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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?

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2 Ways to Represent data

• On the spherical earth (globe)

• On flat maps

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Syracuse

-76.19 W 43.07N

Where is it?How do we locate it on earth?

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Flat Map

-76.19, 43.07

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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!

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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

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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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Coordinates on EarthNorth Pole

South Pole

Latitude

Longitude

Equator

Meridians

Parallels

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Syracuse

-76.12, 43.08

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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?

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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 these

and each has its own properties

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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.

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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) = NAD84

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Recent Spheroids

• Clark 1866 not earth centered• WGS 1966• WGS 1972 TBE• WGS 1972• WGS 1982• WGS 1984 (= GRS 1980)

WGS = World Geodetic System

GRS = Geodetic Reference System

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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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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

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NAD 83

• Based on earth centered WGS 72• WGS 72 is mathematically moved

to make it fit a specific location

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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

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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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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

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The Problem

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The Mercator Projection Making a Projection

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Mercator

• The equations for mapping objects (math term here) on a sphere onto a flat paper are, for Mercator, surprisingly simple:X =, X is Mercator value, is longitudeAnd

Y = ln Tan ( /2 + /4), is latitude

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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. maps 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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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

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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 coordinated system• The State Plane coordinate system

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UTM Coordinate Systems

• 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

Prime MeridianErrors are Zero!

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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

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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!

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UTM Zones

Most of NY is in UTM Zone 18

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UTM Coordinate

Easting

Northing

• The units in UTM are usually Meters

• You need to specify the zone

• Example: Location of CCC 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

1 UTM ZONE OF 6 DEGREES

OFFSET

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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 and SPC. • States running N-S (VT) are in

Transverse Mercator• States running E-W (TN) are in Lambert

Conformal

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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)

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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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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??

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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/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

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.• 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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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

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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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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

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How you convert• Using ArcToolbox • In Toolbox you can

– a) create a .prj file or– b) change the data in the .prj file.

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The 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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The toolboxTo Project a feature that

already has a projection

To Project a feature that does

not have a projection

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Change to State Plane

• Use Project tool 1 - Browse

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Spatial Reference Properties

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Add output System

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Final Steps

Add Datum Transformation

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Last little booby trap

GeographiGeographic SCALEc SCALE

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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

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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!

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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!

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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

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