Map Projections and Datums of the Atlantic Provinces Making it Fit - or - Having a Fit by M. Donnelly

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Map Projections and Datumsof the Atlantic
ProvincesMaking it Fit - or - Having a Fit by
M. Donnelly D. Raymondrevised - 2002With
selected slides from Vic Dohar, Geoscience
Information Division, Cartography Section,
Natural Resources Canada, Ottawa
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(No Transcript)
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Map Projection Basics

• Map projections are mathematical formulas for
  transforming coordinates from a three-dimensional
  space to a two-dimensional space.
• The two-dimensional space is referenced in a
  Cartesian coordinate system, where feature
  coordinates are represented in distances measured
  from the X and Y axis. The origin has an X and Y
  value of 0, and coordinates may be represented in
  either positive or negative values.

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Map Projection Basics

• The purpose of a map projection is to represent
  features on the Earths surface as accurately as
  possible in relationship to the spatial
  properties of shape, area, scale and direction.
• Map projections that preserve these properties
  are known as conformal, equal-area, equidistant
  and azimuthal respectively.
• Some level of distortion is always present in a
  map projection. By definition, they are a
  compromise of error and distortion.

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Projection Properties

• SHAPE Conformal maps preserve local shape,
  
• AREA Equal-area or equivalent maps retain
  all areas at the same scale
• SCALE Equidistant maps maintain certain
  distances
• DIRECTION Azimuthal maps express certain
  accurate directions.

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SHAPE - Conformal
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AREA - Equal-Area
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SCALE - Equidistant
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AZIMUTHAL - Direction
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Map Projection Basics

• The categories are
• 1) Cylindrical
• 2) Conic
• 3) Planar or azimuthal
• 4) Mathematical
• can be constructed graphically - from a sphere

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Map Projection Basics

• Cylindrical projections are conformal.
• UTM and MTM are examples of cylindrical
• Projections.

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Map Projection Basics

• Conic projections can be either conformal,
  equal-area or equidistant, depending on the
  complexity.

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Map Projection Basics

• Planar or Azimuthal projections display
  true-direction.

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Source of ProjectionORTHOGRAPHIC
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Source of ProjectionSTEREOGRAPHIC
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Source of ProjectionGNOMONIC
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Map Projection Basics

• The three main projections may intersect and pass
  through the earth.
• These are called secant projections
• 1) Secant Cylindrical 2) Secant Conic 3)
  Secant Planar or azimuthal

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Map Projection Basics
Secant Cylindrical projections have 2 lines of
intersection
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Map Projection Basics
Secant Conic projections have 2 standard
parallels
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Map Projection Basics

• Secant Planar or Azimuthal projections have
• a radius of intersection from the origin.

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Projections

• Conformal Transverse Mercator, Stereographic,
• Lambert Conformal Conic
• Equal-Area Albers
• Equidistant Equidistant Conic (Simple Conic)
• Azimuthal Stereographic

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Nova Scotia Projections

• Commonly used projections for Nova Scotia
• 1) UTM - Universal Transverse Mercator
• 125000 (old) 150000 1250000 1500000
• 2) MTM - Modified Transverse Mercator
• 11000 12000 15000 110000
• 3) Lambert - Lambert Conformal Conic
• 12000000

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Universal Transverse Mercator

• Nova Scotia 6º UTM
• The UTM is a world wide military mapping
  projection that divides the Earth into 60 zones
  of 6 degrees of longitude.
• UTM is a secant cylindrical projection.

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Universal Transverse Mercator
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Northings and Eastings

• The scale factors in each UTM zone varies from
  0.999600 at the central meridian values are
  greater than 1.0 on east and west outer portions
  of the zones.

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Universal Transverse Mercator
Across Nova Scotia there are 3 UTM zones numbered
19, 20, and 21 from West to East. Only small
amounts of Nova Scotia fall within zones 19 and
21. Therefore it is reasonable to push all of
Nova Scotia into ZONE 20 with tolerable scale
error.
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Modified Transverse Mercator

• Nova Scotia 3º Modified Transverse Mercator
• (3º MTM)
• Provincial base mapping and legal surveys are
  referenced to the 3º MTM projection.
• The scale factors in each MTM zone varies from
  0.999900 at the central meridian values greater
  than 1.0 on east and west outer portions of the
  zones.

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Modified Transverse Mercator

• 3 wide MTM Zones in Nova Scotia

Zone 5 Zone 4
- 64.5 - 61.5
Across Nova Scotia there are 2 zones numbered 4
and 5 from East to West. False Easting for zone
4 is 4,500,000. False Easting for zone 5 is
5,500,000.
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Newfoundland Labrador 3MTM
Note that Zone 3 is calculated with the
Stephenville Shift, CM 5830, to accommodate
the community of Stephenville. False Easting for
each Zone is 304800m.
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New Brunswick PEIOblique Stereographic Double
Projection

• This is a conformal projection selected to
  provide slightly higher accuracy than other
  solutions (i.e. MTM)
• Reasonable distribution of error
• Single zone solution
• Secant Azimuthal

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New Brunswick PEIOblique Stereographic Double
Projection
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New Brunswick PEIOblique Stereographic Double
Projection
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New Brunswick PEIOblique Stereographic Double
Projection
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New Brunswick PEIOblique Stereographic Double
Projection
New Brunswick Origin 4630 N 6630 W False
Northing 800000mN False Easting 300000mE Scale
at centre of projection 0.999912 Prince Edward
Island Origin 4715 N 6300 W False
Northing 400000mN False Easting 700000mE Scale
at centre of projection 0.999912
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Datum Basics

• A datum is a set of parameters defining a
  coordinate system, and a set of control points
  whose geometric relationships are known, either
  through measurement or calculation. All datums
  are based upon an ellipsoid (or spheroid), which
  approximates the shape of the Earth.
• Required for accurate mapping at scales larger
  than 1500,000 (local maps)
• Smaller scale maps are derived from the Sphere

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Spheroid Definition

• The size of a circle is defined by its radius.
  The size and shape of an ellipse is defined by
  two different radii, a semi-major and semi-minor
  axis. Just as rotating a circle about an axis
  defined by its diameter will create a sphere,
  rotating an ellipse about its axis will produce
  an ellipsoid. An ellipsoid that approximates a
  sphere is called a spheroid. These two terms are
  used interchangeably in the literature, despite
  their technical differences.
• An ellipsoid used to derive coordinates for
  mapping purposes is sometimes called a reference
  ellipsoid.

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The Reference Ellipsoid
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Latitude Longitude Shifts
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Atlantic Provinces

• Datums used almost exclusively in Atlantic
  Canada
• 1) North American Datum of 1927 (NAD27)
• 2) Average Terrestrial System of 1977
  (ATS77)
• 3) North American Datum of 1983 (NAD83)

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North American Datum 1927

• The North American Datum of 1927 uses the Clarke
  spheroid of 1866 to represent the shape of the
  Earth. The origin of this datum is a point on the
  Earth - Meades Ranch, Kansas. Many NAD27 control
  points were calculated from observations taken
  during the 1800s. These calculations were done
  manually and in sections over many years,
  therefore errors varied from station to station
  and were cumulative.

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Local Datum (NAD 27)
North American Datum 1927 (NAD27) Reference point
at Meades Ranch, Kansas
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Average Terrestrial System of 1977 (ATS77)

• The Maritime Provinces have used a DATUM
  definition called ATS77 or Average Terrestrial
  System. This definition was realized in 1979 and
  implemented by LRIS under the Council of Maritime
  Premiers. ATS77 was seen as an interim definition
  (pending release of NAD83) - much more accurate
  than NAD27.
• This local datum has been supported only by
  Canadian software vendors (CARIS/USL, NSGC and
  FME) until recently.
• The close resemblance to WGS - World Geodetic
  System 1972 (WGS72) permits spheroid substitution
  where sub-metre accuracy is not required over a
  large region.

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North American Datum 1983

• Many technological advances in surveying and
  geodesy have revealed weaknesses in the network
  of control points in NAD27, particularly when
  linking existing control with newly established
  surveys. NAD83 allows for a single datum or
  control network to cover North America
  consistently, by having the origin of the datum
  as the Earths center of mass (Geocentric).
• NAD83 is derived from both Earth and satellite
  observations and uses the GRS80 spheroid.

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Commonly used Spheroids/Ellipsoids

• Name Semi-major Semi-minor Assoc.
  Projection/Datum
• Sphere 6370997 6370997 Geographic
• Clarke 1866 6378206.4 6356583.8 UTM(NAD27)
• WGS72 1972 6378135 6356750.519915
• ATS77 1977 6378135.0 6356750.305 MTM(ATS77)
• GRS80 1980 6378137 6356752.3141 UTM(NAD83)
• WGS84 1984 6378137 6356752.31 GPS
• Notes
• Because WGS72 and ATS77 are almost identical we
  can obtain sub-metre accuracy using WGS72 for
  ATS77. In software packages not supporting
  ATS77, this is the only option.

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Earth-Centred Ellipsoid vs. Local Datum
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Know your data

• Understanding the coordinate system defined in
  NTS data is critical in geo-referencing and
  overlaying thematic data. Geomatics Canada
  includes a header file that defines the
  coordinate system of NTS data. The following
  example lists NTS data in NAD83 on the UTM
  projection
• The North American Datum of 1983 (NAD83) is used
  as the reference system for the planimetric
  coordinates (X,Y) of NTDB entities.
• The coordinates are projected on the Universal
  Transverse Mercator (UTM) grid, which is based on
  the GRS80 reference ellipsoid.
• Elevations are expressed in reference to mean sea
  level (Canadian Vertical Geodetic Datum).

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Datum Transformations

• Datum transformations are defined shifts in
  latitude and longitude values at specific points
  on the Earths surface. Transformations exist
  between NAD27, ATS77 and NAD83.
• CAUTION Significant errors can result when
  attempting to convert one datum to another if no
  official transformation exists between them.
  Even though your software will allow it, the
  results will be incorrect.

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Datum Transformations

• A datum transformation alters two things
• 1) The location of longitude and latitude
  lines,
• due to the change in reference ellipsoid
• 2) The shift in features due to different
  datums

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Datum Transformations
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Datum Transformations
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Datum Transformations

• The following diagrams display the datum
  transformation performed by Geomatics Canada on
  an NTS sheet from NAD27 to NAD83. These
  illustrations show why there will always be data
  that is missing or extending beyond the neatline
  of your map when performing datum transformations.

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Datum Transformations

• The NTS sheet in NAD27. Longitude and latitude
  lines are based on the Clarke 1866 spheroid and
  form the neatline of the map.

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Datum Transformations

• The NTS sheet with the datum transformation
  applied.

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Datum Transformations

• The NTS sheet in NAD83 with latitude and
  longitude lines based on GRS80 spheroid. These
  form the neatline for the NTS sheet in NAD83.

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Datum Transformations

• Areas in red are clipped and appended to
  adjoining sheets.

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Datum Transformations

• Areas in orange are appended from adjoining NTS
  sheets to complete NTS sheet in NAD83.

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Datum Transformations

• Actual neatline from 11D/12 (1996-UTM NAD83) with
  hydrography layer shown in blue

DX 9.51mm DY -3.31mm
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THANK YOU
Selected References 1989 - J.P. Snyder, Map
Projections - A Working Manual 1993 - J.P.
Snyder, Flattening the Earth 1950 - W.
Chamberlin, Round Earth on Flat Paper 1979 - P.
McDonnell, Jr., Introduction to Map
Projections 1976 - H. Roblin, Map Projections