Lecture Outline
Geography 12: Maps and
Mapping
Lecture 2:
Describing the Earth
The Earth is Round!
Geodesy: Size and Shape of the Earth
Latitude and Longitude
Datums
Reference Grids
Universal Transverse Mercator
State Plane Coordinate System
Earth measured in ~250 BC by
Eratosthenes
24,902 miles in
circumference
7,926 miles in
diameter
These numbers
are taken at
equator
BTW, Eratosthenes’s
“World” Map
Sources of Error
What’s a stadia?
157.5m
• Leads to correct
solution to within 1%
185m – Greek
• 16% overestimation
210m – Egyptian
• 32% overestimation
Syene is close to, but
not quite on the Tropic
of Cancer (Aswan is
~40 mi north, ~ .5
deg)
Alexandria not quite
directly north (3
degrees west of north)
Overland distance a
pretty tough guess!
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But It’s a Little More
Complicated…
The Earth is Spherical, but not a Sphere
It is closer to an Ellipsoid, flattened 1/298
F is Flattening Ratio
F = (A – B) / A
Oblong due to rotation of the earth
Elliptical Earth
Radius
a=6,378,137.0m, b=6,356,752.3m
Equatorial Circumference
c=40,075.01668 km (24,901.46089 miles)
Polar Circumference
c=40,030.23642 km (24,873.63573 miles)
1 meter originally defined as 1/10,000,000 of the
distance from the equator to north pole
1 nautical mile was originally 1 minute of
latitude
1 * 60 * 360 * 1.15 (conversion factor to “normal”
miles)
Geoid
Geoid – The mathematical figure of the
earth
Literally – “Earth-like”
Rougher than the ellipsoid
Varies by up to +/- 100m from ellipsoid
Smoother than the earth in full detail
Does not refer to relief. Relief varies about
20km from highest peak to lowest ocean trench
Geoid
NOAA technical definition: The
equipotential surface of the Earth's gravity
field which best fits, in a least squares
sense, global mean sea level
Caused by variations in density on the earth
Think of it like an idealized surface of the
earth
Exaggerated Geoid -15000:1
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GRACE Measurements
Early GRACE Results
Gravity Recovery and Climate Experiment
Two satellites spaced apart sense distance from one another
Increases in local gravity speed up first satellite, increasing
distance
Allow for much more precise measurements of local gravity
http://www.csr.utexas.edu/grace/
Latitude
Finding Latitude
You can find latitude by
Measuring sun angle, and accounting for date
In the northern hemisphere, measuring the
angle from the horizon to Polaris (the North
Star)
Relationship of Polaris to Earth
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Polaris
Longitude is trickier
The equator is “real”
90 degrees from axis
12 hour days/nights all year round
But the Prime Meridian is not
You need one meridian for reference and timekeeping,
but why Greenwich, England?
Other “prime meridians” Copenhagen, Jerusalem, Paris,
Rome, Saint Petersburg, Madrid
Internationally adopted in 1884 (well, France adopted
in 1911)
Royal Observatory, Greenwich
Measuring Longitude
Possible to do it using the moons of Jupiter and
very long calculations, but this was impractical at
sea
John Harrison developed an accurate time piece
(chronometer) that could keep very accurate time
at one’s home port (1761)
By comparing difference in time locally with the
chronometer, you can determine longitude (1
hour=15 degrees)
The Importance of Longitude
Format of Lat/Long
Divided into degrees, minutes, seconds,
hemisphere
H DDMMSS.SS
But often displayed in decimal degrees
H DD.DDDDD
Or degrees and decimal minutes
H DDMM.MMM
Must include N/S for Latitude E/W for Longitude
(or sometimes +/-)
42 degrees North
Henricus Hondius World Map, 1630
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The graticule
The network of lines
of latitude and
longitude upon
which a map is
drawn
From the Latin
craticula meaning
fine latticework
Determining Accurate Locations
Datum – A reference ellipsoid with an
offset
Use one ellipsoid, but match it up locally so the
offset doesn’t have to be so big
Some ellipsoids:
•
•
•
•
Clark(1866) – 1:294.98
Hayford (1924) – 1:297.00
World Geodetic System (1972) – 1:298.26
Geodetic Reference System (1980) – 1:298.25722
Difference in NAD83 and
WGS84
Three Important Datums
North American Datum of 1927 (NAD27)
Initial point at Meade’s Ranch, Kansas
Used Clarke 1866 Ellipsoid
North American Datum of 1983 (NAD83)
Used the Earth-centered GRS80 Ellipsoid
World Geodetic System of 1984 (WGS84)
Widely used worldwide for GPS mapping
Very similar to NAD83, but a few differences in
ellipsoid (both are geocentered)
Vertical Datums
Can just use height above ellipsoid (or geoid), but
results odd near the coast
Sea level – a moving target
National Geodetic Vertical Datum of 1929
(NGVD29)
Approximation of sea level surface for United States
based on tidal records.
North American Vertical Datum of 1988
(NAVD88)
Mean Lower Low Water
http://www.co-ops.nos.noaa.gov/
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Vertical Datums near SB, CA
Datum
Height (m) Height (ft)
Mean Higher High Water 1.643
5.39
Mean High Water
1.413
4.64
Mean Sea Level
0.850
2.79
NGVD29
Mean Low Water
0.834
0.030
2.74
0.10
NAVD88
0.030
0.10
0.00
Mean Lower Low Water 0.000
Reference Grids
Reference Grid – A regular grid superimposed on
a map used for locational purposes
Not much different than the ones you find on city
maps (Letters and Numbers to locate roads, etc.)
We’ll talk about three in detail
GEOREF – World Geographic Reference System
UTM – Universal Transverse Mercator (and UPS –
Universal Polar Stereographic)
SPC – State Plane Coordinate System
Control Networks
Establish two start
locations with careful
observation
Make a baseline
between the two
Used to triangulate,
but now trilaterate to
establish new
locations marked by
monuments
GEOREF (Military System)
Globe is tiled is
15x15 degree cells
Each Row and
Column is labeled
with a letter
Zoom in for more
accuracy
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GEOREF
Each 15x15 degree cell is divided again 15x15 producing 1
degree cells
Further accuracy achieved by noting minutes east and north of
reference lines
Point of Ayre then: MK LK 385250
UTM and UPS
UTM is used for most places, UPS used for polar
regions
Each zone defined by a central meridian and six
degree width
60 north-south zones
Each North and South zone has a False Origin
“X” coordinate is an Easting, “Y” is a Northing
Example Coordinate:
236 000 mE, 3 809 000 mN, Zone 11, S
UTM Zones in the US
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Example Map
State Plane Coordinate System
Used for mapping local, substate, state sized
areas
Large states divided into smaller subregions
Projection used varies based on state
orientation (Generally N/S or E/W running)
125 zones – CA has 6
Like UTM, also uses a false origin
Continental SPCS Zones
Black tic marks outside of map neatline
Notation
1 440 000 feet E, 330 000 feet N, CA, Zone V
always positive, in feet, and increase to the East
and to the North
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