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TheUse of ReferenceSurfaces to Determine Repeat-OrbitVariability in SatelliteAltimetry

W. Cudlip,H.A. Phillips,and A.H.W.Kearsley

Abstract topography and radar backscatterare constant.Previous re- searchinto altimeter measurementsover land has shown that Two alternative techniquesfor estimating the variability of the there are several regions in radial orbit error for collinear tracks arc investigated using large, uniform desert the world that give "good-quality" radar echoes(Rapley et ol., L987i Geosataltimeter data. The first usessinusoidal fitting to ocean height differences around an orbit, and the second usesrela- Guzkowska et a1.,1990). For example, areasof the Libya tively flat areas of land (in the Simpson Desert, Australia, and Sand Sea,Taklimakan Shamo,and the Kalahari and Simpson the Antarctic Plateau).using a non-oceansurface rcquires Desertsare uniform over hundreds of kilometres and are- knowledge of the local surface slope, and we obtain ihis very flat (i.e., have large-scalesurface slopes less than 0.1'). principle, through the fitting of a plane to the set of repeat height meas- In these deserts,together with the flatter regions in urements. The difference in the relative-orbit-enor estimates Greenlandand on the Antarctic Plateau.could be used to de- from the two techniques is 12 cm root-mean-square(nus), termine the relative orbit error at a number of points around from which we conclude that relative orbit etor can be re- an orbit arc. The relative orbit error at other locations around the orbit could then be determined through sinusoidal duced to less than 9 cm using ocean fitting, and to between 9 inter- polation, as in the and 1.2cm using land fitting. The Antarctic p)ateau could not oceantechnique. Many orbits will not be used as a reference as the orbit error appeared correlated cross suitable referencesurfaces, and this may be a drawback with the cross-trackdisplacement of repeat backs, preventing compared to using the ocean for certain applications.The ef- the determination of the local surface slope. The land analysis fect of the distribution of suitable referencesurfaces is not was also limited by lack of waveform data and Geosatoff- addressedhere as it is application dependent. pointing; current altimeter mr'ssions(e.g., ERS-1and Topex/Po- The two techniqueshave relatively independent sources seidon) should be able to achieve higher accuracies. of error, and so their merits and accuracyare assessedby comparing the relative orbit error derived using the ocean with that derived at two land referencesites for the same set Introduction of orbits. The Simpson Desertin central Australia was cho- Radial orbit error is the single largestsource of error in de- sen as one of the r-eferencesites because it was already termining surface heights from satellite radar altimetry. How- known to provide "well-behaved" altimeter returns (Chua ef ever, for many applications of altimeter data requiring repeat o1.,fssf); and Australia has extensiveocean on three sides, observations, e.g., determining changesin large-icaleocean enabling good interpolation of the oceanresults. A region on topography or measuringthe variation in water level in lakes the Antarctic Plateauaround 56o8,72oS was chosen as the or wetlands, it is sufficient to know the variation in the satel- other referencearea because it was crossedby two of the or- lite orbit rather than its absolutevalue. This can be achieved bits that passedover the Simpson. In principle, much of the through the use of height referencesurfaces that are assumed Antarctic Plateaucould be used as a referencesurface due to to be fixed or varying in a known way. In this paper, we in- the uniformity of its terrain and its low surfaceslopes. Geo- vestigatetwo alternative techniquesfor estimating the varia- sat GeophysicalData Records(Cnns) for four orbits with re- bility of the radial orbit error for collinear tracks using peat data in 1987 and 19BBwere used in the analysis. Geosatdata. The first technique uses the mean ocean surface,cor- TheGeosat Data rected for tides, etc., as a reference.The effect of the dy- The Geosataltimeter satellite, Iaunched bv the U.S. Naw in namic topography of the ocean surfaceis reduced by taking 1985, had the primary objective of mapping the marine ge- advantage of the fact that difference in height measurements oid. Initially, it performed a classifiedGeodetic Mission be- repeat (the for orbits relative orbit error) has a once per cycle tween 1 April 1985 and 30 September1986. During this sinusoidal (Cartwright form and Ray, 1990).A number of re- period, the satellite was in a very long repeat orbit, with a searchershave used collinear repeat tracks to estimateorbit -5 km cross-trackspacing at the equator,in order to perform in (e.g., error this way Cheney ei al., 1991:Van Geysenef fine-resolutiongeoid mapping. The second phase of the mis- o1.,1992). sion beganon B November 1986 and was known as the exact The secondtechnique uses land surfacesfor which the repeat mission (nntra).During this period the satellite was placed in a 17-day repeat orbit with a -160 km cross-track W. Cudlip is with the Mullard SpaceScience Laboratory, University CollegeLondon, Holmbury St. Mary, Docking, PhotogrammetricEngineering & Remote Sensing, Suney, RH59 6NT, United Kingdom. vol. 6r, No. 7, July 1995,pp. BB1-8S0. H.A. Phillips and A.H.W. Kearsleyare with the School of 0099-1112l95/6107-BB1$3.00/0 Surveying,University of New South Wales, P.O. Box 1, Ken- O 1995 American Society for Photogrammetry sington, New South Wales 2033, Australia. and RemoteSensing PEER.REVIEWED ARIICTE

p ( \ ) 4 t '1/ \ 7 \.4 ( I h /t l r/ ) ) r\ 1 \ f \ 16 it a ) (-, \ ) ( r \ \ \ 8t'

Figure1. Globalground tracks for the four Geosatorbits that crossthe SimpsonDesert in Australia.The tracks are labeledwith the track numberassigned sequentially to the 243 orbits within each I7-day repeatperiod.

spacing at the equator,resulting in the orbit ground track re- the antenna not pointing to the nadir, causes a change in the peating every 243 orbits. Sixty-two repeat cycles (usually re- pattern of radar illumination of the surface, and this distorts ferred to as ERMs)were completed before the satellite finally the shape of the return echo. This has an effect on the on- failed in fanuary 1990, almost five years after launch. The or- board height tracker that is dependent on the surface topog- bit of the satellite was controlled by rocket burns, with up- raphy. Over the ocean, the topography is quantified using the datesbeing required every few weeks, to ensure that the significant wave height (swu) parameter. The SWH itself can ground tracks repeatedto within + 1 km. The data from this also alter the tracking characteristics, and so the combined part of the mission are not classified,and 1 Hz averageddata effect of off-pointing and sWH is theoretically calculated be- (GeophysicalData Records)are available from the NOAANa- fore the mission and entered into look-up tables. Off-pointing tional OceanographicData Center in the U.S.A. (Cheneyef and swu estimates derived from the return-echo waveform o1.,19911. shape are used to extract the appropriate conection from the There are four Geosatground tracks that crossthe Simp- tables, and the value is inserted into the cDR data. son Desert,two ascending(tracks 81 and 1,24)and two de- In this analysis, when calculating the surface heights, scending (tracks 16 and 21,7).The track numbers used here the ionospheric corrections and the Fleet Navy Operational refer to the orbit number within each tz-day repeat period. Center (r'Noc) atmospheric corrections given in the GnR data Figure L shows the location of the ground tracks on a map of were used. Data over the ocean were also corrected for tides the world. The results from the analysis of track 16 are pre- and the swu/off-pointing correction. For data over the land, sented in this paper. The Antarctic Plateauis crossedonly only the Earth tide correction was added. The swtt/off-point- by the two descendingtracks due to the asymmetric distribu- ing correction was not applied because the off-pointingesti- tion of land around the South Pole, and the latitudinal limit mates are known to be incorrect over land. This is a result of of 72" for Geosat.The ERS-1satellite has a larger latitudinal the return-echo waveform shape being non ocean-like, and Iimit (82') which will result in over half of its orbits crossing the long averaging time of -2 minutes required for the off- the Antarctic Plateau. pointing calculation. The land data are therefore uncorrected Geosatcompleted 62 ERMsin all. Improvedorbit ephem- for Geosat off-pointing. This can introduce errors of up to eris data, based on the GEM-T2geopotential model (Hainesef + 17 cm in individual surface height measurements for SWH o1.,1390), were available to us for only the first 43 ERMs values of up to S m (the maximum value allowed in the (covering1987 and most of 19BB).Data error problemsmeant analysis). that ERMs1, 5, and 20 could not be included in the analysis, resulting in 40 ERMsof data for processing.Excluding the re- AltimeterConections maining ERMsllom the analysis is not a serious drawback be- Many corrections have to be applied to convert the time de- causetowards the end of 19BBthe stability of the spacecraft lay measured by a radar altimeter into first a range measure- began to be seriously affectedby the increasedsolar activity ment and then a surface height measurement, The associatedwith the maximum of the sunspot cycle which oc- corrections required and their accuracies have been dis- curred in 1989. The pendulum motion of the satellite in- cussed extensively elsewhere (SeasatSpecial Issue I, 1982; creased,resulting in hore frequent "off-pointing," which Geosat Special Issue I, 1990; Guzkowska ef al.,'1990; Cheney causeda loss of data quality and the instrument to loose lock et al., 19s1), and a brief but comprehensive overview of the- of the surfacemore often. operating principles and terminology of space borne radar al- Satellite off-pointing, which results in the boresightof timeters can be found in Rapley (1990).

882 PE&RS PEER.REVIEWED ARIICTE

The surface height, -h, relative to the Earth's reference el- this gradient constitutes the largest potential source of error lipsoid is given by in the use of land as a height reference. Errors derived from /-4,,-,and /.h",.o"do not appea-rin Equa- ft : (1i".,+ Ah..b) - (r- + * A4,,", 4r^,,",," tion 2 becausethey constitute a constant bias that cancelsfor * 4r.o + Ahti,r"+ Aftdy,,+ Ah"r"p.) (1) repeat observations.The magnitudes and effectsof the error where terms in Equation 2 are discussedin detail in later sections. ft"", is the altitude of the satellite above the Reference Ellipsoid 0ceanReference Surfaces at the instant of measurement; Theoretical calculations fCartwright and Ray {1990)and ref- dft..u is the radial orbit error (including the effect of time-tag bias error): erencestherein) have shown that radial orbit error has a r,,, is the range estimate derived directly from the telemetered dominant frequency of 1 cycle/revolution, and height differ- time-delay measurement; encesfor collinear tracks can be expressedas /4"", is the net instrument correction, which includes the h(t) : A(t) cos Ot + B(f) sin At + C(t) (3) center-of-gravity correction, antenna corrections, electronic de- lays, etc.; where A : 2n/orbital period, and A(t), B(t), C(t) are coeffi- dr.,-." is the net atmospheric correction and includes cients which vary with time but on a time scalelong com- contributions from the dry, wet, and liquid water tropospheric corrections, together with the ionospheric correction; and pared with ,f)f.For single-orbitheight differences,A(f), B(f), zlr"", is the net correction derived from estimatinq the location and C(t) can be regardedas constants.Note that Equation 3 is : within the range window of the point on the leading edge of functionally identical to h(f) D(t) sin(J2f+ d) + C(t),where the return echo corresponding to the mean surface; it includes D(t) is the amplitude and d the phaseof a single sinusoid. the on-board tracker error (or retrack error if the data are re- For repeatsof ground track 16, we used ERM22 as the tracked (Martin et o1., 19s3)), the swH/off-pointing correction, referencetrack as it is near the median of the cross-track and a surface bias correction (referred to as the sea-state bias spread of orbits, and it is towards the middle of the period of correction, over the oceanl. the data being analyzed.The height differenceswere gener- The remaining corrections are concerned with the conversion ated using the time into the orbit after aligning the orbits at of range to surface height: the ascendingnode equatorcrossing. The repeat data were linearly interpolated from adjacent 1-Hz values to the refer- Afi,,,,"is the net tidal correction (including Ocean, Ocean Load- ing, and Earth tides) required to convert the height ence times, and subsequentlyaveraged over 17 data points measurement at the time of observation to the mean heieht (-1,1,2.2km) in order to reduce the data volume for further (over lime): analysis.Averaging over L7 samplesgives a point spacingof dfi.,,, (only applicable over water) accounts for the height about 1oand about 200 points per orbit for fitting. changes produced by such things as eddies and currents, and Visual inspection of the sinusoidal fits to the height differ- the depressing effect of high pressure systems (the barometric encesappear satisfactoryeven when over half the ocean data correction): and were lost due to excessivelylarge satellite off-pointing. This oc- (only Ah",.o" significant over land) accounts for the fact that the cured mainly towards the end of 19BBwhen the solar activity altimeter ranges to the nearest point on the surface rather than was increasing and was affecting the stability of the spacecraft. the nadir point. The correction is usually referred to as slope- induced error. Figure 2 illustrates two fits to ocean height differences. There are a number of factorswhich can affect the oual- The bias component of many of these corrections will be ity of the fit, as indicatedby the componentsof Equation2. canceled out when height differences are calculated. We can write the relationship between height difference, 6ft, and rel- CollocationEnor (Aina) ative orbit error, 6ft..n, as follows: As mentioned earlier, the surfacegradients over the ocean - are sufficiently small that the effect of the -r 1 km cross-track 6fi 6ft-b * Isina * 6r*-* * 6r*, * 6lld",, + 6h,i.r" Q) where

I is the horizontal distance between the measurement ooints. and lsina is the vertical displacement between the meisure- 1.00 ERM19 ment points assuming the loial topography is uniform and can 0.50 be characterized by a mean surface gradient, a; 0.00 5r*-* is the error in the atmospheric corrections; 3000.00 4000-00 6r"., is the error in the tracking and surface-bias corrections; 6i0"" onll' applies to ocean data and is the height difference (-) resulting from changes in dynamic effects (eddies, currents, at- 1.ooT-ditt mospheric pressure, etc.). The features extend typically just a 0.50 0.00 few hundred kiiometres and constitute the "noise" sienal- ob- served in height difference plots over the ocean; and 6i,,o. is the error in the tidal corrections. It can be several me- in coastal tres regions. It is insignificant over land. Figure2. Typicalsinusoidal fits to oceanheight differ- Typical large-scale surface gradients over the ocean are ences (h-diff) for track 16. The x-axisis the time in sec- -2 cmlkm; therefore, the + 1-km cross-track displacement of ondsfrom the staft of the orbit(ascending equator repeat orbits introduces a height variation of <2 cm, which crossing).Four segments of oceandata are usuallyseen is small enough to be ignored. Observations in the vicinity of (e.9.,ERM 19) althoughfor some orbitsless data are ocean trenches and seamounts, where larger surface gradi- available(e.9., ERM 39) due to the altimeterlosing lock of ents exist, are excluded from this analysis. Generally, surface the surfacethrough satellite off-pointing. gradients over land are much larger, and the uncertainty in

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displacementof repeat orbits can be ignored. However, be- timates is obtained through a comparisonwith values de- causewe use the time into the orbit to match reDeatdata. rived independently over land referencesurfaces. rather than the location itself, there is a small albng-tracker- For the ERMsof track 16, the standard deviation of the r_orintroduced by changesin the orbit timing. Analysis of residual from the fit is typically 15 cm, reflecting mainly the the effect shows that, although the orbit period is constant to variability in the surfacedue to dynamic features,etc. The about 0.01 seconds,the differencein the time spent in the amplitudes of the fitted functions (the maximum relative or- northern and southern hemispheresvaries seasonallywith bit error) have a mean of 4b cm, and a maximum amplitude peak to peak amplitude of about 0.3 seconds.However, given of 1.06 m. This is consistentwith the published precision for -6.0 the satellite velocity of km/sec and typical basin-scale the GEM-T2orbit ephemerisof 10 to 25-cm root-mean-square gradientsof 2 cm/km, the resulting error is^atmost a few (nrrls)initially, rising to 40 to 60 cm through roaA (Cheneyet centimetresand so can be ignored. o1.,1991J. Having derived the functional form of the relative orbit AtmospheilcConection Enor (Dr*,*) error for each uRtr,t,the values over the Simpson Desert were The main componentsof the atmosphericresidual errors will calculated and are displayed in Figure S. The variation has an be due to the wet tropospheric correction and the iono- RYI of -30 cm (1.6 m peak to peak),indicating the extremes spheric correction. The ionospheric correction in the geosat of the orbit error tend not to occur over the Simpson Desert. cDRsis discussedin detail in Cheney et 01.(1991). They con- clude that the Geosationospheric model underestimatedthe landRefelence Surfaces global ionosphereas the soiar maximum approachedthrough Determination of relative orbit error using Iand referencesur- 19BBand 1989. Errors of a few centimetresare likelv. Emerv- faces has the advantage that the surface topography is static, et o1.(1S90) discuss the FNoCwet tropospheric correction i.e., has no significant tidal or dynamic signal ai there is and conclude that the FNOCmodel consistentlv underesti- over the ocean.A complication, however, is that over land mates water vapor in the tropics by as much as t0 cm, with the effect of the cross-tracksurface slope cannot be ignored. the error varying with time. The maximum error in the at- With a cross-trackdisplacement of rep^eatorbits of uf to * r mospheric correction difference is thereforelikely to be on , km, to achieve a target orbit error meisurement accu-racyof s the order of 10 cm. cm, the cross-tracksurface slope must be known to an Jccu- racy of about 5 cm/km (0.003").In this analysiswe deter- RangeEstimation Corection Enor (6r"",) mine the overall slope at a point by fitting a plane surfaceto The contribution to this term from the performance of the the set of repeat heilht measurements accum'ulated about on-boardtracker is insignificant over the oceanbecause the that point. The residuals from the plane fit are then taken to data are averagedalong track. It is not insignificant over land be the relative orbit error associatedwith each repeat obser- becauseonly limited along-trackaveraging is possible. vation. Successiveestimates of the orbit errors ca^nbe ob- The error in the SWH/off-pointingcorrection is also in- tained along track and the results averagedto reduce the cluded in this term, although, over the ocean,the error in effect of random noise. this couection is assumedto be small, However, Hayne and For a set of repeat tracks, the height measurementscan Handcock (1990)have shown that further correctionscould be representedby lr(xu),i : L to N,/ I r to M, wherex,, is be "standard" applied to the swH/off-pointing corrections the latitude and longitudeposition vector of the lh sa-plu given in the cDR data. Theseadditional corrections,although on the rlh track. For a typical reference surface. ihe reoeat typically (10 cm, can be as large as Z0 to 30 cm for com- tracksare effectively pa.ittet and have equal sample spacing bined extremesof off-pointing and significant wave height. (-0.0 tm for 1-Hz data),although the actual along-tracksari- However, there will be a reduction in the associatederror ple location varies from track to track. Using a set-of reference when a whole orbit is analyzedbecause the typical wave- points, r, parallel to the along-track direction and with a spac- length of the off-pointing variation is less than an orbit. ing equal to the sample spacing of the altimeter measure- Similarly, the sea-statebias correction is also included ments, each repeat height measurementcan be assignedto the in this term, but a correction is not applied in this analysis nearestreference point. Figure 4 illustrates the geometry of the becauseit is of sufficiently short wavelength to be averaged situation. If we now assumethat the local surface around each out around the orbit. referencepoint can be representedby a plale over the 6.6- by 2-km area of the repeat observations,we have TidalConection Enor (6/4,0") fi(x,;) : + - The Schwiderski Tide Model given in the GDRsis likely to fi"(r/ b(r).(r, x,) + Ah,, (4) contain errors of 10 cm or so in the open ocean,increasing to a metre or more in coastalregions.

OceanDynamic Feature Enor (6/or") The ocean surfacehas dynamic featuressuch as eddies and curents which can have relatively large amplitudes of -50 0.5 cm, over scalesof 100's of kilometres, and changing on a 0 time scale of days. -u5 One advantageof the oceanfitting is that all these errors have typical wavelengthsthat are short compared to the length of an orbit and so the effect of the enors is reduced Figure3. The relativeorbit error at the SimosonDes- when data from a whole orbit are fitted. It is difficult to ert derivedfrom the sinusoidalfits to repeat-tracx quantify this reduction becausethe behavior of the errors heightdifferences over the ocean.ERM 22 was used around the orbit depends on many factors.Therefore, the as the referenceorbit. best measureof the uncertainty in the relative orbit error es-

884 PE&RS PEER.REVIEWED ARIICIE

6h",0..Note that the uncertainty in the relative orbit error es- timates can be reduced to some extent by averagingthe re- siduals along track. .\. Variations over time in the radar backscattercoeffrcient o of the surfacemay also introduce changesin altimeter-meas- N. ured heights through a changein the relationship between d the mean radar surfaceand the mean geometric surface.The variability of the backscattercoefficient in desertsand the high Antarctica plateau is difficult to determine using Geosat data becauseof the severeeffect of satellite off-pointing on backscattermeasurements. Given the arid and unchanging .\. nature of the areasunder consideration,the effect is not ex- o" o Reference Point pected to be significant at the levels of accuracybeing con- . MeasurementsamPle of backscatterstability \' sidered here. Further investigation and its effect on height measurementshould be carried out Figure 4. A schematicdrawing with data from ERS-1and Topex/Poseidon. showingthe relationshipbetween the samplesof repeat-track measurementsand a set of refer- SimpsonDesert Analysis encepoints. The barsdelineate The sandy area of the Simpson Desertextends approximately the areasover which a olaneis between latitudes 23.5'S and 27oSand between longitudes fitted to the repeatedheight 136'E and 138'E. Figure 5 shows the location of the four dif- measurements. ferent Geosatground tracks that pass over this area.Figure 6 gives the parameterprofiles for height, backscattercoeffi- cient, and significant wave height (swH) for track 16 of ERM22as an example of the typical behavior of the observa- where h.(r,) is the height at the referencepoint, b(r,) is the tions. The height profile revealsthat the surfacegradient is local gradient vector of the surface,and Aft,,is the residual of uniform and relatively smooth with a mean of -27 cm/k;rn the measurement.We assumethat 4h,, can be regardedas (<0.02'). However, there are a few undulations towards the having a constant and a variable comfonent center of the profile where the swH value is particularly high (-20 Ah':57' *UO. (5) m). The return-echowaveforms in the Simpson area are known to be ocean-like (Guzkowskaef a1.,1990; Chua ef ol., 6ft',is the constant element with componentsfrom both 1991);therefore, the SWHvalues can be interpreted as repre- the altimeter measurementcorrections and the radial orbit senting the typical dune heights in the region. error. 6.h,,represents the variable componentsof the correc- The main steps in the analysisare tions and radial orbit error and is assumedto be a zero-mean random variable. Substituting Equation 5 into Equation 4 and rearranging gives ft(x,i) = [h.(r,)+6li',1+ b(r/.(q - xu) + 6hu. (6) Fitting a plane surfaceto the set of repeat height meas- urements around each referencepoint allows the height, []r"(r/ + 6h'/, the gradient, b(r,), and the residuals, 6hu,to be determined. The residuals,6hu, have three main components (seeEquation 2): 6h,, : 6ir*u, a 6r,,or+ 6r*"."", (7) 6h",0.is the variable component of the orbit error for which w.euse the term relative orbit error. Given the size of a typical referencesurface, the relative orbit enor can be re- garded as being constant along track (henceno 7 subscript)as its variation around the orbit is relatively slow. 6r"",..is the error in the range-estimationcorrections and is com'posed mainly of the tracker noise and the off-pointing error. 6ru,,,o". is the error arising from the atmosphericand ionospheric corrections.It can also be regardedas being constantalong track for a typical referencesurface, Assuming the componentsof Equation 7 are independ- 133" 134' 135' 136" 1370 ent, then the variance of the required parameter,6h",n., is Figure5. Locationof the four Geosatground tracks that equal to the sum of the variancesof the other parameters, passover the SimpsonDesert superimposed on an ex- Providing there are a sufficient number of repeat observa- tract from The TimesAtlas (Bartholomew,1986). The re- tions to give a reasonableestimate of the surfacegradient, gionwith the dottedoutline shows the mainarea of sand and the variancesof 6r.",--and 6r",,,.".are small, then the re- ounes. sidual, 6ft,,,will be a gooil estimatebf the relative orbit error, ER.REVIEWED ARTICTE

Latltude Simpson Desed: track 16 ERM22 -26.44 - heisht (m) .26.45

-26.46

-26.47

tt -26.48 I a .26.49 'rj

136.54 136.58 136.62 136.66 Longitude

swh (m) Figure7. Typicaldistribution of repeat- track samplesabout each reference pointfor track 16 overthe Simpson Desert.

3440 3470 3480 Lat: .24-11 -26-37 Lohgr 137.73 136.66 TrackerNoise Figure6. Typicalparameter profiles for track 16 over the The precision of Geosatheight measurementsis dominated SimpsonDesert. The x-axis is the time in secondsfrom by "tracker noise" and is 5 to 10 cm over the ocean for 1-Hz the start of the orbit (ascendingequator crossing). The samples (a mean value every 6.6 km) (Cheneyet al.,1s87). heightand radar backscattercoefficient (o.) profilesare The precision is worse over the Simpson Desertbecause the relativelyuniform, whereas the significantwaveheight dune height is larger than typical oceanwaves and the ter- (swH)shows a markedincrease towards the centerof the rain is more variable. An examination of very close repeat desert. tracks (i.e., whose sampleswere within 50 m) showed the height tracker noise rangesfrom 30 to 50 cm RMSfor dune areaswith SWHtypically <5 m. Differencesof severalmetres were observedin areasof larger dunes. In order to further investigate o ground-track the effect of tracker noise Establish a set of reference points for the refer- and the averaging ence alea, of data in the GDRdata set, a number of . Extract a set of repeat height measurements for each reference tracks of waveform data for track 81 were processed,Analy- point and fit plane surfaces, and sis of a close repeat of threshold-retrackedwaveform data re- o Identify reference points with "acceptable" fit and average sulted in a height noise in the range 14 to 30 cm for dune the residual along track for each nRv. areaswith swH <5 m, i.e., about half the value recorded for the non-retrackeddata in the GDRs.Clearly, the orbit-error Sixty-two referencepoints for the track-16 repeatswere analysis would be greatly improved if carried out with re- establishedusing the locations of the samplesfor ERM22. tracked waveform data. However, such data are not readily ERM22 was chosenbecause it was known from the ocean available for the Geosatmission. The few reDeattracks of analysis to lie at the median of the spread of possible cross- waveform data for track 81 available to us were provided by track positions. The repeat height measurements about each special arrangementwith the Applied Physics Laboratory, of these referencepoints were extracted,and fitted with a lohn Hopkins University. plane using a standard least-squaresmethod. Figure 7 shows Tracker noise is obviously a significant contributor to the the distribution of the samplesabout each referencepoint. observedRIras of the residuals.To limit the effect of tracker The samplesspread over a rectangleof dimensions 6.6 km noise, the sectionsof track with the lowest Swrt have to be by 2 km as a result of the along-track1-Hz sample spacing and the + 1-km cross-trackvariation. The goodness-of-fitstatistic for each referencepoint showed that the assumption of the surfacebeing a plane over the area of the samplesis a reasonableone for most of the rms of residuals (m) points. However, the RMSof the residuals at each reference 2.00 point varied widely from 0.28 m (Point 58) to more than 2 m 1.50 (Point (see 32) Figure 8). Becausethe relative orbit error is 1.00 effectively constant for each referencepoint over the length 0.50 of the Simpson, then the RMSof the residuals should also be 0.00 constant.Clearly, the additional sourcesof error (from the range-estimationcorrection and the atmosphericcorrection) identified in Equation 7 are not insignificant. The error in the Figure8. The root-mean-squareof the residualsfrom a range-estimationcorrection has two main parts, namely, the planefit to the heightmeasurements around each of tracker noise and the off-pointing error. These two compo- the 62 referencepoints established for track 16 over nents, togetherwith the atmosphericcorrection error, are the SimpsonDesert. now discussed.

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the area of the fit. To test this assumption,the interpolated Correction (m) relative orbit errors from oceanfitting were assumedcorrect and assignedto the relevant samplesabout an arbitrary refer- ence Doint. If the relative orbit error is a zero-meanrandom variable, then the fitted plane would show no significant slope. In addition, the differencebetween the residualsand 0.t0 the input values gives an indication of the effect of the error in the slope estimate.The results of the fitting were 0.0s No. of samples in fit =40 Lat. gradient {m,) : 5.4 +5 cm/km 0 10 20 30 40 ERM 50 Long. gradient [m,) = 73.4 +13 cm/km I 1987 | 1984 St. dev. of input/residual Figure9. Variationof the FNocWet and Drytropo- differences = 6.0cm sphericcorrections and the lonosphericcorrection overthe periodof the analysis.The Drycorrection has The observed latitude and longitude gradients are not -2.L beenoffset by m to placeit on the same scale significant given the error associated with the fit, showing as the othercorrections. the zero-mean random variable assumption to be valid. The differences between the input values and the measured resid- uals have a standard deviation of 6 cm. This implies that, when fitting a plane to the real observations, the variation of used and its effect further reduced by averagingthe results the orbit error over the olane will contribute -6 cm RMS to- along track. wards the overall error 6udget. This is acceptable given the size of other contributing errors. It must be pointed out that Satellite0ff-Pointing this error analysis applies for 40 repeats with the given The effect of Geosatoff-pointing contributes to the residuals, ground pattern for track 16 (Figure 7), and the result may be and this will be exaggeratedby the relatively large SWHin different for a different number of repeats with a different the Simpson Desert,particularly towards the center of the re- ground pattern (see Antarctic analysis in next section). gion. It was mentioned earlier that an off-pointing correction was applied over the ocean,but not over land, becauseit is Relative0rbit EnorCalculation difficult to estimateconectly. The is calculated off-pointing Despite the large variation in the residuals seen in Figure B, the ocean of over from the slope the trailing-edgeof the re- there are a number of points, mostly Iying towards the end turn echo. rlowever,However, over land the turn ecno. over land tne tlarlrng-eclgetrailing-edge slope rsis of the track, where the RMS of the height residuals is less dominated by effectsand terrain the standard off-pointing than 40 cm. This is close to the expected value of about 30 calculationcalculatlon doesooes not grvegive thetne couectcorrectcorlect result. Iortunately, e) eive result. Fortunatelv.Fortunately, e:ex- cm for the GEM-Tz orbit, and. as the SWH is less than 5 m amination of the off-pointing llom the ocean either side of here, the residual is almost certainly dominated by orbit er- Australia indicates that it rarelvrarely exceeded 0.5o over the ror rather than tracker noise and off-pointing. The four Simpson, so for dune areas with <5 SWH m, the off-pointing points with the lowest residuals were selected and the mean was nearly in range error always the LOIo 17 cm. In addi- iesidual for each ERM was calculated (Figure 10). We inter- did tion, there not appear to be a significant correlation be- pret these mean residuals as the relative orbit error as de- off-pointing tween the angle and the differencebetween the rived over land, and in a later section we compare them with land ocean and orbit-error estimatesderived later. We con- the ocean-derived values, Averaging the residuals from these clude thereforethat the effect of off-pointing is less than that four points helps to reduce the effect of tracker noise, but the to tracker due noise for this area. off-pointing and atmospheric correction errors act as a bias over short track lengths and will not be reduced. This is one AtmosphericConection Enor of the drawbacks of using land reference surfaces as opposed As discussedfor ocean data, the wet tropospheric correction to the ocean surface around an orbit. is likely to be the main source of error in the atmospheric correction. However, one of the advantagesof using an arid AntarcticAnalysis region as a referencesurface is that the water-vapor content Data from the section of track 16 that passes over the Antarc- of the atmosphereis Iikely to be low, so the error in the cor- tic Plateau appear to be relatively smooth and uniform. Data rection will be correspondinglysmall. Figure g shows the variability of the wet, dry, and ionospheric correctionsver- sus ERM(i.e., every 17 days) for the period of the analysis.

The wet tropospheric correction revealsthat during 19BB Relalive orbit error (Land) there was significantly more water vapor in the atmosphere compared to 1987. Nevertheless,the correction rarely ex- 0.5 ceeds 15 cm, and even assigninga 50 percent error to the 0 FNoCvalues gives a maximum error of B cm. The contribu- RNRsE '0.5 tion to the RMSof the relative orbit error is a few centi- lust ERM number metres.This is acceptablegiven the other sourcesof eror. -1 Figure10. The relativeorbit error at the SimpsonDes- Distributionof 0dit Enor ert derivedfrom the meanof the residualsfrom plane One of the assumptionsrequired for the plane-fitting tech- fits to the heightmeasurements around four reference nique is that the relative orbit error is a zero-meanrandom polnts. variable, that is, its value does not depend on location over PEER.REVIEWED ARIICTE

spanning the longitude range of 4B'E to Sb'E near the latitu- dinal limit of -72" for Geosatwere extractedand orocessed. Figure 11 illustrates typical profiles for the pu.u..r"t"rt height, radar backscattercoefficient (o.), and SwH taken from ERM22. It can be seenthat the o. is relativelv constant and that the SWHis lower than that over the Simpson, suggesting that the region should be good for surfacefitting. Unfortunately, as a result of increasedGeosat off-point- 4500 ing in polar regions,about half the passesin the Antaictic (dE data set fail to maintain lock of the surface.This loss of data, 20 while obviously reducing the number of orbits that can be analyzed,also increasesthe enor associatedwith estimating the iurface slooe. To determine the effect of the reduced number of orbits 4500 and to test again if the relative orbit error behavesas a zero- swh ( mean random variable, the interpolated relative orbit error ,OI from the oceanwas assignedto the repeat observations 'u around an arbitrary referencepoint 'oI / as describedfor the ll Simpson analysis.For the full set of repeat observations,the 5y results of the plane fitting were ^,I 4500 4510 4520 4530 4540 No. of samples in fit :4O Latt -72.03 -72-04 Long: 54.76 48.87 Lat. gradient (m,) : -45.3 + 14 cm/km Long. gradient {m.) : O.5 +2 cmlkm Figure17. Typicalparameter profiles for track 16 (ERM St. dev. of input/residual 22]'over the sectionof the AntarcticPlateau considered :11cm differences as a referencesurface. The x-axis is the time in seconds from the start of the orbit (ascendingequator crossing). In contrast to the Simpson result, there appearsto be a marked comelationbetween the latitude (cross-tracklocation) of the point and the orbit enor. This results in a significant slope to the fitted plane, and the standard deviation of the Our inability to use the Antarctic Plateauas a reference differencebetween the input orbit error and output residuals surfaceis unfortunate becausethe plateau has the potential is 1.1cm, compared to 6 cm for the Simoson. to act as a referencesurface for many orbits and is almost es- The situation is made worse by the iact that half the sential if interpolated relative orbit errors are to be derived data are lost through Ioss of lock. Ii we just 20 points use the from land referencesurfaces. for which we actually have Antarctic observations,then the discrepanciesare larger, the standard deviation of the differ- ence being an unacceptable24 cm, as shown below: Comparisonof0cean and Land Results Figure 12 shows the ocean-derivedvalue of relative orbit er- No. of samples in fit :2O ror for each ERM(as shown in Figure 3) plotted againstthe Lat. gradient (m,) : -67.7 + 16 cm/km correspondingland-derived value (as shown in Figure 10). A Long. gradient (m.) : 1.3 +3 cm/km consistentrelationship is revealed,with a mean offset of 30 St. dev. of input/residual cm due to the fact that the oceanvalues were derived rela- differences :24cm tive to ERM22 whereasthe land values were derived relative to a mean orbit error. For the land observations,ERM z2 is 25 The relative orbit error shows a significant gradient over cm from the mean, which is consistentwith the 30-cm offset, the area of the fit, so the residuals from a plane fit to the given the error in the individual altimeter measurements. height measurements cannot be interpreted as orbit error. The presenceof such an offset is not relevant for relative or- The relationship between orbit error ind cross-track location bit error analysis. is surprising, given the small size of the cross-track displace- Figure 13 shows the difference between the ocean and ment. The effect may be related to the fact that the data are land derivations (after the subtraction of the 3O-cmoffset). The '12 near the latitudinal limit of the orbit and that errors in the nvs of the differenceis cm (St cm peak to peak),and this geoid models used in calculating the orbit ephemeris are representsthe worst-caseuncertainty in using either tech- larger near the poles. This problem may not be as severe for nique. The differences should be the nMS sum of the errors in the ERS-1altimeter because the latitudinal limit of -82' will the individual techniques,because the main sourcesof error allow observations over flatter regions of the plateau away are independent. Assigning the error equally suggestsan accu- from the limit. Geoid models with improved representation racy of about I cm RMSin the use of either technique.How- of the Antarctic will also be used in the orbit cilculations. ever, there are a number of reasonsto suggestthat this We have to conclude that these Geosat data over the ola- combined error is dominated bv errors in the land measure- teau cannot be used to estimate relative orbit error because ment: of our inability to determine the cross-track surface slope. . The tracker Further work will be required to investigate whether alierna- noise is significant because only limited along- track averaging of the data has been possible; tive techniques could be used to determine the slope, Possi- o The errors associated with off-pointing have not been ble alternatives include using adjacent orbits, or regions of accounted for over land; and the Antarctic with particularly low surface slopes, such as . In some of the cases that have a large discrepancy between the ice shelves or areas with sub-slacial lakes. Iand and ocean estimate, the ocean fit looks particularly good.

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improvement would come from the use of retracked wave- Flelativeorbit error comparison form data. Discussion This analysishas demonstratedthat the mean oceansurface

I around an orbit provides a better reference surface for the al- ?, . timeter than doei a desertregion. However, many of the prob- E t .ta Land lems associatedwith the land may be particular to the use of

1.0(m) Geosatdata. Current altimeter missions (e.8.,ERS-1 and Topex/ Poseidon)should have improved attitude control and better accessto waveform data (for retracking).Eventually, the limi- ting factor in the use of land surfacesas height referenceswill be the ability to determinethe cross-tracksurface slope. For some applications, it may be possibleto select land Figuret2. Comparisonof the surfacesknown to have zero surfaceslope, such as salarsor ocean-derivedrelative orbit error clay pans. However, this would severelylimit the number of estimateswith those obtainedus- orbits that could be analyzed.Lakes with monitored water ingthe SimpsonDesert height Ievels might also be used as a height reference,but the effect measurements.The non-zerointer- of wind set-up and denivellations,which could introduce er- cept is not relevantfor relativeor- rors of severaldecimetres, might be significant.Further re- bit erroranalvsis. searchis reouired in this area. The curient advantageof Geosatdata over data from cur- rent altimetric satellitesis the large quantity of repeat data available.Although later altimeter missions are likely to pro- duce better land observationsthan Geosat,it will be several The use of ocean data around the orbit as a reference years before the number of repeat orbits available is suffi- surfaceis likely thereforeto give better results than using de- cient for self cross-trackslope determination.In the mean- sert data, at least for Geosatobservations over regions con- time, it should be possibleto use Geosatdata to determine taining dunes a few metres or more in height. The quality of the local slope at, for example,Geosat/eRs-r orbit cross- relative orbit error estimatefrom the ocean data is therefore overs. This will allow the determination of relative orbit er- likely to be better than the 9-cm equal division of error ror for later satelliteswith very little repeat data. might suggest. In the longer term, Topex/Poseidonhas the best prospect There are a number of ways in which the analysis of the for accuratelocal slooe estimation becauseit is intended that data could be improved. Over the ocean,the residual after this satellite will accumulate 5 years of altimetric data in a the fit could be analyzedto exclude regions of high variabil- 10-day repeat cycle. Unfortunately, the orbit separationis ity, improved wet tropospheric corrections (availablein the rather large (-300 km), which may limit some of the appli- cD-RoMedition of the cDR data (Cheneyet al., 1991))and the cations of the data. The ERS-1satellite, in its 35-day repeat barometric correction could be applied, togetherwith the re- phase,wiII give better ground coveragewith B0-km orbit vised Swrt correctionsof Hayne and Handcock (rggO).Over spacing,but will acquire less than 20 repeats.ERS-1 will ob- the land, the distribution of points around the reference tain about 30 repeatsin each of the two 3-month ice-phases point could be improved by repositioning the 1-Hz height of the mission, 6ut again the large orbit separationmiy limit values by recalculatingthe means from the 10-Hz height data the applicability of the data. available in the GDRproduct. In addition, the surfaceslope estimatecould be improved by using a more recent Geosat Summaryand Conclusions orbit ephemeris,e.g., the University of Texas GeosatERM The analysis demonstrates that both ocean and land refer- Ephemeriswhich is available for the first 44 ERMsand has a ence surfaces can be used to improve on the relative orbit er- '1.7 quoted radial accuracyof cm RMS(C. Shum, private com- ror of the Geosat orbit ephemerides currentlv available. munication). However. none of these improvements are Assigning the error from the comparison equally gives g cm worth pursuing while the land analysisiJ dominated by the RMS enor compared with the -2O to -50 cm RMS radial or- tracker noise inherent in the cDR data. The most significant bit error over the Simpson for the GEM-Tzorbit ephemeris used in the analysis. The ocean technique appears slightly superior to that of land because some of the contributing er- rors are reduced through the averaging effect of analyzing data from a whole orbit, Also, the Geosat land data used here suffered from tracker noise and off-pointing. 0.50 The Antarctic Plateau cannot be recommended as a ref- 0.00 erence surface because our analysis revealed that the Geosat @ooNr@69d bNoFO location -0.50 orbit error was correlated with the cross-track of the orbit and so did not behave as a zero-mean random variable ERM number over the 2-km spread of ground tracks. This prevented the Figure13. The differencesbetween the ocean-and land- determination of the cross-track surface slope, an essential derivedestimates for relativeorbit versus ERMnumber. A prerequisite for the use of land reference surfaces. It has yet 3O-cmmean differencebetween the estimateshas been to be determined whether all Geosat orbits over the Antarctic removed. are affected in this way. Using the ocean also has the advantage that it is easy to PEER.REVIEWED ARTICTE

interpolate the result to any location. For land, unless the of SignificantWave Height and Attitude on GeosatRadar Altim- referencesurface is close to the area under analysis,then etet Measurements,l. Geophys. Res,,95(C3):2837-2842. two or more suitable land referencesites along the orbit are Martin, T.V., A.C. Brenner,H.f. ZwaIIy, and R.A. Bindschadler, required for interpolation, and this may not be easyto 1983.Analysis and Retrackingof ContinentalIce SheetRadar achieve given the problems with the Antarctic data and the Altimeter Waveforms,l. Geophys..Res.,88(C3):1608-1616. effect of large dunes in deserts. Rapley, C.G.,1990. Microwave Remote Sensingfor Oceanographic Data from later altimetric missions such as ERS-1and To- and Marine Weather-ForecastModels (R.A. Vaughn, editor), KIu- pex/Poseidonwill potentially yield better results over land wer Academic Publishers,pp. a5-63. than those presentedhere becausethese altimeters have better Rapley,C.G., M.A.J. Guzkowska, W. Cudlip, and I.M. Mason,1987. satelliteattitude control and there should be better accessto An Exp)oratory Study of Inland Water and Land Altimetry Using waveform data for retracking. The land technique is important SeasatData, ESA ContractReport 6483/85/NL/BI,ESA Scientific for some ocean-relatedapplications because the relative orbit and Technical Publ. Branch, ESTEC,Noordwijk, Holland. error is determinedcompletely independentlyof the ocean SeasatSpecial Issue I, GeophysicalEvaluation, 7582.J. Geophys. surface.In the longer term, it may be possibleto use land sur- fies.,87(C5):1. faces as a reference datum for sea-levelchange measurements. Tapley, 8.D., G.H. Born, and M.E. Parke,1982. The SeasatAltimeter The accuracy of the relative orbit error determination sug- Data and its Accuracy Assessment,l. Geophys.-Res., 87(C5): geststhat desertareas could also be used as absoluteheight 3173-3 188. referencesfor orbit determination if the surface height was Van Gysen,H., R. Coleman,R. Morrow, B. Hirsh, and C. Rizos, 1992. known in the samereference frame as the satelliteorbit (e.g., Analysis of Collinear Passesof SatelliteAltimeter DaIa,I. Geo- phys. Res.,97 (C2):2265-227 7. using cPS)and the relevantaltimeter biases were also known. (Received29 April 1993;accepted 10 August 1993;revised 10 No- Acknowledgments vember1993) Thanks to Justin Mansley and Ellen Mason for help with the data processing.W. Cudlip acknowledgesthe assistanceof Wyn Cudlip the British Council in funding his visit to the University of Wyn Cudlip received the B.S. degreein Physics New South Wales, and wishes to thank the membersof staff and Astronomy from LeicesterUniversity, U.K., at the School of Surveying for their help. This work was sup- in 1975 and a Ph.D. degreein Infrared Physics ported in the main by a giant from the Australian Research from University CollegeLondon, U.K., in 1980. Council. He joined the RemoteSensing Group at the Mullard SpaceScience Laboratory in 1985 where he is now a Senior ResearchFellow. From 19BBto 1991 he was resDon- Refelences sible for the specificationof the ERS-1altimeter data proc-ess- ing algorithms to be used at the ERS-1UK Processingand Barthoiomew & Son Ltd., 1985. Tlre Times Atlas of the World,Times Archive Facility. His main researchinterest is developing Books Ltd, London. new applications for satellite radar altimeter data over non- Cartwright, D.E., and R.D. Ray, 1990. Ocean Tides ftom Geosat Al- ocean surfaces. timetry, I. Geophys. fies., 95(C3):3069-3090. Chua, P.K., A.H.W. Kearsley, f.K. Ridley, W. Cudlip, and C.G. Rap- Helen Phillips ley, 1991. The Determination and Use of Orthometric Heights Helen Phillips received the B.S. degreein Phys- Derived from the Seasat Radar Altimeter over Land, Photogram- ics from University CollegeLondon, U.K., in metfic Engineering & Remote Sensing, 57(4):437445. 1990. She is currently working at the School of Cheney, R.E., B.C. Douglas, R.W. Agreen, L. Miller, D.L. Porter, and Surveying,University of New South Wales, N.S. Dovle. 1.987. Geosat Altimeter Geoohvsical Data Record (GDR) []ser Handbook, NOAA Technicil Memorandum NOS Australia. Her researchinterests include satellite NGS-46, Natl. Ocean Serv., N/CG112, NOAA, Rockville, Mary- altimetry and cps surveying. She has taken part in two cPS land, 32 p. field campaignsto test sites in the Simpson Desert,the latest joint Cheney, R.E., N.S. Doyle, B.C. Douglas, R.W. Agreen, L. Miller, E.L. being a venture with MSSLcoinciding with the flying of Timmerman, and D.C. McAdoo, 1991-.The Complete Geosat Al- the NASA/TPLAirsar over the site. timeter GDR Handbook, NOAA Technical Memorandum NOS NGS-7, Natl. Ocean Serv., N/CG112, NOAA, Rockville, Maryland, Bill Kearsley Bop' BiIl Kearsleyreceived the B. Serv. and M. Serv. GeosatSpecial Issue I, 1990./. Geophys.Res., 95(C3):1. degreesin surveying from the University of Guzkowska,M.A.J., C.c. Rapley,J.K, Ridley, W. Cudlip, C.M. Bir- New South Wales,Australia, in 1963and 1969, kett, and R.F. Scott, 1.99O.Developments in Inland Water and respectively,followed by a Ph.D. degreein Land Altimetry, ESA CR-7839l88lFlFL,ESA Scientific and Tech- wi,illl|wirw!;! Physical Geodesy in 1976. He is cunently an nical Publ. Branch, ESTEC,Noordwiik, Holland. Associate Professor at the School of Surveving, University of Emery,W.J., G.H. Born, D.G. Baldwin, and C.L.Norris, 1990. Satel- New South Wales. His research and professional interests in Iite-DerivedWater Vapor Correctionsfor GeosatAltimetry, /. geodetic surveying include optimum evaluations of gravimet- Geophys.-Res., 9s(C3l :2953-2564. ric geoids; combination of gravimetric geoid heights, GPSel- Haines,B.J., G.H. Born, Rosborough,J.G, Marsh, and R.G.William- lipsoidal heights, and conventional leveling in height son, 1990.Precise Orbit Computation for the GeosatExact Re- networks; optimum geopotential models for regional geoid peat Mission, l. Geophys.Res., 95(C3):2871-2886. determinations; and the use of satellite radar altimetry to Hayne, G.S.,and D.W. Hancock III, 1990.Corrections for the Effects determine topographic heights over land.

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