Geographic Coordinate Systems
A GCS uses a sphere to locate you on Earth’s surface.1 YES, I know, the Earth is not a sphere, but more of a potato… we’ll get to that.
2 Viz taken from this amazing reference.
Have you ever wondered why longitude and latutide are measured in degrees? This is why! Your location on the globe is described using the angle at which we can find your location relative to midway between the poles (that’s the equator y’all) and a fairly arbitrary (Euro-centric?) prime meridian.3 The prime meridian was established in 1884 at the International Meridian Conference in DC, one of the coolest conferences ever held. The intersection of the equator and the prime merdian form coordinates (0,0)`in our GCS. Latitude ranges from -90 degrees at the South Pole to 90 degrees chez Santa Claus. This should make sense if you look at the figure above. Longitude runs from 180 degrees when heading east of the prime meridian and -180 degrees when traveling west. This leaves parts of Fiji and the Chukotka Autonomous Okrug with some confusing coordinates.
There are many different GCS, each defined by the way we think of Earth’s shape. Some GCS project latitude and longitude onto a sphere, others a spheroid. They are also defined by the way we think of the (0,0) point in the middle of the earth. A datum defines the position of our abstract Earth in sphere or spheroid form relative to the center of the Earth. The following is the best visualization I’ve found of this, also taken from this amazing reference:
What’s important to understand here is that while lat and lon make it easy to locate exact positions on our planet’s surface, they are NOT UNIFORM, repeat NOT UNIFORM. Look at the globe… as latidude moves north, the regions defined by each grid cell become smaller. Take home? Don’t measure distances or areas using latitude and/or longitude. Let’s move on to something that will let do just that…
Projected Coordinate Systems
PCS, unlike GCS, are defined on a two dimensional surface, i.e. lengths, angles, and areas are constant across these two dimensions. PCS are generally tailored to the pecularities of specific regions. This is a way of addressing Eath’s lumpiness and non-spherical distortions. To translate a 3D shape onto a 2D surface, we use map projections. Imagine a light shining through Earth onto a 2D surface, as shown below. Yet again, the amazing reference I recommend you go read illustrates this very well. One of the most important things you can remember about map projections is that any time you transform a 3D object into a 2D object, you will distort shape, area, and representation of the 3D object. Map projections, therefore, are not neutral. The projection you choose to use reflects choices about the over/under representation regions. For example, conformal projections preserve local shape at the expense of distorting larger regions. Equal area projections preserve the area of shapes displayed at the expense of angle and scale. Equidistant projections preserve distance between points but distorts scale.
Projection in R
You can determine the projection of any sf object by calling the st_crs() function:
library(sf)
states <- st_read("./data/states.shp")## Reading layer `states' from data source `C:\Users\eburchf\OneDrive - Emory University\Teaching\ENVS 270 Environmental Data Science\03_ESDA\data\states.shp' using driver `ESRI Shapefile'
## Simple feature collection with 51 features and 5 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: -178.2176 ymin: 18.92179 xmax: -66.96927 ymax: 71.40624
## geographic CRS: NAD83plot(st_geometry(states))
st_crs(states)## Coordinate Reference System:
## User input: NAD83
## wkt:
## GEOGCRS["NAD83",
## DATUM["North American Datum 1983",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["latitude",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["longitude",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",4269]]This string contains all of the information needed to describe the projection of this data. This shapefile is projected in a Geographic Coordinate System (i.e. using latitude and longitude to describe location). Really, we can think of this dataset as unprojected since it’s being displayed using a GCS. Our datum is NAD83, or the North American Datum of 1983, a commonly used reference for the US. We’re using the Geodetic Reference System 1980 as our model of Earth’s shape and indicating this by ELLIPSOID["GRS80.... This also contains the EPSG which is a reference number for this projection.This comes from the European Petroleum Survey Group (now Oil and Gas Producers), who, starting in the 1980s, began collecting and standardizing geodetic parameters to help normalize projection. Yes, big gas and oil even influences projections. You can also just use the EPSG code to build your projection information in the case of unprojected data. The full list of EPSG entries can be found here. www.spatialreference.org is another great reference.