2.7.1.13 RA2 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:
  eq 2.80 
  eq 2.81 
where f_Ku and f_S are the
emitted frequencies (in Hz)
The RA2 total electron
content expressed in 101 TEC units (1
TEC unit = 1016 e/m2).is given by :
TEC_RA2 =  Iono_Alt_Ku *
(f_Ku)2 / 40250   eq 2.82 
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):
  eq 2.83 
  eq 2.84 
where σ(RKu) and
σ(RS) are respectively the 1Hz
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 1Hz range
standard deviations σ(RKu) and
σ(RS) as function of
waveheight SWH.
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
frequencydependent corrections.
The above equation shows that an error
of 5.5 cm on the difference bC  bKu
leads to a 1cm 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
1cm 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
Imel, D., Evaluation of
the TOPEX/POSEIDON dualfrequency
ionosphere correction, J. Geophys. Res.,
99, 24,89524,906, 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) :
  eq 2.87 
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 dualfrequency 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
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. Multimission altimeter
intercalibration 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:
  eq 2.88 
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
dualfrequency 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
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 SolarTerrestrial
Physics 61 (1999) 12051218
Jason GIM Ionosphere Correction Study
Report, CLS.DOSNT04194
Comparison IRI2001 / IRI95 in
altitude correction for GIM based
ionospheric corrections on
EnviSat CLS.DOSNT04193
2.7.1.17 Atmospheric attenuation correction
The Ku and Sband backscatter
coefficient twoway 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 RA2
time tag, σ_Ku is the
ocean backscatter coefficient for
Kuband (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:
2.103 dB for the atmospheric
attenuation of the S band backscattering
coefficient and 8.103 dB for the Ku band
backscattering coefficient.
As there are no measurements performed, no
upper bound of the errors can be given.
Reference
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 Kuband rain attenuation
The rain attenuation (dB) is
calculated using the ocean backscatter
coefficient for Kuband, σ0_Ku (dB)
Ref. [2.27 ]
by :
Rain_Att = Exp_Sigma0_Ku  σ0_Ku   eq 2.89 
Where the expected Kuband
backscatter coefficient, Exp_Sigma0_Ku,
is determined by linear interpolation in the
input table, as function of the Sband
backscatter coefficient.
Applicability

The Kuband rain
attenuation is computed for FDGDR,
IGDR and GDR product

The computation of
the Kuband rain attenuation is
performed continuously for all
surface types (over land and ocean)
Reference
Tournadre, J., and J.C.
Morland, The effects of rain on
TOPEX/POSEIDON Altimeter data, IEEE
Trans. Geosci. Remote Sensing, vol. 35,
pp 11171135, 1998.
2.7.1.19 Squared Off nadir angle of the
satellite computed from platform data
The squared
offnadir angle (Off_Nadir in radians) is
derived from the interpolated
pitch and roll mispointing angles by :
  eq 2.90 
Applicability

The platformderived
squared
offnadir angle is computed
for FDGDR, IGDR
and GDR products.

The computation of
the
platformderived squared
offnadir 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.
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 socalled "Spline
interpolation of grid values".
The mean sea surface has been computed using
a 7year TOPEX/POSEIDON mean
profile, a 5year ERS1/2 mean profile,
a 2Year GEOSAT mean profile and the 2
168day non repeat cycle data of
the ERS1 geodetic phase. All these data
have been preprocessed in order
to be
 more homogeneous, and referenced to the
7year T/P mean profile
 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 19931999).
This mean sea surface contains:
 Over ocean, the mean geoid plus the mean
ocean dynamic topography (19931999)
 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
More information can be obtained at: http://www.cls.fr/mss/
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 2.53
cm rms.
Reference
Hernandez, F. and P.
Schaeffer, 2000: Altimetric Mean Sea
Surfaces and Gravity Anomaly
maps intercomparisons,AVINT0115242CLS,
48 pp. CLS Ramonville St Agne.
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 socalled "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
Lemoine, F.G. et al.,
1998 : The development of the joint
NASA GSFC and NIMA Geopotential model
EGM96, NASA/TP1998206861, 575 pp, July 1998
