Coordinate systems

Coordinate systems

COORDINATE SYSTEMS

Geographic (GCS)◦ Degrees……

Projected (PCS)◦ Meters, feet….

GEOGRAPHIC COORDINATE SYSTEMS

A GCS is a three dimensional “spherical” surface used to define a location on the earth by:◦ Equator◦ Prime meridian


A point on the earth is referenced by longitude and latitude values, angles expressed in degrees

LONGitude: angle measured on the sphere from the prime meridian

LATitude: angle measured from the equator

equator

Prime meridian


Parallels: horizontal lines of equal latitude The line of latitude midway between the

poles of the sphere is the equator (latitude =0)

The equator (latitude =0) divides the sphere in north (top) and south (bottom) latitude sides

Meridians: vertical lines of equal longitude The conventional line of 0 longitude is the

prime meridian The prime meridian divides the meridians in

a west (left) and east (right) sides of longitude

Parallels and Meridians form the geographical grid with the origin (0,0) at the intersection of the equator and the prime meridian

For most of the GCSs, the prime meridian is the line of longitude passing through

Greenwich (UK)


GEOGRAPHIC COORDINATE SYSTEMS Latitude and longitude are

measured in degrees, minutes and seconds (DMS) or decimal degrees (DD)

Longitude ranges between -180° (or 180 west) and +180° (or 180 east)

Latitude ranges between -90° (or 90° south) and +90° (or 90° north)

Above and below the equator the latitude lines (circles) gradually become smaller

Only along the equator one degree of latitude represents the 111.12 Kilometers)

GEOGRAPHIC COORDINATE SYSTEMS The GCS surface is:

◦ Ellipse defined by two radii, the longer radius is the semi major axis (a), the shorter is the semi minor axis (b)

◦ The rotation of an ellipse around its semiminor axis creates an ellipsoid

◦ An ellipsoid is defined by the two axes, a and b or by an axis and the flattening, f

f= (a-b)/a

ab

GEOGRAPHIC COORDINATE SYSTEMS The earth has been surveyed many times,

by many topographers we have many ground measured ellipsoids

representing the shape of the earth (International 1909, Clarke 1866, Bessel)

Each of them has been chosen to better fit and cartographically represent one limited region in the world

Because of gravitational and surface feature variations, the earth can not be a perfect ellipsoid; satellite technnology allowed the creation of new and more accurate ellipsoids for worldwide use

the most recent and the most widely used is the one defined in the World Geodetic System of 1984 (WGS 1984 or WGS84)

A geographic position on the earth is defined by:◦ Latitude from the equator◦ Longitude from a prime meridian◦ A specific GCS

A position on the earth could have different longitude and latitude if the GCS is different

The difference is always around seconds or fractions of a second

The error of setting a wrong GCS in a GPS system could affect the coordinates on a map even of hundred meters


equator

Prime meridian

An ellipsoid approximates the shape of the earth.It is the mathematical or geometrical reference surface of the earth. A Datum

◦ defines the ellipsoid and the position of the ellipsoid relative to the center of the earth

◦ The center of the earth is defined as its center of mass as calculated by satellite measurements

◦ Provides a frame of reference for combining data from different GCS

◦ The most widely used datum is the WGS84◦ WGS84 it is the framework for locational measurements worldwide



A geographic position on the earth is defined by:◦ Latitude from the equator◦ Longitude from a prime

meridian◦ A specific DATUM or GCS

Ellipsoid Relative position according to

WGS84

PROJECTED COORDINATE SYSTEMS To preserve or measure some

properties (distance, area, shape,..) on maps we need a PCS

A PCS is defined on a flat two dimensional surface

Locations based on x,y(,z) coordinates on a grid/cartesian plane

The grid is made by a network of equally spaced lines (same distances between horizontal and vertical)

Based on a GCS

PROJECTED COORDINATE SYSTEMS The ellipsoid is transformed from

a three dimensional surface to create a flat map sheet

This mathematical transformation is commonly referred to as a map projection

Like shining a light through the earth surface casting its shadow onto a map sheet wrapped around the earth itself

Unwrapping the paper and laying it flat produces the map

A map projection uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates.

Representing the earth’s surface in two dimensions causes distortion in the shape, area,distance, or direction of the data.

Different projections cause different distortions

Projections could be:◦ Conformal

Preserve local shapes, mantaining angles Meridians and parallels intersect at 90° angles

◦ Equal area Preserve the area Meridians and parallels may not intersect at right

angles◦ Equidistant

Preserve distances betweeen certain points No projection is equidistant for all points in the map

PROJECTED COORDINATE SYSTEMS

PROJECTED COORDINATE SYSTEMS Some of the

simplest projections are made onto developable shapes as cones, cylinders, and planes, tangent or secant to the earth ellipsoid

PROJECTED COORDINATE SYSTEMS Samples of

projections

PROJECTED COORDINATE SYSTEMS Universal Transverse

Mercator: Central meridian as the tangent

contact Developing the cylinder creates

distortion:◦ used for an area spanning 3° east

and 3° west from the central meridian

◦ Used for representing lands below 80° of latitude

The earth is divided into 60 zones each covering 6° of longitude

PROJECTED COORDINATE SYSTEMS a

COORDINATE TRANSFORMATIONS

x,y x,y

Why considering coordinate systems, projections and transformations?

◦ Locating correctly a GPS point onto a map◦ Overlaying different map data sources (a vegetation map,

a soil map, etc. )◦ Performing spatial analysis◦ Deriving coordinates using a topographic map in the field◦ Specifying coordinates without errors

GIS & COORDINATE SYSTEMS

equipotential surface of the Earth gravitational field that most closely approximates the mean sea surface

The geoid surface is described by geoid heights that refer to a suitable Earth reference ellipsoid

Geoid heights are relative small, the minimum of some -106 meters is located at the Indian Ocean, the maximum geoid height is about 85 meters.

Elevation/altitude is measured above mean sea level (AMSL)

GEOID

GEOID

GEOID

GEOID

global map with geoid heights of the EGM96 gravity field model, computed relative to the GRS80 ellipsoid

Coordinate systems

Science