RA2/MWR LOP CLS.OC/NT/96.038 Issue 2rev1 Toulouse, 14 ...RD4 : Numerical Recipes : The Art of Scientific Computing in C (Edition 2). William H. Press, Brian P. Flannery, Saul A. Teukolsky,

RA2/MWR LOPCLS.OC/NT/96.038Issue 2rev1 Toulouse, 14 November 1997Nomenclature : PO-NT-RAA-0004-CLS

Algorithms Definition and Accuracy

PREPARED BY COMPANY DATE VISA

J.P. DUMONTJ. STUMO.Z. ZANIFE

CLSCLSCLS

QUALITY VISA A. BLUSSON CLS

APPROVED BY O.Z. ZANIFE CLS

APPLICATIONAUTHORIZED BY

J. BENVENISTEP. VINCENT

ESRINCNES

CLS 18 Av. Edouard Belin 31401 TOULOUSE CEDEX 4 FRANCETel. (0)5 61 39 47 00 FAX (0)5 61 75 10 14

CLSRA2/MWR LOP

Algorithms Definition and AccuracyPage : i2

Date : 14/11/97

Source ref. : CLS.OC/NT/96.038 Nomenclature : PO-NT-RAA-0004-CLS Issue : 2rev1

Proprietary information : no part of this document may be reproduced, divulgedor used in any form without prior permission from CLS.

DOCUMENT STATUS SHEET

Project controlvisa

Issue Date Reason for change

1/0

2/0

2/1

20/12/96

20/01/97

14/11/97

First issue

Second issue : accounting for ESRINand CNES comments about the firstissue.

Second issue, first revision

D : Page deleted I : Page inserted M : Page modified

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LIST OF ACRONYMS

ADx : Applicable Document xCNES : Centre National d’Etudes SpatialesCLS : Collecte Localisation SatellitesCSR : Centre for Space ResearchDS : Data SetDSR : Data Set RecordESA : European Space AgencyESRIN : European Space Research InstituteESTEC : European Space Research and Technology CentreFDGDR : Fast Delivery Geophysical Data RecordFES : Finite Element SolutionFOS : Flight Operation SegmentGDR : Geophysical data RecordCOG : Centre of GravityGRGS : Groupe de Recherche en Géodésie SpatialeIGDR : Interim Geophysical Data RecordLOP : Level 2 Ocean ProcessingLS : Least SquareMDS : Measurement Data SetMJD : Modified Julian DateMPH : Main Product HeaderMSS : Mean Sea SurfaceMWR : MicroWave Radiometer (ENVISAT)NGDC/WDC-A : National Geophysical Data Centre/World Data Centre ANRT : Near Real TimeOFL : Off-LinePF : PlatformPTR : Point Target ResponseRA2 : Radar Altimeter (ENVISAT)RMS : Root Mean SquareRDx : Reference Document xSGDR : Sensor Geophysical Data RecordSNR : Signal to Noise RatioSPH : Specific Product HeaderSV : State VectorSWH : Significant WaveheightTEC : Total Electron ContentTBC : To Be Confirmed

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TBD : To Be DefinedUTC : Universal Time Co-ordinated

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APPLICABLE DOCUMENTS / REFERENCE DOCUMENTS

AD1 : Software Prototyping for RA-2/MWR Level 2 Ocean Processing ; Technical,Management, Administrative and Financial Proposal ; Response to request forquotation RFQ/3-8785/96/NL/GS. CLS

AD2 : RA-2/MWR Level 2 Ocean Processing - Product Assurance PlanPO-AQ-RA-0001-CLS

AD3 : Envisat-1 Products Format GuidelinesPO-TN-ESA-GS-0242

AD4 : Envisat-1 RA-2 and MWR products SpecificationPO-TN-ESA-GS-0178

AD5 : ENVISAT-1 Orbit Propagator. S/W I/F and Installation GuidePPF-TN-ESA-GS-00248

AD6 : Input / Output Data DefinitionPO-ST-RA-0005-CLS

AD7 : ENVISAT-1 products specifications. Vol. 14 : RA-2 products specificationsPO-RS-MDA-GS-2009, Red Marked Copy from 26/09/97

RD1 : Definition of the RA-2 level 2 ocean and ice retracking algorithmsPO-NT-RAA-003-CLS, Issue 1rev0, 15/01/97

RD2 : RA-2 retracking comparisons over ocean surface by CLSCLS.OC/NT/95.028, Issue 3.1

RD3 : Etude du retracking des formes d’ondes altimetriques au dessus des calottes polaires,CNES report CT/ED/TU/UD/96.188, CNES contract 856/2/95/CNES/0060, B.Legresy, 1995.

RD4 : Numerical Recipes : The Art of Scientific Computing in C (Edition 2). William H.Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling

RD5 : Algorithms specifications (ocean and ice2 FDGDR processing)PO-SP-RAA-0006-CLS, issue 3rev0, 14/11/97

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TABLE OF CONTENTS

1. INTRODUCTION .......................................................................................................................................... 1

2. INPUT AND OUTPUT DATA ...................................................................................................................... 3

2.1. INPUT DATA..............................................................................................................................................................................................................3

2.1.1. Product data................................................................................................................................ 3

2.1.2. Auxiliary data............................................................................................................................. 3

2.2. OUTPUT DATA.........................................................................................................................................................................................................5

2.3. SUMMARY OF THE INTERFACES...................................................................................................................................................................5

3. PROCESSING OVERVIEW......................................................................................................................... 7

3.1. GENERAL FLOWCHART......................................................................................................................................................................................7

3.2. BRIEF DESCRIPTION.............................................................................................................................................................................................9

3.2.1. FDGDR processing .................................................................................................................... 9

3.2.2. IGDR processing...................................................................................................................... 10

3.2.3. GDR processing .......................................................................................................... ............. 12

4. ALGORITHMS .................................................................................................................. .......................... 12

4.1. TO COMPUTE THE AVERAGED TIME TAGS............................................................................................................................................13

4.2. TO COMPUTE THE AVERAGED ALTITUDE, ALTITUDE RATE AND LOCATION.....................................................................14

4.3. TO COMPUTE ALTITUDE, ALTITUDE RATE AND LOCATION FROM ORBIT FILES...............................................................16

4.4. TO COMPUTE THE DOPPLER CORRECTIONS.........................................................................................................................................19

4.5. TO PERFORM THE ICE 2 RETRACKING......................................................................................................................................................21

4.6. TO PERFORM THE OCEAN RETRACKING.................................................................................................................................................26

4.7. TO COMPUTE THE PHYSICAL PARAMETERS.........................................................................................................................................31

4.8. TO CORRECT THE ALTIMETER RANGE FOR DOPPLER EFFECTS.................................................................................................35

4.9. TO AVERAGE THE OCEAN ESTIMATES.....................................................................................................................................................37

4.10. TO DETERMINE THE SURFACE TYPE.......................................................................................................................................................39

4.11. TO INTERPOLATE THE MWR DATA TO ALTIMETER TIME TAG.................................................................................................41

4.12. TO COMPUTE THE BACKSCATTER COEFFICIENT ATMOSPHERIC ATTENUATION..........................................................43

4.13. TO COMPUTE THE 10 METERS ALTIMETER WIND SPEED.............................................................................................................45

4.14. TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE ALTIMETER................................................................................47

4.15. TO COMPUTE THE 10 METERS MODEL WIND VECTOR..................................................................................................................49

4.16. TO COMPUTE THE SEA STATE BIASES....................................................................................................................................................51

4.17. TO COMPUTE THE DUAL-FREQUENCY IONOSPHERIC CORRECTION.....................................................................................53

4.18. TO COMPUTE THE DORIS IONOSPHERIC CORRECTION.................................................................................................................56

4.19. TO COMPUTE THE BENT MODEL IONOSPHERIC CORRECTION..................................................................................................58

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4.20. TO COMPUTE THE MODEL WET AND DRY TROPOSPHERIC CORRECTIONS........................................................................60

4.21. TO COMPUTE THE INVERTED BAROMETER EFFECT......................................................................................................................67

4.22. TO COMPUTE THE MEAN SEA SURFACE PRESSURE OVER THE OCEAN...............................................................................69

4.23. TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THE ORTHOTIDE ALGORITHM.....................71

4.24. TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THE HARMONIC COMPONENTSALGORITHM...................................................................................................................................................................................................................73

4.25. TO COMPUTE THE HEIGHT OF THE TIDAL LOADING......................................................................................................................75

4.26. TO COMPUTE THE SOLID EARTH TIDE AND THE LONG PERIOD EQUILIBRIUM TIDE HEIGHTS................................77

4.27. TO COMPUTE THE POLE TIDE HEIGHT....................................................................................................................................................80

4.28. TO COMPUTE THE MEAN SEA SURFACE HEIGHT.............................................................................................................................82

4.29. TO COMPUTE THE GEOID HEIGHT............................................................................................................................................................84

4.30. TO COMPUTE THE OCEAN DEPTH / LAND ELEVATION..................................................................................................................86

4.31. TO INTERPOLATE THE ALTIMETER WIND SPEED DATA TO RADIOMETER TIME TAG..................................................88

4.32. TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE RADIOMETER ...........................................................................90

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1. INTRODUCTION

This document is aimed at defining the level 2 processing of the ENVISAT RA-2 and MWRdata, consisting in the framework of this study (see AD1), of the following processing limited tothe so-called "ocean" and "ice2" processes (see AD4) :

• FDGDR processing : Near Real Time processing aimed at providing RA-2 / MWR level 2Fast Delivery GDR (or FDGDR) products, from level 1b unconsolidated products, usingpredicted auxiliary data. "Unconsolidated" means parameters which do not account for thefinal instrumental calibration data.

• IGDR processing : Off-Line processing aimed at providing RA-2 / MWR level 2 InterimGDR (or IGDR) products, within a few days (3 to 5), from level 1b unconsolidated products,using restituted auxiliary data (meteorological fields, solar activity indexes, pole location,platform data, DORIS ionospheric data) and a DORIS preliminary orbit.

• GDR processing : Off-Line processing aimed at providing RA-2 / MWR level 2 GDRproducts, within a few weeks (3 to 4), from level 1b consolidated products, using the bestrestituted auxiliary data (meteorological fields, solar activity indexes, pole location, platformdata, DORIS ionospheric data) and a DORIS precise orbit. "Consolidated" means parameterswhich account for the updated instrumental calibration data.

• SGDR processing : Off-Line processing aimed at providing RA-2 / MWR level 2 SensorGDR (or SGDR) products including waveforms, within a few weeks (3 to 4), from level 2GDR products and the corresponding level 1b consolidated products. This processingconsists of the acquisition of the level 1b data (averaged and burst waveforms) and of thelevel 2 GDR data, and of the merging of these data in a single product. It does not request anycritical algorithm and thus will not be described in this document.

This document is aimed at defining these processings, i.e. to identify and describe their mainfunctions. It must be considered as the basic input for the detailed requirements of theprocessings, and not of course as the detailed requirements themselves.

The product tree (see AD4) pointing out the main features of these processings and products isgiven in figure 1-a.

The interfaces of FDGDR, IGDR and GDR processings (input and output data) are defined insection 2. An overview of the processings is then given in section 3. It consists of thepresentation of the general flowchart, and of a brief description of FDGDR, IGDR and GDRprocessings. The detailed description of the algorithms is finally given in section 4, where eachalgorithm is defined through the following items :− Name of the algorithm− Function of the algorithm− Input data− Output data− Mathematical statement− Applicability to the various processings and products, and to the surface types− Accuracy

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− Comments− References

Terminology

In all the document, a RA-2 "elementary measurement" represents one datablock (55.7 ms),while a RA-2 "averaged measurement" represents one source packet, i.e. twenty elementarymeasurements (1.114 s). There is no ambiguity about MWR measurements which are averagedmeasurements (1.2 s) only.

Figure 1-a : Product tree (FDGDR, IGDR, GDR, SGDR)

Level 1b product(RA-2 / MWR + waveforms)

Level 2 FDGDR product(RA-2 / MWR)

Level 2 FDGDR processing

Level 2 IGDR processing

Level 2 GDR product(RA-2 / MWR)

Level 2 IGDR product(RA-2 / MWR)

Level 2 GDR processing

Restitutedgeophysicalcorrections

Predictedgeophysicalcorrections

Preciseorbit

Preliminaryorbit

RA-2 and MWR DORIS orbitAuxiliary dataDelay

Off_line3-4 weeks

Off_line3-5 days

Near RealTime

Near RealTime

Consolidated

Level 2 SGDR processing

Level 2 SGDR product(RA-2 / MWR + waveforms)

Off_line3-4 weeks

Unconsolidated

Unconsolidated

Consolidated

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2. INPUT AND OUTPUT DATA

2.1. INPUT DATA

Input data consist of two types of data (see AD3) :− Product data, which may be :

⋅ RA-2/MWR level 1b product data (for FDGDR, IGDR and GDR processings)

⋅ DORIS orbit product data (DORIS orbit data for IGDR and GDR processings)− Auxiliary data, which may be dynamic or static :

⋅ Dynamic auxiliary data are the unforeseeable data which vary during the mission life

⋅ Static auxiliary data are constant or foreseeable data.

Level 2 processings are operated by product. For FDGDR processing, a product represents asequential set of RA-2 / MWR measurements, whose maximum length is about one revolutionof the satellite (i.e. about one orbit). For IGDR and GDR processings, a product represents onepass (i.e. half an orbit from pole to pole).

2.1.1. Product data • RA-2 / MWR Level 1b data :

The level 1b product is described in AD7. Generally speaking, it is assumed that level 1bproducts contain time ordered data without overlapping, whatever the nature of the product is(i.e. unconsolidated, consolidated or other if it exists).

• FDGDR Level 2 data :

The FDGDR level 2 product is described in section 2.2.

• DORIS orbit data :

The DORIS orbit data are described in AD6. They correspond to DORIS preliminary orbitand to DORIS precise orbit.

2.1.2. Auxiliary data

• Dynamic data :

Dynamic auxiliary data are described in AD6. They consist of :− TBD orbit data (preliminary or precise backup orbit data)− Meteorological data (predicted or restituted data)− Solar activity data− Pole location data

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− Platform data (antenna pitch and roll angles and COG motion)− DORIS-derived TEC maps

Generally speaking, the dynamic auxiliary data requested on input of the level 2 processingsare the data which cover the time span of the input product to be processed (with additionalpoints before and after for the orbit data, due to the orbit interpolation method).

• Static data :

Static auxiliary data are described in AD6. They do not depend on the type of level 2processing. They consist of :− Universal constant data ("constant file" described in AD6)− RA-2 instrumental characterisation data ("characterisation files" described in AD7)− Processing parameters (all the constant parameters used in the processing stored in the

"system file", such as backscatter coefficient to wind speed conversion, electromagneticbias coefficients, thresholds, etc)

− The data contained in the following files :

⋅ Sea state bias table

⋅ Modified dip map

⋅ Coefficients for the model ionospheric correction

⋅ Cartwright’s amplitudes for the solid earth tide calculation

⋅ Coefficient maps for the non-equilibrium ocean tide calculation (solution 1)

⋅ Coefficient maps for the non-equilibrium ocean tide calculation (solution 2)

⋅ Coefficients for the tidal loading effect calculation

⋅ Geoid height

⋅ Mean sea surface height

⋅ Bathymetry / topography map (ocean depth, land elevation)

⋅ Map of the altitude of meteorological grid points

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2.2. OUTPUT DATA

Generally speaking, it is assumed that level 2 processings do not modify the organisation of theinput data, and in particular that they do not account for the organisation of data from orbitrevolution to passes. Level 2 processings output thus one level 2 product (FDGDR, IGDR orGDR product), structured as the level 1b input product. Level 2 products are described in AD6.They consist of :− One Main Product Header (MPH)− One Specific Product Header (SPH)− Two Measurement Data Sets (MDS), consisting of a serie of Data Set Records (DSR)

⋅ MDS1 : RA-2 averaged measurements

⋅ MDS2 : MWR averaged measurements

2.3. SUMMARY OF THE INTERFACES

The interfaces of the FDGDR, IGDR and GDR processings are summed up in figure 2.3-a.

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Figure 2.3-a : Interfaces of the FDGDR, IGDR and GDR processings

(1) TBD orbit data as backup solution

Productdata

DynamicAuxiliary

Data

StaticAuxiliary

Data

Level 1b (unconsolidated)

Meteo. : predicted

Solar activity

Pole location

FDGDRprocessing FDGDR product

PF data

Productdata

DynamicAuxiliary

Data

StaticAuxiliary

Data

Meteo. : restituted

Solar activity

Pole location

GDRprocessing GDR product

PF data

Productdata

DynamicAuxiliary

Data

StaticAuxiliary

Data

Level 1b (consolidated)

Meteo. : restituted IGDRprocessing IGDR product

DORIS precise orbit (1)

Level 1b (unconsolidated)

DORIS preliminary orbit (1)

Solar activity

Pole location

DORIS-derived TEC maps

PF data

DORIS-derived TEC maps

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3. PROCESSING OVERVIEW

3.1. GENERAL FLOWCHART

A general flowchart of the FDGDR, IGDR and GDR level 2 processings is given in figure 3.1-a.Each function (i.e. algorithm) is represented by a box, and a table indicates to which type oflevel 2 processing(s) it belongs (grey if the algorithm is performed). Moreover, the rhythm ofactivation of the algorithms (RA-2 elementary measurements, RA-2 averaged measurements orMWR averaged measurements) is pointed out.

Algorithms which proceed with data management or quality check, such as :− to get and prepare the input data− to check the input data (presence, conformity, compatibility of input files)− to convert units− to modify reference systems− to check the data at various levels of the processing− to build the output product (including statistics)− to manage the end of the processing− etcare not represented in this document, because they are not considered as critical items in theframework of the present processing definition. They will be represented and described duringthe processing detailed requirements phase.

Generally speaking, the algorithms defined hereafter only concern RA-2 measurements intracking modes, i.e. measurements in "tracking" mode (nominal measurement mode), or in"preset tracking" mode, or in "preset loop output" mode (see AD7).

It is assumed that the level 1b data to be processed in the level 2 processing (time-tag, location,waveforms, window delays, scaling factors for sigma0 evaluation, etc.) have the same meaningfor the "tracking", "preset tracking" and "preset loop output" modes, so that the level 2processing of these measurements is exactly the same. It is thus assumed that the specificities ofthe three tracking modes (if any) are accounted for and managed in the level 1b processing.

For non tracking measurements, only the time-tag, the location (longitude and latitude) and theinstrument mode identifier will be provided in the output data set record, while the other fieldswill be set to default values.

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Figure 3.1-a : General flowchart of the FDGDR, IGDR and GDR level 2 processings

TO AVERAGE THE OCEAN ESTIMATES

TO INTERPOLATE THE MWR DATA TO ALTIMETER TIME TAG

TO COMPUTE THE BACKSCATTER COEFFICIENT ATMOSPHERIC ATTENUATION

TO COMPUTE THE 10 METERS ALTIMETER WIND SPEED

TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE ALTIMETER

TO COMPUTE THE SEA STATE BIASES

TO COMPUTE THE DUAL FREQUENCY IONOSPHERIC CORRECTION

TO DETERMINE THE SURFACE TYPE

TO COMPUTE THE MEAN SEA SURFACE PRESSURE OVER THE OCEAN

TO COMPUTE THE DORIS IONOSPHERIC CORRECTION

TO COMPUTE THE BENT MODEL IONOSPHERIC CORRECTION

TO COMPUTE THE MODEL WET AND DRY TROPOSPHERIC CORRECTIONS

TO COMPUTE THE INVERTED BAROMETER EFFECT

RA-2averaged

measurements

RA-2elementary

measurements

TO COMPUTE THE PHYSICAL PARAMETERS

TO CORRECT THE ALTIMETER RANGE FOR DOPPLER EFFECTS

TO COMPUTE THE 10 METERS MODEL WIND VECTOR

l ll

l ll

TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THE ORTHOTIDE ALGORITM

TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THE HARMONIC COMPONENTS ALGORITHM

TO COMPUTE THE HEIGHT OF THE TIDAL LOADING

TO COMPUTE THE SOLID EARTH TIDE AND THE LONG PERIOD EQUILIBRIUM TIDE HEIGHTS

TO COMPUTE THE POLE TIDE HEIGHT

TO COMPUTE THE MEAN SEA SURFACE HEIGHT

TO COMPUTE THE GEOID HEIGHT

TO COMPUTE THE OCEAN DEPTH / LAND ELEVATION

TO INTERPOLATE THE ALTIMETER WIND SPEED DATA TO RADIOMETER TIME TAG

TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE RADIOMETER

MWRaveraged

measurements

FDGDR GDRIGDR

TO COMPUTE THE AVERAGED ALTITUDE, ALTITUDE RATE AND LOCATION

TO COMPUTE ALTITUDE, ALTITUDE RATE AND LOCATION FROM ORBIT FILES

TO COMPUTE THE DOPPLER CORRECTIONS

TO PERFORM THE ICE 2 RETRACKING

TO PERFORM THE OCEAN RETRACKING

TO COMPUTE THE AVERAGED TIME TAGS

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3.2. BRIEF DESCRIPTION

A brief overview of the main functions of the nominal level 2 processings is given in thissection. A detailed description of the algorithms is provided in section 4.

3.2.1. FDGDR processing

• The time-tag of the averaged measurements is derived from the time-tags of the elementarymeasurements.

• The elementary values of the location (latitude, longitude), the orbit altitude and the orbitaltitude rate are interpolated at the time tag of the averaged measurements.

• The ice2 and ocean retrackings are performed in Ku and S bands. The ocean retrackingalgorithm is nominally initialised by the outputs of the ice2 retracking algorithm, and itaccounts for the mispointing information derived from the platform data (antenna pitch androll angles which precede the measurement).

• Elementary physical parameters are derived from the ocean and ice2 retrackings outputs,combined with the input tracker range corrected for COG motion and from which the level1b correction is removed, and with the input scaling factors for Sigma0 evaluation (in Ku andS bands). These parameters consist of :− Ocean and ice2 altimeter ranges corrected for COG motion− Significant waveheight− Ocean and ice2 backscatter coefficients− Square of the off-nadir angle derived from Ku-band waveforms (using an estimate of the

slope of the trailing edge of waveforms computed within the ice2 retracking algorithm)• The elementary estimates of the ocean and ice2 altimeter ranges are corrected for the Doppler

effects (adding of the input correction)• The ocean physical parameters (altimeter range, significant waveheight, backscatter

coefficient) and the square of the off-nadir angle are then edited and averaged to provide 1-Hz estimates. Moreover, the averaged off-nadir angle is derived.

• The surface type "ocean" or "land" is determined, first by using information provided by abathymetry / topography file, and then in case of ambiguity, by information from thealtimeter itself. It will be used in the following to sort data to be accounted for in thealgorithms relevant to ocean surfaces only.

• The MWR brightness temperatures (2 channels) and the radiometer land flag are interpolatedto the altimeter time tag of the averaged measurements.

• The backscatter coefficient atmospheric attenuations are computed in Ku and S bands, usingbrightness temperatures

• The Ku and S bands ocean backscatter coefficient are corrected for the atmosphericattenuation and the 10 meters altimeter wind speed is derived (from the Ku-band estimates)

• Then, the MWR level 2 parameters (wet tropospheric correction, water vapour and cloudliquid water contents) are computed from the brightness temperatures, using in particular thealtimeter wind speed as a correction term.

• The two components (U and V) of the 10 meters wind vector are computed using forecastedmeteorological fields.

• The sea state bias is computed in Ku and S bands.

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• Two types of ionospheric corrections are computed in Ku and S bands :− Dual-frequency correction− Correction derived from Bent model using sunspot numbers.

• The following parameters are computed using analysed meteorological fields :− The wet and dry tropospheric corrections due to permanent gases of the troposphere, and

the sea surface atmospheric pressure at measurement− The sea surface height correction due to atmospheric loading (the so-called inverted

barometer effect)− The mean sea surface pressure over the ocean.

• The non-equilibrium ocean tide height is computed from two algorithms :− The orthotide algorithm (using CSR model)− The harmonic components algorithm (using Grenoble hydrodynamical model FES).

• The following tide heights are also computed :− The height of the tidal loading induced by the ocean tide− The solid earth tide height and the height of the long period equilibrium tide

• The pole tide height (geocentric tide height due to polar motion) is computed using polelocations.

• The height of the mean sea surface above the reference ellipsoid is computed• The height of the geoid is computed.• The ocean depth or land elevation is computed using a bathymetry / topography file.• Finally, the parameters of the MWR data set records of the output product are computed :

− The altimeter wind speed is interpolated to radiometer time tags− The MWR level 2 parameters (i.e. the wet tropospheric correction due to water vapour in

the troposphere, and the water vapour and cloud liquid water contents), are computed atMWR time tag, from the MWR brightness temperatures and using the altimeter windspeed interpolated at MWR time tag as a correction term.

3.2.2. IGDR processing

• The time-tag of the averaged measurements is derived from the time-tags of the elementarymeasurements.

• The elementary and averaged orbit altitudes and orbit altitude rates, and the averaged locationof measurements are recomputed from DORIS preliminary orbit data (or TBD preliminaryorbit data in backup solution).

• The elementary Doppler corrections on the altimeter range are computed in Ku and S bandsfrom the altitude rates derived from DORIS preliminary orbit data.

• The ice2 and ocean retrackings are performed in Ku and S bands. The ocean retrackingalgorithm is nominally initialised by the outputs of the ice2 retracking algorithm, and itaccounts for the mispointing information derived from the platform data (antenna pitch androll angles which precede the measurement).

• Elementary physical parameters are derived from the ocean and ice2 retrackings outputs,combined with the input tracker range corrected for COG motion and from which the level1b correction is removed, and with the input scaling factors for Sigma0 evaluation (in Ku andS bands). These parameters consist of :− Ocean and ice2 altimeter ranges corrected for COG motion− Significant waveheight

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− Ocean and ice2 backscatter coefficients− Square of the off-nadir angle derived from Ku-band waveforms (using an estimate of the

slope of the trailing edge of waveforms computed within the ice2 retracking algorithm)• The elementary estimates of the ocean and ice2 altimeter ranges are corrected for the Doppler

effects previously computed from DORIS preliminary orbit data.• The ocean physical parameters (altimeter range, significant waveheight, backscatter

coefficient) and the square of the off-nadir angle are then edited and averaged to provide 1-Hz estimates. Moreover, the averaged off-nadir angle is derived.

• The surface type "ocean" or "land" is determined, first by using information provided by abathymetry / topography file, and then in case of ambiguity, by information from thealtimeter itself. It will be used in the following to sort data to be accounted for in thealgorithms relevant to ocean surfaces only.

• The MWR brightness temperatures (2 channels) and the radiometer land flag are interpolatedto the altimeter time tag of the averaged measurements.

• The backscatter coefficient atmospheric attenuations are computed in Ku and S bands, usingbrightness temperatures

• The Ku and S bands ocean backscatter coefficient are corrected for the atmosphericattenuation and the 10 meters altimeter wind speed is derived (from the Ku-band estimates)

• Then, the MWR level 2 parameters (wet tropospheric correction, water vapour and cloudliquid water contents) are computed from the brightness temperatures, using in particular thealtimeter wind speed as a correction term.

• The two components (U and V) of the 10 meters wind vector are computed using analysedmeteorological fields.

• The sea state bias is computed in Ku and S bands.• Three types of ionospheric corrections are computed in Ku and S bands :

− Dual-frequency correction− DORIS-derived ionospheric correction (computed from DORIS-derived TEC maps)− Correction derived from Bent model using sunspot numbers.

• The following parameters are computed using analysed meteorological fields :− The wet and dry tropospheric corrections due to permanent gases of the troposphere, and

the sea surface atmospheric pressure at measurement− The sea surface height correction due to atmospheric loading (the so-called inverted

barometer effect)− The mean sea surface pressure over the ocean.

• The non-equilibrium ocean tide height is computed from two algorithms :− The orthotide algorithm (using CSR model)− The harmonic components algorithm (using Grenoble hydrodynamical model FES).

• The following tide heights are also computed :− The height of the tidal loading induced by the ocean tide− The solid earth tide height and the height of the long period equilibrium tide

• The pole tide height (geocentric tide height due to polar motion) is computed using polelocations.

• The height of the mean sea surface above the reference ellipsoid is computed• The height of the geoid is computed.• The ocean depth or land elevation is computed using a bathymetry / topography file.

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• Finally, the parameters of the MWR data set records of the output product are computed :− The altimeter wind speed is interpolated to radiometer time tags− The MWR level 2 parameters (i.e. the wet tropospheric correction due to water vapour in

the troposphere, and the water vapour and cloud liquid water contents), are computed atMWR time tag, from the MWR brightness temperatures and using the altimeter windspeed interpolated at MWR time tag as a correction term.

3.2.3. GDR processing

The GDR processing is the same as the IGDR processing excepted for the following points :

• Orbit data consist of DORIS precise orbit data (or TBD precise orbit data in backupsolution), instead of preliminary data.

• The pole tide height is computed from improved pole location data (with respect to the polelocation data used in the IGDR processing).

4. ALGORITHMS

The following descriptions do not account for reference systems and units. The parameters ofthe mathematical formulae are assumed to be consistent. These items will be accounted for inthe detailed requirements of the software.

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4.1. TO COMPUTE THE AVERAGED TIME TAGS

Function

To compute the time tag of averaged RA-2 measurements.

Input data

• Product data :− Elementary RA-2 time tags− Data block number and source sequence count (source packet number)

• Computed data : None• Dynamic auxiliary data : None• Static auxiliary data :

− Processing parameters

Output data

− Averaged RA-2 time tags

Mathematical statement

The elementary time-tag associated to a data block represents the time when the middle of the100 averaged corresponding Ku-band waveforms is on the ground. The averaged measurementsprovided in the level 2 output product correspond to the source packets of the telemetry. Thetime-tag of the averaged measurements are computed by linear regression of the correspondingelementary RA-2 time tags, at the middle of the source packet.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the averaged time tags is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the averaged time tags is relevant to all surface types.

Accuracy

The elementary time-tags within a source packet are derived from the on-board datation of thesource packet. As the level 1b algorithm is such as these time-tags are equidistant, there will beno error due to the interpolation method (linear regression).

Comments NoneReferences None

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4.2. TO COMPUTE THE AVERAGED ALTITUDE, ALTITUDE RATE ANDLOCATION

Function

To interpolate the elementary altitude, altitude rate and location at the time-tag of the averagedRA-2 measurements.

Input data

• Product data :− Elementary longitudes, latitudes, altitudes and altitude rates− Data block number and source sequence count (source packet number)

• Computed data : None• Dynamic auxiliary data : None• Static auxiliary data :


Output data

− Longitude, latitude, altitude and altitude rate at the RA-2 averaged time-tags− Altitude differences from the averaged altitude (differences between the orbit altitudes of

elementary measurements and the orbit altitude of the averaged measurement).


The averaged parameters are computed by regression of the corresponding elementary RA-2time tags, at the middle of the source packet (linear regression for the latitudes, longitudes andaltitude rates, parabolic regression for the altitude). The differences between the elementary andthe averaged values of the altitude are computed and stored in the output product.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the averaged location, altitude and altitude rate is performed in FDGDRprocessing only.

• Surface type :The computation of the averaged location, altitude and altitude rate is relevant to all surfacetypes.

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Accuracy

The error due the interpolation algorithm is negligible. Indeed, it is :− smaller than 0.20 10-3 degrees on the latitude and 0.85 10-3 degrees on the longitude, which

are the maximum errors, corresponding to measurements close to the poles, observed fromone orbit of ERS OPR measurements when the location of 1-Hz points is replaced by theresult of the linear interpolation of the location of the 1-Hz points just before and just after(worst case with respect to the proposed method)

− about 0 on the altitude and altitude rate, assuming a constant radial acceleration within asource packet, i.e. a parabolic altitude and a linear altitude rate. With these assumptions, alinear regression on the altitude would lead to an error of about 3 mm for an radialacceleration of 5 cm/s2.

Comments

One of the advantage of the regression is the automatic management of missing elementary data.

References None

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4.3. TO COMPUTE ALTITUDE, ALTITUDE RATE AND LOCATION FROMORBIT FILES

Function

To compute the orbit altitude above reference ellipsoid, the orbit altitude rate and location fromorbit files.

Input data

• Product data :− Elementary RA-2 time tags− DORIS orbit data covering the time span of the input product (position and velocity of the

satellite on its orbit at regular time steps)• Computed data :

− From "To compute the averaged time tags":⋅ Averaged RA-2 time tag

• Dynamic auxiliary data :− TBD orbit data (as backup solution only)

• Static auxiliary data :− Processing parameters

Output data

− Orbit altitude (altitude of COG above reference ellipsoid) and orbit altitude rate for theaveraged RA-2 measurements.

− Altitude differences from the averaged altitude (differences between the orbit altitudes ofelementary measurements and the orbit altitude of the averaged measurement).

− Orbit altitude rate of the elementary measurements− Latitude and longitude of the averaged RA-2 measurements.


The orbit altitude (h), the orbit altitude rate (h’) and the location (latitude, longitude)corresponding to an input (elementary or averaged) altimeter time-tag t are computed asfollows:

• N (typically N=8) position vectors are selected from the input orbit file (N/2 before and N/2after the altimeter time tag). These vectors are interpolated at the altimeter time tag using the

Everett’s formula. The interpolated positionrP P P PX Y Z= ( , , ) of the satellite is then projected

onto the reference ellipsoid to provide the latitude, longitude and orbit altitude h (i.e. thealtitude of the platform centre of gravity above the reference ellipsoid).

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• M (typically M=8) velocity vectors are selected from the input orbit file (M/2 before andM/2 after the altimeter time tag). These vectors are interpolated at the altimeter time tagusing the Everett’s formula. The orbit altitude rate (h’) is then obtained by forming a scalar

product of the interpolated satellite velocity vector rV V V VX Y Z= ( , , ) with the normalised

position vector (see section "accuracy"), i.e. by :

hV P V P V P

P P P

X X Y Y Z Z

X Y Z

’. . .

=+ +

+ +2 2 2(1)

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of altitude, altitude rate and location from orbit files is performed in IGDRand GDR processings only.− IGDR : the processing is performed from a DORIS preliminary orbit (backup solution

with a TBD preliminary orbit)− GDR : the processing is performed from a DORIS precise orbit (backup solution with a

TBD precise orbit)• Surface type :

The computation of altitude, altitude rate and location from orbit files is relevant to allsurface types.

Accuracy

• The error due to the Everett’s interpolation method is negligible if the number N of orbitpoints taken into account is large enough (typically N=8, i.e. 4 points before and 4 pointsafter the altimeter time).

• The driving parameter for the Doppler range effect is the velocity component of the satellitein the light of sight of the observer, i.e. in the direction NS defined by the satellite (S) andthe corresponding nadir point (N). However, this direction may be merged with the directionOS of the position vector (defined by the earth centre O and the satellite S). Indeed, themaximum angle γ between these two directions is about 0.17 degrees, leading to an error ofabout 5.10-6 h’.

In the worst case, assuming a satellite altitude of 800 km and a radial velocity of ± 25 m/s atthe point where γ is maximum, the error on the radial velocity will thus be 1.25 10-4 m/s,leading to an error on the Doppler correction always smaller than 2 microns whatever theemitted bandwidth is.

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Comments

• A backup solution to compute the altitude, altitude rate and location from orbit files consistsof the use of TBD orbit files. If these files contain a series of position and velocity of thesatellite on its orbit at regular time steps, then the processing is the same as for DORIS files.If they contain only one state vector at equator ascending node, then the computation will beperformed using the ESA orbit propagator (see AD5).

References None

S

N

O

y

x

γ

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4.4. TO COMPUTE THE DOPPLER CORRECTIONS

Function

To compute the Doppler corrections (Ku band and S band) on the altimeter range.

Input data

• Product data :− Elementary Ku bandwidth identifier

• Computed data :− From "To compute altitude, altitude rate and location from orbit files" :

⋅ Orbit altitude rate of the elementary RA-2 measurements• Dynamic auxiliary data : None• Static auxiliary data :

− RA-2 instrumental characterisation data

Output data

− Doppler correction in Ku band− Doppler correction in S band


For each elementary measurement, the Doppler correction δh to be added on the altimeter rangeis computed in Ku and S bands, by :

δ εhf T

Bh=

.. ’ (ε = ±1) (1)

where : h’ = altitude ratef = emitted frequencyT = pulse durationB = emitted bandwidth (consistent in Ku band with the Ku bandwidth identifier)

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the Doppler corrections is performed in IGDR and GDR processings.

• Surface type :The computation of the Doppler corrections is performed whatever the surface type may be.Nevertheless, the Doppler corrections being computed from the radial velocity of the RA-2antenna with respect to the reference ellipsoid (which is derived from the orbit data), it isfully consistent with ocean measurements, but not with measurements relative to othersurfaces.

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Accuracy

Assuming an altitude rate variation of ± 25 m/s, the Doppler correction variation will be about:± 2.1 cm in Ku band 320 MHz± 8.5 cm in Ku band 80 MHz± 34.0 cm in Ku band 20 MHz± 1.0 cm in S band (160 MHz)

Assuming an accurate knowledge of the instrumental parameters, the accuracy of the Dopplercorrection only depends on the accuracy on the orbit altitude rate and thus on the accuracy of theorbit data.

Comments

The FDGDR product will contain in particular (see AD6) :− the elementary tracker altimeter ranges (after removal of the level 1b Doppler correction)− the elementary and averaged altimeter ranges including the retracking correction and the

Doppler correction (computed in level 1b processing)− the elementary Doppler corrections (computed in level 1b processing)The operation of the IGDR and GDR processings is similar to the operation of the FDGDRprocessing, but the elementary Doppler corrections applied to the altimeter ranges (and providedin the level 2 product) are recomputed accounting for DORIS orbit data (preliminary orbit datafor IGDR, precise orbit data for GDR).

This solution allows the accounting for possible Ku bandwidth changes within a source packet.

References None

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4.5. TO PERFORM THE ICE 2 RETRACKING

The ice2 retracking algorithm is performed on the Ku and on the S waveforms. The onlydifference in the retracking of Ku and S waveforms is the processed data (waveform, processingand instrumental parameters), while the processing is the same. A single description is thusgiven below.

Function

To perform the ice2 retracking on the waveform (Ku band or S band).

Input data

• Product data :− Waveform (128 FFT samples + 2 DFT samples in Ku band, 64 FFT samples in S band)− Ku bandwidth identifier in Ku band− Noise power measurement

• Computed data : None• Dynamic auxiliary data : None• Static auxiliary data (see RD1) :

− Processing parameters− RA-2 instrumental characterisation data

Output data

− Epoch or "range offset" (τ)− Width of the leading edge (σL)− Amplitude or "power" (Pu)− Mean amplitude or "mean power" (Pt)− Slope of the first part of the logarithm of the trailing edge (sT1)− Slope of the second part of the logarithm of the trailing edge (sT2)− Slope of the first part of the logarithm of the trailing edge for mispointing estimation (sT1m)− Thermal noise level (Pn)− Mean quadratic error between the normalised waveform and its model


Background

The ice2 retracking algorithm is an adaptation to the ENVISAT RA-2 background, of thealgorithm designed by GRGS to process ERS data over continental ice sheets (see RD3).

Generally speaking, the aim of the ice2 retracking algorithm is to make the measured waveformcoincide with a return power model, according to Least Square estimators. The expression of themodel versus time (t), derived from Brown’s model (Brown, 1977), is given by :

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( )[ ]Vm tP

erft

s t Pu

LT n( ) . .exp .= +

−

− +

21

τσ

τ (with : erf x e dttx

( ) .= ∫ −2 2

0π) (1)

where the parameters to be estimated are :− τ : the epoch − σL : the width of the leading edge − Pu : the amplitude − sT : the slope of the logarithm of the trailing edge− Pn : the thermal noise level (to be removed from the waveform samples)

Basic principle

The ice2 retracking algorithm is defined in RD1. Its basic principle is described hereafter :

• Waveform normalisation and leading edge identification :Depending on the option for thermal noise determination (processing parameter), the thermalnoise level (Pn) is either the input noise power measurement (NPM), or it is computed froman arithmetic average of samples of the first plateau, or it is a default value (processingparameter).Pn is removed from the waveform samples which is then normalised (i.e. divided by anestimate of the maximum amplitude of the useful signal). Finally, the beginning and the endof the leading edge are identified from an analysis of the shape of the waveform (accountingin particular for the frequent case of a trailing edge with a positive slope), and an estimationwindow is built around the detected leading edge.

• Coarse estimation stage (τ, σL) :

A coarse estimation of the epoch (τ) of the waveform in the estimation window and of thewidth of the leading edge (σL), is then derived from Least Square estimators by fitting theprocessed waveform to a mean return power model with a flat trailing edge. This fit isperformed in the estimation window i.e. around the leading edge of the waveform. Theseestimates are the values which minimise the residual in the estimation window, between thenormalised waveform and the corresponding model. For each possible value of τ(corresponding to a position varying between the beginning and the end of the estimationwindow, with a predefined step) and of σL (varying between two thresholds, with apredefined step) :− the normalised model (Vmn) is computed in the estimation window− the amplitude Pu of the normalised waveform is estimated by minimising the mean

quadratic error between the normalised waveform (Vn) and the weighted normalisedmodel (Pu.Vmn) in the estimation window (linear regression between the waveform and thenormalised model)

− the residual R between Vn and Pu.Vmn is computed in the estimation window− the estimates are updated if R is smaller than the previous minimum value

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• Fine estimation stage (τ, σL, Pu) : A fine estimation of τ, σL and Pu (amplitude) is finally derived. The coarse and fine

estimation stages are very similar. The particularities of the fine estimation process are thefollowing :− the simulated values of τ and σL correspond to a position and a width, centred on the

coarse estimates, with left and right deviations equal to the half of the coarse resolutions,and with predefined steps (smaller than those used in the coarse estimation process).

− the estimated amplitude is provided in output

• Estimation of the slope of the trailing edge (sT1, sT2) : The estimation of the slope of the trailing edge is intentionally fully decorrelated from the

estimation of the other parameters (τ, σL, Pu), because slopes variations may be veryimportant from a waveform to another, and because the uncertainty on its estimate is veryimportant due to speckle effects. Indeed, over ice surfaces, the slope of the trailing edgedepends on several parameters among which the slope and the curvature of the overflownsurface, the signal due to the penetration of the radar wave in the snow pack (Legresy andRemy, in press), and of course instrumental features (e.g. antenna). The slope is estimated bylinear regression of the logarithm of the normalised waveform samples in two windows partof the trailing edge: the first one (sT1) just after the end of the leading edge with a predefinedwidth, and the second one (sT2) in a contiguous window with a predefined width. The firstestimation is aimed at pointing out a possible volume signal existing at the end of the leadingedge.

A third slope (sT1m) is estimated as sT1, with an other predefined width aimed at pointing outa mispointing angle over ocean surfaces (see section 4.7).

• Estimation of the mean amplitude (Pt) :

The mean amplitude of the waveform is estimated by an arithmetic average of the waveformsamples (thermal noise level removed) in a window limited by the beginning of the leadingedge and the end of the first window used in the slope estimation.

Finally, outputs are converted (the epoch τ is referred to the analysis window, the amplitude Pu

is denormalised, etc.)

Detailed operation

A full description of the algorithm is given in RD1. The detailed specifications of the algorithmfor the FDGDR processing are given in RD5.

Applicability

• Products (FDGDR, IGDR, GDR) :The ice2 retracking algorithm is performed in FDGDR, IGDR and GDR processings.

• Surface type :The ice2 retracking algorithm is performed whatever the surface type may be. Nevertheless,it is optimised for continental ice sheets surfaces, except the computation of the slope of thetrailing edge for the mispointing estimation which is relevant to ocean surfaces only.

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Accuracy

The performances of the ice2 retracking algorithm have been valued in RD1 (see section 6.2),from ice waveforms built from the model given in formula (1), including speckle, and usingnominal values of the RA-2 instrumental parameters. The on-board tracker operation and thusthe jitter on the position of the waveform in distance and amplitude has not been simulated.

The main results obtained in standard conditions, i.e. with :− σL = .761 m (equivalent to an ocean waveheight of 2 m)− SNR = 15 dB− sT = -13.34 km-1 (ocean-like slope of the trailing edge),are summarised below. The dependency of these results with the various parameters (i.e. widthof the leading edge, slope of the trailing edge and signal to noise ratio) are described in RD1.

• Epoch (τ) :The mean error is about 2 cm in Ku band 320 MHz, 3 cm in Ku band 80 MHz, 30 cm in Kuband 20 MHz and -4 cm in S band 160 MHz. It becomes more important when the slope ofthe trailing edge is positive (e.g. in Ku band 320 MHz, it is about -1 cm for sT = 0 and -11 cmfor sT = 13.34 km-1).The standard deviation is about 6 cm in Ku band 320 MHz, 8 cm in Ku band 80 MHz, 23 cmin Ku band 20 MHz and 22 cm in S band 160 MHz. It increases with the width of the leadingedge (σL) and decreases with SNR. The high values observed in S band proceed from anincrease of the speckle on the waveforms samples by a factor of 2 in S band, due to thenumber of averaged individual echoes.

• Width of the leading edge (σL) : For low values of σL, the mean error logically increases with the sampling interval in Ku

band. For σL = 0, it is about -2 cm at 320 MHz, -28 cm at 80 MHz and -177 cm at 20 MHz. Itshould consequently be between -2 cm and -28 cm at 160 MHz. Actually, it is moreimportant (about -38 cm) because of the absence of the two additional DFT samples in Sband, which improve the resolution in Ku band. For these reasons, the estimate of σL can notbe accurate in Ku band 20 MHz, whatever the conditions are. In standard conditions, theerror is small for the other bandwidths. It is about 0.5 cm in Ku band 320 MHz, 7 cm in Kuband 80 MHz and 3 cm in S band 160 MHz. It does not depend on SNR, and its dependencywith the slope of the trailing edge is small.

The standard deviation is about 12.5 cm in Ku band 320 MHz, 17 cm in Ku band 80 MHz,38 cm in Ku band 20 MHz and 44 cm in S band (high value due to the speckle features in Sband). It increases with σL, except in Ku band 20 MHz where it is constant because the wholeleading edge is always included in one FFT filter. It also increases with the slope of thetrailing edge, but does not depend on the signal to noise ratio.

• Amplitude (Pu) :

In standard conditions but with a flat trailing edge (sT=0), the mean error is small (i.e.between -0.01 and -0.1 dB) whatever the bandwidth is. It becomes important in case of anegative and overall a positive slope (e.g. for sT = 13.34 km-1, the error is about -0.5 to -0.6dB in Ku bands 320 and 80 MHz and in S band, and about -0.9, dB in Ku band 20 MHz).

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This error should be smaller for real waveforms, due to the existence of a volume signal atthe end of the leading edge over continental ice sheets (not accounted for in the simulation).

In Ku bands, the standard deviation is about 5 to 7% of the amplitude for a flat trailing edge,and it does not depend on σL or SNR. In S band, it is higher in standard conditions (about11% of the amplitude) and its dependency with σL is important, due to the speckle features(the standard deviation is about 25% of the amplitude for an equivalent significantwaveheight of 8 m).

• Mean amplitude (Pt) :

The accuracy of the estimate of the mean amplitude of the waveform has not be assessedbecause the reference value is unknown (it is not an input parameter of the simulation).Nevertheless, the order of magnitude of the mean amplitude is satisfactory in regard with thesimulated amplitude Pu, and with the tests conditions.

• Slope of the trailing edge (sT1, sT2) :Generally speaking, the standard deviation on the slope estimates are important due to thespeckle affecting the waveforms and to the limited number of samples which can beaccounted for. The interpretation of the mean errors is thus not obvious from a limitedamount of simulated measurements. In standard conditions and for a 320-MHz bandwidth,the standard deviation on sT1 is about 2 km-1.

Comments

In Ku band, all the processing systematically accounts for the two additional DFT samples.

References

− G.S. Brown : "The Average Impulse Response of a Rough Surface and its Applications".IEEE Trans. on Antennas and Propagation, Vol. AP-25, Jan. 1977

− B. Legresy and F. Remy : "Surface characteristics of the Antarctic ice sheet and altimetricobservates", UMR5566 / GRGS (CNES-CNRS) : In press J. of Glacio.

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4.6. TO PERFORM THE OCEAN RETRACKING

The ocean retracking algorithm is performed on the Ku and on the S waveforms. The onlydifference in the retracking of Ku and S waveforms is the processed data (waveform, processingand instrumental parameters), while the processing is the same. A single description is thusgiven below.

Function

To perform the ocean retracking on the waveform (Ku band or S band).

Input data

• Product data :− Waveform (128 FFT samples + 2 DFT samples in Ku band, 64 FFT samples in S band)− Ku bandwidth identifier in Ku band− Noise power measurement

• Computed data :− From "To perform the ice2 retracking" :

⋅ Outputs corresponding to the processed waveform (epoch, width of the leading edge,amplitude, mean quadratic error)


• Dynamic auxiliary data :− Attitude data (antenna pitch and roll angles)

• Static auxiliary data (see RD1):− Processing parameters− RA-2 instrumental characterisation data

Output data

− Epoch (τ)− Information relative to the waveheight (σc)− Amplitude (Pu)− Thermal noise level (Pn)− Mean quadratic error between the normalised waveform and its model− Number of iterations


Background

The ocean retracking algorithm has been defined by CLS, from a comparative study of thevarious standard ocean retracking algorithms (see RD2), i.e. of :− CNES/CLS algorithm designed to process Poseïdon altimeter data

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− JPL algorithm designed to process TOPEX altimeter data− ESTEC algorithm designed to process ERS altimeter data− ALENIA algorithm designed to process ENVISAT altimeter data

Generally speaking, the aim of the ocean retracking algorithm is to make the measuredwaveform coincide with a return power model, according to weighted Least Square estimators.The expression of the model versus time (t) is derived from Hayne’s model (Hayne, 1980).

Accounting for a skewness coefficient (λs = processing parameter), and assuming a gaussianpoint target response (Hamming weighting performed on-board the RA-2 altimeter), it is givenby :

( ) ( )[ ] ( )[ ] [ ] ( )Vm t aP

v erf u erf u c u c u c u Pu s s

cc c c n( ) exp exp= − + +

+ − + + − −

+ξ ξ ξ ξ

λ σσ

σπ

σ σ2

16

12

2 3 2 3 13

3 3 2 2 2 2 (1)

with : erf x e dttx

( ) .= ∫ −2 2

0π

γ θ=1

2 22

0Ln( ).sin , α

γ=

+

4

1

c

hh

R e

θo = antenna beamwidth, c = light velocity, h = satellite height, Re = earth radius

σ σ σc p s2 2 2= + , σp = PTR width , SWH

cs=

24. .σ

aξξ

γ=

−

exp

sin4 2

, ( ) ( )bξ ξ

ξγ

= −cossin

222

, c bξ ξα= , ξ = mispointing

ut c c

c

=− −τ σ

σξ

2

2, v c t

c c= − −

ξ

ξτσ2

2

and where the parameters to be estimated are :− τ : the epoch− σc : the information relative to the significant waveheight (SWH)− Pu : the amplitude− Pn : the thermal noise level (to be removed from the waveform samples)

Basic principle

The ocean retracking algorithm is defined in RD1. Its basic principle is described hereafter :

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• Waveform normalisation :Depending on the option for thermal noise determination (processing parameter), the thermalnoise level (Pn) is either the input noise power measurement (NPM), or it is computed froman arithmetic average of samples of the first plateau, or it is a default value (processingparameter).

Pn is removed from the waveform samples which is then normalised (i.e. divided by anestimate of the maximum amplitude of the useful signal).

• Initialisation of the weighted Least Square fit : Initial values (τ0, σc0, Pu0) of the parameters to be estimated are then computed. Depending

on the features of the ice2 retracking for the processed waveform (i.e. algorithm performed ornot, value of the mean quadratic error OK or not), these initial values will be :− either derived from the ice2 retracking estimates (nominal solution)− or from an estimation process (backup solution).In the backup solution, σc0 is set to a default value, while τ0 and Pu0 are derived from aniterative uniform Least Square fit of the normalised waveform with the mean return powermodel, using Levenberg-Marquardt’s method which allows a smooth variation between theextremes of the inverse-Hessian method and the steepest descent method (see RD4). Theiterative estimation process is initialised from initial coarse guesses of the epoch andamplitude (derived from an analysis of the shape of the waveform). It is stopped when theconvergence is assumed, or when a maximum number of iterations is reached.

• Estimation (weighted Least Square fit) : Then, the fine estimates of the epoch (τ), the information relative to SWH (σc) and the

amplitude (Pu) are derived from an iterative weighted Least Square fit, initialised from theresults of the previous step of the processing (i.e. by τ0, σc0, Pu0). This estimation process isperformed using Levenberg-Marquardt’s method. It is stopped when the convergence isassumed or when the value of the mean quadratic error between the normalised waveformand the corresponding model is stable enough (with a minimum number of iterationsperformed), or finally when a maximum number of iterations is reached. To account for thedistribution of the useful information in the waveform, the weighting function should be suchas little weight is given to the first plateau, maximum weighting is applied to the leadingedge itself, and an intermediate weighting is given to the trailing edge.

Finally, outputs are converted (the amplitude Pu is denormalised, etc.)

Detailed operation

A full description of the algorithm is given in RD1. The detailed specifications of the algorithmfor the FDGDR processing are given in RD5.

Applicability

• Products (FDGDR, IGDR, GDR) :The ocean retracking algorithm is performed in FDGDR, IGDR and GDR processings.

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• Surface type :The ocean retracking algorithm is performed whatever the surface type may be. Nevertheless,it is optimised for ocean surfaces.

Accuracy

The performances of the ocean retracking algorithm have been valued in RD1 (see section 6.3),from ocean waveforms built from the model given in formula (1), including speckle, and usingnominal values of the RA-2 instrumental parameters. The on-board tracker operation and thusthe jitter on the position of the waveform in distance and amplitude has not been simulated.

The main results obtained in standard conditions, i.e. with :− SWH = 2 m− SNR = 15 dB− ξ = 0 (no mispointing),are summarised below. The dependency of these results with the various parameters (i.e.significant waveheight, signal to noise ratio and mispointing) are described in RD1.

• Epoch (τ) :In Ku bands 320 and 80 MHz and in S band, the mean error is nearly independent of thesignificant waveheight (SWH) and of the signal to noise ratio (SNR). It is always smallerthan 1 cm in Ku band 320 MHz, 4 cm in Ku band 80 MHz and 8 cm in S band (160 MHz).The standard deviation increases with SWH and decreases with SNR. In standard conditions,it is about 4 cm in Ku band 320 MHz, 8 cm in Ku band 80 MHz and 18 cm in S band . Thehigh values in S band proceed from an increase of the speckle due to the number of averagedindividual echoes.In Ku band 20 MHz, the behaviour of the estimator is different. First, the mean error and thestandard deviation decrease when SWH becomes important, due to the correlation of theestimates, and to the sampling interval of the waveforms which prevents an accurateestimation of SWH for low waveheights. Then, the mean error and the standard deviationincrease when SNR grows. These features are linked to the error on the estimate of thesignificant waveheight. They become better when the error on SWH is smaller.Finally, as expected the mean error and the standard deviation do not depend on themispointing, which is taken into account in the mean return power model used in the LeastSquare fit.

• "Waveheight" (σc) :In Ku band 320 and 80 MHz and in S band, the error is nearly independent of SWH and ofSNR. Moreover, it is always very small. In standard conditions, the mean estimate is about2.00 m in Ku band 320 MHz, 1.92 m in Ku band 80 MHz and 1.99 m in S band. For nullwaveheights, the mean estimate is about 0.30 m in Ku band 320 MHz, 1.20 m in Ku band 80MHz and 1.50 m in S band. The important error in S band with regard to the error in Ku band80 MHz is probably due to the absence of the two additional DFT samples in S band.The error is important in Ku band 20 MHz at low waveheights, due to the sampling intervalof the analysis window for this bandwidth. In standard conditions, the mean estimate is about4.8 m for SWH = 0 m, 5.1 m for SWH = 2 m, 4.8 m for SWH = 4 m and 7.0 for SWH = 8 m.

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The standard deviation on SWH lightly increases with SWH and decreases with SNR. Hereagain, the high noise level observed in S band is due to the speckle features. In standardconditions, the standard deviation on σc is about 8 cm in Ku band 320 MHz, 18 cm in Kuband 80 MHz and 33 cm in S band . The high values in S band proceed from an increase ofthe speckle due to the number of averaged individual echoes.Finally, as expected the mean error and the standard deviation on SWH do not significantlydepend on the mispointing, which is taken into account in the mean return power model usedin the Least Square fit.

• Amplitude (Pu) :In Ku bands 320 and 80 MHz and in S band, the mean error on the amplitude is always verysmall (less than 0.03 dB whatever the conditions may be). The standard deviation is nearlyindependent of SWH and SNR. In standard conditions, the standard deviation on Pu is about0.2 in Ku band 320 and 80 MHz, and 0.4 in S band, assuming a total amplitude equal to 10FFT units. The high noise level observed in S band is due to the speckle features, and asexpected results do not depend on the mispointing.In Ku band 20 MHz, the error is more important as for the other estimates (about 0.05 dB instandard conditions).

Comments

− The mispointing information (derived from the input antenna pitch and roll angles whichprecede the altimeter measurement) is taken into account in FDGDR, IGDR and GDRprocessings, through the mean return power model used in the Least Square fits.

− In Ku band, all the processing systematically accounts for the two additional DFT samples.

References

Hayne G.S. 1980 : "Radar Altimeter Mean Return Waveforms from Near-Normal-IncidenceOcean Surface Scattering". IEEE Trans. on antennas and propagation, Vol. AP-28, n°5, pp.687-692

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4.7. TO COMPUTE THE PHYSICAL PARAMETERS

Function

To compute (in Ku and S bands) :− the tracker altimeter range corrected for COG motion and decorrected for Doppler effects− the ocean and ice2 altimeter ranges corrected for COG motion− the significant waveheight− the ocean and ice2 backscatter coefficientsTo compute (in Ku band) :− the square of the off-nadir angle

Input data

• Product data (in Ku and S bands) :− Tracker altimeter range ht

− Scaling factor for sigma0 evaluation Kcal

− Doppler correction on the altimeter range δh1b

• Computed data :− From "To perform the ocean retracking" :

⋅ Epoch τocean in Ku and S bands⋅ Information relative to the waveheight σc in Ku and S bands

⋅ Amplitude Puocean

in Ku and S bands

− From "To perform the ice2 retracking" :

⋅ Epoch τ ice in Ku and S bands

⋅ Amplitude Puice

in Ku and S bands

⋅ Mean amplitude Pt in Ku and S bands⋅ Slope sT1m of the first part of the logarithm of the trailing edge

• Dynamic auxiliary data :− Distance d between the RA-2 antenna reference point for the range measurement and the

position of the satellite COG (from the COG file)• Static auxiliary data :


Output data

− Tracker altimeter range corrected for COG motion and decorrected for Doppler effects (Kuand S bands)

− Ocean physical parameters (Ku and S bands) :⋅ Ocean altimeter range⋅ Significant waveheight⋅ Ocean backscatter coefficient

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⋅ Square of the off-nadir angle (Ku band only)− Ice2 physical parameters (Ku and S bands ) :

⋅ Ice2 altimeter range⋅ Ice2 backscatter coefficient⋅ Ice2 leading edge backscatter coefficient


For each elementary measurement in Ku and S bands :

− The tracker altimeter range corrected for COG motion and decorrected for Doppler effects (tobe stored in the output product) is computed by :

h h d ht t b’ = + − δ 1 (1)

where δh1b is the input level 1b Doppler correction.

− The altimeter ranges (h= hocean for ocean, h= hice for ice) are computed by :

h ht= +’ .ε τ (ε = +1) (2)

where τ τ= ocean for ocean and τ τ= ice for ice, and where h’t corresponds to the range settingapplied on-board to the waveform to which τ has been derived.

− The significant waveheight SWH is computed by :

SWH c c p= −2 2 2. σ σ (3)

where σc is expressed in time units (see RD1), σp is the PTR width (expressed in time units)and c is the light velocity.

− The backscatter coefficients (σ σ0 0= ocean for ocean, σ σ0 0= ice for ice) are computed by :

σ0 1010= +K Pcal .log ( ) (4)

where P Puocean= for ocean and P Pt= for ice, and where Kcal is relative to the amplitude

setting AGC applied on-board to the waveform from which Pu has been derived.The ice2 leading edge backscatter coefficient is also computed from formula (4),

using P Puice= .

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For each elementary measurement in Ku band :

− The square of the off-nadir angle (ξ2) is computed from the slope of the logarithm of thetrailing edge sT1m, by :

ξ α

γ

2

1

1

2

1

12

=+

+.

sT m

(5)

This expression is derived from Hayne’s model (see (1) in "To perform the oceanretracking"), assuming that the impact of the part of the model which depends on theskewness coefficient is negligible on the trailing edge.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the ocean physical parameters is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the ocean (respectively ice2) physical parameters is performed whateverthe surface type may be. Nevertheless, it is relevant for ocean (respectively ice) surfaces only.

Accuracy

• Regarding the estimates derived from the ocean retracking algorithm combined with the on-board tracking algorithm, the performances have been valued using the RASS simulator anda prototype of the ocean retracking algorithm.In standard conditions over ocean surfaces (SWH = 2 m, σ0 = 10 dB, no mispointing), thestandard deviation on the 20-Hz estimates are the following in Ku-band 320 MHz :− Altimeter range : σ = 8 cm− Significant waveheight : σ = 40 cm− Backscatter coefficient : σ = 0.1 dBThese results are consistent with those observed from the analysis of real data measured bythe Poseidon altimeter, whose instrumental features are close to those of ENVISAT.

• Regarding the estimates derived from the ice2 retracking algorithm combined with the on-board tracking algorithm, the performances have been valued using the RASS simulator anda prototype of the ice2 retracking algorithm.In standard conditions over ocean surfaces (SWH = 2 m, σ0 = 10 dB, no mispointing), thestandard deviation on the 20-Hz estimates are the following in Ku-band 320 MHz :− Altimeter range : σ = 10 cm− Backscatter coefficient : σ = 0.1 dB− Leading edge backscatter coefficient : σ = 0.3 dB

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Comments

SWH will be set to 0 when the argument of the square root is negative. It means that at lowwaveheights, estimates of σc such as σc < σp (which may be statistically correct) will be forcedto σc = σp. Nevertheless, (TBC) this operation should not lead to a significative error on thesignificant waveheight in Ku band, due to the existence of the two additional DFT samples onthe leading edge.

References None

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4.8. TO CORRECT THE ALTIMETER RANGE FOR DOPPLER EFFECTS

Function

To correct the ocean and ice2 altimeter ranges (in Ku and S bands) for the Doppler effects.

Input data

• Product data (in Ku and S bands) :− For FDGDR processing : Doppler correction on the altimeter range δh1b

• Computed data :− From "To compute the physical parameters" :

⋅ Ocean altimeter range hocean in Ku and S bands

⋅ Ice2 altimeter range hice in Ku and S bands

− For IGDR and GDR processings, from "To compute the Doppler corrections" :⋅ Doppler correction in Ku and S bands (δhIGDR for IGDR, δhGDR for GDR)

• Dynamic auxiliary data : None• Static auxiliary data : None

Output data

− Ocean altimeter range corrected for Doppler effects (Ku and S bands)− Ice2 altimeter range corrected for Doppler effects (Ku and S bands)


For each elementary measurement, the corrected altimeter ranges (hc= hcocean for ocean, hc= hc

ice

for ice) are computed in Ku and S bands by :

h h hc = + δ (1)

where h hocean= for ocean and h hice= for ice2, and where δh is :− the input level 1b Doppler correction (δh1b) in the FDGDR processing− the computed Doppler correction in the IGDR and GDR processings (δhGDR or δhIGDR).

Applicability

• Products (FDGDR, IGDR, GDR) :The correction of the altimeter range for Doppler effects is performed in FDGDR, IGDR andGDR processings.

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• Surface type :The Doppler correction is performed whatever the surface type is. Nevertheless, the Dopplercorrections being computed from the radial velocity of the RA-2 antenna with respect to thereference ellipsoid (which is derived from the orbit data), it is fully consistent with oceanmeasurements, but not with measurements relative to other surfaces.

Accuracy

Irrelevant

Comments

See comments of the algorithm "To compute the Doppler corrections".

References None

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4.9. TO AVERAGE THE OCEAN ESTIMATES

Function

To select and average the elementary ocean estimates of the altimeter range, the significantwaveheight, the backscatter coefficient and the off-nadir angle (Ku band and S band).

Input data

• Product data :− Ku bandwidth identifier in Ku band

• Computed data :− From "To perform the ocean retracking" :

⋅ Mean quadratic error in Ku and S bands− From "To compute the physical parameters" :

⋅ Significant waveheight in Ku and S bands⋅ Ocean backscatter coefficient in Ku and S bands⋅ Square of the off-nadir angle (Ku band only)

− From "To correct the altimeter for Doppler effects" :⋅ Ocean altimeter range in Ku and S bands

• Dynamic auxiliary data : None• Static auxiliary data :


Output data

− Ocean altimeter range in Ku and S bands : mean value, standard deviation, number of validpoints and map of valid points.

− Significant waveheight in Ku and S bands : mean value, standard deviation and number ofvalid points

− Ocean backscatter coefficient in Ku and S bands : mean value, standard deviation andnumber of valid points

− Ku bandwidth identifier for the averaged measurement− Off-nadir angle


Generally speaking, the first stage of the process consists of the identification of the validelementary estimates. It will be performed thanks to criteria such as :− the comparison of the mean quadratic errors with thresholds− the comparison of the estimates themselves with thresholds− the detection of outliers with respect to the standard deviation of the estimates, etc.

In Ku band, the possible change of the emitted bandwidth within a source packet will also betaken into account. Only one bandwidth will be accounted for in the averaging process. This

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bandwidth will be identified in the output product (a Ku bandwidth identifier for the averagedmeasurement will be built in this algorithm).The number of valid points (for the altimeter range, the significant waveheight, and thebackscatter coefficient) will be computed, and the map of valid points for the altimeter rangewill be drawn up.Then statistics will be derived from the valid estimates.− Altimeter range : the mean value is computed by linear regression (consistent with the time

tag definition), and the standard deviation is computed with respect to the linear model.− Significant waveheight and backscatter coefficient: statistics are performed using an

arithmetic averaging.− Off-nadir angle : the mean value is computed by arithmetic averaging of the square of the

off-nadir angle, and by extracting its square root.

Applicability

• Products (FDGDR, IGDR, GDR) :The averaging of the ocean estimates is performed in FDGDR, IGDR and GDR processings.

• Surface type :The averaging of the ocean estimates is performed whatever the surface type may be.Nevertheless, it is optimised for ocean surfaces.

Accuracy

For the altimeter range, a linear regression is requested because of the high radial velocity(maximum value about ± 25 m/s). A parabollic regression is not recommended because thenoise of the 20-Hz estimates is largly greater than the signal induced by the acceleration. Theparabollic regression has been tested by JPL for TOPEX measurements, but it has not beenretained because of the instability of the second order coefficient (acceleration).

For the other parameters, an arithmertic averaging is the most appropriate method, due to thelack of signal over one second.

Assuming the estimates are fully decorrelated due to the retracking algorithm, the standarddeviation of the 1-Hz estimates will be equal to the standard deviation of the 20-Hz estimatesreduced by a factor of the square root of the number of samples (nominally 20).

Comments

Statistics relative to the backscatter coefficient are performed from elementary estimatesexpressed in dB. This operation is correct over ocean surfaces where the variation of thebackscatter coefficient is small enough within one source packet so as the logarithmic transferfunction may be considered linear.

References None

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4.10. TO DETERMINE THE SURFACE TYPE

Function

To determine the type (ocean or land) of the surface overflown by the altimeter, by usinginformation provided by a bathymetry / topography file, and information from the altimeteritself.

Input data

• Product data : None• Computed data :

− For FDGDR processing, from "To compute the averaged altitude, altitude rate andlocation" :⋅ Location of the measurement (latitude, longitude)

− For IGDR and GDR processings, from "To compute the altitude, altitude rate and locationfrom orbit files :⋅ Location of the measurement (latitude, longitude)

− From "To average the ocean estimates" :⋅ Number of valid points (for the altimeter range in Ku band)⋅ Standard deviation (for the altimeter range in Ku band)⋅ Ku bandwidth identifier for the averaged measurement


− Processing parameters (bathymetry / topography map)

Output data

− Type of the surface overflown by the altimeter (ocean or land).


The latitude and longitude of the altimeter measurement are used to determine the foursurrounding gridpoints in the bathymetry / topography file :− If the elevation of each of the four points is negative, then the surface type is set to « ocean ».− If the elevation of at least one of the four points is zero or is positive, then the values of the

number of valid points (elementary measurements) and of their range standard deviation arechecked against some given threshold :

⋅ if the number of valid points is greater than a threshold (e.g. 10) and if the range standarddeviation is smaller than a threshold (chosen according to the Ku bandwidth identifier)then the surface type is set to « ocean »

⋅ else it is set to « land ».

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Applicability

• Products (FDGDR, IGDR, GDR) :The surface type is determined in FDGDR, IGDR and GDR processings.

• Surface type :/

Accuracy

The surface type results from the combination of two independent informations, namely a landelevation file and the quality of the altimetric measurement itself. The surface type may beerroneously set in the following cases :− It may be erroneously set to « ocean » in place of « land » in ocean areas if some small islets

are not included in the 5’x5’ land elevation file.− It may be erroneously set to « ocean » in place of « land » in land areas in some known places

of the world where the altitude is below the sea level.− It may be erroneously set to « ocean » in place of « land » in land areas if the quality of the

altimetric measurement over land is good enough to be considered as « ocean like ». This willbe fortunately the case for lakes, but also unfortunately the case of some continental ice areasor some sand desert areas.


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4.11. TO INTERPOLATE THE MWR DATA TO ALTIMETER TIME TAG

Function

The MWR operates independently of the RA-2, and although the MWR data rate is close to thealtimeter rate (about 1/sec), they are asynchronous. In order to apply MWR-derived correctionsto the altimeter, the MWR data must therefore be first interpolated to the desired altimeter time.This algorithm acts as a synchroniser between the MWR and the altimeter processing.

Input data

• Product data :− MWR time tag− MWR nadir brightness temperatures− MWR land flag

• Computed data :− From "To compute the averaged time tags" :

⋅ Averaged RA-2 time tags− From "To determine the surface type" :

⋅ The surface type (ocean/land) seen by the altimeter• Dynamic auxiliary data : None• Static auxiliary data :


Output data

− MWR brightness temperatures and MWR land flag at averaged RA-2 time tag.


The MWR brightness temperatures are computed at the altimeter time tag by linear interpolationof the two nearest valid bracketing MWR measurements found within ± 16 s of the altimetertime. The MWR land flag is assigned to the altimeter time tag from the nearest available MWRmeasurement.If two MWR measurements are not found within ± 16 s of the altimeter time but if only onevalid MWR point is found within ± 8 s of the altimeter time, the corresponding brightnesstemperatures and MWR land flag are assigned to the altimeter time tag. The quality of theinterpolation will be "good" if the linear interpolation is successful and if there is no gapbetween MWR measurements, it will be "bad" otherwise.

The valid MWR measurements considered depend on the altimeter surface type :− if the surface type seen by the altimeter is «ocean», in a first step only MWR measurements

having the MWR land flag set to « ocean » are considered. If no ocean MWR measurement isfound within the above defined time spans, then MWR measurements having the MWR landflag set to « land » are considered in a second step.

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− if the surface type seen by the altimeter is «land», in a first step only MWR measurementshaving the MWR land flag set to « land » are considered. If no land MWR measurement isfound within the above defined time spans, then MWR measurements having the MWR landflag set to « ocean » are considered in a second step.

Applicability

• Products (FDGDR, IGDR, GDR) :The interpolation of the MWR data to altimeter time is performed in FDGDR, IGDR andGDR processings.

• Surface type :The interpolation of the MWR data to altimeter time is relevant to all surface types.

Accuracy

Experience with TOPEX data has shown that, in order to avoid out-of-bounds interpolationvalues, linear interpolation is preferred to cubic interpolation. The authorised time spans of ± 16s and ± 8 s used in the algorithm allow for the radiometer to altimeter correspondence to work incase of missing ocean MWR measurements. Selecting only ocean radiometer points within thesetime spans for the interpolation to ocean altimetric points, will permit ocean altimetermeasurements between small islands or at land/sea transitions to get a non land-contaminatedradiometer measurement. An estimate of the wet tropospheric correction error induced by theinterpolation of MWR data in the worst case (i. e., interpolation at RA-2 time from twoequidistant MWR data spaced by 32 s) has been performed using one 35-day ERS-2 cycle. Thestandard deviation of the difference between the interpolated value and the true value is 13 mm.In case of extrapolation, the same worst case feature is obtained with ± 8 s.


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4.12. TO COMPUTE THE BACKSCATTER COEFFICIENT ATMOSPHERICATTENUATION

Function

To compute the backscatter coefficient atmospheric attenuation for Ku band and S band.

Input data


− From «To interpolate the MWR data to altimeter time » :⋅ MWR brightness temperatures⋅ MWR land flag

− From «To determine the surface type » :⋅ Surface type (ocean / land)



Output data

− Backscatter coefficient two-way atmospheric attenuation (Ku band)− Backscatter coefficient two-way atmospheric attenuation (S band)


The Ku-band backscatter coefficient two-way atmospheric attenuation is computed (in dB) by :

Att sigma Ku c_ _ .0 2= τ (1)

where τc is the opacity in dB:

τ γ γ γc P LVap Cont Cloud Liq= + +0 7 7. _ _ . _ _ (2)

where : γ0 = 0.042 dB (Ku-band), 0.038 dB (S-band)γp = 0.023 dB/g.cm-2 (Ku-band), 0.00092 dB/g.cm-2 (S-band)γL = 0.145 dB/kg.m-2 (Ku-band), 0.00863 dB/kg.m-2 (S-band)

Vap_Cont_7 and Cloud_Liq_7 are respectively the MWR water vapour content in g.cm-2 andthe MWR cloud liquid water contents in kg.m-2, derived for a constant 7 m/s wind speed. Theyare computed from the MWR 23.8 GHz and 36.5 GHz brightness temperatures (TB23 andTB36), if the MWR land flag is set to « ocean », according to :

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Vap Cont c c Log TB c Log TBe e_ _ . ( ) . ( )7 280 23 280 360 1 2= + − + − (3)

Could Liq b b Log TB b Log TBe e_ _ . ( ) . ( )7 280 23 280 360 1 2= + − + − (4)

where ci and bi are retrieval coefficients.

γ0, γp and γL have been calculated by using the analytical expressions for the oxygen, watervapour and non-raining clouds absorption coefficients given in Ulaby et al. (1981). The USStandard atmosphere was used to compute the oxygen opacity γ0. The Arctic, US Standard andTropical atmospheres were used to compute the water vapour opacity and finally γp was derivedby regression against the columnar water content of the three atmospheres. γL was computedassuming a constant mean cloud temperature of 275 K.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the backscatter coefficient atmospheric attenuation is performed inFDGDR, IGDR and GDR processings.

• Surface type :The computation of the backscatter coefficient atmospheric attenuation is relevant to oceansurfaces only .

Accuracy

For the oxygen opacity γ0, considering the arctic and the tropical atmosphere (instead of the USstandard atmosphere) leads to values of 0.0469 dB and 0.0394 dB respectively (instead of 0.042dB) for Ku-band. The accuracy on the oxygen opacity γ0 is then 0.005 dB.

Comments

Computed from (1), the largest backscatter coefficient attenuation values (0.1 dB in S-band and0.6 dB in Ku-band) are encountered for a tropical atmosphere (6 g/cm2 water vapour content)with deep cloud (1 kg/m2 liquid water content).

References

− Ulaby, F.T., R.K. Moore and A.K. Fung, Microwave Remote Sensing, Volume 1, Addison-Wesley Publishing Company, Reading, Massachusetts, 1981

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4.13. TO COMPUTE THE 10 METERS ALTIMETER WIND SPEED

Function

To compute the altimeter wind speed from the Ku band backscatter coefficient.

Input data


− From «To average the ocean estimates » :⋅ Ocean backscatter coefficient in Ku band

− From «To compute the Ku band backscatter coefficient atmospheric attenuation » :⋅ Backscatter coefficient atmospheric attenuation in Ku band



− Backscatter coefficient to wind speed conversion

Output data

− Wind speed corrected for atmospheric attenuation− Backscatter coefficient corrected for atmospheric attenuation


First, the atmospheric attenuation is added to the backscatter coefficient to correct it. Then windspeed is computed (in m/s) according to the modified Chelton and Wentz algorithm (Witter andChelton, 1991).

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of wind speed is performed in FDGDR, IGDR and GDR processings.

• Surface type :The computation of wind speed is relevant to ocean surfaces only.

Accuracy

The derived wind speed is considered to be accurate to the 2 m/s level.

Comments None

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References

− Witter, D.L., and D.B. Chelton : A Geosat altimeter wind speed algorithm and a method foraltimeter wind speed algorithm development, J. Geophys.Res., 96, 8853-8860, 1991

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4.14. TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE ALTIMETER

Function

To compute the wet tropospheric correction due to water vapour in the troposphere, to be addedto the altimeter range, and the water vapour and cloud liquid water contents, from the MWRbrightness temperatures and using the altimeter wind speed as a correction term.

Input data


− From «To interpolate the MWR data to altimeter time tag » :⋅ MWR brightness temperatures⋅ MWR land flag

− From «To compute the 10 meters altimeter wind speed » :⋅ Wind speed (corrected for atmospheric attenuation)




Output data

− MWR wet tropospheric correction (Wet_H_Rad)− Water vapour content (Vap_cont)− Cloud liquid water content (Cloud_Liq)


The MWR wet tropospheric correction Wet_H_Rad, water vapour content Vap_Cont and cloudliquid water content Cloud_Liq are given by, if the MWR land flag is set to "ocean" :

Wet H Rad a a Log TB a Log TB a We e_ _ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (1)

Cloud Liq b b Log TB b Log TB b We e_ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (2)

Vap Cont c c Log TB c Log TB c We e_ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (3)

where TB23 and TB36 are the 23.8 GHz and 36.5 GHz brightness temperatures (in K), W is thealtimeter wind speed (in m/s), and where ai, bi and ci are retrieval coefficients.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the MWR level 2 parameters for the altimeter is performed in FDGDR,IGDR and GDR processings.

• Surface type :The computation of the MWR level 2 parameters for the altimeter is relevant to oceansurfaces only.

Accuracy

In the above two equations, the correction term due to wind speed is small (for example, a3 isabout 1.3 mm per m/s). The MWR wet tropospheric correction accuracy is about 1 to 2 cm, andthe water vapour content accuracy is about 0.3 g/cm2. The cloud liquid water accuracy has neverbeen assessed, due to the lack of comparison data.


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4.15. TO COMPUTE THE 10 METERS MODEL WIND VECTOR

Function

To compute the 10 meters wind vector components from the meteorological model.

Input data


− From "To compute the averaged time tags" :⋅ Averaged RA-2 time tag


− For IGDR and GDR processings, from "To compute the altitude, altitude rate and locationfrom orbit files" :⋅ Location of the measurement (latitude, longitude)

− From "To determine the surface type" :⋅ Surface type (ocean / land)

• Dynamic auxiliary data :− Meteorological data : U- and V-components of the 10 meters wind vector. For each of

these 2 parameters, the data consist in two data files bracketing the time of measurement.(Each file contains the parameter given on a 1° x 1° geographical grid).

• Static auxiliary data :− Processing parameters− Map of the altitude of meteorological grid points (on the same 1° x 1° geographical grid as

for the meteorological data).

Output data

− The two components U and V of the 10 meters model wind vector at measurement.


The two components U and V of the 10 meters model wind vector at measurement are obtainedby linear interpolation in time between two consecutive meteorological files, and by bilinearinterpolation in space from the four nearby grid values. If the surface type of the altimetermeasurement is set to « ocean », only « ocean »grid points are used in the interpolation. If nosuch « ocean »grid points are found, then the four « land » grid points are used. If the altimetermeasurement is over land, only « land » grid points are used in the interpolation. If no such« land »grid points are found, then the four « ocean » grid points are used. A grid point isdeclared as being « land » if its altitude is > 0, else it is declared as being « ocean ».

Applicability

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• Products (FDGDR, IGDR, GDR) :The computation of the U- and V-components of the 10 meters wind vector is performed inFDGDR, IGDR and GDR processings :− FDGDR : the processing is performed from forecasted meteorological fields.− IGDR and GDR : the processing is performed from analysed (more accurate)

meteorological fields.• Surface type :

The computation of the 10 meters model wind vector is relevant to all surface types.

Accuracy

The best accuracy for wind vector is achieved for analysed fields and varies from about 2 m/s inmodulus and 20° in direction in northern Atlantic to more than 5 m/s in modulus and 40° indirection in southern Pacific. When forecasted fields are used, it is expected that these typicalerrors get worse, but remain at a reasonable level at the global scale. For both cases, the errorintroduced by space and time interpolation under the satellite track is probably small comparedwith the intrinsic inaccuracy of the sea level pressure.


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4.16. TO COMPUTE THE SEA STATE BIASES

Function

To compute the sea state bias for Ku band and S band. Sea state bias is the difference betweenthe apparent sea level as « seen » by an altimeter and the actual mean sea level.

Input data


− From «To average the ocean estimates » :⋅ Significant waveheight in Ku band (SWH_Ku)⋅ Significant waveheight in S band (SWH_S)⋅ Backscatter coefficient in S band (σ0_S)

− From «To compute the 10 meters altimeter wind speed » :⋅ Backscatter coefficient in Ku band corrected for atmospheric attenuation (σ0_Ku)⋅ Wind speed (W)

− From «To compute the 10 meters model wind vector » :⋅ Components U and V of the 10 meters model wind vector

− From «To compute the backscatter atmospheric attenuation »:⋅ S- band backscatter atmospheric attenuation



− Processing parameters (coefficients ai and bi)

Output data

− Sea state bias in Ku band (SSB_Ku)− Sea state bias in S band (SSB_S)


The S-band backscatter cross-section atmospheric attenuation is first added to the S-bandbackscatter cross-section to correct it. The sea state biases for Ku band and S band are computed(in mm) by :

( )( )

SSB Ku f a SWH Ku Ku SWH S S U V W

SSB S g b SWH Ku Ku SWH S S U V W

i

i

_ , _ , _ , _ , _ , , ,

_ , _ , _ , _ , _ , , ,

=

=

σ σ

σ σ0 0

0 0

(1)

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where f and g are functions provided either under analytical form or under tabulated form. As afirst algorithm version, the SSB will be bilinearly interpolated from a table given as function ofSWH_Ku and W, with same values for Ku-band and S-band.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the sea state biases is performed in FDGDR, IGDR and GDRprocessings :− FDGDR : the two components U and V of wind vector are issued from forecasted

meteorological fields.− IGDR and GDR : the two components U and V of wind vector are issued from analysed

(more accurate) meteorological fields.• Surface type :

The computation of the sea state biases is relevant to ocean surfaces only.

Accuracy

Few is known on the underlying physics of sea state bias. For Ku band, the 4-parameter modelby Gaspar et al. (1994) :

SSB_Ku = SWH_Ku x (a1 + a2.SWH_Ku + a3.W + a4.W2)

seems the best suited both for TOPEX and POSEIDON. The estimated global RMS accuracy isabout 2 cm.

Comments None

References

− Gaspar, P., F. Ogor, P.Y. Le Traon and O.Z. Zanife, Estimating the sea state bias of theTOPEX and POSEIDON altimeters from crossover differences. J. Geophys. Res., 99, 24,981-24,994, 1994.

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4.17. TO COMPUTE THE DUAL-FREQUENCY IONOSPHERIC CORRECTION

Function

To combine the Ku band and S band altimeter ranges (both corrected from sea state bias), so asto derive the Ku band and S band ionospheric corrections.

Input data


− From «To average the ocean estimates » :⋅ Ocean altimeter range in Ku band⋅ Ocean altimeter range in S band

− From «To compute the sea state biases » :⋅ Ku band sea state bias correction⋅ S band sea state bias correction




Output data

− Ku band ionospheric correction (Iono_Alt_Ku)− S band ionospheric correction (Iono_Alt_S)


The following formulae assume input parameters in mm.

The Ku band and S band sea state bias corrections are first added to the Ku band and S bandaltimeter ranges to correct them, because sea state bias may be different for the two frequencies.Let RKu and RS be the corresponding corrected values.

The range R corrected for ionospheric delay is given for the two frequencies by the followingequations :

R R Iono Alt KuKu= + _ _ (1)R R Iono Alt SS= + _ _

where the ionospheric corrections Iono_alt_Ku and Iono_alt_S are obtained (in mm) by usingthe first order expansion of the refraction index :

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Iono Alt KuTEC

f Ku_ _ .

_= −40250 2 (Ku band) (2)

Iono Alt STEC

f S_ _ .

_= −40250 2 (S band)

where f_Ku and f_S are the emitted frequencies (in Hz), and where TEC is the columnar totalelectron content of the ionosphere, expressed in e-/m2.

Combining equations (1) and (2) leads to :

( )( )

Iono Alt Ku f R R

Iono Alt S f R R

Ku Ku S

S Ku S

_ _ .

_ _ .

= −

= −

δ

δ(3)

with :

δff S

f Ku f SKu =−

≈_

_ _.

2

2 2 0 0588 (4)

δff Ku

f Ku f SS =−

≈_

_ _.

2

2 2 10588

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the dual-frequency ionospheric correction is performed in FDGDR,IGDR and GDR processings.

• Surface type :The computation of the dual-frequency ionospheric correction is relevant to ocean surfacesonly.

Accuracy

From (3), one can derive the standard deviation of Ku band and S band ionospheric corrections σ(Iono_Alt_Ku) and σ(Iono_Alt_S) :

σ δ σ σ( _ _ ) . ( ) ( )Iono Alt Ku f R RKu Ku S= +2 2

σ δ σ σ( _ _ ) . ( ) ( )Iono Alt S f R RS Ku S= +2 2

where σ(RKu) and σ(RS) are respectively the 1-Hz range standard deviation for Ku band and Sband.

Table below gives the values of σ(Iono_Alt_Ku) and σ(Iono_Alt_S), assuming probable valuesfor Ku band and S band 1-Hz range standard deviation σ(RKu) and σ(RKu) as function ofwaveheight SWH :

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SWH(m)

σ(RKu)(cm)

σ(RS)(cm)

σ(Iono_Alt_Ku)(cm)

σ(Iono_Alt_S)(cm)

2 1.5 4.5 0.3 5.04 3.3 10 0.6 11.18 5.5 16.5 1.0 18.4

These values represent the expected noise in the retrieved ionospheric corrections, given thenoise in the input altimeter ranges.

The range combination algorithm assumes that the other range corrections are independent ofthe altimeter frequency. For the TOPEX altimeter, the dual frequency ionospheric correction isgiven by equation (8) in Imel’s paper (Imel, 1994) :

( ) ( )[ ]∆r f R b R bion c c Ku Ku= − − −δ . , with δff

f fc

Ku c

=−

≈2

2 2 0179. for TOPEX

In the above equation, ∆rion is the derived ionospheric correction, RC and RKu are the measuredC and Ku ranges respectively, bC and bKu represent all the other frequency-dependentcorrections. The above equation shows that an error of 5.5 cm on the difference bC - bKu leads toa 1-cm error on the derived ionospheric correction. For the ENVISAT altimeter, the situation isbetter because the gap between the two bands is larger : an error of 17 cm on the difference bS -bKu leads to a 1-cm error on the derived ionospheric correction. Such errors on the difference bS

- bKu could be due to errors on the absolute range bias difference between the two bands, or dueto inaccuracies in the sea state bias parameterisation for one of the frequencies.

Comments

An alternate way to the proposed algorithm would be to deal with 18-Hz ranges, correct themfrom 18-Hz sea state bias (evaluated using 18-Hz significant wave height and wind speed),combine them to derive 18-Hz dual-frequency ionospheric corrections, and then correct the 18-Hz ranges for sea state bias and ionospheric corrections and compute a 1-Hz corrected range bylinear regression on the 18 individual measurements. The gain in accuracy of such a method isquestionable and would require a specific study (using the complete TOPEX Ku-band and C-band waveforms processing), to assess the impact of introducing noisy 18-Hz significant waveheight or sigma nought estimates in the (inaccurate) sea state bias parameterisation, and toassess the robustness of the linear regression performed on the noisy-enhanced, correctedranges.

References

− Imel, D., Evaluation of the TOPEX/POSEIDON dual-frequency ionosphere correction, J.Geophys. Res., 99, 24,895-24,906, 1994.

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4.18. TO COMPUTE THE DORIS IONOSPHERIC CORRECTION

Function

To compute the ionospheric correction from DORIS-derived TEC maps.

Input data



− From "To compute altitude, altitude rate and location from orbit files" :⋅ Location of the measurement (latitude, longitude)

• Dynamic auxiliary data :− DORIS-derived TEC maps

• Static auxiliary data :− Processing parameters− RA-2 instrumental characterisation data

Output data

− DORIS-derived ionospheric correction for Ku band (Iono_Dor_Ku)− DORIS-derived ionospheric correction for S band (Iono_Dor_S)


The TEC from DORIS maps is interpolated, bilinearly in latitude and longitude, and linearly intime at the altimeter measurement. It is then used in the two following equations to derive theionospheric corrections (in mm) :

Iono Dor KuTEC

f Ku

Iono Dor STEC

f S

_ _ ._

_ _ ._

= −

= −

40250

40250

2

2

(1)

where f_Ku and f_S are the emitted frequencies (in Hz), and where TEC is the columnar totalelectron content of the ionosphere, expressed in e-/m2.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the DORIS ionospheric correction is performed in IGDR and GDRprocessings only.

• Surface type :The computation of the DORIS ionospheric correction is relevant to all surface types.

Accuracy

Comparison with the TOPEX dual-frequency altimeter estimates show that the global meandifference between the two ionospheric corrections is about 1 cm, with a standard deviation lessthan 2 cm (Le Traon et al., 1996).

Comments None

References

− Le Traon, P.Y., J.P. Dumont, J. Stum, O.Z. Zanife, J. Dorandeu, P. Gaspar, T. Engelis, C. LeProvost, F. Remy, B. Legresy and S. Barstow, 1996. Multi-mission altimeter inter-calibrationstudy, CLS/ESTEC contract number 11583/95/NL/CN.

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4.19. TO COMPUTE THE BENT MODEL IONOSPHERIC CORRECTION

Function

To compute the ionospheric path delays for Ku and S bands due to free electrons of theionosphere.

Input data





• Dynamic auxiliary data :− Solar activity data : two monthly sunspot numbers bracketing the time of measurement.

(These sunspot numbers should be the observed 12-month running average of the monthlysunspot number. As the observed 12-month running average is available only 6 monthsafter the month of measurement, predicted values are used).

• Static auxiliary data :− Processing parameters :

⋅ Two monthly coefficients datasets corresponding to the months of the two sunspotnumbers (these coefficients datasets are extracted from an input file containing the 12datasets of coefficients).

⋅ Tables of parameters− RA-2 instrumental characterisation data

Output data

− Ionospheric corrections for Ku band (Iono_Mod_Ku)− Ionospheric corrections for S band (Iono_Mod_S)− Sunspot number interpolated to the altimeter time tag (to be written in SPH)


The ionospheric corrections are obtained (in mm) by using the first order expansion of therefraction index :

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Iono Mod KuTEC

f Ku

Iono Mod STEC

f S

_ _ ._

_ _ ._

= −

= −

40250

40250

2

2

(1)

where f_Ku and f_S are the emitted frequencies (in Hz), and where TEC is the columnar totalelectron content of the ionosphere, expressed in e-/m2. TEC is computed for each altimetermeasurement from the Bent model (Llewellyn and Bent, 1973).

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the Bent model ionospheric correction is performed in FDGDR, IGDRand GDR processings.

• Surface type :The computation of the Bent model ionospheric correction is relevant to all surface types.

Accuracy

The ionospheric correction retrieved with the Bent model is accurate to the 2-cm level for lowsolar activities, but errors as high as 10 cm may occur in high solar activities during the day nearthe geomagnetic equator.

Comments None

References

− Llewellyn, S.K. and R.B. Bent, 1973 : Documentation and description of the Bentionospheric model, AFCRL-TR-73-0657

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4.20. TO COMPUTE THE MODEL WET AND DRY TROPOSPHERICCORRECTIONS

Function

To compute the wet and dry tropospheric corrections due to permanent gases of the troposphere,from meteorological model.

Input data






• Dynamic auxiliary data :− Meteorological data : mean sea level pressure, relative humidity profile, geopotential

profile and temperature profile. For each of these 4 parameters, the data consist in twometeorological data files bracketing the time of measurement (each file contains theparameter given on a 1° x 1° geographical grid).

• Static auxiliary data :− Processing parameters− Map of the altitude of meteorological grid points (on the same 1° x 1° geographical grid as


Output data

− Dry tropospheric correction (δhdry)− Model wet tropospheric correction (δhwet)− Sea surface atmospheric pressure at measurement (Psurf)


The excess propagation path, also called path delay, induced by the neutral gases of theatmosphere between the backscattering surface and the satellite is given by :

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δh = (n(z) - 1) Hsurf

Hsat

dz∫ (1)

where n(z) is the index of refraction of air, Hsurf and Hsat are respectively the altitudes of thesurface and of the satellite above mean sea level.The index of refraction is conveniently expressed in terms of the refractivity N(z), defined as :

N(z) = 10-6 (n(z) - 1) (2)

N(z) is given by Bean and Dutton (1966) :

N(z) = 77.6 P

Td + 72

e

T + 3.75 105

e

T2 (3)

where Pd is the partial pressure of dry air in hPa, e is the partial pressure of water vapour in hPa,and T is temperature in K.As the partial pressure of dry air is not easily measured, it is desirable to obtain an expressionfunction of the total pressure of air. For deriving it, we have to consider that the dry air and thewater vapour are ideal gases, i.e., they obey to the Mariotte-Gay Lussac law :

for dry air : Pd

ρd

= RT

M d

(4)

for water vapour : e

ρw

= RT

M w

(5)

where ρd and ρw are the volumic masses of dry air and water vapour respectively, Md and Mw

are the molar masses of dry air (28.9644 10-3 kg) and water vapour (18.0152 10-3 kg)respectively, R is the universal gas constant (8.31434 J.mole-1.K-1).Combining (4), (5) and (3) leads to :

N(z) = 77.6 Rρd

dM + 72 R

ρw

wM 3.75 105

e

T2 (6)

The volumic mass of wet air is the sum of the volumic masses of dry air and water vapour :ρ = ρd + ρw (7)

Introducing the volumic mass of wet air given by (7) into (6) leads to :

N(z) = 77.6 Rρ

M d

+ (72 - 77.6 M

Mw

d

) R ρw

wM + 3.75 105

e

T2 (8)

Reintroducing (5) into (8) leads to the final expression of refractivity N(z) :

N(z) = 77.6 Rρ

Md

+ (72 - 77.6 M

Mw

d

) e

T + 3.75 105

e

T2 (9)

Combining this expression with (1) and (2) leads to the following equation for δh :

δh = 77.6 10-6 R

Md

ρ dzHsurf

Hsat

∫ + (72 - 77.6 M

Mw

d

)10-6 e

T dz

Hsurf

Hsat

∫ + 3.75 10-1 e

T dz2

Hsurf

Hsat

∫ (10)

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The first term will be called the dry tropospheric correction δhdry :

δhdry = 77.6 10-6 R

Md

ρ dzHsurf

Hsat

∫ (11)

The sum of the two remaining terms will be called the wet tropospheric correction δhwet :

δhwet = (72 - 77.6 M

Mw

d

)10-6 e

T dz

Hsurf

Hsat

∫ + 3.75 10-1 e

T dz2

Hsurf

Hsat

∫ (12)

1- Calculation of the dry tropospheric correction

It is commonly assumed that the atmosphere is in hydrostatic equilibrium :dP

dz= -ρ g (13)

where g is the acceleration due to gravity.

Combining (11) and (13) leads to the following equation for δhdry :

δhdry = 77.6 10-6 R

Md

1

g dP

0

Psurf

∫ (14)

where Psurf is the atmospheric pressure at the ground surface.

The acceleration of gravity is a function of latitude and altitude. This function can be modelledby :

[ ]g g . 1 - 0.0026 cos(2 ) - 0.00031 z0= φ (15)

where φ is the latitude, z is altitude in km, and g0 = 9.80664

The variation of g with altitude is small and can be neglected by considering an mean value forg = 9.783 constant with altitude. This leads to the final expression for δhdry :

[ ]δ φhdry s urf= − +2 277 1 0 0026 2. . . cos( ) P (16)

(16) is the expression obtained by Saastamoinen (1972), where Psurf is in hPa, and δhdry is in mmand is set here with a negative sign to be added to the altimeter range.

The main input for (16) is the atmospheric pressure at the ground surface, Psurf. Over ocean,Psurf, is the mean sea level pressure, Pmsl. Over terrestrial surfaces, the pressure at the groundsurface Psurf can be derived from the pressure of the first upper level above the ground surface,Plev , knowing the temperature and humidity of the atmospheric layer between the surface andthis first upper level. To establish it, we have to consider the Mariotte-Gay Lussac law for wetair:

P

ρ =

RT

M(17)

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Combining again (13) and (17) leads to (18 ) :dP

P = −

M g

R T dz (18)

Integrating (18) between the altitude above mean sea level of the first upper pressure level Hlev,and the altitude above mean sea level of the ground surface Hsurf leads to :

Ln(P

P)lev

surf

= −1

R

M g

T dz

Hsurf

Hlev

∫ (19)

The molar mass of wet air M depends on the water vapour content of the atmosphere :

M = Md + e

P(Mw - Md) (20)

The problem of variation of molar mass M with altitude is commonly solved by considering theair as free of water vapour (i.e., M = Md), with the same pressure and density as wet air, but withthe so-called virtual temperature Tv :

Tv = T

1 + e

P(M - M

M)w d

w

(21)

This leads to :

Ln(P

P)lev

surf

= −M

Rd

g

Tv dz

Hsurf

Hlev

∫ (22)

For solving (22), it is assumed that the virtual temperature decreases linearly with altitude, witha vertical gradient of 6.5°/km (a mean value commonly used in meteorology). A mean valueTvm is taken for Tv, corresponding to the middle of the atmospheric layer between the surfaceand the first upper level above the surface:

Tvm = Tv(z = Hlev) + 6 5

2

. 10-3

(Hlev - Hsurf) (23)

The virtual temperature at the first upper level above the surface is computed from (21) by usingthe temperature T(z = Hlev) and the water vapour partial pressure e(z = Hlev) which is deducedfrom relative humidity H by :

e = H es(T) (24)

where es(T) is the saturation water vapour pressure at temperature T, obtained in hPa fromTetens formula :

es(T) = 6.1115 exp22.542 (T - 273.15)

273.48 + (T - 273.15) for T < 273.15 (25)

es(T) = 6.1121 exp17.368 (T - 273.15)

238.88 + (T - 273.15) for T ≥ 273.15 (26)

Computing from (15) a mean value for g, gmean, leads to the final expression for Psurf :

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Psurf = Plev exp(Ma g (H - H )

R Tvmmean lev surf ) (27)

The following steps are used for computing the dry tropospheric correction at the altimetermeasurement :

For each input Pmsl map :

• The Psurf map is computed from the Pmsl map :− if the altitude of grid point Hsurf (given as a static auxiliary file) is 0 (« ocean grid point),

then Psurf = Pmsl.− else, Psurf is given by (27)

• The dry tropospheric correction map is computed from (16)• The dry tropospheric correction is obtained at the altimeter measurement from by linear

interpolation in time between two consecutive dry tropospheric correction maps, and bybilinear interpolation in space from the four nearby grid values. If the surface type of thealtimeter measurement is set to « ocean », only « ocean » grid points of the map are used inthe interpolation. If no such « ocean »grid points are found, then the four « land » grid pointsof the map are used. If the surface type of the altimeter measurement is set to « land », only« land » grid points of the map are used in the interpolation. If no such « land »grid points arefound, then the four « ocean » grid points are used.

2) Calculation of the wet tropospheric correction

Introducing the numerical values for Md and Mw into (12) leads to the following equation forδhwet in m :

δhwet = 23.7 10-6e

T dz

Hsurf

Hsat

∫ + 3.75 10-1 e

T dz2

Hsurf

Hsat

∫ (28)

Because the first term in (28) is only about 1% of the second term, (28) can be simplifiedwithout loss of accuracy by introducing a mean temperature Tm (Elgered, 1993), defined as :

Tm =

e

Tdz

e

Tdz

Hsurf

Hsat

2Hsurf

Hsat

∫

∫(29)

Considering a value of 288 K for Tm leads to the final expression for δhwet :

δhwet = -381.5e

T dz2

Hsurf

Hsat

∫ (30)

where δhwet is in mm and is set as being a negative quantity to be added to the altimeter range.

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Maximum difference in δhwet between (28) and (30) is about 0.3 mm.In (30), e is given in hPa by (24) to (26). The altitude z of the pressure levels above the groundsurface is deduced from geopotential φ as follows :

z = φg

- Hsurf (31)

where g is given by (11)

The integral is computed by trapezoidal rule, by using the values of relative humidity andtemperature given at the discrete vertical pressure levels of the model. When negative humidityvalues are found, they are set to zero. When humidity values greater than 100% are found, theyare set to 100%. Pressure levels considered in the summation are those lying between thesurface (having positive altitude) and the altitude corresponding to the 200 hPa pressure level,above which the contribution of humidity is negligible. The temperature value at the surfaceitself is extrapolated from the temperature value at the first selected pressure level, assuming avertical gradient of 6.5°/km. The humidity value at the surface is simply set to the humidityvalue found for the first selected pressure level.

The following steps are used for computing the wet tropospheric correction at the altimetermeasurement :

• The wet tropospheric correction map is computed from the relative humidity, geopotentialand temperature profile maps, as detailed above.

• The wet tropospheric correction at the altimeter measurement is obtained by linearinterpolation in time between two consecutive wet tropospheric correction maps, and bybilinear interpolation in space from the four nearby grid values. If the surface type of thealtimeter measurement is set to « ocean », only « ocean » grid points of the map are used inthe interpolation. If no such « ocean »grid points are found, then the four « land » grid pointsof the map are used. If the surface type of the altimeter measurement is set to « land », only« land » grid points of the map are used in the interpolation. If no such « land »grid points arefound, then the four « ocean » grid points are used.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the dry and wet tropospheric corrections is performed in FDGDR, IGDRand GDR processings :− FDGDR : the processing is performed from forecasted meteorological fields.− IGDR and GDR : the processing is performed from analysed (more accurate)


The computation of the dry tropospheric correction is relevant to all surface types.

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Accuracy

The accuracy of the dry tropospheric correction primarily depends on the accuracy of the inputmean sea level pressure. The best accuracy for mean sea level pressure is achieved for analysedfields. Typical errors vary from 1 hPa in northern Atlantic to more than 10 hPa in southernPacific. A 1 hPa error on pressure translates in a 2 mm error on the dry tropospheric correction.When forecast fields are used, it is expected that these typical errors get worse, but remain at areasonable level at the global scale. For both cases, the error introduced by space and timeinterpolation under the satellite track is probably small compared with the intrinsic inaccuracy ofthe sea level pressure. For land surfaces, additional error is induced by the calculation of thesurface pressure from the upper level pressure, due to assumptions on the mean virtualtemperature of the atmospheric layer between the surface and the first upper level above theground surface, and due to inaccurate knowledge of the TerrainBase digital elevation model(DEM) used for computing the altitude of the grid points above mean sea level. This additionalerror may be as large as the intrinsic error of the mean sea level pressure.The mean standard deviation of the difference between radiometer-derived and model-derivedwet tropospheric corrections is about 3 cm. This is a mean value over the global ocean. Largermodel errors are found in the tropics (up to 10-cm errors) and smaller ones in high latitudes. Thebest accuracy will probably be achieved for analysed fields.

Comments

The processing described above is the standard level 2 processing which corresponds toFDGDR and GDR processings. In the case of the IGDR processing, the averaged RA-2 timetags and the surface type come from the input FDGDR product, instead of "To correct andaverage time tags", and "To determine the surface type".

References

− Bean, B. R., and E. J. Dutton, Radio Meteorology, U.S. NBS Monogr., 92, March 1966.− Elgered, G., 1993 : Tropospheric radio path delay from ground-based microwave radiometry,

in Atmospheric Remote Sensing by Microwave Radiometry, M. A. Janssen, Ed., New York :Wiley, ch. 5.

− Saastamoinen, J., 1972 : Atmospheric correction for the troposphere and stratosphere in radioranging of satellites, Geophys. Monogr., 15, American Geophysical Union, Washington D.C.

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4.21. TO COMPUTE THE INVERTED BAROMETER EFFECT

Function

To compute the sea surface height correction due to atmospheric loading (the so-called invertedbarometer effect).

Input data





− From "To compute the model wet and dry tropospheric correction" :⋅ Sea surface atmospheric pressure at measurement


• Dynamic auxiliary data : None• Static auxiliary data : None

Output data

− Inverted barometer height (H_Baro)


The inverted barometer height correction is computed (in mm) according to the followingformula :

( )H Baro b p p_ .= − − (1)

where b = 1 cm/HPa, p is the sea surface atmospheric pressure at measurement, and p is theglobal mean sea level atmospheric pressure (= 1013 HPa).

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the inverted barometer effect is performed in FDGDR, IGDR and GDRprocessings :− FDGDR : the processing uses mean sea level pressure from forecasted meteorological

fields.− IGDR and GDR : the processing uses mean sea level pressure from analysed (more

accurate) meteorological fields.• Surface type :

The computation of the inverted barometer effect is relevant to ocean surfaces only.

Accuracy

Extensive modelling work by Ponte et al. (1991) confirms that over most open ocean regions theocean response to atmospheric pressure forcing is mostly static. Typical deviations from theinverted barometer response are in the range of 1 to 3 cm rms, with most of the varianceoccurring at high frequencies. Inverted barometer correction is not reliable for pressurevariations with very short periods (< 2 days) and in coastal regions.

Comments None

References

− Ponte, R.M., D.A. Salstein and R.D. Rosen, Sea level response to pressure forcing in abarotropic numerical model. J. Phys. Oceanog., 21, 1043-1057, 1991

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4.22. TO COMPUTE THE MEAN SEA SURFACE PRESSURE OVER THE OCEAN

Function

To compute the mean of sea surface pressure over the ocean for each input mean sea levelpressure field.

Input data


− From "To compute the averaged time tags" :⋅ Averaged RA-2 time tag of the first measurement of the input product


• Dynamic auxiliary data :− Meteorological data : the mean sea level pressure file which is the nearest in time relative

to the time tag of the first measurement of the input product. (The mean sea level pressureis given on a geographical grid).

• Static auxiliary data :− Map of the altitude of meteorological grid points (on the same 1° x 1° geographical grid as


Output data

− Mean sea surface pressure over the ocean (Pmean, to be written in SPH).


Pmean (in hPa) is obtained for each meteorological field by a weighting average of the mean sealevel pressure values from all grid points over the ocean (grid points having a negative or zeroaltitude) :

PP

meanmsl= ∑

∑.cos( )

cos( )

φφ

(1)

where Pmsl and φ are respectively the mean sea level pressure and the latitude of grid points.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the mean sea surface pressure over the ocean is performed in FDGDR,IGDR and GDR processings :− FDGDR : the processing is performed from forecasted meteorological fields.− IGDR and GDR : the processing is performed from analysed (more accurate)


The computation of the mean sea surface pressure over the ocean is relevant to oceansurfaces only.

Accuracy

The accuracy on Pmean is about 2 HPa


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4.23. TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THEORTHOTIDE ALGORITHM

Function

To compute the height of the ocean tide from the orthotide algorithm (using CSR model).

Input data







− Tidal orthoweights map (geographical grid providing at each gridpoint 6 weighting factorsU and 6 weighting factors V).


Output data

− Non-equilibrium ocean tide height (solution 1)


The non-equilibrium ocean tide is computed from the model developed at the University ofTexas (Ma et al., 1994). This model uses the formulation described by Cartwright and Ray(1990). This formulation is based on orthotide functions. The computed tide is composed of the30 largest spectral lines within both the diurnal and semidiurnal bands, sufficient forrepresenting all major constituents including nodal modulations. The model is based onempirical determination of orthoweights maps, derived from the TOPEX mission.

For the Mediterranean sea, the tide solution from the model by Canceil et al. (1995) isincorporated in the input orthoweights map.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the non-equilibrium ocean tide height from the CSR model is performedin FDGDR, IGDR and GDR processings.

• Surface type :The computation of the non-equilibrium ocean tide height from the CSR model is relevant toocean surfaces only.

Accuracy

The comparison by Le Provost et al. (1996) of the tide model prediction with tide gaugeobservations from 59 sites distributed over the world ocean showed that the overall RMSdifference is 3.48 cm for CSR model (3.86 cm for FES model).

Comments

It must be pointed out that the non-equilibrium ocean tide height derived from the CSR model isactually the sum of ocean tide height and tidal loading height.

References

− Canceil, P., R. Agelou and P. Vincent, Barotropic tides in the Mediterranean Sea from afinite element numerical model, submitted to J. Geophys. Res., 1995

− Cartwright, D.E., and R.D. Ray, Oceanic tides from Geosat altimetry,, J. Geophys.Res., 95,3069-3090, 1990.

− Le Provost, C., F. Lyard, J.M. Molines, M.L. Genco and F. Rabilloud, A hydrodynamicalocean tide model improved by assimilating a satellite altimeter derived dataset, submitted toJ. Geophys. Res., 1996

− Ma, X.C., C.K. Shum, R.J. Eanes, and B.D. Tapley, Determination of ocean tides from thefirst year of TOPEX/POSEIDON altimeter measurements, 99, 24809-24280, 1994.

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4.24. TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THEHARMONIC COMPONENTS ALGORITHM

Function

To compute the height of the ocean tide from the harmonic components algorithm (usingGrenoble hydrodynamical model FES).

Input data







− Harmonic coefficients maps of the 8 principal tide waves. .− Processing parameters

Output data

− Non-equilibrium ocean tide height (solution 2).


The non-equilibrium ocean tide is the sum of 27 tide constituents hi :

[ ]h F A Bi i i i i i= +. ( , ).cos( ) ( , ).cos( )φ µ ψ φ µ ψ (i=1,27) (1)

with : ψ σi i i it X U= + +.

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− Fi is the tide coefficient of amplitude nodal correction (depends only on the altimeter time)− Ui is the tide phase nodal correction (depends only on the altimeter time)− Xi is the tide astronomical argument (depends only on the altimeter time)− σi is the tide frequency− t, φ and µ are respectively the altimeter time tag, latitude and longitude− Ai(φ,µ) and Bi(φ,µ) are harmonic coefficients bilinearly interpolated at the altimeter location

(φ,µ) from the input harmonic coefficients map given by the FES model by Le Provost et al.(1994, 1996), and by the model by Canceil et al. (1995) for the Mediterranean sea.Coefficients 9 to 27 are computed by admittance from the principal constituents 1 to 8, usingprocessing parameters

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the non-equilibrium ocean tide height from the FES model is performedin FDGDR, IGDR and GDR processings.

• Surface type :The computation of the non-equilibrium ocean tide height from the FES model is relevant toocean surfaces only.

Accuracy

The comparison by Le Provost et al. (1996) of the tide model prediction with tide gaugeobservations from 59 sites distributed over the world ocean showed that the overall RMSdifference is 3.86 cm.

Comments None

References

− Canceil, P., R. Agelou and P. Vincent, Barotropic tides in the Mediterranean Sea from afinite element numerical model, submitted to J. Geophys. Res., 1995

− Le Provost, C., M.L. Genco, F. Lyard, P. Vincent and P. Canceil, Tidal spectroscopy of theworld ocean tides from a finite element hydrodynamical model, J. Geophys. Res., 99, C12,24,777-24,798, 1994.

− Le Provost, C., F. Lyard, J.M. Molines, M.L. Genco and F. Rabilloud, A hydrodynamicalocean tide model improved by assimilating a satellite altimeter derived dataset, submitted toJ. Geophys. Res., 1996

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4.25. TO COMPUTE THE HEIGHT OF THE TIDAL LOADING

Function

To compute the height of the tidal loading induced by the ocean tide.

Input data







− Harmonic coefficients maps of the 8 principal tide waves. .

Output data

− Height of the tidal loading.


The height of the tidal loading is the sum of 27 constituents hi :

[ ]h F C Di i i i i i= +. ( , ).cos( ) ( , ).cos( )φ µ ψ φ µ ψ (i=1,27) (1)

with : ψ σi i i it X U= + +.

− Fi is the tide coefficient of amplitude nodal correction (depends only on the altimeter time)− Ui is the tide phase nodal correction (depends only on the altimeter time)− Xi is the tide astronomical argument (depends only on the altimeter time)− σi is the tide frequency− t, φ and µ are respectively the altimeter time tag, latitude and longitude− Ci(φ,µ) and Di(φ,µ) are harmonic coefficients bilinearly interpolated at the altimeter location

(φ,µ) from the input harmonic coefficients map. This map has been computed from theFrancis and Mazzega’s method (1990) : this method consists in evaluating a convolution

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integral over the loaded region (the oceans) with a kernel (so-called Green’s function) whichis the response of the media (the Earth) to a mass-point load. The used ocean tides model isthe FES model. Coefficients 9 to 27 are computed by admittance from the principalconstituents 1 to 8.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of height of the tidal loading is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the height of the tidal loading is relevant to ocean surfaces only.

Accuracy

Other methods have been used for Geosat and TOPEX/Poseidon missions for the evaluation ofthe tidal loading. The Ray and Sanchez’s method (1989) for the Cartwright and Ray tide modelused a high-degree spherical harmonic method. The method of Francis and Mazzega is probablymore accurate (no cut-off due to spherical harmonics expansion, no ocean to landdiscontinuities). Empirical determination of tidal loading was also derived fromTOPEX/Poseidon using the same method as for the ocean tide. This empirical solution and theFrancis and Mazzegas’s solution are very similar.

Comments None

References

− Francis, O., and P. Mazzega, Global charts of ocean tide loading effects, J. Geophys. Res.,Vol. 95, 11,411-11,424, 1990.

− Ray, R.D., and B.V. Sanchez, Radial deformation of the Earth by oceanic tidal loading,NASA Tech. Memo, 100743, July, 1989.

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4.26. TO COMPUTE THE SOLID EARTH TIDE AND THE LONG PERIODEQUILIBRIUM TIDE HEIGHTS

Function

To compute the solid earth tide height and the height of the long period equilibrium tide.

Input data







− Cartwright’s tables, frequencies ωi and phases φi of the 6 astronomical variables at thereference epoch (22 May 1960 at 12H).


Output data

− Height of the solid Earth tide (H_Solid)− Height of the long period equilibrium tide (H_Equi)


The gravitational potential V induced by an astronomical body can be decomposed intoharmonic constituents s, each characterised by an amplitude, a phase and a frequency. Thus, thetide potential can be expressed as :

V V snsn

= ∑∑=

∞( )

2(1)

where the tide potential of constituent s, Vn(s), is given by :

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[ ][ ]

V s c s W s t s m for m n even

V s c s W s t s m for m n odd

n n nm

n n nm

( ) ( ). .cos ( ). ( ) . ( )

( ) ( ). .sin ( ). ( ) . ( )

= + + ← + =

= + + ← + =

ω φ λ

ω φ λ(2)

where the phase ω(s).t + φ(s) of constituent s at altimeter time tag t (relative to the referenceepoch), is given by a linear combination of the corresponding phases of the 6 astronomicalvariables ωi.t + φi :

[ ]ω φ ϖ φ( ). ( ) ( ). .s t s k s ti i ii

+ = +∑=1

6

(3)

where λ is the altimeter longitude, and where Wmn is the associated Legendre polynomial

(spherical harmonic) of degree n and order m (Wmn (sin )θ , with θ altimeter latitude).

The Cartwright’s tables provide for degree n=2 and order m=0,1,2, and for degree n=3 and orderm=0,1,2,3 the ki(s) coefficients and the amplitudes cn(s) for each constituent s (only amplitudesexceeding about 0.004 mm have been computed by Cartwright and Tayler (1971), andCartwright and Edden (1973)). This allows for the potential to be computed.

The solid Earth tide height and the height of the long period equilibrium tide are bothproportional to the potential. The proportionality factors are the so-called Love number Hn andKn.

The solid Earth tide height H_solid is thus :

H Solid HV

gH

V

g_ . .= +2

23

3(4)

with :H2 = 0.609H3 = 0.291g = 9.80V2 = V20 + V21 + V22

V3 = V30 + V31 + V32 + V33

The height of the long period equilibrium tide H_Equi is thus :

( ) ( )H Equi H KV

gH K

V

g_ . .= − + + − +1 12 2

203 3

30(5)

with :K2 = 0.302K3 = 0.093

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the solid earth tide height and of the height of the long periodequilibrium tide is performed in FDGDR, IGDR and GDR processings.

• Surface type :The computation of the solid earth tide height is relevant to all surface types, while thecomputation of the height of the long period equilibrium tide is relevant to ocean surfacesonly.

Accuracy

The accuracy of the solid earth tide height and of the height of the long period equilibrium tideis better than 1 mm.

Comments None

References

− Cartwright, D.E., and R.J. Tayler : New computations of the tide-generating potential,Geophys.J.R.Astr.Soc, v23, 45-74, 1971

− Cartwright, D.E., and A.C. Edden : Corrected tables of tidal harmonics,Geophys.J.R.Astr.Soc, v33, 253-264, 1973

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4.27. TO COMPUTE THE POLE TIDE HEIGHT

Function

To compute the geocentric tide height due to polar motion.

Input data




• Dynamic auxiliary data :− Pole location data (in arcseconds) :

⋅ x (along the 0° meridian)⋅ y (along the 90°W meridian)

• Static auxiliary data :− Processing parameters :

⋅ average pole position in arcseconds (x_avg, y_avg)⋅ scaled amplitude factor (A)

Output data

− Height of the pole tide (H_Pole)


The Earth’s rotational axis oscillates around its nominal direction with apparent periods of 12and 14 months. This results in an additional centrifugal force which displaces the surface. Theeffect is called the pole tide. It is easily computed if the location of the pole is known (Wahr,1985), by :

[ ]H Pole A x x avg y y avg_ .sin( ). ( _ ).cos( ) ( _ ).sin( )= − − −2φ λ λ (1)

where H_Pole is expressed in mm, and where λ and φ are respectively the longitude and latitudeof the measurement.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the pole tide height is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the pole tide height is relevant to all surface types.

Accuracy

This algorithm uses predicted pole locations. The use of restituted pole locations instead ofpredicted ones has negligible impact on the pole tide height accuracy.A pole location accuracy of about 50 cm is needed to get a 1-mm accuracy on the pole tideheight.

Comments None

References

− Wahr, J. : J. Geophys. Res., Vol. 90, pp. 9363-9368, 1985.

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4.28. TO COMPUTE THE MEAN SEA SURFACE HEIGHT

Function

To compute the height of the mean sea surface (MSS) at the location of the altimetermeasurement, from the MSS input file.

Input data






− MSS file (geographical grid)

Output data

− Height of the mean sea surface above the reference ellipsoid.


The height of the MSS is computed at altimeter measurement, from the most precise MSSavailable at the time of ENVISAT launch, by bilinear interpolation in latitude and longitude ofthe gridded values at the altimeter measurement.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the mean sea surface height is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the mean sea surface height is relevant to ocean surfaces only.

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Accuracy

The most accurate MSS available, provided in the ERS-2 and TOPEX GDR, is the OSUMSS95.Its global standard deviation of the difference between altimeter sea surface height and mean seasurface height is about 10 cm.


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4.29. TO COMPUTE THE GEOID HEIGHT

Function

To compute the height of the geoid at the location of the altimeter measurement, from the geoidinput file.

Input data






− Geoid file (geographical grid)

Output data

− Height of the geoid.


The height of the geoid is computed at altimeter measurement, from the most precise geoidavailable at the time of ENVISAT launch, by bilinear interpolation in latitude and longitude ofthe gridded values at the altimeter measurement.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the height of the geoid is performed in FDGDR, IGDR and GDRprocessings.

• Surface type :The computation of the height of the geoid is relevant to all surface types.

Accuracy

The most accurate geoid model available, provided in the ERS-2 and TOPEX GDR, is theJGM3/OSU91A geoid.

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4.30. TO COMPUTE THE OCEAN DEPTH / LAND ELEVATION

Function

To compute the ocean depth or land elevation from a bathymetry / topography file.

Input data






− Bathymetry / topography file, from NGDC (TerrainBase).

Output data

− Ocean depth / land elevation.


The ocean depth / land elevation is obtained by bilinear interpolation in space from theTerrainBase gridded values. If the altimeter measurement is over ocean, only negative values ofgrid points are used in the interpolation. If the altimeter measurement is over land, only positiveor null values of grid points are used in the interpolation.

Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the ocean depth / land elevation is performed in FDGDR, IGDR andGDR processings.

• Surface type :The computation of the ocean depth / land elevation is relevant to all surface types.

Accuracy

The TerrainBase global digital elevation model contains a complete matrix of land elevation andocean depth for the entire world gridded at 5-minute intervals. NGDC/WDC-A developed the

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model using the best public domain data available. In particular, for oceans, data are fromETOPO5 bathymetry. Accuracy of the data set is hard to define, due to the disparate sources ofdata. In general, the data sets for the USA, Western Europe, Korea/Japan, Australia and NewZealand are the most precise, having a horizontal resolution of five minutes of latitude andlongitude, and vertical resolution of 1 meter. Data for Africa, Asia, and South America vary invertical resolution from a few meters to 150 meters. Very little detail is contained in the oceanicdata shallower than 200 m. All oceanic data are coded at least -1 m, excepted below 78 S, wherethe ETOPO5 bathymetry model terminates. Ocean cells south of 78 S were filled with nullvalues. This problem produces discontinuity but only affects the southernmost coastal areas ofthe Ross and Weddel Seas. Land data are coded at 0 or greater, except where lake bottoms orother landlocked features go below sea level (e.g., Dead Sea, Death Valley, and in centralAustralia).

Comments None

References

More information can be extracted at the NGDC W3 server :(http ://www.ngdc.noaa.gov/mgg/global/global.html)

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4.31. TO INTERPOLATE THE ALTIMETER WIND SPEED DATA TORADIOMETER TIME TAG

Function

The altimeter operates independently of the MWR, and although the altimeter data rate is closeto the MWR rate (about 1/sec), they are asynchronous. In order to apply altimeter-derived windspeed to the MWR level 2 processing, we must therefore first interpolate the altimeter data tothe desired MWR time. Thus, this algorithm acts as a synchroniser between the altimeter and theMWR processing.

Input data

• Product data :− MWR time tag− MWR land flag

• Computed data :− From "To compute the averaged time tags" :

⋅ Averaged RA-2 time tags− From "To determine the surface type" :

⋅ The surface type (ocean/land) seen by the altimeter− From "To compute the 10 meters altimeter wind speed" :

⋅ Altimeter wind speed• Dynamic auxiliary data : None• Static auxiliary data : None

Output data

− Altimeter wind speed at MWR time tag.


The altimeter wind speed is computed at the radiometer time tag by linear interpolation of thetwo nearest valid bracketing wind speed measurements found within ± 16 s of the radiometertime. Valid means that only altimeter measurements with the surface type set to « ocean » areconsidered .If two altimeter wind speed measurements are not found within ± 16 s of the radiometer timebut if only one valid altimeter point is found within ± 8 s of the radiometer time, thecorresponding wind speed is assigned to the radiometer time tag. The quality of theinterpolation will be "good" if the linear interpolation is successful and if there is no gapbetween altimeter measurements, it will be "bad" otherwise.wind speed

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Applicability

• Products (FDGDR, IGDR, GDR) :The interpolation of the altimeter wind speed to the radiometer time is performed in FDGDR,IGDR and GDR processings.

• Surface type :The interpolation of the altimeter wind speed to the radiometer time is relevant to oceansurfaces only (MWR land flag set to « ocean »).

Accuracy

Experience with TOPEX data has shown that, in order to avoid out-of-bounds interpolationvalues, linear interpolation is preferred to cubic interpolation.


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4.32. TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THERADIOMETER

Function

To compute at MWR time tag, the wet tropospheric correction due to water vapour in thetroposphere, and the water vapour and cloud liquid water contents, from the MWR brightnesstemperatures and using the altimeter wind speed interpolated at MWR time tag as a correctionterm.

Input data

• Product data :− MWR brightness temperatures− MWR land flag

• Computed data :− From «To interpolate the altimeter wind speed to radiometer time tag » :

⋅ Altimeter wind speed• Dynamic auxiliary data : None• Static auxiliary data :

Processing parameters

Output data

− MWR wet tropospheric correction (Wet_H_Rad)− Water vapour content (Vap_cont)− Cloud liquid water content (Cloud_Liq)


The MWR wet tropospheric correction Wet_H_Rad, water vapour content Vap_Cont and cloudliquid water content Cloud_Liq are given by :

Wet H Rad a a Log TB a Log TB a We e_ _ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (1)

Cloud Liq b b Log TB b Log TB b We e_ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (2)

Vap Cont c c Log TB c Log TB c We e_ . ( ) . ( ) .( )= + − + − + −0 1 2 3280 23 280 36 7 (3)

where TB23 and TB36 are the 23.8 GHz and 36.5 GHz brightness temperatures (in K), W is thealtimeter wind speed (in m/s), and where ai, bi and ci are retrieval coefficients.

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Applicability

• Products (FDGDR, IGDR, GDR) :The computation of the MWR level 2 parameters for the radiometer is performed in FDGDR,IGDR and GDR processings.

• Surface type :The computation of the MWR level 2 parameters for the radiometer is relevant to oceansurfaces only (MWR land flag set to « ocean »).

Accuracy

In the above two equations, the correction term due to wind speed is small (for example, a3 isabout 1.3 mm per m/s). The MWR wet tropospheric correction accuracy is about 1 to 2 cm, andthe water vapour content accuracy is about 0.3 g/cm2. The cloud liquid water accuracy has neverbeen assessed, due to the lack of comparison data.


Documents

RA2/MWR LOP CLS.OC/NT/96.038 Issue 2rev1 Toulouse, 14 ...RD4 : Numerical Recipes : The Art of Scientific Computing in C (Edition 2). William H. Press, Brian P. Flannery, Saul A. Teukolsky,