1 Spheroids, datums, Projections, etc.

2

3 Syracuse W 43.07N  How do we locate Syracuse on earth? degrees west of meridian through Greenwich, England degrees N of the equator

4 Flat Map , 43.07

5 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!

6 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)

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

8 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°

9 The world in Geographic Coordinates Is Antarctica Really that big? Remember: all non- global maps have some kind of distortion

10 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

11 Earth Earth Centered Spheroid Spheroid Best fit over the entire earth World geodetic system of ‘72 (WSG72) and of ’84 (WSG84) = NAD83

12 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

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

14 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

15 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 = ~185 meters

to -40 m

17 0 to 10 m

18 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

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

20 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

21 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 

22 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 

23 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)

24 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

25 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

26 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 of true scale. This occurs about 180 kilometers east and west of the central meridian.

27 UTM Zones Most of NY is in UTM Zone 18

28 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!

29 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

30 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 OFFSET - 200K M 1 UTM ZONE OF 6 DEGREES ~668K m

31 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

32 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)

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

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

35 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

36 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??

37 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…

38 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!

39 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!

40 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

41 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

42 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] )

43 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

44 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.

45 And.. How this is done, in detail, is covered in Thursday's session And you will “Exercise” this skill in Exercise 4

46 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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