RADAR ALTIMETER CALIBRATION USING GROUND BASED TRANSPONDERS ABSTRACT

A.R. Birks

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon. OX11 0QX, U.K.

Email: a.r.birks@rl.ac.uk

ABSTRACT

An important long-term objective of satellite radar altimeter measurements of the oceans is to provide truly global sealevel measurements within a global geodetic system. Essential prerequisites of this goal are the accurate calibrationand long-term monitoring of the range bias of the radar altimeter. The latter in particular requires an absolutecalibration technique; relative calibration, by the comparison of sea surface measurements by different altimeters,cannot distinguish between a trend in the altimeter bias and a genuine trend in mean sea level.

Experiments in which transponders have been deployed beneath the ERS-1 satellite have shown that the radaraltimeter can measure the range to a transponder deployed beneath it with sub-centimetre resolution. The accuracy ofthe range measurement then depends principally on the accuracy of the available water vapour path correction. Thiscapability permits a number of applications to vertical position monitoring, orbit studies, and radar altimetercalibration.

Applied to altimeter bias calibration, the technique eliminates error sources such as tides and sea state bias. Bestresults are obtained when the range window of the radar altimeter is preset to a fixed value during the transponderoverpass, and this technique has been in regular use on ERS-1 and ERS-2. A transponder also provides a target ofstable radar cross-section, which can be directly measured, and can be used for calibration of the radar cross-sectionmeasurement. Transponder deployments beneath ENVISAT can make an independent contribution these calibrationobjectives.

Transponders offer a unique means to inter-compare the bias calibrations of satellite altimeters, capable of extensionto future missions to maintain the continuity of radar altimeter data sets in the long term, and may be used asreference targets for the inter-comparison of radar cross-section measurements in a similar way.INTRODUCTION

The use of ground-based transponders as reference targets relative to which radar altimeter (RA) measurements ofsurface elevation accurate to a few centimetres might be attained was suggested by Powell [1]. The transponderappears to the radar altimeter as a point target, and so the effects of 'speckle' (that is to say, the interference effects thatarise when multiple scatterers contribute to the radar echo) do not limit the accuracy with which its position can bedetermined. Precise range measurements as the altimeter passes overhead permit the transponder range at closestapproach to be determined, relative to the range tracker of the radar altimeter, with a precision of a few millimetres(depending on the operating mode of the altimeter). Consequently the accuracy of the range measurement is limited inpractice by factors external to the radar measurement; principally by the accuracy with which the propagation delayswithin the troposphere and ionosphere can be measured or estimated.

Successful application of the technique permits a range of applications to orbit studies and to a variety of geodetic andgeophysical studies in which the precise measurement of vertical position is a factor. In addition a transponder mayact as a precise reference target, whose position and radar cross-section are accurately known, for use in radaraltimeter calibration. For altimeter range bias calibration the transponder technique presents a number of advantages;it is not affected by the problems of geoid extrapolation and sea state bias, and can allow an additional degree offlexibility in the choice of calibration sites.

The use of transponders has been developed at the Rutherford Appleton Laboratory with the ERS-1 and ERS-2satellites over a number of years. Several quantitative experiments have enabled the technique to be demonstrated andvalidated.

During the Commissioning Phase of the ERS-1 mission, two transponders were deployed beneath ERS-1 at locationsin Europe. This experiment was intended to demonstrate and validate the technique in a situation in which thetransponder deployments were well supported with environmental data and at sites where, owing to the high density oflaser tracking stations in the region, it was hoped that orbit calculations of high quality would be available. Theanalysis of data over the European sites directly confirmed the expected high accuracy (< 3 cm) attainable in radaraltimeter range measurements to transponders [2].

Other experiments [3, 4] have demonstrated the reliability of the technique, and in particular a trial in 1994, in whicha transponder was located on an oil platform in the North Sea, further demonstrated the potential centimetric accuracyof the technique [5]. The accuracy of relative height determinations by this technique is comparable to that of GPSdeterminations but with benefits including possible unattended operation and automatic collection of data and deliveryto users.

Transponder deployments beneath ENVISAT can make an independent contribution to the calibration objectives ofthe RA-2 instrument, and could both contribute to the commissioning phase and provide long-term monitoring of therange bias or radar cross-section measurement. To contribute in this way a transponder should be deployed at asuitable permanent location at the start of the ENVISAT mission and remain in place throughout the mission. Thispaper considers some quantitative aspects of this scenario.

TRANSPONDERS AS BENCHMARKS IN RADAR ALTIMETRY

A transponder is an active radar target that re-transmits an incident signal with minimum distortion, so behaving as apoint radar target. The transponder should be located within a few kilometres of the satellite ground track. Then, asthe radar altimeter passes overhead, echoes from the transponder are received when the target is simultaneously withinthe range window and the antenna footprint of the altimeter. During this period, the range from the altimeter to thetransponder varies according to

r2=r02+[v(t−t0)]2

(1)

where r is the range to the transponder at time t, r0 is the range to the transponder at the time t0 of closest approach,when the line of sight to the transponder is orthogonal to the orbit, and where v is the apparent velocity of the satellite(which differs from the true orbital velocity by a correction for the curvature of the orbit).

Thus the echoes from the transponder trace out a characteristic quadratic locus in delay. In the case of the ERS-1 andERS-2 altimeters, each telemetry waveform represents the average of 50 received pulses. Each waveform i representsan independent measurement of the range ri to the transponder at the corresponding time ti. If the data is free fromclutter (power from natural targets close to the transponder in delay), a precise range ri can be derived from eachwaveform. By a least squares fit of the expected locus (1) to the data points

(ri, ti), i = 1, ... N

(2)

the parameters of (1), and in particular the range at closest approach r0, may be determined. A detailed illustrationwas given in [3]. More generally, a fit of a modelled power envelope to the waveform samples gives a robustdetermination of the parameters.

The accuracy of the derived parameters depends on the accuracy with which the range can be derived from eachwaveform, and can be estimated from the residuals of a least squares fit as described above. Theoretical studiesindicate that the errors due to receiver noise are very low, and it appears that in the case of the ERS altimeters thelimiting error source is the quantization of the radar altimeter waveforms. It is this that limits the precision of theretrieval to typically 5 mm when the ERS ice mode window is used.

The radar altimeters on ERS-1 and ERS-2 allow for the use of a preset mode, in which the delay of the range windowis set to a precalculated value and held fixed for a pre-determined period. In other words, the range tracker does not

operate during the fixed period. ERS-1 allows the use of either of two range windows, of widths 29 and 116 metres;these are intended for tracking over ocean or ice surfaces respectively. Either can be used in preset mode to observetransponders. The principal error sources within the measurement scale in proportion to the window width.

Although transponders can be observed using the ordinary tracking modes of the radar altimeter, preset operation, inwhich the range window is set to match the predicted range to the transponder, is a very advantageous way to observetransponders, both because it simplifies the data analysis and it allows the deployment site to be chosen to minimiseclutter. Almost all transponder experiments with the ERS satellites have used this mode, with the co-operation of theESA operational staff to uplink the necessary commands. This has proved to be very successful.

The technique is equally applicable to any radar altimeter, transmitting in the same frequency band and in particularshould be applicable to the ENVISAT RA-2.RANGE BIAS CALIBRATION

In order to use a transponder for RA calibration, it is deployed on the satellite ground track at a point where preciseshort-arc orbit measurements may be obtained, in a geodetic frame of reference, by an independent technique such asSatellite Laser Ranging (SLR). Thus the transponder might be deployed close to an SLR station, where a short-arcsolution would give a measurement of the orbit with high precision, comparable to that of the transponder rangemeasurement. Of course the position of the transponder must be accurately known in the reference frame of the SLRstation. GPS can be used to relate the position of the transponder to that of the SLR station in a precisely definedInternational Terrestrial Reference Frame (ITRF).

The methods outlined above may then be used to derive an uncorrected range to the transponder at closest approachfrom the altimeter data. Corrections for altimeter internal delay and offset from the satellite centre of gravity,transponder internal delay, and atmospheric propagation effects are then applied to convert this to a measurement ofthe true range. This range is then compared with the range calculated from the satellite orbit and the known positionof the transponder. and the residual determined.

In general the range residuals so derived can be thought of as radial orbit errors, and may be used to assess the qualityof the orbit used at the transponder location. (Strictly the range residual is measured along the line of sight at closestapproach, but if the transponder is close to the ground track the difference between this and the radial orbit error willbe insignificant.) If the orbit quality is sufficiently high, the mean residual will represent the uncorrected bias of theradar altimeter.Error Budget

Contributions to the error of an altimeter bias determination fall into two categories; those that vary randomly frompass to pass, and those that are constant at a particular deployment site. Errors of the first type include orbit errors anderrors in the atmospheric propagation corrections; their effect will be reduced by averaging as more passes becomeavailable. Transponder position errors, and errors in the determination of the transponder internal delay, will beconstant at a deployment site; if present they will give rise to systematic error on the absolute determination ofaltimeter bias, but would not affect the determination of a long-term drift. If transponders were to be deployed at morethan one site, the presence of such systematic error will be evident as a systematic difference between the biasdeterminations at the different sites. Supporting measurements must be made at each pass over the deployment site toenable propagation corrections to be determined with maximum accuracy.Dry Troposphere correction.

The contribution of the dry troposphere to the altimeter path delay depends solely on the surface pressure, and this canbe measured directly at the deployment site. The sensitivity to errors of measured surface pressure is 2.3 mm per mb,so provided the surface pressure is measured to better than 1 mb, the dry path correction is known to better than 5 mm.

Wet Troposphere Correction.

Data from the Microwave Radiometer instrument on ENVISAT cannot be used to determine this correction where thetransponder deployment site is on land. The correction must be derived from measurements made at or near thedeployment site. The most satisfactory way to determine the wet path correction is to use an upward-lookingradiometer to measure the water vapour content. The variability of a typical series of measurements suggests anaccuracy of 3%, corresponding to errors of less than 1 cm in the path correction. However, the absolute accuracy maybe reduced to between 1 and 2 cm by uncertainty in the radiometer calibration.

If a microwave radiometer is not available, radiosonde measurements of the temperature and humidity profiles may beused to determine the integral of refractivity, and hence the wet path correction. Measurements of humidity areaccurate to typically 5% to 10%, and so we might conservatively estimate the error of the wet path correction as about10% for a collocated radiosonde. For a typical wet path correction of 15 cm, this gives an error of about 1.5 cm. GPStechniques may also be used. A regional modelling exercise, incorporating as much of the available data as possible,may represent the best approach to determining the most accurate estimate possible of the wet troposphere correction.Ionosphere Correction

The magnitude of this correction depends on the time of day, season, and solar activity. Typical mid-day values mayrange between 7 and 30 cm, depending upon the phase of the solar cycle; night-time values are lower. Values of up to5.5 cm have been reported for ascending (night-time) passes at middle latitudes between 1991 and the present [3, 5,6]. The correction may be derived from GPS observations or other dual frequency measurements close to thedeployment site.

Transponder Position Error

An error in the vertical position of the transponder will give rise to an error of the same magnitude in the derivedrange, while an across-track position error will give an error that depends on the across-track displacement of thetransponder from the ground track of the satellite. If the transponder is close to the ground track, the effect of anacross-track position error on the range will be negligible, but if it is displaced from the ground track by 2 km, aposition error of 4 m would give rise to a range error of 1.0 cm. Errors in transponder position would be systematic,provided the transponder remained at a fixed location. It should be possible to derive the horizontal position of thetransponder to centimetres by GPS techniques, and in the light of this, the effects of cross-track position errors will beignored in the following.Orbit Error

A radial orbit error will map directly into an error of the same magnitude on the derived bias. If for example weassume that SLR data enables the orbit to be derived with a radial error of 3 cm, the derived bias will also be accurateto 3 cm. Errors will be random from pass to pass, so their impact will be reduced if several passes are observed andtheir results averaged.

Across-track orbit error will give rise to a variable range error the magnitude of which depends on the total across-track displacement in the same way as for a transponder position error. Table 1 shows the range error, in mm, as a

Table 1. Range error (mm) as a function of the across-track displacement Xof the transponder, for across-track orbit errors dx of 1 and 5 metres.

X (km)12345

dx = 1 m1.25 mm2.503.755.006.25

dx = 5 m 6.25 mm12.5018.7525.0031.25

function of the across-track displacement X of the transponder, for across-track orbit errors dx of 1 and 5 metres.It is thus very important that the across-track orbit error is as small as possible. However, the availability of good locallaser tracking in a calibration experiment should permit the reduction of this error to an acceptable level, and it willnot be considered further here.Transponder Internal Delay

To analyse the transponder data it is necessary to know the internal delay within the transponder. This represents thedelay within the transponder, from the upper radome surface above the receiving antenna to that above the transmitantenna. It includes the free space path between the radomes and the antennas, together with the group delay withinthe internal waveguide, coaxial cables and RF components. Most of the delay arises in passive components. It can bemeasured independently, and will cancel in a difference measurement. Although the internal delay of the transpondermight be expected to vary with temperature, all our experience confirms that in practice it is very stable.Typical Error Budget

A typical error budget is given in Table 2. The table gives the effect of those errors that vary randomly from pass topass on a single measurement of the altimeter range bias, and on the average from 3 and 6 passes. The table is basedon the assumption that the troposphere and ionosphere corrections can be estimated to 15 mm and 10 mm (rms)respectively.

The table also assumes that the range to the transponder can be measured with an accuracy of 10 mm. This is aconservative assumption, since experience with ERS-1 showed internal consistency of 5 mm in ice mode; the mainsource of this error is believed to be quantisation in the radar altimeter and this error source should not be present inthe improved RA-2.

Use of preset mode with ENVISAT is assumed, since although use of ordinary tracking modes is possible, the need fortracker reconstruction complicates the analysis and may lead to difficulties. No assessment has been made of whetheruse of the ‘burst’ mode of the RA-2 over transponders may permit improvements to the range accuracy.We assume that the radial orbit error has a standard deviation of 1.5 cm, typical of that expected to be achieved bytracking with multiple SLR stations as proposed for the RA-2 regional calibration campaign. Larger orbit errors woulddegrade the precision of the calibration, and the ability to detect trends.

The accuracy with which a trend in range bias can be measured depends on those errors that vary randomly from passto pass. From Table 2, the random component of the error on the range bias (RSS of random terms) is 25 mm for asingle pass, and 8 mm on the average of 10 passes. If then 30 measurements were made over a 3 year period, the trendwould be estimated to 5.0 mm/year. If the transponder is located at an orbit crossing point, twice as many passes canbe measured, and the error falls to 3.5 mm/year.

Table 2. Error budget for absolute measurement of range bias, including constant errors.

Quantity

Measured Range to transponderTransponder internal delay

Tropospheric correction (Dry + Wet)Ionospheric correction

RSS of random errors on range to transponderCorrected Range to transponderOrbit height error

Transponder position in SLR frameRange bias error (random terms only)Range bias error

rms (mm)101510212315

20

2534

1527

1025

Systematic10

9612169

9136

Ave 36

Ave

Table 2 also illustrates the effects of systematic errors, such as the error in the vertical height of the transponder in theSLR frame, plus any calibration error of the transponder internal delay. These do not affect the measurement of trend,but determine the absolute accuracy of the calibration. The result where 6 passes are available is dominated by thesystematic bias resulting from these error sources. If two or more transponders are deployed, systematic errors at onesite may be detected when results from different sites are compared, since they will differ at the different sites.RADAR CROSS-SECTION CALIBRATION

Provided the transponder is deployed at a site free of ground clutter, the radar cross-section of the transponder can bederived from the altimeter data. Thus if an independent measurement of the radar cross-section of the transponder isavailable, an absolute calibration of the radar cross-section measurement of the RA-2 is possible. The absolute value ofthe transponder radar cross-section may be determined either by an overall measurement on a test range, relative to acube corner reflector of known size, or by laboratory measurements of the components. This measurement is difficultand it is not clear what absolute accuracy is achievable. Nevertheless, if the absolute cross-section is not available arelative calibration is still possible. This would permit long-loop monitoring and cross-calibration of differentaltimeters.

In practice, the integrated signal should be determined from each waveform received by the radar altimeter. This isproportional to the total energy received by the radar altimeter, and the proportionality coefficient (properly defined) isthe calibration coefficient of the radar altimeter, multiplied by an antenna beam correction. The integral under thereturned waveform is in fact independent of the tracker evolution (provided the returned energy is wholly within therange window) because the individual echoes contribute to the waveform linearly. This means that the method doesnot (unlike the range measurement) require either the reconstruction of the tracker or the use of preset mode, althoughit obviously requires that ground clutter be effectively removed, and this may significantly constrain the selection of adeployment site.

The Transponder as a standard of radar cross-section

In general the gain of the active transponder will vary with ambient temperature, so that if it is to be used as a radarcross-section reference, these variations must be monitored (or eliminated by a feedback method). The presenttransponder provides a reference target whose variations are characterised to 0.1 dB; it incorporates an internalmonitoring system that permits variations in the gain to be determined to < 0.1 dB, and measurements confirm thatthe system is repeatable at this level. (The gain at a single frequency is determined with an accuracy of 0.08 dB, andthe average gain over the frequency band will be more accurate than this.) Its measured coefficient of RF gain withrespect to amplifier temperature variations is -0.1 dB per degree C. This was well within the procurement specificationof ± 0.2 dB per degree C. The error budget for a radar cross-section calibration will then be dominated by other,external, effects.Error Sources

The radar equation for a point target (ignoring atmospheric propagation loss) is

2

GPtGλPr=σ2

4πR(4π)2R2

(3)

where Pt is the transmitted power, Pr is the power received by the radar, λ is the wavelength, G is the gain of the RA

antenna in the direction of the target, R is the range to the target, and σ is the radar cross-section of the target in thedirection of incidence.

For a distributed target, the back-scattered power received by the pulse-limited radar altimeter at height R isproportional to

σ=(πRcτ)σ0

(4)

Table 3. Radar cross-section errors (dB) resulting from satellite roll offset dθ, for

a transponder displaced by X km from the ground track.

X (km)1234

θ (deg.)0.07350.1470.2200.294

dθ = 0.030.063 dB0.126 dB0.188 dB0.251 dB

0.060.126 dB0.251 dB0.377 dB0.502 dB

0.090.188 dB0.377 dB0.565 dB0.754 dB

0.120.251 dB0.502 dB0.754 dB1.005 dB

where c is the velocity of light, τ is the effective pulse-length of the radar, and where σ0 is the radar cross-section perunit area of the surface. Thus if the radar altimeter has been calibrated with a point target σ, the calibration of σ0follows in terms of known quantities.

The range R is known to high accuracy from delay measurement, and the accuracy of the calibration will depend onthe accuracy with which the other factors in (3) can be determined. The potential error sources are discussed in thefollowing.Satellite Attitude

The radar altimeter antenna gain G in (3) must be evaluated in the direction of the line of sight to the transponder.Uncertainty in the satellite attitude will lead to uncertainty in G, and this uncertainty will be greater the further thetransponder is from the antenna boresight. Along-track pointing errors (pitch errors) may be derived from the receivedpower profile. However across-track (roll) errors cannot be treated in this way.

Suppose that the transponder is displaced from the ground track by a distance X. If the satellite is in nominal attitude,this will correspond to an angular displacement θ from the RA antenna boresight, and the gain G will be evaluated atangle θ. However, if the satellite is rotated from its nominal position through a roll angle dθ the correct value of G in(3) should be G(θ + dθ), and use of G(θ) will give rise to an error in the derived radar cross-section σ. The error in σ,expressed in dB, will be proportional to (sin2θ dθ). The dependence of radar cross-section error dσ on roll error dθ fora typical satellite borne RA, for values of X from 1 to 4 km, is shown in Table 3.

Clearly if the harmonic and random components of the roll error dθ exceed 0.03 degrees, the error in σ becomesunacceptably large when X > 2 km, and so the deployment site should certainly not be displaced by more than 2 kmfrom the ground track. The longer trailing edge of ENVISAT RA-2 may allow total attitude bias to be derived fromthe ocean return, but it is desirable that transponder be as close to ground track as possible, more so than for rangebias calibration.Transponder Pointing

Mispointing of the transponder antennas will contribute to the error budget in a similar way to satellite attitude errors,although the antenna beams are wider, so the effect of a given displacement will be smaller than for the RA antennacase. The transponder antenna beamwidths are of the order of 2.5 degrees. The estimated vertical pointing accuracyachievable is 0.05 beam widths (about 0.1 deg.) and this corresponds to dσ = 0.07 dB at X = 1 km.

If the orbit repeated itself exactly, and the transponder were permanently in place, this would be a systematic error, butin fact X will vary from pass to pass, and so it will have a random component.Polarization Alignment

The plane of polarisation of the transponder should be aligned with that of radar signal for maximum power andminimum sensitivity to misalignment. If the transponder is deployed at a crossing point, this is not possible for bothorbit arcs, but a suitable compromise is to orientate the transponder plane of polarization to bisect the ascending anddescending orbit directions. A transponder that transmitted and received circular polarization might be used; thiswould render the results insensitive to orientation and to the possibility of ionospheric Faraday rotation, but at theexpense of a 6 dB reduction in signal strength. Faraday rotation is actually a very small effect (up to 0.3 degrees).

Table 4. Sample error budgets transponder radar cross-section measurements. Twoversions are given, for transponder displacements of 1 and 2 km from the ground

track.

Effect

Satellite AttitudeTransponder pointingTransponder gain

Polarization alignmentTropospheric AttenuationRSS of relative calibration

Absolute calibration of transponderRSS of absolute calibration

Error (dB) X= 1 km0.130.060.050.050.070.170.100.20

Error (dB)X = 2 km0.250.100.050.050.070.290.100.30

If the nominal alignment of the transponder polarization is parallel to that of the RA, an alignment error of 5 degreeswill. correspond to a cross-section error of 0.07 dB. If the transponder polarization were aligned to bisect theascending and descending ground tracks at a crossing point, such that the angle between the planes of polarizationwere 15 degrees, then an error of 0.10 dB would result from an alignment error of 1.23 degrees, but the (systematic)error would be in the opposite sense for ascending and descending passes, and so should average out.Atmospheric Effects

Gaseous attenuation contributes about 0.14 dB, which may be modelled. Clouds may contribute a variable path loss ofabout 0.15 dB/km per 1 g/m3 of water, a typical contribution of 0.12 to 0.20 dB, and so only clear sky observationsshould be used for maximum accuracy.Clutter

Clutter may affect the measurement in two ways: direct superposition of power; and non-linear effects within thereceiver. Careful site selection must be used to minimise the impact of clutter, .since the radar cross-section calibrationis likely to be more sensitive to ground clutter than the range bias measurement.Error budget

Table 4 shows sample error budgets for transponders displaced by 1 and 2 km with respect to the ground track. Thedominant effects are errors in knowledge of satellite attitude, which will affect both relative and absolute calibrations,and in the case of an absolute calibration, the accuracy of the absolute measurement of the radar cross-section of thetransponder itself.

The challenge in reducing the error of the absolute calibration to a target level of 0.2 dB is to reduce the absolutemeasurement of the transponder radar cross-section to 0.1 dB. However, the random error of a relative calibration canbe reduced to 0.17 dB on a single pass. This would enable detection of trends of 0.19 dB per year if the transponderwere in place for 1 year, and 0.04 dB per year from 3 years of data.CONCLUSION

Since the launch of ERS-1 the technique of transponder altimetry has been extensively demonstrated and validatedusing the ERS satellites. A transponder provides a reference target the range of which can be measured by the radaraltimeter with sub-centimetre resolution and with an accuracy dependent on the accuracy with which the propagationdelay is known. Transponder altimetry can make an independent contribution to the calibration and long-termmonitoring of the range bias and radar cross-section of the ENVISAT RA-2.

In a wider context, the use of transponders provides a unique means to inter-compare the bias calibrations of satellitealtimeters, capable of extension to future missions to ensure the long term consistency of their data sets. Transpondersmay also be used as reference targets for the inter-comparison of radar cross-section measurements in a similar way.REFERENCES

[1] R.J. Powell, 'Relative Vertical Positioning Using Ground-Level Transponders with the ERS-1 Altimeter'. IEEETrans. Geoscience and Remote Sensing, GE24, 421-425, 1986.[2] P.H. Denys, A.R. Birks, P.A. Cross, R.J. Powell, P. Pesec and B. Burki. 'Transponder Altimetry: Precise heightmeasurements over land'. Journal of Geophysical Research, 100 (B12), 24347-24359, 1995.

[3] R.J. Powell, A.R. Birks, W.J. Bradford, C.L. Wrench and J. Biddiscombe. 'Using Transponders with the ERS-1Altimeter to Measure Orbit Altitude to ± 3 cm.' Proceedings of the First ERS-1 Symposium (4 - 6 November 1992,Cannes, France), ESA SP-359, 511-516, March 1993.

[4] A.R. Birks, W. Cudlip, J. Hayball and J. Fisher. 'ERS-1 Orbit Determination and Assessment, Final Report',Contract Report to DRA Farnborough. Document Ref. EOS-94/097-110000-FR-001, Earth Observation Sciences Ltd.,June 1994.

[5] P.H. Denys, A.R. Birks, P.A. Cross and R.J. Powell. 'The Brent Alpha Transponder Altimetry Trial, NorthernNorth Sea - Switzerland July 1994'. Department of Surveying, University of Newcastle upon Tyne and RutherfordAppleton Laboratory, Report 94/1014 for Shell UK Exploration and Production, Version 3.0, April 1995.

[6] C.R. Francis. The Calibration of the ERS-1 Radar Altimeter. ESA Report ER-RP-ESA-RA-0257, Issue 2.0, 1993March 1.