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2.7 RA-2/MWR Level 2 Products And Algorithms

2.7.1 RA-2 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 (Off-Line product, available within 3 to 5 days) and the GDR (Off-Line 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 (RA-2 elementary measurements, RA-2 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

 

RA-2 - 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 sea-ice retracking

 

 

 

 

To perform the ice-1 retracking

 

 

 

 

To perform the ice-2 retracking

 

 

 

 

To perform the oceaN retracking

 

 

 

 

TO COMPUTE THE PHYSICAL PARAMETERS

 

 

 

 

To correct the RA-2 range for Doppler effects

 

 

 

 

To compute the Doppler slope correction (ICE SURFACES)

 

 

 

 

TO EDIT AND COMPRESS THE OCEAN ESTIMATES

 

RA-2 - 1 Hz

 

 

 

 

To determine the surface type

 

 

 

 

To interpolate MWR data to RA-2 time tags

 

 

 

 

To compute the BACKSCATTER COEFFICIENT atmospheric attenuations

 

 

 

 

To compute the 10 meter RA-2 wind speed

 

 

 

 

To compute the MWR geophysical parameters at RA-2 time tag

 

 

 

 

To compute the 10 meter MODEL wind vector

 

 

 

 

To compute the sea state biases

 

 

 

 

To compute the dual-frequency 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 RA-2 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 RA-2 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 Levenberg-Marquardt'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 on-board the RA-2 altimeter), it is given by :

 

image eq 2.1
 

 

with :
image eq 2.2

image eq 2.3
,
image eq 2.4

θo = antenna beamwidth, c = light velocity, h = satellite height, Re = earth radius

image eq 2.5
, σp = PTR width ,
image eq 2.6

image eq 2.7
,
image eq 2.8
,
image eq 2.9
, ξ = mispointing

image eq 2.10
,
image 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 antenna-COG (Ant_COG) selected for the averaged measurement which contain the processed elementary measurement:

    eq 2.12

    Where for each RA-2 nominal tracking data, the Ku-band and the S-band tracker ranges are computed (in seconds) from the input window delays and from offsets computed, by:

    image eq 2.13

    image eq 2.14

    where

    image eq 2.15

    image eq 2.16

    image 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:

    image eq 2.18

    Where the updated Ku-band and S-band Doppler compensations (Doppler_Comp_Update_Ku, Doppler_Comp_Update_S) are computed from the altitude rate (Sat_Alt_Rate(i) in m/s), by:

    image eq 2.19

    Where:

    • Wavelength (10-6 m) is the radar wavelength (RA-2 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/10-6 s) is the chirp slope (RA-2 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
    image eq 2.20
    then:

       
    image 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
    image eq 2.22
    then
    image eq 2.23

    Else:

    image 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.

 

Accuracy

TBD

 

References

Ref 2.1
"RA-2 retracking comparisons over ocean surface by CLS", CLS.OC/NT/95.028, Issue 3.1

 

Ref 2.2
Numerical Recipes : The Art of Scientific Computing in C (Edition 2). William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling

 

Ref 2.3
Hayne G.S. 1980 : "Radar Altimeter Mean Return Waveforms from Near-Normal-Incidence Ocean Surface Scattering". IEEE Trans. on antennas and propagation, Vol. AP-28, n°5, pp. 687-692

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 RA-2 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 ]

 

image eq 2.25
 

 

(with :
image 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

 

image  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:

    image 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
    image eq 2.29
    then:

    image eq 2.30

    The ice2 backscatter coefficient (Sigma0_Ice2 in dB) related to the integrated signal over the waveform is computed by:

    If
    image eq 2.31
    then:

    image eq 2.32

Applicability

  • The Ice-2 retracking algorithm is performed for FDGDR, IGDR and GDR product.
  • The Ice-2 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.

 

Accuracy

TBD.

 

References

Ref 2.4
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.

 

Ref 2.5
G.S. Brown : "The Average Impulse Response of a Rough Surface and its Applications". IEEE Trans. on Antennas and Propagation, Vol. AP-25, Jan. 1977

 

 

 

2.7.1.3 Level 2 Ice Algorithms : General

A sub-set of the level 2 processing is concerned with improving the accuracy of measurements over non-ocean surfaces.

 

The ICE1 Retracking algorithm is a range estimation technique suitable for echoes returned from non-ocean 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 on-board 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 non-linear 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 pre-processing.

 

There are two independent retracking algorithms. The first is the Offset Centre-of-Gravity (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 Ku-band 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 Pre-processing

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 non-ocean 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.

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:

image 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.

 

The OCOG Retracking Algorithm

The retracker offset and COG offset are added to the telemetered range for output thus:

image 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 image (Fields 25 and 26), as follows:

image 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, image 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 Sea-Ice Retracking

Description: In this algorithm, waveform parameterisation based on peak threshold retracking is applied to the Ku-band 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 sea-ice waveform amplitude is determined by finding the maximum value of the waveform samples thus:

 

image 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 sea-ice 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

 

The Sea-ice Retracking Algorithm

The retracker offset and COG offset are added to the telemetered range for output thus:

image 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 Sea-ice 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 image (Field 25), as follows:

image 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 slant-range to a point offset from Nadir. To use this measurement it must be corrected for the slant and re-located 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 co-ordinate 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 co-ordinate system for the slope models. The transformation maps any function defined in the conventional altimetric (geodetic ellipsoidal) co-ordinate system onto a plane. This is accomplished via a pair of transformations which implement the Lambert equal-area 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 co-ordinate frame) the returned echo power came. If no slope model is found, the nadir direction is used.

 

  • The slope-corrected 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 Co-ordinate Conversion

Description: This algorithm determines the location of the spacecraft in a hemispherical Cartesian co-ordinate frame. The first step is a straight-forward calculation of the meridional radius of curvature of the ellipsoid using the standard expression:

 

eq 2.42
image

This quantity is then used in the equations for the Lambert equal-area projection:

 

eq 2.43
image

image 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. semi-major 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 image in a local Cartesian co-ordinate frame (x,y) with its origin at the sub-satellite 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:

image eq 2.45

image eq 2.46

 

First, the spacecraft position (in global hemispherical Cartesian co-ordinates - see Co-ordinate 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:

image eq 2.47

image eq 2.48

 

Where f is an interpolation formula (six-point bivariate interpolator - which is exact if second order derivatives are zero or negligible) , with:

 

image eq 2.49
;
image eq 2.50

where
image eq 2.51
is the resolution of the ith slope model, and
image eq 2.52
and
image eq 2.53
are the co-ordinates of a slope value within the model. The parameter p,q are given by:

image eq 2.54
 

image 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 ).

image 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 co-ordinates (x,y ):

 

image eq 2.57

eq 2.58
image

 

The last step of the algorithm involves the calculation of the echo direction angles in local co-ordinates, thus:

image eq 2.59

image eq 2.60

 

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 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 single-precision, 32-bit floating-point 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 RA-2 , 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 (Ku-band) retracked range (see OCOG Retracking 2.7.1.1. ) and the echo direction are used to calculate the slope-corrected elevation in the geodetic (i.e. altimetric) ellipsoidal reference frame. We must transform the local co-ordinates 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:

 

image eq 2.61

 

We then evaluate 3 expressions to determine the slope-corrected latitude, longitude and elevation of the echoing point, in global geodetic ellipsoidal co-ordinates, i.e. the altimeter reference frame:

image eq 2.62

image eq 2.63

image 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' vertical-component 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 vertical-component Doppler correction from our general Doppler correction to arrive at a delta-Doppler 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 delta-Doppler range correction.

 

Non-tracking data are not a problem, as the orbit information is always included, but as no elevation data are available the delta-Doppler 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 co-ordinates, are converted to Cartesian co-ordinates, in order to manipulate vector components:

image 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 co-ordinates:

image eq 2.66

image eq 2.67

 

We then determine the velocity by differentiation, e.g. for the X component we have:

image eq 2.68

 

Next we determine the Cartesian components of the position vector of the echoing point, determined in the slope correction algorithm:

image 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:

image 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 line-of-sight vector thus:

image eq 2.71

image eq 2.72

 

The Doppler range correction (Ku and S band) for the altimeter may now be found in the normal way from:

image eq 2.73

 

where
image eq 2.74

 

In order to convert this to a delta-Doppler range correction, the conventional flat-surface range correction from the Level 1b product is required. (
image eq 2.75
comes from the L1b data in the NRT processing but is the value recomputed at Level 2 in the off-line processing.)

image 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 100ms-1 . 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 S-band 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 line-of-sight 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 Ku-band is approximately 10 km, and at S-band this increases to approximately 60 km.

 

Thus at Ku-band, 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 S-band (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.

 

 

Ref 2.6
RA-2 Ice Algorithms: Retracker Trade-Off Study, MSSL, UCL-TN-0002 v 1a, 17/04/96

Ref 2.7
RA-2 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 :

 

image 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 (10-6 m) is the radar wavelength (provided by the RA-2 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/10-6 s) is the chirp slope (provided by the RA-2 instrumental characterisation file: effective value (positive for Ku-Band and negative for S-Band), 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 so-called 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 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, 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 radiometer-derived and model-derived 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 10-cm errors) and smaller ones in high latitudes.

 

Reference

Ref 2.8
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 semi-diurnal) atmospheric tides. Two main reasons have governed this choice:

  • S1 and S2 signals are poorly retrieved in 6-hourly 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

Ref 2.9
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

 

Ref 2.10
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.

Ref 2.11
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.

Ref 2.12
Boone C., " Etudes SALP pour GDR 2i�me generation Jason. Partie 1 : Signaux diurne et semi-diurne de pression ", CLS-DOS-NT-03.909, CLS, Ramonville Saint-Agne, 2003.

Ref 2.13
Dorandeu J., "Impact of S1 and S2 athmospheric signals on T/P and Jason SSH variability", minutes of SWT meeting at Arles, Nov.18-21, 2003.

Ref 2.14
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 so-called 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

Ref 2.15
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.

Ref 2.16
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 RA-2 time tag, s0_Ku is the ocean backscatter coefficient for Ku-band (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

Ref 2.17
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 Ku-band significant wave height and the RA-2 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

Ref 2.18
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

Ref 2.19
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, 15803-15814, 1998

Ref 2.20
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, 1690-1707, 2002.

Ref 2.21
Labroue S., RA2 Ocean and MWR measurement long term monitoring. Final report for WP3, Task2 SSB estimation for RA2 altimeter, CLS_DOS-NT-04-284


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