Massachusetts Institute of Technology
Department of Urban Studies and Planning

11.520: A Workshop on Geographic Information Systems

11.188: Urban Planning and Social Science Laboratory

Lecture 3: Map Projections and Coordinate Systems

October 6, 2010, Prof. Joseph Ferreira

(based on notes by Prof. Mike Flaxman and former Visting Prof. Zhong-Rhen Peng
with contributions from Prof. Peter Dana's (U. of Colorado) web pages)

Administrative notes:

  • Homework #1 is now due on Wednesday, Oct. 13 (instead of today)
  • Lab Exercise #5 due Monday, Oct. 18 (next Monday is a holiday)
  • Recitations this week: (MS-Access queries and ArcMap usage; file management strategies; your questions)
    • Wed. 4-5 pm (primarily for undergrads) in Room 2-131 *TODAY*
    • Thurs. 2-3 pm (primarily for MCP1s) in Room 9-450A
    • Fri. 9:30 - 10:30 am (primarily for MCP2s and all others) in Room 9-450A
    • Recitation notes: Recitation 2

Today's Topics:

  • Datums, Map Projections, and Coordinate Systems
    • Basic concepts and links to detailed discussion
    • Coordinate systems and projections in ArcGIS and Google Earth
  • Examples of GIS mapping and spatial analysis
    • MBTA 'heat maps' of transit ridership
    • MassGIS: http://www.mass.gov/mgis/
      • MassGIS presentations: http://www.mass.gov/mgis/mgispres.htmap
    • Metro Boston data commons: http://www.metrobostondatacommon.org/
      • Town summaries: http://www.metrobostondatacommon.org/html/gallery.htm#1-06
    • A recent PhD thesis: Mi Diao, Sustainable Metropolitan Growth Strategies: Exploring the Role of the Built Environment
      • See maps of vehicle miles travelled and neighborhood characteristics in metro Boston (by 2550x250m grid cells)

     

Datums, Map Projections, & Coordinate Systems

      What is the minimum information needed to precisely determine
      location on the surface of the planet?

Need *both* a known coordinate system
and a known model of the earth’s surface

If you only know one, you can be hundreds of meters off target

      -literally

An Ellipsoid or a Datum are abstractions of the surface of the earth

WG84 (the World Geodetic System of 1984) is a standard ellipsoid.

In North America, the most recent ellipsoid data it is called the North American Datum of 1983 (NAD83) (the earlier version is NAD27).

Difference between measurements between NAD27 & NAD83 vary by location
but commonly 10 – 100 ft

 

Geographic Reference System: Latitude and Longitude

Axis: the center of earth rotation.

Equator: The plane through the center of mass perpendicular to the axis.

Longitude: lines slicing the earth parallel to the axis, and perpendicular to the plane of equator.

The line goes through Greenwich has 0 longitude.

Range from 0 to 360 degrees, or 180 degree west (-) to 180 degree east (+).

Latitude

Latitude is defined based on ellipsoid representing the shape of the earth.

See: Prof. Peter Dana's notes on projections and coordinate systems (U. of Colorado) http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html

<Click the images below to enlarge...>

 

 

Latitude definition:

A line drawn through a point of interest perpendicular to the ellipsoid at that location, the angle made by this line with the plane of Equator is the latitude of that point.

Ranges from 90 degree south (-) to 90 degree north (+).

 

What do Latitude and Longitude mean?

Two points on the same longitude, separated by one degree of latitude are 1/360 of the circumference of earth apart, or about 111 km apart.

One minute latitude is 1.86 km.

One second latitude is 30 m.

For the same latitude, one minute of longitude separation corresponds to different distances depending on the latitude (111 km at equator, nothing at the poles!).

Nowadays, latitude/longitude often expressed in decimal degrees.

Distance calculation using latitude and longitude

n       Latitude -90≤Ø≤90

n       Longitude -180≤λ≤180

n       Arc distance between two points on the earth surface (spherical):

n        Rcos-1[sinØ1sinØ2+cosØ1cosØ2cos(λ1-λ2)]

n        R is the radius of the spherical earth

 

Cartesian Coordinate System

n       Assign two coordinates to every point on a flat surface.

Map Projections

n       Map projections transform the curved, 3-D surface of the planet into a flat, 2-D plane. Note, that Map projections distort map scale in various ways

n       Transform a position on the Earth’s surface identified by latitude and longitude (Ø, λ) into a position in Cartesian coordinates (x, y).

n        x = f (Ø, λ)

n        Y = g (Ø, λ)

n       Map projections necessarily distort the Earth and the map scale.


Example using Prof. Peter Dana's notes (U. of Colorado)
http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj.html

Example using ArcMap

  • ESRI sample data map of 50 US states
  • Convert to Mass state plane and compare results

Map Projection Classifications based on preservation properties

n       The conformal property, preserves the shapes of small features on the Earth’s surface (directions). This is useful for navigation. E.g., Mercator projection and Gnomonic projection.

n       The equal area property, preserves the areas. This is useful for analysis involving areas like the size of a land parcel, e.g., Goode’s projection.

n       Any projection can have either conformal property or equal area property, but not both.

 

Map Projection classifications based on physical surface models

n       Cylindrical projections -- wrapping a cylinder of paper around the Earth, projecting the Earth’s features onto it, and then unwrapping the cylinder;

n       Azimuthal or planar projections -- touching the Earth with a sheet of flat paper;

n       Conic projection -- wrapping a sheet of paper around the Earth in a cone.

n       All three types can have either conformal property or equal area property, but not both.

 

Unprojected projection: Plate Carrée or Cylindrical equidistance Projection

n       Just maps longitude as x and latitude as y.

n       Heavily distorts image of the Earth.

n       It does not have either conformal or equal area property.

n       But it maintains the correct distance between every point and the Equator.

n       Serious problems (distorted area, direction and other properties) can occur when doing analysis using this projection.

 

The Universal Transverse Mercator (UTM) Projection

n       Projected by wrapping a cylinder around the Poles, rather than around the Equator.

n       There are 60 zones. Each zone is 6 degree wide and wrapped along a particular line of longitude.

n       The projection is conformal, the scale is the same in all directions.

n       UTM coordinates are in meters, making it easy to make accurate calculations of short distances between points.

n       UTM projections have more problems at high latitudes.

 

State Plane Coordinates and other local systems

n       UTM is still not accurate enough for small area surveying.

n       During 1930s, each US state adopt its own projection and coordinate system, generally known as State Plane Coordinates (SPC).

n       Each state chose its own projection based on its shape to minimize distortion over the area of the state.

n       Some states have more than one internal zone.

n       The North American Datum 1983 (NAD83) is commonly used for SPC.

 

Converting Georeferences

n       Two datasets can differ in both the projection and the datum, so it is important to know both for every dataset (and the data can be expressed in feet or meters with different origins!)

n       Use coordinate conversion to combine datasets that use different systems of georeferencing. Keep in mind, changing projections means the system must convert projected coordinates back to lat/lon (geographic) and then re-project into another projection/datum.

n       Convert into projections that have desirable properties, e.g., no distortion of area, for analysis.

More info on Coordinate systems and projections

Review of Layer & Database tools in ArcGIS (& new look at 'field calculate' choices)

  • Examine ArcMap menus and dialog boxes regarding attribute table manipulation
  • Layer Properties:
    • Fields (visibility and formatting)
    • Definition Query (What to include in data frame; SQL query builder)
  • Selection (from main menu)
    • select by attributes
    • select by location
  • Selection (from attribute viewing table)
    • Options...
    • Add field
    • Show all/selected
  • Adding new fields
    • read-only issues - can't change read-only table
    • Data types & field calculation options (area, geometry,...)
    • export original as DBF table (or shapefile)
    • Add saved table and edit
    • Join edited table to original shapefile

Examples of GIS mapping and spatial analysis

 


Last modified 6 October 2010 by Joe Ferreira

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