Outline

 

  1. Measuring the Earth

  2. Cartography and Map Overlays

Measuring the Earth

 

 

Where are we?

  • latitude: 38.90894,
  • longitude: -77.07458

but what does that mean?

 

  1. Latitude (vertical coordinate)

    • \(\phi\) (“phi”): angle between equator & straight line from center of Earth to location
    • positive in Northern hemisphere
    • negative in Southern hemisphere

  2. Longitude (horizontal coordinate)

    • \(\lambda\) (“lambda”): angle between Prime Meridian & straight line from center of Earth to location
    • positive east of Prime Meridian
    • negative west of Prime Meridian


\(\phi=\) lat, \(\lambda=\) lon

Prime Meridian

The Shape of Earth

What is the shape of the earth?

Wrong!


Wrong!


 

 

 

Also wrong?

 

 

 

  1. Geoid
    1. surface of equal gravitational potential (\(\sim\) mean sea level)
    2. measured, interpolated surface


Geoid

 

 

 

  1. Ellipsoid
    1. ellipsoidal model that is best fit to Earth’s shape
    2. ellipsoid \(=\) ellipse rotated around its short axis


Ellipsoid

 

 

 

  1. Topography
    1. Earth’s height, relative to mean sea level
    2. measured with satellite or aerial photography


Topography vs. Geoid vs. Ellipsoid

 

 

Geodetic datum

  • coordinate system that references ellipsoid to geoid
  • examples:
ellipsoid datum
WGS 1984 NAD 1983
Clarke 1866 NAD 1927
  • translates positions on maps to real positions on Earth


Geodetic survey marker

 

 

World Geodetic System 1984

  • international standard for GPS, satellite navigation systems
  • developed by DoD, international network of scientists
  • refinement of GRS 80 reference ellipsoid
  • associated with North American Datum 1983 (NAD 1983)
  • radius at Equator \(=\) 6378.14 km
  • default in most GIS


 

 

 

WGS 84

Projections and Coordinate Systems

 

 

How to squeeze 3 dimensions into 2?

 

What are projections?

  • transformations from Earth’s 3D surface to 2D plane

 

  1. Cylindrical projection

    • “wrap cylinder around Equator”
    • more distortion near poles

  2. Conic projection

    • “put cone on top of Earth”
    • latitudes as arcs, longitude as straight lines

  3. Azimuthal projection

    • “put flat plane on top of Earth”
    • projection outward from single central point


 

Azimuth, cone, cylinder

 

 

  1. “Unprojected” projection

    • raw geographic coordinates
    • latitude \(\to\) vertical axis
    • longitude \(\to\) horizontal axis
    • effectively a cylindrical projection
    • less distortion near Equator
    • more distortion near poles


 

No free lunch

 

Distortion

  • all projections distort Earth
  • area, distance, direction, shape

 

  1. Conformal/conic projections
    (e.g. Lambert Conformal Conic)

    • preserves angles, shapes
    • distorts area

  2. Equal area projections
    (e.g. Albers Conic Equal Area)

    • preserves area
    • distorts angles, shapes

  3. Azimuthal projections
    (e.g. Azimuthal Equidistant)

    • preserves direction, distance
    • distorts shapes


 

Funhouse mirrors

Common coordinate systems

 

  1. Universal Transverse Mercator (UTM)

    • global system of 60 zones
    • cylindrical projection


 

UTM

 

 

 

  1. Military Grid Reference System (MGRS)

    • derived from UTM, with different labeling convention
    • NATO military standard


 

MGRS

 

 

 

  1. State Plane Coordinate Systems

    • defined separately for each U.S. state
    • high local accuracy


 

 

SPRS

In QGIS, your map’s projection information is found in the lower-right corner
(EPSG \(=\) European Petroleum Survey Group code)

  • EPSG:4326 is the code for World Geodetic System (WGS84)
  • this is the default in QGIS, and a standard for satellite navigation systems

Click on the EPSG code to open CRS Properties (Coordinate Reference System)

Let’s change the CRS to Mercator (e.g. EPSG:900913, EPSG:3785). Click OK.

Greenland should now appear larger than the entire continent of Africa…

Let’s change the CRS to Equal Area (EPSG:54034, EPSG:5070).

Greenland shrinks. Overcorrection or no?

Let’s change the CRS to World Azimuthal Equidistant (EPSG:54032).

Now it looks more like a globe than a map… but better for studying the Arctic.

Here’s how to check and change projections in R.

 

Suppose we have 2 sf objects: world (world map) and grat (graticules).

world = sf::read_sf("Data/World/ne_110m_admin_0_countries.geojson")
grat = sf::read_sf("Data/World/ne_50m_graticules_10.geojson")

We can check their CRS with st_crs() from the sf library.

sf::st_crs(world)
## Coordinate Reference System:
##   User input: WGS 84 
##   wkt:
## GEOGCRS["WGS 84",
##     DATUM["World Geodetic System 1984",
##         ELLIPSOID["WGS 84",6378137,298.257223563,
##             LENGTHUNIT["metre",1]]],
##     PRIMEM["Greenwich",0,
##         ANGLEUNIT["degree",0.0174532925199433]],
##     CS[ellipsoidal,2],
##         AXIS["geodetic latitude (Lat)",north,
##             ORDER[1],
##             ANGLEUNIT["degree",0.0174532925199433]],
##         AXIS["geodetic longitude (Lon)",east,
##             ORDER[2],
##             ANGLEUNIT["degree",0.0174532925199433]],
##     ID["EPSG",4326]]

Here’s how these datasets look unprojected (WGS 84).

plot(world["geometry"],reset=FALSE)
plot(grat["geometry"],add=TRUE)


 

We can change projections with the st_transform() function (sf library).

 

Let’s transform to Mercator projection (e.g. EPSG:3785), and plot the result.

world_ = sf::st_transform(world, crs="EPSG:3785")
grat_ = sf::st_transform(grat, crs="EPSG:3785")
plot(world_["geometry"],reset=FALSE)
plot(grat_["geometry"],add=TRUE)

 


 

Let’s transform to Equal Area projection (e.g. EPSG:5070).

world_ = sf::st_transform(world, crs="EPSG:5070")
grat_ = sf::st_transform(grat, crs="EPSG:5070")
plot(world_["geometry"],reset=FALSE)
plot(grat_["geometry"],add=TRUE)


 

Let’s transform to Azimuthal Equidistant projection (e.g. ESRI:54032).

world_ = sf::st_transform(world, crs="ESRI:54032")
grat_ = sf::st_transform(grat, crs="ESRI:54032")
plot(world_["geometry"],reset=FALSE)
plot(grat_["geometry"],add=TRUE)

 


 

You can look up a projection’s EPSG code here: spatialreference.org

Cartography and Map Overlays

Overlays

 

 

 

What is an overlay?

  • combination of multiple layers of spatial data
  • each layer represent some set of features of the real world
    (e.g. elevation, roads, violence)
  • when superimposed on top of each other, layers can reveal patterns and relationships between variables
    (e.g. are mountainous areas more violent?)
  • all layers must be on a common projection!


Multiple layers

This week’s lab will be focused on map overlays

Last week: Single-layer map


 

 

 

This week: Multi-layer map

What Makes a Good Map?

AOR’s of U.S. Combatant Commands

A good map should clearly communicate information.

Vignelli’s 1972 NYC Subway Map

A good map should direct attention toward information of primary interest.

(Bad) Map of Mendocino Complex Fire

A good map should be not too complex (especially if audience is general public).

Complementary colors


 

 

Map with complementary colors

A good map should use contrasting colors/shades (e.g. complementary colors).

Primary uses of maps

  1. Reference map
    (general information)

 

Interstate highways around NYC


  1. Thematic map
    (focuses on specific theme/subject)

 

2016 presidential elections in NYC