Lecture 1(Class 2)

1. GISC3325-Geodetic Science 20 January 2009 Lecture 1(Class 2)

2. Course Update • Reading assignment for this week: Chapters 1-3 of the text. • Lab 1 must be received by midnight 21 January 2009. • Next two labs deal with NGS monument recovery. Details are posted to the class web page. It involves on-line research and field work. Points recovered will be used in subsequent labs.

3. Topics for today • Definitions of geodesy • Divisions of geodesy • Reference surfaces for heights • Experiment of Eratosthenes, the Father of Geodesy

4. Geodesy defined • The discipline that deals with the measurement and representation of the earth, including its gravity field, in a three-dimensional time-varying space. (Vanicek and Krakiwsky) • The problem of geodesy is to determine the figure and the external gravity field of the earth and of other celestial bodies as functions of time; as well as ,to determine the mean earth ellipsoid from parameters observed on and exterior to the earth's surface. (Torge)

5. Why is geodesy important to land surveyors? • Surveyors often required to establish vertical and horizontal control project. • Use of GPS fundamentally linked to geodetic issues of coordinates, reference frames, etc. • GIS should have as base layer geodetic control. • SPCS based on reference ellipsoid • Coordinate transformations (e.g. between NAD 27 and NAD 83) are geodetic problems.

6. Datum • A geodetic datum is represented by a set of physical monuments on the earth's surface, published coordinates for these monuments, and a reference surface upon which the spatial relationships between the monuments are known. (textbook)

7. Another and better definition • Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle. Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements. • From Peter Dana's site: http://www.colorado.edu/geography/gcraft/notes/datum/datum.html

9. Divisions of Geodesy • Areas of emphasis in geodesy include: • Geometric • Physical • Satellite • Astronomy • Getting positions and heights from GPS involves all these areas. • Remember: h – H – N = 0 plus errors in h,H, and N

10. Reference Surfaces • Topographic surface • Geometric reference surface • Physical reference surface

11. Their Characteristics • Topographic surface is where we live and work. It usually corresponds with neither the geometic nor physical reference surface. • Geometric reference surface is the mathematical reference system used for making calculations. • Sphere – used in astronomical computations and for approximate results. • Ellipse – more precise but more complex. The Earth as an ellipsoid of revolution takes into account for flattening of the sphere.

12. Physical reference Surface • Geoid, is from the Greek for "Earth-shaped", is the common definition of our world's shape. This recursive description is necessary because no simple geometric shape matches the Earth. • Our definition: The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level.

13. Geoid model from GRACE data

14. Heights

15. Heights • Point on topographic surface (terrain) • Ellipsoid height (h) is the distance from the ellipsoid reference surface to the terrain. • H – Orthometric height (NAVD88) is the distance from the geoid to the terrain. • N – Geoid height is the distance between the geoid and the ellipsoid reference surface.

16. From below: -23.949(h) – 1.83(H) - (-25.75)(N) = 0.029 error AH1762 *********************************************************************** AH1762 HT_MOD - This is a Height Modernization Survey Station. AH1762 CBN - This is a Cooperative Base Network Control Station. AH1762 TIDAL BM - This is a Tidal Bench Mark. AH1762 DESIGNATION - 877 5870 H TIDAL AH1762 PID - AH1762 AH1762 STATE/COUNTY- TX/NUECES AH1762 USGS QUAD - CRANE ISLANDS SW (1975) AH1762 AH1762 *CURRENT SURVEY CONTROL AH1762 ___________________________________________________________________ AH1762* NAD 83(2007)- 27 35 17.26666(N) 097 13 22.29500(W) ADJUSTED AH1762* NAVD 88 - 1.83 (meters) 6.0 (feet) GPS OBS AH1762 ___________________________________________________________________ AH1762 EPOCH DATE - 2002.00 AH1762 X - -711,246.902 (meters) COMP AH1762 Y - -5,612,090.901 (meters) COMP AH1762 Z - 2,936,118.126 (meters) COMP AH1762 LAPLACE CORR- 0.94 (seconds) DEFLEC99 AH1762 ELLIP HEIGHT- -23.949 (meters) (02/10/07) ADJUSTED AH1762 GEOID HEIGHT- -25.75 (meters) GEOID03

17. Experiment of Eratosthenes • Measured earth's radius/circumference in 220 BCE • At local noon on the summer solstice it was possible to see to the bottom of a well in Syene. • On the same day/time he measured the angle of sun's rays in Alexandria. • He then measured the distance between Syene and Alexandria. • Using simple geometry, he calculated the radius and the circumference of the Earth.

19. Details • The angle was measured by solving the right triangle using the known height of a staff and the shadow formed by the sun. • The angle was found to be 7.2 degrees. • The distance (S) between the two cities was 5000 stade (1 stade ≈ 160 m) • Use equivalent fractions to solve. • (7.2deg/360deg) = (S / circumference of earth(C))

20. How good was the result?

21. Scilab Code - http://www.scilab.org/

22. Complications • We don't really know the length of a stade. • Syene and Alexandria are not on the same meridian making the angle inaccurate. • Angle seems surprisingly convenient (7.2 degrees is 1/50 of a circle).

23. Unit questions • We still see problems with unit conversions. • US Survey foot is equal to 3927/1200 exactly • Or 3.2808333333... approximately • International foot is based on relationship of 2.54 cm = one inch. • i.e. (0.0254 * 12) = 0.3048 cm/ft • Or 3.28083989501 meters in one foot • If we confuse the two we get bad results converting SPCS values.