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Home , Figure of the Earth, Geomatics, History of geodesy, Physical geodesy, Satellite geodesy

Introduction to

Alexander Braun

Byrd Polar Research Center and Laboratory of and The Ohio State University, Columbus, OH, USA [email protected] Undergraduate course Dept. of Engineering, University of Calgary

<< >> What is Geodesy?

Geodesy (greek) - divide the ⇒ F.R. Helmert (1880) - “The science of measuring the size and shape ⇒ of the Earth and of mapping of the Earth”

Torge (1975) - added and reference frame “Geodesy aims at ⇒ determining the size and shape of the Earth globally as well as its intrinsic gravity field, also generated by other celestial bodies, and the International Reference as global reference frame, all as function of time.”

<< >> What is Geodesy?

Determination of the size and shape of the Earth ⇒ by measuring distance and >> coordinates → Time dependency of distance and angle >> dynamics, reference ⇒ frame caused by Earth rotation, , plate motions, , → tides

Gravity field >> determines the and drives the dynamical ⇒ processes distribution, external bodies, Earth and ocean tides, → atmospheric mass variations

GEOMETRY - DYNAMICS - GRAVITY OF THE EARTH

<< >> What are the objectives?

Provide fundamental parameters for life on Earth and in space ⇒ ⇒ Gravity field ⇒ Variations in time ⇒ Provide reference frame and coordinates ⇒ Provide projections, coordinate transformations, and reference ⇒ systems

<< >> What are the tools?

Theodolite, , compass, laser levels ⇒ GPS - global positioning, clock ⇒ Gravity field - , airborne, terrestrial, space-borne ⇒ Reference frame, coordinates, projections - mathematical description ⇒ of the size and shape, or measurements, or analytical relationships

sensors - GPS, altimetry, laser ranging, VLBI, DORIS, SAR ⇒

<< >> Who is using geodesy?

engineering - , transportation, GPS, , ⇒ monitoring of deformations, cadastral information, GIS

and geology - mineral exploration, crustal and earthquake ⇒ deformation,

- change, tides, ship routing, ⇒ physics - linear collider, Synchrotron Radiation Facilities, no-gravity ⇒ experiments

“Geodetic sciences” uses geodesy for solving scientific problems “Geomatics engineering” uses geodesy for solving engineering problems.

<< >> Course title: Introduction to Geodesy ⇒ Lectures: 3 times per week, 1 hour each, total: 39 hours ⇒

Laboratory: 1 per week, 2-3 hours, total: 26-39 hours ⇒

Pre-requisites ⇒ AMAT217: Calculus for engineers and scientists → ENGG233,ENGG335: Computing I + II → AMAT309: Vector calculus → High-school physics →

<< >> Grading ⇒ Final exam: 40% Labs: 30% Quiz: 20% Presentation: 10%

Literature ⇒ W. Torge, Geodesy, 2001, Paperback 416 pp, Walter de Gruyter, ISBN: 3110170728 Heiskanen, W.A. and H. Moritz, 1967: , W.H. Freeman, San Francisco, 364 pp J. A. Elithorp Jr and D. D. Findorff, Geodesy for Geomatics and Geographic Information System Professionals, paperback: 259 pages, ISBN: 1-59399-087-1

<< >> Section Title lecture hours 1 What is geodesy? 1 2 and coordinate systems 4 3 Reference system and reference frame 4 4 Coordinate transformations and 3 5 Gravity field 5 6 Geodynamics 3 7 geodesy 2 8 Gravity missions 2 9 Altimetry and SAR 2 10 VLBI, GPS, and 3 11 Basic applications in engineering 3 12 Course summary 1 13 Lectures used for quiz preparation/ repetition and student presentations 6 << >> Labs

# Title 1 Trigonometry, coordinate systems, reference frame, transformations 2 Gravity field and geodynamics 3 and sensors 4 Selected geodetic problems

<< >> Quiz and Final Exam

# Title 1 Quiz after lecture section 4 including Trigonometry, coordinate systems, reference frame, transformations 2 Final exam including entire course and lab material

<< >> Outline of the course

1-1 lecture: What is geodesy? ⇒ of Geodesy, famous geodesists, geodesy as a link between natural sciences and engineering.

2-4 Trigonometry and coordinate systems ⇒ space-fixed, Earth fixed, non-geocentric, celestial, geocentric, topo- centric coordinate systems spherical and ellipsoidal coordinates

3-4 Reference system and reference frame ⇒ IERS, celestial and terrestrial reference frame, WGS84, GRS80, height systems, numbers, orthometric heights, normal heights, , ellipsoid, rotational ellipsoid, , vertical deflections

<< >> 4-3 Coordinate transformations and vertical datum ⇒ , orthometric and ellipsoidal height, map projections

5-5 Gravity field ⇒ , geopotential, centrifugal forces, Laplace and Poisson equation, spherical harmonic expansions, normal gravity, Brun’s formula, gravity anomalies, Vening-Meinesz transformation, gravimetry, gradiometry, abs. and relative gravimetry, networks, Bouger gravity, , temporal gravity variations

6-3 Geodynamics ⇒ motion in a celestial systems, motion in a terrestrial system, Earth rotation, precession and nutation, Earth deformations, Earth tides and ocean tides, tidal loading, plate tectonics, Earthquakes, driving forces of geodynamic processes, pole tides, length of day variations

7-2 Satellite geodesy ⇒ << >> Satellite mission concept, determination, sensor technology, what can we measure better from space and what not?

8-2 Gravity missions ⇒ satellite orbitography, measuring gravity from space (distance, velocity and acceleration methods), CHAMP, GRACE, GOCE, current gravity field models, accuracy, resolution

9-2 Altimetry and SAR ⇒ principles of altimetry, applications, SAR imagery, SAR interferometry, Digital models, JASON-1, , ICESat, CryoSat, ALOS, RADARSAT-2

10-3 VLBI, GPS and satellite laser ranging ⇒ radio-sources, Quasars, VLBI stations and principle of long- baseline interferometry, basics of GPS constellation and positioning, principles of DORIS and station distribution, satellite laser ranging, station coordinates and velocities, ITRF

<< >> 11-3 Applications of geodesy in engineering ⇒ positioning, navigation, transportation, deformation monitoring, hydrography

12-1 Course summary ⇒ 13-6 Lectures used for quiz preparation/repetition and student ⇒ presentations

<< >> Example lecture: Satellite Altimetry

<< >> What is an ?

altus (latin) - height metron (greek) - to measure

An altimeter is an instrument to measure height, altitude or elevation.

Altimeters are based on two physical principles:

Barometric altimeter - pressure difference ⇒ Range altimeter using the distance-velocity-travel time relation ⇒

<< >> A barometric altimeter is a pressure sensor to detect the barometric pressure at instrument altitude.

The difference of the barometric pressure and the pressure at sea level can be converted into the altitude.

altitude = 1000 (SLP BP )) (1) ∗ − e.g. altitude = 1000 (30 in/Hg 28 in/Hg) = 2000 feet (2) ∗ − or in SI units - meters and Pascal:

altitude(m) = 0.09 (m/P a) (SLP (P a) BP (P a)) (3) ∗ − << >> The range altimeter based on a distance-velocity-travel time relation is measuring the two-way travel time of a signal with a known velocity. The distance or the “range” can be derived:

velocity TWT distance = ∗ (4) 2

<< >> Where do we need to measure a distance?

Autofocus in cameras - infrared light (10000 GHz) ⇒ Navigation and positioning - GPS (1.575 Ghz, 1.227 GHz) ⇒ Traffic control, speeding tickets - radar (1 MHz - 3 GHz) ⇒ Aviation - barometric, GPS ⇒ Engineering and construction - GPS, laser (400-800 nm) ⇒

<< >> Electromagnetic waves travel with the speed of light: v = 3 108 m/s ∗

<< >> Satellite altimetry

<< >> Orbit determination

Once we know the travel time and the velocity, we can derive the distance between satellite and Earth surface. To derive the , we need to know the position of the satellite at the time of the measurement, the orbit.

Satellite Laser Ranging - SLR ⇒ DORIS, PRARE ⇒ GPS ⇒

<< >> SLR and DORIS network

>>> Jason - Instruments movie

<< >> What changes the satellite orbit?

Earth gravity field ⇒

Third-body gravitational attraction from the Sun, Moon, other ⇒ planets

Atmospheric drag ⇒

Direct solar radiation pressure ⇒

Albedo radiation reflected from the Earth’s surface ⇒

>>> Orbit and gravity movie

<< >> << >> Mission Operational accuracy cycle/d altitude/km

Skylab 1973 9 month 100 m 435 GEOS-3 1975-1978 1-2 m 30 days 840 1978 3 month 10 cm 762 1986-90 5 cm 800 Topex/Poseidon 1992 - present < 5 cm 9.9 1337 ERS-1 1991 - 2000 5 cm 35, 163 780 ERS-2 1995 - 2003 5 cm 35 780 GFO-1 1998 - present 5 cm 800 Jason-1 Dec 2001 - pres. < 5 cm 9.9 1337 ENVISAT Mar 2002 - pres. < 5 cm 35 796

<> Laser altimetry missions

MGS 1996-2000 2-30 m 378 ICESat Earth Jan 2003 - present < 10 cm 8, 91 600 SELENE Moon Sep 2004 5 m 100 km

<< >> Altimetry data coverage

Depending on the orbit characteristics, the satellite is flying in different patterns. Projected onto the Earth’s surface, the flight lines are called tracks. Compromise of temporal and spatial resolution

<< >> Radar or Laser?

Radar altimetry Laser altimetry - footprint 2-20 km - footprint 40-70 meters - vertical accuracy < 5cm - vertical accuracy < 10cm - weather independent - weather dependent, clouds - robust - energy consuming, not robust - long history, 18 years - short missions only - operates on most altimetry - operates on ICESat, MGS and missions - works over water and SELENE - works over water, ice ice and land

<< >> Applications

Satellite altimetry has applications in oceanography, geophysics, geodesy, glaciology, atmospheric and space science, and, since ICESat also in hydrology, and forestry.

Highly dynamic processes need to be observed as often as possible and require a short orbital cycle, e.g. ocean currents. Static processes require maximum spatial resolution, but no temporal resolution, e.g. marine gravity anomalies.

<< >> Mean sea surface height

Knudsen and Andersen

<< >> Marine gravity anomalies

<< >> Global bathymetry - Smith and Sandwell

<< >> EL Nino Southern Oscillation

<< >> Sea level change

<< >> from altimetry

<< >> Ground truth

<< >> Ground truth

<< >> Mars topography - MOLA

<< >> ICESat over Cleveland

<< >> Virtual satellite mission

What do you want to study? ⇒ Is the process static or dynamic? ⇒ What spatial resolution is required? ⇒ What temporal resolution is required? ⇒ What ground-truth can you provide for calibration? ⇒ How long do you need to observe - mission duration? ⇒ ...... ? ⇒

<< >> You can answer all of these questions? ⇒ Write it down and contact a space agency? ⇒ and then ...... ⇒ You can answer all of these questions? ⇒ Write it down and contact a space agency? ⇒ and then ...... ⇒

GOOD LUCK and thanks for your attention!!!!

Pictures, movies and data have been provided by NASA, JPL, ESA, CNES, JAXA, GFZ

Figures made with iGMT, GMT, gnuplot. Presentation created by pdflaTeX and PPower4.

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