Coordinate Systems Spheroids and spheres. Datums. Coordinate systems. GIS and Remote Sensing Coordinate Systems Spheroids and spheres. Datums. Coordinate systems. geographic coordinate system. projected coordinate system. Universal Transfer Mercator System. refer to map_projections.chm

Definition of a spheroid Sphere Spheroid A sphere is based on a circle, while a spheroid (or ellipsoid) is based on an ellipse.

Definition of a spheroid Major Minor Semi-minor, b Semi-major, a The shape of an ellipse is defined by two radii. The longer radius is called the semi-major axis, and the shorter radius is called the semi-minor axis. A spheroid is defined by either the semi-major axis, a, and the semi-minor axis, b, or by a and the flattening. The flattening is the difference in length between the two axes expressed as a fraction or a decimal. The flattening, f, is: f = (a - b) / a

Datums While a spheroid approximates the shape of the earth, a datum defines the position of the spheroid relative to the center of the earth. Earth’s surface Earth-centered (WGS84) datum Local (NAD27) datum

Coordinate System North Prime Meridian (Longitude) 60º 40º (80ºE 55ºN) 20º 55º Lat. West 0º East 80º Long. -40º 80º -20º 60º 0º 20º 40º Equator (Latitude/ Parallel) South

Coordinate systems There are two types of coordinate systems: geographic and projected. Z (80ºE 55ºN) 80º Long. 55º Lat. Spheroid Y X + = geographic coordinate system 80º Long. 55º Lat. 0º +20º +40º -20º -40º +180º -180º … +90º -90º projected coordinate system

Geographic Coordinate Systems A GCS uses a three-dimensional spherical surface to define locations on the earth. A GCS is often incorrectly called a datum, but a datum is only one part of a GCS. A GCS includes an angular unit of measure, a prime meridian, and a datum (based on a spheroid).

Geographic Coordinate Systems Description The earth is modeled as a sphere or spheroid. The sphere is divided into equal parts usually called degrees; some countries use grads. A circle is 360° or 400 grads. Each degree is subdivided into 60 minutes, with each minute composed of 60 seconds. The geographic coordinate system consists of latitude and longitude lines. Each line of longitude runs north-south and measures the number of degrees east or west of the prime meridian. Values range from -180 to +180°. Lines of latitude run east-west and measure the number of degrees north or south of the equator. Values range from +90° at the North Pole to -90° at the South Pole.

Projected coordinate systems A projected coordinate system is defined on a flat, two-dimensional surface. It is always based on a geographic coordinate system that is based on a sphere or spheroid. In a projected coordinate system, locations are identified by x, y coordinates on a grid, with the origin at the center of the grid. Each position has two values that reference it to that central location. One specifies its horizontal position and the other its vertical position. The two values are called the x-coordinate and y-coordinate. Using this notation, the coordinates at the origin are x = 0 and y = 0. X<0 Y>0 X>0 Y<0 X Y (0,0)

Map Projection Projection Method Cylindrical Projection

Universal Transfer Mercator For the Universal Transfer Mercator System, the globe is divided into 60 zones; each zone has its own central meridian. each spanning 6 degrees wide of longitude (3 degrees west and 3 degrees east) X-and Y-coordinates are recorded in meters. The limits of each zone are 84 degree Northern, 80 degree Southern. Regions beyond these limits are accommodated by the Universal Polar Stereographic projection. The value given to the central meridian is the false easting (500, 000m), and the value assigned to the Equator is the false northing (0m for Northern, 10 000 000m for Southern). A scale factor is applied to cylindrical coordinates to average scale error over the central area of the map while reducing the error along the east and west boundaries. The scale factor has the effect of recessing the cylinder into the earth so that it has two lines of intersection. Scale is true along these lines of intersection. You may see the scale factor expressed as a ratio, such as 1:2500. In this case it is generally called the scale reduction. The relationship between scale factor and scale reduction is: Scale factor = 1-scale reduction In this case the scale factor would be 1-(1/2500) or 0.9996

UTM Span North Equator East West The Universal Transverse Mercator (UTM) system have 60 north and south zones, so each spanning or zoning 6° of longitude. South

Coordinate Systems REFERENCES Geographic Information System and Science, www.gis.com, www.wiley.co.uk/gis, www.wiley.com/gis Melita Kennedy n Steve Kopp, 2000 at USA; Understanding Map Projection,. www.esri.com