RA2/MWR LOP CLS.OC/NT/ Issue 2rev1 Toulouse, 14 November 1997 Nomenclature : PO-NT-RAA-0004-CLS. Algorithms Definition and Accuracy

Transcription

1 CLS.OC/NT/ Issue 2rev1 Toulouse, 14 November 1997 Nomenclature : PO-NT-RAA-0004-CLS PREPARED BY COMPANY DATE VISA J.P. DUMONT J. STUM O.Z. ZANIFE CLS CLS CLS QUALITY VISA A. BLUSSON CLS APPROVED BY O.Z. ZANIFE CLS APPLICATION AUTHORIZED BY J. BENVENISTE P. VINCENT ESRIN CNES CLS 18 Av. Edouard Belin TOULOUSE CEDEX 4 FRANCE Tel. (0) FAX (0)

2 Page : i2 DOCUMENT STATUS SHEET Project control visa 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 ESRIN and CNES comments about the first issue. Second issue, first revision D : Page deleted I : Page inserted M : Page modified

3 Page : i3 LIST OF ACRONYMS ADx CNES CLS CSR DS DSR ESA ESRIN ESTEC FDGDR FES FOS GDR COG GRGS IGDR LOP LS MDS MJD MPH MSS MWR NGDC/WDC-A NRT OFL PF PTR RA2 RMS RDx SGDR SNR SPH SV SWH TEC TBC : Applicable Document x : Centre National d Etudes Spatiales : Collecte Localisation Satellites : Centre for Space Research : Data Set : Data Set Record : European Space Agency : European Space Research Institute : European Space Research and Technology Centre : Fast Delivery Geophysical Data Record : Finite Element Solution : Flight Operation Segment : Geophysical data Record : Centre of Gravity : Groupe de Recherche en Géodésie Spatiale : Interim Geophysical Data Record : Level 2 Ocean Processing : Least Square : Measurement Data Set : Modified Julian Date : Main Product Header : Mean Sea Surface : MicroWave Radiometer (ENVISAT) : National Geophysical Data Centre/World Data Centre A : Near Real Time : Off-Line : Platform : Point Target Response : Radar Altimeter (ENVISAT) : Root Mean Square : Reference Document x : Sensor Geophysical Data Record : Signal to Noise Ratio : Specific Product Header : State Vector : Significant Waveheight : Total Electron Content : To Be Confirmed

4 Page : i4 TBD UTC : To Be Defined : Universal Time Co-ordinated

5 Page : i5 APPLICABLE DOCUMENTS / REFERENCE DOCUMENTS AD1 : Software Prototyping for RA-2/MWR Level 2 Ocean Processing ; Technical, Management, Administrative and Financial Proposal ; Response to request for quotation RFQ/3-8785/96/NL/GS. CLS AD2 : RA-2/MWR Level 2 Ocean Processing - Product Assurance Plan PO-AQ-RA-0001-CLS AD3 : Envisat-1 Products Format Guidelines PO-TN-ESA-GS-0242 AD4 : Envisat-1 RA-2 and MWR products Specification PO-TN-ESA-GS-0178 AD5 : ENVISAT-1 Orbit Propagator. S/W I/F and Installation Guide PPF-TN-ESA-GS AD6 : Input / Output Data Definition PO-ST-RA-0005-CLS AD7 : ENVISAT-1 products specifications. Vol. 14 : RA-2 products specifications PO-RS-MDA-GS-2009, Red Marked Copy from 26/09/97 RD1 : Definition of the RA-2 level 2 ocean and ice retracking algorithms PO-NT-RAA-003-CLS, Issue 1rev0, 15/01/97 RD2 : RA-2 retracking comparisons over ocean surface by CLS CLS.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, 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

6 Page : i6 TABLE OF CONTENTS 1. INTRODUCTION INPUT AND OUTPUT DATA INPUT DATA Product data Auxiliary data OUTPUT DATA SUMMARY OF THE INTERFACES PROCESSING OVERVIEW GENERAL FLOWCHART BRIEF DESCRIPTION FDGDR processing IGDR processing GDR processing ALGORITHMS TO COMPUTE THE AVERAGED TIME TAGS 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 PHYSICAL PARAMETERS TO CORRECT THE ALTIMETER RANGE FOR DOPPLER EFFECTS TO AVERAGE THE OCEAN ESTIMATES TO DETERMINE THE SURFACE TYPE 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 10 METERS MODEL WIND VECTOR TO COMPUTE THE SEA STATE BIASES TO COMPUTE THE DUAL-FREQUENCY IONOSPHERIC CORRECTION TO COMPUTE THE DORIS IONOSPHERIC CORRECTION TO COMPUTE THE BENT MODEL IONOSPHERIC CORRECTION...58

7 Page : i TO COMPUTE THE MODEL WET AND DRY TROPOSPHERIC CORRECTIONS TO COMPUTE THE INVERTED BAROMETER EFFECT TO COMPUTE THE MEAN SEA SURFACE PRESSURE OVER THE OCEAN TO COMPUTE THE NON-EQUILIBRIUM OCEAN TIDE HEIGHT FROM THE ORTHOTIDE ALGORITHM 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...90

8 Page : 1 1. INTRODUCTION This document is aimed at defining the level 2 processing of the ENVISAT RA-2 and MWR data, consisting in the framework of this study (see AD1), of the following processing limited to the so-called "ocean" and "ice2" processes (see AD4) : FDGDR processing : Near Real Time processing aimed at providing RA-2 / MWR level 2 Fast Delivery GDR (or FDGDR) products, from level 1b unconsolidated products, using predicted auxiliary data. "Unconsolidated" means parameters which do not account for the final instrumental calibration data. IGDR processing : Off-Line processing aimed at providing RA-2 / MWR level 2 Interim GDR (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 GDR products, within a few weeks (3 to 4), from level 1b consolidated products, using the best restituted auxiliary data (meteorological fields, solar activity indexes, pole location, platform data, DORIS ionospheric data) and a DORIS precise orbit. "Consolidated" means parameters which account for the updated instrumental calibration data. SGDR processing : Off-Line processing aimed at providing RA-2 / MWR level 2 Sensor GDR (or SGDR) products including waveforms, within a few weeks (3 to 4), from level 2 GDR products and the corresponding level 1b consolidated products. This processing consists of the acquisition of the level 1b data (averaged and burst waveforms) and of the level 2 GDR data, and of the merging of these data in a single product. It does not request any critical 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 main functions. It must be considered as the basic input for the detailed requirements of the processings, and not of course as the detailed requirements themselves. The product tree (see AD4) pointing out the main features of these processings and products is given in figure 1-a. The interfaces of FDGDR, IGDR and GDR processings (input and output data) are defined in section 2. An overview of the processings is then given in section 3. It consists of the presentation of the general flowchart, and of a brief description of FDGDR, IGDR and GDR processings. The detailed description of the algorithms is finally given in section 4, where each algorithm 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

9 Page : 2 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 elementary measurements (1.114 s). There is no ambiguity about MWR measurements which are averaged measurements (1.2 s) only. Off_line 3-4 weeks Level 2 SGDR product (RA-2 / MWR + waveforms) Level 2 SGDR processing Consolidated Off_line 3-4 weeks Level 2 GDR product (RA-2 / MWR) Level 2 GDR processing Precise orbit Off_line 3-5 days Consolidated Level 2 IGDR product (RA-2 / MWR) Restituted geophysical corrections Near Real Time Level 2 IGDR processing Unconsolidated Level 2 FDGDR product (RA-2 / MWR) Level 2 FDGDR processing Predicted geophysical corrections Preliminary orbit Unconsolidated Near Real Time Level 1b product (RA-2 / MWR + waveforms) Delay RA-2 and MWR Auxiliary data DORIS orbit Figure 1-a : Product tree (FDGDR, IGDR, GDR, SGDR)

10 Page : 3 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 a sequential set of RA-2 / MWR measurements, whose maximum length is about one revolution of the satellite (i.e. about one orbit). For IGDR and GDR processings, a product represents one pass (i.e. half an orbit from pole to pole) Product data RA-2 / MWR Level 1b data : The level 1b product is described in AD7. Generally speaking, it is assumed that level 1b products 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 orbit and to DORIS precise orbit 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

11 Page : 4 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 processings are the data which cover the time span of the input product to be processed (with additional points 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 2 processing. 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, electromagnetic bias 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

12 Page : OUTPUT DATA Generally speaking, it is assumed that level 2 processings do not modify the organisation of the input data, and in particular that they do not account for the organisation of data from orbit revolution to passes. Level 2 processings output thus one level 2 product (FDGDR, IGDR or GDR 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.

13 Page : 6 Product data Level 1b (unconsolidated) Dynamic Auxiliary Data Static Auxiliary Data Meteo. : predicted Solar activity Pole location PF data FDGDR processing FDGDR product Product data Level 1b (unconsolidated) DORIS preliminary orbit (1) Dynamic Auxiliary Data Static Auxiliary Data Meteo. : restituted Solar activity Pole location PF data DORIS-derived TEC maps IGDR processing IGDR product Product data Level 1b (consolidated) DORIS precise orbit (1) Dynamic Auxiliary Data Static Auxiliary Data Meteo. : restituted Solar activity Pole location PF data DORIS-derived TEC maps GDR processing GDR product Figure 2.3-a : Interfaces of the FDGDR, IGDR and GDR processings (1) TBD orbit data as backup solution

14 Page : 7 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 of level 2 processing(s) it belongs (grey if the algorithm is performed). Moreover, the rhythm of activation of the algorithms (RA-2 elementary measurements, RA-2 averaged measurements or MWR 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 etc are not represented in this document, because they are not considered as critical items in the framework of the present processing definition. They will be represented and described during the processing detailed requirements phase. Generally speaking, the algorithms defined hereafter only concern RA-2 measurements in tracking 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 meaning for the "tracking", "preset tracking" and "preset loop output" modes, so that the level 2 processing of these measurements is exactly the same. It is thus assumed that the specificities of the 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 the instrument mode identifier will be provided in the output data set record, while the other fields will be set to default values.

15 Page : 8 FDGDR IGDR GDR TO COMPUTE THE AVERAGED TIME TAGS TO COMPUTE THE AVERAGED ALTITUDE, ALTITUDE RATE AND LOCATION TO COMPUTE ALTITUDE, ALTITUDE RATE AND LOCATION FROM ORBIT FILES RA-2 elementary measurements TO COMPUTE THE DOPPLER CORRECTIONS TO PERFORM THE ICE 2 RETRACKING TO PERFORM THE OCEAN RETRACKING TO COMPUTE THE PHYSICAL PARAMETERS TO CORRECT THE ALTIMETER RANGE FOR DOPPLER EFFECTS TO AVERAGE THE OCEAN ESTIMATES TO DETERMINE THE SURFACE TYPE 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 10 METERS MODEL WIND VECTOR TO COMPUTE THE SEA STATE BIASES l l l TO COMPUTE THE DUAL FREQUENCY IONOSPHERIC CORRECTION RA-2 averaged measurements 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 TO COMPUTE THE MEAN SEA SURFACE PRESSURE OVER THE OCEAN l l l 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 MWR averaged measurements TO INTERPOLATE THE ALTIMETER WIND SPEED DATA TO RADIOMETER TIME TAG TO COMPUTE THE MWR LEVEL 2 PARAMETERS FOR THE RADIOMETER Figure 3.1-a : General flowchart of the FDGDR, IGDR and GDR level 2 processings

16 Page : BRIEF DESCRIPTION A brief overview of the main functions of the nominal level 2 processings is given in this section. A detailed description of the algorithms is provided in section FDGDR processing The time-tag of the averaged measurements is derived from the time-tags of the elementary measurements. The elementary values of the location (latitude, longitude), the orbit altitude and the orbit altitude 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 retracking algorithm is nominally initialised by the outputs of the ice2 retracking algorithm, and it accounts for the mispointing information derived from the platform data (antenna pitch and roll 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 level 1b correction is removed, and with the input scaling factors for Sigma0 evaluation (in Ku and S 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 a bathymetry / topography file, and then in case of ambiguity, by information from the altimeter itself. It will be used in the following to sort data to be accounted for in the algorithms relevant to ocean surfaces only. The MWR brightness temperatures (2 channels) and the radiometer land flag are interpolated to the altimeter time tag of the averaged measurements. The backscatter coefficient atmospheric attenuations are computed in Ku and S bands, using brightness temperatures The Ku and S bands ocean backscatter coefficient are corrected for the atmospheric attenuation 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 cloud liquid water contents) are computed from the brightness temperatures, using in particular the altimeter wind speed as a correction term. The two components (U and V) of the 10 meters wind vector are computed using forecasted meteorological fields. The sea state bias is computed in Ku and S bands.

17 Page : 10 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 pole locations. 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 at MWR time tag, from the MWR brightness temperatures and using the altimeter wind speed interpolated at MWR time tag as a correction term IGDR processing The time-tag of the averaged measurements is derived from the time-tags of the elementary measurements. The elementary and averaged orbit altitudes and orbit altitude rates, and the averaged location of measurements are recomputed from DORIS preliminary orbit data (or TBD preliminary orbit data in backup solution). The elementary Doppler corrections on the altimeter range are computed in Ku and S bands from the altitude rates derived from DORIS preliminary orbit data. The ice2 and ocean retrackings are performed in Ku and S bands. The ocean retracking algorithm is nominally initialised by the outputs of the ice2 retracking algorithm, and it accounts for the mispointing information derived from the platform data (antenna pitch and roll 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 level 1b correction is removed, and with the input scaling factors for Sigma0 evaluation (in Ku and S bands). These parameters consist of : Ocean and ice2 altimeter ranges corrected for COG motion Significant waveheight

18 Page : 11 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 a bathymetry / topography file, and then in case of ambiguity, by information from the altimeter itself. It will be used in the following to sort data to be accounted for in the algorithms relevant to ocean surfaces only. The MWR brightness temperatures (2 channels) and the radiometer land flag are interpolated to the altimeter time tag of the averaged measurements. The backscatter coefficient atmospheric attenuations are computed in Ku and S bands, using brightness temperatures The Ku and S bands ocean backscatter coefficient are corrected for the atmospheric attenuation 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 cloud liquid water contents) are computed from the brightness temperatures, using in particular the altimeter wind speed as a correction term. The two components (U and V) of the 10 meters wind vector are computed using analysed meteorological 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 pole locations. 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.

19 Page : 12 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 at MWR time tag, from the MWR brightness temperatures and using the altimeter wind speed interpolated at MWR time tag as a correction term 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 backup solution), instead of preliminary data. The pole tide height is computed from improved pole location data (with respect to the pole location data used in the IGDR processing). 4. ALGORITHMS The following descriptions do not account for reference systems and units. The parameters of the mathematical formulae are assumed to be consistent. These items will be accounted for in the detailed requirements of the software.

20 Page : 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 the 100 averaged corresponding Ku-band waveforms is on the ground. The averaged measurements provided in the level 2 output product correspond to the source packets of the telemetry. The time-tag of the averaged measurements are computed by linear regression of the corresponding elementary 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 GDR processings. 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 the source packet. As the level 1b algorithm is such as these time-tags are equidistant, there will be no error due to the interpolation method (linear regression). Comments References None None

21 Page : TO COMPUTE THE AVERAGED ALTITUDE, ALTITUDE RATE AND LOCATION Function To interpolate the elementary altitude, altitude rate and location at the time-tag of the averaged RA-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 : Processing parameters 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). Mathematical statement The averaged parameters are computed by regression of the corresponding elementary RA-2 time tags, at the middle of the source packet (linear regression for the latitudes, longitudes and altitude rates, parabolic regression for the altitude). The differences between the elementary and the 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 FDGDR processing only. Surface type : The computation of the averaged location, altitude and altitude rate is relevant to all surface types.

22 Page : 15 Accuracy The error due the interpolation algorithm is negligible. Indeed, it is : smaller than degrees on the latitude and degrees on the longitude, which are the maximum errors, corresponding to measurements close to the poles, observed from one orbit of ERS OPR measurements when the location of 1-Hz points is replaced by the result 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 a source packet, i.e. a parabolic altitude and a linear altitude rate. With these assumptions, a linear regression on the altitude would lead to an error of about 3 mm for an radial acceleration of 5 cm/s 2. Comments One of the advantage of the regression is the automatic management of missing elementary data. References None

23 Page : TO COMPUTE ALTITUDE, ALTITUDE RATE AND LOCATION FROM ORBIT FILES Function To compute the orbit altitude above reference ellipsoid, the orbit altitude rate and location from orbit 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 the averaged RA-2 measurements. Altitude differences from the averaged altitude (differences between the orbit altitudes of elementary 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. Mathematical statement 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 as follows: N (typically N=8) position vectors are selected from the input orbit file (N/2 before and N/2 after the altimeter time tag). These vectors are interpolated at the altimeter time tag using the r Everett s formula. The interpolated position P = ( PX, PY, PZ)of the satellite is then projected onto the reference ellipsoid to provide the latitude, longitude and orbit altitude h (i.e. the altitude of the platform centre of gravity above the reference ellipsoid).

24 Page : 17 M (typically M=8) velocity vectors are selected from the input orbit file (M/2 before and M/2 after the altimeter time tag). These vectors are interpolated at the altimeter time tag using the Everett s formula. The orbit altitude rate (h ) is then obtained by forming a scalar r product of the interpolated satellite velocity vector V = ( VX, VY, VZ) with the normalised position vector (see section "accuracy"), i.e. by : VX. PX + VY. PY + VZ. PZ h = (1) P + P + P Applicability X Y Z Products (FDGDR, IGDR, GDR) : The computation of altitude, altitude rate and location from orbit files is performed in IGDR and 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 all surface types. Accuracy The error due to the Everett s interpolation method is negligible if the number N of orbit points taken into account is large enough (typically N=8, i.e. 4 points before and 4 points after the altimeter time). The driving parameter for the Doppler range effect is the velocity component of the satellite in the light of sight of the observer, i.e. in the direction NS defined by the satellite (S) and the corresponding nadir point (N). However, this direction may be merged with the direction OS of the position vector (defined by the earth centre O and the satellite S). Indeed, the maximum angle γ between these two directions is about 0.17 degrees, leading to an error of about h. In the worst case, assuming a satellite altitude of 800 km and a radial velocity of ± 25 m/s at the point where γ is maximum, the error on the radial velocity will thus be m/s, leading to an error on the Doppler correction always smaller than 2 microns whatever the emitted bandwidth is.

25 Page : 18 y S γ N O x Comments A backup solution to compute the altitude, altitude rate and location from orbit files consists of the use of TBD orbit files. If these files contain a series of position and velocity of the satellite 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 be performed using the ESA orbit propagator (see AD5). References None

26 Page : 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 Mathematical statement For each elementary measurement, the Doppler correction δh to be added on the altimeter range is computed in Ku and S bands, by : δh = ft. ε. B h (ε = ±1) (1) where : h = altitude rate f = emitted frequency T = pulse duration B = 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-2 antenna with respect to the reference ellipsoid (which is derived from the orbit data), it is fully consistent with ocean measurements, but not with measurements relative to other surfaces.

27 Page : 20 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 Doppler correction only depends on the accuracy on the orbit altitude rate and thus on the accuracy of the orbit 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 FDGDR processing, but the elementary Doppler corrections applied to the altimeter ranges (and provided in the level 2 product) are recomputed accounting for DORIS orbit data (preliminary orbit data for IGDR, precise orbit data for GDR). This solution allows the accounting for possible Ku bandwidth changes within a source packet. References None

28 Page : TO PERFORM THE ICE 2 RETRACKING The ice2 retracking algorithm is performed on the Ku and on the S waveforms. The only difference in the retracking of Ku and S waveforms is the processed data (waveform, processing and instrumental parameters), while the processing is the same. A single description is thus given 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 (σ L ) Amplitude or "power" (P u ) Mean amplitude or "mean power" (P t ) Slope of the first part of the logarithm of the trailing edge (s T1 ) Slope of the second part of the logarithm of the trailing edge (s T2 ) Slope of the first part of the logarithm of the trailing edge for mispointing estimation (s T1m ) Thermal noise level (P n ) Mean quadratic error between the normalised waveform and its model Mathematical statement Background The ice2 retracking algorithm is an adaptation to the ENVISAT RA-2 background, of the algorithm 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 waveform coincide with a return power model, according to Least Square estimators. The expression of the model versus time (t), derived from Brown s model (Brown, 1977), is given by :

29 Page : 22 P u t τ 2 x 2 Vm() t =. + erf.exp[ s ( t ) t 1 T. τ ] + Pn (with : erf ( x) =. e dt ) (1) 2 σ L π 0 where the parameters to be estimated are : τ : the epoch σ L : the width of the leading edge P u : the amplitude s T : the slope of the logarithm of the trailing edge P n : 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 thermal noise level (P n ) is either the input noise power measurement (NPM), or it is computed from an arithmetic average of samples of the first plateau, or it is a default value (processing parameter). P n is removed from the waveform samples which is then normalised (i.e. divided by an estimate of the maximum amplitude of the useful signal). Finally, the beginning and the end of the leading edge are identified from an analysis of the shape of the waveform (accounting in particular for the frequent case of a trailing edge with a positive slope), and an estimation window is built around the detected leading edge. Coarse estimation stage (τ, σ L ) : A coarse estimation of the epoch (τ) of the waveform in the estimation window and of the width of the leading edge (σ L ), is then derived from Least Square estimators by fitting the processed waveform to a mean return power model with a flat trailing edge. This fit is performed in the estimation window i.e. around the leading edge of the waveform. These estimates are the values which minimise the residual in the estimation window, between the normalised waveform and the corresponding model. For each possible value of τ (corresponding to a position varying between the beginning and the end of the estimation window, with a predefined step) and of σ L (varying between two thresholds, with a predefined step) : the normalised model (V mn ) is computed in the estimation window the amplitude P u of the normalised waveform is estimated by minimising the mean quadratic error between the normalised waveform (V n ) and the weighted normalised model (P u.v mn ) in the estimation window (linear regression between the waveform and the normalised model) the residual R between V n and P u.v mn is computed in the estimation window the estimates are updated if R is smaller than the previous minimum value

30 Page : 23 Fine estimation stage (τ, σ L, P u ) : A fine estimation of τ, σ L and P u (amplitude) is finally derived. The coarse and fine estimation stages are very similar. The particularities of the fine estimation process are the following : the simulated values of τ and σ L 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 (s T1, s T2 ) : The estimation of the slope of the trailing edge is intentionally fully decorrelated from the estimation of the other parameters (τ, σ L, P u ), because slopes variations may be very important from a waveform to another, and because the uncertainty on its estimate is very important due to speckle effects. Indeed, over ice surfaces, the slope of the trailing edge depends on several parameters among which the slope and the curvature of the overflown surface, the signal due to the penetration of the radar wave in the snow pack (Legresy and Remy, in press), and of course instrumental features (e.g. antenna). The slope is estimated by linear regression of the logarithm of the normalised waveform samples in two windows part of the trailing edge: the first one (s T1 ) just after the end of the leading edge with a predefined width, and the second one (s T2 ) in a contiguous window with a predefined width. The first estimation is aimed at pointing out a possible volume signal existing at the end of the leading edge. A third slope (s T1m ) is estimated as s T1, with an other predefined width aimed at pointing out a mispointing angle over ocean surfaces (see section 4.7). Estimation of the mean amplitude (P t ) : The mean amplitude of the waveform is estimated by an arithmetic average of the waveform samples (thermal noise level removed) in a window limited by the beginning of the leading edge 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 P u is denormalised, etc.) Detailed operation A full description of the algorithm is given in RD1. The detailed specifications of the algorithm for 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 the trailing edge for the mispointing estimation which is relevant to ocean surfaces only.

31 Page : 24 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 using nominal values of the RA-2 instrumental parameters. The on-board tracker operation and thus the 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 : σ L =.761 m (equivalent to an ocean waveheight of 2 m) SNR = 15 db s T = km -1 (ocean-like slope of the trailing edge), are summarised below. The dependency of these results with the various parameters (i.e. width of 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 Ku band 20 MHz and -4 cm in S band 160 MHz. It becomes more important when the slope of the trailing edge is positive (e.g. in Ku band 320 MHz, it is about -1 cm for s T = 0 and -11 cm for s T = km -1 ). The standard deviation is about 6 cm in Ku band 320 MHz, 8 cm in Ku band 80 MHz, 23 cm in Ku band 20 MHz and 22 cm in S band 160 MHz. It increases with the width of the leading edge (σ L ) and decreases with SNR. The high values observed in S band proceed from an increase of the speckle on the waveforms samples by a factor of 2 in S band, due to the number of averaged individual echoes. Width of the leading edge (σ L ) : For low values of σ L, the mean error logically increases with the sampling interval in Ku band. For σ L = 0, it is about -2 cm at 320 MHz, -28 cm at 80 MHz and -177 cm at 20 MHz. It should consequently be between -2 cm and -28 cm at 160 MHz. Actually, it is more important (about -38 cm) because of the absence of the two additional DFT samples in S band, which improve the resolution in Ku band. For these reasons, the estimate of σ L can not be accurate in Ku band 20 MHz, whatever the conditions are. In standard conditions, the error is small for the other bandwidths. It is about 0.5 cm in Ku band 320 MHz, 7 cm in Ku band 80 MHz and 3 cm in S band 160 MHz. It does not depend on SNR, and its dependency with 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 S band). It increases with σ L, except in Ku band 20 MHz where it is constant because the whole leading edge is always included in one FFT filter. It also increases with the slope of the trailing edge, but does not depend on the signal to noise ratio. Amplitude (Pu) : In standard conditions but with a flat trailing edge (s T =0), the mean error is small (i.e. between and -0.1 db) whatever the bandwidth is. It becomes important in case of a negative and overall a positive slope (e.g. for s T = km -1, the error is about -0.5 to -0.6 db in Ku bands 320 and 80 MHz and in S band, and about -0.9, db in Ku band 20 MHz).

32 Page : 25 This error should be smaller for real waveforms, due to the existence of a volume signal at the 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 σ L or SNR. In S band, it is higher in standard conditions (about 11% of the amplitude) and its dependency with σ L is important, due to the speckle features (the standard deviation is about 25% of the amplitude for an equivalent significant waveheight of 8 m). Mean amplitude (P t ) : The accuracy of the estimate of the mean amplitude of the waveform has not be assessed because 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 the simulated amplitude P u, and with the tests conditions. Slope of the trailing edge (s T1, s T2 ) : Generally speaking, the standard deviation on the slope estimates are important due to the speckle affecting the waveforms and to the limited number of samples which can be accounted for. The interpretation of the mean errors is thus not obvious from a limited amount of simulated measurements. In standard conditions and for a 320-MHz bandwidth, the standard deviation on s T1 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 B. Legresy and F. Remy : "Surface characteristics of the Antarctic ice sheet and altimetric observates", UMR5566 / GRGS (CNES-CNRS) : In press J. of Glacio.

33 Page : TO PERFORM THE OCEAN RETRACKING The ocean retracking algorithm is performed on the Ku and on the S waveforms. The only difference in the retracking of Ku and S waveforms is the processed data (waveform, processing and instrumental parameters), while the processing is the same. A single description is thus given 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) From "To compute the averaged time tags": Averaged RA-2 time tag 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 (σ c ) Amplitude (P u ) Thermal noise level (P n ) Mean quadratic error between the normalised waveform and its model Number of iterations Mathematical statement Background The ocean retracking algorithm has been defined by CLS, from a comparative study of the various standard ocean retracking algorithms (see RD2), i.e. of : CNES/CLS algorithm designed to process Poseïdon altimeter data