APG4001S Geodesy 2024 Lecture Notes PDF

APG4001S GEODESY - 2024 Lectures ▪ Monday –Friday 9 – 9:45 am (GTL) Tutorials: ▪ Wednesdays: 2 – 5 pm (GCL) Patroba Odera Room: 5.06 [email protected] APG4001S Geodesy  Assessments Test-1: Wednesday 28 August 2024 Test-2: Wednesday 9 October 2024 ❖ E...

APG4001S GEODESY - 2024 Lectures ▪ Monday –Friday 9 – 9:45 am (GTL) Tutorials: ▪ Wednesdays: 2 – 5 pm (GCL) Patroba Odera Room: 5.06 [email protected] APG4001S Geodesy  Assessments Test-1: Wednesday 28 August 2024 Test-2: Wednesday 9 October 2024 ❖ Examination: Wed. 30 Oct – Wed. 20 Nov. 2024 DP requirements: Completion of all lessons, assignments and tests with a minimum average of 40% (from combined marks for all tests and assignments). Assessment: Tests count 15%, practical assignments count 25%, examination of 3 hours counts 60% Recommended Texts: Geodesy, 3rd Edition: W Torge GPS Theory & Practice: B Hofmann-Wellenhof, H Lichtenegger & J Collins GPS for Geodesy: A Kleusberg & P Teunissen(Eds) Satellite Geodesy, 2nd Ed: G Seeber Physical Geodesy: B Hofmann-Wellenhof & H Moritz APG4001S Geodesy OUTLINE: 1. Introduction to Geodesy 2. Earth’s Gravity Field / Physical Geodesy 3. Satellite Geodesy / Satellite Positioning 4. Geodetic Networks 5. Datum Transformation Evaluation: Pracs/Assignments: 25% Tests: 15% Examination 60% APG4001S Geodesy Introduction to Geodesy The discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three- dimensional time-varying space APG4001S Geodesy Basic Components of Geodesy Geometry of the Earth Earth Rotation Geodesy Polar Motion Earth’s Gravity Field APG4001S Geodesy Geometry of the Earth Global, Regional and National geodetic control networks Triangulation and Trilateration (accurate angles/distances) Reduction of observations to the reference ellipsoidal and map projections Adjustment of geodetic control networks Mapping of land, sea & ice surface geometry. APG4001S Geodesy APG4001S Geodesy APG4001S Geodesy Plate tectonics movement APG4001S Geodesy  Earth Rotation and Polar Motion o Positional astronomy – geodetic astronomy o Reference frame transformations o Ocean-atmosphere-solid earth coupling o Space geodesy APG4001S Geodesy DORIS - Doppler Orbitography and Radio- positioning Integrated by Satellite LEO – Low Earth Orbiter (e.g. TOPEX/Poseidon) APG4001S Geodesy Earth’s Gravity Field ▪ Potential theory and GBVP ▪ Gravimetry (Terrestrial, Satellite, Air borne and Ship track) ▪ Establishment of Height Datums and Unification APG4001S Geodesy Global gravity anomalies from GRACE APG4001S Geodesy Global geoid model from GOCE APG4001S Geodesy Geodesy in Partnership with International Organizations (a) International Service Organizations International GNSS Service (IGS) Geodesy International Altimetry International Gravimetric Service (IAS) Bureau (BGI) International Bureau on Weights and Measures(BIPM) APG4001S Geodesy  (b) Related International Organizations International Union of Geodesy and Geophysics (IUGG) -American Geophysical Geodesy International Astronomic Union (AGU) Union (IAU) - European Geosciences Union (EGU) International Association of Geodesy (IAG) APG4001S Geodesy FIGURE OF THE EARTH APG4001S Geodesy GEOID: The geoid is that equipotential surface of the Earth's actual gravity field which on average coincides with mean sea level terrain geoid MSL N ( 100m) ellipsoid APG4001S Geodesy  HISTORY OF GEODESY Flat Earth - Spherical Earth – Ellipsoidal Earth – Geoidal Earth Flat Earth -Flat Earth with hemispherical sky-Initial shape of the earth - (Homer) before 625 BC -Disc floating on an ocean - Thales of Miletus (Asia, current Milet in Turkey) (625-547 BC) -Cylinder with the land on its curving surface - Anaximander of Melitus (611-547 BC) APG4001S Geodesy  Spherical Earth -Postulated by Pythagoras (c.580-550 BC) based on philosophical considerations only -First attempt to describe the dimension of the spherical Earth – Aristotle (c. 384 – 322 BC) – diameter of the earth (400,000 stades approx. 84,000 – 63,000 km) -Second guess by Archimedes (321 BC) – diameter of the earth (400,000 stades approx. 63,000 – 47,000 km) -Eratosthenes: First scientific description of the figure of the earth (276–195 BC)  Alexandria R d  Syene (Aswan) – the sun is directly overhead during summer solstice (21 June ) Value obtained 6267km, d Accepted value of 6371km R= (2% error)  APG4001S Geodesy  USE OF LATITUDE:  = 2 − 1 (observed)  d R=  to star    d R     =  + The latitude, , is determined by measuring the zenith angle, , (at transit) for a star with known declination,  APG4001S Geodesy Other Determinations ❖ Posidonius - 100BC ❖ Caliph al-Mamon - 820AD ❖ Fernel - 1524 New Technology ❖ Triangulation (Frisius, 1540) ❖ Telescope (Kepler, 1611) APG4001S Geodesy Triangulation: ❖ Snellius - 1615 ❖ Picard - 1670 APG4001S Geodesy Ellipsoidal Earth ❖ Pendulum (Jean Richer – 1672): Clock running correctly in Paris (France) runs too slow in Cayenne (French Guiana): T = 2 g This implies that gravity decreases towards the equator ❖ Newton (1687) derives from theoretical considerations that a rotating fluid body (Earth) would assume an ellipsoidal shape: b a −b 1 f =  (Newton) a a 310 - Huygens (1690) – Similar conclusion APG4001S Geodesy  Prolate or Oblate? Newton Cassini French Academy expeditions to Lapland (Finland) (1736-1738) and to Peru (1734-1744), together with recalculated French arc (1740) resolved the question APG4001S Geodesy  ARC MEASUREMENTS B1  1.1 B2   2.2 a (1 − e 2 ) where = 3 (1 − e 2 sin 2  ) 2 Key result (oblate ) Two equations in a, e2 , to solve for for a, e2 B1 > B2 APG4001S Geodesy Determination of "best" reference ellipsoid: ❖ Longer arcs ❖ More precise angles and directions ❖ Least squares ❖ Meridian and parallel arcs ❖ Impact of military mapping needs Recent reference Results: ellipsoids Mason and Dixon 1761 -GRS67 Delambre and Mechain 1798 -GRS72 -GRS80 Gauss 1821 -WGS84 Everest 1841 Very Recent reference Clarke 1866, 1880 Systems/Frames Helmert 1870 -ITRS -ITFR APG4001S Geodesy Geoidal Earth ❖ In the 1880's Helmert proposed that a better model for the Earth would be the geoid  ellipsoid deflection of the vertical N geoid N = geoidal height   Line integral of  provides difference in geoidal height APG4001S Geodesy GEOID Determination: R ❖ Stokes' (1849) : N= 4  g.S ( ).d g = g −  (needs extensive gravity coverage, plus powerful computer) Because of the lack of data (especially in southern oceans, Russia, China, Africa), not very successful as a stand-alone method ❖ Other key contributions, Molodensky 1945-1964, Bjerhammar 1965, Sanso 1977, Moritz 1980 Other Technologies: ❖ EDM – late 1950's - provided scale for geodetic networks ❖ Computers – late 1960's – provided means of rigorous adjustments APG4001S Geodesy Use of Satellites: ❖ Perturbations in satellites' orbits are caused by variations in the Earth's gravity field. Hence, measure perturbations, deduce gravity variations and deduce variations in geoid (shape of Earth), (Recently, CHAMP, GRACE, GOCE) ❖ Direction and range measurements to and from satellites are also used to determine precise relative positions (e.g. GPS) APG4001S Geodesy SOUTH AFRICAN GEODETIC HISTORY-1 NETWORKS: ❖ 1751: LaCaille's arc from Cape Town to Piketberg ❖ 1841: Maclear's arc from Agulhas to Kamieskroon ❖ 1859: Bailey's survey of the Cape South coast ❖ 1883: Gill/Morris geodetic survey of Cape & Natal ❖ 1906: Gill/Morris geodetic survey of Transvaal and Orange River Colony ❖ 1900 – 1960's: Infill and densification of networks Introduction of plane co-ordinate system ❖ 1970's: EDM traverses to provide scale ❖ 1980's: TRANSIT doppler system ❖ 1990's: GPS control network ❖ 1999: New South African datum – Hartebeesthoek 1994 APG4001S Geodesy SOUTH AFRICAN GEODETIC NETWORKS - 1 APG4001S Geodesy SOUTH AFRICAN GEODETIC NETWORKS - 2 APG4001S Geodesy SOUTH AFRICAN GEODETIC NETWORKS (TrigNet) - 3 APG4001S Geodesy  Hartebeesthoek 1994 (HART94 Datum) ❖ Uses WGS84 ellipsoid: a = 6378137,000m, b = 6356752,314m ❖ Initial point is VLBI telescope at Hartebeesthoek - ITRF91(1994.0) ❖ National GPS network (> 100 points) adjusted in 3D - (X, Y, Z) ❖Relative accuracies of the order of 1ppm ❖From 1 January 1999 Due to crustal motion the Hart94 co-ordinates are not consistent with the co- ordinates used for TrigNet (ITRF2005(2008.002) – average shifts of 36cm () and 14cm () Also errors in Hart94 (10-20cm horizontal, 30-40cm vertical)  Cape Datum This datum was used in South Africa prior to 1999: ❖ Uses modified Clarke 1880 ellipsoid: a = 6378249.145m b: 6356514.967m ❖ Initial point is Buffelsfontein, near Port Elizabeth  = -33o 59' 32“.000;  = 25o 30' 44“.622;  = 3o 58' 15",000 (to Zuurbergh from North)) ❖ Zero deflections, zero geoidal height ❖ Non-rigorous piecemeal adjustment of terrestrial data spanning > century X0   −136m   −135.4m  -134.7m  Y   −108m   −106.7m  -110.9m   0        Z0   −292m  NGA  −291.7m  UCT -292.7m  CDSM  Arc Datum Basically, these are re-adjustments of portions of the southern and east African geodetic triangulation: ❖ Uses modified Clarke 1880 ellipsoid: a = 6378249.145m b: 6356514.967m ❖ Initial point is Buffelsfontein, near Port Elizabeth ❖ Selected chains of triangulation, coinciding roughly with the 30th meridian arc, extending from Buffelsfontein to Uganda were adjusted ❖ Arc 1950 adjustment provided datum for Zambia, Malawi, Rwanda, Burundi ❖ Arc 1960 adjustment provided datum for Uganda, Tanzania and Kenya  SOUTH AFRICAN GEODETIC HISTORY - 2 GRAVITY & GEOID: ❖ 1818: First gravity measurements ❖ 1950's: First national gravity surveys ❖ 1960's: Geoidal profile at 30° south from astronomic observations ❖ 1985: First geoid model for South Africa, from gravity and satellite data ❖ 2006: Refined geoid model for southern Africa SPACE: ❖ 1970 - : VLBI measurements at Hartebeesthoek ❖ 1993: First SLR measurements; permanent SLR at HartRAO in 2000 ❖ 1990 - : GPS control networks; IGS; TrigNet APG4001S Geodesy GRAVITY & GEOID APG4001S Geodesy SPACE GEODESY IN SOUTH AFRICA APG4001S Geodesy SPACE GEODESY IN SOUTH AFRICA source: HartRAO APG4001S Geodesy