1. 0/27 Merriam-Webster: a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field

2. 1/27 Basically it is what we use to geo- reference or position our civil works projects with respect to other related projects such as SLOSH models, historical high water marks, ADCIRC models, DFIRMS, Bridges, etc.

3. 2/27 Eratosthenes Egypt about 240 BC Syene Alexandria 500mi 7 º 12’ or 1/50 th of a circle Eratosthenes had observed that on the day of the summer solstice, the midday sun shone to the bottom of a well in the Ancient Egyptian city of Swenet (known in Greek as Syene). Sun not directly overhead To these observations, Eratosthenes concluded that the circumference of the earth was 50 x 500 miles, or 25000 miles. The accepted value along the equator is 24,902 miles, but, if you measure the earth through the poles the value is 24,860 miles He was within 1% of today’s accepted value Eratosthenes' conclusions were highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. He knew that at the same time, the sun was not directly overhead at Alexandria; instead, it cast a shadow with the vertical equal to 1/50th of a circle (7° 12'). He also knew that Alexandria and Syene were 500 miles apart

4. 3/27 Gravity: Local Attraction not Unfortunately, the density of the earth’s crust is not uniformly the same. Heavy rock, such as an iron ore deposit, will have a stronger attraction than lighter materials. Therefore, the geoid (or any equipotential surface) will not be a simple mathematical surface. Vertical Datums The Geoid

5. 4/27 What is the GEOID? “The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, global mean sea level.”“The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, global mean sea level.” Can’t see the surface or measure it directly.Can’t see the surface or measure it directly. Modeled from gravity data.Modeled from gravity data. Vertical Datums The Geoid

6. 5/27 Equipotential Surfaces Reference Surface (Geoid) Topography The Geoid Vertical Datums

7. 6/27 An ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. The GRS80 ellipsoid is used for the NAD83. a= 6378137.00000 meters b= 6356752.31414 meters f= 1/(a-b)/a = 298.2572220972 So we squash the sphere to fit better at the poles. This creates a spheroid a = 6,378,137.00000 m b = 6,356,752.31414 m Close Fit At The Equator But The Poles Are Out NAD83 uses the GRS80 Ellipsoid GRS80 fits geoid to about +/- 300’

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9. 8/27 h Earth’s Surface P

10. 9/27 A point, line, or surface used as a reference, as in surveying, mapping, or geology.

11. 10/27 GRS80-WGS84 CLARKE 1866 GEOID Earth Mass Center Approximately 236 meters Local vs. Global Reference Ellipsoid Basic Geodesy

12. 11/27 UNITED STATES ELLIPSOID DEFINITIONS CLARKE 1866 a = 6,378,206.4 m 1/f = 294.97869821 GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) a = 6,378,137 m 1/f = 298.257222101 WORLD GEODETIC SYSTEM 1984 - (WGS 84) a = 6,378,137 m 1/f = 298.257223563 BESSEL 1841 a = 6,377,397.155 m 1/f = 299.1528128 Basic Geodesy

13. 12/27 Ellipsoid vs. Geoid Ellipsoid –Simple Mathematical Definition –Described by Two Parameters –Cannot Be 'Sensed' by Instruments Geoid –Complicated Physical Definition –Described by Infinite Number of Parameters –Can Be 'Sensed' by Instruments Vertical Datums

14. 13/27 Ellipsoid vs. Geoid Vertical Datums High Density Low Density ellipsoid geoid Earth’s surface

15. 14/27 N = separation between geoid and ellipsoid (Geoid03) h = elevation relative to ellipsoid (GRS80) This is what we reference our project elevations to. These are the elevations you get from the NGS datasheets and traditionally were obtained from geodetic leveling h = H + N The geoid is the equipotential surface of the earth’s attraction and rotation which, on the average, coincides with mean sea level in the open ocean. They are instead referenced to the GRS80 ellipsoid, that squashed sphere that best fits the earth and is used for NAD83 Let’s take a look at the difference between NAVD88 elevations (orthometric heights) and the ellipsoid heights from GPS H GPS heights are not related to either orthometric or hydraulic/tidal elevations. h N To convert GPS derived heights to NAVD88 you must use the latest geoid model (currently Geoid03) H = elevation relative to geoid (orthometric or NAVD88)

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17. 16/27 Geoid Model

18. 17/27 H is measured traditionally h is measured with GPS Observations N is modeled using Gravity Models Vertical Datums h = H + N

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20. 19/27 NSRS Coordinate Systems Latitude & Longitude State Plane Coordinates UTM Coordinates NAD 83 NAD 27

21. 20/27 Surfaces Used In State Plane Coordinate Systems Lambert ProjectionTransverse Mercator Projection East-West North-South EARTH IMAGINARY CYLINDER A C B D A CD B IMAGINARY CONE EARTH Conformal (preserve distances and directions within defined limits)Conformal (preserve distances and directions within defined limits) 158 miles for 1:10,000 Basic Geodesy 158 miles wide

22. 21/27 Conic Projections (Lambert) The lines where the cone is tangent or secant are the places with the least distortion.

23. 22/27 Cylindrical Projections (Mercator) Transverse Oblique The lines where the cylinder is tangent or secant are the places with the least distortion. Panhandle of Alaska

24. 23/27 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 168W 162 156 150 144 138 132 126 120 114 108 102 96 90 84 78 72 66 60 54W UTM Zones Basic Geodesy

25. 24/27 UTM Zone 14 Equator -120° -90 ° -60 ° -102°-96° -99° Origin 6° Basic Geodesy

26. 25/27 NAD83 State Plane Coordinate Zones State Plane Coordinate System - 1983 Basic Geodesy

27. 26/27 NAD83 State Plane Units of Measure Basic Geodesy 2007

28. 27/27 Additional Information Available at: http://crunch.tec.army.mil/information/SM_CoP/ndsp mark.w.huber@usace.army.mil