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2.7.1.13 RA-2 ionospheric correction

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

The ionospheric corrections Iono_alt_Ku and Iono_alt_S (in mm) are given for the two frequencies by the following equations :

 eq 2.79
(1)

with:

where f_Ku and f_S are the emitted frequencies (in Hz)

The RA-2 total electron content expressed in 10-1 TEC units (1 TEC unit = 1016 e-/m2).is given by :

## Applicability

• The dual frequency ionospheric correction and the total electron content are computed for FDGDR, IGDR and GDR products.
• The computation of the dual frequency ionospheric correction and the total electron content are performed, continuously for all surface types (over land and ocean), although it is relevant to ocean surfaces only.

## Accuracy

From equation (1) of the mathematical statement, one can derive the standard deviation of Ku band and auxiliary band ionospheric corrections σ(Iono_Alt_Ku) and σ(Iono_Alt_Aux):

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

The table below gives the values of σ(Iono_Alt_Ku) and σ(Iono_Alt_S), assuming probable values for Ku band and S band 1-Hz range standard deviations σ(RKu) and σ(RS) as function of waveheight SWH.

##### Table 2.5
 SWH (m) σ(RKu) (cm) σ(RS) (cm) σ(Iono_Alt_Ku)(cm) σ(Iono_Alt_S) (cm) 2 1.5 4.5 0.3 5.0 4 3.3 10 0.6 11.1 8 5.5 16.5 1.0 18.4

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

The range combination algorithm assumes that the other range corrections are independent of the altimeter frequency. For the dual frequency TOPEX altimeter, the ionospheric correction for the Ku band is given by equation (8) in Imel's paper Ref. [2.22 ] :

 eq 2.85
, with
 eq 2.86
for TOPEX

In the above equation, Δrion is the derived ionospheric correction, RC and RKu are the measured C and Ku ranges respectively, bC and bKu represent all the other potentially frequency-dependent corrections. The above equation shows that an error of 5.5 cm on the difference bC - bKu leads to a 1-cm error on the derived ionospheric correction. For the ENVISAT altimeter, the situation is better because the gap between the two bands is larger: an error of 17 cm on the difference bS - bKu leads to a 1-cm error on the derived ionospheric correction. Such errors on the difference bS - bKu could be due to errors on the absolute range bias difference between the two bands, or due to inaccuracies in the sea state bias parameterization for one of the frequencies.

## Reference

##### Ref 2.22
Imel, D., Evaluation of the TOPEX/POSEIDON dual-frequency ionosphere correction, J. Geophys. Res., 99, 24,895-24,906, 1994

2.7.1.14 DORIS ionospheric correction

The ionospheric corrections are obtained (in mm) by using the TEC (Total Electron Content, in e-/m2), from DORIS maps, which is interpolated, bilinearly in latitude and longitude, and linearly in time at the altimeter measurement. It is then used in the two following equations to derive the ionospheric corrections (in mm) :

where f_Ku and f_S are the emitted frequencies (in Hz). This algorithm is relevant only for GDR and IGDR products.

## Applicability

• The Doris ionospheric correction is computed for IGDR and GDR product.
• The computation of the Doris ionospheric correction is performed continuously for all surface types (over land and ocean).

## Accuracy

Comparison with the TOPEX dual-frequency altimeter estimates show that the global mean difference between the two ionospheric corrections (TOPEX and DORIS) is about 1 cm, with a standard deviation less than 2 cm .

## Reference

##### Ref 2.23
Le Traon, P.Y., J.P. Dumont, J. Stum, O.Z. Zanife, J. Dorandeu, P. Gaspar, T. Engelis, C. Le Provost, F. Remy, B. Legresy and S. Barstow, 1996. Multi-mission altimeter inter-calibration study, CLS/ESA contract number 11583/95/NL/CN

2.7.1.15 BENT model ionospheric correction

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

where f_Ku and f_S are the emitted frequencies (in Hz), and where TEC is the columnar total electron content of the ionosphere, expressed in e-/m2. TEC is computed for each altimeter measurement from the Bent model 2.7.1.15. .

2.7.1.16 GIM Ionospheric correction

The GIM ionospheric correction is based on Total Electron Content (TEC) grids which are operationally produced by JPL in delayed time (5 days) as well as in near real time (10 hours). The TEC is an integrated content (basically from 0km to >1400km). So an altitude correction factor is used to take account the EnviSat altitude. IRI95 was recommended by Iijima and al, 99 Ref. [2.24 ] . Studies drawn at CLS Ref. [2.25 ] had demonstrated that GIM correction is an efficient alternative to the dual-frequency ionospheric correction.

## Applicability

• The GIM correction is computed for IGDR and GDR product
• The computation of GIM correction is performed continuously for all surface types (over land, ice and ocean). Nevertheless, it is applicable only for ocean surfaces.

## Reference

##### Ref 2.24
Automated daily process for global ionospheric total electron content maps and satellite ocean altimeter ionospheric calibration based on Global Positioning System data B.A Iijima et al Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1205-1218

##### Ref 2.25

Jason GIM Ionosphere Correction Study Report, CLS.DOS-NT-04-194
Comparison IRI2001 / IRI95 in altitude correction for GIM based ionospheric corrections on EnviSat CLS.DOS-NT-04-193

2.7.1.17 Atmospheric attenuation correction

The Ku and S-band backscatter coefficient two-way MWR atmospheric attenuation (Att_σ_Ku and Att_σ_S in dB) are computed with neural algorithms as a function of TB23_Int, TB36_Int and σ_Ku.

where TB23_Int and TB36_Int are the 23.8 GHz and 36.5 GHz brightness temperatures (in K) interpolated to RA-2 time tag, σ_Ku is the ocean backscatter coefficient for Ku-band (dB).

## Applicability

• The MWR atmospheric attenuation correction is computed for FDGDR, IGDR and GDR product
• The computation of the atmospheric attenuation correction is performed continuously for all surface types (over land, ice and ocean). Nevertheless, it is applicable only for ocean surfaces.

## Accuracy

As this algorithm has been formulated over a representative database [RD], a minorant of the error is the rms difference obtained when applying directly the algorithm over the database: 2.10-3 dB for the atmospheric attenuation of the S band backscattering coefficient and 8.10-3 dB for the Ku band backscattering coefficient.

As there are no measurements performed, no upper bound of the errors can be given.

## Reference

##### Ref 2.26
S. LABROUE and E. OBLIGIS, "Neural network retrieval algorithm for the Envisat/MWR", report CLS/DOS/NT/03.848 of ESA contract n�13681/99/NL/GD, January 2003.

2.7.1.18 Ku-band rain attenuation

The rain attenuation (dB) is calculated using the ocean backscatter coefficient for Ku-band, σ0_Ku (dB) Ref. [2.27 ] by :

Where the expected Ku-band backscatter coefficient, Exp_Sigma0_Ku, is determined by linear interpolation in the input table, as function of the S-band backscatter coefficient.

## Applicability

• The Ku-band rain attenuation is computed for FDGDR, IGDR and GDR product
• The computation of the Ku-band rain attenuation is performed continuously for all surface types (over land and ocean)

None

## Reference

##### Ref 2.27
Tournadre, J., and J.C. Morland, The effects of rain on TOPEX/POSEIDON Altimeter data, IEEE Trans. Geosci. Remote Sensing, vol. 35, pp 1117-1135, 1998.

2.7.1.19 Squared Off nadir angle of the satellite computed from platform data

The squared off-nadir angle (Off_Nadir in radians) is derived from the interpolated pitch and roll mispointing angles by :

## Applicability

• The platform-derived squared off-nadir angle is computed for FDGDR, IGDR and GDR products.
• The computation of the platform-derived squared off-nadir angle is performed continuously for all surface types.

## Accuracy

At present, an interpolation mechanism is implemented as follows:

The absolute value of the difference between the input averaged L1b time to be processed and the State Vector time is calculated. If two records from the Envisat wide attitude file are found such that they embrace the time difference, the pitch and roll angles from the two records are extracted and used to obtain the interpolated pitch and roll angles.

## Reference

None

2.7.1.20 Mean sea surface height

The mean sea surface used is from CLS (Collecte Localisation Satellite), CLS01 Ref. [2.28 ] .

The mean sea surface has been estimated on a 1/30 (2 minutes) of a degree grid using a local inverse method, which also provides an estimation and an associated error field.

The height of the MSS is computed at altimeter measurement by spline interpolation in latitude and longitude of the gridded values at the altimeter measurement, using the mechanism so-called "Spline interpolation of grid values".

The mean sea surface has been computed using a 7-year TOPEX/POSEIDON mean profile, a 5-year ERS-1/2 mean profile, a 2-Year GEOSAT mean profile and the 2 168-day non repeat cycle data of the ERS-1 geodetic phase. All these data have been pre-processed in order to be

1. more homogeneous, and referenced to the 7-year T/P mean profile
2. less contaminated by the ocean topography variable signal (the mean ocean topography signal contained in the surface is thus corresponding to the mean sea level during the period 1993-1999).

This mean sea surface contains:

• Over ocean, the mean geoid plus the mean ocean dynamic topography (1993-1999)
• Over land, the EGS96 mean geoid
• In coastal areas (between ocean and land)... A smooth extrapolation/relaxation of the ocean values (geoid+mean dynamic topography) toward the EGM96 geoid

## Applicability

• The computation of the mean sea surface is performed for FDGDR, IGDR and GDR products.
• The computation of the mean sea surface is performed continuously for all surface types.

## Accuracy

To validate these MSS, the CLS01 and GSFC00.1 MSS were interpolated along the groundtracks of the T/P (7 years), ERS (5 years), and GEOSAT (2 years) mean profiles. The statistics show a systematic height difference between the two surfaces, characterised by mean difference of the order of 2.5-3 cm rms.

## Reference

##### Ref 2.28
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.

##### Ref 2.29
Hernandez and P. Schaeffer , The CLS01 Mean Sea Surface: A validation with the GSFC00.1 surface., December 2001, CLS, Ramonville St Agne.

2.7.1.21 Geoid height

The geoid model used is the EGM96 model Ref. [2.30 ] . The height of the geoid is computed at altimeter measurement by spline interpolation in latitude and longitude of the gridded values at the altimeter measurement, using the mechanism so-called "Spline interpolation of grid values".

## Applicability

• The geoid height is computed for FDGDR, IGDR and GDR products.
• The computation of the geoid height is performed continuously for all surface types.

## Accuracy

The geoid model used is the EGM96 model (Lemoine et al., 1998)

## Reference

##### Ref 2.30
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

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry

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