some some are compressed. We can see this distortion when we look at a map of the entire globe.

The mathematical calculations used in spatial projections are designed to optimize the relative size and shape of a particular region on the globe.

projection surfaces graphic
The 3-dimensional globe must be transformed to create a flat 2-dimensional map. How that transformation or projection occurs changes the appearance of the final map and the relative size of objects in different parts of the map. Source: CA Furuti, progonos.com/furuti

About UTM

The Universal Transverse Mercator (UTM) system is a commonly used projected coordinate reference system. UTM subdivides the globe into zones, numbered 0-60 (equivalent to longitude) and regions (north and south).

Data Note: UTM zones are also defined using bands, lettered C-X (equivalent to latitude) however, the band designation is often dropped as it isn’t essential to specifying the location.

While UTM zones span the entire globe, UTM uses a regional projection and associated coordinate system. The coordinate system grid for each zone is projected individually using the Mercator projection.

The origin (0,0) for each UTM zone and associated region is located at the intersection of the equator and a location, 500,000 meters east of the central meridian of each zone. The origin location is placed outside of the boundary of the UTM zone, to avoid negative Easting numbers.

utm zone characteristics
The 0,0 origin of each UTM zone is located in the Bottom left hand corner (south west) of the zone - exactly 500,000 m EAST from the central meridian of the zone. Source: Penn State E-education

Nasa image showing the UTM x and y zones
The gridded UTM coordinate system across the globe. Source: NASA Earth Observatory
The UTM zones across the continental United States. Source: Chrismurf, wikimedia.org.
UTM zones across the continental United States. Source: Chrismurf, wikimedia.org.

Understand UTM Coordinates

Let’s compare coordinates for one location, but saved in two different CRS’s to better understand what this looks like. The coordinates for Boulder, Colorado in UTM are:

UTM Zone 13N easting: 476,911.31m, northing: 4,429,455.35

Remember that N denotes that it is in the Northern hemisphere on the Earth.

Let’s plot this coordinate on a map.

# create a data.frame with the x,y location
boulder_df <- data.frame(lon=c(476911.31),
                lat=c(4429455.35))

# plot boulder
ggplot() +
                geom_point(data=boulder_df,
                aes(x=lon, y=lat, group=NULL), colour = "springgreen",
                      size=5)

Plot location - wgs84

# convert to spatial points
coordinates(boulder_df) <- 1:2

class(boulder_df)
## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"
crs(boulder_df)
## CRS arguments: NA

# assign crs - we know it is utm zone 13N
crs(boulder_df) <- CRS("+init=epsg:2957")

Note what the projection string for our data in UTM looks like: +init=epsg:2957 +proj=utm +zone=13 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs

If we spatially project our data into a geographic coordinate reference system, notice how our new coordinates are different - yet they still represent the same location.

boulder_df_geog <- spTransform(boulder_df, crs(worldBound))
coordinates(boulder_df_geog)
##         lon   lat
## [1,] -105.3 40.01

Now we can plot our data on top of our world map which is also in a geographic CRS.

boulder_df_geog <- as.data.frame(coordinates(boulder_df_geog))
# 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")

# map boulder
worldMap +
        geom_point(data=boulder_df_geog,
        aes(x=lon, y=lat, group=NULL), colour = "springgreen", size=5)

global map in wgs84 with points

Important

While sometimes UTM zones in the north vs south are specified using N and S respectively (e.g. UTM Zone 18N) other times you may see a letter as follows: Zone 18T, 730782m Easting, 4712631m Northing vs UTM Zone 18N, 730782m, 4712631m.

Data Tip: The UTM system doesn’t apply to polar regions (>80°N or S). Universal Polar Stereographic (UPS) coordinate system is used in these area. This is where zones A, B and Y, Z are used if you were wondering why they weren’t in the UTM lettering system.

Optional Challenge

The Penn State e-Education Institute has a nice interactive tool that you can use to explore UTM coordinate reference systems.

View UTM Interactive tool Note: You will need Adobe Flash Player to use this tool.

Datum

The datum describes the vertical and horizontal reference point of the coordinate system. The vertical datum describes the relationship between a specific ellipsoid (the top of the earth’s surface) and the center of the earth. The datum also describes the origin (0,0) of a coordinate system.

Frequently encountered datums:

  • WGS84 – World Geodetic System (created in) 1984. The origin is the center of the Earth.
  • NAD27 & NAD83 – North American Datum 1927 and 1983, respectively. The origin for NAD 27 is Meades Ranch in Kansas.
  • ED50 – European Datum 1950

NOTE: All coordinate reference systems have a vertical and horizontal datum which defines a “0, 0” reference point. There are two models used to define the datum: ellipsoid (or spheroid): a mathematically representation of the shape of the earth. Visit Wikipedia’s article on the earth ellipsoid for more information and geoid: a model of the Earth’s gravitatinal field which approximates the mean sea level across the entire Earth. It is from this that elevation is measured. Visit Wikipedia’s geoid article for more information. We will not cover these concepts in this tutorial.

Coordinate Reference System Formats

There are numerous formats that are used to document a CRS. In the next tutorial we will discuss three of the commonly encountered formats including: Proj4, WKT (Well Known Text) and EPSG.

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