Geographic vs Projected CRS

On the previous page, you explored the basic concept of a coordinate reference system. You 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)

On this page, you will learn about the differences between these CRSs in more detail.

As you 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 CRSs 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 you need to locate places on the Earth. Or when you need to create global maps. 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.

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.

You will review what data projected in a geographic CRS look like.

import os
from glob import glob
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.ticker import ScalarFormatter
import geopandas as gpd
from shapely.geometry import Point
import earthpy as et
import seaborn as sns

# Adjust plot font sizes
sns.set(font_scale=1.5)
sns.set_style("white")

# Set working dir & get data
data = et.data.get_data('spatial-vector-lidar')
os.chdir(os.path.join(et.io.HOME, 'earth-analytics'))

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 CRSs

Projected Coordinate Reference Systems

As you 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 (your 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 are compressed. You can see this distortion when you 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.

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.

Understand UTM Coordinates

Compare coordinates for one location, but saved in two different CRSs 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.

Plot this coordinate on a map.

boulder_df = np.array([[476911.31,  4429455.35]])
geometry = [Point(xy) for xy in boulder_df]

boulder_loc = gpd.GeoDataFrame(geometry,
                               columns=['geometry'],
                               crs={'init': 'epsg:2957'})

/opt/conda/lib/python3.8/site-packages/pyproj/crs/crs.py:53: FutureWarning: '+init=<authority>:<code>' syntax is deprecated. '<authority>:<code>' is the preferred initialization method. When making the change, be mindful of axis order changes: https://pyproj4.github.io/pyproj/stable/gotchas.html#axis-order-changes-in-proj-6
  return _prepare_from_string(" ".join(pjargs))

fig, ax = plt.subplots(figsize=(10, 10))
boulder_loc.plot(ax=ax)
ax.set_title("Plot of Boulder, CO Location")

# Turn off scientific notation
plt.ticklabel_format(useOffset=False)
plt.show()

# View crs
boulder_loc.crs

<Projected CRS: EPSG:2957>
Name: NAD83(CSRS) / UTM zone 13N
Axis Info [cartesian]:
- E[east]: Easting (metre)
- N[north]: Northing (metre)
Area of Use:
- name: Canada - 108°W to 102°W
- bounds: (-108.0, 48.99, -102.0, 84.0)
Coordinate Operation:
- name: UTM zone 13N
- method: Transverse Mercator
Datum: NAD83 Canadian Spatial Reference System
- Ellipsoid: GRS 1980
- Prime Meridian: Greenwich

Note the projection of your data in UTM is EPSG code 2957

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

# Reproject the data to WGS84
boulder_df_geog = boulder_loc.to_crs(epsg=4326)
boulder_df_geog.crs

<Geographic 2D CRS: EPSG:4326>
Name: WGS 84
Axis Info [ellipsoidal]:
- Lat[north]: Geodetic latitude (degree)
- Lon[east]: Geodetic longitude (degree)
Area of Use:
- name: World
- bounds: (-180.0, -90.0, 180.0, 90.0)
Datum: World Geodetic System 1984
- Ellipsoid: WGS 84
- Prime Meridian: Greenwich

# View the coordinate values of the newly reprojected data.
boulder_df_geog

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

fig, ax = plt.subplots(figsize=(10, 5))

worldBound.plot(cmap='Greys',
                ax=ax)

ax.set(title="World map with Boulder, CO location \n Geographic WGS84 CRS",
       xlabel="X Coordinates (Decimal Degrees)",
       ylabel="Y Coordinates (Decimal Degrees)")

boulder_df_geog.plot(ax=ax,
                     markersize=52,
                     color='springgreen')
plt.show()

Important Tips

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.

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. You 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 you will discuss three of the commonly encountered formats including: Proj4, WKT (Well Known Text) and EPSG.