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Practical Vector GIS

Globe to map

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The where is it…

• How do we locate Syracuse in space on the earth’s surface?

• On a FLAT surface?

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The where is it…

• How do we locate Syracuse in space on the earth’s surface?

• On a FLAT surface?

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Syracuse

-76.19 W 43.07N

How do we locate Syracuse on earth?

-76.19 degrees west of meridian through Greenwich, England

43.07 degrees N of the equator

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-76.19 degrees west of meridian through Greenwich, England

43.07 degrees N of the equator

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Earth’s Coordinate SystemX is Longitude and is measured E and W from Greenwich, England. West is negative, East is positiveY is latitude and is measured N and S from the equator. North is positive and S is negative.

These are called Geographic Coordinates

North Pole

South Pole

Lat = 0º

Lat = -30º

Long = -6 0º

Lat = 30º

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Coordinates on EarthNorth Pole

South Pole

Latitude

Longitude

Equator

Meridians

Parallels

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X, Y = Longitude, Latitude

Lines of constant LongitudeLines of constant Latitude

0-90 +90-180 +180

0

-30

30

-90

90

-60

60

Equator

Stretch the top

Stretch the bottom

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X, Y = Longitude, Latitude

Lines of constant LongitudeLines of constant Latitude

0-90 +90-180 +180

0

-30

30

-90

90

-60

60

Equator

90E, 30N

90W, 30S

+90, +30

-90 -30

W76.15° N43.04°

-76.12° 43.08°

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The world in Geographic Coordinates

IsAntarcticaReally that

big?

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The where is it…

• How do we locate Syracuse in space on the earth’s surface?

• On a FLAT surface?

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The where is it…

• How do we locate Syracuse in space on the earth’s surface?

• On a FLAT surface?

• What we just did, plot Long, Lat coordinates, put the globe on a flat surface but DISTORTION

• Why distorted?

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Maps are Flat

• The globe is an ideal model of the earth (almost)

• But you can’t put a useful one in your pocket usless

• So the problem is to put data from a sphere (almost) onto a flat surface

• Xerox can’t do it

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Overview

1. There are a number of problems that apply when converting to flat maps

• Geographic coordinate systems• #1 problem – Datums• #2 problem – Projection• #3 problem – Scale• #4 problem – Generalization

2. Here they are, 1 by 1

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Problem #1, Datums

• Earth is NOT a sphere!• It is more pear shaped• To accommodate this geographers and

surveyors have created models of the earth’s surface

• These are called Datums• And this is booby trap #1 because…• Different shapes different coordinates

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Trees Don’t Move Much• But their coordinates

can change• The Long/Lat of this

tree will be different depending on which datum is being used!

• Could be up to ~50m different in the US

• There are lots of different datums to contend with!

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Problem #2

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Mercator

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The Projection Problem

• There are many mathematical ways of projecting the spherical surface onto a flat surface.

• For the earth these have names likeMercator

AlbersPolyconic

Lambert equal area Azimuthal

Peters

Albers equal area

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Other Projections

Wrong Question – they are all right, just different.

And they all have different properties

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Problem #3

GeographiGeographic SCALEc SCALE

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DefinitionScale =

distance on map(distance unit)distance on ground (distance unit)

A Scale of 1/24,000 means

1 inch (or foot, or furlong) on the map =

24,000 inches (or feet or furlongs) on the ground.

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2,600 Mi

3.5”

Numeric or Ratio scale =1/47,067,429

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Living Room

Kitchen

Dining Room

2.6” / 25’

Scale = 1/115

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Living Room

Kitchen

Dinning Rm.

Scale1/47,000,000

1/46,000

1/115

Is a smaller number than

Is a smaller number than

=0.000000021

=0.000022

=0.008696

Small Scale dataLarge

area/sheetLeast

accurate

Large Scale data

Small area / sheetMost

accurate

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Living Room

Kitchen

Dinning Rm.

Scale1/47,000,000

1/46,000

1/115

Is a smaller number than

Is a smaller number than

=0.000000021

=0.000022

=0.008696

Small Scale dataLarge

area/sheetLeast

accurate

Large Scale data

Small area / sheetMost

accurate

8888

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Problem #4 -Accuracy & Generalization

• When a paper map is made at a very small scale the cartographer is limited by the pen being used

• Can’t draw anything finer than the width of the pen line.

• At a scale of 1/1,000,000 a line 0.05 cm wide = 0.05x1,000,000 cm or 50,000 cm or 500 meters or 19,850” or 1,640’ wide!

• What road is 1,640’ wide!!!• So on the map the road is much, much too

wide

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Accuracy & Generalization

• Take the case of a winding stream

• Shrink it to a Smaller scale (large area, small paper

• Now it is hard to see what is there

• So the cartographer simplifies the stream

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Accuracy & Generalization

• The generalized stream is not as accurate a representation of the stream as the original

• And if you try to mix data of different scale common lines are NOT going to match

Original

Generalized

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Booby Trap Summary

• Using a GIS is more than just combining various data layers – just knowing what buttons to push is NOT sufficient!!!

• You have to be careful that the basic 4 booby traps outlined above do not cause problems

• And 4 possible sources of error give Murphy a field day since problems encountered go up as n2

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Booby Trap Summary

• Using a GIS is more than just combining various data layers

• You have to be careful that the basic three booby traps outlined here do not cause problems

• And 3 possible sources of error give Murphy a field day since problems encountered go up as n2

•Datum

•Projection

•Scale

•Generalization

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icebergAnd that was

just this!

This topic will be a major part of the course!