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

A Map……record of location of objects in geographic

space.…each location is unique and can be

represented in different ways. Pair of longitude and latitude to locate a

place on earth surface. ZIP code of a location (Zone Improvement

Plan)

Plane Coordinate Systems

All these methods of fixing locations relates to the mathematical concepts of Coordinates.

A coordinate is one of a set of numbers that determines the location of a point in a space of

a given dimension.

Plane Coordinate Systems

Two basic types of coordinate reference system on a plane (two-dimensional space):

1. Plane rectangular coordinate system

2. Plane polar 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.

Plane Rectangular Coordinate System (Cartesian Coordinate System)

Global Cartesian Coordinates (x,y,z)

O

X

Z

Y

GreenwichMeridian

Equator

•

The Polar Coordinate System…… a two dimensional coordinate

system in which each point on a plane is determined by an angle and a distance.

especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance;

in the more familiar Cartesian or rectangular coordinate system, such a relationship can only be found through trigonometric formulation.

Plane Polar Coordinate System

Geographic Coordinate Systems of EarthIn 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 EarthWe 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.

LatitudeLongitude

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 meridian is 0 degrees longitude. This imaginary line runs through the United Kingdom, France, Spain, western Africa, and Antarctica.

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

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)Y

X

(9,5)

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

X

Y

(-X,+Y)

(+X,-Y)

(+X,+Y)

(-X,-Y)

(0,0)

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

S

EW

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) (N, E)

(S, W) (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.

Y

X

90°S

90°N

What is Latitude?• Each degree of

latitude is divided into 60 minutes.

• Each minute is divided into 60 seconds.

Y

X

90°S

90°N

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?

• The earth is divided into 360 equal slices (meridians)

• 180 west and 180 east of the prime meridian

Y

X

180°W 180°E

What is Latitude?

• Our latitude and longitude might be:

• 37°, 03’,13’’N• 76°, 29’, 45’’W

Y

X

90°S

90°N

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

Parallel of latitude

X

Y

ZN

EW

=0-

90°S

P

OR

=0-180°E

=0-90°N

•

Greenwichmeridian

=0°

•

Equator =0°

•

•=0-180°W

- Geographic longitude - Geographic latitude

R - Mean earth radius

O - Geocenter

Lat/long system measures angles on spherical surfaces

e.g.

• 60º east of PM• 55º north of equator

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.

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

Clarke 1866 Clarke 1880

GRS80 WGS60

WGS66 WGS72

WGS84 Danish

Ellipsoid or SpheroidRotate an ellipse around an axis

O

X

Z

Ya ab

Rotational axis

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

Earth surface

EllipsoidSea surface

Geoid

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

Ocean

Geoid

Earth surface

Ellipsoid

Gravity Anomaly

Gravity anomaly is the elevation difference betweena standard shape of the earth (ellipsoid) and a surface

of constant gravitational potential (geoid)

Definition of Elevation

Elevation Z

•

Pz = zp

z = 0

Mean Sea level = Geoid

Land Surface

Elevation is measured from the Geoid

Standard Ellipsoids

Ellipsoid Majoraxis, a (m)

Minoraxis, b (m)

Flatteningratio, f

Clarke(1866)

6,378,206 6,356,584 1/294.98

GRS80 6,378,137 6,356,752 1/298.57

Ref: Snyder, Map Projections, A working manual, USGSProfessional 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

SelectedEllipsoids

and Datums

Source: http://maic.jmu.edu/sic/standards/datum.htm