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Satellite Altimetryaltimetry Andand Gravimetrygravimetry:: Theory and Applications C.K SatelliteSatellite AltimetryAltimetry andand GravimetryGravimetry:: Theory and Applications C.K. Shum1,2, Alexander Bruan2,1 1,2 Laboratory for Space Geodesy & Remote Sensing 2,1Byrd Polar Research Center The Ohio State University Columbus, Ohio, USA [email protected], [email protected] http://geodesy.eng.ohio-state.edu Norwegian Univ. of Science and Technology Trondheim, Norway 21–25 June, 2004 Satellite Altimetry and Gravimetry: Theory and Applications Tuesday, 22 June 2004 • Orbital Dynamics & Orbit Determinations II (AM) By C.K. Shum – Nonlinear orbit determination & parameter recovery – Force, measurement, and Earth orientation models • Satellite Altimetry II (AM) By C.K. Shum – Principles of satellite altimetry, mission design, waveforms – Geographically correlated orbit errors and POD – Instrument, media and geophysical corrections • Altimeter Collinear Analysis (PM) By Alexander Braun – Stackfile method for oceanography and marine geophysics – Mean sea surface, marine gravity field determinations – Models accuracy evaluations and limitations • Radar Altimeter Data Processing (PM) By Alexander Braun • Tutorial on iGMT (continued) (PM) By Alexander Braun Background and History: Satellite Altimetry NASANASA’’SS EarthEarth ObservingObserving SystemSystem Satellites:Satellites: Terra,Terra, AquaAqua 15 February 2004 C. Shum 9 Credit: NASA/GSFC NASANASA’’SS EarthEarth ObservingObserving SystemSystem Satellites:Satellites: Terra,Terra, AquaAqua Example15 February temporal 2004 and spatialC. Shumsampling of 10 satellite (LEO) measurements from space Credit: NASA/GSFC SATELLITESATELLITE ALTIMETRYALTIMETRY Radar altimetry concept was formulated in the Williamstown Conference [William Kaula et al.] in 1969. NASA’s GEOS-3 is the first radar altimeter demonstrating the measurement of sea surface heights of the global ocean. Initially designed to measure ocean, radar altimetry has been demonstrated to be useful in the measurement of land and sea ice, land topography, lake and rivers, etc Measurement Coverage: TOPEX/POSEIDON, JASON: 660 latitude coverage ERS-1/2, Envisat 820 latitude coverage Seasat, Geosat, GFO Jason 720 latitude coverage CRYOSAT 940 latitude coverage ICESAT (Laser) ICESAT 940 latitude coverage Altimeter measures geocentric sea level and ice sheet elevation change Courtesy: A. Braun 15 February 2004 C. Shum 12 Earth Satellite Altimeters Ku-band altimeter (multiple antennas) capable of nadir, SAR, and InSAR mode. CRYOSAT Potential15 February tracking 2004 closer to C. Shum 13 coastlines. No radiometer. Courtesy, ESA Satellite Altimetry and Gravimetry: Theory and Applications Tuesday, 22 June 2004 • Orbital Dynamics & Orbit Determinations II (AM) By C.K. Shum – Nonlinear orbit determination & parameter recovery – Force, measurement, and Earth orientation models • Satellite Altimetry II (AM) By C.K. Shum – Principles of satellite altimetry, mission design, waveforms – Geographically correlated orbit errors and POD – Instrument, media and geophysical corrections • Altimeter Collinear Analysis (PM) By Alexander Braun – Stackfile method for oceanography and marine geophysics – Mean sea surface, marine gravity field determinations – Models accuracy evaluations and limitations • Radar Altimeter Data Processing (PM) By Alexander Braun • Tutorial on iGMT (continued) (PM) By Alexander Braun EarthEarth SatelliteSatellite AltimetryAltimetry MissionsMissions Mission Launch Date Skylab 1973 GEOS 3 1974 SeaSat 1978 GEOSAT GM*/ERM 1984 ERS-1* (Geodetic phase) 1991 TOPEX/POSEIDON 1992 ERS-2 1995 GFO 1998 JASON 2001 *Non-repeat ENVISAT 2002 ground tracks ICESAT (laser) 2003 15 February 2004Planned: CRYOSAT C.(2004), Shum JASON or OSTM (2007) 16 Proposed: ABYSS, NPOESS, GAMBLE NASA/CNESNASA/CNES JASON-1JASON-1 AltimeterAltimeter MissionMission (2001)(2001) Altitude: 1354 km 10-day repeat orbit 660 Inclination 15 February 2004 C. Shum 17 Credit: NASA/JPL Principle of Satellite Altimetry • Fundamental design • Radar principle • Temporal-spatial sampling (ground track patterns) Radar altimeter operates in Ku- band, 13.6 GHz (λ=2.21 cm), C- band (5.6 GHz), & S-band (4.2 GHz) L-band (1.0–1.5 GHz), S-band (1.5–4.2 GHz), C-band (4.2–5.4 GHz), X-band (5.7–10.9 GHz), Ku-band (10.9–22.0 GHz) [Low –>high] Electromagnetic Spectrum [Source: NASA/JPL] Radar Altimeter Geometry Measurement Concept: Altimeter Crossover • Active (2-way) nadir pointing microwave (radar) instrument • Accurate clock • Altimeter range (halt)= c(2∆t) where c=speed of light Implies that the clock needs to be accurate to < 1 µsec for halt to be accurate to < 1 cm • Mean Sea Surface: –100 m to +80 m • Geoid ~ MSS • Ocean topography: ~ several meters • Ellipsoid: ~6378 km • Altimeter altitude: 800 – 1300 km Radar Altimeter Footprint radius of footprint R : R = cτh c – speed of light τ – pulse width (pulse duration) , actual h – satellite hight Geos-3: h =840, τ =12.5 ns =12.5×10−9 second , R = 3.6 Seasat: h =800, τ =3ns =3×10−9 , R = ? 16H 2 ln 2 τ 2 = τ 2 + p c2 τ : radar’s theoretical pulse width p pulse-length-limited H :standard deviation of wave height beamwidth-limited Effect of SWH 1.94 SWH 0.56M SWH time(gate) SWH will cause electromagnetic bias (emb) .The higher the SWH , the lower received pulse energy OceanOcean surfacesurface reflectivityreflectivity andand atmosphericatmospheric attenuationattenuation Maul [1985] Clear sky attenuation, Courtesy: Chelton et al. [2001] radar affected by rain, cloud Pulse-LimitedPulse-Limited RadarRadar AltimetryAltimetry Beam-limited (L) and pulse-limited (R) altimeter designs. For T/P (1350 km, 13.6 GHz) the Pulse-Limited Altimeter Footprint and antenna diameter would be ~8 m for beam- operations limited altimeter design. Pulse-limited altimeters issue many short-pulses and provides an average. E.g. antenna width for T/P is ~1.5 m. T/P: bandwidth ~0.3 Ghz (3 ns pulse) Courtesy: Chelton et al. [2001] Pulse-LimitedPulse-Limited RadarRadar AltimetryAltimetry Plane views of illuminated pattern Averaged waveform return of radar with various pulse duration for 2 different wave heights Courtesy: Chelton et al. [2001] DevelopmentDevelopment at at APL APL ofof the the original original satellite-basedsatellite-based navigationnavigation system system (1959-1998,(1959-1998, TransitTransit)) Courtesy: K. Raney Conventional radar altimetry: Pulse-Limited Power (F0) Surface response function Slope (SWH) Track point Pulse length (Time delay) Time Quasi-flat sea SWH > pulse length Plan view of Pulse-limited illumination annuli footprint 97/10/13 rkr Courtesy: K. Raney Altimeters Compared DDA: More averaging => x2 better precision, x10 better efficiency Advantage: along-track incidence and Doppler equivalence Processing: remove Conventional (modulo PRF) extra delay due to Delay/Doppler wavefront curvature, which converts all Pulse length Pulse length data along-track to height measurements Doppler modulation Along track Pulse Doppler segmentation limited Pulse- permits closer approach to Annuli of footprint equal areas Doppler land and vegetation limited footprint Two-dimensional section of the 0 0 angular scattering function at each 1 1 Multi-looks at each location and every 2 2 subsatellite point 3 3 Relative time delay ~250 m Courtesy: K. Raney Repeat orbits: designed (+/-1 km spacing at equator) for mesoscale oceanography and sea level, 35-day repeat orbits): optimize temporal sampling and sacrifice spatial coverage Non-repeat (Geodetic) orbits: designed for fine-spatial sampling, suffers from temporal sampling (Geosat GM, ERS-1 Geodetic phase, proposed ABYSS mission) 10-day Repeat 35-day Repeat 17-day Repeat GEOSATGEOSAT GEODETICGEODETIC MISSIONMISSION GROUNDGROUND TRACKTRACK PATTERNPATTERN Orbit Determination: Dynamic, reduced dynamic, kinematic Equation of Motion: r ← vector ˙r˙ = −µ r3 ← scalar + ∇U + F U - conservative (gravitational) forces F - Non-conservative forces € PRECISION ORBIT DETERMINATION METHODS Dynamical Equations of Motion: GMr &r&= + ∑ f (r,v,c,t) r 3 r,v - Position and Velocity Vectors ∑ f (r,v,c,t) - Perturbation Forces Gravitational: • Non-spherical Earth • Luni-solar and planetary • Solid Earth tides • Ocean tides • General relativity Nongravitational: • Atmospheric drag • Direct solar radiation pressure • Earth albedo radiation pressure • Empirical forces c - Constant Parameters • Dynamical • Kinematical DOMINANTDOMINANT PERTURBATIONSPERTURBATIONS ONON NEAR-EARTHNEAR-EARTH ORBITINGORBITING SATELLITESSATELLITES • Gravitational – Geopotential, N-body, solid Earth and ocean tides (astronomical) – Cryospheric, oceanic, hydrological, atmospheric mass variations* – Secular mass variations due to postglacial rebound, sea level, etc.* – General relativity • Nongravitational *Currently not modeled – Atmospheric drag – Solar radiation pressure (includes Earth eclipsing) – Earth radiation pressure (optical and infrared) • Non-rotating (Inertial) and Terrestrial reference frames – Station positions, horizontal velocities, vertical motion* – Precession, nutation, Earth rotation, polar motion – Geocenter motion* and loading (tidal, atmospheric*, hydrological*) • Satellite thrust/thermal radiation models • S/C attitude (CM motion wrt tracking sensors and instrument) Accelerations on Satellite Orbits Chelton et al. [2001] SLR Tracking System Chelton et al. [2001] DORIS Tracking System Chelton et al. [2001] GlobalGlobal PositioningPositioning SystemSystem SatellitesSatellites GeosatGeosat OrbitOrbit ErrorError Spectra:Spectra: heightheight vsvs SlopeSlope Radial Orbit Error of ~5 m at 40,000 km scale (once per revolution), is about
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