level 2 sral mwr algorithm theoretical ... - sentinel online · centre (mpc) for the copernicus...

PREPARATION AND OPERATIONS OF THE MISSION PERFORMANCE

CENTRE (MPC) FOR THE COPERNICUS SENTINEL-3 MISSION

Sentinel-3 Level 2 SRAL MWR Algorithm Theoretical

Baseline Definition

Ref.: S3MPC.CLS.PBD.005

Issue: 2.0

Date: 01/07/2019

Contract: 4000111836/14/I-LG

Customer: ESA Document Ref.: S3MPC.CLS.PBD.005

Contract No.: 4000111836/14/I-LG Date: 01/07/2019

Issue: 2.0

Project: PREPARATION AND OPERATIONS OF THE MISSION PERFORMANCE CENTRE (MPC)

FOR THE COPERNICUS SENTINEL-3 MISSION

Title: Level 2 SRAL MWR Algorithm Theoretical Baseline Definition

Author(s): STM ESLs

Approved by: S. Labroue Authorized by J. Bruniquel, Service Manager

Distribution: Sentinel Online

Accepted by ESA P. Féménias, ESA TO

Filename S3MPC.CLS.PBD.005 - i2r0 - S3 L2 SRAL MWR ATBD.docx

Copyright ©2017 – CLS, CNES, MSSL

All rights reserved.

No part of this work may be disclosed to any third party translated, reproduced, copied or

disseminated in any form or by any means except with the written permission of CLS, CNES and MSSL

Disclaimer

The work performed in the frame of this contract is carried out with funding by the European Union.

The views expressed herein can in no way be taken to reflect the official opinion of either the

European Union or the European Space Agency.

Sentinel-3 MPC

Level 2 SRAL MWR Algorithm

Theoretical Baseline Definition


Issue: 2.0

Date: 01/07/2019

Page: i

Changes Log

Version Date Changes

1.0 13/07/2017 First version

2.0 01/07/2019 Update with changes up to PB2.49A_1.21B

List of Changes

Version Section Answers to RID Changes

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Table of content

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

1.1 AIM ............................................................................................................................................................... 1

1.2 BACKGROUND .................................................................................................................................................. 1

2 ALGORITHMS DEFINITION AND SPECIFICATION ............................................................................................ 3

2.1 ALT_COR_BAC_01 - TO COMPUTE THE CORRECTED RETRACKED BACKSCATTER COEFFICIENTS ....................................... 3

2.2 ALT_COR_GEN_01 - TO COMPUTE THE MODELED INSTRUMENTAL CORRECTIONS ON THE RETRACKED PARAMETERS (KU-

BAND) 4

2.3 ALT_COR_GEN_02 - TO COMPUTE THE MODELED INSTRUMENTAL CORRECTIONS ON THE RETRACKED PARAMETERS (C-

BAND) 7

2.4 ALT_COR_MIS_01 - TO COMPUTE THE CORRECTED SQUARED MISPOINTING ANGLE .................................................... 9

2.5 ALT_COR_RAN_01 - TO COMPUTE THE DOPPLER CORRECTION ............................................................................ 10

2.6 ALT_COR_RAN_02 - TO COMPUTE THE GENERAL DOPPLER CORRECTION (ALL)....................................................... 12

2.7 ALT_COR_RAN_03 - TO COMPUTE THE CORRECTED RETRACKED ALTIMETER RANGES ................................................ 14

2.8 ALT_COR_RAN_04 - TO COMPUTE THE SEA STATE BIASES ................................................................................... 16

2.9 ALT_COR_RAN_05 - TO COMPUTE THE DUAL-FREQUENCY IONOSPHERIC CORRECTIONS ............................................ 17

2.10 ALT_COR_RAN_06 – TO CALCULATE THE APPLICABLE SET OF CORRECTIONS (LRM ICE; SAR SEA-ICE, MARGIN) ........... 19

2.11 ALT_COR_RAN_07 - TO COMPUTE THE FILTERED IONOSPHERIC CORRECTION .......................................................... 21

2.12 ALT_COR_SWH_01 - TO COMPUTE THE CORRECTED RETRACKED SIGNIFICANT WAVEHEIGHTS .................................... 23

2.13 ALT_MAN_INT_01 – TO PERFORM SHORT-ARC ALONG-TRACK INTERPOLATION ....................................................... 24

2.14 ALT_MAN_TIM_01 – TO COMPUTE 1-HZ TIME TAGS ........................................................................................ 26

2.15 ALT_MAN_WAV_02 – TO DISCRIMINATE WAVEFORMS ..................................................................................... 28

2.16 ALT_PHY_BAC_01 - TO COMPUTE THE RETRACKED BACKSCATTER COEFFICIENTS ...................................................... 30

2.17 ALT_PHY_BAC_02 - TO COMPUTE THE BACKSCATTER COEFFICIENT (SAR, SEA-ICE, MARGIN) .................................... 31

2.18 ALT_PHY_BAC_03 - TO COMPUTE THE BACKSCATTER COEFFICIENT (LRM, ICE) ....................................................... 33

2.19 ALT_PHY_GEN_01 - TO COMPUTE THE ELEVATION AND LOCATION OF ECHOING POINTS (LRM, ICE ; SAR, MARGIN) ..... 34

2.20 ALT_PHY_GEN_02 - TO COMPUTE THE RAIN FLAG ............................................................................................. 36

2.21 ALT_PHY_GEN_03 - TO COMPUTE THE RAIN RATE ............................................................................................. 38

2.22 ALT_PHY_RAN_01 - TO COMPUTE THE RETRACKED ALTIMETER RANGES ................................................................ 40

2.23 ALT_PHY_RAN_02 – TO COMPUTE THE SURFACE HEIGHT ANOMALY (SAR, SEA-ICE) ............................................... 41

2.24 ALT_PHY_RAN_03 – TO COMPUTE THE FREEBOARD .......................................................................................... 42

2.25 ALT_PHY_SNR_01 - TO COMPUTE THE SNR FROM THE ESTIMATES OF THE AMPLITUDE AND OF THE THERMAL NOISE LEVEL

OF THE WAVEFORMS .................................................................................................................................................... 43

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2.26 ALT_PHY_SWH_01 - TO COMPUTE SWH FROM THE RETRACKED COMPOSITE SIGMA ............................................... 45

2.27 ALT_PHY_WIN_01 - TO CORRECT THE BACKSCATTER COEFFICIENTS FOR ATMOSPHERIC ATTENUATION AND TO COMPUTE

THE 10 METER ALTIMETER WIND SPEED ............................................................................................................................ 47

2.28 ALT_RET_ICE_01 – TO PERFORM THE ICE-1 (OCOG) RETRACKING (SAR SEA-ICE, MARGIN ; LRM ICE) ....................... 49

2.29 ALT_RET_ICE_02 - TO PERFORM THE ICE-2 RETRACKING (LRM) .......................................................................... 51

2.30 ALT_RET_ICE_03 – TO PERFORM THE “FUNCTION FIT” RETRACKING (SAR, SEA-ICE) ................................................ 55

2.31 ALT_RET_ICE_04 - TO MERGE MLE4 RESULTS INTO THE ICE CHAIN (LRM ICE) ....................................................... 57

2.32 ALT_RET_ICE_05 - TO PERFORM THE SAR ICE-MARGIN WW RETRACKING (SAR ICE SHEETS) .................................... 58

2.33 ALT_RET_ICE_06 – TO PERFORM THE DIFFUSE RETRACKING (SAR, NON-LEAD) ....................................................... 59

2.34 ALT_RET_OCE_01 - TO PERFORM THE OCEAN RETRACKING (LRM) ....................................................................... 62

2.35 ALT_RET_OCE_02 - TO PERFORM OCEAN/COASTAL ZONE RETRACKING (SAR) ........................................................ 67

2.36 GEN_COR_ORB_01 - TO DERIVE THE ORBITAL ALTITUDE RATE WITH RESPECT TO THE REFERENCE MSS/GEOID .............. 77

2.37 GEN_COR_RAN_01 - TO COMPUTE THE 10 METER WIND VECTOR, THE SURFACE PRESSURE AND THE MEAN SEA SURFACE

PRESSURE FROM ECMWF MODEL, THE DRY AND WET TROPOSPHERIC “OPERATIONAL” CORRECTIONS (OCEAN SURFACES) AND THE DRY

AND WET TROPOSPHERIC “PSEUDO-OPERATIONNAL” CORRECTIONS (CONTINENTAL SURFACES).................................................... 78

2.38 GEN_COR_RAN_02 - TO COMPUTE THE HIGH FREQUENCY FLUCTUATIONS OF THE SEA SURFACE TOPOGRAPHY FROM

MOG2D MODEL ......................................................................................................................................................... 85

2.39 GEN_ENV_BAT_01 - TO COMPUTE THE OCEAN DEPTH / LAND ELEVATION .............................................................. 87

2.40 GEN_ENV_DIS_01 - TO COMPUTE DISTANCE TO SHORE ...................................................................................... 88

2.41 GEN_ENV_ECH_01 - TO DETERMINE THE ECHO DIRECTION (SAR, MARGIN) .......................................................... 89

2.42 GEN_ENV_ECH_02 - TO DETERMINE THE ECHO DIRECTION (LRM, ICE) ................................................................. 92

2.43 GEN_ENV_GEO_01 - TO COMPUTE THE GEOID HEIGHT ...................................................................................... 94

2.44 GEN_ENV_MDT_01 - TO COMPUTE THE MEAN DYNAMIC TOPOGRAPHY HEIGHT ..................................................... 95

2.45 GEN_ENV_MET_01 - TO COMPUTE THE INVERTED BAROMETER EFFECT ................................................................. 97

2.46 GEN_ENV_MSS_01 - TO COMPUTE THE MEAN SEA SURFACE HEIGHT (SOLUTION 1) ................................................. 99

2.47 GEN_ENV_MSS_02 - TO COMPUTE THE MEAN SEA SURFACE HEIGHT (SOLUTION 2) ............................................... 101

2.48 GEN_ENV_SUR_01 - TO DETERMINE THE RADIOMETER SURFACE TYPE ................................................................ 103

2.49 GEN_ENV_SUR_02 - TO COMPUTE THE OCEAN/SEA-ICE FLAG AND CLASSES MEMBERSHIPS ................................... 105

2.50 GEN_ENV_SUR_03 - TO COMPUTE THE CONTINENTAL ICE FLAG ........................................................................ 108

2.51 GEN_ENV_SUR_04 - TO DETERMINE THE SURFACE CLASSIFICATION FLAG ............................................................ 110

2.52 GEN_ENV_TID_01 - TO COMPUTE THE SOLID EARTH AND THE EQUILIBRIUM LONG PERIOD OCEAN TIDE HEIGHTS .......... 111

2.53 GEN_ENV_TID_03 – TO COMPUTE THE TIDE HEIGHTS (SOLUTION 2 – GENERIC COMPUTATION) ............................... 114

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2.54 GEN_ENV_TID_04 - TO COMPUTE THE DIURNAL AND SEMIDIURNAL ELASTIC OCEAN TIDE HEIGHT AND THE LOAD TIDE

HEIGHT (SOLUTION 1 – 28 COMPONENTS) ..................................................................................................................... 116

2.55 GEN_ENV_TID_05 - TO COMPUTE THE POLE TIDE HEIGHT ................................................................................. 119

2.56 RAD_PHY_ATT_01 - TO COMPUTE THE SRAL SIGMA0 ATMOSPHERIC ATTENUATIONS ............................................ 121

2.57 RAD_PHY_GEN_01 - TO COMPUTE THE MWR GEOPHYSICAL PARAMETERS AT SRAL TIME TAG ............................... 123

2.58 RAD_PHY_GEN_02 - TO COMPUTE THE WET TROPOSPHERE CORRECTION AT SRAL TIME TAG (USING SST AND GAMMA

PARAMETERS) ........................................................................................................................................................... 124

2.59 RAD_PHY_GEN_03 – TO COMPUTE THE WET TROPOSPHERIC COMPOSITE CORRECTION .......................................... 126

2.60 RAD_PHY_TEM_01 – TO CO-LOCALIZE THE RADIOMETER PIXELS ........................................................................ 129

3 ACRONYMS ................................................................................................................................................ 131

List of Figures

Figure 1 : Observation scenario with and without mispointing ----------------------------------------------------- 68

Figure 2 : Flight dynamics coordinate system assumed for mispointing calculation --------------------------- 69

Figure 3 - SAR ocean retracker global software structure ------------------------------------------------------------ 71

Figure 4 - Geographical masks: in blue for winter and in red for summer. -------------------------------------- 106

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1 Introduction

1.1 Aim

This document is aimed at defining the “scientific” algorithms used in the Level 2 processing of the

Sentinel-3 Surface Topography Mission SRAL and MWR data.

“Scientific” algorithms represent the core of the processing. They are dissociated from “Data

management” algorithms, ensuring functions such as data acquisition, data selection and preparation,

units conversions, general checks, products generation, processing management, etc., which strongly

depend on the format of the input and output data.

The definition of the altimeter Level 2 scientific algorithms, provided in this document, consists of the

identification and the description of their main functions. It will provide the reader with an overview of

the procedures and a global understanding of the algorithms.

Each scientific algorithmis is defined, using the following items:

• Name and identifier of the algorithm

• Heritage (mission for which the algorithm is used or derived)

• Function

• Algorithm Definition:

Input data Output data Mathematical statement

• Accuracy (if any)

• Comments (if any)

• References (if any)

1.2 Background

1.2.1 Products levels

Level 1b products – issued from L1b processing - correspond to geo-located engineering-calibrated

products, while Level 2 products – issued from L2 processing - correspond to geo-located geophysical

products.

1.2.2 Delivery Delay

As far as Sentinel-3 Topography Mission is concerned, three products delivery delays are considered:

• Near Real Time (NRT): delivered less than 3 hours after data acquisition, and mainly used for marine meteorology and ocean-atmosphere gas transfer studies

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• Slow Time Critical (STC): delivered within 48 hours after data acquisition, due mainly to the consolidation of some auxiliary or ancillary data (e.g. preliminary restituted orbit data) and mainly used for geophysical studies and operational oceanography

• Non Time Critical (NTC): delivered within typically 1 month after data acquisition, due mainly to the consolidation of some auxiliary or ancillary data (e.g. precise orbit data), and mainly used for geophysical studies and operational oceanography.

1.2.3 Ancillary/Auxiliary and Dynamic/Static Data

Besides instrumental data (SRAL, MWR, GNSS), additional data are requested on input of the various

processings aimed at building user products:

• Ancillary data corresponds to data internal to the Sentinel-3 system (e.g. orbit, instrumental LUT, configuration data i.e. processing parameters)

• Auxiliary data corresponds to data exterrnal to the Sentinel-3 system (e.g. meteo fields, land/sea mask)

Both types of data may be dynamic or static:

• Dynamic data corresponds to time-varying data (e.g. orbit, meteo fields)

• Static Data corresponds to constant data (e.g. instrumental LUT, land/sea mask, configuration data)

1.2.4 Altimeter Terminology

Altimeter measurements are performed either in Low Resolution Mode (LRM) or in Synthetic Aperture

Radar (SAR) mode.

• In LRM mode, pulses are transmitted at the Pulse Repetition Frequency (PRF about 1924 Hz) rythm, following a typical pattern of 3 Ku-band pulses / 1 C-band pulse / 3 Ku-band pulses. These pulses are processed and averaged on-board to provide a power waveform (128 I2+Q2 samples) every about 50.9 ms, corresponding to the averaging of 84 Ku-band pulses and of 14 C-band pulses. This measurement is called an elementary measurement or a 20-Hz measurement. It contains Ku-band and C-band waveforms and associated parameters.

• In SAR mode, the Pulse Repetition Frequency (PRF) is about 17 800 Hz. Pulses are transmitted by a series of 66 (64 Ku-band pulses and 2 C-band pulses), called a burst, corresponding to a duration about 12.74 ms. A burst corresponds thus to a 80-Hz measurement, and contains 64 Ku-band and 2 C-band waveforms (128 I and Q samples for each of them).

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2 Algorithms Definition and Specification

2.1 ALT_COR_BAC_01 - To compute the corrected retracked backscatter

coefficients

2.1.1 Heritage

Jason-1, Jason-2

2.1.2 Function

To compute the corrected retracked backscatter coefficients (main and auxiliary bands).

2.1.3 Algorithm Definition

2.1.3.1 Input data

• Altimeter configuration data

• Backscatter coefficient:

Retracked backscatter coefficient and associated validity flag

• Instrumental correction:

Backscatter modeled instrumental coefficient correction AGC instrumental errors correction Internal calibration correction

• Processing parameters (SAD):

Backscatter coefficient system bias

2.1.3.2 Output data

• Corrected retracked backscatter coefficients

• Net instrumental correction

2.1.3.3 Mathematical statement

The estimates of the retracked backscatter coefficients are already corrected through the scaling factors

for Sigma0 evaluation, for the AGC errors and the internal calibration. The two following corrections are

added:

• The modeled instrumental correction • The system bias

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2.2 ALT_COR_GEN_01 - To compute the modeled instrumental corrections on

the retracked parameters (Ku-band)

2.2.1 Heritage

TOPEX/POSEIDON, Jason-1, Jason-2

2.2.2 Function

To compute the modeled corrections of the instrumental errors on the altimetric estimates (altimeter

range, altimeter range rate, significant waveheight, backscatter coefficient and square of the mispointing

angle - (main band), using correction tables depending on significant waveheight and signal to noise ratio.


2.2.3.1 Input data


• Signal to noise ratio:

Signal to noise ratio and associated validity flag

• Significant waveheight:

Significant waveheight and associated validity flag

• Instrumental correction tables (SAD) (1):

Main band altimeter range correction table Main band significant waveheight correction table Main band backscatter coefficient correction table Main band squared mispointing angle correction table


Default value for the inputs of the correction tables

2.2.3.2 Output data

• Main band altimeter range modeled instrumental correction

• Main band significant waveheight modeled instrumental correction

• Main band backscatter modeled instrumental coefficient correction

• Main band squared mispointing modeled instrumental coefficient correction

(1) Including features such as lower bound, upper bound and step for each input

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Principle

The imperfections of the altimeter components lead to errors on the altimetric estimates. To provide

accurate measurements, a complete knowledge of these errors (source and quantization of their effects)

is required.

The following errors are accounted for:

Errors of the on-board software Errors due to the low-pass filtering Errors due to the leakage spikes Errors due to the on-board FFT Errors due to the PTR

Nevertheless, the linearity of these errors is not obvious at all, and a separate correction for each effect

is probably not consistent with the instrument behavior. An integrated modeling of these errors is thus

necessary.

All these effects are accounted for in a simulator (including the ocean retracking), which provides

correction tables depending on significant waveheight and signal to noise ratio. The correction (x,y)

corresponding to a given significant waveheight x and a given signal to noise ratio y, will be computed by

bilinear interpolation of the corresponding correction table, i.e. by:

( )( ) ( )( )

( )( ) ( )( ))y,x(.

s.s

yyxx)y,x(.

s.s

yyxx

)y,x(.s.s

yyxx)y,x(.

s.s

yyxx)y,x(

nnyx

pppn

yx

np

npyx

pnpp

yx

nn

−−

+−−

+

−−

+−−

=

where:

• xp and xn are the abscissa just before and just after x, and sx is the corresponding step (xn - xp) • yp and yn are the abscissa just before and just after y, and sy is the corresponding step (yn - yp)

Be aware that the errors due to the low-pass filtering are not accounted for in the simulator aimed at

building the correction tables, because the waveforms from which the altimetric parameters are derived

in the retracking processing have already been corrected for these effects. Moreover, no mispointing

correction on the backscatter coefficient is accounted for (because mispointing is managed through the

retracking algorithm).

Computation of the corrections

The processing consists of a bilinear interpolation of the corresponding input correction tables versus the

significant waveheight and the signal to noise ratio. If the significant waveheight or the signal to noise

ratio values are out of range, then these values will be set to the appropriate minimum or maximum

authorized value.

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2.2.4 Comments

This algorithm is used for both LRM and SAR modes with tables dedicated to the mode.

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2.3 ALT_COR_GEN_02 - To compute the modeled instrumental corrections on

the retracked parameters (C-band)

2.3.1 Heritage


2.3.2 Function

To compute the modeled corrections of the instrumental errors on the altimetric estimates (altimeter

range, altimeter range rate, significant waveheight and backscatter coefficient - (auxiliary band), using

correction tables depending on significant waveheight and signal to noise ratio.


2.3.3.1 Input data


• Signal to noise ratio:

Signal to noise ratio and associated validity flag


Significant waveheight and associated validity flag

• Instrumental correction tables (SAD) (1):

Auxiliary band altimeter range correction tables Auxiliary band significant waveheight correction tables Auxiliary band backscatter coefficient correction tables


Default value for the inputs of the correction tables

2.3.3.2 Output data

• Auxiliary band altimeter range modeled instrumental correction

• Auxiliary band significant waveheight modeled instrumental correction

• Auxiliary band backscatter modeled instrumental coefficient correction

(1) Including features such as lower bound, upper bound and step for each input

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Principle

The imperfections of the altimeter components lead to errors on the altimetric estimates. To provide

accurate measurements, a complete knowledge of these errors (source and quantization of their effects)

is required.

The following errors are accounted for:

Errors of the on-board software Errors due to the low-pass filtering Errors due to the leakage spikes Errors due to the on-board FFT Errors due to the PTR

Nevertheless, the linearity of these errors is not obvious at all, and a separate correction for each effect

is probably not consistent with the instrument behavior. An integrated modeling of these errors is thus

necessary.

All these effects are accounted for in a simulator (including the ocean retracking), which provides

correction tables depending on significant waveheight and signal to noise ratio. The correction (x,y)

corresponding to a given significant waveheight x and a given signal to noise ratio y, will be computed by

bilinear interpolation of the corresponding correction table, i.e. by:

( )( ) ( )( )

( )( ) ( )( ))y,x(.

s.s

yyxx)y,x(.

s.s

yyxx

)y,x(.s.s

yyxx)y,x(.

s.s

yyxx)y,x(

nnyx

pppn

yx

np

npyx

pnpp

yx

nn

−−

+−−

+

−−

+−−

=

where:

• xp and xn are the abscissa just before and just after x, and sx is the corresponding step (xn - xp) • yp and yn are the abscissa just before and just after y, and sy is the corresponding step (yn - yp)

Be aware that the errors due to the low-pass filtering are not accounted for in the simulator aimed at

building the correction tables, because the waveforms from which the altimetric parameters are derived

in the retracking processing have already been corrected for these effects. Moreover, no mispointing

correction on the backscatter coefficient is accounted for (because mispointing is managed through the

retracking algorithm).

Computation of the corrections

The processing consists of a bilinear interpolation of the corresponding input correction tables versus the

significant waveheight and the signal to noise ratio. If the significant waveheight or the signal to noise

ratio values are out of range, then these values will be set to the appropriate minimum or maximum

authorized value.

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2.4 ALT_COR_MIS_01 - To compute the corrected squared mispointing angle

2.4.1 Heritage

Jason-1, Jason-2

2.4.2 Function

To compute the corrected squared mispointing angle (main band).


2.4.3.1 Input data


• Squared mispointing angle:

Retracked squared mispointing angle and associated validity flag


Squared mispointing modeled instrumental correction (main band)


Squared mispointing system bias

2.4.3.2 Output data

• Corrected retracked square of the mispointing angle


The modeled instrumental correction and system bias are added to the input squared mispointing angle.

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2.5 ALT_COR_RAN_01 - To compute the Doppler correction

2.5.1 Heritage

Jason-1 (Poseidon-2), Jason-2, ENVISAT

2.5.2 Function

To compute the Doppler corrections on the altimeter range.


2.5.3.1 Input data

• Orbit:

Orbital altitude rate


• Altimeter instrumental characterization data, i.e. for each band (Ku, C):

Emitted frequency Pulse duration Emitted bandwidth Sign of the slope of the transmitted chirp

2.5.3.2 Output data

• Ku-band Doppler correction

• C-band Doppler correction


For each band, the Doppler correction to be added to the altimeter range is computed by:

'h.B

T.f.hDoppler −=

where:

h' is the altitude rate f is the emitted frequency T is the pulse duration B is the emitted bandwidth

= 1 is the sign of the slope of the transmitted chirp

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2.5.4 Accuracy

Assuming instrumental features such as:

f = 13.575 GHz (Ku) and 5.41 GHz (C) B = 320 MHz (Ku) and 290 MHz (C)

T = 44.8 s

• An error of 0.1 mm on the Ku band Doppler correction will be reached for an orbital altitude rate error exceeding 5 cm/s for Ku band.

• An error of 0.1 mm on the C band Doppler correction will be reached for an orbital altitude rate error exceeding 12 cm/s.

2.5.5 Comments

In order to ensure the continuity of the Doppler correction whatever the surface type is, the altitude rate

involved in its expression originates from the orbit, and is not the tracker estimate or an estimate derived

from the altimeter range retracked estimates (e.g. slope of these estimates over 1 second, as it was done

for POSEIDON-1).

2.5.6 References

• Chelton D.B., Walsh E.J., and MacArthur J.L., 1989, Pulse compression and sea-level tracking in satellite altimetry, J. Atmos. Oceanic Technol., 6, 407-438.

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2.6 ALT_COR_RAN_02 - To compute the General Doppler Correction (all)

2.6.1 Heritage

ENVISAT, Cryosat-2

2.6.2 Function

This algorithm determines the generalised Doppler correction to range, due to the effects of the

spacecraft orbit and due to line of sight variations arising over sloping surfaces. This is known as the

generalised-Doppler range correction.


2.6.3.1 Input data

• Slope corrected latitude:

• Slope corrected longitude:

• Slope corrected height: h

• Orbit (DAD)

Values extracted via the CFI [CFI-S-01]

Position of the satellite in the ITER frame: P

Velocity of the satellite in the ITER frame: v

• Geophysical constants

Speed of light: c

• Altimeter instrumental characterization data

Wavelength: c

Chirp slope: cS

2.6.3.2 Output data

• General Doppler correction: generalD


• Calculate the line of sight vector from the spacecraft to the echoing point

• Using the CFI supplied functions, convert the echoing point coordinates from geodetic to Cartesian ITER reference frames

• Form the line of sight unit vector: l

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• Calculate the component of the spacecraft velocity in the line of sight vector

lvvs

•=

• Calculate the generalised Doppler correction:

cc

sgeneral

S

cvD

=

2.6.4 Accuracy

The correction due to the slope may have a magnitude of the same order as the line of sight correction.

The accuracy of the correction is dominated by the accuracy of the slope model, which is variable. The

orbit accuracy is a factor, but is negligible compared to that of the slope model.

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2.7 ALT_COR_RAN_03 - To compute the corrected retracked altimeter ranges

2.7.1 Heritage

Jason-1, Jason-2

2.7.2 Function

To compute the corrected retracked altimeter ranges (main and auxiliary bands).


2.7.3.1 Input data


• Altimeter range:

Retracked altimeter range and associated validity flag

• Instrumental corrections:

Doppler corrections on the altimeter range (computed at L1b and L2 levels) Modeled instrumental correction on the retracked altimeter range USO drift correction Internal path correction

• Platform data:

Distance antenna – COG


Altimeter range system bias

2.7.3.2 Output data

• Corrected retracked altimeter range



The L1b estimates of the retracked altimeter range are already corrected through the tracker range

estimates, for the USO frequency drift and the internal path correction. The three following corrections

are added:

• The modeled instrumental correction • The system bias • The distance antenna – COG

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In addition for both LRM and SAR modes, the Doppler correction corresponding to the L1b processing at

the measurement location is first removed from the altimeter range and the Doppler correction estimated

during the L2 processing (cf.ALT_COR_RAN_01 - To compute the Doppler correction) is then applied.

2.7.4 Comments

Given the relative slow variations of the orbit state vector within the temporal window of the SAR mode

multi-look (less than 3 seconds), we can assume that the orbital rate does not vary significantly along the

bursts in view from a reference surface location.

A variation of 0.1 mm on the Ku-band Doppler correction is reached when the orbital altitude rate varies

of about 5 cm/s, which is above the maximum variations of the orbital altitude rate observed within 1

second in past altimetry missions (around 4 cm/s for ENVISAT and 2.5 cm/s for Jason-2). This upper bound

of the variation in Doppler correction obtained for nadir-looking case (LRM) holds also for the multi-look

case (i.e., in SAR mode, when the projection of the orbital altitude rate on the steering direction is

applied).

Therefore, we can consider that the variations of the Doppler correction within the multi-look process will

not exceed 0.3 mm, which is in average low compared to the magnitude of this correction (e.g., +- 7 cm

for Jason-2).

It thus appears relevant to update the Doppler range correction in SAR mode with more accurate orbit

data at the reference surface location, which can be considered as an overall correction for all the bursts

contributing to the measurement.

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2.8 ALT_COR_RAN_04 - To compute the sea state biases

2.8.1 Heritage

TOPEX/Poseidon, ERS-1, ERS-2, Jason-1, Jason-2, ENVISAT

2.8.2 Function

To compute the sea state bias in the main and in the auxiliary frequency bands. The sea state bias is the

difference between the apparent sea level as "seen" by an altimeter and the actual mean sea level.


2.8.3.1 Input data


Significant waveheight (main band) Associated validity flag

• Wind speed:

Wind speed corrected for atmospheric attenuation (W)

• Sea state bias table (SAD)

2.8.3.2 Output data

• Sea state bias in main and in auxiliary bands


The SSB is bilinearly interpolated from a SAD table that is provided as a function of significant waveheight

(main band) and of wind speed, with same values for the main and the auxiliary bands.

2.8.4 Accuracy

The underlying physics of the sea state bias is not completely understood. The estimated global RMS

accuracy is about 2 cm.

2.8.5 References

• Gaspar, P., and J.P. Florens, 1998 : Estimation of the sea state bias in radar altimeter measurements of sea level : Results from a new nonparametric method.J. Geophys. Res, Vol 103, NO. C8, 15803-15814.

• Gaspar, P., and F. Ogor, 1996: Estimation and analysis of the Sea State Bias of the new ERS-1 and ERS-2 altimetric data (OPR version 6). Report of task 2 of IFREMER Contract n° 96/2.246002/C.

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2.9 ALT_COR_RAN_05 - To compute the dual-frequency ionospheric

corrections

2.9.1 Heritage

Jason 1, Jason 2, ENVISAT

2.9.2 Function

To combine the altimeter ranges in the main and auxiliary frequency bands, so as to derive the main band

ionospheric correction and the auxiliary band ionospheric correction. The altimeter ranges are first

corrected for sea state bias before being combined.


2.9.3.1 Input data

• Altimeter range:

Corrected altimeter range (main and auxiliary bands) Associated validity flag (main and auxiliary bands)

• Sea state bias:

Sea state bias correction (main and auxiliary bands)

• Altimeter instrumental characterization data:

Main and auxiliary band emitted frequencies

2.9.3.2 Output data

• Ionospheric correction (main and auxiliary bands)


The following formulae assume input parameters in mm.

The main band and auxiliary band sea state bias corrections are first added to the input main band and

auxiliary band altimeter ranges to correct them, because these corrections may be different for the two

frequencies. Let RMain and RAux be the corresponding corrected values.

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

Main_Alt_IonoRR Main += , uxIono_Alt_ARR Aux +=

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where the ionospheric corrections Iono_alt_Main and Iono_alt_Aux are obtained (in mm) by using the

first order expansion of the refraction index:

2Main_f

TEC.40300Main_Alt_Iono −= (Main band)

2Aux_f

TEC.40300Aux_Alt_Iono −= (Auxiliary band)

where f_Main and f_Aux are the emitted frequencies (in Hz), and where TEC is the columnar total electron

content of the ionosphere, expressed in electrons/m2.

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

( )( )AuxMainAux

AuxMainKu

RR.fAux_Alt_Iono

RR.fMain_Alt_Iono

−=

−=

with: 22

2

MainAux_fMain_f

Aux_ff

−= and

22

2

AuxAux_fMain_f

Main_ff

−=

For LRM mode, the algorithm is run from 20-Hz Ku- and C- band altimeter estimates.

For SAR mode, it is run from 20-Hz Ku-band altimeter estimates and 20-Hz C-band filtered estimates

(computed by linear regression of 1-Hz related estimates, at the Ku-band time tag).

2.9.4 Comments

The total electron content, TEC_Alt, is output in e-/m2.

In SAR mode, the input auxiliary band range is an interpolated value computed at the time tag of the main

band measurement.

A flag must be provided in the L2 product to indicate the validity of the ionospheric correction depending

of the overflown surface (e.g. invalid estimate over ice surfaces).

2.9.5 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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2.10 ALT_COR_RAN_06 – To calculate the applicable set of corrections (LRM Ice;

SAR Sea-Ice, Margin)

2.10.1 Heritage

CryoSat-2

2.10.2 Function

A single corrections value is created by summing all of the applicable meteorological and geophysical

corrections. The snow depth, sea-ice concentration and snow density values are also computed.


2.10.3.1 Input data

• Corrections

GIM Ionospheric Correction (IONO) Inverse Barometric (IB) Ocean Tide (OT) Loading Tide (OLT) Solid Earth Tide (SET) Polar Tide (PT) Model Wet Tropospheric (WET) Model Dry Tropospheric (DRY)

• Corrections status flags

• Application flags and model choices

• Surface type

• Auxiliary Data Files:

Snow Depth climatology Sea-ice concentration file

2.10.3.2 Output data

• Corrections

• Snow depth

• Sea-ice concentration

• Snow density

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Corrections

• Select an ocean tide model (GOT or FES) based on PCONF flag

• Form the summed correction as :

Ocean or Sea-Ice : DRY + WET + IB + IONO + OT + OLT + SET + PT Land : DRY + WET + IONO + OLT + SET + PT Extract snow depth and sea-ice concentration from aux

files with bilinear interpolation

Note that the Mog2d is not appropriate over these surfaces and the radiometer wet correction is not

available.

Snow depth, sea-ice concentration and snow density

Snow depth and sea-ice concentration are computed by bilinear interpolation from the corresponding

auxiliary files.

Snow density is currently passed through from a default configuration parameter. This is done to allow a

future possible update to use a climatology file.

2.10.4 Comments

If corrections values are bad, zero should be passed in. Note that individual corrections can be omitted by

use of the Boolean configuration parameters.

Regarding the sea-ice concentration auxiliary data, either a static input (climatology files) or a dynamic

input are possible for the computation. The algorithm performs the choice of the data source to use,

considering that the dynamic data is to be used if present in input and the static solution (climatology

files) is selected in case of absence of dynamic input.

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2.11 ALT_COR_RAN_07 - To compute the filtered ionospheric correction

2.11.1 Heritage

ENVISAT

2.11.2 Function

To compute a filtered ionospheric correction from a main-band altimeter-derived ionospheric correction

using an iterative process based on median and Lanczos filtering.


2.11.3.1 Input data

• Time-tags (internal source)

• Locations (internal source):

− Latitudes

− Longitudes

• Altimeter-derived ionospheric corrections for main band (internal source)

• On-ground retracked range parameter (internal source)s:

− Standard deviation of the measurements

− Number of valid estimates

• Ocean/Sea-ice flags

• Processing parameters (SAD)

• Universal constants (SAD)


• Filtered altimeter-derived ionospheric corrections for main band

• Filtered altimeter-derived ionospheric corrections validity flags


An iterative filtering method in two steps is applied on a set of data over ocean with a preliminary

selection on surface type and on range standard deviation.

The first step of the iterative process (filtering) consists in the application of a median filter and a

Lanczos filter.

The second step of the iterative process consists in a selection of filtered data based on differences

between filtered and not filtered data. The filtered data which difference with non filtered value is not

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included in a range of [-3σ,3σ] are rejected, σ corresponding to the global standard deviation of

filtered/not filtered difference values.

If values are rejected, a new iteration of these two steps is performed on the new set of selected values.

The process ends when no more value is rejected on the selection criteria.

An interpolation by spline is then performed wherever the ionospheric correction is not defined

(considering a limited number of missing points). The filtered correction is thus defined for each

measurement of the input dataset.

2.11.4 Accuracy

N/A

2.11.5 Comments

None.

2.11.6 References

• M. Ablain, JF.Legeais: SLOOP Tache 2.4 : Amélioration du filtrage de la correction ionosphérique bifréquence, CLS-DOS-NT-10-0098 / SALP-NT-P-EA-21834-CLS, 07/06/2010

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2.12 ALT_COR_SWH_01 - To compute the corrected retracked significant

waveheights

2.12.1 Heritage

Jason-1, Jason-2

2.12.2 Function

To compute the corrected retracked significant waveheights (main and auxiliary bands).


2.12.3.1 Input data


Significant waveheight: Retracked significant waveheight and associated validity flag


Significant waveheight modeled instrumental correction


Significant waveheight system bias


• Corrected retracked significant waveheight



The two following corrections are added to the input significant waveheights:

• The modeled instrumental correction • The system bias

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2.13 ALT_MAN_INT_01 – To perform short-arc along-track interpolation

2.13.1 Heritage

CryoSat-2

2.13.2 Function

An estimation of the height of the sea surface that would be present in the absence of sea ice is

performed.

This algorithm needs continuous data i.e. from across the Arctic. Therefore, as an input to this processor

we need data that is either not partitioned at the pole or multiple datasets to provide continuity. The

current design of the PDS means that data is partitioned at the pole and data is processed one file at a

time. In this situation, extrapolation as well as interpolation should be used to compute the interpolated

sea-surface height anomaly.


2.13.3.1 Input data

• For all records

Sea surface height anomaly: shah

Surface type: surfd

Timestamp of the records: 𝑡𝑟𝑒𝑐 Flags

• For the current record

Timestamp of the current record: t

• Processing parameters:

Maximum interpolation time delta from current time: ir

Maximum absolute value of SHA: ℎ𝑚𝑎𝑥


• Interpolated sea-surface height anomaly: shah


• For each record, select those records that are of ocean type and which have a timestamp within the interpolation delta of the timestamp of the current record, and form arrays:

1N:0h isha − surface height anomaly

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1N:0t isha − timestamp

where iN is the count of records found and skipping the current record if this value is too small.

• Perform a linear fit to the selected records

=i

shai

sha itN

1t

=i

shai

sha ihN

1h

( )

( )

+

−

=

i

2i

2sha

i

shashaisha

1tNit

htNit

b

sha1sha0 tbhb −=

• Sample the fitted function at the current location and assign the result as the sea-surface height anomaly at this location:

( ) tbbth 10sha −=

2.13.4 Comments

When implementing the fitting routine for this module ensure that the method of implementing the

algorithm chosen is free from patents or licensing requirements that conflict with project requirements.

2.13.5 References

• Numerical Recipes in C: The Art of Scientific Computing, 2nd Edition. William H. Press, et.al. fit() Section 15.2

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2.14 ALT_MAN_TIM_01 – To compute 1-Hz time tags

2.14.1 Heritage

None

2.14.2 Function

To build the averaged measurements from sets of continuous elementary measurements and to compute

their time-tags.


2.14.3.1 Input data

• For each elementary measurement (LRM mode, SAR mode Ku-band, SAR mode C-band):

Time tag {ti}

• Processing parameter (SAD):

Duration of the averaged measurement (t)


• For each averaged measurement:

Time tag Operating mode (LRM, SAR, LRM and SAR) Number of elementary measurements in the averaged measurement (for each frequency band)

• For each elementary measurement:

Index of the associated averaged measurement


The averaged (so-called 1-Hz) measurements time-tags are built from the reference time (01-01-2000 0h)

an a duration (t, processing parameter close to 1 second) as shown in the figure below. This strategy is

used to guarantee a single definition of the 1-Hz measurements, independent of the existing elementary

(so-called 20-Hz) measurements, avoiding thus a change of 1-Hz datation in case of reprocessing (e.g. NRT

processing from a given data set vs STC processing with additional measurements , …).

The 20-Hz measurements (time tags ti) belonging to a given 1-Hz measurement (time-tag T) are the

measurements such as :2

tTt

2

tT i

+

− .

The number of 20-Hz measurements per 1-Hz measurement is computed, and an operating mode (LRM,

SAR or both modes) is associated to each 1-Hz measurement.

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The possible gaps of elementary measurements within the data set, leading to empty 1-Hz measurements

are managed.

20-Hz meas.

Origin Time

1-Hz meas.

k.t t t

LRM Operating Mode SAR Operating Mode

Time

20-Hz Ku-band measurements in LRM operating mode

20-Hz Ku-band measurements in SAR operating mode

20-Hz C-band measurements in SAR operating mode

1-Hz measurements

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2.15 ALT_MAN_WAV_02 – To discriminate waveforms

2.15.1 Heritage

CryoSat-2

2.15.2 Function

Records must be assigned a surface type classification based upon the record contents. This enables

surface type specific processing to occur later in the algorithm chain.


2.15.3.1 Input data

• Power waveform: binsN:1P

• Beam behaviour parameters: bbN:1

• Processing parameters

Min/max bounds for each classification metric for each surface type:

surfmetricsmaxsurfmetricsmin N:1N:1M,N:1N:1M

• Sea-ice concentration for the current location and time

This is used as one of the classification metrics for the current location. The dataset is indexed for the current location via a CFI call.


• Surface type classification: surfd

Open ocean Sea-ice Lead Unclassified


• Form a classification vector of classification metrics metricsN:1M from the results of applying a set of

classification functions to the values within the record and the values from auxiliary datasets.

Current metrics are:

Waveform peakiness (from power waveform)

Sea-ice concentration

The list of metrics is to be updated following CryoSat-2 commissioning.

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• Determine whether this classification vector falls within one of a set of surfN non-overlapping regions

within an metricsN -dimensional classification space

If it does, assign the surface type represented by that region to the record If it does not, assign the ‘unclassified’ type to that record The regions are defined as boxes with their minimum and maximum extent in each dimension found

from surfmetricsmaxsurfmetricsmin N:1N:1M,N:1N:1M

2.15.4 Accuracy

The accuracy of this algorithm is dependent on post-launch commissioning with actual data. The

boundaries for the parameters must be adjusted to remove records for which the surface height does not

represent the sea surface (i.e. those containing sea-ice) from the set of records that are interpolated

during the short arc interpolation.

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2.16 ALT_PHY_BAC_01 - To compute the retracked backscatter coefficients

2.16.1 Heritage

Jason-1, ENVISAT, Jason-2

2.16.2 Function

For each elementary measurement, to compute the retracked estimates of the backscatter coefficient

(main and auxiliary bands).


2.16.3.1 Input data

• Scaling factor:

Scaling factor for sigma0 evaluation (corrected in level 1b processing)

• Retracking outputs (amplitude):

Amplitude Execution flag (valid / invalid)


• Backscatter coefficient and associated validity flag


For each elementary measurement in both bands, the backscatter coefficient is computed as follows,

where Pu represents the amplitude estimate output by the retracking algorithm and where Kcal is the

scaling factor for Sigma0 evaluation.

)P(log.10K u10cal0 +=

The validity of the retracked backscatter coefficients is determined from the retracking execution flags.

Default values are provided in case of invalidity of the retracked backscatter coefficient estimates.

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2.17 ALT_PHY_BAC_02 - To compute the backscatter coefficient (SAR, Sea-Ice,

Margin)

2.17.1 Heritage

CryoSat-2

2.17.2 Function

To calculate the backscatter value for the surface, 0 .

We start with the baseline for this algorithm as described below. However, a new study about to start

with ESA for CryoSat-2 will produce a new method for this algorithm that we intend to use later.


2.17.3.1 Input data

• Retracked waveform power estimate: fitP

• Scaling factor from L1b: Kcal


Linear bias: refb

Multiplicative bias: refa


• Backscatter: 0


Backscatter is :

( ) refreffit100 baPlog10 −= + Kcal

2.17.4 Accuracy

The accuracy of the backscatter value derived here is primarily dependant on the accuracy of the scaling

factor computed at L1. The two scaling parameters provide an ability to tune the computation during

commissioning.

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2.17.5 Comments

The issue with calculating the backscatter in SAR mode is that the waveform shape is different and

therefore retrackers will give a different value for backscatter. The output of the study mention above for

CryoSat will be a new method of calculating amplitude which can be inserted into the SAR chain upstream

of this algorithm, without requiring modification of this algorithm.

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2.18 ALT_PHY_BAC_03 - To compute the backscatter coefficient (LRM, Ice)

2.18.1 Heritage

CryoSat-2

2.18.2 Function

To calculate the backscatter value for the surface 0 .


2.18.3.1 Input data

• Retracked waveform power estimate: fitP

• Scaling factor from L1b: Kcal


Linear bias: refb

Multiplicative bias: refa


• Backscatter: 0


Backscatter is :

( ) refreffit100 baPlog10 −= + Kcal

2.18.4 Accuracy

The accuracy of the backscatter value derived here is primarily dependant on the accuracy of the scaling

factor computed at L1. The two scaling parameters provide an ability to tune the computation during

commissioning.

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2.19 ALT_PHY_GEN_01 - To compute the elevation and location of echoing

points (LRM, Ice ; SAR, Margin)

2.19.1 Heritage

ENVISAT, CryoSat-2.

2.19.2 Function

The corrected echo direction and range are used to compute the height, latitude and longitude of the

actual echoing point.


2.19.3.1 Input data

• Uncorrected latitude: 0

• Uncorrected longitude: 0

• Range estimate from retracker: R

• Echo position altitude ( ) and azimuth ( )

• Meridional radius of curvature of the ellipsoid 0

• Radius of parallel circle at geodetic latitude 0


• Slope corrected latitude:

• Slope corrected longitude:

• Slope corrected height: h


0

cossinR0

+=

0

sinsinR0

+=

( )

+−=

2

sinRcosRhh

2

e

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2.19.4 Accuracy

It is unusual to calculate an elevation at Level 2, as this is normally left up to the user, as he or she will

correct the range with a mixture of atmospheric and geophysical corrections appropriate to an

application, before determining the elevation. However, the transformation equations in this algorithm

are linear to a good approximation with respect to constant offsets applied to range. Within the range of

correction values likely to be encountered, the position is unaffected to better than microdegree accuracy,

and the range corrections (applied in the correct sense) can be applied to elevation a-posteriori, with error

less than 1 mm.

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2.20 ALT_PHY_GEN_02 - To compute the rain flag

2.20.1 Heritage

ENVISAT

2.20.2 Function

To compute a 6-states rain flag (“no rain”, “rain”, “high rain probability from altimeter”, “high probability

of no rain from altimeter”, ” ambiguous situation (possibility of ice)” or “evaluation not possible”) from

main and auxiliary bands altimeter backscatter coefficients.

2.20.3 Algorithm definition

2.20.3.1 Input data

• Location:

Latitude of the altimeter measurement


Corrected backscatter coefficient (main and auxiliary bands) Associated validity flag (main and auxiliary bands)

• Integrated liquid water content

• Altimeter surface type

• Radiometer interpolation quality flag

• Table providing, for an input value of auxiliary band backscatter coefficient, the expected main band backscatter coefficient with its associated uncertainty (SAD)



• Rain flag

• Rain attenuation


The rain flag, initialized to “evaluation not possible”, is updated if both altimeter and radiometer data are

available, if both main and auxiliary bands backscatter coefficients are valid and positive, and if the

altimeter surface type is set to “open ocean or semi-enclosed seas” or to “enclosed seas or lakes”.

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This update is determined from the expected main band backscatter coefficient and its associated

uncertainty which are computed by linear interpolation in the input table, as function of the auxiliary band

backscatter coefficient:

• If the interpolation of radiometer data to the altimeter measurement failed, then:

If the rain attenuation – i.e. the difference between the expected main band backscatter coefficient and the measured main band backscatter coefficient - exceeds a threshold (which depends on the uncertainty in the expected main band backscatter coefficient), then the rain flag is set to “high rain probability from altimeter”

Else, the rain flag is set to to “high probability of no rain from altimeter”

• Else if the rain attenuation exceeds the above-mentionned threshold and if the integrated liquid water content from the radiometer exceeds some given threshold, then:

If the latitude exceeds a given threshold, then the rain flag is set to “ambiguous situation” Else, the rain flag is set to “rain”

• Else, the rain flag is set to “no rain”

The input main and auxiliary bands backscatter coefficients to be used are not corrected for atmospheric

attenuation.

2.20.4 Accuracy

See “References”.

2.20.5 Comments

For ENVISAT, initial values for Rain_Coef, Rain_Cloud_Liq and Rain_Delta_Sigma0 are 1.8, 0.2 kg/m2 and

0.5 dB respectively.

2.20.6 References

• ENVISAT RA-2 & MWR Product and Algorithm evolution studies -WPs 3100/3200/3300 report CLS-DOS-NT-07-042, V1.2

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2.21 ALT_PHY_GEN_03 - To compute the rain rate

2.21.1 Heritage

None

2.21.2 Function

To compute the rain rate.


2.21.3.1 Input data

• Datation:

Altimeter time-tag (1 Hz)

• Location:

Latitude of the altimeter measurement (1 Hz) Longitude of the altimeter measurement (1 Hz)

• Rain flag

• Rain attenuation

• Brightness temperatures (interpolated at altimeter time tags):

23.8 GHz brightness temperature (1 Hz) 36.5 GHz brightness temperature (1 Hz)



• Auxiliary data tables (SAD)


• Rain rate


For each sample indicated as rainy by the rain flag, the freezing level (FL) is inferred by the inversion of

the radiometer brightness temperatures or from seasonal maps of FL, if the inversion process fails. The

rain rate is then computed from the FL and attenuation using the Marshal-Palmer relation [1948]:

RR = ( ) b/10 aFL2/

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a and b are frequency-dependent coefficients and whose values are a = 0.02038 dB.km-1 and b = 1.203

[Quartly et al, 1999]. Comparison of Topex, Jason-1 and ENVISAT dual-frequency rain rate estimates by

[Tournadre 2006] showed that ENVISAT overestimated low rain rates. Therefore, the rain rate value is

corrected with an inter-calibration relation with Jason-1 rain rate estimates that significantly reduces the

differences between the mean annual rain rate computed from ENVISAT and those from both Topex and

Jason-1 missions.

2.21.4 Accuracy


2.21.5 References

• Marshall J. and W. M. Palmer, 1948: The distribution of rain-drops with size. J. Meteor., 5, 165-166.

• Quartly, G.D., M.A. Srokosz, and T.H. Guymer, 1999: Global precipitation statistics from dual-frequency TOPEX altimetry. J. Geophys. Res., 104, 31489-31516.

• Tournadre J., 2006: Improved level-3 oceanic rainfall retrieval from dual-frequency spaceborne radar altimeter systems, J. Atmos. Oceanic Technol., 23, 1131-1149.

• Tran N., J. Tournadre and P. Féménias, Validation of ENVISAT rain detection and rain rate estimates by comparing with TRMM data, IEEE GRS letters, doi:10.1109/LGRS.2008. 2002043, 5 (4), 658-662, 2008.

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2.22 ALT_PHY_RAN_01 - To compute the retracked altimeter ranges

2.22.1 Heritage

Jason-1, Jason-2, ENVISAT

2.22.2 Function

For each elementary measurement, to compute the retracked estimates of the altimeter range (main and

auxiliary bands).


2.22.3.1 Input data

• Tracker range:

Tracker range (corrected in the level 1b processing)

• Retracking outputs:

Epoch Execution flag (valid / invalid)

• Universal constants (SAD):

Light velocity


• Altimeter range and associated validity flag


For each elementary measurement in main and auxiliary bands, the altimeter range is as follows, where

ht represents the input tracker range and where is the epoch estimate output by the retracking

algorithm.

+= thh

The validity of the retracked altimeter ranges is determined from the retracking execution flags. Default

values are provided in case of invalidity of the retracked altimeter range estimates.

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2.23 ALT_PHY_RAN_02 – To compute the surface height anomaly (SAR, Sea-Ice)

2.23.1 Heritage

CryoSat-2

2.23.2 Function

Provide a surface height anomaly relative to the mean sea surface and corrected for retracker height error

and other effects.


2.23.3.1 Input data

• Platform altitude: eh

• Range corrected for fitting retracker: fitR

• Mean sea surface: MSSh


• Surface height: h

• Sea surface height anomaly: shah


• The surface height is calculated as :

fite Rhh −=

• This gives the surface height anomaly :

MSSsha hhh −=

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2.24 ALT_PHY_RAN_03 – To compute the freeboard

2.24.1 Heritage

CryoSat-2

2.24.2 Function

For records identified as containing sea-ice, the difference between the calculated height and estimated

sea-surface is taken and used to estimate the freeboard.


2.24.3.1 Input data

• Surface height: h

• Interpolated sea-surface height anomaly: shah

• Discriminated surface type: surfd


• Ice freeboard: frebh

• In the case where freeboard is not computed, it will be set to the appropriate fill value in the L2 product.


For records discriminated as sea-ice, calculate freeboard shafreb hhh −= i.e. the difference between the

measured surface height and the expected sea-surface height at this location.

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2.25 ALT_PHY_SNR_01 - To compute the SNR from the estimates of the

amplitude and of the thermal noise level of the waveforms

2.25.1 Heritage


2.25.2 Function

To compute the signal to noise ratio (main and auxiliary bands) from the estimates of the amplitude and

of the thermal noise level of the waveforms.


2.25.3.1 Input data


• AGC:

Corrected AGC: AGCc

• Retracking outputs (power):

Amplitude of the waveforms (Pu ) and associated validity flag Thermal noise level of the waveforms (Pn) and associated validity flag


Minimum value of AGC requested to set SNR to AGC in case of null thermal noise: AGCmin Bias between SNR and AGC: Bias


• Signal to noise ratio


For each band, the signal to noise ratio is computed by:

=

n

u10

P

Plog.10SNR

The input validity flags are managed. Moreover, if the thermal noise level is set to 0, the signal to noise

ratio is set to AGCc + Bias (if AGCc exceeds a threshold, AGCmin), or otherwise to Pu (in dB) (i.e. that Pn is set

to the amplitude resolution of the analysis window).

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2.25.4 Accuracy

The signal to noise ratio is requested in the level 2 processing to access the modeled instrumental

corrections tables. Its value is derived from the estimates of amplitudes of the waveform provided by the

ocean retracking algorithm (the thermal noise level Pn is derived from an averaging of samples of the first

plateau, while the amplitude Pu is derived from a fit of the waveform with a mean return power model).

This parameter is thus consistent with the one used in the simulator to build the corrections tables.

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2.26 ALT_PHY_SWH_01 - To compute SWH from the retracked composite Sigma

2.26.1 Heritage

Jason-1, ENVISAT, Jason-2

2.26.2 Function

For each elementary measurement, to derive the estimates of the significant waveheight (main and

auxiliary bands) from the retracked estimates of the composite Sigma.


2.26.3.1 Input data


• Retracking outputs (composite Sigma):

Composite Sigma Execution flag (valid / invalid)


Sampling interval of the analysis window Ratio between the PTR width and the sampling interval of the analysis window


Light velocity


• Significant waveheight and associated validity flag


For each elementary measurement in main and auxiliary bands, the significant waveheight SWH is

computed as follows:

2p

2c.c2SWH −=

where:

c is the composite Sigma (expressed in time units)

p is the PTR width (expressed in time units) c is the light velocity

The validity of the significant waveheights is determined from the retracking execution flags.

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2.26.4 Comments

• SWH will be set to 0 when the argument of the square root is negative.

• The averaged significant waveheight is derived from the averaged value of c, while the standard deviation of the significant waveheight is derived from the elementary estimates of the significant waveheight.

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2.27 ALT_PHY_WIN_01 - To correct the backscatter coefficients for atmospheric

attenuation and to compute the 10 meter altimeter wind speed

2.27.1 Heritage

GEOSAT, TOPEX/POSEIDON, ERS-1, ERS-2, ENVISAT

2.27.2 Function

To correct the backscatter coefficients (Ku and C bands) for atmospheric attenuation and to compute the

altimeter wind speed from the corrected Ku-band backscatter coefficient.


2.27.3.1 Input data


Ku-band ocean backscatter coefficient C-band ocean backscatter coefficient Ku-band ocean backscatter coefficient validity flag C-band ocean backscatter coefficient validity flag

• Atmospheric attenuation:

Ku-band backscatter coefficient atmospheric attenuation C-band backscatter coefficient atmospheric attenuation

• Backscatter coefficient to wind speed conversion (SAD, look-up tables: one for LRM mode and one for SAR mode)


• Backscatter coefficients (both bands) corrected for atmospheric attenuation

• Wind speed corrected for atmospheric attenuation


First, atmospheric attenuation is added to the backscatter coefficient to correct it (in both bands). Then

the wind speed is computed (in m/s) from a model depending on the Ku-band corrected backscatter

coefficient.

2.27.4 Accuracy

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

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2.27.5 References

• Abdala, S., Ku-band radar altimeter surface wind speed algorithm, European Space Agency, (Special Publication) ESA SP, 2007.

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2.28 ALT_RET_ICE_01 – To perform the ice-1 (OCOG) retracking (SAR sea-ice,

margin ; LRM ice)

2.28.1 Heritage

ENVISAT, CryoSat-2.

2.28.2 Function

A standard OCOG retracking is performed on the power waveform.

The OCOG retracking method is the same for all forms of this algorithm, however the processing

parameters may be tuned independently. This tuning is performed by loading a set of processing

parameters that are appropriate to the mode and surface type.


2.28.3.1 Input data

• Power waveform: 1N:0P s −

• trR tracker range from L1b

• CoG correction CoGd


bind size of a range window bin in metres

TPi nominal tracking point

First_bin first gate to consider in the window Last_bin last gate to consider in the window


• OCOG Retracker range correction : OCOGR

• OCOG Retracker range estimate : OCOGR

• OCOG Retracker power estimate : OCOGP

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• Calculate OCOG amplitude as

−

=

−

==1N

0i

2

1N

0i

4

OCOGs

s

]i[P

]i[P

P

• Search the power waveform array to locate the index of first bin containing more power than OCOGP as

0i

• Calculate OCOG retrack bin : ( )

1iPiP

1iPP1ii

00

0OCOG0OCOG

−−

−−+−=

• The OCOG range correction is : ( ) binTPOCOGOCOG diiR −=

• Calculate the OCOG corrected range as : 𝑅𝑂𝐶𝑂𝐺 = 𝑅𝑡𝑟 + 𝛿𝑅𝑂𝐶𝑂𝐺 + 𝑑𝐶𝑜𝐺 +𝑐𝑡𝐹𝐹𝑇

2𝐹𝑖𝑟𝑠𝑡_𝑏𝑖𝑛

2.28.4 Accuracy

The waveform samples are quantised in FFT power units. It is very difficult to predict the extrema of the

actual range of values that will be present in the filter bank. However, the filters are short integers. This

means that potentially at least, the accumulated squares and fourth powers can get extremely large, 322128 & 642128 respectively for Ku band. Hence, care must be taken to prevent wraparound. The

implementation must also preserve tracker offset precision to its theoretical maximum (i.e. consistent

with the on board tracking precision).

2.28.5 References

• Bamber J. L. : “Ice sheet altimeter processing scheme”, International Journal of Remote Sensing, 15(4), pp 925-938, 1994.

• Wingham, D. J., Rapley, C. G., & Griffiths, H. (1986). New techniques in satellite altimeter tracking systems. Proceedings of IGARSS’86 Symposium, Zu ̈rich, 8–11 Sept. 1986, Ref. ESA SP-254 (pp. 1339–1344)

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2.29 ALT_RET_ICE_02 - To perform the ice-2 retracking (LRM)

2.29.1 Heritage

ENVISAT, Jason-2

2.29.2 Function

To perform the ice-2 retracking (the so-called ice_erf algorithm) on the waveforms.


2.29.3.1 Input data

• Altimeter configuration data and quality information

• Waveform:

Waveform (128 FFT samples for Ku and C bands)


Altimeter instrumental characterization data for the preparation of data for the ice-2 retracking Sampling interval of the analysis window



Light velocity


For each band, the following 20-Hz parameters:

• Epoch or "range offset":

• Width of the leading edge: L

• Amplitude: Pu

• Mean amplitude: Pt

• Thermal noise level: Pn

• 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 (Ku band only)


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• Mean quadratic error between the normalized waveform and its model

• Quality information, such as an execution flag (valid / invalid)


The ice-2 retracking algorithm is performed on the Ku and on the C band waveforms. The only difference

in the retracking of Ku and C waveforms is the processed data (waveform, processing and instrumental

parameters). A single description is thus given below.

Background

The ice-2 retracking algorithm is based on the ENVISAT RA-2 ice-2 retracking. The aim of the ice-2

retracking algorithm is to make the measured waveform coincide with a return power model, according

to Least Square estimators.

The expression of the return power as a function of time is given Brown (Brown, 1977):

( ) nTL

u Pt.sexp.t

erf1.2

P)t(Vm +−

−+= (with:

−

=

x

0

t dte.2

)x(erf2

)

where the parameters to be estimated are:

: the epoch

L : 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 and main steps of the processing

The basic principle and the main steps of the processing are defined hereafter.

• Identification of the waveform validity:

The validity of the waveform is determined from the input waveform quality information. The

retracking is then performed only if the input waveform is valid.

• Waveform normalization and leading edge identification:

Depending on the option for thermal noise determination (processing parameter), the thermal noise

level (Pn) 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).

Pn is removed from the waveform samples which is then normalized (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 (, L):

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A coarse estimation of the epoch () of the waveform in the estimation window and of the width of

the leading edge (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 minimize the

residual in the estimation window, between the normalized waveform and the corresponding model.

For each possible value of (corresponding to a position varying between the beginning and the end

of the estimation window, with a predefined step) and of L (varying between two thresholds, with a

predefined step):

The normalized model (Vmn) is computed in the estimation window The amplitude Pu of the normalized waveform is estimated by minimizing the mean quadratic error

between the normalized waveform (Vn) and the weighted normalized model (Pu.Vmn) in the estimation window (linear regression between the waveform and the normalized 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

• Fine estimation stage (, L, Pu):

A fine estimation of , L and Pu (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 and L correspond to a position and a width, centered 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 logarithm of the trailing edge (sT1, sT2):

The estimation of the slope of the logarithm of the trailing edge is intentionally fully decorrelated from

the estimation of the other parameters (, L, Pu), 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, 1997), and of course instrumental features

(e.g. antenna). The slope is estimated by linear regression of the logarithm of the normalized waveform

samples in two windows part of the trailing edge: the first one (sT1) just after the end of the leading

edge with a predefined width, and the second one (sT2) 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.

For Ku band, a third slope (sT1m) is estimated as sT1, with an other predefined width aimed at pointing

out a mispointing angle over ocean surfaces.

• Estimation of the mean amplitude (Pt):

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.

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

denormalized, etc.)

2.29.4 Comments

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

2.29.5 References

• "Etude du retracking des formes d'ondes altimétriques au dessus des calottes polaires", CNES report, CT/ED/TU/UD/96.188, CNES contract 856/2/95/CNES/0060, B. Legresy, 1995.

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

• Legresy and F. Remy: "Surface characteristics of the Antarctic ice sheet and altimetric observates", UMR5566 / GRGS (CNES-CNRS), J. of Glacio, 43 (144), 265-275, 1997.

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2.30 ALT_RET_ICE_03 – To perform the “function fit” retracking (SAR, Sea-Ice)

2.30.1 Heritage

CryoSat-2

2.30.2 Function

The power waveform is retracked by fitting a function that models the expected power return to the

waveform.

The retracking method is the same for both the sea-ice and ice-sheet forms of this algorithm, however

the processing parameters may be tuned independently.


2.30.3.1 Input data




• Applicable geophysical and meteorological corrections C




Initialisation values for function parameters (may be static from configuration files or dynamic from

prior waveform QA or OCOG retracking): 1N:0 −

Amplitude 0a0 =

Tracking point 1t0 = ( fiti when expressed in bins)

Sigma of Gaussian 2=

Exponential 3k =

iterN maximum number of iterations to perform

2finish stop iterating if the fit converges to this level

iterr stop iterating if the improvement in the fit is less that this ratio

stuckN stop iterating if the fit does not improve for this many consecutive iterations


• Final (fitted) value of function parameters: 1N:0 −

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• Retracker waveform power estimate: fitP

• Retracker range correction: fitR

• Retracker range estimate: fitR

• Retracker quality measurement: 2fit


• Fit ( ) ( )= ,tftP by non-linear least-squares method (Levenberg-Marquard).

The fitted function ( ),tf is a three-part piecewise function:

Leading edge ( )

20tt

01 ea,tf

−−

=

Linking function ( )

( )( )

( )( ) ( )

2

02

0b

302

b

tt1

ttct2

c4k5tt

ct2

c2k3

02 ea,tf

−

+−

+−−−

−−−

= , where

2b kt =

bktc =

Trailing edge ( ) ( )0ttk03 ea,tf −−=

( )

tt

ttt

tt

for

for

for

)t(P

)t(P

)t(P

tP

b

b0

0

3

2

1

= (note that 0t and bt are defined above)

• The range correction for the fitted retracker is

( ) binTPfitfit diiR −=

• The range corrected for the fitted retracker is CoGfittrfit dCRRR +++=

2.30.4 Comments



Note that the use of a waveform model renders this algorithm applicable only to Ku-band.

2.30.5 References

Numerical Recipes in C: The Art of Scientific Computing, 2nd Edition. William H. Press, et.al. mrqmin()

Section 15.5

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2.31 ALT_RET_ICE_04 - To merge MLE4 results into the ice chain (LRM Ice)

2.31.1 Heritage

2.31.2 Function

Usage of the CryoSat retracker CFI has been removed as the software is no longer supported. The

functionality will be replaced by using the results of the MLE4 retracker (which are read from the input L2

file). This algorithm now simply maps the MLE4 results onto the variables previously filled by the CFI

retracker.

The processing is described below.

2.31.2.1 Input data




• MLE4 retracking ‘epoch’: 4MLER

• MLE4 power estimate: 4MLEP


• MLE4 Retracker range estimate: CFIR

• MLE4 power estimate: CFIP


Calculate the MLE4 corrected range as :

CoG4MLEtrCFI dCRRR +++=

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2.32 ALT_RET_ICE_05 - To perform the SAR ice-margin WW retracking (SAR ice

sheets)

2.32.1 Heritage

CryoSat-2.

2.32.2 Function

A model of the SAR mode waveform is fitted to the received power. The amplitude and retracking offset

are derived from analysis of the fitted waveform. The method is that used for waveforms received in the

SARin degraded case for CryoSat where the phase and coherence information is unavailable.


2.32.3.1 Input data









• WW Retracker range correction: WWR

• WW Retracker range estimate: WWR

• WW Retracker power estimate: WWP


The retracking algorithm has been designed to exploit least squares fitting of a semi-analytical model of

the echo. The echo model is a modified gaussian of the form:

( ) ( )tfaetP −=

where f is a 5-part piecewise continuous function whose form addresses different regions of the echo

thus:

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( ) ( ) ( )( ) +−−+−= ntt where ntgmttgtf 0001

( ) ( ) ( ) ( ) 203

1032

10210102 tttnt where tt-tbtt-tbtt-tbbtf ++−+−+−+=

( )( ) 1020

103 ttttt where

ttt

1tf −+

−−=

( ) ( ) ( ) ( ) 30103

1032

102104 ttttt where tt-tatt-tatt-t1

tf −−−+−+−

=

( )( )

30

21

0

tt

5 ttt where tta

celogtf

0

+

−−=

−−

A Levenberg-Marquart non-linear least-squares fit is performed to derived the parameters t,c,n,,,a .

Then:

)Pmax(aPWW =

( )TPbinWW itdR −=

CoGWWtrWW dCRRR +++=

2.32.4 Accuracy

The accuracy of this retracker will be fully validated during the commissioning phase of CryoSat-2. Any

improvements in the method at that time will feed-forwards to Sentinel-3.

2.32.5 Comments



Note that the use of a waveform model in this algorithm makes it inapplicable to C-band.

2.32.6 References


Section 15.5.

2.33 ALT_RET_ICE_06 – To perform the diffuse retracking (SAR, Non-lead)

Algorithm under MSSL Background Intellectual Property Rights (BIPR).

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2.33.1 Heritage

Cryosat2

2.33.2 Function

The power waveform is retracked using a threshold of first maximum retracker.

The retracking method is used only for returns over ocean that have not discriminated as lead by

ALT_MAN_WAV_02 (i.e. for all non-lead records).


2.33.3.1 Input data

• Power waveform: 𝑃[0: 𝑁𝑆 − 1]

• tracker range from L1b: 𝑅𝑡𝑟

• CoG correction: 𝑑𝑐𝑜𝑔

• Summed, applicable geophysical and meteorological corrections: 𝐶


size of a range window bin in metres: 𝑑𝑏𝑖𝑛

nominal tracking point: 𝑖𝑡𝑝


• Retracker waveform power estimate: 𝑃𝑑𝑖𝑓

• Retracker range correction: 𝛿𝑅𝑑𝑖𝑓

• Retracker range estimate: 𝑅𝑑𝑖𝑓


• Smooth the input waveform with a 3-bin moving average filter

• Locate the bin containing the maximum value

• Locate the first bin that contains a power value greater than diffuse_peak_frac of the maximum value

and also contains more power than the two adjacent bins on either side (first maximum)

• Perform a threshold retrack to find the point where the power rises to diffuse_first_frac of the value

of the first maximum.

• Repeat this process to find the diffuse_second_frac point.

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• Reject any waveforms for which the distance between the two power points is more than

diffuse_width_thresh bins.

2.33.4 Accuracy

N/A.

2.33.5 Comments

Waveforms are retracked EITHER by this algorithm, if discriminated as open-ocean, sea-ice, or unknown,

OR by the model-fit retracker for specular waveforms ALT_RET_ICE_03, if they are discriminated as leads.

They are not retracked by both.

2.33.6 References


Section 15.5

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2.34 ALT_RET_OCE_01 - To perform the ocean retracking (LRM)

2.34.1 Heritage

Jason-2

2.34.2 Function

To perform the ocean retracking (hereafter called “ocean-3” retracking from Jason heritage) on the

waveforms (main and auxiliary bands), i.e. to estimate the altimetric parameters (epoch, composite

Sigma, amplitude, square of the mispointing angle).

In this algorithm, the resolution of the set of m linear equations is based on a least-square method and

utilizes the standard routine “F04AMF” of the NAG library, simulated by the routines “dgeqrf” and

“dormqr” from the public LAPACK library (www.netlib.org/lapack) and the routines "dtrsm", "dgemv" and

"dnrm2" from the BLAS library (www.netlib.org/blas). Thus, a wrapper (provided by CLS) will be used to

call these routines with the interfaces expected from the “F04AMF” routine of the NAG library.


2.34.3.1 Input data


• Waveform:

Waveform Waveform validity flag

• Off-nadir angle:

Off-nadir angle (square value)

• Orbit:

Orbit altitude (20-Hz)


Altimeter instrumental characterization data for the preparation of data for the ocean retracking Abscissa of the reference sample for tracking Sampling interval of the analysis window Antenna beamwidth Ratio between the PTR width and the sampling interval of the analysis window



Light velocity Earth radius

http://www.netlib.org/lapack

http://www.netlib.org/blas

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For each band, the following 20-Hz parameters:

• Epoch:

• Composite Sigma: c

• Amplitude: Pu


• Square of the mispointing angle: 2 (relevant for Ku-band only)

• Mean quadratic error between the normalized waveform and its model

• Number of iterations

• Quality information, such as an execution flag (valid / invalid)


The ocean-3 retracking algorithm is performed on the Ku-band and on the C-band waveforms. For each

20-Hz measurement, the Ku-band waveform must be processed first, because the Ku-band estimate of

the square of the mispointing angle is requested on input of the processing of the C-band waveform.

Background

The aim of the ocean-3 retracking algorithm is to make the measured waveform coincide with a return

power model, according to weighted Least Square Estimators derived from Maximum Likelihood

Estimators. Regarding mispointing, the return power model accounts for the second order terms.

Moreover, within the Ku-band ocean-3 retracking, the square of the off-nadir angle is estimated together

with the three standard altimetric parameters (epoch, composite Sigma and amplitude).

The expression of the return power as a function of time is given by Amarouche (Amarouche, 2003).

Accounting for a skewness coefficient (s: processing parameter), and assuming a Gaussian Point Target

Response, it is given by:

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) n222

3c

322

3

c

ss22

u

211

3c

311

3

c

ss11u

Puexpw2

uerf16

uerf1vexp2

PA

uexpw2

uerf16

uerf1vexpAP)t(Vm

+

−

−+

++−−

−

−+

++−=

with: −

=

x

0

t dte.2

)x(erf2

−=

2sin4expA , )

2(sin.

)2(Log

2 02

e

= , o = antenna beamwidth

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( )

+

= 2sin.

R

h1h

c.

4

e

, ( )

+

= 2cos.

R

h1h

c4

e

, 8

2

1

−= , =2

with: c = velocity of light, h = mean (raw) satellite altitude, Re = earth radius

p = PTR width (expressed in time), sc2SWH = (significant waveheight), 2s

2p

2c +=

c

2c1

12

tu

−−= ,

−−=

2tv

2c1

11 , 13u23u2w 2c

211c1

21 1 −++=

c

2c2

22

tu

−−= ,

−−=

2tv

2c2

22 , 13u23u2w 2c

222c2

22 2 −++=

and where the parameters to be estimated are:

: the epoch

c : the composite Sigma Pu : the amplitude

: the mispointing angle (Ku-band only) Pn : the thermal noise level (estimated from an arithmetic average of samples of the first plateau)

Basic principle

The problem to solve is the estimation of a set of N=4 parameters ={1=,2=c,3=Pu,4=2} for Ku-band,

and N=3 parameters ={1=,2=c,3=Pu} for C-band. The system to solve results from the maximization

of the logarithm of the likelihood function (), i.e. from the system:

0)(Ln)(C =−=

where C is the total cost function and is the gradient function.

This system is reduced to weighted Least Square Estimators, and is equivalent to set the Least Square

function 2 to 0, where the merit function 2 is defined by:

2

i i

ii2 Vm_V

=

where V represents the measured waveform, and where the weighting function is {i} = {Vmi}.

This system may also be represented by the following set of N equations:

0Vm

.VVm

k

i

i2i

ii =

− )

An iterative solution is obtained by developing the total cost function in a Taylor series at the first order

about an initial set ={01=,02=c0,03=Pu0,40=20} of estimates (for C-band, 40 is the Ku-band estimate

of the square of the mispointing angle, and the square of the mispointing angle is not estimated) :

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+ −= .gn1n

with: BD)BB( 1T − = (valued to the current values n)

k

i

iik

Vm.

1B

= , ( )ii

i1i VVm.

1D −

=

and where g is a loop gain (positive value, unique to the parameter being estimated).

Using {i} = {Vmi}, the Least Square Estimators method described above would put the most weight on

the regions with the least power, i.e. on the regions with the least information regarding the parameters

to be estimated. For this reason, the weighting function is superseded by a factor constant over a

waveform ({i} = ). In order to normalize the residuals ({Vmi-Vi}), this factor is set to the current

estimate of the amplitude.

Main steps of the processing

The main steps of the nominal processing are the following:

• Identification of the waveform validity:

The validity of the waveform is determined from the input waveform quality information. The

retracking is then performed only if the input waveform is valid.

• Thermal noise estimation:

The thermal noise level (Pn) is computed from an arithmetic average of samples of the first plateau (in

a predefined gate).

• Initialization:

A default value of the epoch (processing parameter) is used when the instrument is operating in closed

loop, while this default value is superseeded by the estimate of the epoch output by

“ALT_MAN_RET_04 - To initialise the LRM ocean retracking” for the processed band when the

instrument is operating in closed loop.

• Estimation (weighted Least Square fit):

The fine estimates of the epoch (), the composite Sigma (c), the amplitude (Pu) and for the Ku-band

the square of the off-nadir angle (2), are derived from the iterative process defined previously, which

is initialized from default values , c0, Pu0 and 20 (input processing parameters, except 2

0 for C-band, which is the Ku-band estimate of the square of the mispointing angle) for each waveform.

This estimation process is stopped when the value of the mean quadratic error between the normalized waveform (i.e. the waveform from which Pn is removed and weighted by 1/Pu) and the corresponding model built from the estimates is stable enough, with a minimum number of iterations performed, or when a maximum number of iterations is reached.

2.34.4 Comments

• As mentioned in section "Mathematical statement", an iterative solution of the system to be solved is given by:

+ −= .gn1n

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with: BD)BB( 1T − = (valued to the current values n),

k

i

iik

Vm.

1B

= , ( )ii

i1i VVm.

1D −

= , g = loop gain

• Solving this system by calculation of including the inversion of matrix BBT, is definitely not recommended. It is the reason why the resolution of the following equivalent system has been preferred:

gX with , DXB n1nT

−

−== +

This system is solved (i.e. vector X = is estimated) using the F04AMF NAG Fortran routine, which

calculates the accurate least-squares solution of a set of m linear equations in n unknowns, m n and

rank = n, with multiple right-hand sides, AX = B, using a QR factorization and iterative refinement.

• An additional weighting of matrices B_Mat and D_Mat is under investigation.

• The first two columns of matrix BT_Mat are scaled by 10-9 to prevent numerical instabilities within the matrix inversion process. For the same reason, the last column of matrix BT_Mat is scaled by 10-5.

• The algorithm is designed to process non-equidistant waveform samples (the input waveform is characterized by a table of abscissa and a table of amplitudes). It will be thus possible to process ENVISAT-like waveforms for example (128 FFT samples and of 2 additional DFT samples), without any modification of the algorithm.

2.34.5 References

• Amarouche L., Thibaut P., Zanife, O.Z., Dumont J.P., Vincent P. and Steunou N.: “Improving the Jason-1 ground retracking to better account for attitude effects”, Marine Geodesy, Volume 27, pp 171-197, 2004.

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2.35 ALT_RET_OCE_02 - To perform ocean/coastal zone retracking (SAR)

2.35.1 Heritage

None

2.35.2 Function

To fit the theoretical multi-looked waveform model to one 20-Hz Level 1B SAR waveform using the

Levenberg-Marquardt method and to retrieve geophysical variables and fitting quality information.


2.35.3.1 Input data

• L1b SAR mode waveforms

• Universal constants

• Instrumental characterization data



• Epoch relative to central gate position

• Sea Surface Significant Wave Height

• Maximum Received Power

• Thermal noise

• Least square fitting routine exit flag

• Number of iterations on exiting least square fitting loop

• Norm between waveform and model on exiting least square fitting loop

• Width of the leading edge (composite Sigma)


Observation scenario

The DDA single-look model, base for the DDA retracker, follows the geometry for Elliptical surface based

on WGS84 with 𝑎 = 6378137 𝑚, 𝑏 = 6356752.3142 𝑚 and as Cartesian system axis (𝑥,,) defined by:

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(1)

Where 𝜃𝑝𝑙𝑎𝑡 corresponds to the parametric latitude and 𝜙𝑝𝑙𝑜𝑛 to the planetographic longitude.

Provided the previous, the new observation scenario follows the following figure :

Figure 1 : Observation scenario with and without mispointing

Scattering points on the surface are referenced by: the 2D vector 𝜌⃗, which is the shorthand for (𝑥,) and

its modulus is equal to 𝜌2=𝑥2+𝑦2; the distance from the satellite to the scatterer can be shown to be:

(2)

Where h is the spacecraft altitude, z is the height of the scatterer and α corresponds to the Earth

curvature effect and shall be related to the altitude and Earth radius as follows:

(3)

The Earth Radius shall be calculated from 𝑎, for an elliptical surface as:

(4)

The effect of mispointing in this model has been introduced as a pointing displacement on the

surface. Therefore, if the antenna is no longer pointing at nadir but different, it will be illuminating

towards a position displaced 𝑥−𝑥𝑝,−𝑦𝑝. Where 𝑥𝑝, are the mispointing coordinates, which can be

easily related to pitch pitch) and roll (𝜃roll) angles; this is done as follows:

(5)

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Note that signs of pitch and roll follow the flight dynamics coordinates system as shown in the

following figure:

Figure 2 : Flight dynamics coordinate system assumed for mispointing calculation

Variables of interest for the single-look and multi-looked models

• Burst Length :

(6)

• Earth Curvature Effect :

(7)

• Inverse of MSS :

(8)

• Antenna gain :

The single-look model is derived assuming elliptical antenna pattern:

(9)

To simplify this expression we wrote it in terms of αxand αy:

(10)

To account for any misalignment of the antenna focal point we have re-defined the previous

accounting for a shape factor, which by default will be set to one (assumed by default non dis-

alignment of the antenna):

(11)

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The final expression of the antenna accounting for the previous results into:

(12)

In the presence of mis-pointing G is written as:

(13)

The power expression of the previous shall be written as:

(14)

Furthermore, shall the antenna be circular, not elliptical, the assumption to be made is 𝜃𝑥=𝜃𝑦=𝜃𝑐,

or 𝛼𝑥=𝛼𝑦, which provides:

(15)

Scenario Parameters & Variables

• EM Scattering model :

EM Scattering model is assumed for simplicity to be isotropic rough surface of Gaussian statistics.

This model is defined as:

(16)

Where σslopes2 is the variance of the total sea surface slope (aka mean square-slope, MSS hereafter)

and θ is the angle of incidence. Note that only a portion of the total mean square-slope of the

ocean surface is included in MSS, these being the mean-square slopes contributed by the ocean

waves whose lengths are greater than the wavelength of the electromagnetic radiation.

• MSS :

(17)

where σs is the rms height of the specular points with reference to MSL and Lc the ocean correlation

length. For convenience, we introduce the parameter ν, which is simply the inverse of the MSS, as

defined in (8).

Mathematical statement

The algorithm consists of the following functional units:

• An initialisation unit (performed in a data management algorithm), INIT, which checks various flags and prepares the waveform measurements according to the specification set by the user in the processing parameters related to INIT.

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• A fitting unit, FIT, which performs the least-square fitting of the SAMOSA theoretical SAR waveform model to the measured waveforms, according to the specification set by the user in the FIT related processing parameters.

The fitting unit relies on two mechanisms (i.e., functional units) to perform the computation of,

respectively, the single-look (SL) and multi-look (ML) theoretical waveforms. Both SL and ML units depend

on input data and are also controlled through processing parameters.

Figure 3 - SAR ocean retracker global software structure

Mathematical assumptions for the derivation of the analytical expression of the Single-Look Model

In SAMOSA 2.5 version of the algorithm, the following assumptions are considered:

• Omission of Sea Surface skewness effect

• Omission of Mean Surface and Electromagnetic Bias height term

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Furthermore, likewise it was described in the previous DPM the analytical expression of the Single-Look

Model is derived accounting for the system point target response of the DDA (Delay Doppler Altimeter),

which we have seen, that has a contribution in range, which shall be approximated by:

(18)

where :

(19)

Note that p is well described in literature and it is a factor resulting from the mathematical

approximation of a sinc squared by a Gaussian, and rB is known as the time resolution and is defined as

the inverse of the reception bandwidth (Br ).

(20)

In the SAMOSA model reference paper, this approximation is written in terms of a new variable:

(21)

Thus:

(22)

where :

(23)

It is important to highlight how 𝜏 (delay time with respect to mean sea level) relates to epoch:

(24)

Single-Look Model

The single-look model analytical expression SAMOSA5, dependent on epoch 𝑡0, 𝜐, αp , Pu and Hs (SWH), is

given by:

(25)

With :

(26)

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(27)

Where:

• Iνsc is the Scaled Spherical Modified Bessel function of first kind and order ν, defined as:

• k is the range delay index (also referred in the altimetry community as the lagged range gate or range bin)

• l is the Doppler frequency index

• σz is surface roughness, given by Hs/4

• Pu is the waveform power amplitude

• gl , Lz, LΓ , Tz and Γk,l(0) will be defined hereafter

Note that we define 𝑘=𝑘′−𝑘0, where 𝑘′ takes a range of values [-(Np)/2+1, +(Np)/2 ], and 𝑘0 (dimensionless

epoch relative to the central gate) is related to 𝑡0 as 𝑘0=𝑡0𝐵𝑟.

Similarly the Doppler index l= 0 corresponds to zero Doppler and the number of pulses per burst and the

SAR mode PRF defines its range of values.

gl is a function of the parameter αp and a function of Hs (SWH), and it is given by:

(28)

Note that Lx, Ly, Lz ,LΓ , ls are calculated from the system parameters:

(29)

(30)

(31)

(32)

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(33)

(34)

(35)

Tk is calculated from the system parameters as:

(36)

k,l(0) is calculated from the system parameters as:

(37)

Where:

(38)

(39)

(40)

(41)

(42)

(43)

(44)

The single-look model in (8) is a 2D matrix representing the distribution of power in Delay and Doppler

space (hence, Delay-Doppler Maps; DDM).

Note that for large values of 𝑔𝑙𝑘 product, the Bessel functions might be approximated as:

(45)

And :

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(46)

Multi-Look Model

For the generation of the multi-look waveforms we need to account for: Neff and Beam_Ang_Stack_TS;

both are provided for each elementary record (approximately 20Hz waveform) in the SAR L1b product.

Neff corresponds to the number of effective looks for a given elementary record. This number represents

the number of looks used for multi-looking at the present ground cell location. Neff can differ from the

maximum number of looks available in principle, because some looks may not be suitable due to low

Signal to Noise Ratio (SNR).

Beam_Ang_Stack_TS is the array of angles of the Doppler beams used for multi-looking for the given

elementary record. It provides in radians the value of the angle of all beams staring at the ground

resolution cell. This array can be easily related to the Doppler frequency of each effective burst beam used

for multi-looking.

First, we will calculate for each angle in Beam_Ang_Stack_TS, the corresponding Doppler frequency:

(47)

This will define the Doppler beams of each burst that must be selected and added to the stack before

incoherent integration.

To convert the Doppler frequency to the index 𝑙 (adimensional), the Doppler frequency must be scaled by

:

, For 1≤n≤Neff

The final expression for the multi-looked waveform is given by:

(48)

2.35.4 Comments

In this current version, the epoch is referenced to the reference sample for tracking, like the LRM epoch.

The detailed processing steps for the SAR waveform fitting is based on the prototype SAR retracker

developed in SAMOSA, which uses un-weighted non-linear least-square fitting and does not require the

explicit knowledge of the partial derivatives of the fitted model. As stated previously, it would take

considerable effort to produce analytical formulas of the first order derivatives of the multi-looked SAR

waveform model.

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There are many numerical implementations of the Levenberg-Marquardt algorithm, which make use of

finite differences to approximate the Jacobian, instead of analytical expressions. Unfortunately, no such

scheme is currently defined as a Mechanism for STM S-3 to perform this type of fitting.

The prototype retracker implemented at NOC is based on a licensed numerical scheme, for which, in the

absence of appropriate S-3 mechanism, we can only provide generic input/output below.

In addition, there are also open source versions of these algorithms freely available.

2.35.5 References

• Gommenginger, C.P. & M.A. Srokosz, WP5.3 Technical Note on Development & Testing of SAR Altimeter waveform theoretical retracker, ESRIN Contract 20698/07/I-LG Development of SAR Altimetry Mode Studies and Applications over Ocean, Coastal Zones and Inland Water (SAMOSA), SAMOSA_WP53_NOC_v1.1, July 2009.

• Martin-Puig, C. & G. Ruffini, Starlab Technical Note for SAMOSA WP5.0 Issue 4, 7th April 2009.

• Gommenginger, C.P & M.A. Srokosz, SAMOSA3 WP2200 Technical Note (D2) on SAMOSA3 Development and Validation, ESRIN Contract 20698/07/I-LG Development of SAR Altimetry Mode Studies and Applications over Ocean, Coastal Zones and Inland Water (SAMOSA), SAMOSA3_WP2200_NOC_v1.0, February 2012.

• Ray, C. & C. Martin-Puig, SAMOSA models trade-off Technical Note, D1 SAMOSA3, Issue 2.00, 16 Jan 2012.

• Brown,G.S. ”The Average Impulse Response of a Rough Surface and Its applications”, IEEE Trans. Antennas Propag., vol. AP-25, pp. 67-74, Jan. 1977. 5, 6, 12, 21, 22, 25.

• Valenzuela,G.R. “Theory for the interaction of electromagnetic and oceanic waves - a review”. 1977.

• Raney, R.K., “The Delay/Doppler Radar Altimeter”, IEEE Trans. Georsci. Remote Sensing, vol. 36, pp. 1578–1588, Sep1998.

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2.36 GEN_COR_ORB_01 - To derive the orbital altitude rate with respect to the

reference MSS/geoid

2.36.1 Heritage

Jason-1, Jason-2

2.36.2 Function

To derive the orbital altitude rate with respect to the MSS/geoid from the orbital altitude rate with respect

to the reference ellipsoid and from the map of slopes of the MSS/geoid with respect to the reference

ellipsoid.


2.36.3.1 Input data

• Location:

Latitude Longitude

• Orbit:

Orbital altitude rate with respect to the reference ellipsoid Orbital rate with respect to the Earth’s centre

• Map of the slopes of the reference MSS/geoid with respect to the reference ellipsoid (SAD)


• Orbital altitude rate with respect to the reference MSS/geoid


• The orbital altitude rate with respect to the reference MSS/geoid is the sum of the two following parameters:

• The input orbital altitude rate with respect to the reference ellipsoid

• The slope of the reference MSS/geoid with respect to the reference ellipsoid, which is derived by bilinear interpolation of the slopes of the input map to the measurement location, accounting for the pass direction (ascending or descending).

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2.37 GEN_COR_RAN_01 - To compute the 10 meter wind vector, the surface

pressure and the mean sea surface pressure from ECMWF model, the dry

and wet tropospheric “operational” corrections (ocean surfaces) and the

dry and wet tropospheric “pseudo-operationnal” corrections (continental

surfaces)

2.37.1 Heritage

Jason-1

2.37.2 Function

To compute at the altimeter time tag and location the 10 meter wind vector components U (zonal

component) and V (meridian component), the surface pressure and mean sea level pressure from the

ECMWF meteorological model fields, the wet tropospheric corrections due to gases of the troposphere

(ocean surfaces), to remove the climatological pressure from the surface pressure and to derive the dry

tropospheric corrections due to gases of the troposphere from this surface pressure to which a model of

S1 and S2 pressure variability is added (ocean surfaces), to compute the wet and dry tropospheric

corrections using a vertical integration of the meteo 3D parameters (continental surfaces).


2.37.3.1 Input data

• Datation:

Altimeter time tag

• Location:

Latitude of the measurement Longitude of the measurement

• Altitude

• Tracker range

• Geophysical corrections

• Meteorological data (DAD):

Meteorological data: U and V components of the 10 meter wind vector, surface pressure and mean sea level pressure. For each of these parameters, the data consist of two data files, 6 hours apart, bracketing the time of measurement (each file, excepted the mean sea surface pressure, contains the parameter given on the so-called Gaussian grid (quasi-regular in latitude, non-regular in longitude).

Humidity and temperature profiles from the vertical levels (see comments in 2.37.5) Table providing the latitudes of the model grid points Table providing the number of grid points in longitude for each model latitude

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• Climatological pressure files (SAD)

The data consists of four data files, corresponding to 0h, 6h, 12h and 18h. Each file contains the climatological pressure referenced to the sea on a cartesian grid, for each of the twelve months of the year.

• S1 and S2 tide grids of monthly means of global amplitude and phase (SAD)



• U-component of the 10 meter model wind vector

• V-component of the 10 meter model wind vector

• Dry tropospheric “operational” and “pseudo-operational” corrections: hdry and hdry-pseudo

• Model wet tropospheric “operational” and “pseudo-operational” corrections: hwet and hwet-pseudo

• Surface pressure (climatological pressure removed)

• Mean sea level pressure


The wet tropospheric correction, the two components U and V of the 10 meter model wind vector, the

surface pressure and the mean sea surface pressure at the altimeter measurement are obtained by linear

interpolation in time between two consecutive (6 hours apart) ECMWF model data files, and by bilinear

interpolation in space from the four nearby model grid values (excepted for the mean sea surface

pressure). The ECMWF model grid is quasi-regular in latitude and non-regular in longitude (the number

of grid points in longitude increases towards lower latitudes).

The climatological pressure (0h, 6h, 12h and 18h for each month) is then removed from the surface

pressure.

Then, the dry/wet tropospheric corrections are computed as follows :

• “operational corrections” : both corrections described below are computed at the “sea level reference” so that coastal points do not suffer from interpolation between ocean and continental points corrections, the drawback being that the non ocean points will be affected with unrealistic values :

The dry tropospheric correction is derived from the mean sea level pressure (climatological pressure removed) to which a model of S1 and S2 pressure variability (R D Ray and R M Ponte, 2003) is added.

The wet troposhperic correction is computed from a “surface“ reference that is the mean sea level pressure and the calculation is based on equation (21) described below.

• “pseudo-operational corrections” : for both corrections, the computation consists in a vertical integration of the 3D meteo parameters performed for each along-track altimeter measurement. The real altitude of the surface terrain along-track is deduced from the altimeter range. This surface altitude is then used inside the 3D meteo fields in order to determine the altitude of the real surface within the model:

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The dry tropospheric correction is computed from equation (15) described below, which requires a value of the surface pressure - corrected for a model of S1 and S2 pressure variability (R D Ray and R M Ponte, 2003) - at the real surface altitude and a value of the gravity at the altitude/latitude of the measurement point for each model layer.

The wet tropospheric correction is computed from equation (21) described below, which requires a value of the surface pressure - corrected for a model of S1 and S2 pressure variability (R D Ray and R M Ponte, 2003) - at the real surface altitude, a value of the gravity at the altitude/latitude of the measurement point for each model layer and a value of specific humidity and temperature (given by the 3D ECMWF meteo fields) for each model layer.

Hereafter are detailed the mathematical statement to compute the surface pressure map and the wet

tropospheric correction map. The input data for computing these maps are the model surface pressure,

and the specific humidity and temperature profiles from the vertical levels of the ECMWF model.

Definitions of the refractive index and of the wet and dry tropospheric corrections

The excess propagation path, also called path delay, induced by the neutral gases of the atmosphere

between the backscattering surface and the satellite is given by:

h = dz 1) - (n(z)Hsat

Hsurf (1)

where n(z) is the index of refraction of air, Hsurf and Hsat are respectively the altitudes of the surface and

of the satellite above mean sea level.

The index of refraction is conveniently expressed in terms of the refractivity N(z), defined as:

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

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

N(z) = 77.6 T

Pd + 72 T

e + 3.75 105

2T

e (3)

where Pd is the partial pressure of dry air in hPa (1 hPa = 100 Pa), e is the partial pressure of water vapor

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 expression function of

the total pressure of air. For deriving it, we have to consider that the dry air and the water vapor are ideal

gases, i.e., they obey to the Mariotte-Gay Lussac law:

For dry air: dd

d

M

RT

ρ

P= (4)

For water vapor: ww M

RT

ρ

e= (5)

where d and w are the volumic masses of dry air and water vapor respectively, Md and Mw are the molar

masses of dry air (28.9644 10-3 kg) and water vapor (18.0153 10-3 kg) respectively, R is the universal gas

constant (8.31434 J.mole-1.K-1).

Combining (4), (5) and (3) leads to:

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N(z) = 77.6 Rd

d

M

ρ + 72 R

w

w

M

ρ + 3.75 105

2T

e (6)

The volumic mass of wet air is the sum of the volumic masses of dry air and water vapor:

= d + w (7)

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

N(z) = 77.6 RdM

ρ + (72 - 77.6

d

w

M

M) R

w

w

M

ρ + 3.75 105

2T

e (8)

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

N(z) = 77.6 RdM

ρ + (72 - 77.6

d

w

M

M)

T

e + 3.75 105

2T

e (9)

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

h = 77.6 10-6 dM

Rdz

Hsat

Hsurf + (72 - 77.6

d

w

M

M)10-6 dz

T

eHsat

Hsurf + 3.75 10-1 dz

T

eHsat

Hsurf

2 (10)

The first term is called the dry tropospheric correction hdry:

hdry = 77.6 10-6 dM

Rdz

Hsat

Hsurf (11)

The sum of the two remaining terms is called the wet tropospheric correction hwet:

hwet = (72 - 77.6 d

w

M

M)10-6 dz

T

eHsat

Hsurf + 3.75 10-1 dz

T

eHsat

Hsurf

2 (12)

Introducing the numerical values for Md and Mw into (12), and multiplying hwet by –1 to get a negative

quantity to be added to the altimeter range, leads to the following equation for hwet in m:

hwet = -23.7 10-6 dz T

eHsat

Hsurf - 3.75 10-1 dz

T

eHsat

Hsurf

2 (13)

Calculation of the dry tropospheric correction as function of the surface pressure

It is commonly assumed that the atmosphere is in hydrostatic equilibrium, i.e. g being the acceleration

due to gravity:

dz

dP= - g (14)

Combining (11) and (14) leads to the following equation for hdry, where Psurf is the atmospheric pressure

at the ground surface:

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hdry = 77.6 10-6 dM

R dP

g

1Psurf

0 (15)

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

z 0.00031 - )cos(2 0.0026 - 1.gg 0 = (16)

where is the latitude, z is altitude in km, and g0 = 9.80665 m/s2

The variation of g with altitude is small and can be neglected by considering a mean value for g = 9.783

m/s2 constant with altitude. This leads to the final expression for hdry:

)2cos(0026.01.P 277.2h urfsdry +−= (17)

(17) is the expression obtained by Saastamoinen (1972), where Psurf is in hPa, and hdry is in mm and is set

here with a negative sign to be added to the altimeter range. Computing the dry tropospheric correction

from (15) instead of from (17) (i.e., taking into account the variation of g with altitude, as given by (16)),

leads to differences below the 1-mm level in dry tropospheric correction (below the 0.5-mm level for

latitudes less than 50°).

Note In GEN_COR_RAN_01 algorithm, the dry tropospheric correction will be computed as described

in (17) but using a surface pressure which is the interpolated surface pressure Psurf from which the

climatological pressure is removed (over the ocean only) and to which a model of S1 and S2 waves

pressure variability (R D Ray and R M Ponte, 2003) is added.

Calculation of the surface pressure map

The main input for (17) is the atmospheric pressure at the ground surface, Psurf. As the ECMWF model

surface is not the true Earth surface, it is necessary to correct the model surface pressure Psol for the height

difference between the ECMWF model surface height Hsol and the true surface height H. The true surface

height H is obtained by removing the altimeter range and the geoid height from the satellite altitude.

Then, Psurf is derived from Psol using (18):

γ R

g aM

sol

solsolsolsurf

T

)H - γ(H T . P P

−

+= (18)

Where is the mean vertical gradient of temperature (6.5°/km), and Tsol is the air temperature at the

model surface, interpolated from the air temperature for the first model level:

−+= 1)

P

P(

g M

Rγ1 . T T

lev

sol

alevsol (19)

Note In GEN_COR_RAN_01 algorithm, the climatological pressure is removed to the surface pressure

to be output. This removal is performed for measurements over the ocean only because the

climatological pressure is referenced to the sea (null altitude).

Calculation of the wet tropospheric correction map

The humidity variable output by the model is the specific humidity q, given by :

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q = wd

w

ρ ρ

ρ

+ (20)

Thus, (13) must be rewritten as function of q. After introducing (5), (7), (14) and (20) into (13), one gets:

hwet = -23.7 10-6 wM

Rdp q

g

1Psurf

Psat - 3.75 10-1

wM

Rdp

T

q

g

1Psurf

Psat (21)

As done for the dry tropospheric correction calculation, the expression for g given by (16) is then

introduced in (21), and the variation of g with altitude is neglected by considering a mean value for g =

9.797 constant with altitude (which corresponds to a mean height of 3 km). This leads to the final

expression for hwet:

hwet = - { 1.116454 10-3 dp qPsurf

Psat + 17.66543928 dp

T

qPsurf

Psat } x )2cos(0026.01 + (22)

The wet tropospheric correction map is computed from (22), where the integrals are evaluated from the

surface pressure Psurf defined above up to the model vertical level pressure Psat above which humidity is

negligible (typically 200 hPa). In (22), pressures are in hPa, temperature is in K, specific humidity q is in

kg/kg and hwet is in m.

2.37.4 Accuracy


2.37.5 Comments

• The computation of the wet and dry tropospheric corrections from ECMWF 3D fields is done by using the surface’s altitude information derived from the altimeter tracker range.

• From a software point of view, the computation of the wet and dry tropospheric corrections from ECMWF 3D fields can be done using a number of model levels M being lower than the original number of model levels output by ECMWF Integrated Forecasting System. Thus, the data provided in input can either contain the full set of model levels or only the M lowest ones. It is however essential that the following inputs are coherently provided to the algorithm:

The 3D-parameters input files The following processing parameters: Number of layers in ECMWF model ECMWF model A and B coefficients used to convert hybrid levels to pressure values (whose size is the

Number of layers in ECMWF model + 1)

Thus, the number of layers in ECMWF model provided in the configuration file (processing parameters) shall be equal to the number of layers in the input 3D data, and the A and B coefficients shall be selected to stick to the elected number of layers.

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2.37.6 References

• Définition et analyse de nouvelles methodes de correction de troposphère humide et sèche issues des données ECMWF. Mise en œuvre de l’utilisation directe des sorties ECMWF. Rapport Technique Tâche 2.3.2, Pistach Project, CNES, F. Mercier, 2008.

• Bean, B. R., and E. J. Dutton, Radio Meteorology, U.S. NBS Monogr., 92, March 1966.

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

• R D Ray and R M Ponte, Barometric tides from ECMWF operational analyses, Annales Geophysicae, 21: 1897-1910, 2003.

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2.38 GEN_COR_RAN_02 - To compute the high frequency fluctuations of the sea

surface topography from MOG2D model

2.38.1 Heritage

Jason-1, Jason-2, ENVISAT

2.38.2 Function

To compute the fluctuations of the sea surface topography at the altimeter time tag and location from

MOG2D model.


2.38.3.1 Input data

• Datation:

Altimeter time tag

• Location:


• MOG2D data: sum of the high frequency variability of the sea surface height and of the low frequency part of the inverted barometer effect (DAD).

• The data consists of two data files, 6 hours apart, bracketing the time of measurement (each file containing the parameter given on regular grid).


• Fluctuations of the sea surface topography (sum of the high frequency variability of the sea surface height and of the low frequency part of the inverted barometer effect) at the altimeter measurement time tag and location


MOG2D parameter (sum of the high frequency variability of the sea surface height and of the low

frequency part of the inverted barometer effect) at the altimeter measurement is obtained by linear

interpolation in time between two consecutive (6 hours apart) MOG2D model data files, and by bilinear

interpolation in space from the four nearby model grid values.

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2.38.4 Comments

• An algorithm (management or specified in the processing steps) may be required to generate the time of the altimeter measurement in the required input format.

• The high frequency fluctuations of the sea surface topography at the altimeter measurement time tag and location to be provided in the product will be obtained by removing the inverted barometer effect from the output of this algorithm

2.38.5 References

• Loren Carrère and Florent Lyard, “Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing – comparison with observations”, Geophysical Research Letters, Vol. 30, N0 6, 1275, doi:10.1029/2002GL016473, 2003

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2.39 GEN_ENV_BAT_01 - To compute the ocean depth / land elevation

2.39.1 Heritage

TOPEX-Poseidon, Jason-1, Jason-2, ENVISAT

2.39.2 Function

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


2.39.3.1 Input data

• Location:


• Surface type (“open ocean or semi-enclosed seas”, “enclosed seas or lakes”, “continental ice”, or “land”)

• Bathymetry / topography configuration file (SAD)


• Ocean depth / land elevation


The ocean depth / land elevation is obtained by bilinear interpolation in space from the input

bathymetry/topographygrid values. If the surface type of the altimeter measurement is set to “open

ocean or semi-enclosed seas”, only grid points having negative altitude are used in the interpolation. If no

such grid points with negative altitude are found, then the four grid points having positive altitude are

used. If the altimeter measurement is set to “enclosed seas or lakes”, “continental ice”, or “land”, all grid

points are used in the interpolation, regardless of their altitude.

2.39.4 Accuracy

The Global Digital Elevation Model ACE2 is described in:

http://tethys.eaprs.cse.dmu.ac.uk/ACE2/shared/documentation

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2.40 GEN_ENV_DIS_01 - To compute distance to shore

2.40.1 Heritage

None

2.40.2 Function

To compute the distance between the measurement location (over sea surface) and the coastline using

bilinear interpolation.


2.40.3.1 Input data

• Location, i.e. latitude and longitudes

• Distance to shore table (SAD)


• Distance to shore at altimeter location


The input SAD table provides the theoretical distance to shore on a lat/lon grid. This algorithm consists of

getting the distance to shore by bilinear interpolation.

2.40.4 Comments

This algorithm was not implemented in past altimetry missions.

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2.41 GEN_ENV_ECH_01 - To determine the echo direction (SAR, Margin)

2.41.1 Heritage

CryoSat-2.

2.41.2 Function

This function takes the standard method of slope correction that is used for LRM data and accounts for

the effect of the footprint shape in SAR mode. The altitude and azimuth that is calculated by the standard

method is projected into the across-track plane. This is used to determine the actual altitude and azimuth

of the echoing point within the SAR footprint.


2.41.3.1 Input data



• Satellite altitude: eh

• Fitting retracker range estimate: fitR

• Slope model(s) (SAD)

• Orbit (DAD)

Values extracted via the CFI [CFI-S-01]; see reference for methods.

Position of the satellite in the ITER frame: P

Velocity of the satellite in the ITER frame: v

Boresite vector of the satellite in the ITER frame: b


Semi-major axis of the reference ellipsoid: ea

Flattening coefficient of the ellipsoid: e


• Echo position altitude ( SAR ) and azimuth ( SAR )



• Flag application of correction

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• Calculate the meridional radius of curvature of the ellipsoid for the nadir location

( )( ) 23

022

2e

sine1

e1a0

−

−=

• Slope model Cartesian frame coordinates are given by:

( )

−=

2

sincos2X 0200

( )

−=

2

sinsin2Y 0200

• Calculate the radius of parallel circle at geodetic latitude

022

0e0

sine1

cosa

−

=

• Range derivatives in local co-ordinates can then be found by interpolating the appropriate slope model (for the current location) to get ( )Y,Xsx and ( )Y,Xsy and calculating:

( ) ( )

+

+=

=

YY,Xs

XY,Xs

h

1s

x

lyx

ex

0x 0

( ) ( )

+

+=

=

YY,Xs

XY,Xs

cosh

1s

y

lyx

0ey

0y 0

• Echo direction angles uncorrected for SAR mode are given as

Azimuth : ( )xyLRM ssatan=

Altitude : 2y

2xLRM ssasin +=

• Calculate the geodetic coordinates of echo point:

LRM2

LRM2

0 cossincos00

00

+

=

0

LRMLRMfit0LRM

cossinR

+=

0

LRMLRMfit0LRM

sinsinR

+=

( )

+−=

2

sinRcosRhh

2LRMfit

LRMfiteLRM

• Form the uncorrected echo vector e

:

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Convert echo position ( )h,, to Cartesian E

using CFI [CFI-S-01]

PEe

−=

• Calculate the across-track component of the uncorrected echo vector:

SAR corrected echo vector ( )

v

vvevd

= (will be in across-track plane)

Corrected azimuth SAR is then calculated using the boresight vector:

Get the component of the SAR corrected echo vector in the plane normal to the boresight

( )b

bbdba

=

Calculate the azimuth angle from the Z axis of the frame (North)

=

a

aacos z

SAR

Corrected altitude is

•

=bd

bdacosSAR

2.41.4 Accuracy

The ellipsoid geometry calculations mix large numbers such as the semi-major/minor axes (a, b) with small

numbers such as eccentricity (e), and calculations are subject to loss of accuracy. Double precision

arithmetic should be used throughout to give accuracy to better than 1 mm.

Slopes of 1 in 10,000 lead to slope corrections at the ~ 5 millimetre level, and so the slopes in the models

may be safely represented as single-precision, 32-bit floating-point numbers, as the 24-bit precision

available translates to approximately 8 decimal significant figures. Slopes of greater than a few degrees

will not be tracked at high precision (if at all) by the altimeter, and so precision in areas of high surface

slope is less important. This keeps the size of the files as low as possible.

2.41.5 References

[CFI-S-01] - Software tools for S-2&S-3 Orbit and Attitude computation

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2.42 GEN_ENV_ECH_02 - To determine the echo direction (LRM, Ice)

2.42.1 Heritage

CryoSat-2, ENVISAT

2.42.2 Function

This function is the standard method of slope correction that is used for LRM data.


2.42.3.1 Input data



• Satellite altitude: eh

• Fitting retracker range estimate: fitR

• Slope model(s) (SAD)


Semi-major axis of the reference ellipsoid: ea

Flattening coefficient of the ellipsoid: e


• Echo position altitude ( SAR ) and azimuth ( SAR )



• Flag application of correction


• Calculate the meridional radius of curvature of the ellipsoid for the nadir location

( )( ) 23

022

2e

sine1

e1a0

−

−=

• Slope model Cartesian frame coordinates are given by:

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( )

−=

2

sincos2X 0200

( )

−=

2

sinsin2Y 0200

• Calculate the radius of parallel circle at geodetic latitude

022

0e0

sine1

cosa

−

=

• Range derivatives in local co-ordinates can then be found by interpolating the approprate slope model (for the current location) to get ( )Y,Xsx and ( )Y,Xsy and calculating:

( ) ( )

+

+=

=

YY,Xs

XY,Xs

h

1s

x

lyx

ex

0x 0

( ) ( )

+

+=

=

YY,Xs

XY,Xs

cosh

1s

y

lyx

0ey

0y 0

• Echo direction angles are given as

Azimuth : ( )xyLRM ssatan=

Altitude : 2y

2xLRM ssasin +=

2.42.4 Accuracy

The ellipsoid geometry calculations mix large numbers such as the semi-major/minor axes (a, b) with small

numbers such as eccentricity (e), and calculations are subject to loss of accuracy. Double precision

arithmetic should be used throughout to give accuracy to better than 1 mm.

Slopes of 1 in 10,000 lead to slope corrections at the ~ 5 millimetre level, and so the slopes in the models

may be safely represented as single-precision, 32-bit floating-point numbers, as the 24-bit precision

available translates to approximately 8 decimal significant figures. Slopes of greater than a few degrees

will not be tracked at high precision (if at all) by the altimeter, and so precision in areas of high surface

slope is less important. This keeps the size of the files as low as possible.

2.42.5 Comments

Zero divides in the atan() function should be trapped, and the angle set to

2 as appropriate.

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2.43 GEN_ENV_GEO_01 - To compute the geoid height

2.43.1 Heritage

TOPEX-Poseidon, ERS-1, ERS-2, Jason-1, Jason-2, ENVISAT

2.43.2 Function

To compute the height of the geoid above the reference ellipsoid at the location of the altimeter

measurement, from the geoid input file.


2.43.3.1 Input data

• Location:


• Geoid (geographical grid, SAD)


Interpolation window size (even)


• Height of the geoid.


The height of the geoid is computed at the altimeter measurement by spline or bilinear interpolation in

latitude and longitude of the grid values at the altimeter measurement.

2.43.4 Comments

EGM2008 is the baseline for the current issue of Sentinel-3 processing.

2.43.5 References

• Lemoine, F.G. et al., 1998 : The development of the joint NASA GSFC and NIMA Geopotential model EGM96, NASA/TP-1998-206861, 575 pp, July 1998

• Nikolaos Pavlis et al., 2008 : An Earth Gravitationnal Model to Degree 2160: EGM2008, Presentation given at the 2008 European Geosciences Union General Assembly held in Vienna, Austria, April13-18, 2008.

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2.44 GEN_ENV_MDT_01 - To compute the mean dynamic topography height

2.44.1 Heritage

Jason-2, Jason-1

2.44.2 Function

To compute the height of the mean dynamic topography (MDT) at the location of the altimeter

measurement, from the MDT input file.


2.44.3.1 Input data

• Location:


• MDT value and accuracy (geographical grid, SAD)


Interpolation window size (even) MDT offset


• Height of the mean dynamic topography

• MDT interpolation flag

• MDT accuracy


The height of the MDT is computed at the altimeter measurement using a squared window of NxN MDT

grid points (typically N = 6) centered on the altimeter point. Spline functions are calculated within the

window as function of grid point latitude for each MDT column. Each of these spline functions is evaluated

at the altimeter latitude. The resulting values are then used for calculating a spline function of grid point

longitude. The height of the MDT is derived by evaluating the spline at the altimeter longitude. When one

MDT grid point has a default value (grid point over land), then a lower N value is tried. If spline

interpolation fails (because N < 4), then bilinear interpolation is performed. An offset may be added to

the computed height of the MDT.

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A MDT flag is also derived. It addresses the quality of the interpolation by providing the number of grid

cells used during the spline (or bilinear) interpolation process. The accuracy is also provided at the location

of the measurement by the MSS accuracy map (calibrated formal errors) using a bi-linear interpolation.

2.44.4 Comments

CNES/CLS 09 is the baseline for the current issue of Sentinel-3 processing.

2.44.5 References

• Rio, M. H., S. Guinehut, and G. Larnicol (2011), New CNES-CLS09 global mean dynamic topography computed from the combination of GRACE data, altimetry, and in situ measurements, J. Geophys. Res., 116.

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2.45 GEN_ENV_MET_01 - To compute the inverted barometer effect

2.45.1 Heritage

TOPEX/Poseidon, Jason-1, Jason-2, ENVISAT

2.45.2 Function

To compute the sea surface height correction due to atmospheric loading (the so-called inverted

barometer effect), using a non constant mean reference pressure.


2.45.3.1 Input data

• Surface atmospheric pressure:

Surface atmospheric pressure p

Mean sea surface atmospheric pressure over the global oceans P Processing parameter (SAD)


• Inverted barometer height


The inverted barometer height correction (H_Baro) is computed (in mm) according to the following

formula:

( )pp.bBaro_H −−=

where b = 9.948 mm/hPa, p is the surface atmospheric pressure at the location and time of the altimeter

measurement, and p is the global mean sea level atmospheric pressure, computed from the surface

pressure field the closest in time from the altimeter measurement.

2.45.4 Accuracy

Extensive modeling work by Ponte et al. (1991) confirms that over most open ocean regions the ocean

response to atmospheric pressure forcing is mostly static. Typical deviations from the inverted barometer

response are in the range of 1 to 3 cm rms, with most of the variance occurring at high frequencies. The

Inverted barometer correction is not reliable for pressure variations with very short periods (< 2 days) and

in coastal regions.

This inverted barometer height calculation uses a non constant mean reference sea surface pressure. As

stated by Dorandeu and Le Traon (1999), this improved inverted barometer height correction reduces the

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standard deviation of mean sea level variations (relative to an annual cycle and slope) by more than 20%

when compared with the standard inverted barometer height correction (i.e. with constant reference

pressure) and no correction at all. It also slightly reduces the variance of sea surface height differences at

altimeter crossover points, and the impact of the improved correction on the mean sea level annual cycle

and slope is also significant.

2.45.5 References

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

• Dorandeu, J., and P.Y. Le Traon, Effects of global mean atmospheric pressure variations on mean sea level changes from TOPEX/POSEIDON, accepted for publication in J. Atmos. Ocean. Technology, 1999.

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2.46 GEN_ENV_MSS_01 - To compute the mean sea surface height (Solution 1)

2.46.1 Heritage

TOPEX-Poseidon, ERS-1, ERS-2, Jason-1, Jason-2, ENVISAT

2.46.2 Function

To compute the height of the mean sea surface (MSS) and the associated accuracy at the location of the

altimeter measurement, from the MSS input file.


2.46.3.1 Input data

• Location:


• MSS value and accuracy (geographical grid, SAD)


Interpolation window size (even) MSS offset


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

• MSS interpolation flag

• MSS accuracy


The height of the MSS is computed at the altimeter measurement using a squared window of NxN MSS


window as function of grid point latitude for each MSS column. Each of these spline functions is evaluated


longitude. The height of the MSS is derived by evaluating the spline at the altimeter longitude. When one

MSS grid point has a default value (grid point over land), then a lower N value is tried. If spline


the computed height of the MSS.

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A MSS flag is also derived. It addresses the quality of the interpolation by providing the number of grid

cells used during the spline (or bilinear) interpolation process. The accuracy is also provided at the location

of the measurement by the MSS accuracy map (calibrated formal errors) using a bi-linear interpolation.

2.46.4 Comments

CNES-CLS-11 is the baseline for the current issue of Sentinel-3 processing.

2.46.5 References

• Hernandez, F. and P. Schaeffer, 2000: Altimetric Mean Sea Surfaces and Gravity Anomaly maps inter-comparisons AVI-NT-011-5242-CLS, 48 pp. CLS Ramonville St Agne.

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2.47 GEN_ENV_MSS_02 - To compute the mean sea surface height (Solution 2)

2.47.1 Heritage

None

2.47.2 Function

To compute the height of the mean sea surface (MSS) at the location of the altimeter measurement, from

the MSS input file.


2.47.3.1 Input data

• Location:


• MSS value (geographical grid, SAD)


Interpolation window size (even) MSS offset


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

• MSS interpolation flag


The height of the MSS is computed at the altimeter measurement using a squared window of NxN MSS


window as function of grid point latitude for each MSS column. Each of these spline functions is evaluated


longitude. The height of the MSS is derived by evaluating the spline at the altimeter longitude. When one

MSS grid point has a default value (grid point over land), then a lower N value is tried. If spline


the computed height of the MSS.

A MSS flag is also derived. It addresses the quality of the interpolation by providing the number of grid

cells used during the spline (or bilinear) interpolation process.

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2.47.4 Comments

DNSC/DTU10 is the baseline for the current issue of Sentinel-3 processing.

2.47.5 References

• Andersen O. B, Knudsen P (2009): The DNSC08 mean sea surface and mean dynamic topography. J. Geophys. Res., 114, C11, 2009.

• Andersen, O. B.: The DTU10 Gravity field and Mean sea surface (2010) Second international symposium of the gravity field of the Earth (IGFS2), Fairbanks, Alaska

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2.48 GEN_ENV_SUR_01 - To determine the radiometer surface type

2.48.1 Heritage

ERS-1/2 (MWR), ENVISAT (MWR), Jason-1 (JMR)

2.48.2 Function

To determine if the surface type corresponding to the radiometer measurement is over land or over

ocean. Two surface types are derived: one for the brightness temperatures and the other one for the

radiometer path delay.


2.48.3.1 Input data

• Location:

Latitude of the radiometer measurement Longitude of the radiometer measurement

• Land/sea mask file (SAD)

• Processing parameters (SAD) :

Characteristics of the reference ellipsoid (semi-major axis, flattening) Radial ground distance data :

The radial ground distance from the sub-satellite point along nadir at which land contamination would be sufficient to corrupt the subsequent path delay estimate by approximately 0.5 cm (used to flag the path delay)

The radial ground distance from the sub-satellite point along nadir from which land contamination of path delay is lower with along-track averaging than without (used to flag the radiometer main beam brightness temperatures for their proper selection in the along-track averaging procedure).


• Land fraction of the radiometer measurement for path delay flag

• Land fraction of the radiometer measurement for main beam brightness temperatures flag

• Radiometer surface type flag


The mathematical statement is detailed in Ruf, 1999a. From the antenna pattern characteristics and an

approximate path delay retrieval algorithm, a single radial ground distance from the sub-satellite point

along nadir can be estimated at which land contamination would be sufficient to corrupt the subsequent

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path delay estimate by approximately 5 mm. This distance is 50 km. It is therefore recommended that

path delay retrievals within 50 km of land be flagged as possibly contaminated. On the other hand, as path

delay retrievals at distances from land greater than approximately 25 km have lower error with along

track averaging than without, it is also recommended that brightness temperature samples be eliminated

from the along track averaging algorithm when they are within 25 km from land. This 25-km distance is

different from the 50-km distance at which the path delay algorithm begins to degrade. The difference is

due to the fact that, even with degraded performance, it is still preferable to maintain along track

averaging between 25 and 50 km from land in order to maximize the partial cancellation of brightness

temperature errors in the path delay algorithm. The present algorithm thus outputs two radiometer

surface type flags. The first one acts as a path delay quality flag : it corresponds to the 50-km distance.

The second one is only used for proper selection of main beam brightness temperatures in the along track

averaging algorithm : it corresponds to the 25-km distance.

Each of these two distances is translated into the number of grid points of the land/sea mask file to include

in a search for land presence around the location of the radiometer measurement (note that the same

land/sea mask file is used in the altimeter processing to determine the surface type for the altimeter). The

percentage of grid points within this search area that are set to “continental ice” or “land” is then

determined. Subsequent computations will assume that if this percentage is > 0, then the measurement

is contaminated by land.

The surface type of the MWR is defined by the surface type of the grid point closest to the MWR sample.

2.48.4 Comments

This algorithm is issued from ENVISAT processing. It is generic enough to be applied to the S3 mission and

can be parametrized according to the specific S3 needs (e.g., no along averaging).

For the L2 processing, the radiometer land fraction to use is the one for main beam brightness

temperatures land contamination.

2.48.5 References

Ruf, C.S., 1999a : Jason Microwave Radiometer – Land Contamination of Path Delay Retrieval. 22 February

1999

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2.49 GEN_ENV_SUR_02 - To compute the Ocean/Sea-Ice flag and Classes

Memberships

2.49.1 Heritage

ENVISAT

2.49.2 Function

To compute a 6-states ocean/sea-ice flag indicating open water or sea-ice type (i.e. first-year ice, multi-

year ice, wet ice, ambiguous / mixture of type) along with an additional “not evaluated” state in case of

failure. This information is completed with the 4 memberships values (between 0 and 1) associated to the

4 classes (open water, first-year ice, multi-year ice, and wet ice) to allow user to set their own threshold

on the membership value.


2.49.3.1 Input data

• Datation:


• Location:




Backscatter coefficient corrected for atmospheric attenuation (main band) Associated validity flag (main band)






• Ocean/Sea-ice flag

• Memberships value associated to the 4 classes (open water, first-year ice, multi-year ice, and wet ice)

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The state of the flag (i.e. the open water/sea-ice type) is derived from a set of measurements that includes

the Ku-band backscatter coefficient and the two brightness temperatures.

First, this set is used to compute the input parameters vector x

(x1, x2, x3) of the clustering algorithm as:

• x 1 = average of TB, • x 2 = Ku-band σ0 • x 3 = TB difference defined as (TB_36.5 – TB_23.8).

Then, the location and time of the measured data is used to identify the concerned polar region (i.e. Arctic

or Antarctic) and the season (i.e. winter or summer) in order to determine the appropriate mask

(seeFigure 4) that specifies where the algorithm has to be used.

Figure 4 - Geographical masks: in blue for winter and in red for summer.

The classes’ memberships are computed from a matrix of tie-point M ( 1pt

, 2pt

, …) that was specified

during the development phase (i.e. determination of the number of cluster and the coordinates of the tie-

point associated to each cluster in the input space, see “References”). The tie-point matrix defines a

partition of the input space into a given number of clusters.

Standard Euclidean distances are used to compute the different membership values between a given

observation x

and each tie-point vector pit

of the clustering algorithm.

Then the observation x

is assigned to the cluster with the closest tie-point vector in term of distance

which can also be said as: the observation x

is assigned to the cluster with the highest computed

membership. The state of the flag can be set.

Finally, the validity mask and a post-classification correction are applied for specific known cases of bad

classification.

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2.49.4 Accuracy


2.49.5 References

Tran N., F. Girard-Ardhuin, R. Ezraty, H. Feng, and P. Femenias, “Defining a sea ice flag for ENVISAT

altimetry mission”, IEEE GRS letters, doi:10.1109/LGRS.2008. 2005275, 6 (1), 77-81, 2009

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2.50 GEN_ENV_SUR_03 - To compute the Continental Ice flag

2.50.1 Heritage

None

2.50.2 Function

To compute a 14-state flag indicating the type of the ice-sheet snow facies (“0: not evaluated”, “1:

Greenland type 1”, “2: Greenland type 2”, “3: Greenland type 3”, “4: Greenland type 4”, “5: Greenland

type 5”, “6: Greenland type 6”, “11: Antarctica type 1”, “12: Antarctica type 2”, “13: Antarctica type 3”,

“14: Antarctica type 4”, “15: Antarctica type 5”, “16: Antarctica type 6”, “17: Antarctica type 7”)


2.50.3.1 Input data

• Datation:


• Location:




Backscatter coefficient corrected for atmospheric attenuation (main band) Associated validity flag (main band) Backscatter coefficient corrected for atmospheric attenuation (auxiliary band) Associated validity flag (auxiliary band)






• Ice-sheet snow facies type flag

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The state of the flag (i.e. the ice-sheet snow facies type) is derived from a set of measurements that

includes the two backscatter coefficients and the two brightness temperatures.

First, this set is used to compute the input parameters vector x

(x1, x2, x3, x4) of the clustering algorithm

as:

x 1 = Ku-band σ0, x 2 = average of TB, x 3 = ratio of TB defined as (TB_23.8 – TB_36.5) / (TB_23.8 + TB_36.5), x 4 = σ0 difference defined as (Ku σ0 – C σ0).

Then, the location of the measured data is used to identify the concerned ice-sheet (i.e. Greenland or

Antarctica) in order to use the appropriate matrix of tie-point M ( 1pt

, 2pt

, …) among the two available

ones that were specified during the development phase (i.e. determination of the number of cluster and

the coordinates of the tie-point associated to each cluster in the input space, see “References”). Each tie-

point matrix defines a partition of the input space into a given number of clusters.

Standard Euclidean distances are computed between a given observation x

and each tie-point vector pit

of the selected clustering algorithm.

Then the observation x

is assigned to the cluster with the closest tie-point vector in term of distance

which can also be said as: the observation x

is assigned to the cluster with the highest computed

membership. The state of the flag can be set.

2.50.4 Accuracy


2.50.5 References

Tran N., F. Rémy, H. Feng, and P. Femenias, “Snow facies over ice sheets derived from ENVISAT active and

passive observations”, IEEE Trans. On Geoscience and Remote Sensing, doi: 101109/TGRS.2008.2000818,

46(11), 3694-3708, 2008.

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2.51 GEN_ENV_SUR_04 - To determine the Surface Classification flag

2.51.1 Heritage

None

2.51.2 Function

To compute a 7-state flag indicating the type of the overflown surface (0: “Open ocean”, 1: “Land“, 2:

“Continental waters“, 3: “Aquatic vegetation“, 4:”Continental ice and snow“, 5:”Floating ice“, 6:”Salted

basin“).


2.51.3.1 Input data

• Location:

Latitude of the altimeter measurement Longitude of the altimeter measurement

• Surface classification mask file (SAD)

• Universal constants (SAD)


• Surface classification flag (7-states)


The surface classification is determined using a grid map with 7 possible states. Considering a

measurement, and its longitude and latitude, the process looks for the 4 grid points surrounding it. Then,

the ground distance to each of these 4 points is computed and the surface classification of the closest one

is assigned to the measurement.

2.51.4 References

Moreau T., Mercier F. Thibaut P., “Développement d’un nouveau masque de surface pour le MNT bord

Altika”,CNES study, January 2010.

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2.52 GEN_ENV_TID_01 - To compute the solid earth and the equilibrium long

period ocean tide heights

2.52.1 Heritage

TOPEX/Poseidon-1, Jason-1, Jason-2, ENVISAT

2.52.2 Function

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


2.52.3.1 Input data

• Datation:

Altimeter time tag

• Location:


• Cartwright and Edden tables of tide potential amplitudes of the 6 astronomical variables at the reference epoch (22 May 1960 at 12H).

• Frequencies i and phases i at 0h on 1/1/1900, of 5 astronomical variables, respectively the mean longitude of the moon, the mean longitude of the sun, the mean longitude of the lunar perigee, the negative of the mean longitude of the lunar ascending node and the mean longitude of the solar perigee


Love numbers


• Height of the solid Earth tide

• Height of the equilibrium long period ocean tide


The gravitational potential V induced by an astronomical body can be decomposed into harmonic

constituents s, each characterized by an amplitude, a phase and a frequency. Thus, the tide potential can

be expressed as:

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=

=2n s

n )s(VV

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

odd)nm(for.m)s(t).s(sin.W).s(c.g)s(V

even)nm(for.m)s(t).s(cos.W).s(c.g)s(V

mn

n

0m

nn

mn

n

0m

nn

=+++=

=+++=

=

=

where the phase (s).t + (s) of constituents at altimeter time tag t (relative to the reference epoch), is

given by a linear combination of the corresponding phases of the 6 astronomical variables i.t + i:

=

+=+6

1i

iii t.).s(k)s(t).s(

where is the altimeter longitude, where nmW is the associated Legendre polynomial (spherical harmonic)

of degree n and order m ( )(sinWnm , with altimeter latitude), and where g is gravity.

The Cartwright and Edden tables provide for degree n=2 and order m=0,1,2, and for degree n=3 and order

m=0,1,2,3 the ki(s) coefficients and the amplitudes cn(s) for each constituent s (only amplitudes exceeding

about 0.004 mm have been computed by Cartwright and Tayler (1971), and Cartwright and Edden (1973)).

This allows for the potential to be computed.

The solid Earth tide height and the height of the equilibrium long period ocean tide are both proportional

to the potential. The proportionality factors are the so-called Love number Hn and Kn.

The solid Earth tide height H_solid is thus:

g

V.H

g

V.HSolid_H 3

32

2 +=

with:

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

V3 = V30 + V31 + V32 + V33

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

( ) ( )g

V.KH1

g

V.KH1Equi_H 30

3320

22 +−++−=

with:

K2 = 0.302 K3 = 0.093

The above described tide contributions do not take into account the permanent tide.

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2.52.4 Accuracy

The accuracy of the solid earth tide height and of the height of the equilibrium long period ocean tide is

better than 1 mm.

We refer the reader to the following references:

• SLOOP Project (CNES), Tâche 2.11 : "Analyse des covariance d'erreur de l'altimétrie", CLS-DOS-NT-09-166-SLOOP-Tache.2.11, 2009

• [J. Dorandeu et al., 2009] “Introduction/Overview: from a global system error budget to application-specific error budgets”, Presentation at the Ocean Surface Topography Science Team, Seatle, 2009.

2.52.5 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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2.53 GEN_ENV_TID_03 – To compute the tide heights (solution 2 – Generic

computation)

2.53.1 Heritage

TOPEX/Poseidon, ERS-1, ERS-2, Jason-1, Jason-2

2.53.2 Function

Using FES model :

• To compute the height of the ocean tide (sum of the diurnal and semidiurnal ocean tide from the harmonic components algorithm). The ocean tide height does not include the load tide height.

• To compute the height of the diurnal and semi-diurnal tidal loading induced by the ocean tide predicted by the model that was also used to compute the ocean tide height, and to compute the height of the long period tidal loading.

• To add the ocean tide and the load tide to compute the elastic ocean tide.

• To compute the height of the total and of the equilibrium long period ocean tides, and to derive the height of the non equilibrium long period ocean tide (accounting also for long period loading tides).

• To add the height of the equilibrium long period ocean tide to the elastic ocean tide to compute the geocentric ocean tide that is provided in output.


2.53.3.1 Input data

• Datation:

1-Hz Altimeter time tag

• Location:


• Static auxiliary data consisting of amplitudes and phases of the various waves to be used


• Geocentric ocean tide height (solution 2, diurnal and semi-diurnal elastic ocean tide-height)

• Total loading tide height (solution 2)

• Equilibrium long period ocean tide height (solution 2)

• Non equilibrium long period ocean tide height (solution 2)

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The ocean tide height, the height of the tidal loading, the total long period tide height and the equilibrium

long period ocean tide height are computed using the FES library distributed by AVISO, with support from

CNES. The total long period tide height is computed by adding the long period ocean tide height and the

long period tidal loading height. The non equilibrium long period tide height is derived by removing the

equilibrium long period ocean tide height to the total long period tide height

2.53.4 Accuracy

/

2.53.5 Comments

/

2.53.6 References

FES2012 and FES2014 were produced by NOVELTIS, LEGOS and CLS Space Oceanography Division, and

distributed by AVISO, with support from CNES (http://www.aviso.altimetry.fr).

http://www.aviso.altimetry.fr/

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2.54 GEN_ENV_TID_04 - To compute the diurnal and semidiurnal elastic ocean

tide height and the load tide height (solution 1 – 28 components)

2.54.1 Heritage

TOPEX/Poseidon, ERS-1, ERS-2, Jason-1, Jason-2, ENVISAT

2.54.2 Function

• To compute the sum total of the diurnal and semidiurnal ocean tide from the GOT4.10 (see “References”) harmonic components algorithm (using GOT4.10 model). The ocean tide height does not include the load tide height.

• To compute the height of the diurnal and semi-diurnal tidal loading induced by the ocean tide predicted by the model that was also used to compute the ocean tide height (solution 1: GOT00 harmonic components).

• To add the ocean tide and the load tide to compute the elastic ocean tide.

• To add the height of the equilibrium long period ocean tide (issued from "GEN_ENV_TID_01 : To compute the solid earth and the equilibrium long period ocean tide heights”) to the elastic ocean tide, to compute the geocentric ocean tide that is provided in output.


2.54.3.1 Input data

• Datation:

Altimeter time tag

• Location:


• Height of the equilibrium long period ocean tide

• Harmonic coefficients maps of the principal tidal waves (SAD)

• Load tide harmonic coefficients maps of the principal tidal waves (SAD)

• The frequencies and the phases at 0h on 1/1/1900 of five astronomical variables, respectively the mean longitude of the moon, the mean longitude of the sun, the mean longitude of the lunar perigee, the negative of the mean longitude of the lunar ascending node and the mean longitude of the solar perigee

• The frequencies of the 28 tidal waves

• The admittance parameters

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• Geocentric ocean tide height (solution 1 = GOT4.10 harmonic components)

• Height of the tidal loading (solution 1 = GOT4.10 harmonic components)


• The height of the ocean tide (semi-diurnal and diurnal tidal waves) is the sum of N tidal constituents hi:

)sin().,(B)cos().,(A.Fh iiiiii += (i=1,N)

with:

iiii UXt. ++= Fi is the tidal coefficient of amplitude nodal correction (depends only on the altimeter time) Ui is the tidal phase nodal correction (depends only on the altimeter time) Xi is the tidal astronomical argument (depends only on the altimeter time)

i is the tidal frequency

t, and are respectively the altimeter time tag, latitude and longitude

Ai(,) and Bi(,) are harmonic coefficients bilinearly interpolated at the altimeter location (,) from the input harmonic coefficients map given by the GOT4.10 model (Ray, 1999). Harmonic coefficients A and B are tidal amplitude x cos(phase) and tidal amplitude x sin(phase) respectively.

• The height of the tidal loading is the sum of N constituents hi:

)sin().,(D)cos().,(C.Fh iiiiii += (i=1,N)

Ci(,) and Di(,) are harmonic coefficients bilinearly interpolated at the altimeter location (,) from

the input harmonic coefficients map. This map has been computed from Ray (1999). N = 26 tidal

constituents were used. Among these 26 tidal constituents, 8 principal ones were given in input

amplitudes and phases maps, the 18 remaining ones were computed by admittance from the principal

constituents 1 to 8, using admittance coefficients.

Two additional principal waves (S1 and M4) are taken into account, leading thus to a total number of

28 components.

• The height of the geocentric ocean tide height is the sum of the height of the ocean tide, the height of the tidal loading and the height of the equilibrium long period ocean tide (input of the algorithm)

2.54.4 Accuracy

The ocean tide model GOT99.2, is essentially an update of the one described by E Schrama and R Ray in

Journal of Geophysical Research, v.99, p 24799, 1994. The new solution is described in detail in Ray (1999).

Solution GOT99.2 used 232 cycles of Topex and Poseidon data, and it solved (among other things) for 8

semidiurnal and diurnal tides (Q1,O1,P1,K1,N2,M2,S2,K2). The tides were computed as adjustments to

the hydrodynamic model FES94.1. Outside the latitude limits of Topex (66 deg), the model defaults (by a

taper) to FES94.1. A comprehensive comparison study of the new tide models available before the JASON-

1 and ENVISAT launch dates has been performed by Dorandeu et al. (2000).

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We also refer the reader to the following references:

• SLOOP Project (CNES), Tâche 2.11 : "Analyse des covariances d'erreur de l'altimétrie", CLS-DOS-NT-09-166-SLOOP-Tache.2.11, 2009

• [J. Dorandeu et al., 2009] “Introduction/Overview: from a global system error budget to application-specific error budgets”, Presentation at the Ocean Surface Topography Science Team, Seatle, 2009.

2.54.5 Comments

• In the specification section, equations (3) to (85) are to be computed for the first processed altimeter measurement, and then only when the day of the altimeter measurement is changing.

• The present algorithm must be implemented in such a way that the diurnal and semi-diurnal ocean tide alone or the load tide alone, can be computed.

• An algorithm (management or specified in the processing steps) may be required to generate the time of the altimeter measurement in the required input format.

• There is a know anomaly on this algorithm over lakes and enclosed sea. This mathematical statement is indeed correct as far as land and ocean are concerned, but lakes and enclosed seas are conspicuously absent from the statement (see PDR RID 159). The anomaly will be corrected in a further issue.

• Moreover, the use of GOT00.2 is the baseline for the first issue of the Sentinel-3 processing, but GOT4.7 or higher will be taken into account in a further issue (see PDR RID 158).

• The present algortihm applies to GOT4.10 model.

2.54.6 References

• Dorandeu, J., M. Ablain, F. Lefèvre and R. Ray (2000) : New tide models evaluation. Preliminary report. AVI-NT-011-0253-CLS, April 2000. Available on Internet at ftp://spike.cnes.fr/pub/poseidon/doc/tide.pdf

• The GOT00.2 ocean tide model , is the latest solution in a series beginning with the work described in: E J O Schrama and R Ray, Journal of Geophysical Research, v.99, p 24799, 1994. Its immediate predecessor (GOT99.2) is desribed in: R Ray, A global ocean tide model from Topex/Poseidon altimetry: GOT99.2, NASA Tech Memo 209478, 58 pages, Sept. 1999. Solution GOT00.2 used 286 10-day cycles of Topex and Poseidon data, supplemented in shallow seas and in polar seas (latitudes above 66deg) by 81 35-day cycles of ERS-1 and ERS-2 data. The solution consists of independent near-global estimates of 7 constituents (Q1,O1,K1,N2,M2,S2,K2, with P1 inferred). An a priori model was used that consisted of the hydrodynamic model FES94.1 of Le Provost et al., and several other local hydrodynamic models, including Mike Foreman's in the Gulf of Alaska. Some effort was devoted to removing the boundary problems in FES94.1, although this was not 100% successful. The ERS data appear most useful in the Norwegian and Barents Seas.

ftp://spike.cnes.fr/pub/poseidon/doc/tide.pdf

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2.55 GEN_ENV_TID_05 - To compute the pole tide height

2.55.1 Heritage

TOPEX/Poseidon, Jason-1, Jason-2, ENVISAT

2.55.2 Function

To compute the geocentric tide height due to polar motion.


2.55.3.1 Input data

• Datation:

Altimeter time tag

• Location:


• Surface type (“open ocean or semi-enclosed seas”, “enclosed seas or lakes”, “continental ice”, or “land”)

• Pole location data (DAD):

Date x (along the 0° meridian - arc second) y (along the 90°W meridian - arc second)


Average pole position (arc second): x_avg, y_avg Scaled amplitude factor: A


• Height of the pole tide: H_Pole


The Earth’s rotational axis oscillates around its nominal direction with apparent periods of 12 and 14

months. This results in an additional centrifugal force which displaces the surface. The effect is called the

pole tide. It is easily computed if the location of the pole is known (Wahr, 1985), by:

)sin().avg_yy()cos().avg_xx().2sin(.APole_H −−−=

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where H_Pole is expressed in m, and where and are respectively the longitude and latitude of the

measurement. x and y are the nearest previous pole location data relative to the altimeter time.

A is the scaled amplitude factor in m:

A = - )K + (1 . 3600 x 180

. g 2

R 2

22 open ocean or semi-enclosed seas

A = - 2

22

H . 3600 x 180

. g 2

R over other surfaces (enclosed seas or lakes, land, continental ice)

where is the nominal earth rotation angular velocity in radian/s, R is the earth radius in m, g is gravity

in m/s2, 3600 x 180

is a conversion factor from arc second to radian, H2 and K2 are Love numbers (H2 =

0.609, K2 = 0.302). Over ocean, A = -69.435 10-3.

2.55.4 Accuracy

NTC processing uses predicted pole locations, whereas STC processing will probably use true (measured)

pole locations. The use of measured pole locations instead of predicted ones has probably little 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 tide height.

2.55.5 Comments

The anomaly on this algorithm over lakes and enclosed sea (see PDR RID 159) identified in issue 3.0 is

corrected in the current issue of the document.

2.55.6 References

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

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2.56 RAD_PHY_ATT_01 - To compute the SRAL sigma0 atmospheric attenuations

2.56.1 Heritage

ENVISAT, Jason-2

2.56.2 Function

To compute the altimeter backscatter coefficient (Sigma0) atmospheric attenuation in both bands.


2.56.3.1 Input data

• Brightness temperatures:

Radiometer brightness temperatures

• Land flag:

Radiometer land flag

• Backscatter coefficient

Ku-band ocean backscatter coefficient Ku-band ocean backscatter coefficient validity flag

• Model wet tropospheric correction



• Backscatter coefficient two-way atmospheric attenuation for Ku band

• Backscatter coefficient two-way atmospheric attenuation for C band

• Flag indicating the use of climatological values for the computation of the Sigma0 atmospheric attenuations


As for the ENVISAT mission, the Ku-band and C-band backscatter coefficient two-way atmospheric

attenuations are computed from the MWR 23.8 GHz and 36.5 GHz brightness temperatures (interpolated

at the SRAL time tag) and from the Ku-band sigma0, using a neural network function.

For non nominal cases (failure of the interpolation of radiometer data to altimeter time-tags, or MWR

measurement over land, or brightness temperatures out-of-range, or invalid backscatter coefficient), the

backscatter coefficient two-way atmospheric attenuations for both bands are computed (in dB) by:

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= .20sigma_Att

where is obtained as a linear function of the model path delay value:

)dB(Delay_Path*kv0k

)dB(Delay_Path*cv0c

ModelMod_Ku

ModelMod_c

+=

+=

c0, cv, k0 and kv being coefficients.

2.56.4 Comments

None

2.56.5 References

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

• Keihm, S. J., M. A. Janssen, and C. S. Ruf, TOPEX/POSEIDON microwave radiometer (TMR): III. Wet troposphere range correction algorithm and pre-launch error budget, IEEE Trans. Geosci. Remote Sensing, 33, 147-161, Jan, 1995

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2.57 RAD_PHY_GEN_01 - To compute the MWR geophysical parameters at SRAL

time tag

2.57.1 Heritage

ERS-1, ERS-2, ENVISAT

2.57.2 Function

To compute the MWR geophysical parameters (wet tropospheric correction, water vapor and cloud liquid

water contents) at SRAL time tag.


2.57.3.1 Input data

• Brightness temperatures:

Radiometer brightness temperatures

• Backscatter coefficient

Ku-band ocean backscatter coefficient Ku-band ocean backscatter coefficient validity flag



• Radiometer wet tropospheric correction

• Water vapor content

• Cloud liquid water content


As for the ENVISAT mission, the MWR geophysical parameters (wet tropospheric correction, water vapor

and cloud liquid water contents) are computed from the MWR 23.8 GHz and 36.5 GHz brightness

temperatures (interpolated at the SRAL time-tag) and from the Ku-band sigma0, using a neural network

function.

2.57.4 Comments

A flag must be provided in the L2 product to indicate the validity of the MWR wet tropospheric correction

depending of the overflown surface (e.g. invalid estimate over ice surfaces).

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2.58 RAD_PHY_GEN_02 - To compute the wet troposphere correction at SRAL

time tag (using SST and Gamma parameters)

2.58.1 Heritage

ENVISAT

2.58.2 Function

To compute the wet tropospheric correction from the radiometer brightness temperatures, from the Ku-

band backscattering coefficient, from the sea surface temperature and from the lapse rate (decreasing

rate of the atmosphere temperature with altitude).


2.58.3.1 Input data

• Time

• Location

• Radiometer measurements :

Brightness temperature at 23.8 GHz interpolated at the altimeter time tag Brightness temperature at 36.5 GHz interpolated at the altimeter time tag


• Altimeter measurement :

Ku-band ocean backscattering coefficient not corrected for the atmospheric attenuation Ku-band ocean backscattering coefficient validity flag


• Additional physical information

Sea surface temperature (4 seasonal tables, 2° resolution) Lapse rate (climatological table, 1° resolution)


• Wet tropospheric correction


The wet tropospheric correction is computed from the 5 inputs using a neural network function.

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2.58.4 Accuracy

See « References ».

2.58.5 Comments

The processing parameters for the neural network algorithm (weights and bias) consider cm units.

2.58.6 References

• Obligis E., A. Rahmani, L. Eymard and S. Labroue, 2008: An improved retrieval algorithm for the water vapor retrieval : Application to the ENVISAT MicroWave Radiometer, IEEE Transactions on Geoscience and Remote Sensing, vol. 47, n°9, pp 3057-3064.

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2.59 RAD_PHY_GEN_03 – To compute the wet tropospheric composite

correction

2.59.1 Heritage

CNES/CLS PISTACH Jason-2 project.

2.59.2 Function

To compute a wet tropospheric correction based on both radiometer and model corrections over areas

where the radiometer wet troposphere correction is missing or supposed as invalid due to the proximity

of emerged lands: coastal areas and/or radiometer gaps in open oceans. The overall principle of this

correction is to take advantage of the dynamics of the model correction where the radiometer correction

cannot be used.

For example, in the basic ocean/land transition case, the composite wet tropospheric correction takes:

• The values of the radiometer correction when the satellite if far enough from the shoreline (50 km for Jason-2, adjustable for S3),

• The values of the model correction plus an offset that corresponds to the bias between the radiometer and the model correction at the place of the last valid radiometer correction.


2.59.3.1 Input data

• Coastal configuration type (SAD)

• Model wet tropospheric correction

• Radiometer wet tropospheric correction



• Composite wet tropospheric correction


The composite wet tropospheric correction is computed for an entire track segment.

The radiometer correction and the model correction must be computed over the entire track segment

before starting the processing of the composite wet tropospheric correction. The coastal configuration

type is also assumed to be defined for the considered track segment.

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The methodology identifies several configuration types combining both the geographical position of the

measurement relative to the coasts and/or the validity of the radiometer correction.

Description of the various configuration:

OPEN_OCEAN:

The nadir of the satellite is far enough (about ~50km) from the closest emerged land.

The radiometer wet tropospheric correction is present and valid.

The composite correction is equal to the radiometer correction:

Composite_Correction(i) = Radiometer_Correction(i)

COASTAL_PATH:

The entire track segment is too close from any emerged land. Therefore, there is no valid radiometer

correction in the immediate vicinity of the measurement locations.

The composite correction is equal to the model correction:

Composite_Correction(i) = Model_Correction(i)

TRANSITION:

One end of the track segment holds a valid radiometer wet tropospheric correction (open ocean end)

The other end of the track segment is located near the coasts.

The composite correction is equal to the values of the model correction plus an offset that corresponds

to the bias between the radiometer and the model correction at open ocean end:

Composite_Correction(i) = Model_Correction(i) – DeltaModRad

where

DeltaModRad = Model_Correction – Radiometer_Correction at the open ocean end of the segment

SHORT_HOLE:

Some radiometer wet tropospheric corrections are missing or are invalid along a short (< ~200km)

track segment.

The composite correction is interpolated along the track segment based on the valid radiometer wet

corrections at each end of the segment:

Composite_Correction(i) = Radiometer_Correction(SegmentStartIndex)

+ ( i - SegmentStartIndex) * Inc

Where :

Inc = ( Radiometer_Correction(SegmentEndIndex) – Radiometer_Correction(SegmentStartIndex) )

/ (SegmentEndIndex – SegmentStartIndex)

LARGE_HOLE:

Some radiometer wet tropospheric corrections are missing or are invalid along a large (> ~200km) track

segment, too large so that the radiometer correction cannot be interpolated.

The model correction is used instead but is “detrented” so that each end of the segment fit the nearby

valid radiometer wet tropospheric corrections:

Composite_Correction(i) = Model_Correction(i) + (i-SegmentStartIndex) * Slope

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+ Radiometer_Correction(SegmentStartIndex)

– Model_Correction(SegmentStartIndex)

Where :

Slope = ( (Radiometer_Correction(SegmentEndIndex)

- Radiometer_Correction(SegmentStartIndex) )

- (Model_Correction(SegmentEndIndex)

- Model_Correction(SegmentStartIndex)) )

/ (SegmentEndIndex – SegmentStartIndex)

2.59.4 Accuracy


2.59.5 Comments

This methodology has been developed at CLS since 2002 and has been recently implemented in the Jason-

2 PISTACH products.

Note that this methodology is very close from the so-called “Dynamically Linked Model” developed by

Fernandes et al, 20031 at the University of Porto.

2.59.6 References

• Mercier (2004) Amélioration de la correction de troposphère humide en zone côtière CLS-DOS-NT-04-084.

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2.60 RAD_PHY_TEM_01 – To co-localize the radiometer pixels

2.60.1 Heritage

ENVISAT

2.60.2 Function

To perform the co-location of radiometer measurements from the two channels


2.60.3.1 Input data

• Radiometer time tags for the two channels

• Brightness temperatures for the two channels

• Latitude, Longitude of the channel 1 measurement

• Minimum number of measurement to be skipped (shift)

• Number of measurements to be checked to account satellite altitude and velocity variations (N_Dshift)


• Co-located Brightness temperature for the two channels

• Latitude, Longitude of the co-located measurements

• Time tag of the co-located measurements

• Flag of valid colocation


Principle

Co-location involves pairing radiometer measurements from the two channels which coincide over the

same point on the Earth’s surface. This is done by matching forward and backward channels with the

same or very similar latitude and longitude.

A first approximation of the number of measurements to skip for alignment of the two channels is

evaluated using the satellite altitude and velocity and the viewing angles of the channels. Moreover, due

to the satellite altitude and velocity variations, it is possible that a variation in localisation could occur. For

this reason, a check in the “N_Dshift” measurements after the “expected” one shall be performed to find

the best fit in terms of datation.

Main steps of the processing

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The 23.8 GHz channel is looking forward and therefore the location is first available for Channel 1 and

then for channel 2. Hence, for every measurement of channel 1 – starting from the first valid data, the

corresponding one of Channel 2 is searched in the record about “shift” samples far from the actual.

First the calculated shift is applied in order to account the mean value of skipped measurement due to

the “hard” mispointing of the two feeds.

j = i + shift

where “i” is the actual index of the channel 1 measurement and “j” is the actual index of the channel 2

measurement about which the correct data will be found

Then, being the evaluation of the shift made, a certain variation of this value is expected inside a fixed

range due to the satellite altitude and velocity variations. So all the time tags of the data inside this

range are checked in order to find the closest to the 23.8 GHz one:

( )k)h2(jTime_Tag_ch1(i)Time_Tag_cmin +− with k=0,N_Dshift

where N_Dshift is the number of measurement to be checked to account the satellite altitude and

velocity variations

Let j+k0 be the index of the channel 2 measurement closest to the actual channel 1 measurement.

Finally, the co-located brightness temperatures, the time tag and the location are computed using the

indexes i and j+k0.

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3 Acronyms

ACQ Acquisition

AD Applicable Document

ATBD Algorithms Theoretical Baseline Definition

CAL Calibration

COG Centre Of Gravity

DAAD Dynamic Anciliary/Auxiliary Data

DAM Data Acquisition and Management

GDR Geophysical Data Record

GNSS Global Navigation Satellite System

GPRW Gain Profile Range Window

GPS Global Positioning System

HK Housekeeping

IGDR Interim Geophysical Data Record

IPF Instrument Processing Facility

IR Impulse Response

ISP Instrument Source Packets

LRM Low Resolution Mode

LTM Long Term Monitoring

MDS Measurement Data Set

MOE Medium precision Orbit Ephemeris

MWR MicroWave Radiometer

N.A. Not Applicable

NRT Near Real Time

NTC Non Time Critical

OB On-Board

PDGS Payload Data Ground Segment

PLRM Pseudo LRM mode measurements from SAR mode pulses

POD Precise Orbit Determination

POE Precise Orbit Ephemeris

PTR Point Target Response

RD Reference Document

RINEX Receiver Independent Exchange Format

RTN Real Time Navigation

SAAD Static Anciliary/Auxiliary Data

SAR Synthetic Aperture radar

SDR Sensor Data Record

SRAL SAR Radar Altimeter

STC Short Time Critical

STM Surface Topography Mission

TAI International Atomic Time

TAS Thales Alenia Space

TBC To Be Confirmed

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TBD To Be Defined

USO Ultra Stable Oscillator

End of document

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