ABSOLUTE AND RELATIVE CALIBRATION OF ERS-2 WITH APPLICATIONS TO ENVISAT P. Moore and G.T. Kilby Department of Geomatics University of Newcastle-upon-Tyne Newcastle, NE1 7RU UK email:
[email protected]
INTRODUCTION Continuous monitoring of the range stability is a pre-requisite for sea-level rise and other demanding applications in satellite altimetry. Range stability may be investigated by either absolute or relative calibration techniques. In this study relative calibration is undertaken through intercomparison against TOPEX/Poseidon and absolute calibration undertaken in the vicinity of 8 tide gauges around the UK. In the former, dual crossover residuals between ERS-2 and TOPEX/Poseidon are analysed for the relative bias along with other spatial and geophysical parameters. The relative bias is subsequently corrected for the observed TOPEX drift as deduced by comparison against the global network of tide gauges. This procedure provides a better estimate of the relative bias than achieved by using the global tide gauge data set, as for TOPEX/Poseidon. In the absolute calibration approach, tide gauge measurements are extrapolated to the sub-satellite points using local models for ocean tides and the geoid; each of the tide gauges having been tied geocentrically to the satellite frame by episodic GPS measurement.
ERS-2 ALTIMETRY The ERS-2 altimetric range and geophysical corrections were taken in the most part from the Precise Ocean Product (OPR) with the following modifications and choice of corrections: • • • • • • •
Radiometric wet tropospheric correction (recomputed after pass 650 of cycle 12 – as recommended by CERSAT); otherwise rejected Pole tide: applied for relative calibration; not applied for absolute calibration Sea state bias: 3 parameter model [1] as recommended by CERSAT Inverse barometric correction: applied for relative calibration; not applied for absolute calibration ERSIN correction for ultra stable oscillator (USO) bias drift: applied ESRIN correction for bias jumps as characterised by SPTR: applied Radial orbit height: AGM98 (relative calibration) and DGM-E04 (absolute calibration)
Bias jumps occur after the altimeter is placed in its safe-mode and then reactivated. The temperature differential over this stand-by period leads to a jump in the range measurement as the clock stabilises to a different temperature regime. According to [2] the Single Point Target Response (SPTR) can quantify the jump. Normal orbital heights were taken from in house NCL orbits using the AGM-98 gravity field [3] and from DEOS DGM-E04 orbits [4].
RELATIVE CALIBRATION The relative calibration procedure is detailed in [5]. Briefly, the relative bias between ERS-2 and the TOPEX altimeter and other geophysical parameters is recovered from dual crossover residuals using AGM-98 orbits for ERS-2 and NASA orbits for TOPEX/Poseidon. In [5] the parameters are estimated per 35 day ERS-2 cycle but here we utilise the
time spans between the SPTR events. Over each time span the altimeter bias is constant relative to the bias jumps but a discontinuity may occur between successive intervals. In this manner we seek to quantify discrepancies between the bias jumps as issued by ESRIN and the observed bias values. SPTR events occurred frequently throughout, especially during the early ERS-2 lifetime, with time intervals varying from a single day to as high as 165 days. The derived ERS2 relative bias was corrected for the observed TOPEX bias drift [6]. Figure 1 plots the derived relative bias and standard deviations for the first 48 ERS-2 cycles, i.e. May 1995 to December 1999.
Figure 1. ERS-2 bias as estimated from DXO data with TOPEX/Poseidon; AGM-98 ERS-2 orbits. Bias corrected for observed TOPEX drift. Mean bias –45.7±1.1 cm; slope 1.5±8.2 mm/yr. The figure reveals both the frequency of the ERS-2 bias jumps and that the altimetric range bias varies substantially over the 5 year period. Low values close to the beginning of 1996 (MJD 50083) are responsible for the spurious mean sea-level change [7] over the ERS tandem period MJD 49853 – 50237 (16 May 1995 – 3 June 1996). A similar conclusion would be drawn from data spanning 1997 – mid 1998 centred on MJD 50800. From MJD 51006 (12 July 1998) onwards, the bias shows greater consistency apart from spurious values over very short time intervals. Overall, there is no clear evidence of contamination at the annual cycle and the conclusion, unchanged from previous work, is that the bias jumps, as inferred from SPTR data, is still the most likely cause of the observed trend.
ABSOLUTE CALIBRATION Absolute calibration of ERS-2 was considered in the vicinity of 14 UK tide gauges. Of these gauges, 6 were subsequently discarded from lack of altimetric data due to location or to the complicated ocean tidal regime in the locality. The 8 tide gauges considered are shown in Figure 2. All sites collect hourly sea-level measurements measured with respect to a local tide gauge benchmark (TGBM). A schematic of the measurements required is given as Figure 3. For each gauge a nearby GPS benchmark was occupied episodically [8] to tie the site into the European fiducial network. Local surveys by the UK Ordnance Survey and Proudman Oceanographic Laboratory provided the height of
all TGBMs relative to the Ordnance Datum Newlyn (ODN). As height differences between the tide gauge benchmarks and ODN are also known the individual heights can be found. The tide gauge measurement was extrapolated to the subsatellite point through differential corrections for mean sea-level change and ocean variability. Locals models for the geoid [9], tides [10] and storm surge [11] can be used for differential corrections between the two sea-levels. However, as the hindsight storm surge values were not currently available for all epochs, the storm surge differential correction was omitted. Given the inevitability of modelling errors in the differential corrections the maximum distance from tide gauge to sub-satellite point was restricted to 45km. The extrapolated tide gauge reading was equated to the altimetric data with the misclosure representing the altimeter bias. Mathematically, the altimeter bias, hbias, is given by hbias = halt – hsat + hsarc +hset + hTGdatum + hTGreading + (hSSPgeoid – hTGgeoid) + (hSSPot – hTGot) + (hSSPss – hTGss)
(1)
where h alt, is the corrected altimeter range, hsat the orbital height, hsarc the short-arc correction to the orbital height, hset the solid earth tide; h TGdatum the tide gauge datum; h TGreading the tide gauge reading; and h geoid, hot and h ss the geoid, ocean tide and storm surge modelled results respectively where the super-script SSP and TG denote the sub-satellite point and tide gauge.
Figure 2. ERS-2 ground tracks and tide gauges for the absolute calibration. Each pass of ERS-2 in the vicinity of the tide gauges yielded a number of 1 Hz altimeter points where a bias estimate can be derived from equation 1. However, accuracy decreases with distance from the tide gauge due to the use of the differential corrections. Conversely, points close to land are unreliable due to contamination of the radiometer by the landmass. Thus, sub-satellite points exceeding 45km from the tide gauge were discarded with a lower limit imposed by the coastline. The orbital height was taken from the DEOS DGM-E04 orbits [4]. Ideally, the long-arc positioning can be enhanced through short-arc corrections computed from 3 or more SLR stations that ranged to ERS-2 near simultaneously. Typically, a radial, along-track and cross-track correction to the long-arc orbit is sought with the radial correction employed within the absolute calibration. Separation of the radial and across-track errors, in particular, requires that the
Figure 3. Schematic of tide gauge and altimetric measurements and datum. geographical distribution of the stations must be favourable with one site either side of the ground track. With SLR tracking from Herstmonceux, Grasse, Graz, Matera, Potsdam, Wettzell and occasionally San Fernando there appeared plentiful opportunities for short-arc enhancements. However, in practice operational difficulties restricted the availability of 3 SLR stations to about 10% of the arcs. For example, in 1996, there were 238 absolute calibration points but of these only 30 passes had short-arc potential, i.e. SLR tracking from 3 or more stations. Of these 30 only 9 provided a correlation coefficient of 0.7 or less between the radial and across-track constant corrections. Four ( i.e. 3 from Holyhead, 1 from Stornaway) of the 9 had tracking from San Fernando in Spain which provided the important station west of the ground track whilst another 4 were from Lerwick, the most northerly of the gauges. An ascending pass over Aberdeen completed the 9. Despite the unfavourable correlations the standard error for the radial correction was often at the 1-2 cm level. As expected most of the 30 short arc possibilities were ascending night-time passes. Also, tt was noted that, even with San Fernando operational, few descending arcs had the required geographical distribution apart from those close to Newhaven and Lowestoft. Due to the infrequency of the short-arc enhancement it was eventually decided to forego the short-arc correction and to utilise all available arcs with the long-arc positioning. In this manner, it was hoped that the less accurate orbits would be compensated by the larger sample. Point 1 2 3 4 mean
Latitude (deg) 56.760914 56.817185 56.873449 56.929691 56.845310
Longitude (deg) -1.984817 -2.017704 -2.050676 -2.083278 -2.034119
Distance from gauge (km) 43.05 36.60 30.21 23.93 33.45
Bias (cm) -40.17 -39.87 -41.78 -41.69 -40.88
Table 1. Absolute calibration of ERS-2 for ascending pass near the Aberdeen tide gauge. MJD 49908 (10 July 1995) Table 1 shows the individual calibrations using the 1 Hz ERS-2 altimetry on the CD ROM for an ascending pass on MJD 49908, 10 July 1995, in the vicinity of the Aberdeen tide gauge. The actual ground track is depicted as Figure 4. A single mean value was recovered for the pass by simply averaging the individual calibrations. Results for all such passes
for the 8 tide gauges of Figure 2 are presented as Figure 5 which distinguishing between ascending and descending passes. The individual passes are colour coded with several gauges having two passes that satisfy the maximum displacement criterion of 45 km. The figure reveals large variations, both within the results for a particular colour-coded pass and between passes from different gauges. Much of the variation is systematic error due to the orbital height although the differential tidal and geoidal corrections and the omission of the storm surge differential corrections will contribute. Of particular note is the 5cm offset between the mean values for all ascending and all descending arcs. This is attributable to the anti-correlated orbital error which changes sign at a given geographical location between ascending and descending arcs. Most of this is due to the time tag bias of about –1.2 ms for ERS-2 altimetry which was not applied at source. At the latitude of the UK this equates to about ±2cm for ascending/descending arcs. The remainder will have a contribution from the geographically anti-correlated orbit error due to gravitational errors in the geopotential model used for orbit determination. The values of Figure 5 can be corrected for the time tag error and time variations in the ERS-2 altimetric centre of figure by using the results for the coefficients A2 – A6 from equation 1 of [5]. Figure 6 plots the modified values. The mean values now agree to within 1cm giving confidence to the correction procedure. On combining results for ascending and descending arcs from Figure 6 the mean bias equated to –45.0 cm with a slope of –2.4 ± 1.6 mm/yr. The results for the above calculations are assembled and summarised in Table2.
Figure 4. Ground track of ERS-2 for ascending pass near the Aberdeen tide gauge. MJD 49908 (10 July 1995) A or D A D A D A&D
Figure 5a 5b 6a 6b -
Tide Gauge # 8 7 8 7 8
Data Points # 524 595 524 595 1119
Rms (cm) 7.2 7.0 7.3 6.9 7.1
Bias (cm) -44.6 ± 0.3 -49.9 ± 0.3 -44.5 ± 0.3 -45.4 ± 0.3 -45.0 ± 0.2
Slope (mm/yr) 4.2 ± 2.4 0.3 ± 2.2 -1.8 ± 2.4 -4.3 ± 2.1 -2.4 ± 1.6
Table 2. Summary of absolute calibrations for the UK
APPLICATIONS TO ENVISAT The relative calibration of ERS-2 against TOPEX/Poseidon, both for the mean bias and for bias signatures, is now a well-established procedure and reported widely in the literature. Two distinct possibilities exist for ENVISAT, namely; (A). (B).
Intercomparison against a TOPEX/Poseidon type mission Comparison against in situ tide gauge data from the global data set.
The essence of the procedure (A) requires • •
Availability of accurate altimetric data and orbits for a TOPEX/Poseidon type mission Independent monitoring of the TOPEX-like altimeter bias through in situ tide gauge data.
For ENVISAT, it is a strong possibility that the science community will have access to TOPEX/Poseidon and/or JASON-1 data altimetry. The best scenario is that TOPEX/Poseidon is still operational for the first few months of ENVISAT (and JASON-1) enabling direct intercomparisons between ERS-2 and ENVISAT. Otherwise, JASON-1 will replace TOPEX/Poseidon within the comparative studies. The worst case scenario is failure of both TOPEX/Poseidon and JASON-1 leaving few opportunities for accurate intercomparisons except for repeat pass possibilities with ERS-2 and intercomparisons with GFO. Since ERS-2 is subject to bias jumps and GFO altimetry is untested we should not be over optimistic there. In (B) one employs comparisons against in situ tide gauge data for ENVISAT as undertaken for ERS-1 and ERS-2 [12]. Unlike the absolute calibration the tide gauge are not connected geocentrically and a relative measure is recovered. This proved highly successful for TOPEX/Poseidon, identifying drift in the total altimetric measurement. The procedure applied to ERS was, however, less accurate than using the dual crossover approach due to the relatively low number of data points for the short time intervals between bias jumps. Figure 7, taken from [12], compares relative calibrations from dual crossover and tide gauges for ERS-2. Overall, the trends are similar. Statistically, on removing outliers where the agreement exceeded 3.0cm, the rms difference was 0.81cm with a correlation coefficient of 0.75. For ENVISAT, with improved orbits from DORIS/GPS, the methodology will be revisited and can complement, or even supplant, the dual crossover approach.
Figure 7. ERS-2 bias drift comparison: DXO and tide gauge solutions. For absolute calibrations the above methodology is still being developed for sites around the UK and investigations are underway to drive down the uncertainty within the bias estimates. Currently, the uncertainty within the UK absolute
calibration is excessive for any deduction apart from mean value and long term drift. Improvements will include • • • •
Use of short-arc orbital enhancements – currently being investigated in more detail. San Fernando is the key SLR station for short-arc refinements. Possible enhancement to differential ocean tidal corrections through TOPEX altimetry Inclusion of storm surge data – currently being investigated Combination with relative calibrations using in situ tide gauge data
REFERENCES [1] P.F. Gaspar and F. Ogor, “Estimation and analysis of the sea-state bias of the new ERS-1 and ERS-2 altimeter data”, Task 2 Rep. Contract 96/2.426 002/C, Inst. Fr. de Rech. Pour l’Exploit de la Mer, Brest, France, 1996. [2] M. Roca and C.R. Francis, “Identification and origin of the on-board bias jumps”, in Minutes of RA and MWR2 CWG(#9), ERSIN, ESA, 1996. [3] P. Moore, “Gravity field enhancement using dual crossovers between ERS and TOPEX/Poseidon with application to the ERS-2 altimeter bias”, in press [4] R. Scharroo and P. Visser, “Precise orbit determination and gravity field improvement for the ERS satellites”, J. Geophys. Res., vol 103, 8113-8127, 1998. [6] P. Moore, “Spatial and temporal errors in ERS-2 radial positioning”, this issue,2000. [7] P. Moore, S. Carnochan and R.J. Walmsley, “Stability of ERS altimetry during the tandem mission”, Geophys. Res. Lett., vol 26, 373-376, 1999. [8] V.R. Ashkenazi, M. Bingley and T.F. Baker, “Monitoring changes in mean sea-level to millimetres using GPR”, ”, Geophys. Res. Lett., vol 20, 1951-1954, 1993. [9] W.E. Featherstone, “ A GPS controlled gravimetric determination of the geoid of the British Isles”, Ph.D thesis, Oxford University, Uk, 1992. [10] R.A. Flather, R. Proctor and J. Wolf, “ Oceanographic forecast models”, In Computer Modelling in the Environmental Sciences, eds D.G. Farmer and M.J. Rycroft, Clarendon, Oxford, England, 1991. [11] J.A. Smith, “ The operational storm surge model data archive”, Report 34, Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, UK, 1994. [12] P. Moore, M.D. Reynolds and R.J. Walmsley, “Monitoring of the ERS-2 radar altimeter range measurement stability”, Final Report, ESA contract no. 12771/98/I/EW, March 1999.
