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Map Projection & Coordinate Systems (review)
● Ellipsoids and Datums● Map Projections● Coordinate Systems● Philippine Coordinate System
Earth’s shape. Without water and clouds, it looks like a sloppily peeled potato. European Remote Sensing satellite, ERS1 from 780 Km.
Ojibwe (Native American) ca. 1820, drawn on birch bark (which accounts for its shape), shows the migration legend of the Ojibwe, from the creation of their people to their home .
Sketch maps on home ranges. Map was made by Chris (middle schooler), who rode bus #71.
The equatorial radius of the earth
3,443.609 – Airy (1830)
3,443.931 – Austrian Nat'lSouth Am. (1969)
3,443.957 – Clark 1866
3,443.980 – Clark (1850)
3,443.939 – Geodetic Reference System (1980)
3,444.054 – International (1924)
3,443.917 – World Geodetic System (1972)
Defense Mapping Agency, Hydrographic Center, American Practical Navigator (1977), Map Projections – A working Manual (1987)
The equatorial radius of the earth
3,443.609 – Airy (1830)
3,443.931 – Austrian Nat'lSouth Am. (1969)
3,443.957 – Clark 1866
3,443.980 – Clark (1850)
3,443.939 – Geodetic Reference System (1980)
3,444.054 – International (1924)
3,443.917 – World Geodetic System (1972)
Defense Mapping Agency, Hydrographic Center, American Practical Navigator (1977), Map Projections – A working Manual (1987)
• How well can we hit Minsk, USSR with a missile from Kansas (circa 1960)?
Minsk (Pulkovo, 1942) N 53° 52' 57.78" E 028° 01' 58.00"
Minsk (NAD27)
N 53° 53' 02.76" E 028° 01' 43.06”
∆ Latitude = ~ 5”, ∆ Longitude = ~15”Around 313 meters of error
These Coordinates Refer to the Same Bridge!
a) 37° 53.423’ N, 126° 43.990’ E, h = 23 mb) 37° 53.423’ N, 126° 43.990’ E, H = 0 mc) 37° 53’ 25.4” N, 126° 43’ 59.4” E, h = 23 md) 37° 53’ 25.4” N, 126° 43’ 59.4” E, H = 0 me) 37.89038° N, 126.73316° E, h = 23 mf) 37.89038° N, 126.73316° E, H = 0 mg) Zone 52, 300669 m E, 4196075 m N, h = 23 mh) Zone 52, 300669 m E, 4196075 m N, H = 0 mi) 52S CG 00668 96075, h = 23 mj) 52S CG 00668 96075, H = 0 mk) 3014326.6 m, 4039148.7 m, 3895863.0 ml) 37° 53.260’ N, 126° 44.116’ E, h ≅ H = 0 mm) 37° 53’ 15.6” N, 126° 44’ 6.9” E, h ≅ H = 0 mn) 37.88767° N, 126.73526° E, h ≅ H = 0 mo) Zone 52, 300872 m E, 4195348 m N, h ≅ H = 0 mp) 52S CS 00870 95350, h ≅ H = 0 mq) 3014213.2 m, 4038687.9 m, 3895223.3 m
Geoid Simplified Representation: Ellipsoid
Projection on developable surface
Planar map withcoordinate system
Shape of the Earth
● Approximated by a mathematical model represented by an ellipsoid (also called spheroid)
● A number of cartographic ellipsoids has been designed for certain portions of the Earth's surface
● Ellipsoids are usually sufficient for horizontal positioning; however, the geoid has to be used for exact elevation calculations
Ellipsoid
Semimajor Axis: a = 6371837 mSemiminor Axis: b = 6356752.3142Flattening Ratio: f=(ab)/a = 1/298.257223563
Rotate Ellipse in 3 Dimensions:
a
b
Ellipsoids in various countries
Ellipsoid Name Region of useAiry 1858 Great BritainAiry modified IrelandAustralian National AustraliaBessel 1841 Austria, Chile, Croatia, Czech Rep., Germany, Greece
Indonesia, Netherlands, Slovakia, Sweden, SwitzerlandBessel modified NorwayClark 1880 Africa, FranceClarke 1866 North America, PhilippinesEverest 1830 Afghanistan, Myanmar, India, Pakistan, Thailand,
other countries in southern AsiaGRS 1980 North America, worldwideHayford (Int'l) 1909 Beguim, Finland, italy, all countire using ED50 systemNew International 1967 many other countiresKrassovsky 1938 Albania, Poland, Romania, Russia and neighboring countiresWGS 1984 North America, worldwideWGS 1972 NASA satellite
Traditional Horizontal Datums
• Many nations established their own regional datum– Used various national standards and procedures– Different time frames– Calculated ellipsoids that fit well locally
• Established initial point location and orientation with astronomic observations
Result:Inconsistent Datums
The Traditional Approach
Traditional Horizontal DatumsLimitations to the Traditional Approach
NAD 27(Clarke Ellipsoid )
ED 50(International Ellipsoid)
Horizontal Datums
• Global replaces regional datums with a common, accurate standard
• One system for maps of the entire planet
Regional vs. Global Approach
DoD’s Satellite Derived Horizontal Datum
WGS 84
NIMA's World Geodetic System 1984
Z
Prime Meridian
X
Y
WGS 84 is an Earth Centred Earth Fixed
An ellipsoid is placed on top of the axis tocreate a geodeticfoundation for the variouscoordinate systems.
Vertical Datums
High Tide
Low Tide
Mean Sea Level
Like horizontal measurements, elevation only has meaning when referenced to some start point.
MSL Elevation
Mean sea level is the most common vertical datum.Mean sea level is the most common vertical datum.
A datum defines the initial point and reference
surface
A coordinate system determines how locations are referenced from
the datum
Map projection
● To transform a curved Earth surface into a plane
● Direct projection of a spherical object to a plane cannot be performed without distortion
The surface of the Earth tears when youpeel and flatten it. Peel a globe and youwill get globe gores.Most map projections stretch and distortthe earth to fill in the tears. The Mercatorprojection preserves angles, andso shapes in limited areas, but it greatlydistorts sizes. Look at the size of Greenlandon the globe compared to the Mercator.
Different projections are designed to minimize the distortion and preserve certain
properties:● conformal preserves angles (shapes for small
areas), used for navigation and most national grids systems
● equidistant preserves certain relative distances, used for measurement of length
● equivalent preserve area, used for measurement of areas
Geometry of a developable surfacecylindricaltransforms the spherical surface to a tangent or secant cylinder
conicuses the tangent or secant cone
azimuthaluse a tangent or secant plane (flat sheet)
Coordinate System
● Accurately identify a location on the Earth
● Defined by its origin (prime meridian, datum), coordinate axes (x, y, z) and untis (angle: degree, gon, radiant; length: meter, feet)
Observer’s
Meridian
PrimeMeridian
Latitude
Longitude
Y
Z
X
Coordinate systems commonly used in GIS
● geographic (global) coordinate system (latitudelongitude)
● planar (cartesian) georeferenced coordinate system (easting, northing, elevation) which includes projection from an allipsoid to a plane, with origin and axes tied to the Earth surface
● planar (cartesian) nongeoreferenced coordinate system, such as image coordinate system with origin and axes defined arbitrarily (e.g. image corner) without defining its position on the Earth.
Geographic coordinate system: latitudelongitude
● Most common for glaoal data coverage● Meridians are the longitude lines connecting the
north and south poles (0180 degrees east from the prime meridian and 0180 degrees west)
● 0 degrees longitude is the prime meridian and 1980 degrees longitude is the international date line
Geographic coordinate system: latitudelongitude
● Parallels are the latitude lines which form a around the Earth parallel with the equator (090 degrees north and 090 degrees south of the equator)
● Decimal values W and S as negative numbers, N and E as positive (1.167 deg, 38.0 deg)
● Sexasgesimal always use positive number together with N, S, E, W (1:10:00W, 38:00:00N)
Equator
Greenwich, UK
N
Prime Meridian
Latitude
Longitude
Universal Transverse Mercator
•Projecting the sphere onto a cylinder tangent to a central meridian.
•Distortion of scale, distance, direction and area increase away from the central meridian.
•If you rotate the cylinder every 6º of longitude you create the UTM projection.
•This projection is used on map scales of 1:500,000 and larger (TPCs, JOGs, and TLMs).
UTM Coordinates
• Flat Grid extending from 84N to 80S• Each zone is numbered Eastward starting at
177°W (6° wide from 180°W to 174°W)• Coordinates are read east then north• Many map products from
foreign countries use UTMs• Most often used on large
scale maps and charts e.g.TLM, JOGs, TPCs
Universal Transverse MercatorThe UTM graticule coverage
180o 180o0o
1 30 60
84o N
80o S
Equator
Each belt is 6O in longitude wide
0 meters N10,000,000m N
Universal Transverse Mercator Grid
2 3 4 5 6 7 8
2 3 4 5 6 7 8
2 3 4 5 6 7 8
2 3 4 5 6 7 8 2 3 4 5 6 7 8 16o
Zone 2 Zone 3156o
168o174o
Central Meridian
2 3 4 5 6 7 8
Zone 4162o
00oo
1,700,0001,700,0001,600,0001,600,0001,500,0001,500,0001,400,0001,400,0001,300,0001,300,0001,200,0001,200,0001,100,0001,100,0001,000,0001,000,000900,000900,000
800,000800,000700,000700,000600,000600,000500,000500,000
400,000400,000300,000300,000200,000200,000100,000100,000
0o
03 508,256mE 0,567,359mN
Sample CoordinatesECEF Cartesian Coordinates:
X= 1,109,928m Y= 4,860,097m Z= 3,965,162mGeographic:
38°.684N, 077°.150W 38° 41.145' N, 077° 08.135’ W
38° 41' 08.73" N, 077° 08’ 08.37" WGEOREF: GJNJ5141
UTM: 18 314,251mE 4,284,069mN
MGRS:18S UH 1425 8406 (New)
18S UT 1421 8385 (Old)
Luzon Datum of 1911
● Origin near San Andres Point on Marinduque island
● Ellipsoid of reference is the Clarke 1866● Controlled by 98 measure baselines, 52
observed azimuths, 49 latitude and longitude stations
● Philippine topographic maps uses the Luzon 1911 datum
Philippine Transverse Mercator
● Divided into 4 zones● False easting at the Central Meridian of 500 km● Scale Factor at Origin = 0.9995● False Northing Latitude of Origin = 04:00:00● Central Meridian of Zones II, III, IV = 121
degrees, 123 degrees, 125 degrees
Philippine Reference System of 1992 (PRS92)
● Determination of seven (70 BursaWolf transformation parameters detween Luzon Datum of 1911 and WGS 84
● So far no accuracy statesments were published● It is still the original Luzon Datum of 1911 with
published transformation parameters frpm WGS84 datum
Datums, Projections, & Coordinates Review
• Know What Datums Exist in AOR• Always Pass Datum w/Coordinate• Understand Map Projection Used for Your
Products• Understand Coordinate System in Use• Know Resources to Transform Datums
and Convert Coordinates
Questions?
References
Neteler, M. & Mitasova, H. 2004. Open source GIS: a GRASS GIS approach, 2nd edition. The Netherlands: Kluwer Academic Publishers
Burrough, P. A. & McDonnel R.A. 1998. Principles of Geographical Information System. New York, USA: Oxford University Press
Dent, B. 1990. Cartography Thematic Map Design, 2nd Edition. USA: Wm. C. Brown Publishers
Datum and Grids. Navigator of the Navy. link: https://www.navigator.navy.mil/navigator/coordinates.ppt
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Emmanuel P. Sambale. November, 2006
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