-
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
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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
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Background and History:Satellite Altimetry
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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
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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
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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
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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
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15 February 2004 C. Shum 13CRYOSAT
Courtesy, ESA
Ku-band altimeter (multipleantennas) capable ofnadir, SAR, and
InSAR mode.Potential tracking closer tocoastlines. No
radiometer.
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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
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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
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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
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Principle of Satellite Altimetry• Fundamental design• Radar
principle
• Temporal-spatial sampling (ground track patterns)
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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]
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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
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Radar Altimeter FootprintRadar Altimeter Footprintradius of
footprint :R
hcR τ=c – speed of lightτ – pulse width (pulse duration) ,
actualh – satellite hightGeos-3: h=840, τ = 5.12 ns = 9105.12 −×
second , 6.3=RSeasat: 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
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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]
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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
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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
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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
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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)
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10-day Repeat
-
35-day Repeat
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17-day Repeat
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GEOSAT GEODETIC MISSION GROUND TRACK PATTERNGEOSAT GEODETIC
MISSION GROUND TRACK PATTERNGEOSAT GEODETIC MISSION GROUND TRACK
PATTERN
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Orbit Determination:Dynamic, reduced
dynamic, kinematic
-
€
˙ ̇ r = −µ r r3← vector← scalar
+ ∇U + F
Equation of Motion:
U - conservative (gravitational) forcesF - Non-conservative
forces
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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
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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 lmlmc
lmplmp
l
p
l
ml
sincos001
)0( −=Δ Φ∑∑∑==
∞
=
&
( )λλ mm SCD lmlms
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 lmlmc
lmplmp
l
p
l
ml
sincos001
+=Δ Φ∑∑∑==
∞
=
&
Geographical variability error about the mean:
( )λλ mmv SCD lmlms
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 lmlmiclmplmpl
p
l
ml
sincos~
001
+Φ= ∑∑∑==
∞
=
( ) ( )λλ mSmCD lmlmiclmplmpl
p
l
ml
sincos~
001
+Φ− ∑∑∑==
∞
=
( ) ( )λλ mSmCD lmlmislmplmpl
p
l
ml
cossin~
001
−Φ∑∑∑==
∞
=
m
( ) ( )λλ mSmCD lmlmislmplmpl
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
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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 723.11027.25 +×=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
-
Atmospheric Refractions on RadarAtmospheric Refractions on Radar
index of the ionosphere_
22
1f
Nn α+=
N = number of free elections per unit volumeα = 80.5 23 −smf =
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
-
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]