# Object’s Location in the World

 Chapter 2 Basic Mapping Processes Introduction

I. Defining an Object’s Location in the World
II. Geographical Coordinate System
III. What is the Earth’s Shape?
IV. Impact of Earth’s Shape on Location
Determination
V. A Datum as a Mapping Framework
I. Horizontal Datum
II. Vertical Datum

How do we define the location of an object in the world?
40.625106o, -73.961446o
40o 37’ 30.3816”, -73o 57’ 41.2056”
40.606789
o, -74.044016o
40o 36’ 24.4404”, -74o 2’ 38.4576”
Chapter 2 Basic Mapping Processes
Geographical Coordinate
System
Chapter 2 Basic Mapping Processes
Types of Coordinate Systems
Geographical Coordinate System
(Spherical Coordinates)
Projected Coordinate System
(Cartesian Coordinates)
Chapter 2 Basic Mapping Processes
source: http://courses.washington.edu
What differences do you see between these?
Types of Coordinate Systems
Projected Coordinate System
(Cartesian Coordinates)
Chapter 2 Basic Mapping Processes
source: http://courses.washington.edu
Geographic Coordinate System
http://www.disam.dsca.mil/pubs/archives.htm Vol 26-4 2004
DISAM Journal
Graticule
The pattern of meridians
and parallels on the earth.
Great Circle
A circle that divides the
earth into two equal halves.
Small Circle
A circle that divides the earth
into two unequal halves.
Chapter 2 Basic Mapping Processes
Latitude is the angular distance north or
south of the
equator.
Geographic Coordinate System
Image Source: Christopherson, Geosystems 6th edition
Parallels connect points of equal latitude. Meridians connect points of equal longitude.
Longitude is the angular distance east or
west of the
Prime Meridian.
Chapter 2 Basic Mapping Processes
Geographic Coordinate System
A degree of latitude or longitude can be subdivided further into minutes and seconds…
One degree is divided into 60
minutes (60’)…
One minute is divided into 60
seconds (60”)….
Example:
44o4206”E
This reads 44 degrees, 42 minutes,
6 seconds East of the Prime
Meridian.
44th degree divided into 60 minutes
42nd minute divided into 60 seconds
42nd minute of 44th degree
6th second of 42nd minute
44oE 45oE
44o43’E
44
o42’E
So, how do you convert between DMS and Decimal Degrees?
Chapter 2 Basic Mapping Processes
What is the Earth’s Shape?
Chapter 2 Basic Mapping Processes
Chapter 2 Basic Mapping Processes
Three Important Shapes of the Earth
“Good Enough” For
General Mapping Purposes
Need to Consider Both in
Detailed Mapping Efforts

Impact of the Earth’s Shape
on Location Determination
Chapter 2 Basic Mapping Processes
An accurate and precise calculation of “the vertical” is required in order to accurately
calculate a locations’ latitude and longitude using traditional methods.
Deflection of the vertical – the
difference between a vertical line
passing through the earth’s center
of gravity (geoid) and a vertical line
passing through the earth’s
geometric center (ellipsoid).
Chapter 2 Basic Mapping Processes
Impact of Earth’s Shape on Latitude / Longitude
Determination

What About a Point’s Elevation Value?
Different elevation values are obtained based on which shape is used.
Which surface do you use?
Chapter 2 Basic Mapping Processes
Horizontal Datum
Chapter 2 Horizontal Datum
Horizontal Datums
Local Horiz. Datum – ellipsoid is constructed as a best fit with the geoid in a specific area.
Global Horiz. Datum – ellipsoid is constructed as a best fit with the geoid globally
Source: http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm
Chapter 2 Horizontal Datum
A Selection of Ellipsoids Used for Mapping Purposes

 Name Date Equatorial Radius (m) Polar Radius (m) Area of Use WGS84 1984 6,378,137 6,356,752.31 Worldwide GRS 80 1980 6,378,137 6,356,752.3 Worldwide (Nad83) Australia 1965 6,378,160 6,356,774.7 Australia Clarke 1880 1880 6,378,249.1 6,356,514.9 France, most Africa Clarke 1866 1866 6,378,206.4 6,356,583.8 North America (Nad27) Airy 1849 6,377,563.4 6,356,256.9 Great Britain

Chapter 2 Horizontal Datum
North American Datum of 1927 (NAD27)
Meades Ranch-Center of the Contiguous US
The base point was the reference point for almost all land survey measurements in the
United States from 1927 until the establishment of the North American Datum of 1983
(NAD 83) and the World Geodetic System of 1984 (WGS84).
Chapter 2 Horizontal Datum
Effect of the Datum Change
The North American Datum of
1983, contains fewer inherent
local distortions than the North
American Datum of 1927
The datum change resulted in the
latitude and longitude locations
throughout the North America.
Chapter 2 Horizontal Datum
Chapter 2 Vertical Datum
Vertical Datum
Chapter 2 Vertical Datum
Vertical Datums and Elevation Measurements
Traditionally, vertical measurements are referenced to a local vertical
datum that has a starting point at a tidal station.
North American Vertical Datum of 1988
Many elevation measurements in North
America are tied to the North American
Vertical Datum of 1988 (NAVD 88)
The zero surface for this datum is defined
by Mean Sea Level at the Rimouski tidal
Mean Sea Level (MSL) is defined by
surveyors as the average of all low and
high tides at a particular starting location
over a
19 (18.6) year lunar period called
Metonic cycle.
Chapter 2 Vertical Datum
Vertical Datums and
Elevation Measurements
A local vertical datum is
implemented through a vertical
control network.
Example: Geodetic leveling in the
Netherlands using the vertical datum
defined by the Amsterdam tidal station
Source: http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm
NO CLASS – Classes Follow MONDAY Schedule Chapter 2 Vertical Datum
Important Dates!
Added to the Calendar on Blackboard:
Tuesday Feb 7th (that’s today) – last
day to drop with 50% refund
Tuesday Feb 14th (one week from
today) – last day to drop with 25%
refund and not receive a “W”
Tuesday Feb 21st – Classes follow the
Monday schedule – No Class Meeting
Thursday Feb 23rd – I will be traveling, I
will pre-record and send out a lecture, I
will be available via email for questions
during our class time (up until the plane
takes off)
After that, no schedule disruptions until
SPRING BREAK

The UTM Zones
Chapter 2 Coordinate Systems Grid Systems: UTM
840N
80
0S
0
0
There are total 60 North-South Zones, starting
from 180ºW and each being 6º wide in longitude
1800W
180
0W
180
0E
180
0E
0
0
00
00
Chapter 2 Coordinate Systems Grid Systems: UTM
Projection: Transverse_Mercator
False_Easting: 500000.000000
False_Northing: 0.000000
Projection: Transverse_Mercator
False_Easting: 500000.000000
False_Northing: 0.000000
Two UTM zones
for New York
But what’s the deal
with this falseness?

Chapter 2 Coordinate Systems Grid Systems: UTM
source: http://www.vidiani.com
Let’s use Manhattan as a model
UTM does not use use negative numbers.
UTM North zones doesn’t use false northing, it uses the equator (black line)
UTM Southzones, rather than measuring south from the equator (negative
numbers) instead it measures up from an imaginary false north (red line)
500k
UTM Meridian UTM Meridian
False Easting
Transverse Mercator
Projection
Used for North – South
trending states
Used for East – West
trending states
Lambert Conformal Conic
Projection
Chapter 2 Coordinate Systems Grid Systems: UTM
Chapter 2 Coordinate Systems Grid Systems: UTM
State Plane Systems
• Lambert Conformal Conic
• Transverse Mercator
Projection: Transverse_Mercator
False_Easting: 350000.000000
False_Northing: 0.000000
Chapter 2 Coordinate Systems Grid Systems: UTM
• A systematic rendering of a
graticule of lines of latitude and
longitude on a flat sheet of paper.
• A mathematic transformation of
the curved earth surface to a flat
sheet of paper
Curved Earth
Geographic coordinates
(Latitude & Longitude)
Flat Map
Cartesian coordinates: x,y
(Easting & Northing)
A Map Projection is …
Chapter 2 Map Projections What is a map projection?
Maps can’t or don’t show
the whole world
• Examples:
– Mercator: usually extends
to 80
o N and 80o S
– Gnomonic, limited
mathematically to cover
less than a hemisphere.
Although maps are useful, they have limitations…
Chapter 2 Map Projections

 0 30W 60E 30E 90E 150E 120E 30N 180E 180W 120W 150W 60N

60W
90W
150N
What is a map projection?
1800W
180
0W
180
0W
90
0N
Point to
Point
Point to line
Continuity
Loss
Breaks in continuity (where the same line forms two edges of the map)
(World from space, modified) (World Miller Cylindrical Projection)
Correspondence and continuity are lost and geographic distortions occur.
Chapter 2 Map Projections
Although maps are useful, they have limitations…
What is a map projection?
(Azimuthal) Plane Cylinder Cone
Developable Surface of Map Projection
Chapter 2 Map Projections Creation of a Map Projection
Choose based on scale, place, other considerations
Plane Projection Orientations
Normal
(Polar)
Transverse (Equatorial)
Oblique
Chapter 2 Map Projections Creation of a Map Projection
Cylindrical Projection Orientations
Transverse
(Along a Meridian)
Oblique
Normal
(Equatorial)
Chapter 2 Map Projections Creation of a Map Projection
Light source at the
center of the earth
Light source at the
infinite distance
Light source sits
exactly opposite the
developable surface’s
point of tangency
Gnomonic Projection
Orthographic Projection
Stereographic Projection
Chapter 2 Map Projections Creation of a Map Projection
Light Type for Map Projections
• Two Major Properties
Properties that can exist at all
points
on certain projections.
Earth Properties to Preserve or Distort
• Two Minor Properties
Properties that can exist in
relation to only one or two
points or lines on certain
projections.
12

 12

12 12
50°
50°
40°
–Conformality: Shape (Angle)
–Equivalence: Area (Size)
–Distance (Scale)
–Direction (Azimuth)
Chapter 2 Map Projections Earth’s Properties S.A.DD
Mercator Conformal Projection
Generating Globe
Chapter 2 Map Projections Earth’s Properties Conformality (Shape)
Another Example: Lambert’s Conic Conformal Projection
Example of a Conformal Projection – preserves shape
Mollweide Equal-area Projection
Chapter 2 Map Projections Earth’s Properties Equivalence (Area)
Sinusoidal Projection
Albert’s Conic Equal-Area Projection
Lambert’s Azimuthal Equal Area
Other Examples:
Generating Globe
Example of an Equal-Area Projection – preserves area
• Conformality (Shape) and Equivalence (Area) are mutually
exclusive, you
CANNOT preserve both on one map.
• However, a map can be both azimuthal (preserving
direction) and equivalent (preserving area) or both
azimuthal and equidistant (preserving scale).
Azimuthal equidistant projection Azimuthal equal-area projection
Chapter 2 Map Projections Earth’s Properties S.A.D.D.
Compromise projections are projections that do not preserve
any of the globe properties but also does not result in extreme
distortion of any property.
• It is impossible and
unnecessary to keep all
or none of the properties
precisely.
• Compromise projections
have better visual
effects as used for the
education purpose.
• Commonly used ones
include Miller
Cylindrical, Robinson,
and Winkel Tripel.
Chapter 2 Map Projections Earth’s Properties Compromise Projections
Chapter 2 Map Projections Earth’s Properties Compromise Projections
Projection Selections
• Purpose of the map
Are aesthetics important?
Are distance and / or direction calculations being made?
• Size of the area being mapped
Is an entire continent being mapped?
f
• Shape of the area being mapped
Does the area being mapped have a “skinny” shape? (e.g. Chile)
Does the area being mapped have a rectangular shape? (e.g. United
States)
• Latitudinal location of the area being mapped
Polar Location?
Mid-Latitude Location?
Equatorial Location?
What considerations do we need to make when selecting
a map projection?
Great Website: http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html