Observing the Ocean using Satellite Altimeter Data · 2018-05-15 · Observing the Ocean using...

Observing the Ocean usingObserving the Ocean using

Satellite Altimeter DataSatellite Altimeter Data

Detlef StammerDetlef StammerInstitut fInstitut füür r MeereskundeMeereskunde

University HamburgUniversity Hamburg

GermanyGermany

31 March 200631 March 2006Faculty of AerospaceFaculty of Aerospace

Engineering, DEOSEngineering, DEOS 22

Satellite altimetrySatellite altimetry

Source: JPL

Atmospheric TransmissionAtmospheric Transmission

MW is all weather

observing system

How altimeters workHow altimeters work

••The altimeter is a radar at vertical incidenceThe altimeter is a radar at vertical incidence

••The return signal is from specular reflectionThe return signal is from specular reflection

••The basic measurement is the distance from theThe basic measurement is the distance from the

satellite to the surface.satellite to the surface.

••This is measured by the travel time of a sent andThis is measured by the travel time of a sent and

receiving radar pulse, receiving radar pulse, h=c t/2h=c t/2

In principle there are two types of altimeter:In principle there are two types of altimeter:

--beam limitedbeam limited

--pulse limitedpulse limited

A Beam Limited AltimeterA Beam Limited Altimeter

In a beamIn a beam

limitedlimited

altimeter thealtimeter the

return pulse isreturn pulse is

dictated by thedictated by the

width of thewidth of the

beam.beam.

A plot of return power versus time for a beamA plot of return power versus time for a beam

limited altimeter looks like the heights of thelimited altimeter looks like the heights of the

specular points, i.e. the probability densityspecular points, i.e. the probability density

function (pdf) of the specular scatterersfunction (pdf) of the specular scatterers

The tracking point is themaximum of the curve

A Pulse Limited AltimeterA Pulse Limited Altimeter

In a pulse limitedIn a pulse limited

altimeter the shape ofaltimeter the shape of

the return is dictatedthe return is dictated

by the length (width) ofby the length (width) of

the pulsethe pulse

A plot of return power versus time for a pulseA plot of return power versus time for a pulse

limited altimeter looks like the integral of thelimited altimeter looks like the integral of the

heights of the specular points, i.e. theheights of the specular points, i.e. the

cumulative distribution function (cdf) of thecumulative distribution function (cdf) of the

specular scatterersspecular scatterers

The tracking point is thehalf power point of the

§§We send out a thin shell of radar energy which isWe send out a thin shell of radar energy which is

reflected back from the sea surfacereflected back from the sea surface

§§The power in the returned sign is detected by aThe power in the returned sign is detected by a

number of gates each at a slightly different timenumber of gates each at a slightly different time

Altimeter MeasurementsAltimeter Measurements

A single pulse

If we add waves ...

Some example waveformsSome example waveforms

§§The total area illuminated is related toThe total area illuminated is related to

the significant wave heightthe significant wave height

§§The formula isThe formula is

The area illuminatedThe area illuminated

where c is the speed of light, ! is the pulse length, Hs

significant wave height, R0 the altitude of the satellite

and RE the radius of the Earth

Hs (m)Hs (m) Effective footprint (km)Effective footprint (km)

(800 km altitude)(800 km altitude)Effective footprint (km)Effective footprint (km)

(1335 km altitude)(1335 km altitude)

00 1.61.6 2.02.0

11 2.92.9 3.63.6

33 4.44.4 5.55.5

55 5.65.6 6.96.9

1010 7.77.7 9.69.6

1515 9.49.4 11.711.7

2020 10.810.8 13.413.4

From Chelton et al (1989)

The effect of mispointingThe effect of mispointing

A real waveformA real waveform

§§Narrow beams require very large antennas andNarrow beams require very large antennas and

at present are impractical in spaceat present are impractical in space

––For a 5 km footprint a beam width of about 0.3° isFor a 5 km footprint a beam width of about 0.3° is

required. For a 13.6GHz altimeter this would imply arequired. For a 13.6GHz altimeter this would imply a

5m antenna.5m antenna.

§§Even more important is the problem ofEven more important is the problem of

mispointing.mispointing.

§§(The laser altimeter on ICESAT has many of the(The laser altimeter on ICESAT has many of the

characteristics of a beam limited altimeter)characteristics of a beam limited altimeter)

§§All the altimeters flown in space to date areAll the altimeters flown in space to date are

pulse limitedpulse limited

§§For the rest of these lectures we only considerFor the rest of these lectures we only consider

the pulse limited designthe pulse limited design

From satellite height to sea surfaceFrom satellite height to sea surface

heightheight

An Altimeter measures:"SSH and thus surface geostrophic currents (travel time)"SWH (from wave form)

"Wind speed (from !o or AGC)

Global wind speed

Sea Level anomaly

Global wave height

Altimetry

§§From the altimeter measurement we know theFrom the altimeter measurement we know the

height of the satellite above the sea surfaceheight of the satellite above the sea surface

§§We want to know the height of the sea surfaceWe want to know the height of the sea surface

above the geoid (ellipsoid)above the geoid (ellipsoid)

§§Therefore we need to know the satellite orbit (toTherefore we need to know the satellite orbit (to

a few cma few cm!!s or less)s or less)

OrbitsOrbits

Inclination determines

geographic range.

i=66 i=98

Day 1-3

Day 4-6

SWH Information agrees well with Buoy DataSWH Information agrees well with Buoy Data

The wave climateThe wave climate

The biggest signalThe biggest signal

in the wavein the wave

climate is ofclimate is of

course seasonal.course seasonal.

Monthly mean wave heightMonthly mean wave height

(90(90’’s)s)

Inter-annual variability (90Inter-annual variability (90’’s)s)

EOF 80EOF 80’’s-90s-90’’ss

Wave Period and the NAOWave Period and the NAO

In a similar way toIn a similar way to

wave height wavewave height wave

period relates to theperiod relates to the

NAONAO

The above shows the

first EOF of period.

On the left we have a

regression of Tm on

the NAO

§§The altimeter measures the altitude of theThe altimeter measures the altitude of the

satellitesatellite

§§The oceanographer wants a measurementThe oceanographer wants a measurement

of sea level and surface currentsof sea level and surface currents

§§Steps that need to be takenSteps that need to be taken

–– Instrument correctionsInstrument corrections

–– Platform correctionsPlatform corrections

–– Orbit determinationOrbit determination

–– The effect of refractionThe effect of refraction

–– Sea surface effectsSea surface effects

–– GeoidGeoid correction. correction.

Processing OverviewProcessing Overview

§§The Earth is not round. The true shape ofThe Earth is not round. The true shape of

the earth is the geoid. As the satellitethe earth is the geoid. As the satellite

orbits the Earth it moves closer and furtherorbits the Earth it moves closer and further

away responding to changes in gravity.away responding to changes in gravity.

§§This means that the satellite is constantlyThis means that the satellite is constantly

moving towards and away from the earth.moving towards and away from the earth.

A Doppler correction is therefore neededA Doppler correction is therefore needed

(applied by the space agencies)(applied by the space agencies)

Platform correctionsPlatform corrections

§§There are other platform There are other platform ""correctionscorrections!!

§§e.g A correction needs to be made for thee.g A correction needs to be made for the

distance between the centre of gravity of thedistance between the centre of gravity of the

spacecraft and the altimeter antennaspacecraft and the altimeter antenna

§§All these corrections are applied by the spaceAll these corrections are applied by the space

agencies and need not worry the scientist (unlessagencies and need not worry the scientist (unless

something goes wrong)something goes wrong)

The problem of the GeoidThe problem of the Geoid

§§The geoid is the surface of equal gravity potentialThe geoid is the surface of equal gravity potential

on the Earthon the Earth!!s surface (the shape of the Earth)s surface (the shape of the Earth)

§§The ellipsoid is an approximation to the shape ofThe ellipsoid is an approximation to the shape of

the Earththe Earth

§§We know the ellipsoid - we do not know the geoidWe know the ellipsoid - we do not know the geoid

The GeoidThe Geoid

Scale: magenta (-107m) to red (84.5m)

§§The geoid is usually expressed in termsThe geoid is usually expressed in terms

of spherical harmonics (sine curves on theof spherical harmonics (sine curves on the

sphere). These have degree and order.sphere). These have degree and order.

Degree and order 360 is approximately aDegree and order 360 is approximately a

resolution of 1°resolution of 1°

§§Sea surface pressure and henceSea surface pressure and hence

geostrophic currents are in terms of seageostrophic currents are in terms of sea

surface height relative to the geoid. Wesurface height relative to the geoid. We

measure currents (sea surface slopes)measure currents (sea surface slopes)

relative to the ellipsoid.relative to the ellipsoid.

§§There are a number of instrument correctionsThere are a number of instrument corrections

that need to be made.that need to be made.

§§These are either applied by the space agenciesThese are either applied by the space agencies

or are available from themor are available from them

Instrument CorrectionsInstrument Corrections

Atmospheric CorrectionsAtmospheric Corrections

-- Ionospheric correctionIonospheric correction

-- Dry tropospheric correctionDry tropospheric correction

-- Wet tropospheric correctionWet tropospheric correction

As the radar signal travels through theatmosphere it is slowed down (refraction). Sincewe are interested in the speed of the radar we

must correct for this effect.

There are three parts of the atmosphere thatmust be taken in to account:

Ionospheric correctionIonospheric correction

§§Caused by free electrons in theCaused by free electrons in theionosphereionosphere

§§Frequency dependent so it can beFrequency dependent so it can bemeasured with a dual frequency altimetermeasured with a dual frequency altimeter

§§Otherwise use a model or otherOtherwise use a model or otherobservations from a dual frequency radarobservations from a dual frequency radarsystem (GPS, DORIS)system (GPS, DORIS)

§§Average value 45mm, s.d. 35mmAverage value 45mm, s.d. 35mm

§§Depends on solar cycleDepends on solar cycle

Low solar

activity

High solar

activity

Annual sunspot

numbers

Monthly sunspot

numbers

Dry Tropospheric CorrectionDry Tropospheric Correction

§§Due to ODue to O22 molecules in the atmosphere molecules in the atmosphere

§§Derived from atmospheric pressureDerived from atmospheric pressure

(from met models) by(from met models) by

––Dry_trop=2.277(p)(1+0.0026cos(2lat))Dry_trop=2.277(p)(1+0.0026cos(2lat))

–– (mm) (hPa) (°) (mm) (hPa) (°)

Winter DJF

Air Pressure

Mean (hPa)

Standard

deviation

Summer JJA

Atmospheric

Pressure

Mean (hPa)

Standard

Deviation

Wet Tropospheric CorrectionWet Tropospheric Correction§§Caused by water vapour in theCaused by water vapour in the

atmosphereatmosphere

§§Obtained by microwave radiometerObtained by microwave radiometer

on satelliteon satellite

––two frequency on ERS and ENVISATtwo frequency on ERS and ENVISAT

––three frequency on T/P and JASONthree frequency on T/P and JASON

§§Or from weather forecastingOr from weather forecasting

modelsmodels

Tropospheric

water vapour

from SSM/I

Mean (g/m2)

Standard

deviation

Sea Surface CorrectionsSea Surface Corrections

§§ Sea State Bias Sea State Bias

§§Not really corrections but signalsNot really corrections but signals

we are not interested inwe are not interested in

––Inverse Barometer CorrectionInverse Barometer Correction

––TidesTides

Sea State BiasSea State Bias

§§Also called EM bias (Electromagnetic)Also called EM bias (Electromagnetic)

§§A bias in the range that is related toA bias in the range that is related to

wave heightwave height

§§Average size 100mmAverage size 100mm

§§In general waves are non-linear. TheIn general waves are non-linear. Thecrests are peakier and the troughscrests are peakier and the troughsrounder than linear theory.rounder than linear theory.

§§For linear waves the pdf of the specularFor linear waves the pdf of the specularpoints is the same as the pdf of thepoints is the same as the pdf of thewater elevationwater elevation

§§For non-linear waves this is not true soFor non-linear waves this is not true sothe median point of the specular pointsthe median point of the specular points(the half power point) is not in the same(the half power point) is not in the sameplace as mean sea level.place as mean sea level.

§§This is one possible explanation for seaThis is one possible explanation for seastate biasstate bias

Non-linear Sea SurfaceNon-linear Sea Surface

§§If there is enhanced power returnedIf there is enhanced power returned

from the wave troughs and reducedfrom the wave troughs and reduced

power from the crests we will also getpower from the crests we will also get

a sea state bias.a sea state bias.

Enhanced reflections from the troughsEnhanced reflections from the troughs

§§An element of the sea state bias comesAn element of the sea state bias comes

from the tracker. Using a different trackerfrom the tracker. Using a different tracker

will give a different value for the sea statewill give a different value for the sea state

biasbias

Tracker BiasTracker Bias

§§There is as yet no theoretical method forThere is as yet no theoretical method for

estimating the sea state bias.estimating the sea state bias.

§§We are therefore forced to use empiricalWe are therefore forced to use empirical

methodsmethods

§§Find the function of HFind the function of Hss (and U (and U1010) that) that

minimises the crossover differencesminimises the crossover differences

State of the art in sea state biasState of the art in sea state bias

§§With parametric methods we have aWith parametric methods we have aspecified function for the SSB and estimatespecified function for the SSB and estimatethe parameters of this function, e.g. thethe parameters of this function, e.g. theBM4 model used for TOPEXBM4 model used for TOPEX

Parametric vs non-parametric methodsParametric vs non-parametric methods

An example non-parametric

With non-parametric

methods we compile

statistics and smooth the

resulting 2-d histogram

Inverse Barometer CorrectionInverse Barometer Correction

§§When air pressure changes the ocean actsWhen air pressure changes the ocean acts

like a barometer (in reverse). High air pressurelike a barometer (in reverse). High air pressure

depresses the sea surface, low air pressuredepresses the sea surface, low air pressure

raises it.raises it.

§§1 mbar (hPa) change in air pressure is1 mbar (hPa) change in air pressure is

approximately equal to a 1cm change in the seaapproximately equal to a 1cm change in the sea

surfacesurface

§§Good in mid and high latitudes not in TropicsGood in mid and high latitudes not in Tropics

§§An alternative to an IB correction is toAn alternative to an IB correction is to

use a correction from a barotropic modeluse a correction from a barotropic model

of the oceanof the ocean

§§Barotropic (non-depth dependent)Barotropic (non-depth dependent)

motions move very quickly and can bemotions move very quickly and can be

aliased by the altimeter ground tracksaliased by the altimeter ground tracks

§§Barotropic models are quick to run butBarotropic models are quick to run but

have proved hard to validatehave proved hard to validate

Barotropic ModelsBarotropic Models

§§If we are going to use altimetry forIf we are going to use altimetry foroceanographic purposes we need tooceanographic purposes we need toremove the effect of the tides.remove the effect of the tides.

§§Alternatively we can use the altimeter toAlternatively we can use the altimeter toestimate the tides (see below).estimate the tides (see below).

§§In general we use global tidal models toIn general we use global tidal models tomake predictions and subtract them frommake predictions and subtract them fromthe signal.the signal.

TidesTides

Aliasing PeriodsAliasing Periods

T/P ERS

Tide Period

(days)

length

(days)

length

M2 12.42 62 9E 95 9E

S2 12 59 180W 0 !

N2 12.65 50 9W 97 4W

K1 23.93 173 360W 365 360E

O1 25.82 46 9.23E 75 9E

P1 24.07 89 360W 365 360W

§§As well as the ocean tide we haveAs well as the ocean tide we have

to considerto consider

1.1. the loading tide (the effect of thethe loading tide (the effect of the

weight of water). This is sometimesweight of water). This is sometimes

included in the ocean tideincluded in the ocean tide

2.2. the solid earth tidethe solid earth tide

3.3. the polar tidethe polar tide

§§On continental shelves the globalOn continental shelves the global

models are not very accurate andmodels are not very accurate and

local models are neededlocal models are needed

Colocating the dataColocating the data

The across track geoid slopeThe across track geoid slope

§§Although the space agencies try to put theAlthough the space agencies try to put the

satellite in a repeat orbit this isnsatellite in a repeat orbit this isn!!t possiblet possible

§§When we colocate the data across the trackWhen we colocate the data across the track

we need to take into account the geoid slopewe need to take into account the geoid slope

§§This comes from a geoid model or a meanThis comes from a geoid model or a mean

sea surfacesea surface

Precise Orbit ComputationPrecise Orbit Computation

§§This is done through a combination of satelliteThis is done through a combination of satellite

tracking and dynamical modelling.tracking and dynamical modelling.

§§A dynamical model is fitted through the trackingA dynamical model is fitted through the tracking

data. Solutions cover a few days at a time.data. Solutions cover a few days at a time.

§§The tracking information comes from DORIS,The tracking information comes from DORIS,

GPS and Satellite Laser ranging (SLR)GPS and Satellite Laser ranging (SLR)

SLR Stations

DORIS stations

§§The quality of orbits are measured by theThe quality of orbits are measured by the

reduction of crossover differences and byreduction of crossover differences and by

comparison to SLR stationscomparison to SLR stations

§§TOPEX/POSEIDON and JASON orbits are goodTOPEX/POSEIDON and JASON orbits are good

to about 3-5 cmto about 3-5 cm

§§ERS-2 and ENVISAT 5-10 cmERS-2 and ENVISAT 5-10 cm

TOPEX Error BudgetTOPEX Error BudgetFrom Chelton et al 2001From Chelton et al 2001

SourceSource ErrorError

Instrument NoiseInstrument Noise 1.7cm1.7cm

IonosphereIonosphere 0.5cm0.5cm

EM BiasEM Bias 2.0cm2.0cm

SkewnessSkewness 1.2cm1.2cm

Dry TroposphereDry Troposphere 0.7cm0.7cm

Wet TroposphereWet Troposphere 1.1cm1.1cm

OrbitOrbit 2.5cm2.5cm

TotalTotal 4.1cm4.1cm

§§The geoid is time invariant (approximately)The geoid is time invariant (approximately)

§§So if we subtract a mean sea surface we willSo if we subtract a mean sea surface we will

remove the geoidremove the geoid

§§But we lose ...But we lose ...

––... the mean circulation... the mean circulation

§§The final part of the processing is toThe final part of the processing is to

subtract a mean sea surfacesubtract a mean sea surface

§§There are two possible sources for thisThere are two possible sources for this

1.1. Averaging the data for that satelliteAveraging the data for that satellite

along trackalong track

2.2. Using a global MSS derived from aUsing a global MSS derived from a

number of missionsnumber of missions

Subtracting the mean sea surfaceSubtracting the mean sea surface

Mean Sea SurfaceMean Sea Surface

Altimeter missions to dateAltimeter missions to date

TOPEX/PoseidonTOPEX/Poseidon

Processing stepsProcessing steps

§§Subtract the orbitSubtract the orbit

§§Correct the altimeter measurementCorrect the altimeter measurement

§§Colocate the measurementsColocate the measurements

§§Remove a mean sea surfaceRemove a mean sea surface

§§HHss - significant wave height - significant wave height

§§tt00 - the time for the radar signal to reach - the time for the radar signal to reach

the Earth and return to the satellite (height)the Earth and return to the satellite (height)

§§!!00 - - the radar backscatter coefficientthe radar backscatter coefficient

What are we measuring?What are we measuring?

Track separation: 300 km at equator!

Date coverage during 10 day repeat cycle.

Geoid Hight+/- 100 m

Mean SSH (+/- 1m)and mean flow field;smoothed!!

(Von TOPEX mehr als 1800 Art.)

SSH Variability can be studied independent of geoid model

SSH AnomaliesSSH Anomalies

Example of SSH eddy statistics from along-track data:Relation eddy scale to Ro.

Time-Longitude PlotsTime-Longitude Plots

ERS-based observationsERS-based observations

North Atl 34°N

Cipollini et al 1997 (North Atlantic): Hughes et al 1998 ( Southern Ocean)

Merged T/P+ERSMerged T/P+ERS

§§Chelton et al 2006Chelton et al 2006

§§Made possible by bothMade possible by both

remarkable improvement in ERSremarkable improvement in ERS

orbits (Scharroo et al 1998, 2000),orbits (Scharroo et al 1998, 2000),

and careful intercalibration +and careful intercalibration +

optimal interpolation techniquesoptimal interpolation techniques

(Le Traon et al 1998, Ducet et al(Le Traon et al 1998, Ducet et al

2000)2000)

§§Good example of synergyGood example of synergy

between different altimetersbetween different altimeters

Westwardphase

speed cpcm/s

observed cp classic theory cp

Westward moving Easrtward moving

Measurements of the ocean surface topography enable scientists to

improved understanding of ocean circulation and its effect on global

climate, and regional and global sea sea level changes (coastal regions,

islands).

Satellite Altimetry is the only means tomonitor global and regional sea level rise.

Sea Surface Height (Altimeter)

altimeter measurements initiated in the early 1990

Courtesy of Remko Scharroo, NOAA,US

Sea level rise

Trend: +3 mm/yr

B. Douglas, 1991

RegionalRegional variabilityvariability previouslypreviously suggestedsuggested by by tidetide gaugesgauges……..

SSH Drift 1993 – 2002 T/P Observations

Variations du niveau moyen de la mer au cours du 20èmeVariations du niveau moyen de la mer au cours du 20ème

sièclesiècle

dd’’après les mesures marégraphiquesaprès les mesures marégraphiques

d’après Church et al.

(2004)

(1993-2005)

Estimating RainEstimating Rain

ERS-1ERS-1

Guymer et al. (1995)

Mechanisms for #0 change:

reflection from rain clouds

change in surface roughness

attenuation by rain

$#0 = 2 H a Rb

Quantify Quantify $#$#00 (1) (1)

Quantify Quantify $#$#00 (3) (3)

Ku-band #0 responds to

wind and rain fields.

Rescaled C-band #0

shows change due to

wind alone.

Why use rain flags?Why use rain flags?

Quartly et al. (1996); Quartly et al. (2000)

Two purposes for rain flagging:

i) edit bad data

ii) study rainfall at sea

Why study rain with altimetry?Why study rain with altimetry?

Not ideal — narrow swath,

long gap between repeats —

in many ways SSM/I,

AVHRR, TRMM are better

1) All rain climatologies have large uncertainties

2) Stable algorithm — good for decadal studies

Coastal ApplicationsCoastal Applications

Jan-Feb

Jan 16, 1999Feb 11, 1999

Dec 11, 1999

Jan 16, 2000New Eddy

Jan 19

Feb 28

Mar 30

Apr 29

Mid-latitude

NE Pacific

Anticyclonic Cyclonic

Jan 19

Feb 28

Mar 30

Apr 29

Mid-latitude

NE Pacific

Anticyclonic Cyclonic

D. Palacios & S Bograd (GRL, 2005) A census of Tehuantepec and

Papagayo eddies in the northeastern tropical Pacific.

2-9 February 2003Criteria:

> ± 20 cm

> 28 days

Mean life times of:

143d (Tehuantepec)

84d (Papagayo)

Mean frequency

3.5 T eddies/yr

2.2 P eddies/yr

Few cyclonic, so

only AC eddies

Considered.

Figure adapted from Pearce & Griffiths 1991

T. Moore, R. Matear, J. Marra & L. Clementson (JGR, submitted).T. Moore, R. Matear, J. Marra & L. Clementson (JGR, submitted).

Phytoplankton variability off the Western Australian Coast:Phytoplankton variability off the Western Australian Coast:

Mesoscale eddies and their role in cross-shelf exchangeMesoscale eddies and their role in cross-shelf exchange..

SeaWiFS with SSHA overlay

May 6th 2000

3/21/03 CCAR

4/21/03

3/21/03

Satellite altimetry and ocean tidesSatellite altimetry and ocean tides

§§ Altimetry:Altimetry:

–– TOPEX/Poseidon (and Jason) provide estimates of ocean tides at oneTOPEX/Poseidon (and Jason) provide estimates of ocean tides at onesecond intervals in the satellite flight (along track) directionsecond intervals in the satellite flight (along track) direction

–– Empirical methods to map the ocean tidesEmpirical methods to map the ocean tides

§§ Quality Models:Quality Models:

–– The quality of tide models can be verified by means of an independentThe quality of tide models can be verified by means of an independentcomparison to in-situ tide gauge datacomparison to in-situ tide gauge data

–– RMS difference for M2: 1.5 cm, S2: 0.94, O1: 0.99, K1: 1.02RMS difference for M2: 1.5 cm, S2: 0.94, O1: 0.99, K1: 1.02

–– RMS minor constituents are well under the 0.65 cm levelRMS minor constituents are well under the 0.65 cm level

§§ Data Assimilation:Data Assimilation:

–– There are various numerical schemes (finite differencing or finiteThere are various numerical schemes (finite differencing or finiteelements) that implement the elements) that implement the LaplaceLaplace Tidal Equations (LTE). Tidal Equations (LTE).

–– At a later stage methods where developed to assimilate altimeterAt a later stage methods where developed to assimilate altimeterinformation in information in barotropicbarotropic ocean tide models. ( ocean tide models. (representerrepresenter method, data method, datanudging, etc)nudging, etc)

M2 ocean tideM2 ocean tide

Dissipation from TPXO51 (GaryDissipation from TPXO51 (Gary

Egbert, OSU)Egbert, OSU)

GOT99.2 inferred dissipations, Richard Ray GSFC

Internal tides (1)Internal tides (1)§§ High frequency oscillation is imposed on the along trackHigh frequency oscillation is imposed on the along track

tide signal, wavelength typically 160 km for Mtide signal, wavelength typically 160 km for M22 (Mitchum (Mitchum

and Ray, 1997).and Ray, 1997).

§§ Feature stands above the background noise level.Feature stands above the background noise level.

§§ It is visible for MIt is visible for M22 and S and S22 (hardly for K (hardly for K11).).

§§ Some contamination in the T/P along track tides in regionsSome contamination in the T/P along track tides in regions

with increased meso-scale variability.with increased meso-scale variability.

§§ ““CleanClean”” Along track tide visible around Hawaii, French Along track tide visible around Hawaii, French

Polynesia and East of Mozambique.Polynesia and East of Mozambique.

§§ AT tides appear near oceanic ridge systems.AT tides appear near oceanic ridge systems.

1900 2000 2100 2200 2300 2400 2500 2600

Track 223Track 223

HawaiiHawaii

Internal tides (2)Internal tides (2)

160 km

AreaArea’’s of interests of interest

Applications: HurricanesApplications: Hurricanes

Level1b productCloud Top Pressure Level 2 product

(Atmospheric pressure at the altitude

of the top of the cloud)

800 hPa

360 hPa

Hurricane Isabel – 8 September 2003 – Category 3 Hurricane

Altimetry

Hurricane Isidore (September 2002)

MERISASAR

Yucatan

(Mexico)

Cancun

Use of altimeter data and ocean models to improve cyclone forecasting

Need multiple altimeters

Left : MERCATOR forecasting system Right: TCHP - Gustavo Goni, NOAA/OAR/AOML

o Ku-band

x S-Band

Hurricane

Katrina

Applications: Bottom TopographyApplications: Bottom Topography

Traditional computations of surfaceTraditional computations of surface

velocities from altimeter data:velocities from altimeter data:

§§Cross-track geostrophic component fromCross-track geostrophic component fromalong-track data.along-track data.

§§Two components at cross-over points.Two components at cross-over points.

§§Two components from gridded SSH fields.Two components from gridded SSH fields.

§§Velocities from model constrained by altimetry.Velocities from model constrained by altimetry.

Typical Surface CurrentsTypical Surface Currents

§§Tidal currents (cm/s to m/s)Tidal currents (cm/s to m/s)

§§Ekman currents (50 cm/s)Ekman currents (50 cm/s)

§§Innertial oscillations (50 cm/s)Innertial oscillations (50 cm/s)

§§Geostrophic currents (10 cm/s)Geostrophic currents (10 cm/s)

§§Other ageostrophic currents (e.g., in coastalOther ageostrophic currents (e.g., in coastalregions)regions)

§§Stokes drift (cm/s)Stokes drift (cm/s)

§§Orbial motions of surface wavesOrbial motions of surface waves

1 Altimeter

Multi-Satellite Missions

Slope variability or eddy kinetic energyfrom along-track data.

Altimeter constellation:

(Stammer and Dieterich, 1999)

Concept of Parallel Track Velocity Computations.

Proposals: The Wittex Concept (K. Rainey and D. Porter, APL) AltiKa (Toulouse)

But: since Sept. 2002,TOPEX and JASON-1

are flying already in a constellation.

delta t ~ 1 min.

delta x ~150 km

Determining GeostrophicDetermining GeostrophicVelocitiesVelocities

SSH gradients can be determinedsimultaneously in two directions from whichthe geostrophic surface flow field follows.

Tandem Mission SSH Data CoverageTandem Mission SSH Data Coverage

Boundary currentregions are undersampled due todata drop outsthere.

Oleander Ship ADCP measurements(T. Rossby) SSH

gradients

Velocity Track

Parallel-Track velocity Comparisons

Tandem, Oleander Velocity Data Tandem, Oleander Velocity Data

Velocity Variance Ellipses:Velocity Variance Ellipses:The magnitude and direction of the eddy variability can be represented in termsof velocity variance ellipses. Anisotropic flow is represented by an elongatedellipse, with the principal orientation of the variance aligned with theorientation of the major principal axis. The orientation " of the principalvariability, measured anticlockwise from east, is:

Oleander ellipses

red: ascendingblue: descending

Variance Ellipses fromOleander and TandemData show similaramplitudes. Both showstrong spatial variations.Adcending and descendingellipses mostly agree withother.

Reynold StressesReynold Stresses

Spatial variation of those eddy velocity correlation terms act in themomentum balance as stresses on the large-scale flow field as:

Knowing the detailed structure of the Reynold stress terms is thereforeof fundamental interest for understanding the interaction between themean and eddy components of the circulation. A completely isotropicand homogeneous eddy field would not have any impact on the meancirculation.

SST gradients

u'v' d(u'v')/dy Morrow et al.

New Technology:

e.g., OSTM (was cancelled)

The EarthThe Earth’’s Gravity Fields Gravity Field

GRACE measures The time-varying geoid:temporal changesof the gravity fieldAre caused by changesin ground water andRedistribution of massin the ocean.

Determine Earth’s gravity field and its

geoid (equipotential surface for a

hypothetical ocean at rest):

high accuracy (1 mgal and 1 cm)

fine spatial resolution (~ 100 km)

Studies in:

Solid Earth Physics - anomalous density

structure of lithosphere and upper mantle

Oceanography - dynamic ocean topography

and absolute ocean circulation

Ice Sheet Dynamics - ice sheet mass balance

Geodesy - unified height systems

Sea Level change

GOCEGOCE

Application: IceApplication: Ice

CryoSat-I: First observations of regional,

seasonal, and interannnual sea ice variability

hi = f!w

(!w" !

hs snow

Launch: Oct. 7, 2005

IceSatIceSat

And ICESat?

no. of points in 1 km cell for combined ERS/GLAS data set

1 km DEM from combined ERS/GLAS with many corrections:

Ross Ice Shelf aspect:Ross Ice Shelf aspect:

CRYOSAT-IICRYOSAT-II

Altimetry over RiversAltimetry over Rivers

Motivation: River Runoff Monitoring

" Volume transports of rivers are of high socio-economic / political relevance

" Fresh water resources

" Vegetation, agriculture, irrigation

" Pollution

" Ship traffic

" Electric power generation

" Safety and security, other political issues

" Oceanography

" Climate research

" Existing / available information is not complete

" Available remote sensing data products are not sufficient

Major Rivers and the GTN-R**) Global Terrestrial Network for River Discharge

http://gtn-r.bafg.de

Global River Runoff Data Acquisitionby the Global Runoff Data Center, Koblenz, Germany

http://grdc.bafg.de

Remote Sensing of Water Levels in Lakes and Riversby radar altimeters (P.A.M. Berry et al., De Montfort University, UK)

Water levels of Lake Michigan:

+ = altimeter, & = in situ TOPEX coverage (&) of the upper Amazon basin

Amazon water level time series at two locations from TOPEX data

The six studied lakes in ChinaThe six studied lakes in China

T/P-derived

(dashed) and

in situ (solid)

lake levels at

the Bosten

Lake (from

Wang et al.,

2002).

Verification of T/P-derived lake level (1): Bosten

Verification of T/P-derived lake level (3):

Hulun Lake

Thank You for your attention!

The Brown Model - IIThe Brown Model - II

§§Under these assumptions the returnUnder these assumptions the return

power is given by a three foldpower is given by a three fold

convolutionconvolution

Pr t( ) = PFS t( )!PPT t( )!PH "z( )

Prt( ) i s thereturned power

PFS t( ) i s theflat surface response

PPT t( ) i s thepointtarget response

PH !z( ) is the pdf of specular points on the sea surface

ConvolutionConvolution

•• The The convolutionconvolution is an integral which expresses the is an integral which expresses theamount of overlap of one function amount of overlap of one function hh as it is shifted as it is shiftedover another function over another function gg -- as a function of the shift! -- as a function of the shift!

•• It has the effect of "blending" the functionsIt has the effect of "blending" the functionstogethertogether

g(t)" h(t) = g(#)h(t $ #)d#$%

&Convolution

y(t) = g(t)" h(t) = g(# )h(t $ # )d#$%

1) Folding of h (take its mirror

image w.r.t. the ordinate axis) !

2) Displacement - shift h(-!) by

amount t so we get h(t-!) !

h(t-!)

3) Multiplication of h(t-!)

by g(!)

h(t-!)

4) Integration - let’s see it for different values of t

so: ' =

Note that the convolution is commutative, i.e. g(t) ( h(t) = h(t) ( g(t)

§§The Flat surface response function is theThe Flat surface response function is the

response you would get from reflecting theresponse you would get from reflecting the

radar pulse from a flat surface.radar pulse from a flat surface.

§§It looks likeIt looks like

§§where U(t) is the Heaviside or indicatorwhere U(t) is the Heaviside or indicator

functionfunction

§§U(t) = 0 t <0 =1 otherwiseU(t) = 0 t <0 =1 otherwise

§§G(t) is the two way antenna gain patternG(t) is the two way antenna gain pattern

The Flat Surface Response FunctionThe Flat Surface Response Function

§§The point target response function is the shape ofThe point target response function is the shape of

the transmitted pulsethe transmitted pulse

§§ItIt’’s true shape is given bys true shape is given by

§§For the Brown model we approximate this with aFor the Brown model we approximate this with a

Gaussian.Gaussian.

The Point Target Response FunctionThe Point Target Response Function

The Brown Model - IIIThe Brown Model - III

T/P ERS

Tide Period

(days)

length

(days)

length

M2 12.42 62 9E 95 9E

S2 12 59 180W 0 !

N2 12.65 50 9W 97 4W

K1 23.93 173 360W 365 360E

O1 25.82 46 9.23E 75 9E

P1 24.07 89 360W 365 360W

Pr t( ) = PFS t ! t0( )"PT 2#$ p

21+ erf

t ! t0( )2$c

t > t0

PFS t( ) =G02 !R2c" 0

4 4#( )2Lph3exp $

%hcos2&

* + , I0

hsin2&

Compare with the Normal cumulative distributionfunction

I0() is a modified Bessel function of the first

§§##RR is the radar wavelengthis the radar wavelength

§§LLpp is the two way propagation loss is the two way propagation loss

§§hh is the satellite altitude (nominal) is the satellite altitude (nominal)

§§GG00 is the antenna gain is the antenna gain

§§$$ is the antenna beam widthis the antenna beam width

§§!!pp is the pulse widthis the pulse width

§§%% is the pulse compression ratiois the pulse compression ratio

§§PPTT is the peak power is the peak power

§§&& is the mispointing angleis the mispointing angle

What are the other parameters?What are the other parameters?

Noise on the altimeterNoise on the altimeter

§§If we simply use the altimeter as a detector weIf we simply use the altimeter as a detector we

will receive a signal.will receive a signal.

§§This is known as the thermal noise.This is known as the thermal noise.

§§The noise on the signal is known as fading noiseThe noise on the signal is known as fading noise

§§It is sometimes assumed to be constant,It is sometimes assumed to be constant,

sometimes its mean is measuredsometimes its mean is measured

§§For most altimeters the noise on the signal isFor most altimeters the noise on the signal is

independent in each gate and has a negativeindependent in each gate and has a negative

exponential distribution.exponential distribution.

§§For a negative exponential distribution theFor a negative exponential distribution the

variance is equal to the mean. Thus thevariance is equal to the mean. Thus the

individual pulses are very noisyindividual pulses are very noisy

§§The pulse repetition frequency is usuallyThe pulse repetition frequency is usually

about 1000 per secondabout 1000 per second

§§It is usual to transmit data to the ground atIt is usual to transmit data to the ground at

20Hz and then average to 1 Hz20Hz and then average to 1 Hz

Averaging the noiseAveraging the noise

How altimeters really workHow altimeters really work

§§It is very difficult (if not impossible) to generate aIt is very difficult (if not impossible) to generate a

pulse of length 3 nspulse of length 3 ns

§§However it is possible to do something veryHowever it is possible to do something very

similar in the frequency domain using a chirpsimilar in the frequency domain using a chirp

§§Modulate the frequency of the carrierModulate the frequency of the carrierwave in a linear waywave in a linear way

What is a chirp?What is a chirp?

For use over land and ice ENVISAT has modes thatuse 80 and 20 MHz for the chirp,

the pulse width =1/chirp bandwidth

§§Assume that the sea surface is a perfectlyAssume that the sea surface is a perfectly

conducting rough mirror which reflects only atconducting rough mirror which reflects only at

specular points, i.e. those points where the radarspecular points, i.e. those points where the radar

beam is reflected directly back to the satellitebeam is reflected directly back to the satellite

The Brown ModelThe Brown Model

The Brown Model - IIThe Brown Model - II

§§Under these assumptions the returnUnder these assumptions the return

power is given by a three fold convolutionpower is given by a three fold convolution

Pr t( ) = PFS t( )!PPT t( )!PH "z( )

Prt( ) i s thereturned power

PFS t( ) i s theflat surface response

PPT t( ) i s thepointtarget response

PH !z( ) is the pdf of specular points on the sea surface

••A chirp is generatedA chirp is generated

••Two copies areTwo copies are

takentaken

••The first isThe first is

transmittedtransmitted

••The second isThe second is

delayed so it can bedelayed so it can be

matched with thematched with the

reflected pulsereflected pulse

Full chirp derampFull chirp deramp

Generatechirp

Transmit Receive

Combine

§§The two chirps are subtracted.The two chirps are subtracted.

§§A point above the mean sea surface givesA point above the mean sea surface gives

returns a frequency lower than would bereturns a frequency lower than would be

expected and a point below the mean seaexpected and a point below the mean sea

surface a higher frequencysurface a higher frequency

§§So a So a ‘‘BrownBrown’’ return is received but with return is received but with

frequency rather than time along the x axisfrequency rather than time along the x axis

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