Coordinate Systems Projections Introduction to Choropleth Maps May

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 *

Arc. Map 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 BP Eratosthenes' Map

Erotosthenes' Calculation Estimate – 40, 500 km (25, 170 mi) Actual – 40, 075 km (24, 960 mi) 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 Angle calc on summer solstice, noon 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 Geoid ● ● 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

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? BREAK Be back in 5 minutes

Definition: Map Projection DEFINITION a: systematic presentation of intersecting coordinate lines on a flat surface upon which features from the curved surface of the earth or the celestial sphere may be mapped b: the process or technique of reproducing a spatial object upon a plane or curved surface or a line by projecting its points; also a graph or figure so formed…. In other words…transformation of a curved surface to a flat one. Image borrowed from the Harvard GSD Website http: //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

DISTORTION You 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 31 st) ● Choropleth Maps (lecture, next week) ● Arc. Map 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