Concept Of Latitude And Longitude

Concept Of Latitude and Longitude

Geodesy and Map Projections • Coordinate systems - (x,y) coordinate systems for map data, Geographic coordinate system • Geodesy - the shape of the earth and definition of earth datums • Map Projection - the transformation of a curved earth to a flat map

Plane Coordinate Systems A Map… …record of location of objects in geographic space. …each location is unique and can be represented in different ways. Ø Pair of longitude and latitude to locate a place on earth surface. Ø ZIP code of a location (Zone Improvement Plan) All these methods of fixing locations relates to the mathematical concepts of Coordinates.

Plane Coordinate Systems

A coordinate is one of a set of numbers that determines the location of a point in a space of a given dimension. Two basic types of coordinate reference system on a plane (twodimensional space): 2. Plane rectangular coordinate system 3. Plane polar coordinate system

Plane Rectangular Coordinate System (Cartesian Coordinate System) §The Cartesian coordinate system(also called rectangular coordinate system) is used; …to determine each point uniquely in a plane through two numbers, usually called: • the x-coordinate or abscissa and • the y-coordinate or ordinate of the point. § Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimension.

Global Cartesian Coordinates (x,y,z) Greenwich Meridian

Z

•

O

Y

X Equator

Plane Polar Coordinate System § The Polar Coordinate System… … a two dimensional coordinate system in which each point on a plane is determined by an angle and a distance. Øespecially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; Øin the more familiar Cartesian or rectangular coordinate system, such a relationship can only be found through trigonometric formulation.

Geographic Coordinate Systems of Earth In order to locate places on earth, a three dimensional coordinate reference system has to be develop that takes into account its shape.

Shape of the Earth We think of the earth as a sphere

It is actually a spheroid, slightly larger in radius at the equator than at the poles

Latitude and Longitude • The earth is divided into lots of lines called latitude and longitude.

Lines • Longitude lines run north and south. • Latitude lines run east and west. • The lines measure distances in degrees.

Longitude

Latitude

Where is 0 degree? • The equator is 0 degree latitude. • It is an imaginary belt that runs halfway point between the North Pole and the South Pole.

Equator

Where is 0 degree? • The prime meridianis 0 degrees longitude. This imaginary line runs through the United Kingdom, France, Spain, western Africa, and Antarctica.

Unnderstanding Longitude & Latitude

Typical Graph • This is an example of a typical graph we are all familiar with. • The graph is made up of different “points” with lines that connect the points.

Typical Graph • Each point has two values: • The “X” value that runs along the horizontal “X” axis • The “Y” value that runs along the vertical “Y” axis

Y axis

X axis

Typical Graph • X value is always Y stated first • Followed by the Y value • The “origin” is the point where the 2 axes intersect with a value of (0,0) (0,0)

(3,8)

(9,5)

X

Typical Graph • A point can also have negative (-) values • Negative X values are to the left of the origin (0,0) • Negative Y values are below the origin

Y (-X,+Y)

(+X,+Y) (0,0) X

(-X,-Y)

(+X,-Y)

East West, North South on The Earth • Let the X axis be the Equator. • Let the Y axis be the Prime Meridian that runs through Greenwich outside of London. • Lat/Long are the 2 grid points by which you can locate any point on earth.

Y

X

East West, North South on the Earth • Let each of the four quarters then be designated by North or South and East or West. N

W

E

S

East West, North South on the Earth

• The N tells us we’re north of the Equator. The S tells us we’re south of the Equator. • The E tells us that we’re east of the Prime Meridian. The W tells us that we’re west of the Prime Meridian.

(N, W)

(S, W)

(N, E)

(S, E)

East West, North South on the Earth

• That means all points in North America will have a North latitude and a West longitude because it is North of the Equator and West of the Prime Meridian.

(N, W)

Prime Meridian

East West, North South on the Earth • What would be the latitude and longitude directions in Australia?

?

Prime Meridian

If you said South and East , you’re right!

What is Latitude? • Latitude is the distance from the equator along the Y axis. • All points along the equator have a value of 0 degrees latitude. • North pole = 90°N • South pole = 90°S • Values are expressed in terms of degrees.

90°N

Y

X

90°S

What is Latitude? • Each degree of latitude is divided into 60 minutes. • Each minute is divided into 60 seconds.

90°N

Y

X

90°S

This is also true of longitude.

What is Longitude? • Longitude is the distance from the prime meridian along the X axis. • All points along the prime meridian have a value of 0 degrees longitude. • The earth is divided into two parts, or hemispheres, of east and west longitude.

Y

X

180°W

180°E

Hemispheres • By using the equator and prime meridian, we can divide the world into four hemispheres, north, south, east, and west.

What is Longitude? Y

• The earth is divided into 360 equal slices (meridians) • 180 west and 180 east of the prime meridian

X

180°W

180°E

What is Latitude? • Our latitude and longitude might be: • 37°, 03’,13’’N • 76°, 29’, 45’’W

90°N

Y

X

90°S

So Where is (0,0)? • The origin point (0,0) is where the equator intersects the prime meridian. • (0,0) is off the western coast of Africa in the Atlantic Ocean.

Latitude and Longitude on a Sphere Meridian of longitude

Z

Greenwich meridian °

N

Parallel of latitude

W

    

P •

O

•

R  



X

• 

•

Equator

=0°

 



 



E

  Y R - Mean earth radius OGeocenter

Lat/long system measures angles on spherical surfaces e.g. • 60º east of PM • 55º north of equator

In Summary!

Positioning on the Earth’s Surface East is the direction of rotation of the Earth

North Pole

Prime Meridian

Latitude: (90oN to 90oS) Longitude: (180oE to 180oW)

0o Longitude

Tropic of Cancer 21st June

22nd Sept 20th March

Equator 22nd December

Tropic of Capricorn Longitude 90o West Longitude 60o West

Longitude 30o West

Latitude 23½o North oW 90 60o90 30 30 Eo 60 90 o 66½23½ o

900

23½o

Latitude 0o Latitude 23½o South Longitude 90oEast Longitude 60o East

Longitude 30o East

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

Now you can find any desired location on a map!

Geographical Coordinate systems • Lat/long values are NOT Cartesian (X, Y) coordinates – constant angular deviations do not have constant distance deviations – 1° of longitude at the equator 1° of longitude near the poles

Globe • Spherical Earth’s surface -radius 6371 km • Meridians (lines of longitude) - passing through Greenwich, England as prime meridian or 0º longitude. • Parallels (lines of latitude) - using equator as 0º latitude. • degrees-minutes-seconds (DMS), • decimal degrees (DD)

True direction, shape, distance, and area

Geographic Latitude/Longitude Coordinate System

Ellipsoidal Parameters

b a

Spheroids and Geoids

Spheroids and Geoids • The rotation of the earth generates a centrifugal force that causes the surface of the oceans to protrude more at the equator than at the poles. • This causes the shape of the earth to be an ellipsoid or a spheroid, and not a sphere. • The nonuniformity of the earth’s shape is described by the term geoid. The geoid is essentially an ellipsoid with a highly irregular surface; a geoid resembles a potato or pear.

The Ellipsoid • The ellipsoid is an approximation of the Earth’s shape that does not account for variations caused by non-uniform density of the Earth. • Examples of Ellipsoids

Ellipsoid or Spheroid Rotate an ellipse around an axis Z b a O a X Rotational axis

Y

The Geoid • A calculation of the earth’s size and shape differ from one location to another. • For each continent, internationally accepted ellipsoids exist, such as Clarke 1866 for the United States and the Kravinsky ellipsoid for the former Soviet Union.

The Geoid • Satellite measurements have led to the use of geodetic datums WGS-84 (World Geodetic System) and GRS-1980(Geodetic Reference System) as the best ellipsoids for the entire geoid.

The Geoid • The maximum discrepancy between the geoid and the WGS-84 ellipsoid is 60 meters above and 100 meters below. • Because the Earth’s radius is about 6,000,000 meters (~6350 km), the maximum error is one part in 100,000.

Representations of the Earth Mean Sea Level is a surface of constant gravitational potential called the Geoid Sea surface

Ellipsoi d

Earth surface

Geoid

Earth Surface: Ellipsoid, Geoid, Topo • • •

The reference ellipsoid surface (a map of average sea level). The reference geoid surface (a mean sea level surface). The real surface of the Earth (the ground) also called the topographic surface.

Geoid and Ellipsoid Earth surface

Ellipsoid

Ocean Geoid

Gravity Anomaly

Gravity anomaly is the elevation difference between a standard shape of the earth (ellipsoid) and a surface of constant gravitational potential (geoid)

Definition of Elevation Elevation Z P •

z = zp

z = 0 Land Surface

Mean Sea level = Geoid Elevation is measured from the Geoid

Standard Ellipsoids

Ref: Snyder, Map Projections, A working manual, USGS Professional Paper 1395, p.12

Geodetic Datum • Geodetic datum defines the size and shape of the ellipsoid earth and the origin (or position) and orientation (or direction) with respect to the Earth. • the direction of the minor axis of the ellipsoid. This is classically defined as being parallel to the mean spin axis of the earth • the position of its centre, either implied by adopting a geodetic latitude and longitude (Φ, λ) and geoid / ellipsoid separation (N) at one, or more points (datum stations), or in absolute terms with reference to the Earth centre of mass; and • the zero of longitude (conventionally the Greenwich Meridian). • True geodetic datums were employed only after the late 1700s when measurements showed that the earth was ellipsoidal in shape. The science of geodesy.

Datums • Commonly used datums in North America – North American Datum of 1927 (NAD27) – NAD83 – Geodetic System of 1984 (WGS84)_

Horizontal Earth Datums • An earth datum is defined by an ellipse and an axis of rotation • NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation • NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation • WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83

Vertical Earth Datums • A vertical datum defines elevation, z • NGVD29 (National Geodetic Vertical Datum of 1929) • NAVD88 (North American Vertical Datum of 1988) • takes into account a map of gravity anomalies between the ellipsoid and the geoid

Selected Ellipsoids and Datums

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