Spheroids, datums,
Projections, etc.
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2
-76.19 degrees west
of meridian through
Greenwich, England
43.07 degrees N of
the equator
How do we locate Syracuse on earth?
3
Flat Map
-76.19,
43.07
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Coordinate Systems
• On the spherical earth (globe)
-Geographic Coordinate Systems are used
• On flat maps
-Projected Coordinate Systems are used
• The distinction between these is important!
• Geographical definitions of these do not
exactly match ESRI'S!
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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
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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
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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
8
The world in Geographic
Coordinates
Is
Antarctica
Really that
big?
Remember: all nonglobal maps have some
kind of distortion
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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 the earth’s
surface and each has its own
properties
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Earth Centered Spheroid
Best fit over
the entire earth
World geodetic system of
‘72 (WSG72) and of ’84
(WSG84) = NAD83
Earth
Spheroid
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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
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Spheroids & Datums
• A spheroid can be moved mathematically
to fit different parts of the earth…
Earth
Spheroid
They then become
datums
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The two common datumsNAD27
• North American Datum of 1927 – NAD27
– Point of perfect fit is Mead’s Ranch in Kansas
– Older data is often in NAD27
• North American Datum of 1983 –NAD83
– Based on earth centered WGS 72
– WGS72 is mathematically moved to make it
fit North America
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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 =
~185 meters
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-20 to -40 m
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0 to 10 m
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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
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Projections: Distortion
• In going from spherical coordinates
(surface) to a flat surface THERE
WILL BE DISTORTIONS in
–
–
–
–
Shape
Area
Distance
Direction
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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: If directions from a central
location to all other points are correct
then the map is Azmuthal
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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
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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
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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 coordinate system (UTM)
• The State Plane coordinate system
(SP)
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UTM Coordinate System
• 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
Central Meridian
There are 60 zones
Each zone is 6°
wide
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UTM coordinate system
• Is 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 tangent to the toilet
paper tube or where the tube intersects the
globe
• two ways to place the tube re earth’s surface
• The further away you are the more inaccurate
the data and the more scale changes
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http://www.uwgb.edu/DutchS/FieldMethods/UTMSystem.htm
Error and Scale
a. A cylinder touching the globe at the
central meridian lies entirely outside the
earth and areas away from the central
meridian project larger than on the globe.
b. A cylinder that touches the outer edges
of the zone lies entirely inside the earth
within the zone, and areas within the zone
project smaller than their true size on the
globe.
c. The scale is actually set to be the best
overall compromise. We not only want the
grid to be useful for specifying location,
but we want distances measured on the
grid to be as close as possible to distances
on the ground.
The scale along a central meridian is 0.9996 of true scale.
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This occurs about 180 kilometers east and west of the central meridian.
UTM Zones
Most of NY is in
UTM Zone 18
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Area of interest…
• 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 NY 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!
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UTM Coordinates
Northing
O(~4,000,000) m in NY
• The units in UTM are usually Meters
• You need to specify the zone
O(~100,000) m
in NY
Easting
• Example: Location of Auburn is:
373,800 Meters E, 4,756,000 Meters N,
Zone 18, N
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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
Central meridian
OFFSET - 200K M
800,000m
700,000m
600,000m
500,000m
400,000m
300,000m
200,000m
1 UTM ZONE OF 6 DEGREES ~668K m
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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, SPC or SP
• States running N-S (VT) are Transverse
Mercator
• States running E-W (TN) are Lambert
Conformal
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State Plane
• Each state has its own origins for its own
system
• States may have multiple zones in
different projections
– NY for example
• LI in Lambert conformal
• Rest of state in Transverse Mercator
• UNITS are usually feet BUT NOT
ALWAYS (another BOOBY TRAP)
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NY East
Zone 4801
NY Central
Zone 4826
State Plane Zones
NY West
Zone 4851
NY Long Island
Zone 4876
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NY East
Zone 4801
NY Central
Zone 4826
State Plane Zones
NY West
Zone 4851
Transverse
Mercator
Lambert
Conformal
NY Long Island
Zone 4876
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Trick
• Many times you will get data without any
metadata
• It is a very good chance it is either UTM
or SP
• In NY
– If Northing is ~4,000,000 meters its UTM
– If Northing is ~ 100,000 feet its SP
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ArcMap Problem (or NOT)
• ArcGIS projects on-the-fly
• By that, we mean that if you add a layer
that is NOT in the same Coordinate
System, Projection, or Datum as the
first layer added to the .mxd ArcMap
will project (verb) it to match the first
layer
• So what’s the problem??
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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…
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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 #$%@ is my data?”
• Bozo then zooms-to-layer – Hmm – it is there!
But not with the rest of my stuff
• Bozo then says “what are the coordinates?’
• Wow – 434,890 degrees East and 4,987,652
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degrees N!
Booby Trap
• Assume that Bozo loaded a layer that was in
Long, lat first (w/a .prj file)
• Now suppose Bozo loads a file that is in UTM
that does not have a .prj file.
• In this case ArcGIS says to itself “Well, Bozo
didn’t tell me different so this one must be DD
also”
• Bozo then says “Where the #$%@ 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
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degrees N!
Rule
• Always have a .prj file for any data
layers you are using.
• Use windows Explorer to verify since you
can have a metadata file (.xml) and no .prj
• 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
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• On_hydro_utm_83
.prj
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]]
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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 (projection [verb] )
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Conversion
• Every layer should have
a .prj file
• This file is what ArcGIS
reads to see what the
projection etc. of the
data is.
• It DOES NOT read the
.xml metadata file
For data in a GCB the projection is defined in the GDB
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How you convert
• Using ArcToolbox
• In Toolbox you can
– a) create a .prj file for a shape that does not have a
.prj file
– b) change the projection etc. of a layer and the
contents of its .prj file if the .prj exists
• Change the datum
• Change the coordinate system
• Change the projection
• Warning: sometime when you use Create
Spatial Reference tool the tool will insist that
a .prj already exists. Why? Who knows.
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And..
• How this is done, in detail, is covered
in Thursday's session
• And you will “Exercise” this skill in
Exercise 4
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Summary
• The process putting global data on a flat
map is full of booby traps!
• There are many (100s) of combinations of
projections, datums, etc.
• For most of us at ESF these two
Coordinate systems are the most common
– UTM
– SPCS
• And NAD27 AND NAD83 are the most
common Datums
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