Satellite Altimetry andSatellite Altimetry andGravimetryGravimetry: : Theory and ApplicationsTheory and Applications
C.K. ShumC.K. Shum1,21,2, Alexander Bruan, Alexander Bruan2,12,1
1,21,2Laboratory for Space Geodesy & Remote SensingLaboratory for Space Geodesy & Remote Sensing 2,12,1Byrd Polar Research CenterByrd Polar Research Center
The Ohio State UniversityThe Ohio State UniversityColumbus, Ohio, USAColumbus, Ohio, USA
[email protected]@osu.eduedu, , [email protected]@osuosu..edueduhttp://geodesy.eng.ohio-state.http://geodesy.eng.ohio-state.eduedu
Norwegian Univ. of Science and TechnologyTrondheimTrondheim, Norway, Norway
2121––25 June, 200425 June, 2004
Satellite Altimetry andSatellite Altimetry and Gravimetry Gravimetry::Theory and ApplicationsTheory and Applications
Tuesday, 22 June 2004Tuesday, 22 June 2004•• Orbital Dynamics & Orbit Determinations II Orbital Dynamics & Orbit Determinations II (AM) By C.K. Shum(AM) By C.K. Shum
–– Nonlinear orbit determination & parameter recoveryNonlinear orbit determination & parameter recovery–– Force, measurement, and Earth orientation modelsForce, measurement, and Earth orientation models
•• Satellite Altimetry II Satellite Altimetry II (AM) By C.K. Shum(AM) By C.K. Shum–– Principles of satellite altimetry, mission design, waveformsPrinciples of satellite altimetry, mission design, waveforms–– Geographically correlated orbit errors and PODGeographically correlated orbit errors and POD–– Instrument, media and geophysical correctionsInstrument, media and geophysical corrections
•• Altimeter Collinear AnalysisAltimeter Collinear Analysis (PM) By Alexander Braun(PM) By Alexander Braun–– Stackfile Stackfile method for oceanography and marine geophysicsmethod for oceanography and marine geophysics–– Mean sea surface, marine gravity field determinationsMean sea surface, marine gravity field determinations–– Models accuracy evaluations and limitationsModels accuracy evaluations and limitations
•• Radar Altimeter Data ProcessingRadar Altimeter Data Processing (PM) By Alexander Braun(PM) By Alexander Braun
•• Tutorial onTutorial on iGMT iGMT (continued)(continued) (PM) By Alexander Braun(PM) By Alexander Braun
Background and History:Satellite Altimetry
15 February 2004 C. Shum 9
NASA’S Earth Observing System Satellites: Terra, AquaNASANASA’’S Earth Observing System Satellites: Terra, AquaS Earth Observing System Satellites: Terra, Aqua
Credit: NASA/GSFCCredit: NASA/GSFC
15 February 2004 C. Shum 10
NASA’S Earth Observing System Satellites: Terra, AquaNASANASA’’S Earth Observing System Satellites: Terra, AquaS Earth Observing System Satellites: Terra, Aqua
Credit: NASA/GSFCCredit: NASA/GSFCExample temporal and spatial sampling ofExample temporal and spatial sampling ofsatellite (LEO) measurements from spacesatellite (LEO) measurements from space
SATELLITE ALTIMETRYSATELLITE ALTIMETRYRadar altimetry concept wasRadar altimetry concept wasformulated in the Williamstownformulated in the WilliamstownConference [William Conference [William Kaula Kaula et al.] inet al.] in1969. NASA1969. NASA’’s GEOS-3 is the first radars GEOS-3 is the first radaraltimeter demonstrating thealtimeter demonstrating themeasurement of sea surface heights ofmeasurement of sea surface heights ofthe global ocean.the global ocean.
Initially designed to measure ocean,Initially designed to measure ocean,radar altimetry has been demonstratedradar altimetry has been demonstratedto be useful in the measurement of landto be useful in the measurement of landand sea ice, land topography, lake andand sea ice, land topography, lake andrivers, etcrivers, etc
15 February 2004 C. Shum 12
MeasurementCoverage:
TOPEX/POSEIDON,JASON:660 latitude coverageERS-1/2, Envisat820 latitude coverageSeasat, Geosat, GFO720 latitude coverageCRYOSAT940 latitude coverageICESAT (Laser)940 latitude coverage
Earth Satellite AltimetersEarth Satellite Altimeters
Altimeter measuresgeocentric sea leveland ice sheetelevation change
Jason
Courtesy: A. Braun
ICESAT
15 February 2004 C. Shum 13CRYOSAT
Courtesy, ESA
Ku-band altimeter (multipleantennas) capable ofnadir, SAR, and InSAR mode.Potential tracking closer tocoastlines. No radiometer.
Satellite Altimetry andSatellite Altimetry and Gravimetry Gravimetry::Theory and ApplicationsTheory and Applications
Tuesday, 22 June 2004Tuesday, 22 June 2004•• Orbital Dynamics & Orbit Determinations II Orbital Dynamics & Orbit Determinations II (AM) By C.K. Shum(AM) By C.K. Shum
–– Nonlinear orbit determination & parameter recoveryNonlinear orbit determination & parameter recovery–– Force, measurement, and Earth orientation modelsForce, measurement, and Earth orientation models
•• Satellite Altimetry II Satellite Altimetry II (AM) By C.K. Shum(AM) By C.K. Shum–– Principles of satellite altimetry, mission design, waveformsPrinciples of satellite altimetry, mission design, waveforms–– Geographically correlated orbit errors and PODGeographically correlated orbit errors and POD–– Instrument, media and geophysical correctionsInstrument, media and geophysical corrections
•• Altimeter Collinear AnalysisAltimeter Collinear Analysis (PM) By Alexander Braun(PM) By Alexander Braun–– Stackfile Stackfile method for oceanography and marine geophysicsmethod for oceanography and marine geophysics–– Mean sea surface, marine gravity field determinationsMean sea surface, marine gravity field determinations–– Models accuracy evaluations and limitationsModels accuracy evaluations and limitations
•• Radar Altimeter Data ProcessingRadar Altimeter Data Processing (PM) By Alexander Braun(PM) By Alexander Braun
•• Tutorial onTutorial on iGMT iGMT (continued)(continued) (PM) By Alexander Braun(PM) By Alexander Braun
15 February 2004 C. Shum 16
Earth Satellite Altimetry MissionsEarth Satellite Altimetry Missions
PlannedPlanned:: CRYOSAT (2004), JASON CRYOSAT (2004), JASON or or OSTM (2007)OSTM (2007)ProposedProposed:: ABYSS, NPOESS, GAMBLE ABYSS, NPOESS, GAMBLE
2003ICESAT (laser)
2002ENVISAT
2001JASON
1998GFO
1995ERS-2
1992TOPEX/POSEIDON
1991ERS-1* (Geodetic phase)
1984GEOSAT GM*/ERM
1978SeaSat
1974GEOS 31973Skylab
Launch DateMission
*Non-repeatground tracks
15 February 2004 C. Shum 17
NASA/CNES JASON-1 Altimeter Mission (2001) NASA/CNES JASON-1 Altimeter Mission (2001) NASA/CNES JASON-1 Altimeter Mission (2001)
Credit: NASA/JPLCredit: NASA/JPL
Altitude: 1354 kmAltitude: 1354 km10-day repeat orbit10-day repeat orbit666600 Inclination Inclination
Principle of Satellite Altimetry• Fundamental design• Radar principle
• Temporal-spatial sampling (ground track patterns)
Electromagnetic Spectrum [Source: NASA/JPL]Electromagnetic Spectrum [Source: NASA/JPL]
Radar altimeter operates in Ku-Radar altimeter operates in Ku-band, 13.6 GHz (band, 13.6 GHz (λλ=2.21 cm), C-=2.21 cm), C-band (5.6 GHz), & S-band (4.2 GHz)band (5.6 GHz), & S-band (4.2 GHz)
L-band (1.0L-band (1.0––1.5 GHz), S-band (1.51.5 GHz), S-band (1.5––4.2 GHz), C-band (4.24.2 GHz), C-band (4.2––5.45.4GHz), X-band (5.7GHz), X-band (5.7––10.9 GHz), Ku-band (10.910.9 GHz), Ku-band (10.9––22.0 GHz) 22.0 GHz) [Low [Low ––>high]>high]
Altimeter CrossoverMeasurement Concept:• 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 tobe accurate to < 1 µsec for haltto be accurate to < 1 cm
Radar Altimeter GeometryRadar Altimeter Geometry
• Mean Sea Surface: –100 m to +80 m• Geoid ~ MSS• Ocean topography: ~ several meters• Ellipsoid: ~6378 km• Altimeter altitude: 800 – 1300 km
Radar Altimeter FootprintRadar Altimeter Footprintradius of footprint :R
hcR τ=c – speed of lightτ – pulse width (pulse duration) , actualh – satellite hight
Geos-3: h=840, τ = 5.12 ns =9105.12 −× second , 6.3=R
Seasat: h=800, τ =3ns =9103 −× , ?=R
2
222 2ln16
cH
p += ττ
:pτ radar’s theoretical pulse width
:H standard deviation of wave height
Effect of SWH
pulse-length-limitedbeamwidth-limited
1.94 SWH
0.56M SWH
time(gate)
SWH will cause electromagnetic bias (emb) .Thehigher the SWH , the lower received pulse energy
Ocean surface reflectivity and atmosphericOcean surface reflectivity and atmosphericattenuationattenuation
Clear sky attenuation,Clear sky attenuation,radar affected by rain, cloudradar affected by rain, cloudCourtesy: Courtesy: Chelton Chelton et al. [2001]et al. [2001]
Maul [1985]Maul [1985]
Pulse-Limited Radar AltimetryPulse-Limited Radar Altimetry
Courtesy: Courtesy: Chelton Chelton et al. [2001]et al. [2001]
Beam-limited (L)Beam-limited (L) and and pulse-limited (R)pulse-limited (R) altimeter altimeterdesigns. For T/P (1350 km, 13.6 GHz) thedesigns. For T/P (1350 km, 13.6 GHz) theantenna diameter would be antenna diameter would be ~8 m for beam-~8 m for beam-limited altimeter designlimited altimeter design. Pulse-limited altimeters. Pulse-limited altimetersissue many short-pulses and provides anissue many short-pulses and provides anaverage. E.g. average. E.g. antenna width for T/P is ~1.5 mantenna width for T/P is ~1.5 m..
Pulse-Limited Altimeter Footprint andPulse-Limited Altimeter Footprint andoperationsoperations
T/P: bandwidth ~0.3 Ghz (3 ns pulse)
Pulse-Limited Radar AltimetryPulse-Limited Radar Altimetry
Courtesy: Courtesy: Chelton Chelton et al. [2001]et al. [2001]
Averaged waveform returnAveraged waveform returnPlane views of illuminated patternPlane views of illuminated patternof radar with various pulseof radar with various pulseduration for 2 different waveduration for 2 different waveheightsheights
Development at APLof the originalsatellite-based
navigation system(1959-1998, Transit)
Development at APLof the originalsatellite-based
navigation system(1959-1998, Transit)
Courtesy: K. Raney
Pulse-limitedannuli
Pulse-Limited
97/10/13 rkr
Pulse length
SWH > pulse lengthQuasi-flat sea
Track point
Time
Power (F0) Surface response function
Plan view ofilluminationfootprint
(Time delay)
Slope (SWH)
Conventional radar altimetry:
Courtesy: K. Raney
Along track
Relative time delay
0
23
Pulse length Pulse length
Annuli ofequal areas
Pulselimitedfootprint
1
23
Pulse-Dopplerlimitedfootprint
1
0
Altimeters Compared
Two-dimensionalsection of theangular scatteringfunction at eachand everysubsatellite point
Processing: removeextra delay due towavefront curvature,which converts alldata along-track toheight measurements
DDA: More averaging => x2 better precision, x10 better efficiency
Conventional Delay/Doppler
Doppler modulation
Advantage:along-trackincidence andDoppler equivalence(modulo PRF)
Multi-looks at each location
Doppler segmentationpermits closer approach to
land and vegetation
~250 m
Courtesy: K. Raney
Repeat orbits: designed (+/-1 km spacingat equator) for mesoscale oceanographyand sea level, 35-day repeat orbits):optimize temporal sampling andsacrifice spatial coverage
Non-repeat (Geodetic) orbits: designedfor fine-spatial sampling, suffers fromtemporal sampling (Geosat GM, ERS-1Geodetic phase, proposed ABYSSmission)
10-day Repeat
35-day Repeat
17-day Repeat
GEOSAT GEODETIC MISSION GROUND TRACK PATTERNGEOSAT GEODETIC MISSION GROUND TRACK PATTERNGEOSAT GEODETIC MISSION GROUND TRACK PATTERN
Orbit Determination:Dynamic, reduced
dynamic, kinematic
€
˙ ̇ r = −µr r3
← vector← scalar
+ ∇U + F
Equation of Motion:
U - conservative (gravitational) forcesF - Non-conservative forces
PRECISION ORBIT DETERMINATION METHODS
Dynamical Equations of Motion:
( )tcvrfr
rGMr ,,,
3∑+=&&
vr , - Position and Velocity Vectors
( )tcvrf ,,,∑ - 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
DOMINANT PERTURBATIONS ONDOMINANT PERTURBATIONS ONNEAR-EARTH ORBITING SATELLITESNEAR-EARTH ORBITING SATELLITES
• 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 modeledCurrently 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]
Global Positioning System SatellitesGlobal Positioning System Satellites
Geosat Geosat Orbit Error Spectra: height vs SlopeOrbit Error Spectra: height vs Slope
OO
Sandwell Sandwell and Zhang, JGR [1989]and Zhang, JGR [1989]
Radial Orbit Error of Radial Orbit Error of ~5 m~5 mat 40,000 km scale (onceat 40,000 km scale (onceper revolution), is aboutper revolution), is about~0.8 ~0.8 µµradrad
After After crossover adjustmentcrossover adjustmentof orbits, the once per revof orbits, the once per reverror reduces to error reduces to ~0.15 ~0.15 µµradrad
SPATIAL REPRESENTATION OF THE RADIAL ORBIT ERRORDUE TO GEOPOTENTIAL PERTURBATION
For 0=q , radial orbit error [Tapley and Rosborough, 1985]
( )λλ mmr SCD lmlm
c
lmplmp
l
p
l
ml
sincos001
)0( −=Δ Φ∑∑∑==
∞
=
&
( )λλ mm SCD lmlm
s
lmplmp
l
p
l
ml
cossin001
−± Φ∑∑∑==
∞
=
&
where
Dlmp - function of satellite altitude and inclination
Φ&c
lmp and Φ&
s
lmp - latitude functions
+ sign denotes satellite is on ascending pass
- sign denotes satellite is on descending pass
Geographical mean radial orbit error:
( )λλγ mm SCD lmlm
c
lmplmp
l
p
l
ml
sincos001
+=Δ Φ∑∑∑==
∞
=
&
Geographical variability error about the mean:
( )λλ mmv SCD lmlm
s
lmplmp
l
p
l
ml
cossin001
−±=Δ Φ∑∑∑==
∞
=
&
SPATIAL REPRESENTATION OF ALTIMETER CROSSOVERERROR DUE TO GEOPOTENTIAL PERTURBATION
Single satellite crossovers:
νΔ=Δ 2x
)cossin(2001
λλ mSmC lmlms
lmplmp
l
p
l
mlD −= Φ∑∑∑
==
∞
=
• Zonals unobservable (to this level of approximation)
Dual satellite crossovers:
jiji vvyyx Δ−Δ+Δ−Δ=Δ
( ) ( )λλ mSmCD lmlmiclmplmp
l
p
l
ml
sincos~
001
+Φ= ∑∑∑==
∞
=
( ) ( )λλ mSmCD lmlmiclmplmp
l
p
l
ml
sincos~
001
+Φ− ∑∑∑==
∞
=
( ) ( )λλ mSmCD lmlmislmplmp
l
p
l
ml
cossin~
001
−Φ∑∑∑==
∞
=
m
( ) ( )λλ mSmCD lmlmislmplmp
l
p
l
ml
cossin~
001
−Φ± ∑∑∑==
∞
=
for satellites i and j
Predicted T/P ErrorDue to Gravity
Courtesy: John Ries
Predicted JASON Orbit Error Due to Gravity
Courtesy: John Ries
Mean rms = 22.4 cmVariability rms = 21.7 cmTotal radial orbit error(EGM96, 50x50) = 31.2 cmEstimated error (150x150)= ~50 cm rms
Note: Geopotential covariance computedto only 50x50, ISS sensitive to ~130x130
International Space Station (ISS)
Error SourceError SourceERS-1/-2ERS-1/-2 Orbit Orbit (cm) (cm)
T/P T/P Geosat Geosat GFO GFO Cryosat Cryosat ISSISS Orbit Orbit Orbit Orbit Orbit Orbit Orbit Orbit Orbit Orbit (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm) (cm)
Constant gravity 2 1 3 3 15 50Constant gravity 2 1 3 3 15 50Radiation forces 2 2 3 3 2Radiation forces 2 2 3 3 2 10 10Atmospheric dragAtmospheric drag 3 <1 3 3 3 50 3 <1 3 3 3 50GM (gravitational constant) 1 1 1 1 1GM (gravitational constant) 1 1 1 1 1 1 1Time variable gravity 2 1 2 2 4 10Time variable gravity 2 1 2 2 4 10Terrestrial reference frame 1 1 3 1 1 1Terrestrial reference frame 1 1 3 1 1 1Center of mass and attitudeCenter of mass and attitude - - - - - 50 - - - - - 50
RSS Absolute Radial Orbit Error 3-5 <3 6- 8 ~5 16 88RSS Absolute Radial Orbit Error 3-5 <3 6- 8 ~5 16 88
Center of mass induced orbit rate error for ISS = 0.025xCoM Dist. Center of mass induced orbit rate error for ISS = 0.025xCoM Dist. µ µradrad Orbits computed using Laser and Doris for T/P, laser and altimeterOrbits computed using Laser and Doris for T/P, laser and altimetercrossover (ERS-1 & T/P) for ERS-1, crossover (ERS-1 & T/P) for ERS-1, Tranet Tranet and crossovers for and crossovers for GeosatGeosat..Accuracy verification: CSR vs. JPL GPS T/P orbit: <2 cm Accuracy verification: CSR vs. JPL GPS T/P orbit: <2 cm rmsrms
ERS-1/-2 and ERS-1/-2 and GeosatGeosat: Altimeter crossover: Altimeter crossover analysis, comparison with T/P analysis, comparison with T/P dynamic topography, ERS-2 with dynamic topography, ERS-2 with PRARE PRARE
CURRENT RADIAL ORBIT ERROR BUDGETCURRENT RADIAL ORBIT ERROR BUDGETFOR ALTIMETRIC SATELLITESFOR ALTIMETRIC SATELLITES
0.88 0.88 µµrad rad ““absoluteabsolute””orbit error, ~0.15 orbit error, ~0.15 µµradrad““relativerelative”” orbit error orbit error
15 February 2004 C. Shum 98
Inferred Sea SurfaceHeights from Altimetry
15 February 2004 C. Shum 101Courtesy: Courtesy: Chelton Chelton et al. [2001]et al. [2001]
15 February 2004 C. Shum 102
Sea Surface Height
wherehorbit the altitude of altimeter orbit;halt the raw altimeter range;hinsru the total of the instrument corrections;hssb the sea state bias correction;hdry the dry troposphere correction;hwet the wet troposphere correction;hion the ionosphere correction;htides the ocean tide correction, solid Earth tide correction and
the pole tide correction;hib the inverted barometer correction;b the altimeter bias;e the contribution of random and systematic errors.
€
hssh = (horbit − halt − hinsru − hssb − hdry − hwet − hiono
€
−htides − hib ) + b + e
Instrument Corrections• Acceleration error
• Doppler-shift error• Oscillator-drift error• Pointing-angle & sea state corrections (altimeter dependent)
• Other drift corrections (Internal calibration, point target response, etc.,
altimeter dependent)• Time tag biases
GFO Timing Stability ComparisonsGFO Timing Stability Comparisons
GFOGFO GeosatGeosat
USO Height Correction ComparisonsUSO Height Correction Comparisons
GFOGFO GeosatGeosat
Timing Bias Estimates - Laser OrbitsTiming Bias Estimates - Laser Orbits
OSU Time Tag BiasOSU Time Tag BiasEstimates(11/00 - 2/01):Estimates(11/00 - 2/01):~1.5 ~1.5 msecmsec
Internal Calibrationcorrections and tidegauge calibrations(RA bias and drift)
Courtesy: G. Hayne and D. Hancock
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
50000000 100000000 150000000 200000000
SPTR Range Corrections to ERS-1 Radar Altimeter
SPTR
Ran
ge C
orre
ction
s
Seconds Past 1990
-40.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
160000000 170000000 180000000 190000000 200000000 210000000 220000000 230000000 240000000
SPTR Range Corrections for ERS-2 RA
SPTR
Ran
ge C
orrec
tion (
mm)
Seconds Past 1990
ERS-1 and ERS-2 (Old) SPTR Range Corrections
Credit: ESA/ESRIN
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
0 5 10 15 20 25 30 35 40
GEOSAT Altimeter Calibration Averaged Per Cycle
GEOSAT Internal Altimeter Height Calibration (cm)GEOSAT Internal Clock Drift Calibration (cm)GEOSAT Total Calibration (cm)
Jan 1, 1987 Jan 1, 1988
Delta
Ran
ge (c
m)
Cycle
GEOSAT Internal Calibration and Oscillator Drift Corrections
Media and Geophysical Corrections• “Correction” is defined as physical
or instrument phenomena that we “understand” and could quantify with specified accuracy • Otherwise, these phenomena are signals
Atmospheric Attenuation of RadarAtmospheric Attenuation of RadarTropsphere Tropsphere (Dry and Wet) and (Dry and Wet) and Ionospere Ionospere Delays [Source: NASA/JPL]Delays [Source: NASA/JPL]
Atmospheric Refractions on RadarAtmospheric Refractions on Radar
R _universal gas constant (8.317 11 −− ⋅⋅ kmolJ )
waterρ _density of water vapor(5.7) Can be written as_( assuming =g constant , =T constant = aT )
as TwPh 723.11027.2 5 +×=Δ − (6.8)dry component wet component
wetdry hh Δ+Δ=
dzzP airs ∫∞
=0
)(ρ (6.9)
∫∞
→=0
)( dzzw waterρ difficult to model
=aT average temperature
cmhcm
meterh
wet
ary
306
31.2
<Δ<
≈Δ
waterρ _density of water vapor(5Can be written as_( assuming =g constant , =T constant = aT )
as TwPh 723.11027.2 5 +×=Δ − (6.8)dry component wet component
wetdry hh Δ+Δ=
dzzP airs ∫∞
=0
)(ρ (6.9)
∫∞
→=0
)( dzzw waterρ
Atmospheric Refractions on RadarAtmospheric Refractions on Radar index of the ionosphere_
22
1f
Nn α+=
N = number of free elections per unit volume
α = 80.5 23 −sm
f = radio frequency in Hertz
Error in range dzNf
dzn ∫∫∞∞
=−=020 2
)1(α
2
2.40fE
= (6.4)
∫∞
→=0NdzE columnar value of free elections (6.5)
1816 1010 << E
If =f 13 GHz (ku-band)
→<Δ< cmhcm 202.0 use of dual-frequency to eliminate it
_
refraction index of air n _
kB
PakATBe
PTA
n
4810
/ 776.0
10)(1 6
=
=
×++= −
:P pressure (in pascals) , 100 =Pa 1 m bar:T temperature in K:e partial pressure of water vapor , in pascals
Range error due to tropo_
dznh ∫∞
−=Δ0
)1(
dzzT
z
mABR
dzzzggmAR water
w
air
a
∫∫−
∞−
+=)(
)(10)()(
10 6
0
6 ρρ (6.7)
difficult to model:g gravity
wm _mean mole culas weight of water vapor = 0.028996 kg _1−mol
(electron/2m )
Troposphere
(6.6)
ATMOSPHERE ATTENUATIONSATMOSPHERE ATTENUATIONS
Chelton Chelton et al. [2001]et al. [2001]
15 February 2004 C. Shum 116
CODE GIM-TOPEX TEC (mean and rms)
1995–2001
COMPARISON OF NCEP(GFO) AND GFO MWR WET DELAY
COMPARISON OF GFO MWR AND ERS-2 MWR (ATSR) WET DELAY
Revised NOAA IGDR Data (Dec 6-22, 1999)
SWH BUOY CALIBRATION (D. Cotton)SWH BUOY CALIBRATION (D. Cotton)Buoy data fit: Buoy data fit: 12 cm 12 cm rms rms (26 cm for TOPEX; 32 cm for ERS-2)(26 cm for TOPEX; 32 cm for ERS-2)Preliminary results (limited calibration data used)Preliminary results (limited calibration data used)
σσ00 BUOY CALIBRATION (D. Cotton) BUOY CALIBRATION (D. Cotton)Buoy data fit : Buoy data fit : 1.28 m/s (1.27 m/s for TOPEX; 1.23 m/s for ERS-2)1.28 m/s (1.27 m/s for TOPEX; 1.23 m/s for ERS-2)Preliminary results (limited calibration data used)Preliminary results (limited calibration data used)
COMPARISONS WITH TOPEX SWH/COMPARISONS WITH TOPEX SWH/σσ0010-day Averages within 66S-66N10-day Averages within 66S-66N
Preliminary results indicate GFO offsetsPreliminary results indicate GFO offsetswith TOPEX SWH and with TOPEX SWH and σσ00 values, confirmingvalues, confirmingD. HancockD. Hancock’’s calibration resultss calibration results
Pressure Field and Inverted Barometer
Chelton et al. [2001]
Tides: Solid Earth tides, (geocentric) ocean tides, pole tides
ASSESSMENT OF TIDE ERROR USINGASSESSMENT OF TIDE ERROR USINGMODEL COMPARISONSMODEL COMPARISONS
Yu et al. [2000]Yu et al. [2000]