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

GIS Data Models, Coordinate Systems and Projections

September 16, 2009, Joseph Ferreira, Jr.

(including 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 regarding lab exercises and schedule

Outline of Today

'Vector' data models for geospatial location

Raster vs. vector data models

Inflation-Adjusted 1989 Cambridge, MA Housing Sales Prices   
Boston/Cambridge Streets superimposed on orthophoto.  Zoomed-in view shows raster nature of the ortho.

Map elements and thematic mapping:
symbology, classification, and normalization

 

Elements of the Map

Scale

Ratio Scales

1:10,000, or 1:100,000 or 1/100,000

Verbal Scales:

     One inch represents 2,000 feet (1:24,000).

     One centimeter represents 20 kilometers (1:2,000,000)

Printout vs. onscreen:

10 foot pixel + 72 pixels per inch onscreen

==> One inch represents 720 feet (1:8,600) -

But some screens have higher/lower pixel densities; not all screens have square pixels; also, screendump to printer will change scale since printer will have different dot-density than the screen

Beware! Good GIS software will try to match screen and printer properties to software settings so screen and printouts will show appropriate scale and show correct scalebars. For the scale to be meaningful, display units and hardware choices must be properly identified.

Large Scale or Small Scale

In general,

         Large scale: >= 1:24,000 (good for *small* area representation - city block)

         Small scale: <= 1:500,000 (good for *large* area representation - metro area)

But scale is relative, depends on the applications

          Large-scale maps are more detailed than small-scale maps

Feature representations at a given scale are product of practical
limits (what can be seen/drawn) and conscious policiesarge-scale maps are more detailed than small-scale maps

          Important concept: “Minimum Mapping Unit" (MMU)

 

Typical Scales Used

In Metric System:

1:10,000 (example: German national basemaps – individual houses shown) 1:25,000 ... 1:100,000 - try changing scale in ArcMap (if coordinate system is known)

In American System:

1:9,600 (one inch represents 800 feet)

1:24,000 (one inch represents 2000 feet) – typical USGS “quad sheet”

1:62,500 (one inch represents (slightly less than) one mile)

 

Key Cartographic Principals

Maps are a medium of communication

              So…know your audience

              Or if you don’t/can’t, use the “10 foot rule”

                     Can an average citizen read & comprehend E sized plot at 10’

                     Or a page print at 8.5x11” – font size at least 12 point

A good map should never be a “GIS Data Dump”

Selective emphasis is key

The hard part is removing data, when in doubt - delete

 

Divide mapped elements into “figure / ground”

       Figure = Foreground elements – the essential story of the map

       Ground = Background elements – provide context, but don’t overwhelm

 

 

Use visual variable (below) to emphasize foreground, minimize clutter background


Colors and Categories

Human cognitive limit / rule of thumb:

Try to limit the number of thematic colors

  • If not possible, try creating logical visual subgroups
    • example: housing in 3 shades of orange, commercial 3 shades of red, etc.
  • Hard to distinguish more than 3-4 tones within same hue
    • Even harder when your map is reproduced in grayscale…

ArcGIS color defaults are *random* saturated colors

  • Tip #1: desaturate colors, especially background colors or those covering large areas of the map
  • Tip #2: reserve bright, saturated colors either for foreground elements, or small polygons
  • Tip #3: turn *off* the outline of polygons, particularly for background polygons or small polygons

Six Principal Visual Variables

Use contrasting symbols to portray geographic differences

For qualitative differences

Use shape, texture and hue (e.g., land use types).

For quantitative differences

Use size to show variation in amount or count
(e.g., population, number of crimes),

Use graytone or hue to show differences in ratio or intensity
(e.g., proportion of household in poverty, population density).

 

Southern New England Counties

Southern New England Counties

Projections

Datums & 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

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 the property, 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 project 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 Spatial Reference Systems

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

Database tools in ArcGIS (Labs #2 and #3 use ArcGIS database tools)

Last modified 16 September 2009 [jf]

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