Spheroids, datums,
Projections, etc.
Spatial data comes in many
forms. So How does a GIS
work with the data so that it
can put it in the right place?
1
2 Ways to Represent data
• On the spherical earth (globe)
• On flat maps
2
Where is it?
How do we locate it on earth?
3
Flat Map
-76.19,
43.07
4
Coordinate Systems
• On the spherical earth (globe)
-Geographic Coordinate System are used
• On flat maps
-Projected Coordinate System are used
• The distinction between these is important!
5
So…
•
•
•
•
That is what this lecture is about
The shape of the earth
The coordinate system of the earth
Models of the earth
– Spheroids
– Datums
• Date projected to flat maps
6
Overview of what you need to know
1.
Spherical earth (globe)
a. Longitude, Latitude (X,Y)
b. Spheroids
c. Datums
 lat, long (Y,X)
2. Flat maps
a. Projections
b. Coordinate Systems
•
•
UTM (Universal Transverse Mercator)
SP (State Plane)
3. Definition and Conversion
7
Coordinates on Earth
North Pole
Meridians
Longitude
Equator
Parallels
Latitude
South Pole
8
9
X, Y = Longitude, Latitude
90
60
30
0
-30
-60
-90
-90Stretch the
0 bottom
+90
+180
Lines of constant Longitude
Lines of constant Latitude
Stretch the top
Equator
-180
10
X, Y = Longitude, Latitude
90E, 30N
Equator
90W, 30S
-180
+90, +3090
60
30
0
-30
-60
-90 -30
-90
-90
0
+90
+180
Lines of constant Longitude
Lines of constant Latitude
11
The world in Geographic
Coordinates
Is
Antarctica
Really that
big?
12
Spheroids & Datums
•
•
•
•
Model the earth with a sphere?
N0! It is more Pear shaped!
So how do we locate stuff on a pear?
Even approximately (since it is a
bumpy pear!)
• Use a model
• There are many models of these and
each has its own properties
13
The Models of the Earth
• Involve…
– Spheroids -the three-dimensional shape
obtained by rotating an ellipse about its
minor axis. This is also called an ellipsoid
– Datums – define a local reference for a
spheroid surface.
14
Earth Centered Spheroid
Best fit over
the entire earth
World geodetic system of
‘72 (WSG72) and of ’84
(WSG84) = NAD84
Earth
Spheroid
15
Recent Spheroids
WGS = World Geodetic System
GRS = Geodetic Reference System
•
•
•
•
•
•
Clark 1866 not earth centered
WGS 1966
WGS 1972 TBE
WGS 1972
WGS 1982
WGS 1984 (= GRS 1980)
16
Datum
• A spheroid does not match the earths
surface everywhere
• A datum is used to align the spheroid with
the surface where you are
• So the datum specifies
– The spheroid
– And the point where it will match the earths
surface exactly
• So you don’t have to worry about Spheroids
much but you do have to worry about
datums
17
Spheroids & Datums
• A spheroid can be moved mathematically
to fit different parts of the earth…
Earth
Spheroid
They then become
datums
18
NAD27
• North American Datum of 1927
• References a surface fit to US
• Point of perfect fit is Mead’s Ranch
in Kansas
• Older data is often in NAD27
19
NAD 83
• Based on earth centered WGS 72
• WGS 72 is mathematically moved to
make it fit a specific location
20
Datum differences
• The change in datum can change your location
measure
• Not your actual location!
• Redlands
– NAD83
• –117° 12' 57.75961" (longitude)
34° 01' 43.77884" (latitude)
– NAD27
• –117° 12' 54.61539" (longitude)
34° 01' 43.72995" (latitude)
~ 1.1 minutes long
~ 1.6 min lat
21
-20 to -40 m
22
0 to 10 m
23
Overview
1.
Spherical earth (globe)
a. Longitude, Latitude (X,Y)
b. Spheroids
c. Datums
2. Flat maps
a. Projections
b. Coordinate Systems
•
•
UTM
SP
3. Conversion
24
PROJECTED COORDS
• Projected Coordinate systems
• Flat maps
• Feature coordinates are
mathematically projected onto flat
surfaces
• There are many projections
• And then there are Coordinate
Systems
25
The Problem
26
27
28
29
The Mercator Projection
Making a
Projection
30
Mercator
• The equations for mapping objects
(math term here) on a sphere onto a flat
paper are, for Mercator, surprisingly
simple:
X = l,
And
X is Mercator value, l is longitude
Y = ln Tan ( t/2 +
p/4), t is latitude
31
Projections: Distortion
• In going from spherical coordinates
(surface) to a flat surface THERE
WILL BE DISTORTIONS in
–
–
–
–
Shape
Area
Distance
Direction
32
Projections: Distortion
• Shape: If shapes look the same on the map
and on the globe then the projection is
conformal
• Area: If area is preserved then you have
an equal area map
• Distance: If distance is preserved then the
map is of uniform scale and you have an
equidistance map.
• Direction. maps If directions from a
central location to all other points are
correct then the map is Azmuthal
33
Summary of Projection Properties
Key:n = Yes x= Partly
Projection
Type
Conformal
Equal
area
Equidi
stant
True
directi
on
n
n
n
Globe
Sphere
n
Mercator
Cylindrical
n
Transverse
Mercator
Cylindrical
n
Persp
ective
Comp
romis
e
x
Straig
ht
rhumb
s
n
Pseudo-
n
Robinson
cylindrical
Gnomonic
Azimuthal
Azimuthal
Equalidistant
Azimuthal
Lambert
Azimuthal
Equal Area
Azimuthal
n
Albers Equal
Area Conic
Conic
n
Lambert
Conformal
Conic
Conic
Polyonic
Conic
n
n
n
n
n
n
x
x
n
34
Summary of Projection Properties
Key:n = Yes x= Partly
Projection
Type
Conformal
Equal
area
Equidi
stant
True
directi
on
n
n
n
Globe
Sphere
n
Mercator
Cylindrical
n
Transverse
Mercator
Cylindrical
n
Persp
ective
Comp
romis
e
x
Straig
ht
rhumb
s
n
Pseudo-
n
Robinson
cylindrical
Gnomonic
Azimuthal
Azimuthal
Equalidistant
Azimuthal
Lambert
Azimuthal
Equal Area
Azimuthal
n
Albers Equal
Area Conic
Conic
n
Lambert
Conformal
Conic
Conic
Polyonic
Conic
n
n
n
n
n
n
x
x
n
35
Common Datums
• NAD27 – N. American datum of 1927
(based on the Clark 1866 spheroid, Mead’s
Ranch, KS is origin)
• NAD83 – N. American datum of 1983 based
on spheroid GRS80
• WGS 1984 (spheroid IS a datum)
• Most GPS systems use WGS spheroids but
can report coordinates based on either of
the NADs
36
Just to make life difficult…
• The term Coordinate System has
TWO (2) meanings
– One we have covered – it can mean
either geographic or projected
coordinate systems
– Within the class of projected coordinate
systems it can specifically mean:
• The UTM coordinated system
• The State Plane coordinate system
37
UTM Coordinate Systems
• The Universal Transverse Mercator or
UTM Coordinate system –
– based on the Mercator projection
– A world wide system
• Toilet Paper
Tube is now
Horizontal so
is tangent to the
earth along its
prime meridian and
and passes through
the Poles
Prime Meridian
Errors are Zero!
38
UTM coordinate system
• A projected coordinate system that
divides the world into 60 north and
south zones, six degrees wide.
• Why?
• The Transverse Mercator is only
bang-on accurate on the meridian
that is tangent to the toilet paper
tube
• The further away you are the more
inaccurate the data
39
UTM coordinate system
• So the way to make accurate maps on flat
surfaces when working with features the
size of, say, states or counties, is to have a
bunch of TM projections
• NY has 3 UTM zones (see handout)
• Usually data for the state is done in Zone
18 (central) without causing too much
error at either end.
• YOU CANNOT USE MORE THAN 1
ZONE IN ANY MAP –Edges won’t match!
40
UTM Zones
Most of NY is in
UTM Zone 18
41
UTM Coordinate
Northing
O(4,000,000) m in NY
• The units in UTM are usually Meters
• You need to specify the zone
Easting
• Example: Location of CCC is:
O(100,000) m
in NY
373,800 Meters E, 4,756,000 Meters N,
Zone 18, N
42
Eastings and Northings in UTM
• Each UTM zone is 6 degrees wide.
• The scheme below is used for Eastings so that no
negative values are present.
• Northings are from the equator
OFFSET
Central meridian
800,000m
700,000m
600,000m
500,000m
400,000m
300,000m
200,000m
1 UTM ZONE OF 6 DEGREES
43
The State Plane Coordinate Sys
• A projected coordinate system used in the
United States
• Divides each state into one or more zones
• Also known as SPCS and SPC.
• States running N-S (VT) are in Transverse
Mercator
• States running E-W (TN) are in Lambert
Conformal
44
State Plane
• Different projections for different states
• Horizontal zones (Tenn) are Lambert
Conformal projections
• Vertical zones are Transverse Mercator
projections
• Each state has its own origins for its own
system
• States may have multiple zones in
different projections
• UNITS are usually feet BUT NOT
ALWAYS
(another BOOBY TRAP)
45
NY East
Zone 4801
NY Central
Zone 4826
State Plane Zones
NY West
Zone 4851
NY Long Island
Zone 4876
46
NY East
Zone 4801
NY Central
Zone 4826
State Plane Zones
NY West
Zone 4851
Transverse
Mercator
Lambert
Conformal
NY Long Island
Zone 4876
47
ArcMap Problem (or NOT)
• ArcGIS can project on-the-fly
• By that, we mean that if you add a
layer that is NOT in the same
Coordinate System, Projection, or
Datum ArcMap will project (verb) it to
match the data already loaded
• So what’s the problem??
48
Booby Trap
• The trap lies in the fact that if you load
data that does NOT have a .prj file
ArcGIS will just say to itself
• “OK, the current coordinate system is
what this Bozo wants to use!”
• This is a problem?
• Yes and no – depends…
49
Booby Trap
• Assume that Bozo loaded a layer that was in
Long, lat first (w/o .prj file)
• Now suppose Bozo loads a file that is in UTM
that does not have a .prj file.
• In this case ArcGIS says to itself “Well, Bozo
didn’t tell me different so this one must be DD
also”
• Bozo then says “Where the #$%@ is my data?”
• Bozo then zooms-to-layer – Hmm – it is there!
But not with the rest of my stuff
• Bozo then says “what are the coordinates?’
• Wow – 434,890 degrees East and 4,987,652
50
degrees N!
Booby Trap
• Assume that Bozo loaded a layer that was in
Long, lat first (w/a .prj file)
• Now suppose Bozo loads a file that is in UTM
that does not have a .prj file.
• In this case ArcGIS says to itself “Well, Bozo
didn’t tell me different so this one must be DD
also”
• Bozo then says “Where the #$%@ is my data?”
• Bozo then zooms-to-layer – Hmm – it is there!
But not with the rest of my stuff
• Bozo then says “what are the coordinates?’
• Wow – 434,890 degrees East and 4,987,652
51
degrees N!
Rule
• Always have a .prj file for any data
layers you are using.
• You can define the .prj file in the
Toolbox
• You can also project data to a new
projection, datum in the tool box
• This actually changes the data
52
Do the math
• Syracuse is at
–
–
–
–
–
4,987,652 N
(DD?)
76 W
(DD?)
Difference is 4,987,576 N
That is the full extent of the data
760 lines means ~7,600 degrees per
pixel
– Never see it when zoomed to full extent
53
Overview
1.
Spherical earth (globe)
a. Longitude, Latitude (X,Y)
b. Spheroids
c. Datums
2. Flat maps
a. Projections
b. Coordinate Systems
•
•
UTM
SP
3. Conversion
54
Conversion
• Every layer should have a .prj file
• It contains the native projection info
• The basic Spatial info in the
metadata is abstracted into the
metadata by ArcCatalog
55
How you convert
• Using ArcToolbox
• In Toolbox you can
– a) create a .prj file or
– b) change the data in the .prj file.
56
• On_hydro_utm_83
.prj
The prj
PROJCS["NAD_1983_UTM_Zone_18N",
GEOGCS["GCS_North_American_1983",
DATUM["D_North_American_1983",
SPHEROID["GRS_1980",6378137.0,298.257222101]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0.0174532925199433]],
PROJECTION["Transverse_Mercator"],
PARAMETER["False_Easting",500000.0],
PARAMETER["False_Northing",0.0],
PARAMETER["Central_Meridian",-75.0],
PARAMETER["Scale_Factor",0.9996],
PARAMETER["Latitude_Of_Origin",0.0],
UNIT["Meter",1.0]]
57
The toolbox
To Project a
feature that
already has a
projection
To Project a
feature that does
not have a
projection
58
Change to State Plane
• Use Project tool
1 - Browse
59
Spatial Reference Properties
60
Add output System
61
Final Steps
Add Datum
Transformation
62
Last little booby trap
Geographic
SCALE
63
Not lining up?
• Obviously data that is not in the same
projection/datum is not going to line
up if there is no .prj file
• Data of different scale, even if the
same projection and datum, may not
line up very well
64
Summary
• This subject area is the most
confusing and complex area of using
GIS.
• Take good notes and do your best to
understand it.
• At GIS conferences sessions on this
topic are always very crowded! That
tells you something!
65
Summary
• Geographic Coordinate Systems are based
on Spheroids (Datums, actually)
• Projected Coordinate Systems are used to
put geo data on flat maps
• There are many Projections
• More commonly, you will run into the class
of Projections called Coordinate Systems
(UTM, SP)
• Projected data is based on a datum and
data in different datums will not (usually)
line up!
66
Acronyms
• NAD – North American
datum
• GCS – Geographic
Coordinate System
• WGS – World Geodetic
System
• UTM – Universal
Transverse Mercator
• SP – State Plane
• GRS –Geodetic
Reference System
• DD – Decimal Degrees
• DMS – Degrees, minutes,
seconds
• HARN – High Accuracy
Reference Network
(State Level)
• NADCON – North
American Datum
Conversion
67
68