1 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?

2 2 Ways to Represent data On the spherical earth (globe) On flat maps

3 Syracuse W 43.07N  Where is it?  How do we locate it on earth?

4 Flat Map , 43.07

5 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!

6 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

7 Overview of what you need to know 1.Spherical earth (globe) a.Longitude, Latitude (X,Y) b.Spheroids c.Datums 2.Flat maps a.Projections b.Coordinate Systems UTM (Universal Transverse Mercator) SP (State Plane) 3.Definition and Conversion  lat, long (Y,X)

8 Coordinates on Earth North Pole South Pole Latitude Longitude Equator Meridians Parallels

9 Syracuse , 43.08

10 X, Y = Longitude, Latitude Lines of constant Longitude Lines of constant Latitude Equator Stretch the top Stretch the bottom

11 X, Y = Longitude, Latitude Lines of constant Longitude Lines of constant Latitude Equator 90E, 30N 90W, 30S +90, W76.15° N43.04°-76.12° 43.08°

12 The world in Geographic Coordinates Is Antarctica Really that big?

13 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

14 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.

15 Earth Earth Centered Spheroid Spheroid Best fit over the entire earth World geodetic system of ‘72 (WSG72) and of ’84 (WSG84) = NAD84

16 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

17 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

18 Earth Spheroids & Datums A spheroid can be moved mathematically to fit different parts of the earth… FIT Fit Spheroid They then become datums

19 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

20 NAD 83 Based on earth centered WGS 72 WGS 72 is mathematically moved to make it fit a specific location

21 Datum differences The change in datum can change your location measure Not your actual location! Redlands –NAD83 –117° 12' " (longitude) 34° 01' " (latitude) –NAD27 –117° 12' " (longitude) 34° 01' " (latitude) ~ 1.1 minutes long ~ 1.6 min lat

to -40 m

23 0 to 10 m

24 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

25 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

26 The Problem

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30 The Mercator Projection Making a Projection

31 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 longitude And Y = ln Tan (  /2 +  /4),  is latitude

32 Projections: Distortion In going from spherical coordinates (surface) to a flat surface THERE WILL BE DISTORTIONS in –Shape –Area –Distance –Direction

33 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

34 Summary of Projection Properties Key: = Yes  = Partly ProjectionType Con- formal Equal area Equidi stant True directi on Persp ective Comp romis e Straig ht rhumb s GlobeSphere  MercatorCylindrical  Transverse MercatorCylindrical  Robinson Pseudo-  cylindrical GnomonicAzimuthal  Azimuthal EqualidistantAzimuthal  Lambert Azimuthal Equal AreaAzimuthal  Albers Equal Area ConicConic  Lambert Conformal ConicConic  PolyonicConic 

35 Summary of Projection Properties Key: = Yes  = Partly ProjectionType Con- formal Equal area Equidi stant True directi on Persp ective Comp romis e Straig ht rhumb s GlobeSphere  MercatorCylindrical  Transverse MercatorCylindrical  Robinson Pseudo-  cylindrical GnomonicAzimuthal  Azimuthal EqualidistantAzimuthal  Lambert Azimuthal Equal AreaAzimuthal  Albers Equal Area ConicConic  Lambert Conformal ConicConic  PolyonicConic 

36 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

37 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

38 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!

39 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

40 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!

41 UTM Zones Most of NY is in UTM Zone 18

42 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

43 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 200,000m300,000m400,000m500,000m600,000m 700,000m800,000m 1 UTM ZONE OF 6 DEGREES OFFSET

44 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

45 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)

46 State Plane Zones NY West Zone 4851 NY Central Zone 4826 NY East Zone 4801 NY Long Island Zone 4876

47 State Plane Zones NY West Zone 4851 NY Central Zone 4826 NY East Zone 4801 NY Long Island Zone 4876 Transverse Mercator Lambert Conformal

48 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??

49 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…

50 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!

51 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!

52 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

53 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

54 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

55 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

56 How you convert Using ArcToolbox In Toolbox you can –a) create a.prj file or –b) change the data in the.prj file.

57 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", , ]], PRIMEM["Greenwich",0.0], UNIT["Degree", ]], PROJECTION["Transverse_Mercator"], PARAMETER["False_Easting", ], 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

58 The toolbox To Project a feature that already has a projection To Project a feature that does not have a projection

59 Change to State Plane Use Project tool 1 - Browse

60 Spatial Reference Properties

61 Add output System

62 Final Steps Add Datum Transformation

63 Last little booby trap Geographic SCALE

64 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

65 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!

66 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!

67 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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