The Globe and Coordinate Systems

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The Globe and Coordinate Systems

• Intro to Mapping GIS

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The Earth Really is Flat!
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Earth as an Inscription

• Day to day, we live life in a flat world
• sun rises in east, sets in west
• sky is above, ground is below
• we orient travel by north-south, east-west
  thinking
• Map Representation or Model of landscape
• A flat map is a perfectly rational model of real
  space on a local or regional scale

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Long History of Mapping

• Prehistoric Renderings, Rock Paintings from the
  KhoiSan People in South Africa
• Traditional Australian Aboriginal Art Symbols
  Communicated Place

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Long History of Mapping

• Ancient tablet from the 7th Century BC depicting
  the world at the time of Sargon (2300 BC) as a
  circle surrounded by water, with Babylon at its
  center. (British Museum)
• Map of known world by Hecataeus
• about 500 BC
• Greeks believed world a sphere

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Mapping on a flat surface is relatively easy
graphic symbols
store
abstraction
house
reality
map
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Map Making (Cartography)

• Cartographic Symbology
• Abstracting spatial reality with graphic
  representation
• Extent
• The area being mapped
• Scalerelationship of size of real world to map
• Prepresentational fraction 1/24,000
• Ratio 124,000
• Written statement 1 inch equals 1 mile
• Bar style
• Generalization
• The amount of detail included in the map
• Depends on the scale

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Formal Definitions

• Mapa representation, usually on a flat surface,
  as of the features of an area of the earth or a
  portion of the heavens, showing them in their
  respective forms, sizes, and relationships
  according to some convention of representation a
  map of Canada.
• Cartographythe production of maps, including
  construction of projections, design, compilation,
  drafting, and reproduction.

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Coordinate Systems
Cartesian

• Numerical systems that specify location in space.
• Types of coordinate systems
• Plane coordinates(i.e. FLAT Surface)
• Cartesian
• Angular/polar
• Global or spherical coordinates

Polar
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Cartesian Coordinates
Y
I
II

• Origin
• Abscissa or X Axis
• Ordinate or Y Axis
• Position X,Y
• Quadrants I through IV
• Point LocationsPoint X Y 1 x1
  y1 2 x2 y2
• Used for most projections.

P1
y1
P2
y2
X
x1
x2
III
IV
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Distance Calculation for Points Measured in
Cartesian Coordinates
Y
I

• Point LocationsPoint X Y
  1 x1 y1 2
  x2 y2
• Distance Formula
• Distance from Point 1 to Point 2

P1
y1
y1 - y2
P2
y2
x1 - x2
X
x1
x2
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Most Flat Maps Utilize a Cartesian Coordinate
System
NORTH SOUTH AXIS
EAST WEST AXIS
Ancient Plan of Jerusalem
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Defining Location on a Sphere the Global
Coordinate System
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Basis of Global Coordinate System

• Earths rotation gives poles and axis as two
  natural points of reference on the sphere.
• Equator locus of points on spheres surface that
  are equidistant from the poles.
• Great Circle
• Pass a plane through a spheres center.
• Connect the points along which plane intersects
  spheres surface.
• Line defined by the points is a great circle.
• Equator is only great circle perpendicular to
  axis of rotation.

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Terms to Specify Position on Globe

• Latitude degrees north and south of equator.
• Longitude degrees east and west of Greenwich,
  England.
• Meridianline of constant longitude.
• Parallelline of constant latitude
• Great circlecircle inscribed on surface by a
  plane passing through earths center.
• Small circlecircle inscribed on surface by a
  plane that passes through earth, but misses the
  center.

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Units of Measure

• Angular Measure
• Degrees360 per circle.
• Minutes60 per degree.
• Seconds60 per minute.

• Great Circle Degree Distances
• Degree 69 miles.
• Minute 1.15 miles.
• Second .02 miles
• One tenth second 10.12 feet
• One hundredth second 1.012 feet.

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Units of Measure

• Traditional Angular Measure
• Degrees 360 per circle.
• Minutes 60 per degree.
• Seconds 60 per minute.

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Decimal Degrees

• Based on decimal fraction of a degree
• Easier to work with
• Can express angles to any precision - to
  hundredths of a degree, to thousandths of a
  degree, and so on
• Better for digital mapping

• Decimal Degree Conversion
• Multiply minutes by 60
• Add seconds to results of minutes multiplied by
  60.
• Divide total by 3,600
• Add result to degrees

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Example of Decimal Conversion
Traditional Measure
45
20
30
1200
60
Convert minutes to seconds
Add seconds to converted minutes
1230

Convert seconds to degree fraction
/ 3600 .3416667
Add whole degree to fraction
.3416667
45
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Global Grid Properties

• All meridians equal length
• All meridians converge at poles (true north
  orientation)
• All lines of latitude are parallel to the equator
• All parallels maintain the same spacing
• Meridians and parallels intersect at right angles
• The scale on a globe is the same everywhere
  (unlike a map)

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Seasonal Variation of Solar Angle

• Axial Parallelism
• Tropics and Polar Circles

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Time and Time Zones
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Concept of Solar Time
Solar times are measures of the apparent position
of the Sun on the celestial sphere. They are not
actually the physical time, but rather hour
angles, that is, angles expressed in time units.
They are also local times in the sense that they
depend on the longitude of the observer.
Celestial sphere
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Apparent Solar Time
Apparent solar time or true solar time is the
hour angle of the Sun. It is based on the
apparent solar day, which is the interval between
two successive returns of the Sun to the local
meridian. Note that the solar day starts at noon,
so apparent solar time 0000 means noon and 1200
means midnight. Solar time can be measured by a
sundial.
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Sundial
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Mean Solar Time
Mean solar time is the hour angle of the mean
Sun. The mean solar time is computed from an
artificial clock time adjusted via observations
of the diurnal rotation of the fixed stars to
agree with average apparent solar time. The
length of a mean solar day is a constant 24 hours
throughout the year even though the amount of
daylight within it may vary. An apparent solar
day may differ from a mean solar day (of 86,400
seconds) by as much as nearly 22 seconds shorter
to nearly 29 seconds longer.
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Time Zones

• Both the mean solar time and the apparent solar
  time differ with longitude.
• Imagine starting in Charlottesville at exactly
  noon.
• As you travel to the west, the Sun will appear
  further east in the sky (i.e. lower and further
  from the meridian).
• Even if you travel only a few miles west, the
  Sun moves off the meridian.
• Each city would have its own time.

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Invention of Time Zones

• With the advent of rapid travel by trains in the
  19th century, it became necessary to standardize
  the time for all cities within a certain region.
• In November 1883, the railroad companies divided
  the United States into four time zones.
• Everyone in a time zone set their clocks to the
  same standard time.

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Time Zones

• In 1884, an international conference was held in
  Washington D.C. by 26 countries.
• The world was divided into 24 times zones, with
  each zone being roughly 15 degrees wide in
  longitude.
• Time zones have been modified for political,
  social and economic reasons.
• Since there are 24 hours in a day, and
  360/1524, the time in each zone differs from the
  time in adjacent zones by one hour.
• Some time zones are not standard (example India)
• China has only 1 time zone

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International Date Line

• Standard time gets earlier as you travel to the
  west.
• The International Date Line line was established
  in the middle of the Pacific Ocean.
• As you go from east to west, you gain a day as
  you cross the line.
• As you go from west to east, you lose a day as
  you cross the line.

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