Cartography: the science of map making

Locating yourself on a Globe

• You need a frame of reference• That is the purpose of Latitude and Longitude• Defining these parameters:

– Earth rotates on an imaginary axis ~ North and South Poles

• Equator: is a great circle that lies equidistant between them.

Great Circles:

• ..are imaginary circles of the surface of the earth who's plane passes through the center of the earth.

 

• The circumference of the earth is 25,000 miles of

40,000 km

• "Great" because it is the largest possible circle

Great Circles:

• 1) cut the earth in half and each half is known as a hemisphere

• 2) are the circumference of the earth• 3) provide the shortest routes of travel on the

earth's surface.– ** Planes travel in great circles.– ** We were always taught a line is the shortest distance

between two points - Not True.

• Small circles: circles whose planes do not pass through the center of the earth.

Latitude

• Latitude: is the angular distance north or south of the equator.

• 1° of latitude = 112 km 360°/40,000 km• 1 degree = 60 minutes • 1 minute = 60 seconds 36°49'52" N• ArcView uses: Decimal Degrees• Sextant measures the angular distance between 2

points (sun & horizon)• **So it easy to determine latitude.

Longitude:

• Longitude: no natural reference point• In 1884 by International Agreement

Greenwich England was the chosen starting point.

• This is called the prime meridian or zero degrees and everything is east or west of that.– (angular distance from Greenwich, England)

The global grid:

• Parallels: lines of latitude, only the equator is a great circle all other parallels are small circles (they never meet)

• Meridians: these are line of longitude and when joined with its mate half way around the globe form great circles

• * the distance between meridians will vary with latitude

Global Coordinate System

• Longitude and Latitude– Degrees, minutes, seconds– 1o latitude = 110.5 km (equator)– 1o longitude = 111.3 cos(latitude)

• Meridian

• Parallel

• Great and Small Circles

How the Earth is Divided

• Hemispheres: Northern, Southern, Eastern, Western

Time Zones

• Solar noon: most towns used this, defined as when a vertical stake cast the shortest shadow.

• By the 19th century transportation and communications (namely railroads and telegraph) connected towns and cities, the adopt of a standard time was necessary.

Time Zones (continued)

• 1884 at the International Meridian Conference 24 time zones were established.

• Greenwich Mean Time (GMT) = Universal time = Zulu time

• 360°/24 = 15° for each time zone, however for convenience many time zones follow state and country lines.

• International Date Line: where each new day begins 180th meridian

• Chronometer 

Time Zones

• 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.

• However globes can not show detail and are big and clumsy.

Globes

Benefits of Maps

• Maps: are the geographers most important tool.• Benefits:

– reproduced easily and inexpensive

– different scales

– can put an enormous amount of information on a map

– roads, buildings, property lines, vegetation, topography

– distribution of land forms

Map Features important in GIS

• 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.

Think of a light bulb

Distortions

• distance

• area

• shape

• direction

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.)

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Map Projection

• Distortions are inherent in maps– Earth is round, map is flat

• Projection is the term used to describe the process of mapping a round surface to flat paper– wide variety of projections possible– each projection causes different distortions to

information

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Map Projections Types

Planar Projection Conical Projection 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.

Variations on Cylindrical Projection

Azimuthal Projection example: Many 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 of Azimuthal Projections

Conic: example:Lambert Conformal Conic Projection

• One or more cones tangent 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 conic projections

Transformations

• The conversion between projections involving mathematical formulas.

• Good GIS packages can do this.

• Overlaying different projections is not possible.