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.
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 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.  used the Geosat altimeter to map the large-scale variability of the Antarctic Circumpolar current, and Nerem et al.  used TOPEX/Poseidon with its superior orbit accuracy to study large-scale variability of the global ocean.
 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 ) 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 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]).
 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 time-variant 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. , 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
 ERS-1 was launched on 17 July 1991 into a near-circular, 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).
2.2. ERS Waveform Product
 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 0.049 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 altimeter-generated 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 low-level altimeter information at this data rate and forms the basis for the work presented here [Cudlip and Milnes, 1994].
2.3. ERS Altimeter Tracking Over Sea Ice
 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 αβ filter. This is described by two coupled equations which generate new values of the height parameter hn and its corresponding rate of change n based on its history
where α and β 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). ɛ is the height error signal generated by the parameter error estimation algorithm, which in Ocean Mode is a Sub-optimal Maximum Likelihood Estimator (SMLE), while in Ice Mode an Offset Centre of Gravity (OCOG) algorithm is used [Francis, 1990; Peacock, 1998]. ɛ 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].
 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, 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
 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 ɛ. For diffuse echoes over the open ocean, a maximum value for ɛ 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 ɛ between its limits of ±4.54 m [Peacock, 1998].
 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 ɛ 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 tracker-generated errors.
3.2. Geometric Errors Over Sea Ice
 A fundamental assumption of pulse-limited altimetry is that the radar backscatter coefficient σ0 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.
3.3. Origin of Radar Echoes in Sea Ice–Covered Regions
 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].
 The peaked nature of satellite radar altimeter returns over sea ice and the fact that radar backscatter is high (typically 20–40 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.
 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 (σ0 = 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  concluded that these strong peaked echoes originate from open water between ice floes. A similar conclusion was drawn by Laxon [1994a].
 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.
 In summary, our understanding of the mechanisms for the backscatter signal over sea ice as detected by a nadir-pointing 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
 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 FES95.2.1 global tide model [Le Provost et al., 1998], which includes a set of solutions for the Arctic Ocean produced by Lyard , 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 Saastamoinen formula [Centre ERS d'Archivage et de Traitement, 1995]).
4.2. Separation of Sea and Ice Surface Elevations
 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
where pmax is the peak waveform power, and pi 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. .
 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 ice-covered region were discarded.
4.3. Waveform Retracking
 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.
4.4. Pulse-Blurring Correction
 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 linear relationship between retracked height error Δhrtk and the height error signal ɛ. Equations (1) and (2) can be combined to give an expression for the height parameter hn at any given time based on its initial value and initial rate of change
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 α = 7.49409 × 10−3 and β = 8.77660 × 10−6 (C. R. Francis and M. Roca, personal communication). h0 and 0 were taken to be zero.
 Pure specular waveforms were used in this simulation. The flat surface impulse response and the surface height pdf were taken as δ functions, which by the convolutional waveform model of Brown  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
Each averaged waveform can therefore be represented as
A series of such averaged waveforms was generated for values of ɛ between −5 m and +5 m, in increments of 10 cm. The height difference Δhavg 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 ɛ 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 ɛ < 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).
 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 ɛ 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 ɛ. Figure 4 shows this final situation when ɛ = +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.
 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 ɛ, 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 ɛ. 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 herr as shown. The simulation shows that the 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 ɛ = 0 axis is due to the fact that we 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.
 The strong linear trend between ɛ and Δhrtk for ɛ less than zero suggests that a correction can be applied to the elevation measurements which is a function of ɛ. Taking the slope of the trend m to be constant for all ɛ over the range of interest, a corrected height hcor can be calculated from the retracked height hrtk as follows
where m is taken to be −3.5 for ERS-1 and −5.0 for ERS-2.
4.5. Additional Processing
 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), a 3σ 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 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, pulse-blurring correction and outlier removal algorithms, and (3) after along-track filtering.
 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 j at a given along-track data point j.
where i is the orbit repeat number, and Nj is the number of data points at j.
 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  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 compared with more sophisticated solutions [Cheney et al., 1989].
5. Accuracy Assessment of Sea Surface Height Data
5.1. Crossover Analysis
 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 Δzij at the location rij where tracks i and j meet is given by
where zi and zj are the observed sea surface heights at the crossover location at times ti and tj, respectively, Δη is the change in dynamic sea surface height between the two times, and Δɛ represents the sum of all measurement errors present in the two measurements.
Figure 6 shows the crossovers computed from cycle 2 of the ERS-2 mission gridded onto a 0.25° × 0.25° 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 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 FES95.2.1 ocean tide model used to correct the altimeter data. The Arctic regional tide model due to Lyard , 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° < ϕ < 75° and −75° < λ < −60°, where ϕ and λ 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.
 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° < ϕ < 80° and −160° < λ < −130°), and again using only data from the ice-free Greenland-Iceland-Norwegian (GIN) Seas (bounded by 60° < ϕ < 75° and −10° < λ < 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 regions.
5.2. Analysis of Collinear Tracks
 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).
 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 ice-covered 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 decorrelate over 1 day, we can divide these values by 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 ice-covered 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.
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.
5.3. Sea Surface Height Measurement Error Budget
 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:
Table 1. Error Budget for Absolute ERS Altimeter Sea Surface Height Retrievals in Ice-Covered Seasa
Error Budget, cm
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.
Radial Orbit Errors
Geographically fully correlated
Geophysical Correction Errors
Dry tropospheric correction
Wet tropospheric correction
Ocean loading tides
Solid Earth tides
5.3.1. Radial Orbit Errors
 The values for the orbit error components are estimated from the values given by Scharroo and Visser , with the nongravitational component remaining the same, and both gravitational components scaled by a factor of 1.5 (R. Scharroo, personal communication).
5.3.2. Tropospheric Corrections
 Mean values for the tropospheric corrections at the poles are typically around 220 cm for the dry correction and 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.
5.3.3. Ionospheric Correction
 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.
5.3.4. Tidal Corrections
 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 FES95.2.1 of Le Provost et al. , the CSR3.0 model of Eanes  and the University of Alaska, Fairbanks model of Kowalik and Proshutinsky ) 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 [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.
5.3.5. Instrument Noise
 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.
 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 , we have added these components in quadrature, with the result that we will most likely be overestimating the resulting error. Scharroo and Visser  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.
6.1. Mean Sea Surface
 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.
 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., 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.
 The detail presented in Figure 8a is similar to that revealed in the Arctic gravity field of Laxon and McAdoo , 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 north-south 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 .
 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-1 168-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 0.25° × 0.25°. 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 0.25° × 0.25° 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 (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.
6.2. Sea Surface Height Variability
 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 1997. 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 0.25° × 0.25° 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 and atmospheric and ocean tide corrections. For comparison, using data from the Seasat altimeter, Cheney et al.  estimated that about 70% of the global ocean observed by this satellite had an RMS variability of less than 5 cm. The increase in variability of almost 2 cm on moving from ice-free to ice-covered ocean would suggest that the additional errors induced by the presence of sea ice are at this level.
 This altimeter-derived variability was compared with the predictions of the NPS coupled ocean-sea ice model. Two years of sea surface height data (1993 and 1994) from an earlier run of the model due to Maslowski et al.  were used. In summary, this model is high resolution with a grid size of 18.52 km and 30 vertical levels, although this resolution is insufficient to resolve eddies in the Arctic Ocean where the Rossby radius is between 5 and 10 km. The output used in this comparison was acquired after 198 years of integration, and was provided in the form of 3 day snapshots of sea surface height from which sea surface height variability was computed. For their comparisons of the results of TOPEX/Poseidon with output from the Parallel Ocean Climate Model (POCM), McClean et al.  subsampled the model's 3 day snapshots to 10 days in order to match the altimeter's repeat period. No distinguishable differences between the quantities computed at the two sampling frequencies were revealed. In the light of this, we retained the model's snapshot interval of 3 days in spite of the fact that the altimeter variability was computed from 35 day repeat cycles. The results of the RMS variability calculation are shown in Figure 10b.
 On comparing the model and altimeter results in Figure 10, it can be seen that there is generally a good qualitative agreement in the spatial distribution of variability. From Figure 10 it would appear that the regions of higher variability in both the model and altimetry show some correlation with bottom topography. The model simulations reveal a strong topographic control, characteristic of barotropic flow in the Eurasian and Canada Basins and in the Arctic marginal seas, where relatively strong transports are confined mainly to the continental shelves. This result is entirely consistent with the patterns of variability observed with the altimeter, although caution must be exercised when interpreting the results in regions where ocean tide model errors may dominate (e.g., the Bering Sea and Canadian Archipelago). The higher variability observed in the shelf regions and marginal seas are in contrast to the lower values in the deep central Arctic waters (in particular the Canada Basin) and the deep water areas of the GIN Seas.
Table 2 shows a quantitative comparison of the variability as determined from ERS-2 and the model in four regions: (1) Canada Basin, 72° < θ < 80° and −160° < λ < −130°, (2) East Siberian Sea, 70° < θ < 80° and 145° < λ < 180°, (3) Barents Sea, 70° < θ < 80° and 15° < λ < 55°, and (4) GIN Seas, 60° < θ < 75° and −10° < λ < 10°.
Table 2. Variability From the ERS-2 Altimeter and the NPS Model Averaged Over the Four Regions Defined in the Text
East Siberian Sea
 After deducting the 2 cm increase in altimeter-derived variability in ice-covered regions (due to additional measurement uncertainties as discussed above), we find that the variability observed from the altimeter is about a factor of 3 to 4 greater than that predicted by the NPS model. This is similar to results obtained by Stammer et al. , who observed that the simulated variability from the global POCM model is a factor of 2 to 4 too low as compared with the results from TOPEX/Poseidon.
 Recently developed data processing techniques for satellite altimeter data acquired in sea ice-covered regions have allowed accurate sea surface height retrievals in the entire region between 60°N and 81.5°N for the first time. Reduction in the quality of these retrievals on moving from ice-free to ice-covered ocean is shown to be at the centimeter level. After detrending, the standard deviation of crossovers over one cycle in the ice-covered Canada Basin was calculated as 9.9 cm, compared with a value of 7.5 cm in the ice-free GIN Seas. An analysis of collinear tracks revealed a combined measurement and tide correction error of 5.7 cm in the Canada Basin, compared with 3.7 cm in the GIN Seas. An error of 9.4 cm has been estimated for the absolute accuracy of these measurements in sea ice-covered regions, which compares with a value of 6.4 cm derived by Scharroo and Visser  for the ice-free global ocean. Each of these analyses indicate that although the residual errors in sea surface height measurements in ice-covered regions are greater than for ice-free regions, it is still small enough to make the data useful for geophysical applications.
 Using measurements obtained from nearly 42 repeat cycles of the ERS-2 mission (a period spanning almost 4 years), an accurate mean sea surface has been computed for the Arctic Ocean. Crossover differences for the mean profiles which made up this surface over the entire region had an RMS value of 7.2 cm, reducing to 4.2 cm in the Canada Basin and 3.8 cm in the GIN Seas. The short wavelength detail revealed by this surface is very similar to that shown in the Arctic gravity field of Laxon and McAdoo . Comparisons were made with the OSUMSS95 mean sea surface in the same region, highlighting significant differences between the two surfaces in permanently ice-covered seas. In the GIN Seas, the two surfaces have an RMS difference of 6.4 cm about a mean of zero after correcting for the bias due to the choice of different reference ellipsoids and altimeter measurement biases. In the Canada Basin, the RMS difference increases to 47.7 cm about a mean of −22.5 cm. The ERS-derived Arctic mean sea surface was shown to offer significant improvements over the existing OSUMSS95 surface in ice-covered seas.
 Two year's of ERS-2 measurements were then used to estimate sea surface height variability in the Arctic Ocean. The mean RMS variability in the ice-covered Canada Basin was estimated to be 7.3 cm, compared with a value of 5.5 cm in the ice-free GIN Seas. It was concluded that the higher variability of about 2 cm observed in ice-covered regions compared with ice-free regions was largely artificial, and a result of additional errors introduced into the sea surface height measurements by the high-powered specular radar echoes received by the altimeter and additional uncertainties in orbit determination and atmospheric and ocean tide corrections. Comparisons with the sea surface height variability computed from two year's of NPS model output were qualitatively favorable. Taking into account the 2 cm increase in altimeter-derived variability in ice-covered regions (due to additional measurement uncertainties), it was found that the variability observed from the altimeter is about a factor of 3 to 4 greater than that predicted by the model. This is in agreement with other altimeter-model comparisons [e.g., Stammer et al., 1996].
 A number of authors have recently identified a dramatic shift in hydrographic fronts within the central and eastern Arctic Ocean [e.g., Carmack et al., 1995; McLaughlin et al., 1996; Steele and Boyd, 1998]. This shift has been associated with changes in the large-scale patterns of sea ice motion, including the shrinking of the Beaufort Gyre and an eastward deflection of the Transpolar Drift [Kwok, 2000]. These two main circulation features are largely controlled by wind patterns and hence changes in atmospheric pressure. Recent modeling efforts by Proshutinsky and Johnson  have demonstrated the existence of two regimes of wind-forced circulation. They showed that the motion in the central Arctic alternates between anticyclonic and cyclonic circulation, with each regime persisting for 5 to 7 years. Atmospheric forcing was highlighted as the key factor in driving variability in the Arctic Ocean. Although it unclear as to whether or not this transition from one regime to the other can be observed using this relatively short altimeter data record, the technique is clearly suited toward this type of study. Another key area which could usefully be studied using altimetry is the East Greenland Current, responsible for the export of cold low-salinity surface water and ice from the Arctic Ocean into the North Atlantic via Fram Strait. This export has major consequences for the convective gyres to the south [Aagaard and Carmack, 1994], which in turn have an effect on the global thermohaline circulation and hence the global climate system. Long-term monitoring of this current system is clearly of enormous benefit, and altimetry is the ideal instrument to achieve this goal. This work has demonstrated a valuable new tool for oceanographic research in the Arctic Ocean. Although we are hampered in some senses by the latitudinal limit of the satellite, a number of key areas including the Canada Basin and Fram Strait can be monitored to examine changes in circulation patterns of the Arctic Ocean.
 We thank Justin Mansley at UCL for the preliminary processing of the WAP data, and acknowledge ESA/UK-PAF for providing the ERS-1/2 data. We would also like to thank Remko Scharroo of the Delft University of Technology for his provision of precise orbits for the ERS missions, and Wieslaw Maslowski of the Naval Postgraduate School for supplying us with sea surface height fields from the NPS coupled ocean-sea ice model. Neil Peacock is funded under the Natural Environment Research Council (NERC) Arctic Ice and Environmental Variability (ARCICE) program, grant number GST/02/2196.