Map Projections and Georeferencing

Coordinate Systems

A geographical coordinate system uses a three-dimensional spherical surface to define locations on the earth.

Divides space into orderly structure of locations.

Two types: cartesian and angular (spherical)

© Paul Bolstad, GIS Fundamentals

Parallels and Meridians

Meridians are great circles of constant longitude

Example is the prime meridian

latitude (φ): angular distance from equator

longitude (λ): angular distance from standard meridian

St. Louis 38° 39' N 90° 38' W New York 40° 47' N 73° 58' W Los Angeles 34° 3' N 118° 14' W Rome 41° 48' N  12° 36' E Sydney 33° 52' S  151° 12' E

Parallels are circles of constant latitude

Example is the equator

Earth’s Shape

The shape of earth can be approximated as a sphere or spheroid. Most often it is modeled as a spheriod.

a

baflattening

)(

ab

WGS 84 (World Geodetic System of 1984)

a = 6378.137 km

b = 6356.752 km

flattening = 1/ 298.257 = 0.00335

Earth’s Expanding Waistline

From the Chronicle of Higher Education Jan 17, 2003

Datum

While a spheroid approximates the shape of the earth, a datum defines the position of the ellipsoid relative to the center of the Earth

The datum provides a frame of reference for measuring locations on the surface of the Earth

A datum is chosen to align a spheroid to closely fit the Earth’s surface in a particular area

Datums

It is important to ensure that the datum of a dataset matches with the datum setting of your GIS and with other data sets being used.

Map Transformations

From one two-dimensional coordinate system to another

Distance Calculations

Great circle distance is the distance of the arc formed by the plane intersecting the two points and the center of the sphere.

Radius = 6378 km

)cos()cos()cos()sin()sin(cos 2121211 lonlonlatlatlatlatRd

212

212 )( yyxxd

1 2

1 2

The distance between two points on a flat plane can be calculated as the square of the coordinate differences summed.

Map Projections: Flattening the Earth

A map projection

is the orderly transfer of positions of places on the surface of the earth to corresponding points on a flat map.

is the systematic arrangement of the earth’s parallels and meridians onto a plane surface.

uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates.

Ty

x

Distortion

All projections introduce distortions in the map.

Some projections minimize distortions in some of these properties at the expense of maximizing errors in others.

Some projections are attempts to only moderately distort all of these properties.

The map properties that are distorted during projection are:

On Earth On Map

Distance (length)

Angle

Area

Scale

Shape

Projection Types

• Equal area – the ratio of areas on the earth and on the map are constant. Shape, angle, and scale are distorted.

• Conformal – the shape of any small surface of the map is preserved in its original form. If meridians and parallel lines are at 90-degree angles, then angles are also preserved.

• Equidistant - preserve distances between certain points. Scale is not maintained correctly, however, typically one or more lines has its scale maintained.

Three general types of projections:

Conceptualizing Projections

Projections can be conceptualized by the placement of paper on or around a globe.

The “location” of the paper is a factor in defining the projection. The paper can be either tangent or secant.

Azimuthal or Plane Projection

With Azimuthal projections, the spherical (globe) grid is projected onto a flat plane, thus it is also called a plane projection.

Planar projections are used most often for polar regions

Lambert Azimuthal Equal-area

Polar Equatorial

Cylindrical Projections

• Cylindrical projections are typically used to represent the entire world. • Mercator is most common cylindrical projection

• Equator is typically the line of tangency• Meridians are of equal space, lines of latitude increases toward poles• Conformal and displays true direction along straight lines• Transverse projections use meridian lines as tangent point, therefore,

North/South lines are preserved

x = λR y = 2R tan (φ /2)

Conic Projections• Conic Projection - tangent to the globe along a line of latitude

distortion increases away from the standard parallel

• The normal aspect is the north or south pole where the axis of the cone (the point) coincides with the pole.

• Conic projections can only represent one hemisphere, or a portion of one hemisphere, for the cone does not extend far beyond the center of the sphere.

• Conic projections are often used to project areas that have a greater east-west extent than north-south, such as the United States.

• Secant Conic projections have two standard parallels which results in less distortion

Projection Aspects

NormalThe standard aspect for a projection. For Equatorial Cylindrical projections the normal is equatorial. For Azimuthal projections normal is polar.

Transverse The transverse aspect places the projection surface 90 degrees from the normal position, e.g., for a Polar Azimuthal projection the equator would be the transverse aspect, while for an Equatorial Cylindrical projection the poles would be the transverse aspect.

Oblique The oblique aspect of a projection surface is placed above or on any position between, but not including, the equator and the poles. It may be centered on a parallel or on a meridian.

The “Unprojected” Projection

• Assigns latitude to the y axis and longitude to the x axis

– A type of cylindrical projection– Is neither conformal nor equal area– As latitude increases, lines of longitude

are much closer together on the Earth, but are the same distance apart on the projection

Also known as the Plate Carrée or Cylindrical Equidistant Projection or

Geographic Projection

Comparing Projections

Pseudocylindrical Projections

Bonne

Universal Transverse Mercator (UTM)

• Implemented as an internationally standard coordinate system– Initially devised as a military standard

• Uses a system of 60 zones– Maximum distortion is 0.04%

• Transverse Mercator because the cylinder is wrapped around the Poles, not the Equator

Zones are each six degrees of longitude numbered from west to east

Military Grid Coordinate System

The Military grid divides the UTM coordinate system into 6X8 degree cells and subdivides each of those cells with lettering and a number system

State Plane Coordinates

• Defined in the US by each state– Some states use multiple zones– Several different types of projections are used by the system

• Provides less distortion than UTM– Preferred for applications needing very high accuracy, such as surveying

Time Zones

Greenwich Mean Time (GMT)

Each Time Zone is measured relative to Greenwich, England.

St. Louis is GMT -6 (GMT -5 during daylight savings [Apr-Oct])

Non-projected Georeferencing

• Is essential in GIS, since all information must be linked to the Earth’s surface

• The method of georeferencing must be:– Unique, linking information to exactly one location– Shared, so different users understand the meaning of a georeference– Persistent through time, so today’s georeferences are still meaningful tomorrow

• A georeference may be unique only within a defined domain, not globally

• There are many instances of Springfield in the U.S., but only one in any state

• The meaning of a reference to London may depend on context, since there are smaller Londons in several parts of the world

Georeferences as Measurements

• Some georeferences are metric– They define location using measures of distance from fixed places

• E.g., distance from the Equator or from the Greenwich Meridian

• Others are based on ordering– For example street addresses in most parts of the world order houses along

streets

• Others are only nominal– Placenames do not involve ordering or measuring

Converting Georeferences

• GIS applications often require conversion of projections and ellipsoids– These are standard functions in popular GIS packages

• Street addresses must be converted to coordinates for mapping and analysis

– Using geocoding functions

• Placenames can be converted to coordinates using gazetteers

Gazetteers provide information about geographical areas or locations using place names and can be linked to coordinate systems .

Map Projection References

Understanding Map ProjectionsMelita Kennedy and Steve KoppEnvironmental Systems Research Institute, Inc 2000

Introduction to Map Projections (http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj.html#Intro)Peter H. DanaDepartment of GeographyUniversity of Texas at Austin

Map Projections(http://www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html)Carlos A. Furuti Prógonos Consulting

Summary

Projections are needed to represent 3-D surface on a flat plane

There are hundreds of projections – choose the one that fits your mapping purpose best

- preserve distance- preserve shape- preserve direction

Choosing a coordinate system is also important (if you have are mapping a dataset, you should know it’s projection and coordinate system)

Different coordinate systems use different datums in order to approximate the shape of the earth.

Vector data is stored in the database, while raster data is referenced.

A geodatabase has three primary componentsfeature classesfeature datasetsnonspatial tables.

•A feature class is a collection of features that share the same geometry type (point, line, or polygon) and spatial reference.

•A feature dataset is a collection of feature classes. All the feature classes in a feature dataset must have the same spatial reference.

•A nonspatial table contains attribute data that can be associated with feature classes.

ArcGIS Geodatabases

All three components are created and managed in ArcCatalog.

Relational Database Example #1

Data Needed this Week

• Folders:• GIStutorial\MaricopaCounty • Gistutorial\RochesterNY• Gistutorial\World • Gistutorial\AlleghenyCounty

• Files:• Tutorial4-2.mxd