Coordinate systems, Projections and Geo-referencing Geog 413 John Masich January 14, 2013

Agenda Questions from last week Modeling the Earth Projections Geo-referencing Article Review

Questions from last week

A quick video

Modeling the Earth Geoid - surface at mean sea level and is used for measuring heights represented on maps’ Ellipsoid (Spheroid) – Measure location (latitude and longitude) of points of interest. Many different ellipsoids have been defined for the world.

Modeling the Earth The earth is not a perfect sphere (don’t tell my globe that!) Datum- a fixed, three-dimensional surface, an oblate spheroid, that is approximately the size and shape of the Earth. From this surface, Latitude, Longitude and Elevation are computed. Reference point

Terrain – Represents the “actual surface of the Earth. The relationship between; The ellipsoid/spheriod The Geoid Mean Sea Level The Terrain Is what Geodesists study to determine measurements on the earth’s surface. This relationship varies ...

Back to the datum Each country or region will develop their own datum. NAD 83 NAD 27

Modeling the Earth – Geoid to Map

Projections In order to display our data in the most representative manner, we project it from the GCS to some form of projection. Projecting from a 3d model to 2d plane results in distortion Area Shape Distance Direction We are trying to represent this amount of the earth on this amount of map space.

Classifications of Map Projections Map projections can be described in terms of their class (cylindrical, conical or azimuthal), point of secancy (tangent or secant), aspect (normal, transverse or oblique), and distortion property (equivalent, equidistant or conformal).

Classes of Projections

Classes of Projections Cylindrical Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant cylinder. The cylinder is then sliced from top to bottom and flattened into a plane. Conic Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant cone that is wrapped around the globe in the manner of a party hat. The cone is then sliced from the apex (top) to the bottom, and flattened into a plane. Planer Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant plane. Because its directions are often true, the planar projection is also known as an azimuthal or zenithal projection.

Point of Secancy (Tangent of Secant) A projection whose surface touches the globe's without piercing it. A tangent planar projection touches the globe at one point, while tangent conic and cylindrical projections touch the globe along a line. At the point or line of tangency, the projection is free from distortion. A projection whose surface intersects the surface of a globe. A secant conic or cylindrical projection, for example, is recessed into a globe, intersecting it at two circles. At the lines of intersection, the projection is free from distortion.

Aspect Normal Traverse Oblique

Classification of map projections Distortion Properties Equal area projections preserve the area of features (popular in GIS) Conformal projections preserve the shape of small features (good for presentations) , and show local directions (bearings) correctly (useful for coastal navigation!) Equidistant projections preserve distances (scale) to places from one point, or along a one or more lines Scale can never be correct everywhere on any map True direction projections preserve bearings (azimuths) either locally (in which case they are also conformal) or from center of map.

Equal Area Projections Albers Conic Lambert cylindrical Equal Area Projections Hammer projection

Conformal Projection Mercator Lambert Conformal Conic

Equidistant Projections Sinusoidal Equi-rectangular

True direction Lamberts Azimuthal

Some interesting map projection links Progonos Atlas of Canada Radical Cartography Kartoweb

How do you determine what projection to use How will the projection of your project and data be determined Data Methods Input\output Manage your data in a manner that is the most efficient for you Considerations Is there a field component What do my field staff use to collect data How challenging will the conversion process be? Can I automate my processes.

Geo-referencing

Georeferencing How do we make sure all our data layers line up Georeferencing How do we make sure all our data layers line up ? Georeferencing: Aligning geographic data to a known coordinate system so it can be viewed, queried, and analyzed with other geographic data. Georeferencing may involve shifting, rotating, scaling, skewing, and in some cases warping, rubber sheeting, or orthorectifying the data. Registration:  lining up layers with each other Rectification: The process by which the geometry of an image is made planimetric (flattened)

If the world was flat, we could use a simple coordinate system with 0,0 in the bottom left corner (or A1) … but alas it isn’t … The edge of the world …

GCS Uses a 3d surface to define locations on the earth This is great if we are using a globe, but impractical Detail Analysis Cumbersome Negative values Harvard School - Projection Fundamentals What are geographic coordinate systems? (ESRI)

Geographic referencing 180 E/W PG: 54N, 123W [54, -123] Geographic referencing is suitable for storing global datasets, but involves negative values south and west of 0, 0 0, 0

Geographic referencing Geographic is not decimal, it is sexagesimal 1 degree = 60 minutes 1 minute = 60 seconds Decimal degrees: 58° 30’ = 58.5 30/60 = 0.5 Decimal degrees: 58° 36’ = 58.6 36/60 = 0.6 Decimal degrees: 58°36’36” = 58.61 36/(60*60) = 0.01 View decimal degrees on pgmap website (use Internet Explorer / Active X)

The main problem with geographic referencing (for GIS data display and analysis) - 1 degree longitude varies from 0 - 111 km (the system is not ‘rectangular’ )

Local example from the phone book 2007 (OK) –scale is consistent 2008: horizontal scale is almost double Local example from the phone book

60º 55.80 Length of One Degree of Longitude Length of a Degree of Latitude Latitude  Kilometres  Miles  Miles 0º  111.32  69.17  0º 110.57 68.71  10º  109.64  68.13  10º 110.61 68.73 20º  104.65  65.03  20º 110.70 68.79 30º  96.49  59.95  30º 110.85 68.88 40º  85.39  53.06  40º 111.04 68.99 50º  71.70  44.55  50º 111.23 69.12 60º  55.80  34.67  60º 111.41 69.23 70º  38.19  23.73  70º 111.56 69.32 80º  19.39  12.05  80º 111.66 69.38 90º  0.00  90º 111.69 69.40 1° Longitude is half the distance at 60N 1° Latitude = ~ 111km anywhere

Earth is not a perfect sphere, it is ellipsoidal. earth is the 'Geoid' Earth is not a perfect sphere, it is ellipsoidal .. earth is the 'Geoid'.  The difference in the major and minor axes has been estimated since ~1830 The latest should be the most accurate, using satellite technology. The difference representing the amount of 'polar flattening' is about 1/300. Estimated ellipsoids   Equatorial Polar Name Date Radius a (metres) Radius b (metres) Flattening WGS 84 1984 6,378,137 6,356,752 1/298 International 1924 6,378,388 6,356,912 1/297 Clarke 1866 6,378,206 6,356,584 1/295 Everest 1830 6,377,276 6,356,075 1/301 Each ellipsoid has a 'Datum'  =  "a set of values that serve as a base for mapping“. For Canadian / North America, we use:     a. North American Datum, NAD27 (1927) based on Clarke 1866     b. North American Datum, NAD 83 (1983) based on WGS 1984 NAD27 was the datum for mapping over most of the 20th century NAD83 is the datum for contemporary GIS / mapping

In BC we use … UTM (Universal Transverse Mercator) BC Albers

Universal Transverse Mercator (UTM) System this bit is hard so pay attention … The world is divided into 60 x 6 º longitude strips - the width of each zone thus varies from 6 x 111km = 666 km at the equator to < 80 km at 84 ° N They are numbered 1 - 60 from 180 º W to 180 º E 180W 180E

Canada: UTM zones

Coordinates repeat for each zone UTM coordinates – in metres - this is the hardest part … Northings (N): from the Equator – increase to the north (to 10,000,000) Eastings (E) – based on the zone Central Meridian at 500,000 Coordinates repeat for each zone In BC, eastings are usually between 300,000-700,000

UTM zone overlap: Topographic map with Geographic and UTM referencing UTM zone Eastings coordinates in BC are generally between 300,000 – 700,000

UTM coordinates may make more sense here : PGMAP: http://pgmap.princegeorge.ca/ (use Internet Explorer / Active X) The UTM system works well for a local area – coordinates in metres

BC: UTM zones How do we deal with multiple UTM zones: Eastings coordinates switch from ~700,000 at the east edge of one zone to ~300,000 at the west edge of the next (= same place)

Albers (conic) projection e.g. Yukon Albers: http://www.environmentyukon.gov.yk.ca/geomatics/techweb/yt-albers-projection.html

BC Albers projection Central meridian: 126 W First Standard Parallel: 50N Second Standard Parallel: 58:30N Latitude of projection origin 45N False northing 0 False easting 1000000 (1million m)

Summary: BC mapping coordinates BC geomatics industry ‘recognises’: 1. Geographic – latitude / longitude – for data storage 2. Universal Transverse Mercator (UTM): zones 7-11 - local / regional 3. BC Albers - for provincial data View all 3 on: http://www.lrdw.ca (imap) (use Internet Explorer-IE) [sometimes!] View Geographic and Albers on http://www.mapplace.ca (use IE / Active X)

Multiple coordinate systems Georeferenced data can be recognized by the coordinates e.g. Prince George Geographic: 53°55′01″N 122°44′58″W UTM zone 10: 512,000 5,972,000 BC Albers: 1,200,000 1000,000 GIS software today can overlay these by projecting ‘on the fly’ Where these would plot if not properly defined: y To be able to do analysis, layers MUST be re-projected into the same projection and datum e.g. UTM -> Albers NAD 27 -> NAD83 UTM A G x