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## Representing the Earth

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**Representing the Earth**RG 620 Week 4 My 03, 2013 Institute of Space Technology, Karachi**Geodesy**Science of measuring the shape of Earth**Modeling the Earth**• The best model of the Earth is 3D globe • For measuring the Earth, Globes have certain drawbacks**Modeling the Earth**• At any point on Earth there are three important surfaces, the Ellipsoid, the Geoid, and the Earth surface**Geoid**Definition: “Three-dimensional surface along which the pull of gravity is constant” OR “A continuous surface which is perpendicular at every point to the direction of gravity”**Geoid**• True shape of the Earth varies slightly from the mathematically smooth surface of an ellipsoid • Differences in the density of the Earth cause variation in the strength of the gravitational pull, in turn causing regions to dip or bulge above or below a reference ellipsoid • This undulating shape is called a Geoid**Ellipsoid**Mathematical surface obtained by revolving an ellipse around earth’s polar axis**Ellipsoid**• Different ellipsoid were adopted in various parts of the world Why difference in Ellipsoidal Estimates? • Because there were different sets of measurements used in each region or continent • These measurements often could not be tied together or combined in a unified analysis • Due to differences in survey methods and data analyses.**Origin, R1, and R2of ellipsoid specified such that**separation between ellipsoid and Geoid is small Examples: Clarke 1880 Local or Regional Ellipsoid**Global ellipsoid selected so that these have the best fit**“globally”, to sets of measurements taken across the globe Example: Geodetic Reference System of 1980 (GRS 1980) World Geodetic System 1984 (WGS84) Global Ellipsoid**Globally Applicable Ellipsoids**• Extremely precise measurements across continents and oceans were possible using data derived from satellites, lasers, and broadcast timing signals • This has led to the calculation of globally applicable ellipsoids such as GRS80, or WGS84**Measuring Heights**• Orthometric Height/Elevation: Vertical distance above a geoid • Ellipsoidal Height: Heights above the ellipsoid • Geoidal Height/Geoidal Separation: The difference between the ellipsoidal height and orthometric height at any location • Geoidal heights vary across the globe • The absolute value of the geoidal height is less than 100 meters at most of the Earth locations • The geoid is not a mathematically defined surface rather it is a measured and interpolated surface**Datum**A fixed 3D surface Provides a frame of reference for measuring locations on the surface of the earth It defines the origin and orientation of latitude and longitude lines Examples: North American Datum of 1983 (NAD 1983 or NAD83), North American Datum of 1927 (NAD 1927 or NAD27), World Geodetic System of 1984 (WGS 1984)**Datum**A spheroid model of the Earth is fixed to a base point Example: For NAD27 Ellipsoid: Clarke 1866 Fixed at Meade's Ranch, Kansas**Datum**• Horizontal Datum • Specify the ellipsoid • Specify the coordinate locations of features on this ellipsoidal surface • Vertical Datum • Specify the ellipsoid • Specify the Geoid –which set of measurements will you use, or which model**Datum**• Many datums have been developed to describe the ellipsoid • Differences between the datums reflect differences in the • control points, • survey methods, and mathematical models and • assumptions used in the datum adjustment**Local Datum**• A local datum aligns its spheroid to closely fit the earth's surface in a particular area • A point on the surface of the spheroid known as the origin point of the datum is matched to a particular position on the surface of the earth • The coordinates of the origin point are fixed, and all other points are calculated from it • The center of the spheroid of a local datum is offset from the earth's center • Not suitable for use outside the area for which it was designed • Examples: • NAD 1927 (designed to fit North America reasonably well) • European Datum of 1950 (ED 1950) (created for use in Europe)**Commonly Used Datums**North American Datum 1927 (NAD27) Uses Clarke 1866 spheroid Fixed at Meade's Ranch, Kansas Yields adjusted latitudes and longitudes for approximately 26,000 survey stations in the United States and Canada North American Datum 1983 (NAD83) Include the large number of geodetic survey points (250,000 stations) GRS80 ellipsoid was used as reference NAD83(1986) uses an Earth-centered reference World Geodetic System of 1984 (WGS84): Earth-centered datum Essentially identical to the North American Datum of 1983 (NAD83) Uses WGS84 ellipsoid**Other Datums**Bermuda 1957 South American Datum 1969 International Terrestrial Reference Frames, (ITRF) Source: http://maic.jmu.edu/sic/standards/datum.htm**Pre-Satellite Datum**• Large errors (10s to 100s of meters), • Local to continental • Examples: Clarke, Bessel, NAD27, NAD83(1986) Post-Satellite Datum • Small relative errors (cm to 1 m) • Global • Examples: NAD83(HARN), NAD83(CORS96), WGS84(1132), ITRF99**Changing the Datum**• The lat/long value of a place on the Earth's surface depends upon the datum • Datum transformation is done to correctly convert data among datums • Changing the datum will change the latitude and longitude of a point on the surface of Earth • Example: • Point: middle of the intersection of Baseline Road and County Line Road near Boulder, Colorado • Location: Latitude and Longitude • NAD27: 40o N, 105o W • NAD83: 39o 59’ 59.97” N, 105o 0’ 01.93” W • Difference between two is 4ft south and 50 ft west**Positions on Globe: Lines of Reference**graticules Figure: 1 Figure: 3 Figure: 2**Measured by Geographical Coordinates (angles) rather than**Cartesian Coordinates Locations are represented by Latitudes and Longitudes Latitudes (Y) and Longitudes (X) are angles Equator is the reference plane used to define latitude Prime Meridian is used to define longitude Positions on Globe**Geographic Coordinate System (GCS)**• GCS uses a three-dimensional spherical surface to define locations on the earth. • Latitude and Longitude are angles denoted by ( °, ', " )**Latitude and Longitude**• The Latitude is measured as the number of degrees from the Equator • The Longitude is measured as the number of degrees from the Prime Meridian • The lines of constant latitude and longitude form a pattern called the Graticule**Example: Measuring Lat and Long**Example: In figure 60° E (longitude), 55° N (latitude)**“Latitude is the angular distance of any point**on Earth measured north or south of the Equator in degrees, minutes and seconds” At poles (North and South Poles) latitudes are 90o North and 90o South At equator latitude is 0° The equator divides the globe into Northern and Southern Hemispheres Each degree of latitude is approximately 69 miles (111 km) (variation because Earth is not a perfect sphere) 90° N 90° S Latitude • 0°**Lines of constant latitude are called parallels of latitude**(horizontal lines) Parallel lines at an equal distance On Globe lines of latitude are circles of different radii Equator is the longest circle with zero latitude also called ‘Great Circle’ (24,901.55 miles) Other lines of latitudes are called ‘Small Circles’ At poles the circles shrink to a point Circle of Equator is divided into 360 degrees Lines of Equal Latitudes In figure, lines of Latitude or Parallels**Some Important Small Circles**• Tropic of Cancer • At 23.5°N of Equator and runs through Mexico, Egypt, Saudi Arabia, India and southern China. • Tropic of Capricorn • At 23.5°S of Equator and runs through Chile, Southern Brazil, South Africa and Australia. • Arctic and Antarctic Circles • At 66° 33′ 39″ N and 66° 33′ 39″ S respectively**Map of the World**Tropical Zone**“Longitude is the angular distance of any point**on Earth measured east or west of the prime meridian in degrees, minutes and seconds” Measured from 0° to 180° east and 180° west (or -180°) The meridian at 0° is called Prime Meridian located at Greenwich, UK Both 180-degree longitudes (east and west) share the same line, in the middle of the Pacific Ocean where they form the International Date Line 1 degree of Longitude= 69.17 mi at Equator 48.99 mi at 45N/S 0.0 mi at 90N/S Prime Meridian 180° E W 180° Longitude**Lines of Longitude (vertical lines/meridians)**They are also called Meridians Meridians converge at the poles and are widest at the equator about 69 miles or 111 km apart On Globe lines of longitude are circles of constant radius which extend from pole to pole Lines of Equal Longitude In figure, lines of longitude or meridian**S**E W Prime Meridian • Royal Astronomical Observatory in Greenwich, England**Latitude/Longitude Formats**• Lat/long coordinates can be specified in different formats: • DD.MM.SSXX (degree, minute, decimal second) • DD.MMXX (degree, decimal minute) • DDXX (decimal degree) How to convert degree, minute, decimal second format into decimal degree? • Decimal degree = (Seconds/3600) + (Minutes/60) + Degrees • In class exercise: DD conversion of24° 48' 58” N 66° 59' E**References**• Bolstad Text Book • http://courses.washington.edu/gis250/lessons/projection/**Solution- Quiz 2 (a)**DD conversion of 38° 20' 20” N 70° 56' 04” E is 38.33889 ° N and 70.93444 ° E The DMS version of 5.23456° is 5 ° 14’ 4.416’’