Coordinate Systems, Projections & Introduction to Choropleth Maps

May 17, 2007

Refer to: Krygier & Wood, pages 92-119

Monmonier, pages 5-18

First: Rapid Review - Concepts

Labs 1 & 3: Illustrator● Pen Tool - Generalize● Closed Path Shapes● Fill, Stroke (simple)● Gradient Fill● Layers● Advanced Methods *

ArcMap Layout

Element placement●Map Layout

– Neatline– Title/Subtitle– North Arrow– Scale *– Legend

Comments from last week

● Type use: In cartography, using decorative type is not desirable.– Distracts from features of importance– Difficult to read

● Legend– May or may not have a title, frame, may include

useful information for understanding the map● Feature symbology

– Adopt consistent conventions

LEGEND Label

Measuring the Earth

Around 2300 BPEratosthenes' Map

??

Estimate – 40,500 km (25,170 mi)

Actual – 40,075 km (24,960 mi)

Erotosthenes' Calculation

Angle calcon summersolstice, noon

Not bad....there is of course dispute:

1. Disagreement on units (500 mi is itself an estimate for stadia, the unit he used)

2. Syene (Cyene) is not exactly on the same meridian as Alexandira

3. Although measured on the solstice, the sun's rays were not exactly parallel because Syene is not on the northern Tropical latitude.

Historically significant best guess...

Eratosthenes' Calculation

The first acknowledged study in geodesy:the determination of the figure and dimensions of the earth

Eratosthenes also did not realize that the Earth is NOT a perfect sphere. Until the 1600's this assumption was not in question (Newton, centrifugal forces).

A dispute ensued (Newton vs Decartes), and after two major expeditions (Lapland, Ecuador) and nine years, it was proven to be an oblate spheroid, bulging at the equatorial region.

Read: Whitaker, R., (2004). The Mapmaker's Wife

Geodesy & The Reference Ellipsoid

● The oblate spheroid has a semimajor (a) and semiminor axis (b)

● The idea of an ellipsoid describes the shape and size of the Earth

● Over 30 ellipsoids exist, depending where on Earth

But what ARE they?

They are local measurements

The ellipsoids you will encounter in the GIS world, most likely are:

WGS 84, GRS 1980 and Clark 1866

Somewhat abstract

● The « Geoid » is a concept that has emerged after the advent of satellite technologies (post 1950's)

● The Earth's surface varies – determine using spherical harmonics

Geoid

Geodetic Datums (or Data)

● A reference point from which measurements are made. Determined by a coincident point between geoid and reference ellipsoid

● Example: Clarke 1866 with single point in Kansas as reference comprises the NAD 27 (North American Datum of 1927 )

The Bottom Line

● These are nice things to know, but what is actually relevant or important to GIS?

● Satellite technology found that NAD 27 is quite erroneous, so a new reference ellipsoid, GRS 80 (Geodetic Reference System of 1980), was created

● Using that ellipsoid, NAD 83 was implemented.

And?

● These differences are often visually negligible in terms of thematic mapping

● Geodesy is more important to navigation, distance and directional applications

● However, these terms will come up repeatedly as you enter GIS positions and it is important to know from where they came and what they mean (generally)

Tired?

BREAKBe back in 5 minutes

DEFINITIONa: systematic presentation ofintersecting coordinate lines on aflat surface upon which featuresfrom the curved surface of the

earthor the celestial sphere may bemapped b: the process ortechnique of reproducing a spatialobject upon a plane or curvedsurface or a line by projecting itspoints; also a graph or figure soformed….

In other words…transformation of a curved surface to a flat one.

Definition: Map Projection

Image borrowed from the Harvard GSD Websitehttp://www.gsd.harvard.edu/geo/manual/projections/fundamentals/index.htm#history

Projection Classes

● There are three classes of projection:– Planar (flattened)– Conic– Cylindrical

There are two cases

The 'tangent' case

The 'secant' case

Aspect

Consequences of Projection

DISTORTION

DISTORTIONYou can never preserve

all of these at once, but you can try.

● Distance - Equidistant● Areas – Equal Area● Angles - Conformal● Shapes - Equivalent● Direction - Azimuthal

More DISTORTION

How do I choose a projection!?

A set of guidelines was developed by Snyder (1987) to help choosing a projection, depending on what you want to preserve in your map

U.S. Geological Survey Professional Paper 1453 John P. Snyder

Planar Geometry

• The x and y axes are the drawing space for a planar map

• Typically, you read units in (x,y)

• The analogous Earth system is longitude and latitude

Earth's Geometric Grid

● Latitude, Longitude● Northing, Easting

– Northing is distance north or south from the Equator in meters

– Easting is the distance from an arbitrary reference line (500,000 m west of the Prime Meridian)

UTM Zones

Military Grid System

GEOREF (World Geographic System)

State Plane System – used often

● State plane systems were developed in order to provide local reference systems that were tied to a national datum.

● They can be a challenge if you are crossing regions while working

Like in this case

Another break

Be back in 5 minutes

Scale

● Just a quick review– Representative Fraction

● Not tied to units– Visual/Graphical– Statement of Equivalency

Finally...

● Introduction to Lab #4● Will span 2 weeks (due May 31st)● Choropleth Maps (lecture, next week)● ArcMap data management

The Choropleth Map

Choropleth Maps

● Very common● Sometimes not well● May be used to

illustrate change● Highly data

dependent● Color scheme is

important

More examples???

Next week, lecture will focus on Choropleth Maps, Color Choices, and more cartographic examples