2.7 RA2/MWR Level 2 Products And Algorithms
2.7.1 RA2 Level 2 Algorithms
The level 2 processing algorithms are used
to generate the three main
level 2 products, namely the FDGDR
(Near Real Time product, available within
3 hours), the IGDR (OffLine
product, available within 3 to 5
days) and the GDR (OffLine product, available
within 3 to 4 weeks). The
relationship between these products is
described in section 2.2.
A general flowchart of the FDGDR, IGDR and
GDR level 2 processings is
given in figure. Each function (i.e.
algorithm) is represented by a box, and a table
indicates to which type of
level 2 processing(s) it belongs (grey
if the algorithm is performed, white if is
not performed). For example, the
algorithm "To Compute the
Doris ionospheric Correction" is performed
during the IGDR and GDR
processings but is not performed during the
FDGDR processing. Moreover, the rhythm of
activation of the algorithms (RA2
elementary measurements, RA2
averaged measurements or MWR averaged
measurements) is indicated. The
first 12 algorithms process the elementary
measurements at a rate of 18Hz while the
remaining 23 algorithms process the
average measurements at a rate
of 1Hz.

Table 2.4 General flowchart of the FDGDR, IGDR and GDR level 2 processings

RHYTHM OF
ACTIVATION

PROCESSING CHAIN

ALGORITHMS

FDGDR

IGDR

GDR

RA2  20 Hz




TO COMPUTE
THE AVERGAED TIME TAGS




To compute
THE AVERAGED
altitude, orbital
altitude rate
and location




To compute
THE altitude,
orbital altitude rate
and
location FROM ORBIT FILES




To compute
the Doppler correctionS




To perform
the seaice retracking




To perform
the ice1 retracking




To perform
the ice2 retracking




To perform
the oceaN retracking




TO COMPUTE
THE PHYSICAL PARAMETERS




To correct
the RA2 range for
Doppler effects




To compute
the Doppler slope
correction (ICE SURFACES)




TO EDIT AND
COMPRESS THE
OCEAN ESTIMATES

RA2  1 Hz




To determine
the surface type




To
interpolate MWR data to
RA2 time tags




To compute
the BACKSCATTER
COEFFICIENT
atmospheric attenuations




To compute
the 10 meter RA2
wind speed




To compute
the MWR
geophysical parameters at
RA2
time tag




To compute
the 10 meter MODEL
wind vector




To compute
the sea state biases




To compute
the dualfrequency
ionospheric corrections




To compute
the doris
ionospheric corrections




To compute
the Bent model
ionospheric corrections




To compute
the MODEL wet and
dry tropospheric corrections




To compute
the inverted
barometer effect




TO COMPUTE
THE MEAN SEA
SURFACE PRESSURE OVER
THE OCEAN




To compute
the NON
EQUILIBRIUM FROM THE
ORTHOTIDE ALGORITHM




To compute
the NON
EQUILIBRIUM FROM THE
HARMONIC
COMPONENTS ALGORITHM




To compute
the solid earth
and the long period
equilibrium
ocean tide heights




TO COMPUTE
THE HEIGHT OF THE
TIDAL LOADING




To compute
the pole tide height




To compute
the mean sea
surface height




To compute
the geoid height




To compute
the ocean depth /
land elevation

MWR  1 Hz




To
interpolate RA2 data to
MWR time tag




To compute
the MWR
geophysical parameters at
MWR
time tag

2.7.1.1 Ocean retracking algorithm
The ocean
retracking algorithm is the result of a
comparative study of the various
standard ocean retracking algorithms
Ref. [2.1 ]
, i.e. of :

CNES/CLS algorithm
designed to process
Poseïdon altimeter data

JPL algorithm designed
to process TOPEX
altimeter data

ESTEC algorithm designed
to process ERS altimeter data

ALENIA algorithm
designed to process
ENVISAT altimeter data
The mathematical
solution of these four retracking are very
close to each other, but the approch used in
the ESTEC algorithm is more
general and complete. So the retracking
implemented to process the ENVISAT RA2
data is based on ESTEC algorithm
improved with some particularities of the
others retracking algorithm.
The ocean
retracking algorithm is performed on the Ku
and on the S waveforms. The only
difference in the retracking of Ku
and S waveforms is the processed data
(waveform, processing and
instrumental parameters), while the
processing is the same.
The ocean
retracking algorithm objective is to make
the measured waveform coincide
with a return power model,
according to weighted Least Square
estimators using the
LevenbergMarquardt's method
Ref. [2.2 ]
. The expression of the model
versus time (t) is derived
from Hayne's model
Ref. [2.3 ]
.
Accounting for a skewness
coefficient (λs =
processing parameter), and assuming a
gaussian point target response (Hamming
weighting performed onboard the
RA2 altimeter), it is given by :
  eq 2.1 
with :
  eq 2.2 
  eq 2.3 
,
  eq 2.4 
θo = antenna
beamwidth, c = light velocity, h
= satellite height, Re = earth radius
  eq 2.5 
, σp = PTR width ,
  eq 2.6 
  eq 2.7 
,
  eq 2.8 
,
  eq 2.9 
, ξ = mispointing
  eq 2.10 
,
  eq 2.11 
and where the
parameters to be estimated are :
τ : the epoch
σc : the information
relative to the significant
waveheight (SWH)
Pu : the
amplitude which is related to the
backscatter coefficient (sigma0)
Pn : the thermal
noise level (to be removed from the waveform samples)
The square of
the mispointing is estimated using the
"ice 2" retracker, see
Ice2 retracking algorithm 2.7.1.2.
Computation of physical parameters

Altimeter range:
The 20Hz tracker altimeter range
corrected for the
COG motion and decorrected for the
Doppler effects
(Range in metres) is computed as
follows, using in
particular the distance antennaCOG
(Ant_COG)
selected for the averaged
measurement which contain
the processed elementary measurement:
  eq 2.12 
Where for each RA2 nominal tracking
data, the
Kuband and the Sband tracker
ranges are computed
(in seconds) from the input window
delays and from
offsets computed, by:
  eq 2.13 
  eq 2.14 
where
  eq 2.15 
  eq 2.16 
  eq 2.17 
(where Chirp_Sl be the selected chirp slope)
The 20Hz ocean altimeter range
corrected for the COG
motion and the Doppler effects
(Range_Ocean in
metres) is computed by:
  eq 2.18 
Where the updated Kuband and Sband
Doppler
compensations
(Doppler_Comp_Update_Ku,
Doppler_Comp_Update_S) are computed
from the
altitude rate (Sat_Alt_Rate(i) in
m/s), by:
  eq 2.19 
Where:
 Wavelength (106 m) is the
radar wavelength
(RA2 instrumental
characterisation data),
to be selected according to
the processed
band (Ku or S) and the
operating RF
subsystem (flag RV_RFSS_Def)
 Chirp_Sl (kHz/106 s) is the
chirp slope
(RA2 instrumental
characterisation data:
effective value (signed)),
to be selected
according to the processed
band (Ku or S),
the emitted bandwidth in Ku
band (flag
Chirp_Id) and the operating
RF subsystem
(flag RV_RFSS_Def).

Backscatter coefficient:
The 20Hz ocean backscatter
coefficient (Sigma0_Ocean
in dB) is computed by:
If
  eq 2.20 
then:
  eq 2.21 
Where Sigma0_scale is the scaling
factor for sigma0
evaluation (dB).

Significant waveheight:
the significant waveheight (SWH_Ocean
in metres) is
computed from the 1Hz SigmaC by:
If
  eq 2.22 
then
  eq 2.23 
Else:
  eq 2.24 
Where PTR_Width is the Point Target
Response width
fixed to 0.53*FFT_Step
Applicability

The ocean retracking
algorithm is
performed for FDGDR, IGDR
and GDR product.

The ocean retracking
algorithm is
performed continuously
whatever the surface
type is. Nevertheless, it is
optimized for ocean surfaces.
References
"RA2 retracking comparisons over
ocean surface by
CLS", CLS.OC/NT/95.028, Issue 3.1
Numerical Recipes : The Art of
Scientific Computing in C
(Edition 2). William H. Press, Brian P.
Flannery, Saul A.
Teukolsky, William T. Vetterling
Hayne
G.S. 1980 : "Radar Altimeter Mean
Return Waveforms
from NearNormalIncidence Ocean Surface
Scattering". IEEE Trans. on
antennas and
propagation, Vol. AP28, n°5, pp. 687692
2.7.1.2 Ice2 retracking algorithm
The ice2
retracking algorithm is performed on the Ku
and on the S waveforms. The only
difference in the retracking of Ku and
S waveforms is the processed data (waveform,
processing and instrumental
parameters), while the processing is the same
The ice2
retracking algorithm is an adaptation to the
ENVISAT RA2 background, of the
algorithm designed by LEGOS to
process ERS data over continental ice sheets
Ref. [2.4 ]
.
The aim of the
ice2 retracking algorithm is to make the
measured waveform coincide with a return
power model, according to Least
Square estimators. The expression of the
model versus time (t), is derived from
Brown's model
Ref. [2.5 ]
  eq 2.25 
(with :
  eq 2.26 
where the parameters to be
estimated are :
τ : the epoch
σL : the width of the
leading edge
Pu : the
amplitude which is related to the
backscatter coefficient (sigma0)
sT : the slope
of the logarithm of the waveform at the
trailing edge
Pn : the thermal
noise level (to be removed from the waveform samples)
Other parameters are also estimated:
The mean
amplitude or "mean power" (Pt) of
the waveform which 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. This
parameter is related to the ice 2 leading
edge backscatter coefficient.
The slope of the
first part of the logarithm of the trailing
edge (sT1) and the slope of the second part
of the logarithm of the trailing
edge (sT2) ). The slope is estimated by
linear regression of the logarithm of
the normalised waveform samples
in two windows part of the trailing edge:
the first one (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.
A third slope
(sT1m) is estimated as sT1, with an other
predefined width aimed at pointing out a
mispointing angle over ocean surfaces
  eq 2.27 
where Gamma is computed from
the antenna beam and where Alpha
is computed from the altitude, the
earth radius, the light velocity and Gamma
Computation of the physical parameters

Altimeter range :
The ice2 altimeter range corrected
for the COG motion
and the Doppler effects (Range_Ice2
in metres) is
computed by:
  eq 2.28 
Where the tracker altimeter range,
Range, is already
described in the Ocean retracking
algorithm paragraph.

Backscatter coefficients :
The ice2 leading edge backscatter
coefficient
(Sigma0_Le_Ice2 in dB) related to
the amplitude of
the waveform fitted at the leading
edge by using the
Erf function is computed by:
If
  eq 2.29 
then:
  eq 2.30 
The ice2 backscatter coefficient
(Sigma0_Ice2 in dB)
related to the integrated signal
over the waveform
is computed by:
If
  eq 2.31 
then:
  eq 2.32 
Applicability

The Ice2 retracking
algorithm is
performed for FDGDR, IGDR
and GDR product.

The Ice2 retracking
is performed
whatever the surface type
is. Nevertheless,
it is optimized for continental ice
sheets surfaces.
The the computation of the slope of
the logarithm of
the trailing edge for the
mispointing
estimation which is relevant to
ocean surfaces only.
References
B.
Legresy : "Etude du retracking des
formes d'ondes
altimetriques au dessus des calottes
polaires". CNES report
CT/ED/TU/UD/96.188, CNES
contract 856/2/95/CNES/0060, 1995.
G.S.
Brown : "The Average Impulse
Response of a Rough
Surface and its Applications". IEEE
Trans. on Antennas and Propagation, Vol.
AP25, Jan. 1977
2.7.1.3 Level 2 Ice Algorithms : General
A subset of the level 2
processing is concerned with improving
the accuracy of measurements over nonocean surfaces.
The ICE1 Retracking
algorithm is a range estimation technique
suitable for echoes returned from nonocean
surfaces. The Sea Ice Retracking algorithm
is the optimal method to apply to echoes
from areas of sea ice.
2.7.1.4 Level 2 Ice Algorithms : Retracking
Physical Justification :
Over topographic surfaces, a radar
altimeter onboard tracking system is unable
to maintain the echo waveform at the nominal
tracking position in the filter bank, due to
rapid range variation. This results in an
error in the telemetered range known as
tracker offset. Retracking is a term used to
describe a group of nonlinear ground
processing estimation techniques which
attempt to determine the tracker offset from
the telemetered echoes, and thereby
estimate the range to the point of closest
approach on the surface. Peaky echoes from
sea ice cause range tracking jitter, which
also results in tracker offsets.
The Ku and S band echo
waveform pairs are examined for quality
prior to elevation retrieval. The waveform
pair is parameterised and the parameters are
compared with thresholds. Flags are set up
to indicate data quality in the output. This
step is referred to as preprocessing.
There are two independent
retracking algorithms. The first is the
Offset CentreofGravity (OCOG) retracker,
intended for data from topographic surfaces.
The waveform pair is parameterised using the
OCOG scheme. From the parameterisation, a
tracker offset is calculated. Also an
estimate of the backscatter is made from the
power in the filter bank.
The second retracker is a
threshold retracker intended for use
with data from sea ice. From the
parameterisation, a tracker offset is
calculated. Again, an estimate of the
backscatter is made from the power in
the filter bank. Although the given
algorithm is general, only the Kuband
calculations are done for sea ice.
Note that for the RA2
instrument the tracker offset is always
measured from the centre of the range window
as this point corresponds to the telemetered
time delay as given in fields 20 and 21 of
the L1b product. The nominal tracking
position (Tp) is however variable and
derived from field 43 in the L1b product.
2.7.1.4.1 Preprocessing
Description:
Preprocessing attempts to determine if
the received echo has a shape
sufficiently recognisable that an
elevation may be determined from it. If
the instrument is not tracking, the
outputs are defaulted, and the
"Waveform OK" flags are set to
bad. Several tests are performed for the
echo at each frequency:
i) the noise power in
the waveforms is determined. This is
done by averaging the power in a set of
range filters in the early part the
waveforms. With echo waveforms from
nonocean surfaces, these power
values may be contaminated by the
surface return, and so thresholding is
used in the next step to reject
waveforms so contaminated, and for
other reasons.
ii) the absolute average
power of the echo is determined. If
this power is smaller than a multiple of
the noise power, the echo is regarded as
not valid.
  eq 2.33 
2.7.1.4.2 OCOG Retracking
Description: In this
algorithm, the Offset Centre of Gravity
waveform parameterisation is applied to
the waveform pair. From this
parameterisation, a tracking offset and
backscatter estimate are determined.
Tests are made on the extent of the
tracking offset, and extreme values are
flagged as retracking failures.
The OCOG waveform
amplitude is determined from the
waveform samples thus:
  eq 2.34 
and the tracking offset
is determined by finding the point
on the waveform (by interpolation) where
the waveform amplitude exceeds a
threshold determined from the OCOG
amplitude. A tracking offset is
determined for both Ku and S band. The
range must also be corrected for the
Centre Of Gravity (COG) offset, which is
the vertical distance from the
satellite centre of mass to the RA
antenna, as this correction factor is
not available in the L2 product.
  eq 2.35 
The retracker offset
and COG offset are added to the
telemetered range for output thus:
  eq 2.36 
The offset itself
can be recovered by subtracting the
telemetered range and the COG
correction. If the offset is outside
a predetermined range, the
retracking is deemed to have failed,
and the corresponding bit in
the ice1 retracking quality flag (L2
fields 134 & 135) is set to true (1).
The backscatter
(sigma0) is estimated using the
instrument link budget, which
is precalculated in the level 1b
parameter
(Fields 25 and 26), as follows:
  eq 2.37 
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
unsigned short integers. This means
that potentially at least, the
accumulated squares and fourth
powers can get extremely
large,
respectively for Ku band. Hence care
must be taken to prevent
wraparound, and the calculation is
best split up to avoid significance
loss even in double precision (a
brutal approach is to use
quadruple precision). The tracker
offset precision must be preserved
to its theoretical maximum (i.e.
consistent with the on board
tracking precision) of 1/256 of a filter.
2.7.1.4.3 SeaIce Retracking
Description: In this
algorithm, waveform parameterisation
based on peak threshold retracking is
applied to the Kuband waveform only.
From this parameterisation, a tracking
offset and backscatter estimate are
determined. Tests are made on the extent
of the tracking offset, and extreme
values are flagged as retracking failures.
The seaice waveform
amplitude is determined by finding the
maximum value of the waveform samples thus:
  eq 2.38 
and the tracking offset
is determined by finding the point
on the waveform (by interpolation) where
the waveform amplitude exceeds a
threshold determined from the above
seaice amplitude. A tracking offset
is determined for Ku band only. The
Centre Of Gravity offset correction must
be included in the range measurement as
the correction is not available
separately in the L2 product
  eq 2.39 
The retracker offset
and COG offset are added to the
telemetered range for output thus:
  eq 2.40 
The offset itself
can be recovered by subtracting the
telemetered range. If the offset is
outside a predetermined range, the
retracking is deemed to have failed,
and the corresponding bit in
the Seaice retracking quality flag
(L2 field 138) is set to true (1).
The backscatter is
estimated using the instrument link
budget, precomputed in the Level 1b
parameter
(Field 25), as follows:
  eq 2.41 
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 filter values are
sourced as unsigned short integers.
The tracker offset precision must be
preserved to its theoretical maximum
(i.e. consistent with the on
board tracking precision) of 1/256
of a filter.
2.7.1.5 Level 2 Ice Algorithms : Slope Correction
Physical Justification: The
Altimeter antenna boresite is pointed at
Nadir and the antenna has a field of view of
about 1.3 degrees (half power). The first
part of the reflected echo will come from
that part of the surface within the field of
view, that is closest to the satellite. Over
flat surfaces the closest point on the
surface is at Nadir but over sloping
terrain that will not be the case. When the
echo waveform is retracked the resulting
range measurement is a slantrange to a
point offset from Nadir. To use this
measurement it must be corrected for the
slant and relocated to the point of first
return offset from Nadir.
The correction is performed
by using models of the surface slope
which enable prediction of the direction of
the point of first return for any given
satellite location. Initially 2 models are
applied: one for Greenland and one for Antartica.
The algorithm is complex and
performed in several steps:

A coordinate
transformation to a hemispherical
Cartesian frame is performed to
facilitate correct interpolation of the
range for the echo direction
determination. The situation arises
because one must work with partial
derivatives of the range, and the range
must be interpolated in a Cartesian
frame in order to compute these
derivatives. It also provides a
convenient coordinate system for the
slope models. The transformation maps
any function defined in the
conventional altimetric (geodetic
ellipsoidal) coordinate system onto a
plane. This is accomplished via a pair
of transformations which implement
the Lambert equalarea map projection,
familiar from cartography.

A check is performed to
determine if a slope model is
present for the point of interest. If a
model is found, it is used to determine
from which direction (in the local
coordinate frame) the returned
echo power came. If no slope model is
found, the nadir direction is used.

The slopecorrected
elevation above the ellipsoid is
determined from the OCOG retracked
rangeand the echo direction by
evaluating some simple expressions. Note
that normally one would not
compute an elevation at Level 2, owing
to the need to correct the range for
propagation delays etc. However in this
case, the range error due to the
atmosphere etc does not disturb the
elevation position (or rather the
disturbances are insignificant), and the
elevation may be corrected a
posteriori. Users must be careful to
apply the range (elevation) correction
in the correct sense however (e.g. if a
correction is to be added to the range
measurement it is subtracted from an
elevation measurement).
2.7.1.5.1 Coordinate Conversion
Description: This
algorithm determines the
location of the spacecraft in a
hemispherical Cartesian
coordinate frame. The first step is a
straightforward calculation
of the meridional radius of
curvature of the ellipsoid
using the standard expression:
This quantity is then
used in the equations for
the Lambert equalarea projection:
  eq 2.44 
Note that this
projection cannot distinguish
the hemisphere of the earth under
consideration. Therefore a
'hemisphere flag' is used in
the slope model files, so
that files from the wrong hemisphere
cannot be accessed.
Accuracy
Some quantities in these
expressions are numerically small
(e.g. eccentricity), and
some are large (e.g. semimajor axis).
The latitude is derived from
the level 1b quantity which is
quantised to microdegrees.
It is converted to double precision
radians before use. The
calculation is all done in double
precision arithmetic to
preserve accuracy which is better than 1
centimetre on the above quantities.
2.7.1.5.2 Echo Direction
Description: This
algorithm determines the
direction from which the power in
the leading edge of the echo
came, by reference to a surface slopes model.
We determine the echo
direction
in a local Cartesian coordinate
frame (x,y) with its
origin at the subsatellite point on the
ellipsoid. This frame is the
tangent plane to the ellipsoid, and
provides a local
approximation to the ellipsoid at the
point in question.
We calculate the
meridional radius of
curvature of the ellipsoid, and the
radius of the corresponding
parallel circle at the geodetic latitude
in question:
  eq 2.45 
  eq 2.46 
First, the spacecraft
position (in global
hemispherical Cartesian coordinates
 see
Coordinate Conversion 2.7.1.5.1.
) is used to determine whether the
overflown surface has an
associated slope model. If not, the
nadir direction is assumed,
and the elevation and azimuth
representing the direction are both set
to zero.
If a slope model is
present, the processing
proceeds. The slope model is
interpolated to get the X
and Y components of slope as follows:
  eq 2.47 
  eq 2.48 
Where f is an
interpolation formula
(sixpoint bivariate interpolator 
which is exact if second
order derivatives are zero or
negligible) , with:
  eq 2.49 
;
  eq 2.50 
where
  eq 2.51 
is the resolution of the ith
slope model, and
  eq 2.52 
and
  eq 2.53 
are the coordinates of a slope
value within the model. The
parameter p,q are given by:
  eq 2.54 
  eq 2.55 
The next stage involves
the computation of a set of
partial derivatives of X and Y with
respect to latitude, and
also longitude, so that the quantities
calculated in the global hemispherical
Cartesian frame (X,Y ) may
be related to the local Cartesian frame
(x,y ).
  eq 2.56 
The interpolated slope
values (in X,Y ) and the set
of partial derivatives are then used
to compute the range
derivatives in local coordinates (x,y ):
  eq 2.57 
The last step of the
algorithm involves the
calculation of the echo direction
angles in local
coordinates, thus:
  eq 2.59 
  eq 2.60 
Accuracy
The ellipsoid geometry
calculations mix large numbers such
as the semimajor/minor axes
(a, b ) with small numbers such as
eccentricity (e ), and calculations are
subject to loss of accuracy.
Double precision arithmetic is 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 are safely
represented as
singleprecision, 32bit floatingpoint
numbers, which 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 RA2 , and so
precision in areas of high surface slope
is less important.
2.7.1.5.3 Elevation Calculation
Description: In this
stage, the OCOG (Kuband)
retracked range (see
OCOG Retracking 2.7.1.1.
) and the echo direction are used
to calculate the
slopecorrected elevation in the
geodetic (i.e. altimetric)
ellipsoidal reference frame. We must
transform the local
coordinates of the echo direction using
the geometry of the
ellipsoid. We calculate the radius
of curvature of the local
ellipse in the direction of the echo
azimuth using:
  eq 2.61 
We then evaluate 3
expressions to determine the
slopecorrected latitude, longitude and
elevation of the echoing
point, in global geodetic ellipsoidal
coordinates, i.e. the altimeter
reference frame:
  eq 2.62 
  eq 2.63 
  eq 2.64 
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.
2.7.1.6 Level 2 Ice Algorithms : Delta
Doppler Correction
Physical Justification: It
is well known that there is a
contribution to range arising from the
Doppler effect due to the vertical component
of spacecraft orbital velocity.
However, over sloping surfaces, there
is an additional contribution to range due
to the Doppler effect, that
arises because the echo direction (line of
sight from the scattering facet) is no
longer to the nadir of the
spacecraft in general. This has the effect
of adding in a component of the
spacecraft forward orbital
velocity in addition to the more generally
appreciated vertical component.
The 'conventional'
verticalcomponent Doppler correction may be
determined using a scalar
calculation by differencing the supplied
vertical orbit altitude. However for the
generalised Doppler, one must
perform a full vector calculation using
the spacecraft velocity and position, and
the echo direction. The position
and velocity vectors are determined
from the available orbit information
supplied in the Level 1b product.
We subtract the
verticalcomponent Doppler
correction from our general Doppler
correction to arrive at a
deltaDoppler correction due to slope.
Description: This algorithm
determines the additional
Doppler correction to range, due to the
effects of sloping surfaces. This is known
as the deltaDoppler range correction.
Nontracking data are not a
problem, as the orbit
information is always included, but as
no elevation data are available
the deltaDoppler correction is
set to zero.
Firstly the spacecraft
velocity vector is found from
two successive 18 Hz data blocks. Hence
the algorithm is initialised at
the start of processing, and
before every data gap.
At several points in the
processing vectors in the
spacecraft frame, i.e. in geodetic
ellipsoidal coordinates, are
converted to Cartesian coordinates, in
order to manipulate vector components:
  eq 2.65 
We first determine the
spacecraft velocity vector by
differentiation of the spacecraft position
vector. This requires two position
determinations at altimetric
sounding N and N+1 (ie the current
record and the next record).
From the orbit parameters we obtain
altitude, latitude and longitude, and
transform these to Cartesian coordinates:
  eq 2.66 
  eq 2.67 
We then determine the
velocity by differentiation,
e.g. for the X component we have:
  eq 2.68 
Next we determine the
Cartesian components of the
position vector of the echoing point,
determined in the slope
correction algorithm:
  eq 2.69 
We determine the line of
sight vector from the echoing
point to the altimeter, using vector
arithmetic with the spacecraft position
vector, and the position vector
of the echoing point. For e.g. the X
component we have:
  eq 2.70 
The driving parameter for
the Doppler range effect is the
velocity component of the satellite in the
line of sight of the observer. This is
obtained by forming a scalar
product of the spacecraft velocity
vector with the unit
lineofsight vector thus:
  eq 2.71 
  eq 2.72 
The Doppler range correction
(Ku and S band) for the
altimeter may now be found in the normal way from:
  eq 2.73 
where
  eq 2.74 
In order to convert this to
a deltaDoppler range
correction, the conventional
flatsurface range correction
from the Level 1b product is required. (
  eq 2.75 
comes from the L1b data in the NRT
processing but is the value
recomputed at Level 2 in the offline processing.)
  eq 2.76 
Accuracy
The magnitude of the Doppler
range correction over flat
surfaces is discussed by Cudlip et
al [S7]. We do not expect the altitude rate
ever to be greater than 100ms1
. At 13.58 Ghz , the Doppler range
correction will not be greater than
approximately ±8.4 cm for a
320 MHz chirp, .34 m for a 80 MHz chirp, and
1.36 m for a 20 MHz chirp.
At Sband at 3.2 GHz, the correction
will not be greater than 4 cm.
However over sloping terrain
there is an additional
contribution, as discussed above, due to the
change in lineofsight to the spacecraft
from the echoing point. From the
geometry of the situation, this
additional contribution could be very large,
but in practice, the antenna
gain function reduces the returned
power effectively to zero at large
displacements from nadir. The
footprint radius at Kuband is approximately
10 km, and at Sband this
increases to approximately 60 km.
Thus at Kuband, the maximum
possible additional contribution
(as output as delta Doppler at
Level 2) is approximately: a) 320 MHz,
±10 cm, b) 80 MHz, ±40
cm, and c) 20 MHz, ±1.6 m. At
Sband (3.2 GHz) at 160 MHz it
is no greater than ±18 cm. The
correction is thus of the same order of
magnitude as the altitude rate
correction, but note that the sign may be
opposite, and may in fact cancel the
altitude rate contribution.
Hence the maximum total Doppler range
correction will be approximately ±20cm,
±80cm, or ±3.2m,
corresponding to 320, 80 and 20 Mhz chirps respectively.
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.
RA2 Ice Algorithms:
Retracker TradeOff Study, MSSL,
UCLTN0002 v 1a, 17/04/96
RA2 Ice Algorithms:
Algorithm Model Description v 1, 13/6/96
2.7.1.7 Doppler correction
The vertical (radial)
velocity of the satellite causes a
frequency Doppler shift which affects the
time delay measurement, thus the range. For
each elementary measurement, the Doppler
correction δh (in m), to be added
on the altimeter range, is computed for Ku
and S bands, from the altitude rate, by :
  eq 2.77 
where:
Sat_Alt_Rate (m/s) is the
satellite altitude rate computed in the
orbit interpolation module for each
elementary measurement.
Wavelength (106 m) is the
radar wavelength (provided by the RA2
instrumental characterisation file), to be
selected according to the processed band (Ku
or S) and the operating RF subsystem (flag RV_RFSS_Def)
Chirp_Sl (kHz/106 s) is the
chirp slope (provided by the RA2
instrumental characterisation file:
effective value (positive for KuBand and
negative for SBand), to be selected
according to the processed band (Ku or
S), the emitted bandwidth in Ku band (flag
Chirp_Id) and the operating RF subsystem
(flag RV_RFSS_Def).
Light_Vel (m/s) is the light
velocity (provided by the constant file)
and Sat_Alt_Rate(i) is the
elementary value of the altitude rate
obtained from the orbit CFI interpolator
routine (if a restituted OSV is available
for the Level 2 processing).
If no restituted OSV file is
available, the Doppler correction is not
calculated at Level 2 but just copied from
the Leve l1b RA2 MDSRs.
2.7.1.8 ECMWF model derived wet and dry
tropospheric corrections, u and v components
of the wind vector, and surface pressure
The input ECMWF
meteorological fields used to calculate
these parameters are different
for the near real time products
(FDGDR and FDMAR) and for the off line
products (IGDR, IMAR, GDR and SGDR).
For the near
real time, the meteorological fields used
are the following: U and V
components of the 10 meter wind vector,
surface pressure, relative humidity profile,
geopotential profile and
temperature profile. These six parameters
are provided on a regular 1 X 1 degree grid.
From the relative humidity,
geopotential and temperature
profiles, the wet tropospheric correction
field is computed, and from the
surface pressure the dry tropospheric
correction is computed.
For the off
line, the meteorological fields used are the
following: U and V components of the 10
meter wind vector, dry
tropospheric correction, wet tropospheric
correction, surface pressure.
These five parameters are provided on
the socalled gaussian grid (quasi regular
in latitude, nonregular in
longitude). This grid is the internal
grid of the ECMWF model used for
the model run. The wet and dry
tropospheric corrections are computed by the
French met office from the
ECMWF humidity and temperature profiles.
The SWT 2004 recommendation was to use the
new tide model FES2004,
which already includes the S1 and S2
waves. Then, in case of offline processing,
the dry tropospheric correction
is now derived from the surface
pressure filtered and corrected
from the S1 and S2 waves.
In both cases,
the wet and dry tropospheric corrections,
the two components U and V of
the 10 meter model wind vector,
the 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. If the
surface type of the altimeter
measurement is set to "open ocean or
semienclosed 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,
whatever their altitude is.
Applicability

These parameters are
computed for
FDGDR, IGDR and GDR product.
For FDGDR,
predicted meteorological fields are
used whereas for
the IGDR and GDR the analysed fields
are used.

These parameters are
computed for all
surface types (over land and ocean).
Accuracy
Generally speaking,
analysed fields are more
accurate than predicted fields.
The error introduced by
space and time interpolation under the
satellite track is small compared with
the intrinsic accuracy
of the meteorological fields.
The best accuracy for
wind vector varies from
about 2 m/s in modulus and
20° in direction in
the northern Atlantic to more than 5 m/s
in modulus and 40°
in direction in the southern Pacific.
The accuracy of the dry
tropospheric correction
primarily depends on the accuracy
of the surface pressure.
Typical errors vary from 1 hPa in
northern Atlantic to more than 10 hPa in
southern Pacific. A 1
hPa error on pressure translates to a 2
mm error on the dry
tropospheric correction. For land
surfaces, additional error is
induced by inaccurate
knowledge of the altitude of the grid
points and of the
altimeter measurements.
The mean standard
deviation of the
difference between
radiometerderived and
modelderived wet tropospheric
corrections is about 3
cm. This is a mean value over the global
ocean. Larger model
errors are found in the tropics (up to
10cm errors) and
smaller ones in high latitudes.
Reference
Saastamoinen, J., 1972: Atmospheric
correction for the
troposphere and stratosphere in radio
ranging of satellites,
Geophys. Monogr., 15, American
Geophysical Union,
Washington D.C.
2.7.1.9 Inverted barometer correction algorithm
The inverted
barometer height correction is computed (in
mm) according to the following
formula :
H_Baro =  b
∗ [Psurf Pbar]   eq 2.78 
Psurf is the surface
atmospheric pressure at the
location and time of the
altimeter measurement, and Pbar is the mean
atmospheric pressure over the
global ocean at the location and time of
the altimeter measurement. Psurf is computed
by bilinear interpolation in
space and linear interpolation in time
from the surface pressure field before and
after the altimeter measurement.
Pbar is computed by linear
interpolation in time from the mean
atmospheric pressure before and
after the altimeter measurement.
Important notice:
Prior to Psurf and Pbar computation at the
time and location of the
altimeter measurement, the surface
pressure fields are filtered for S1 and S2
(diurnal and semidiurnal)
atmospheric tides. Two main reasons have
governed this choice:
 S1 and S2 signals are poorly retrieved
in 6hourly pressure
fields (S2 is sampled at its exact
Nyquist frequency).
 Radiational and gravitational tides are
undistinguishable when computing an
ocean tide model. For
instance, previous ocean tide models
(GOT99, FES2002) already included the
full S2 tide effect.
Thus the following strategy has been decided,
as proposed by Ponte and Ray (2002):
 Let the full S1 and S2 signals (both
radiational and
gravitational effects) in the ocean tide models
 Remove the radiational part from the
surface pressure fields
(otherwise, it would be applied twice).
S1 and S2 filtering:
A climatology (ancillary data files) of S1
and S2 has been built from a
long series of surface pressure
fields. It is then simply subtracted from
the input pressure fields to
obtain an output pressure field
without S1 and S2 effects.
Applicability

The inverted barometer
effect is computed for
FDGDR, IGDR and GDR product

The computation of the
inverted barometer
effect is performed continuously
for all surface types
(over land and ocean), although it is
relevant to ocean surfaces only
Accuracy
Extensive modeling work by
Ponte et al.
Ref. [2.9 ]
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, Pbar. As stated by
Dorandeu and Le Traon
Ref. [2.10 ]
, this improved inverted
barometer height correction
reduces the 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.
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, 10431057, 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.
Ponte,
R.M. and Ray, R.D.,
"Atmospheric pressure corrections in
geodesy and oceanography: A
strategy for handling air tides",
Geophys. Res. Letters, 29 (24), 2002.
Boone
C., " Etudes SALP pour GDR
2i�me generation Jason. Partie 1
: Signaux diurne et semidiurne de pression
", CLSDOSNT03.909, CLS,
Ramonville SaintAgne, 2003.
Dorandeu J.,
"Impact of S1 and S2 athmospheric
signals on T/P and Jason SSH
variability", minutes of SWT meeting at
Arles, Nov.1821, 2003.
Dorandeu J.,
"EnviSat data quality: Envisat GDR
evolutions, Third QWG meeting,
Marsh 2004.
2.7.1.10 Combined atmospheric correction from
MOG2D and IB
High frequency atmospheric signals are badly
retrieved by altimeters, due to
poor time sampling. High frequency
signals are thus aliased by altimeter
measurements and translate into
apparently lower frequency signals
undistinguishable from other ocean signals
of interest. Therefore, it is
important to remove these effects.
As a first approximation, the socalled
Inverse Barometer correction is
conventionally used to correct altimeter
data. This simple correction
assumes a static ocean response to
atmospheric pressure forcing. Neither
dynamical effects at high
frequency nor wind effects are taken into
account in this correction.
In order to take account of dynamical effects
and wind forcing, a new
correction is computed from the MOG2D
(Carrere and Lyard, 2003) barotropic model
forced by pressure and wind.
Only the high frequency part of these
model outputs are retained and combined to
the low frequency inverse
barometer. This new correction provides a
great improvement in terms of
ocean variability reduction (Carrere
doctoral thesis, 2003)
The difference between this new correction
and the Inverse Barometer is
computed and set in the GDR product. The
users are advised to add this
difference to the Inverse Barometer.
Applicability
 The difference between the new
correction and the
Inverse Barometer is computed for GDR product
 The computation of the difference
between the new
correction and the Inverse Barometer is
performed continuously
for all surface types (over land, ice
and ocean).
Nevertheless, it is applicable only for
ocean surfaces.
Reference
Carrère L. and
Lyard F., " Modelling the barotropic
response of the global ocean to
atmospheric wind and pressure forcing 
comparisons with observations
", GRL, 30(6), pp1275, 2003.
Carrère L.,
"Etude et modélisation de la
réponse haute
fréquence de l'océan global
aux forçage
météorologiques", Doctoral
Thesis, 24 Nov. 2003.
2.7.1.11 MWR wet tropospheric correction
The MWR wet tropospheric correction, Dh_RA2,
is obtained with a neural
algorithm. A global and representative
database has been built using
ECMWF analyses from surface and atmospheric
parameters, and simulations of the
brightness temperatures and
backscattering coefficient in Ku band. Then
the architecture of the network
(one layer of 8 hidden neurons)
and the weights of each neuron are
determined to produce the most
accurate estimation of the wet tropospheric
correction (in mm) from
brightness temperatures (TB23_Int and
TB36_Int) and s0_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, s0_Ku is the ocean
backscatter coefficient for Kuband (dB).
Applicability
 The MWR wet
tropospheric correction
is computed for FDGDR, IGDR and
GDR product
 The computation of the MWR wet
tropospheric 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, i.e. 0.5 cm.
Comparisons between retrievals obtained with
the Envisat algorithm applied to
ERS2 measurements and radiosounding
measurements, indicate an rms difference of
1.5 cm. As this error contains
the error on radiosounding measurements, it
gives an upper bound of the error for the
wet tropospheric correction.
Reference
S. LABROUE and E.
OBLIGIS, "Neural network retrieval
algorithm for the
Envisat/MWR", report CLS/DOS/NT/03.848
of ESA contract 13681/99/NL/GD,
January 2003.
2.7.1.12 Sea state bias
Sea state bias is the difference between the
apparent sea level as "
seen " by an altimeter and the actual
mean sea level.
The sea state biases for Ku band and S band
are computed, in mm, by bilinear
interpolation from a table given as function
of Kuband significant wave height and the
RA2 wind speed, (SWH_Ku and W).
The look up table in Ku band has been derived
from ten cycles of ENVISAT data
(cycle 17 to 26), using residuals relative
to a mean sea surface as proposed by
Vandemark et al.
Ref. [2.18 ]
and applying the non
parametric estimation technique as developed
by Gaspar et al.
Ref. [2.19 ]
,
Ref. [2.20 ]
. All the details on the data
set and the method used for the
estimation can be found in the study
report
Ref. [2.21 ]
.
Applicability
 The sea state bias is computed for
FDGDR, IGDR and GDR product
 The computation of the sea state bias is
performed continuously
for all surface types (over land and
ocean), although it is relevant to ocean
surfaces only.
Accuracy
The underlying physics of the sea state bias
is not completely understood.
Nevertheless, the non parametric
estimate is more suitable than a parametric
model, since the non parametric
SSB reduces the crossover variance with a
gain of about 1 cm2, compared to a BM3 model
fitted on ENVISAT data.
References
Vandemark, D., N.
Tran, B. Beckley, B. Chapron and P. Gaspar,
Direct estimation of sea state
impacts on radar altimeter sea level
measurements. Geophysical Research Letters,
29, n�24, 2148, 2002
Gaspar, P. and J.P.
Florens, Estimation of the sea state bias in
radar altimeter measurements of
sea level: Results from a new non parametric
method. J. Geophys. Res., 103, 1580315814, 1998
Gaspar, P., S.
Labroue, F. Ogor, G. Lafitte, L. Marchal and
M. Rafanel, Improving non
parametric estimates of the sea state bias
in radar altimeter measurements
of sea level. JAOT, 19,
16901707, 2002.
Labroue S., RA2 Ocean
and MWR measurement long term monitoring.
Final report for WP3, Task2 SSB
estimation for RA2 altimeter, CLS_DOSNT04284
