Maps, Coordinate Systems and GIS -...

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Geodesy Geodesy Map Projections Map Projections Geodesy Geodesy - - the shape of the earth and definition the shape of the earth and definition of earth of earth datums datums Map Projection Map Projection - - the transformation of a curved the transformation of a curved earth to a flat map earth to a flat map Coordinate systems Coordinate systems - - (x,y) coordinate systems (x,y) coordinate systems for map data for map data

Transcript of Maps, Coordinate Systems and GIS -...

GeodesyGeodesy

Map ProjectionsMap Projections

Geodesy Geodesy -- the shape of the earth and definition the shape of the earth and definition of earth of earth datumsdatumsMap Projection Map Projection -- the transformation of a curved the transformation of a curved earth to a flat mapearth to a flat mapCoordinate systems Coordinate systems -- (x,y) coordinate systems (x,y) coordinate systems for map datafor map data

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Determination the Earth’s size (geometry), shape (gravity) and figure (surface).

Determination of the Earth’s motions (in space: polar motion, variations in rotation rate), its deformations (e.g., plate tectonic motion, plate boundary deformation, volcanoes, land subsidence), and gravity variations.

Definition and maintenance of terrestrial reference frames (datums) for precise 3D positioning, thus providing the backbone for mapping, surveying, and GIS.

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Triangulation from Dunkirk to Barcelona

Jean Baptiste Delambre measuredthe stations between Dunkirk and Rodez, France. The southern segment,from Rodez to Barcelona, was measured by Pierre Méchain. They began theproject in 1792.

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Spherical EarthSpherical Earth

Authalic SphereAuthalic SphereBasic figure for mappingBasic figure for mappingRadius = 6371 kmRadius = 6371 kmMeridians from pole to Meridians from pole to polepoleEquator and small circles Equator and small circles perpendicular to the perpendicular to the meridiansmeridiansGeographic grid of Geographic grid of meridians and small meridians and small circlescircles

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PrimePrime meridian meridian –– Greenwich from 1884Greenwich from 1884

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Latitude and Longitude on a SphereLatitude and Longitude on a Sphere

Meridian of longitude

Parallel of latitude

ϕ

λ

X

Y

N

E

ϕ

Z

W

ϕ=0-90°S

P

OR

λ=0-180°E

ϕ=0-90°N

Greenwichmeridian

λ=0°

Equator =0°

•λ=0-180°W

λ - Geographic longitudeϕ - Geographic latitude

R - Mean earth radius

O - Geocenter

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Spherical Earth ApproximationSpherical Earth Approximation

Y: Right-handed

Z = Pole of Rotation

X = Greenwich Meridian

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What kind of ellipsoid?What kind of ellipsoid?

Cassini's report to the Academy, that the length of a degree seemed to get shorter towards the pole, generated an intense controversy between French and English scientists and resulting in arc measurement expeditions to Lapland (1736/37, average latitude 66°20’) and Peru/Ecuador (1739-1743, (average latitude 1° 31' S).

Oblate? Prolate?

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French triangulationin Lapland

1736

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Ellipsoid or SpheroidEllipsoid or SpheroidRotate an ellipse around an axisRotate an ellipse around an axis

O

X

Z

Ya ab

Rotational axis

The earth is flattened slightlyThe earth is flattened slightlyat the poles and bulges at the poles and bulges somewhat at the equatorsomewhat at the equator

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Definition of Latitude,Definition of Latitude, φφ

(1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn(2) Define the line pq through S and normal to thetangent plane(3) Angle pqr which this line makes with the equatorialplane is the latitude φ, of point S

O φ

Sm

nq

p

r

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By the early 19th century, scientists like Laplace (1802), Gauss (1828), Bessel (1837) recognized that the assumption of an ellipsoidal earth model was untenable under sufficiently high observational accuracy. One could no longer ignore the deviation of the physical plumb line, to which measurements refer, from the ellipsoidal normal.

CM

CE

Geoid – Figure of the Earth

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Different ellipsoids for different areason the globe

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Standard EllipsoidsStandard Ellipsoids

Ellipsoid Major axis, a (m)

Minor axis, b (m)

Flattening ratio, f

Airy (1830)

6377,563 6356,257 1/299,32

Clarke (1866)

6,378,206 6,356,584 1/294.98

WGS 84 (1984)

6,378,137 6,356,752 1/298.57

Ref: Snyder, Map Projections, A working manual, USGSProfessional Paper 1395, p.12

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Position shifts from datum differences

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What is a Projection?What is a Projection?If you could project light from a source through the If you could project light from a source through the earth's surface onto a twoearth's surface onto a two--dimensional surface, you dimensional surface, you could then trace the shapes of the surface features could then trace the shapes of the surface features onto the twoonto the two--dimensional surface. dimensional surface. This twoThis two--dimensional surface would be the basis for dimensional surface would be the basis for your map.your map.

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Projections always distort the mapProjections always distort the map

Rectangularform

Sides of different lenght

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MapMap projectionsprojections

The The characteristicscharacteristics normallynormally consideredconsidered in in choosingchoosing a a mapmap projectionprojection are as are as followsfollows::

1. Area 1. Area -- equalequal--areaarea 2. 2. ShapeShape –– conformalconformal

3. 3. ScaleScale –– oneone or or moremore lineslines on the on the mapmap alongalong whichwhich thethescalescale remainsremains truetrue

4. 4. DirectionDirection –– conformalconformal, , azimuthalazimuthal

5. Special 5. Special –– gnomonicgnomonic 6. 6. MethodMethod of of constructionconstruction

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Earth to Globe to MapEarth to Globe to Map

Representative Fraction

Globe distanceEarth distance

=

Map Scale: Map Projection:

Scale Factor

Map distanceGlobe distance

(e.g. 0.9996)

=

(e.g. 1:50,000)

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Types of ProjectionsTypes of Projections

ConicConic (Albers Equal Area, Lambert (Albers Equal Area, Lambert Conformal Conic) Conformal Conic) -- good for Eastgood for East--West West land areasland areasCylindricalCylindrical (Transverse Mercator) (Transverse Mercator) -- good good for Northfor North--South land areasSouth land areasAzimuthalAzimuthal (Lambert (Lambert AzimuthalAzimuthal Equal Area) Equal Area) -- good for global viewsgood for global views

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Conic ProjectionsConic Projections(Albers, Lambert)(Albers, Lambert)

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Cylindrical ProjectionsCylindrical Projections(Mercator)(Mercator)

Transverse

Oblique

Normal

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AzimuthalAzimuthal(Lambert)(Lambert)

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Projection onto a Flat SurfaceProjection onto a Flat Surface

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Lambert equal-area projection

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Conic equal-area projection

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MercatorMercator (Normal (Normal cylindriccylindric))

Conformal

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Great circle navigation

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Equal-area

Mollweide

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South AmericaSouth America

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Types of Coordinate SystemsTypes of Coordinate Systems

(1) Global Cartesian(1) Global Cartesian coordinates (X,Y,Z) coordinates (X,Y,Z) for the whole earthfor the whole earth(2) Geographic(2) Geographic coordinates (coordinates (φ, λφ, λ, z) , z) (3) Projected(3) Projected coordinates (x, y, z) on a coordinates (x, y, z) on a local area of the earthlocal area of the earth’’s surfaces surfaceThe zThe z--coordinate in (1) and (3) is coordinate in (1) and (3) is defined defined geometricallygeometrically; in (2) the z; in (2) the z--coordinate is defined coordinate is defined gravitationallygravitationally

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Global CartesianGlobal Cartesian Coordinates Coordinates (X,Y,Z)(X,Y,Z)

O

X

Z

Y

GreenwichMeridian

Equator

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Geographic CoordinatesGeographic Coordinates ((φ, λφ, λ, z), z)

Latitude (Latitude (φφ) and Longitude () and Longitude (λλ) defined ) defined using an using an ellipsoidellipsoid, an ellipse rotated about , an ellipse rotated about an axisan axisElevation (z) defined using Elevation (z) defined using geoidgeoid, a , a surface of constant gravitational potentialsurface of constant gravitational potentialEarth Earth datumsdatums define standard values of define standard values of the ellipsoid and the ellipsoid and geoidgeoid

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CoordinateCoordinate SystemSystem

(φo,λo)(xo,yo)

X

Y

Origin

A planar coordinate system is defined by a pairof orthogonal (x,y) axes drawn through an origin

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Cartesian Coordinate SystemCartesian Coordinate System

Planar coordinate systems are based on Planar coordinate systems are based on Cartesian coordinates.Cartesian coordinates.

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Any projected data that you add to Any projected data that you add to ArcMapArcMap, or that , or that you project within you project within ArcMapArcMap, is associated with a , is associated with a projected coordinate system (PCS) in addition to its projected coordinate system (PCS) in addition to its underlying Geographic Coordinate System (GCS). underlying Geographic Coordinate System (GCS).

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Universal Transverse MercatorUniversal Transverse Mercator(UTM)(UTM)

Divide the world into sixty vertical strips, each spanning Divide the world into sixty vertical strips, each spanning six degrees of longitude. Apply a custom Transverse six degrees of longitude. Apply a custom Transverse Mercator projection to each strip and use false Mercator projection to each strip and use false eastingseastingsand and northingsnorthings to make all projected coordinates positive. to make all projected coordinates positive.

Data that crosses zones is subject to distortion.Data that crosses zones is subject to distortion.

A comprehensive system for identifying locations and making measurements over most of the earth's surface.

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UTM-zones

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UTM-zones

Sweden lies in 6zones

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UPS – (Universal Polar Stereographic grid)

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ArcGISArcGIS Reference FramesReference FramesDefined for a Defined for a feature feature datasetdataset in in ArcCatalogArcCatalogCoordinate SystemCoordinate System

ProjectedProjectedGeographicGeographic

X/Y DomainX/Y DomainZ DomainZ Domain

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Coordinate SystemsCoordinate Systems

GeographicGeographiccoordinates (decimal coordinates (decimal degrees)degrees)ProjectedProjected coordinates coordinates (length units, ft or (length units, ft or meters)meters)

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Datum Transformations7-parameter transformation

Geodetic tools available at: http://www.ngs.noaa.gov/TOOLS/

NAD27 to NAD 83

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Summary ConceptsSummary Concepts

Two basic Two basic locationallocational systems: systems: geometricgeometricor Cartesian (x, y, z) and or Cartesian (x, y, z) and geographicgeographic or or gravitational (gravitational (φ, λφ, λ, z), z)Mean sea level surface or Mean sea level surface or geoidgeoid is is approximated by an ellipsoid to define an approximated by an ellipsoid to define an earth earth datumdatum which gives (which gives (φ, λ) φ, λ) and and distance above distance above geoidgeoid gives (z)gives (z)