Cartography: the science of map making A Round World in Plane Terms

Geographic Coordinate System The earth is modeled as a sphere or spheriod. The GCS consists of latitude and longitude lines to describe location on a spherical surface. When latitude and longitude are projected on to a flat piece of paper distortions occur.

The Globe is a nearly perfect representation of the earth, it shows the shape and spatial relationships of land and water. Problem: –Can only look at 1/2 at a time. –Globes can not show detail and are big and clumsy. Globes

Benefits of Maps (including electronic maps) Maps: are the geographers most important tool. Benefits: –reproduced easily and inexpensive –can create different scales –can put an enormous amount of information on a map roads, buildings, property lines, vegetation, topography, etc.

Important Map Features Areas Lines –width exaggeration Points –size exaggeration

On a globe four properties are true: 1) parallels of latitude are always parallel 2) parallels are evenly spaced 3) meridians of longitude converge at the poles 4) meridians and parallels cross everywhere at right angles

Map Projection: A map projection is a mathematical formula for representing the curved surface of the earth on a flat map. –wide variety of projections possible –each projection will create a different type of distortion

Think of a light bulb

Distortions distance area shape direction Distortions are inherent in maps The Earth is round, a map is flat

14 Map Projections Types

Variations of Azimuthal Projections (Planar)

Azimuthal Projection example: most Polar projections Plane is tangent to the globe at some point N or S of the equator or one point on the equator. No distortion at the point of tangency but it increases moving away. All directions from the center are accurate. It is like a view from space. Can only see half the world at once. All great circles passing through the point of tangency appear as straight lines. Good for knowing the great circle path (I.e. shortest distances, important to navigators.

Variations on conic projections

Conic: example: Lambert Conformal Conic Projection One or more cones tangent (or secant) to one or more parallels. Best for mid- latitudes in an E-W direction (U.S.) A straight line is almost a perfect great circle route (planes use this) Can be conformal or equivalent

Variations on Cylindrical Projection

Cylindrical Projection: example: Mercator Tangent to the globe at the equator. No distortions at the equator but it increases moving North or South. Nice rectangular grid. Why are they used in Navigation? *A straight line drawn anywhere on a Mercator projection is a true compass heading: this is called a rhumb line. However, the distance along this line may vary.

There are many map projections and each one is good at representing one or more spatial properties, but no projection preserves all four properties. Mercator projection: maintains shape and direction Sinusoidal and Equal- Area Cylindrical projections: both maintain area, but look quite different from each other. Robinson projection does not enforce any specific properties but is widely used because it makes the earth’s surface and its features "look right."

GCS - unprojected Geographic coordinates displayed as if the Latitude-longitude values are linear units

You must make a choice between: Equivalence: equal area relationship throughout the map, however you get distorted shapes. Conformal: shapes are true and meridians and parallels are at right angles, however land masses are greatly enlarged at high latitudes. Except for very small areas Conformality and Equivalence are mutually exclusive. There are over 1000 different projections.

Other types of considerations Equidistant projections – However scale is not maintained correctly by any projection throughout an entire map True-direction projections or azimuthal projections, maintain some of the great circle arcs. (The shortest distance between 2 points on a globe is the great circle route.)

Transformations The conversion between projections involving mathematical formulas. Good GIS packages can do this. Overlaying different projections is not possible unless the GIS program has “on- the-fly” reprojection capabilities.

Sphere vs. Spheroid A sphere is okay for small scale maps (<1:5,000,000). For larger scale maps a spheroid is necessary, the spheroid used will depend upon the purpose, location, and accuracy of the data.

Datums A reference frame for locating points on Earth’s surface It consist of: 1)A spheroid (ellipsoid) with a spherical coordinate system and an origin. 2)A network of points that have been meticulously surveyed.

Position of the Capital of Texas

N. American Datums NAD27 –Clarke 1866 spheroid –Meades Ranch, KS –Local datum NAD83 –GRS80 spheroid –Earth-centered datum –GPS-compatible NAD27 NAD83 up to 500’ shift WGS84 (very similar to NAD83)

Datums and Elevation Horizontal and Vertical Datums Is the Sea level? –Panama Canal Height Above Ellipsoid (HAE) Height Above Geoid (HAG) Common Vertical Datums: National Geodetic Vertical Datum of 1929 ((NGVD29) North American Vertical Datum of 1988 (NAVD88)