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Spheroids, datums, Projections, etc.

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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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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. Spheroidsc. Datums

2. Flat mapsa. Projectionsb. Coordinate Systems

• UTM (Universal Transverse Mercator)• SP (State Plane)

3. Definition and Conversion

lat, long (Y,X)

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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?

Remember: all non-global 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

Earth Centered Spheroid

Spheroid

Best fit over the entire earth

World geodetic system of ‘72 (WSG72) and of ’84 (WSG84) = NAD83

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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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Earth

Spheroids & Datums• A spheroid can be moved mathematically to

fit different parts of the earth…

FITFit

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. Spheroidsc. Datums

2. Flat mapsa. Projectionsb. 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: = Yes = Partly

Projection TypeCon-

formalEqual area

Equidistant

True directi

on

Perspective

Compromis

e

Straight

rhumbs

Globe Sphere

Mercator Cylindrical

Transverse Mercator Cylindrical

Robinson

Pseudo-

cylindrical

Gnomonic Azimuthal

Azimuthal Equalidistant Azimuthal

Lambert Azimuthal Equal Area Azimuthal

Albers Equal Area Conic Conic

Lambert Conformal Conic Conic

Polyonic Conic

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Summary of Projection Properties

Key: = Yes = Partly

Projection TypeCon-

formalEqual area

Equidistant

True directi

on

Perspective

Compromis

e

Straight

rhumbs

Globe Sphere

Mercator Cylindrical

Transverse Mercator Cylindrical

Robinson

Pseudo-

cylindrical

Gnomonic Azimuthal

Azimuthal Equalidistant Azimuthal

Lambert Azimuthal Equal Area Azimuthal

Albers Equal Area Conic Conic

Lambert Conformal Conic Conic

Polyonic Conic

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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 PaperTube is nowHorizontal sois tangent to theearth along its prime meridian andand passes throughthe Poles

Central MeridianThere are 60

zonesEach 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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Error and Scalea. 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. This occurs about 180 kilometers east and west of the central meridian.

http://www.uwgb.edu/DutchS/FieldMethods/UTMSystem.htm

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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

Easting

Northing

• The units in UTM are usually Meters

• You need to specify the zone

• Example: Location of Auburn is: 373,800 Meters E, 4,756,000 Meters N, Zone 18, N

O(~4,000,000) m in NY

O(~100,000) m in NY

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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

200,

000m

300,

000m

400,

000m

500,

000m

600,

000m

700,

000m

800,

000m

OFFSET - 200K M

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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State Plane ZonesNY West

Zone 4851

NY CentralZone 4826

NY EastZone 4801

NY Long IslandZone 4876

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State Plane ZonesNY West

Zone 4851

NY CentralZone 4826

NY EastZone 4801

NY Long IslandZone 4876

Transverse

Mercator

Lambert Conform

al

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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

degrees N!

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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

degrees N!

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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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PRJ?...

• On_hydro_utm_83

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]]

.prj

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Overview

1. Spherical earth (globe)a. Longitude, Latitude (X,Y)b. Spheroidsc. Datums

2. Flat mapsa. Projectionsb. 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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