Sea surface height determination in the Arctic Ocean from ERS altimetry

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2001jc001026, 2004 Sea surface height determination in the Arctic Ocean from ERS altimetry Neil R. Peacock and Seymour W. Laxon Department of Space and Climate Physics, University College London, London, UK Received 14 June 2001; accepted 12 April 2002; published 1 July [1] Accurate sea surface height measurements have been extracted from ERS altimeter data in sea ice covered regions for the first time. The data have been used to construct a mean sea surface of the Arctic Ocean between the latitudes of 60 N and 81.5 N based on 4 years of ERS-2 data. An RMS value for the crossover differences of mean sea surface profiles of 4.2 cm was observed in the ice-covered Canada Basin, compared with 3.8 cm in the ice-free Greenland-Iceland-Norwegian Seas. Comparisons are made with an existing global mean sea surface (OSUMSS95), highlighting significant differences between the two surfaces in permanently ice-covered seas. In addition, we present the first altimeter-derived sea surface height variability map of the Arctic Ocean. Comparisons with a high-resolution coupled ocean sea ice general circulation model reveal a good qualitative agreement in the spatial distribution of variability. Quantitatively, we found that the observed variability was on average a factor of 3 4 greater than model predictions. INDEX TERMS: 1243 Geodesy and Gravity: Space geodetic surveys; 4275 Oceanography: General: Remote sensing and electromagnetic processes (0689); 4512 Oceanography: Physical: Currents; 6969 Radio Science: Remote sensing; KEYWORDS: Arctic, ocean, satellite, altimetry, ERS Citation: Peacock, N. R., and S. W. Laxon (2004), Sea surface height determination in the Arctic Ocean from ERS altimetry, J. Geophys. Res., 109,, doi: /2001jc Introduction Copyright 2004 by the American Geophysical Union /04/2001JC [2] Satellite altimetry is used to measure sea surface height relative to a reference ellipsoid of the Earth. These height measurements are composed of two components: a time-variant one (due to ocean current variability) and a time-invariant one (due to a combination of spatial variations in the Earth s gravity field and mean ocean dynamic topography). The time-variant component can be separated further into signals of differing temporal and spatial scales. Altimetry has been successfully used to extract information concerning the mesoscale or eddy-containing band, defined to encompass spatial scales of between 50 and 500 km, and periods of between 20 and 150 days [McClean et al., 1997], although the upper limit of the spatial scales is extended to 1000 km by some authors [Fu and Cheney, 1995]. Generally, the largest errors in the altimeter measurement system are due to poor orbit determination, introducing uncertainties at wavelengths greater than 1000 km. At shorter wavelengths the effect of these errors is reduced. Even the early, relatively crude altimeters such as Geos-3 and Seasat were used to study mesoscale signals [e.g., Cheney et al., 1983; Fu et al., 1987]. Until recently, altimetry has been used with limited success to study the large-scale ocean circulation variability, which generally refers to length scales greater than 1000 km. At these longer wavelengths, errors due to poor orbit determination, tide models, and propagation delay corrections begin to dominate. However, by carefully removing residual orbit error, several authors have been successful in mapping large-scale variability. For example, Chelton et al. [1990] used the Geosat altimeter to map the large-scale variability of the Antarctic Circumpolar current, and Nerem et al. [1994] used TOPEX/Poseidon with its superior orbit accuracy to study large-scale variability of the global ocean. [3] In addition to the study of ocean variability, satellite altimetry has been applied to the measurement of the time invariant component of sea surface height, or mean sea surface, on a global basis [e.g., Marsh et al., 1992; Marsh and Martin, 1982]. This mean sea surface is composed of two components. First, the geopotential surface (geoid) which is related to the distribution of mass within the Earth, and at shorter wavelengths bathymetry. Second, the mean ocean dynamic topography which is related to the general ocean circulation. The former dominates the vertical deflection by 2 orders of magnitude (100 m versus 1 m), and can therefore be used in lieu of a geoid when a direct estimate of the geoid is not available. Altimetry can also be used to generate gravity fields of the Earth s surface (e.g., the Arctic gravity field of Laxon and McAdoo [1994]) which essentially reveal short wavelength features of the Earth s upper crust. The combination of orbit and geoid error make a determination of the mean ocean dynamic topography very difficult using altimetry. Geographically correlated orbit error, which cannot be reduced by averaging in time, must be reduced by improving gravity models. The accuracy of the TOPEX/Poseidon orbits, and recent improvements in the accuracy of the ERS orbits [Scharroo and Visser, 1998] have made the determination of the dynamic topography a 1of14

2 feasible option [e.g., Nerem et al., 1994; Stammer and Wunsch, 1994; Tapley et al., 1994]. Such studies are currently hampered by the fact that the geoid is poorly known at wavelengths of less than about 2500 km [Nerem et al., 1994], resulting in a contamination of the dynamic topography at wavelengths shorter than this. Future satellite missions aimed at improving our knowledge of the Earth s gravity field at shorter wavelengths will permit a more detailed study of the mean dynamic topography (e.g., the NASA Gravity Recovery and Climate Experiment (GRACE) mission [Wahr et al., 1998] and the ESA Gravity Field and Steady state Ocean Circulation Explorer Mission (GOCE) [Rebhan et al., 2000]). [4] The extension of mean sea surface measurements and studies of ocean variability into the Arctic Ocean has previously been hindered not only by the latitudinal limit of previous altimeter missions (the most northerly coverage being provided by Seasat and Geosat to 72 N), but also by the presence of both seasonal and permanent sea ice cover. With the advent of the ERS-1 and 2 satellite missions, coverage was extended for the first time to 81.5 N. The presence of sea ice has always presented a problem for users of altimeter data, and editing has usually been required where sea ice is suspected [e.g., Chelton et al., 1990]. In this paper, we apply recent improvements in the understanding and processing of altimeter data acquired over sea ice to generate an accurate mean sea surface in the latitude band 60 N to 81.5 N using nearly 4 years of ERS-2 data. This is compared with the Arctic portion of an existing global mean sea surface produced by the Ohio State University (OSUMSS95) [Rapp and Yi, 1997; Yi, 1995]. In addition, we isolate the timevariant component of sea surface height to provide quantitative estimates of ocean variability in the Arctic Ocean over a 2 year period. These are compared with the variability predictions of a high-resolution coupled ocean sea ice general circulation model due to Maslowski et al. [2000], which we will refer to as the Naval Postgraduate School (NPS) model. Such model-data comparisons are a necessary first step in using model results to further our understanding of the general ocean circulation [Stammer et al., 1996]. 2. ERS Radar Altimetry 2.1. ERS Mission Phases [5] ERS-1 was launched on 17 July 1991 into a nearcircular, Sun synchronous orbit at 98.5 inclination and an altitude of between 782 and 785 km [European Space Agency/Earthnet, 1992], and carried a radar altimeter as part of its suite of instruments. It provided altimeter coverage to ±81.5 latitude for the first time. ERS-2 was launched on 21 April 1995, into the same orbital plane as ERS-1. It follows the ERS-1 satellite along the same orbital path, acquiring data along the same ground track one day after ERS-1. Both satellites operate in exactly repeating orbits which retrace their paths over the surface of the Earth at a well defined interval, the orbits being maintained such that the repeat tracks are coincident to within ±1 km in the across-track direction. ERS-2 will remain in a 35 day repeat configuration for the entirety of its lifetime. The period of overlap of the two missions during the Tandem Phase, between May 1995 and June 1996, provides an opportunity for cross comparison of the two instruments. All data used in this work was obtained while the altimeters were operating in their highest-resolution mode (Ocean Mode) ERS Waveform Product [6] The ERS altimeters transmit radar pulses at a frequency of 1020 Hz, and average 50 return echoes at a time to generate waveforms. These are then used as input to the relevant parameter error estimation algorithm in order to generate the error signals which drive the tracking loops. Parameters such as surface elevation are estimated at intervals of s (approximately 330 m on the ground), resulting in a data telemetry rate of approximately 20 Hz. For this study, it was necessary to use all altimetergenerated information at this rate, including the waveforms, in order to correct tracking errors and apply quality controls to the data acquired where sea ice is present. The Waveform Product (WAP), produced by the UK-PAF, contains lowlevel altimeter information at this data rate and forms the basis for the work presented here [Cudlip and Milnes, 1994] ERS Altimeter Tracking Over Sea Ice [7] In order to maintain the leading edge of the return echoes within the range window, a height tracking loop (HTL) is used, which continually adjusts the position of the window on the basis of the history of return echoes. (There are two additional tracking loops, one to estimate the slope of the leading edge, and another to estimate the amplitude of the return echo, neither of which will concern us here.) The HTL produces smoothed predictions of surface height, used to adjust the position of the range window, by employing a second-order low-pass ab filter. This is described by two coupled equations which generate new values of the height parameter h n and its corresponding rate of change _ h n based on its history h n ¼ h n 1 þ ae þ T _ h n _h n ¼ _ h n 1 þ be T where a and b are the filter parameters and T is the filter update interval, which for the HTL is equal to 1/PRF (where PRF is the pulse repetition frequency of 1020 Hz). e is the height error signal generated by the parameter error estimation algorithm, which in Ocean Mode is a Suboptimal Maximum Likelihood Estimator (SMLE), while in Ice Mode an Offset Centre of Gravity (OCOG) algorithm is used [Francis, 1990; Peacock, 1998]. e is updated each time the relevant parameter error estimation algorithm is invoked, which is at the end of each 50 waveform averaging sequence [Francis, 1990]. Neither estimation algorithm is specifically designed for tracking returns over sea ice, but the more robust nature of the OCOG algorithm resulted in better tracker performance over sea ice when operating in Ice Mode during the early months of the ERS-1 mission [Scott et al., 1994]. [8] During the first months of operation of ERS-1, the tracker constants used often resulted in the leading edge of the waveform migrating out of the range window, a phenomenon known as loss of lock [Strawbridge and Laxon, ð1þ ð2þ 2of14

3 Figure 1. Typical ERS altimeter waveforms acquired from (a) a sea ice covered sea (specular waveform) and (b) open ocean (diffuse waveform). These waveforms show received power at the altimeter versus time. Note that the y axes of these waveforms are not to scale and that the peak power of specular waveforms can be up to 3 orders of magnitude greater than for diffuse waveforms. 1994]. This resulted in a data loss of approximately 35% during the first part of the mission when operating in Ocean Mode over sea ice [Scott et al., 1994]. Adjustments to the tracker parameters were performed by a series of uplinks to the satellite in order to remedy this poor performance. On 23 October 1992, the gain applied to the return echo immediately following acquisition was lowered, resulting in a reduction of the data loss to 25%. A further uplink was performed on 17 June 1993, which imposed limits on the height error signal, resulting in a reduction of the data loss to less than 1%. With the tracking algorithms stabilized over sea ice, ERS-1 and ERS-2 were able to successfully operate in the higher-resolution Ocean Mode over the Arctic Ocean. 3. Radar Altimetry Over Sea Ice 3.1. Tracking Errors Over Sea Ice [9] The vast majority of waveforms acquired over sea ice show a much more specular response than returns from the open ocean, and are characterized by an initial sharp rise in power, followed by a rapid fall off within the range window [Laxon, 1994a]. Figure 1a shows a typical specular waveform, and for comparison Figure 1b shows a waveform characteristic of those obtained over open ocean, which we label as diffuse. It is this deviation of specular echo shape from that of ideal diffuse echoes, for which the SMLE algorithm is designed, which results in the generation of a large range of height error signals e. For diffuse echoes over the open ocean, a maximum value for e of 10 cm is expected [Wingham et al., 1986]. A full simulation of the ERS tracking system with specular echoes resulted in a much larger range of values, with frequent saturation of e between its limits of ±4.54 m [Peacock, 1998]. [10] It can be shown from equations (1) and (2) that the range window moves quadratically during each waveform averaging sequence. If a large height error signal is generated by the SMLE algorithm, then it can be seen that this quadratic movement is quite significant. This results in a poor overlay between the echoes which make up the average waveform, a phenomenon known as pulse blurring. Since e is updated at the end of these averaging sequences, sudden changes in the direction and speed of the range window are possible before the beginning of the next sequence, resulting in what is called tracker oscillation. An analysis of height measurements acquired over the Salar de Uyuni salt pan in Bolivia (which is effectively a flat surface generating specular reflections similar to these observed over sea ice), reveal that the tracking noise for uncorrected data is around 1 m [Peacock, 1998]. As a consequence, these onboard height estimates are rendered useless for geophysical and oceanographic applications and are usually deleted. Section 4 deals with the processing algorithms which are used to correct for these trackergenerated errors Geometric Errors Over Sea Ice [11] A fundamental assumption of pulse-limited altimetry is that the radar backscatter coefficient s 0 varies slowly within the altimeter footprint. In situations where the surface is inhomogeneous on scales similar to the altimeter footprint, the origin of the echo becomes unclear and it is no longer possible to unambiguously identify returns from nadir. For example where the altimeter passes from a highly reflective surface to a less reflective surface the tracker will preferentially track the return from the bright surface, despite the fact that it originates some way off-nadir. Threshold retracking algorithms will also tend to follow such features leading to large errors in the estimates for surface height, a phenomenon known as snagging [Fetterer et al., 1992]. Snagging events can be detected by a careful analysis of waveform shape, and a statistical analysis of data over sea ice shows that they cause problems relatively infrequently Origin of Radar Echoes in Sea Ice Covered Regions [12] Normal incidence radar reflection from any surface is strongly dependent on the surface roughness on scales similar to the wavelength at which the radar is operating (2.2 cm in the case of ERS-1 and 2). Returns over sea ice show a high degree of specularity [Robin et al., 1983]. For a surface to produce a purely specular reflection, the Rayleigh criterion must be satisfied, which for the ERS altimeters occurs when the surface roughness is less than 3 mm throughout the altimeter footprint [Fetterer et al., 1992]. It can be shown theoretically that even if a fraction of one percent of the surface is flat to 3 mm it can dominate the return signal received by the altimeter [Drinkwater, 1991; Robin et al., 1983]. [13] The peaked nature of satellite radar altimeter returns over sea ice and the fact that radar backscatter is high (typically db) indicates that some degree of coherence is typically observed in areas of sea ice cover. This poses the question as to whether or not these returns originate from water or ice surfaces. Although in principle this question might be answered using radar theory, very few measurements of sea ice and water roughness in the polar regions at the millimeter scale exist. The few that exist over sea ice show that only the smoothest ice types, for example over young ice in the Gulf of Bothnia, can result in a significant coherent component [Fetterer et al., 1992]. In the more typical dynamic areas, the surface roughness of ice is normally too large to generate the coherent or even quasi-coherent returns observed in spaceborne altimetry, indicating that the likely source of specular echoes is reflection from calm water or new ice between older ice floes. 3of14

4 Figure 2. An ATSR-2 infrared (12 mm) image from 12 December 1995, 0242 UT, with the exactly coincident altimeter track overlaid. The black and white circles show the locations of the diffuse and specular waveforms, respectively, and their size represents the approximate extent of the altimeter footprint to scale. Transitions over consolidated ice (A) result in diffuse echoes, while transitions over leads (B) result in specular returns. In areas of mixed ice/water surfaces (C) specular echoes are observed where specular reflection from subpixel leads dominates the diffuse return from ice floes. Gaps in the altimeter track occur where a clear distinction between water and ice echoes is not possible. [14] Experiments on artificial sea ice at 13.6 GHz show that backscatter from a calm water surface can exceed that from rough ice by almost 20 db [Gogineni et al., 1990], in agreement with the results of in situ experiments [Onstott, 1992]. Airborne measurements of the radar backscatter at 13.3 GHz made during March 1970 show the strongest returns at nadir (s 0 = 15 db) originating from open water within the pack ice, with backscatter decreasing from 6 to 0 db as the ice thickness increased from 5 to 360 cm [Parashar et al., 1974]. Comparisons of Seasat and Geosat altimetry with SAR revealed peaked waveforms with a backscatter of between 25 and 40 db over new ice and leads [Fetterer et al., 1991; Ulander, 1987]. By comparing Ku band airborne radar altimeter observations with coincident aerial photography, Drinkwater [1991] concluded that these strong peaked echoes originate from open water between ice floes. A similar conclusion was drawn by Laxon [1994a]. [15] Diffuse waveforms with lower backscatter (similar to those obtained over the open ocean) are also observed when the altimeter footprint is entirely filled with consolidated ice such as fast ice and vast floes. These events have been observed using coincident Geosat altimetry and infrared AVHRR imagery [Laxon, 1994a] and coincident airborne altimetry and aerial photography [Drinkwater, 1991]. Figure 2 shows the locations of diffuse and specular waveforms, along with time-coincident imagery from the ATSR-2 instrument also on-board ERS-2. ATSR is the only source for exactly coincident imagery with the ERS radar altimeter although its resolution is limited to 1 km. Diffuse echoes occur where large floes are observed in the imagery and specular echoes are seen where transitions over leads occur. In areas of mixed small floes and leads, specular echoes from smooth water can dominate even at high ice concentrations because of a much higher backscatter from water than from ice. Where neither ice nor water dominates the return, resulting in a distorted echo shape, data are rejected leading to gaps in the altimeter track. [16] In summary, our understanding of the mechanisms for the backscatter signal over sea ice as detected by a nadirpointing satellite radar altimeter are somewhat limited from a theoretical viewpoint. We can say however that (1) coherent or quasi-coherent reflections are present in satellite altimeter observations over sea ice, and (2) even if coherent reflections originate from only a small fraction (<1%) of the surface, they can dominate the return echo observed by the altimeter [Robin et al., 1983; Drinkwater, 1991]. In addition, direct and synergistic measurements point to the fact that such returns originate from calm water or thin ice, rather than from typical surfaces found on first-year and multiyear ice. Once retracked, the range measurements associated with these waveforms can therefore be used to directly measure sea surface height. When very new ice is present, these measurements are within a few centimeters of the true sea surface height. 4. Data Processing 4.1. Preprocessing [17] The ERS-2 data set used to construct the mean sea surface spans the period from 3 May 1995 to 28 June 1999, corresponding to cycles 0 to 41 of the satellite s 35-day repeat mission. The first stage in WAP preprocessing is the application of a waveform filter designed to remove waveforms which would result in erroneous or misleading range measurements, such as loss of lock events where the altimeter has failed to keep track of the leading edge of the waveform [Strawbridge and Laxon, 1994]. Empty waveform windows and waveforms containing bins with negative powers resulting from numerical overflows were also discarded. The satellite orbital position was calculated by interpolating the orbits provided by the Delft University of Technology (DUT) which use the DGM-E04 gravity model [Scharroo and Visser, 1998]. Satellite altitudes were referenced to an ellipsoid of the Earth based on the WGS-84 reference system. Additionally, orbits which are known to contain maneuvers were removed from any further analysis, using the orbit maneuver information compiled by DUT based on data acquired from ESA/ESOC. The following corrections were then applied to the 20 Hz data: ionospheric delay (using the International Reference Ionosphere (1994)), wet and dry components of the troposphere delay (computed from 6-hourly ECMWF surface pressure, humidity and temperature grids), ocean tides (using the FES global tide model [Le Provost et al., 1998], which includes a set of solutions for the Arctic Ocean produced by Lyard [1997], ocean loading tide (from the CSR3.0 model [Eanes, 1994], long-period equilibrium tides and Earth body tides (estimated from the Cartwright-Tayler- Edden tables [Cartwright and Tayler, 1971; Cartwright and Edden, 1973]), and the inverted barometer effect (estimated from the dry tropospheric correction, by inverting the 4of14

5 Saastamoinen formula [Centre ERS d Archivage et de Traitement, 1995]) Separation of Sea and Ice Surface Elevations [18] In Section 3 we discussed the types of return echo which produce range estimates to sea level in both open and ice-covered oceans, along with range estimates to ice floe surfaces. The Pulse Peakiness (PP) parameter defined by Laxon [1994b] was used to distinguish between these waveform types, and is given by PP ¼ 31:5 p max X 64 p i i¼5 where p max is the peak waveform power, and p i is the power in the ith bin. Waveforms with a peakiness of less than 1.8 were processed as diffuse (originating from either open ocean or ice floe surfaces), and those with a peakiness greater than 1.8 were processed as specular (originating from the sea surface in areas of high ice concentration). This threshold was selected on the basis of studies of the variability of this parameter over open ocean. Note that this threshold is slightly greater than the value of 1.7 chosen by Knudsen et al. [1992]. [19] To distinguish diffuse echoes originating from open ocean from those due to ice floes, ice concentrations derived from brightness temperatures obtained from the Special Sensor Microwave/Imager (SSM/I) radiometer were used. This instrument is carried on-board the US Defense Meteorological Satellite Program (DMSP) satellite F-13, and the data was provided on CD-ROM by the EOS Distributed Active Archive Center (DAAC) at the National Snow and Ice Data Center (NSIDC), University of Colorado, Boulder. The NASA Team algorithm [Cavalieri et al., 1984] was used to estimate daily grids of ice concentration from brightness temperature at a resolution of 25 km. An ice concentration threshold of 40% was used to delineate the ice edge, and any diffuse echoes occurring within this icecovered region were discarded Waveform Retracking [20] Because of the presence of high-powered specular echoes, the ERS Ocean Mode tracking system generates large height error signals compared with echoes from the open ocean. Although the system is generally successful at retaining the echo within the range window, it is usually offset by a significant amount from the centre of the range window, which corresponds to the onboard range estimate. This offset is estimated using a threshold retracker operating at 50% of the peak power [Laxon, 1994a]. For diffuse waveforms, a similar threshold retracking scheme was adopted, except that the waveform amplitude was estimated using the Offset Centre Of Gravity (OCOG) algorithm [Bamber, 1994], making the correction less sensitive to noise in individual bins Pulse-Blurring Correction [21] An additional correction to counter the effect of pulse blurring was also applied. The correction was derived from a simulation of the waveform averaging process under the control of the height tracking loop (HTL), which revealed a ð3þ linear relationship between retracked height error Dh rtk and the height error signal e. Equations (1) and (2) can be combined to give an expression for the height parameter h n at any given time based on its initial value and initial rate of change h n ¼ h 0 þ nae þ nt _x 0 þ n ð 2 n þ 1 Þbe ð4þ Repeated application of equation (4) over the period of waveform averaging (that is with n ranging from 0 to 49) formed that basis of the simulation. The filter parameters were chosen to match those of the ERS-2 tracking system, with a = and b = (C. R. Francis and M. Roca, personal communication). h 0 and _ h 0 were taken to be zero. [22] Pure specular waveforms were used in this simulation. The flat surface impulse response and the surface height pdf were taken as d functions, which by the convolutional waveform model of Brown [1977] results in a return pulse identical to the system point target response (SPTR) [Francis, 1990]. Each waveform at the PRF of 1020 Hz was modeled on the SPTR using a Gaussian function, and can therefore be represented as " ð p n ðþ¼exp h h h nþ 2 # cs p where s p = ns [Francis, 1990] and h n is given by ð5þ h n ¼ nae þ n ð 2 n þ 1 Þbe ð6þ Each averaged waveform can therefore be represented as Ph ðþ¼ 1 X n¼0 " exp ð h hn Þ 2 # cs p A series of such averaged waveforms was generated for values of e between 5 m and +5 m, in increments of 10 cm. The height difference Dh avg between the telemetered height at the time of the 37th pulse and the retracking point, at 50% of the peak power, was calculated for each averaged waveform. A plot of the height error signal e against this height difference can be seen in Figure 3a, which reveals a linear trend similar to that seen in ERS-2 data over sea ice, as shown in Figure 3b. The slope of the trend for e < 0 was measured as 5.0 (similar experiments for ERS-1 reveal a trend of 3.5, due to the different filter parameters used by this system). [23] As the averaging process takes place, the range window moves quadratically in time, its position being governed by equation (6). The degree of movement between the arrival of individual pulses depends entirely on the HTL error signal e for a given set of tracking parameters. Because of the movement of the range window, the pulses are not perfectly superimposed and are effectively smeared across the range window, a phenomenon we term pulse blurring. After the arrival of the 50th pulse, at the end of the averaging sequence, the final averaged waveform will be in a position determined purely by e. Figure 4 shows this ð7þ 5of14

6 have chosen to retrack to the half-power point on the leading edge. The choice of retracking point is in fact arbitrary, and a different point would yield different results. [25] The strong linear trend between e and Dh rtk for e less than zero suggests that a correction can be applied to the elevation measurements which is a function of e. Taking the slope of the trend m to be constant for all over the range of interest, a corrected height h cor can be calculated from the retracked height h rtk as follows h cor ¼ h rtk e m ðe < 0Þ ð8þ Figure 3. ERS-2 HTL error signal e versus retracked height error Dh rtk for (a) HTL simulation and (b) specular sea ice data. The greater spread in the ERS-2 data includes the additional effect of tracker noise. final situation when e = +4 m, 0 m and 4 m. Also shown is the position of the centre of the range window when n = 36, that is when the range is written to the telemetry, and the 50% threshold retracking point. [24] It can be seen from Figure 4 that in each case a distinct offset exists between the 50% threshold retracking point and the range window centre. In this simulation, we know that the waveform is initially at the correct tracking position, and that the averaged waveform is offset from this true tracking point because of the motion of the range window. This simulation therefore tells us where the averaged waveform will be located with respect to the centre of the range window for a complete range of e, when the first waveform in the averaging sequence is at the correct tracking point. The current retracking algorithms work under the assumption that waveforms should be retracked to the centre of the range window, but this result tells us that they should be retracked to a position dependent on e. In Figure 4c, a typical averaged waveform is shown which requires retracking in order to make the associated range measurement meaningful. The current 50% threshold retracking scheme has the effect of increasing the range by an amount h err as shown. The simulation shows that the 0 range should be increased by an amount h err, which takes into account the additional offset due to the range window motion. It should also be noted that the asymmetry in Figure 3 about the e = 0 axis is due to the fact that we where m is taken to be 3.5 for ERS-1 and 5.0 for ERS Additional Processing [26] Following the retracking and pulse-blurring corrections, quality controls were applied on the width of the leading edges of each waveform and the power deviation in bins on the trailing edge of diffuse waveforms. After the removal of biases between the retracked specular and diffuse echoes (important in areas of seasonal ice cover), a3s outlier removal scheme was applied on a pass-by-pass basis. Short wavelength noise was removed by applying an along-track low-pass data filter. A linear regression was performed at each data point using the 40 points either side, and replacing the elevation at that point by the value of the least squares fit. This resulted in an effective filter width of 81 points, and a corresponding cutoff wavelength of approximately 27 km. Figure 5 gives an example of a profile Figure 4. Positions of the final averaged waveforms and retracking points relative to the center of the range window in the HTL simulation for (a) e =+4m,(b)e = 0 m, and (c) e = 4 m. A typical averaged waveform that requires retracking is also shown in Figure 4c. 6of14

7 compared with more sophisticated solutions [Cheney et al., 1989]. Figure 5. A profile of ERS-2 altimeter data over sea ice (1) before retracking (upper profile), (2) after retracking and application of the waveform shape quality control, pulse blurring correction, and outlier removal algorithms (shaded), and (3) after along-track filtering. All three profiles are shown at the full data rate of 20 Hz. The unretracked data have a bias of between 1 and 2 m and short wavelength noise (<30 km) of about 1 m. Retracking removes the majority of this bias and reduces the noise to about 25 cm. of ERS-2 altimeter data over sea ice at various stages in the processing: (1) before retracking, (2) after retracking and application of the waveform shape quality control, pulseblurring correction and outlier removal algorithms, and (3) after along-track filtering. [27] Further analysis of the data required the averaging of repeat tracks to generate mean sea surface height profiles, using standard altimetry techniques [e.g., Cheney et al., 1983; Snaith, 1993]. Cycles 0 to 41 of ERS-2 sea level data, spanning a period of nearly 4 years between May 1995 and April 1999, were used to generate 1 Hz mean sea surface profiles for each of the 501 tracks which go to make up one cycle. Equation (9) shows the method used to calculate the mean sea surface height z j at a given along-track data point j. 5. Accuracy Assessment of Sea Surface Height Data 5.1. Crossover Analysis [29] Crossovers are formed at the points where ascending and descending altimeter tracks coincide. At such locations, two measurements of the sea surface height (including measurement error) are available. The time difference between the acquisition of the two measurements varies considerably from one crossover location to another, and therefore the extent of evolution of sea surface height and correlation of measurement errors is also markedly varied. The crossover difference Dz ij at the location r ij where tracks i and j meet is given by Dz ij ¼ z i z j ¼ Dh t i ; t j ; r ij þ De ð10þ where z i and z j are the observed sea surface heights at the crossover location at times t i and t j, respectively, Dh is the change in dynamic sea surface height between the two times, and De represents the sum of all measurement errors present in the two measurements. [30] Figure 6 shows the crossovers computed from cycle 2 of the ERS-2 mission gridded onto a grid. Although these crossovers contain differences due to real oceanographic signals at a range of timescales, they also provide a way of assessing the magnitude of measurement z j ¼ 1 N j X Nj z ij i¼1 ð9þ where i is the orbit repeat number, and N j is the number of data points at j. [28] An important source of error in satellite altimeter data is due to uncertainties in the satellite s altitude. In spite of the high-quality orbits used in this work (Scharroo and Visser [1998] estimate a radial root mean square orbit accuracy using the DGM-E04 model of 5 cm), long wavelength errors are still present in the data. A correction is applied to individual tracks using a simple linear tilt and bias method, after removal of the corresponding mean sea surface height profile, which has the effect of not only reducing long wavelength orbit error, but also long wavelength errors associated with the geophysical corrections. Arc lengths in the observation region were typically less than 6000 km, and the errors associated with applying a simple linear fit have been shown to be less than 5% when Figure 6. Gridded crossover differences for cycle 2 of the ERS-2 mission. Also shown is the 20% contour of total sea ice concentration derived from SSM/I observations over the same period (19 June to 24 July 1995), which delineates the ice boundary. 7of14

8 error. Also shown in Figure 6 is the 20% contour of mean sea ice concentration derived from SSM/I observations over the same time period, which delineates the ice boundary. The first point to note is that there is very little observable change between the crossover differences on moving from open ocean to ice-covered seas. Second, there are a number of regions for which the crossover differences are quite large (with a magnitude greater than 30 cm), in particular Baffin Bay and the Bering Sea. These differences are thought to be largely due to errors in the FES ocean tide model used to correct the altimeter data. The Arctic regional tide model due to Lyard [1997], which is included in this global model does not include the Baffin Bay and Bering Sea regions, which are therefore likely to be poorly represented. In Baffin Bay (defined as the region bounded by 70 < j <75 and 75 < l < 60, where j and l are latitude and longitude, respectively), the mean crossover difference is 33.9 cm. After application of the University of Texas CSR3.0 tide model [Eanes, 1994], this difference reduces to 25.0 cm. Application of the recent ERS-derived Arctic tide model [Peacock, 1998] reduces this difference still further to 20.2 cm. [31] Crossover differences were then computed for ERS-2 cycles 1 to 11 (a period spanning just over 1 year) using all data south of 80 N. A total of 232,642 crossovers were computed, with a resulting overall standard deviation of 17.4 cm (16.9 cm after detrending). In order to quantify the difference in our capability to observe sea surface heights in ice-free and ice-covered seas, we recomputed these standard deviations using only data from the ice-covered Canada Basin (bounded by 72 < j <80 and 160 < l < 130 ), and again using only data from the ice-free Greenland- Iceland-Norwegian (GIN) Seas (bounded by 60 < j < 75 and 10 < l <10 ). From 21,466 crossovers in the Canada Basin, a standard deviation of 12.4 cm was obtained (9.9 cm after detrending), and from 12,495 crossovers in the GIN Seas, a corresponding value of 10.2 cm was obtained (7.5 cm after detrending). These figures imply a very small degradation in the quality of sea surface height retrievals in ice-covered seas compared with ice-free seas, assuming that the sea surface height variability is of similar magnitude in these two region Analysis of Collinear Tracks [32] During the Tandem Mission, ERS-2 followed ERS-1 in the same near-circular orbit, acquiring data along the same ground track one day after ERS-1. This provides us with another way of assessing improvements to the altimeter data due to the enhanced processing scheme by comparing collinear tracks with a temporal separation of 1 day from the two satellites. The observed differences between two collinear tracks include contributions from the change in sea surface height over the time period between the two measurements, orbit error and errors in the applied geophysical corrections. For the Tandem Mission the short temporal separation of 1 day between the two tracks means that the nonconservative component of orbit error and the wet tropospheric correction will be highly correlated over this time period, and so the difference due to these components will be small [Scharroo and Visser, 1998]. Changes in sea surface height due to nontidal oceanographic signals will also be highly correlated. The gravity-induced orbit errors will be the same along two collinear passes, and will therefore cancel during the differencing procedure (neglecting the small across-track variations from one track to the next). [33] The largest contributions to the difference between two collinear tracks will therefore result from errors in the tide correction and height measurement error. Figure 7a shows the gridded collinear track differences for ERS-1 cycle 147 and ERS-2 cycle 2, after along-track filtering and detrending. The ice boundary for this period is also shown. As was the case for the crossover analysis of the same ERS-2 cycle, very little change in collinear height difference is observed on moving from ice-free to icecovered seas. Using all data from ERS-2 cycles 1 to 11 south of 80 N (as for the crossover analysis), we obtain a standard deviation of collinear height differences of 11.5 cm (11.2 cm after detrending). In the Canada Basin a value of 10.0 cm was obtained (8.1 cm after detrending), and in the GIN Seas this figure reduced to 7.5 cm (5.2 cm after detrending). Assuming that the short wavelength signals which make up these differences pffiffi decorrelate over 1 day, we can divide these values by 2 to obtain an estimate of the combined measurement error and tide correction error over one cycle. Taking the standard deviation of 8.1 cm in the Canada Basin after detrending, we obtain a combined measurement and tide correction error of 5.7 cm. The corresponding value in the GIN Seas is 3.7 cm. This analysis indicates that although the residual measurement error in icecovered regions is greater than for ice-free regions, the data have the potential to provide useful oceanographic measurements in ice-covered areas for the first time. [34] Figure 7b shows a similar comparison using two cycles of ERS-2 data, one of which was acquired during the winter, and the other during the summer after the onset of melt. It is interesting to note that in the region of permanent sea ice cover, no significant differences in elevation can be observed, indicating that the effect of meltponds on sea surface height recovery during the summer has to some extent been reduced by the application of our outlier removal scheme discussed in section 4.5. Assuming an average ice thickness in the central Arctic region of 3 m, we would expect to see differences of roughly 10% of this (the approximate ratio of ice freeboard to thickness) if the summer sea surface height measurements originated from meltponds on the surface of the ice when compared with measurements from the sea surface itself during winter Sea Surface Height Measurement Error Budget [35] An estimate of the total error budget for altimeter sea surface height retrievals in ice-covered seas derived from specular waveforms is shown in Table 1. The main contributory factors discussed here are residual orbit error (before detrending), atmospheric and tide correction errors, and instrument noise: Radial Orbit Errors [36] The values for the orbit error components are estimated from the values given by Scharroo and Visser [1998], with the nongravitational component remaining the same, and both gravitational components scaled by a factor of 1.5 (R. Scharroo, personal communication) Tropospheric Corrections [37] Mean values for the tropospheric corrections at the poles are typically around 220 cm for the dry correction and 8of14

9 less than 10 cm for the wet correction, both of which are less than the respective values at lower latitudes [Zlotnicki, 1994]. The errors associated with the dry and wet corrections have been estimated to be ±5.6 mm and ±48 mm, respectively, in the Northern Hemisphere [Cudlip et al., 1994]. However, it is likely that these errors are even higher in the Arctic because of the paucity of meteorological data. Globally the dry tropospheric correction has an average value of about 230 cm, the corresponding value for the wet tropospheric correction being around 30 cm. Assuming that the percentage errors in the Arctic are at worst comparable with the global estimates, we arrive at errors of 1 cm and 1.6 cm for the dry and wet tropospheric corrections, respectively Ionospheric Correction [38] Mean values of this correction are small at the poles (between 1 and 2 cm) compared with the tropics [Zlotnicki, 1994]. The variable nature of the coupling between the solar winds and the magnetosphere results in unpredictable variations in the electron content on timescales ranging from a few hours to several days. As a result, variations in the electron content of up to 50% about the monthly mean value are possible [Cudlip et al., 1994]. The linear relationship between the total electron content and the ionospheric range correction means that this unpredictability could result in errors of up to 1 cm in the Arctic Tidal Corrections [39] The latest global tide models developed with the use of TOPEX/Poseidon altimetry have accuracies in the range of 2 3 cm [Shum et al., 1997]. An intercomparison of three models in the Arctic Ocean (the FES of Le Provost et al. [1998], the CSR3.0 model of Eanes [1994] and the University of Alaska, Fairbanks model of Kowalik and Proshutinsky [1994]) would indicate that the main tidal constituents predicted by these models collectively agree to within about 6 8 cm [Peacock, 1998]. The magnitude of the ocean loading tide correction is typically less than 10 cm, with an accuracy of better than 1 cm [Cudlip et al., 1994]. Finally, the solid Earth tide varies globally in the range ±30 cm, with an uncertainty of much less than 1 cm Table 1. Error Budget for Absolute ERS Altimeter Sea Surface Height Retrievals in Ice-Covered Seas a Error Source Error Budget, cm Radial Orbit Errors Geographically anticorrelated 2.3 Geographically fully correlated 5.0 Nongravitational 3.5 Figure 7. (a) Gridded collinear track differences between ERS-1 cycle 147 and ERS-2 cycle 2 after along-track filtering and detrending. Also shown is the ice boundary for this period. (b) Similar differences between ERS-2 cycle 19 (February 1997) and ERS-2 cycle 24 (August 1997). Geophysical Correction Errors Dry tropospheric correction 1.0 Wet tropospheric correction 1.6 Ionospheric correction 0.5 Ocean tides 6.0 Ocean loading tides 1.0 Solid Earth tides 0.5 Measurement Errors Instrument noise 2.2 Total error 9.4 a Note that the radial orbit errors have not been reduced by detrending and that the altimeter measurements have been filtered to remove signals with wavelengths of less than 27 km. 9of14

10 [Cudlip et al., 1994]. Observations of this correction in the Arctic indicate that the values are generally less than 2 cm, considerably less than the typical global values. We assign a corresponding error of 0.5 cm to this correction Instrument Noise [40] A value for the measurement noise for specular echoes was estimated using output from a full ERS tracker simulation over sea ice [Peacock, 1998]. The waveforms were first retracked, and the resulting height measurements corrected for pulse-blurring and low-pass filtered to remove short wavelength signals of less than about 27 km. [41] In this analysis, it is assumed that all of the error sources are uncorrelated and therefore their contributions to the total error can be added in quadrature. The total error budget for altimetric sea surface height measurements in the Arctic is therefore 9.4 cm, excluding the error associated with the inverted barometer correction and the effects of neglecting sea state bias. It should be noted that strictly speaking, we should be using a single figure for radial orbit accuracy based on both contributions from the geographically correlated and anticorrelated orbit error, since these two components are not completely independent of one another. However, for the purposes of comparison with Scharroo and Visser [1998], we have added these components in quadrature, with the result that we will most likely be overestimating the resulting error. Scharroo and Visser [1998] derive an error of 6.4 cm for the ice-free global ocean (neglecting the contribution due to sea surface height variability). Sea state bias was not neglected in their analysis, and the error introduced by its estimation is included in this value. [43] Individual detrended mean sea surface height profiles were then combined into a single gridded data set. Figure 8a shows the short wavelength features in the Arctic mean sea surface, artificially illuminated from the east. These features reflect the topography of the seafloor plus the density of the oceanic crust and uppermost mantle [Laxon and McAdoo, 1994]. As a consequence, there is often a strong correlation between short wavelength (50 to 300 km) variation in the mean sea surface and the ocean bathymetry [Dixon et al., 6. Results 6.1. Mean Sea Surface [42] A mean sea surface height profile was generated for each of the 501 orbit tracks covered by ERS-2 during each 35-day repeat cycle, as described in Section 4. As an initial estimate of the accuracy of this mean sea surface, crossover differences were computed using the method described in Section 5. The standard deviation of these differences was calculated to be 7.2 cm over the region covered by our measurements (between 60 and 81.5 N). In the ice-covered Canada Basin and ice-free GIN Seas (defined in the crossover analysis in Section 5), the corresponding values were 4.2 cm and 3.8 cm, respectively. Figure 8. (a) Short wavelength features in the Arctic mean sea surface after subtraction of the EGM96 geoid, expanded to degree and order 20. Artificial illumination from the east has been added. The continuous curvature surface gridding algorithm provided as part of the Generic Mapping Tools (GMT) software package [Smith and Wessel, 1990; Wessel and Smith, 1991] was used to generate a grid with a longitude spacing of 1/8 and a latitude spacing of 1/20. Also note the striping pattern visible in certain areas (particularly in the Bering Sea, the Canadian Archipelago, and Baffin Bay). This is due to small differences in the heights obtained from adjacent tracks used to generate local averages. (b) Bathymetry contours at an interval of 1000 m drawn from the NOAA/NGDC Global Gridded Elevation and Bathymetry database (ETOPO5). 10 of 14

11 1983]. The long wavelength components have been computed from a low-order expansion of the global solution of the National Aeronautics and Space Administration/ National Imagery and Mapping Agency Earth Gravity Model, EGM96 [Lemoine, 1997], and removed from the altimetric surface. This model is complete to degree and order 360, but only the spherical harmonic components with degree and order less than or equal to 20 were used in the geoid undulation computation to retain only the long wavelength geoid features (>2000 km). Note that this choice of cutoff is purely arbitrary, but is in line with that of other authors [e.g., Marsh et al., 1992; Marsh and Martin, 1982]. Removal of these long wavelength components using this method allows an illustration of the higher-frequency components of our new mean sea surface, and is not meant as a quantitative comparison with the EGM96 model. [44] The detail presented in Figure 8a is similar to that revealed in the Arctic gravity field of Laxon and McAdoo [1994], which was derived by computing along-track slopes of ERS-1 altimeter data, thereby effectively filtering out long wavelength signals. For reference, Figure 8b shows bathymetry contours at an interval of 1000 m drawn from the National Oceanic and Atmospheric Administration/ National Geophysical Data Center Global Gridded Elevation and Bathymetry database (ETOPO5) [National Geophysical Data Center, 1988]. The mean sea surface delineates sections of the Arctic Basin margin as well as the tips of the Lomonosov and Arctic mid-ocean ridges. Several important tectonic features of the Amerasia Basin are also clearly expressed, including the Mendeleev Ridge, the Northwind Ridge, the Chukchi Borderland, and the northsouth linear feature in the centre of the Canada Basin which represents an extinct spreading centre, first observed in the gravity field of Laxon and McAdoo [1994]. [45] The ERS Arctic mean sea surface is compared with the existing global mean sea surface model produced by the Ohio State University (OSUMSS95). OSUMSS95 is computed from one year average sea surface heights from TOPEX/Poseidon, Geosat and ERS-1 (35-day repeat), and incorporates data from the ERS day repeat phase [Rapp and Yi, 1997; Yi, 1995]. The resolution of the mean sea surface is 1/16 1/16, but has been subsampled here to a resolution of Bilinear interpolation was used to estimate the value of OSUMSS95 at the location of each altimeter-derived mean sea surface point (after detrending), and the differences were gridded onto a grid as shown in Figure 9. In the GIN Seas, a standard deviation of height differences between the two mean sea surfaces of 6.4 cm was observed (about a mean of 0 m). In the ice-covered Canada Basin, a significantly larger standard deviation of 47.7 cm about a mean of 22.5 cm is obtained. The altimeter data contributing to OSUMSS95 at latitudes greater than 72 comes purely from ERS-1. Two thirds of the ERS-1 35-day repeat period data used was acquired before the tracking problems over sea ice were remedied (on 17 June 1993), and the use of the interim geophysical data record (IGDR) suggests that the additional processing required over sea ice (such as retracking) may not have been applied. Since no alternative independent validation of either mean sea surface exists, it is impossible to prove beyond doubt which model is the more accurate. Nevertheless, we believe from the evidence presented so far Figure 9. Difference between the ERS-2 mean sea surface and OSUMSS95 in the Arctic displayed on a 0.25 resolution grid. A constant bias of cm has been added to OSUMSS95 to account for the fact that it is referenced to the TOPEX/Poseidon ellipsoid, whereas the ERS surface is referenced to the WGS-84 ellipsoid. This correction also includes biases in the altimeter measurements that make up both surfaces and possible errors in the ellipsoid parameters adopted for the contributing altimeter missions. (crossover and collinear track analyses) that accurate retrieval of sea surface height in ice-covered seas is possible irrespective of season or location. On this basis, we believe that the new ERS Arctic mean sea surface offers significant improvements over the existing OSUMSS95 surface in the ice-covered Arctic Ocean Sea Surface Height Variability [46] After generating mean sea surface height profiles, the RMS variability of individual detrended repeat tracks was computed using cycles 1 to 21 of ERS-2, spanning a period of 2 years between May 1995 and May The resulting variability contains signals due to oceanographic phenomena, as well as tide model error, residual orbit error, geophysical correction error and measurement error, and is shown in Figure 10a on a grid. The mean RMS variability over the entire region was computed to be 10.2 cm. Considering just the ice-covered Canada Basin and ice-free GIN Seas, this value was reduced to 7.3 cm and 5.5 cm, respectively. It is likely that the higher RMS values observed when sea ice is present are due to additional errors introduced into the sea surface height measurements by the high-powered specular radar echoes received by the altimeter and additional uncertainties in the orbit determination 11 of 14