Concept of Geographic coordinate systems and map projections

Objectives

- Understand the concept of coordination system

- Understand the map projections

Why it is important?

X

Y

(-X,+Y)

(+X,-Y)

(+X,+Y)

(-X,-Y)

Y

X

X - Equator.Y - Prime MeridianLat/Long are the coordinate of point on earth.

N

EW

S

(N, W)

(S, W)

(N, E)

(S, E)

What are the latitude and longitude directions of Kazakhstan?

Latitude and Longitude

Latitude - distance from the equator along the Y axisLongitude - distance from the prime meridian along the X axis.

.

Exercise In Which Quarter These Lon/Lats Are Located

43 °N, 21°E 78°S, 111°W 4°S, 23°E 15°N, 29°E

Coordination systems

Other coordinate systems

If two datasets are not referenced to the same geographic coordinate system, you may need to perform a geographic (datum) transformation.

This is a well-defined mathematical method to convert coordinates between two geographic coordinate systems. As with the coordinate systems, there are several hundred predefined geographic transformations that you can access.

Equator Latitude 0o

Latitude: (90oN to 90oS)

Latitude 23½o NorthTropic of Cancer

Latitude 23½o SouthTropic of Capricorn

Longitude 30o East

Longitude 60o East

Longitude 30o West

Longitude 60o West

Positioning on the Earth’s SurfaceEast is the direction of rotation of the Earth North Pole

South Pole

23½o 23½o

66½o 90o

900

21st June

22nd December

22nd Sept

20th March

30oE60oE90oE90oW30oW60oW

Longitude 90oEastLongitude 90o West

Prime Meridian

0o Longitude

Longitude: (180oE to 180oW)

Latitude and Longitude together enable the fixing of position on the Earth’s surface.

Geographical coordination system

Map Projection 3D surface is transformed to create a flat surface

This transformation, usually by a mathematical conversion, is commonly referred to as map projection

A 2D surface is imagined around the Earth and is referred as projection surface

Which projection is the best

Projection for accurate mapping

• Earth is neither a perfect sphere nor a spheroid• Local irregularities• Earth surveyed many times to determine semi-

minor and semi-major axis• Semi-minor and semi-major axis that fits well one

region may not fit well another region

Type of Projection

• Projection surfaces– Conic, cylindrical, and planar

• ARC/INFO supports 46 projections

ARC / INFO supports

• 26 spheroids• Each region is represented by a unique semi-

minor and semi-major axis• Measurements vary but by a little amount

relative to the magnitude of the Earth

Name Date

Semi-major Axis(a)

Semi-minor Axis(b) Use

Airy 1830 6377563 6356257 Great BritainAustralian National 6378160 6356775

Bessel 1841 6377397 6356079Chile, most parts of Central Europe, and Indonesia

Clarke 1866 6378206 6356584 North America and PhilippinesClarke 1880 6378249 6356515 France, and most of Africa

Everest 1830 6377276 6356075 India, Burma, Ceylon, Malaysia (part)Everest 1956 6377301 6356100 India and NepalEverest 1969 6377296 6356095

Everest (Sabah and Sarawak) 6377299 6356098 Brunei and E. MalaysiaFischer 1960 6378166 6356784Fischer 1968 6378150 6356768GRS80 1980 6378137 6356752 North AmericaHayford 1909 6378388 6356912Helmert 1906 6378200 6356818 EgyptHough 6378270 6356794

International 1909 6378388 6356912 = International 1924

Krasovsky 1940 6378245 6356863 USSR and some East European countriesModified Airy 6377340 6356034

Modified Everest 1948 6377304 6356103 W. Malaysia and SingaporeModified Fischer 1960 6378155 6356773Modified Mercury 1968 6378150 6356768Mercury 1960 6378166 6356784

New International 1967 6378158 6356772South American 1969 6378160 6356775

Southeast Asia 6378155 6356773Sphere 6370997 6370997Walbeck 6376896 6355835WGS66 1966 6378145 6356760WGS72 1972 6378135 6356751 World wideWGS84 1984 6378137 6356752 World wide

Table of Ellipsoids (Source: E.S.R.I., ArcGIS on-line help files)

Conic Projection

• The most simple conic projection is tangent to the globe along a line of latitude

• This is called a standard parallel for a projection

• The meridians are projected onto the conical surface, meeting at the apex

• latitudes are projected as rings onto the conical surface

Cylindrical projections

Cylindrical projections may also have one line of tangency or two lines of secancy around the globe.

Mercator projection is one of the most common cylindrical projections, and the Equator is usually its line of tangency.

Meridians are Geometrically projected onto the cylindrical surface, and latitude parallels are mathematically projected, producing graticular angles of 90 degrees.  

For more complex cylindrical projections the cylinder is rotated thus changing the lines used for tangency or secancy.

The cylinder can be 'cut' along, any meridian to produce the final cylindrical projection.

The meridians are equally spaced, while the spacing between parallel lines of latitudes increases toward the poles.

 

This projection is conformal and display true direction along straight lines.

Transverse Mercator uses meridians as their tangential contact line.

 

Oblique Cylinders are rotated around a great circle line located anywhere between the Equator and the meridians. In these complex projections most meridians and the lines of latitudes are not straight.

 

In all cylindrical projections, the line of tangency or lines of secancy have no distortion and thus are lines of equidistance. Other geographical properties vary depending on the specific projection.

Assignment

Literature for reading

Explain in 2 pages which map projection are you using and compare with another projection which you are not using

- http://en.wikipedia.org/wiki/Geographic_coordinate_system

^ a b c d e f A Guide to coordinate systems in Great Britain v1.7 October 2007 D00659 accessed 14.4.2008^ The International Meridian Conference^ Haswell, Charles Haynes (1920). Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas. Harper & Brothers. Retrieved 2007-04-09.^ University of New South Wales Instrument Collection Wild T4^ The NGS [1] gives the NAD83 co-ordinates of the water tank; [2] estimates the vertical deflection, the difference between NAD83 and lat-lon by the stars.^ Minor light of Hawai'i - Keahole Point, HI LightHouse Friends^ NGS [3] gives the NAD83 co-ordinates and [4] again converts to astro lat-lon.^ http://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=tu1252