Coordinate System and Projection System Flashcards
coordinate systems
a system which uses one or more numbers to uniquely determine the position of a point or other element within a space
properties that define a coordinate system
definition of axis: number, name, order/sequence
definition of measurements: unit, direction (positive/negative)
3 kinds of coordinate systems
observer based - azimuth and altitude
earth based - latitude and longitude
celestial - declination and right ascension
earths rotation
counter clockwise
- provides an axis connecting north and south poles
- provides the basis for a system to determine location
- geographic coordinate systems or geographic grid
one rotation takes
a solar day (24hrs)
parallels define
degrees latitude relative to the equator
meridians define
define degrees longitude relative to prime meridian
network of lines
- east-west (parallels)
- north-south (meridians)
construction of parallels
Starting point is the axis of rotation
Equatorial plane
Imaginary plane through center of the earth
Perpendicular to the axis of rotation
Latitude
The angular distance towards north or south of the equator from the equatorial plane
00 at the equator and +900 at the North pole and -900 at the South pole
concept of small circles
circles produced by a plane passing through a sphere anywhere except its center are referred to as small circles
all parallels except the equator are small circles
concept of great circles
if a sphere is divided exactly in half by a plane passing through its centre, the intersection of the plane with the sphere represents the largest circle that can be drawn on the sphere
properties of great circles
- great circles are the largest circles that can be drawn on a spherical surface
- an infinite number of great circles can be drawn on a sphere
- Only one great circle can be drawn to pass through two points on the surface of a sphere – unless
the two points are the ends of the same diameter - An arc of a great circle is the shortest distance of two points on the surface of a spheroid
Construction of meridians
Construction of meridians Meridians are halves of great circles Extend from north pole to south pole No convenient place to start Arbitrary starting point Meridian passing through Greenwich, England is the 0 meridian or prime meridian Longitude Angle between prime meridian plane and the meridian plane from the point of interest.
longitude is expressed in
degrees, minutes and seconds Indicate east-west position West of prime meridian: W East of prime meridian: E Prime meridian 0o Meridians are between 0o -180o Western hemisphere Eastern hemisphere
shortest distance between two points always
lies on a great circle
distance from the lat/long
Along the meridian (north-south) = Earth’s Circumference/360 = 111 Km (approx.) Along the parallel (east-west) = depends of the latitude = cos(latitude in degree) * (111)
what is projection
is a method of transferring features of the spherical Earth to a flat surface
map projections define
the spatial relationship between locations on earth and their relative locations on a flat map
methods of projection
A method of projection provides an orderly system of parallels and meridian that is used to model the relative location of earth surface features on a two dimensional media.
i. e., mathematica system - Robinson projection, mollweide projection
i. e., geometric - lambert conformal conic, north pole azimuthal equidistan projection
i. e., Mercator projecting
conceptual model of deriving map projections
- a transparent globe with geographical grid and may be continents are drown on it
- a light source placed inner side (center…) of the globe
- a paper placed on the surface of the globe in flat or conical or cylindrical shape
why different types in conic, planar and cylindrical projection systems
Mapmakers and mathematicians have devised almost limitless ways to project the image of the globe onto papers to serve various purposes
For Navigation (Mercator)
To show different parts of the world more accurately
To show world map more accurately
To show distribution patterns (Robinson)
For Administration………
ArcGIS supports 66 different types of map projections
Which projection is the best?
No matter how we model our Earth, as spheroid, or on a two-dimensional flat surface, - each a less accurate than the preceding shape.
Every projection has its own set of advantages and disadvantages.
There is no “the best” projection.
Spatial properties of earth surface features
No single projection can preserve, simultaneously, all of the main spatial properties –
angle, direction, distance, shape, area
On a map, the direction is correct means the bearing between two points is correct on anywhere on the map
If a projection preserves shape and area on the map, an area is uniformly proportional to the real world that they represent.
Conformal Projection
– preserves the correct shapes of small areas.
Equal Area Projection
- quadrilaterals formed by meridians and parallels have an area on the map proportional to their area on the globe.
Equidistant Projection
- distance from a single location to all other locations are preserved.
Azimuthal Projection
– directions from a single location to all other locations are preserved
Compromise Projection
attempt to balance between the above characteristics, and is often used in thematic mapping.
popular map projections
Mercator (Cylindrical)
Lambert conical conformal (Conical)
Transvers Mercator (transvers Cylindrical)
Some projections cannot be expressed geometrically, have only mathematical descriptions
Goodes
Robinson
Molleweide
Eckert
Gerardus Mercator Projection
a cylindrical projection with rectangulargrid
Distance between parallel increase with latitude
Polar cut-of at 800 N and 800 S
High distortion of shape and area toward pole,e.g.: Greenland shows same size as Africa
Scale on 600 latitude is 2 times (on 800, it 6X)of that on the equator
Impotent properties preserves direction (bearing), which makes it Indispensable for navigation
Other uses to show linier features like wind flow line, ocean currents, global temperature and pressure patterns
Polar Projection
Can be centred on either the North or South Pole
Meridians are straight lines radiating outward from the pole
Parallels are nested circles centred on the pole
Parallels with the meridians intersect at right angles
The space between the parallels increases outward from the centre
shows the true shapes of small areas,such as islands
Scale increases away from the centre
shapes look disproportionately larger toward the edge of the map
Goodes Projection
Uses two sets of mathematical curves to form its meridians
Between the 40th parallels, it uses sine curves
Beyond the 40th parallel, towards the poles, it uses ellipses
Ellipses converge to meet at the pole, so the entire globe can be shown
Commonly used to show regional distributions of geographical features such as socials and vegetation.
Shows area in correct proportion.
It distorts the shapes of areas, particularly in high latitudes.
Why is projection necessary?
Data often comes in geographic, or spherical coordinates (latitude and longitude) and cant be used for area calculations in most GIS software applications
Angular Parameters
Central meridian or longitude of origin
Latitude of origin or central parallel
Longitude of center
Latitude of center
Standard Parallel
Linear Parameters
False easting
False northing
Scale factor
How to choose projections
Follow the lead of people who make maps of the area you are interested in.
For a map of Canada Lambert Conical Conformal projection is commonly used.
State plane is a common projection for all states in the USA.
UTM is commonly used and is a good choice hen the east-west width of area does not exceed degrees.
Commonly used Datum Systems in Canada
WGS84 (World Geodetic System of 1984) - geodetic coordinate reference system (datum) developed and used by GPS. No physical monuments.
NAD83 (North American Datum of 1983) - developed based on GRS 1980.
The ellipsoid defined through the use of satellites.
Tied to the North American tectonic plate, meaning over time it diverges from WGS84.
NAD27 (North American Datum of 1927)-developed based on the Clarke Ellipsoid of 1866.
Discontinued from use but there are still use.
It coordinate difference from NAD83 depends on the location
~20 m around Thunder Bay.
Transverse Mercator
Whole Earth can be shown, but all distances, direction, shapes, and areas are reasonably accurate within 15 degrees of the central meridian.
Distances are true only along the central meridian selected by the mapmaker or else along two lines parallel to it
This is an ellipsoid cylindrical projection that divides the world into numbered zones in longitude.
20 latitudinal zones from 80 degrees south to 84 degrees north denoted by letters C to X, omitting the letters I & O.
Each zone is 8 ^^0 south-north (except the “X” is 12 degrees)
Areas are referenced by quoting the longitudinal zone number, followed by the latitudinal zone letter.
UTM Coordinates - Northern Hemisphere
UTM projection use easting and northing in metres for coordinates.
The central meridian’s coordinate is always 500,000
The Equators coordinate is designated 0 for quadrangles in the Northern Hemisphere
UTM Coordinates - Southern Hemisphere
The central meridian’s coordinate is always 500,000
The equator’s coordinate is designated 10,000,000 for quadrangles in the southern hemisphere
UTM Accuracy
Each zone is separately projected using the ellipsoidal form of the transverse Mercator projection with a secant case:
- scale of the central meridian is reduced by 0.04% so two lines about 1 degree 37” east and west of it have true scale
The UTM grid was designed for large-scale topographic mapping in separate sheet, not for world or regional maps
Earth Orbital Revolution
An elliptical path around the Sun
Earth-Sun distance varies between aphelion and perihelion points
23.5 degrees with the ecliptic plane
Celestial Coordinate System
North & South celestial pole - point in sky directly about north/south pole on Earth
Celestial Equator - circle surrounding earth
Ecliptic - a path followed by the sun through the sky over the course of the year.
Declination - angle from celestial equator (0^^0), positive UP, negative going DOWN
Celestial Prime Meridian - point where sun is located
at the vernal equinox (Spring)
Right Ascension (RA) - angle (degree) form the celestial “Prime Meridian” (equivalent of celestial longitude)
