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 Satellite altimetry provides high-quality sea surface height data that have been successfully used to study the variability of sea level and surface geostrophic circulation at different spatial and temporal scales. However, the high-latitude regions have traditionally been avoided due to the persistent sea ice cover. Most of the validation studies have focused on the areas below the polar circles. In this paper we examine the quality and performance of a gridded satellite altimetry product in the Nordic, Barents, and Kara seas. The altimetric sea level in coastal areas is validated using available tide gauge records. We show that at most locations in the Nordic seas the altimetry and tide gauge measurements are in a good agreement in terms of the root-mean square differences and the amplitudes and phases of the seasonal cycle. The agreement deteriorates in the shallow areas of the Barents and Kara seas subject to the seasonal presence of sea ice, and where the altimetry data are contaminated by the residual aliasing of unresolved high-frequency signals. The comparison of linear trends at the locations of tide gauges reveals discrepancies that need to be taken into account when interpreting long-term changes of sea level in the region. Away from the coast the altimetry data are compared to drifter trajectories, corrected for Ekman currents. The drifter trajectories are found consistent with the mesoscale variability of the altimetric sea level. This study provides the first comprehensive validation of a gridded satellite altimetry data product in the high-latitude seas.
 Sea level is a natural integral indicator of climate variability. Satellite altimetry providing continuous, nearly global, and high-accuracy measurements of sea surface height (SSH) has become the main tool to study the variability of sea level at different spatial and temporal scales [Fu and Cazenave, 2001]. However, the use of altimetry data in the polar oceans has been limited due to the seasonal presence of sea ice and temporally sparse altimetry measurements.
 Owing to the 66° orbital inclinations of the former TOPEX/POSEIDON (TP) and present Jason-1 and OSTM/Jason-2 missions, radar altimeters on these satellites do not acquire measurements above the polar circles. The European Space Agency's (ESA's) former ERS-1 and ERS-2 and present Envisat satellites with 98° inclination orbits have sampled the polar oceans up to latitudes of 82° starting from July 1991. The U.S. Navy Geosat Follow-On (GFO) satellite sampling extends to 72° latitude. The National Aeronautics and Space Administration's (NASA's) ICESat satellite was providing the sea surface topography measurements up to 86°N from 2003 to 2010, based on which Kwok and Morison  constructed the mean dynamic topography over the ice-covered areas of the Arctic Ocean. The ESA's Cryosat-2 altimetry satellite was launched on 8 April 2010 with an inclination of 92°. The French-Indian SARAL/AltiKa mission is scheduled for launch in early 2012 and will fly on ERS/Envisat orbit to insure the continuity of altimetry observations in the long-term.
 Although much attention is being paid to polar regions at the present time, most of satellite altimetry data products in the polar oceans are based on measurements by one particular satellite mission at a time, while at lower latitudes the combination of simultaneous measurements from several satellites has provided a better representation of the mesoscale variability [Le Traon et al., 1998; Le Traon and Dibarboure, 1999; Ducet et al., 2000; Pascual et al., 2006]. In this study we assess the data that above the polar circle originate either from ERS-1/2 or Envisat satellites. These satellites have flown on the same orbit thus providing the longest continuous record. Although ICESat data are not part of the product we use, we acknowledge that the combination of ICESat data and, when sufficiently long records become available, Cryosat-2 data with ERS-1/2 and Envisat measurements may improve the quality of future altimetry products. For example, recently Farrell et al.  combined ICESat and Envisat altimetry data to construct the high-resolution mean sea surface of the Arctic Ocean and used it to derive mean dynamic topography.
 ERS-1/2 and Envisat have flown on a 35-day repeat cycle orbit meaning that signals at one particular location along a satellite track with periods shorter than 70 days are not resolved. The unresolved signals, mainly tides, the barotropic variability of sea level forced by high-frequency winds, and part of the mesoscale variability, alias into lower frequencies and corrupt altimetry measurements [Fukumori et al., 1998; Stammer et al., 2000]. The tidal aliasing is routinely corrected for by using tidal models that assimilate altimetry data [Le Provost, 2001]. The aliasing due to the high-frequency barotropic variability is largely suppressed by subtracting model-simulated high-frequency variability [Carrere and Lyard, 2003; Volkov et al., 2007]. Nevertheless, it is well known that ERS-1/2 and Envisat measurements are not optimal for recovering ocean tides [Andersen, 1999, 1994]. The dynamic atmospheric correction applied to altimetry data reduces aliasing from signals with periods less than 20 days, which is optimal for TOPEX/POSEIDON, Jason-1, and Jason-2/OSTM missions, but not for ERS-1/2, Envisat, and GFO satellites.
 The above considerations indicate that the quality of satellite altimetry products in high-latitude regions remains uncertain. Tide gauges have routinely been used to validate altimetry measurements [Mitchum, 1998; Volkov et al., 2007; Pascual et al., 2009; Vinogradov and Ponte, 2010]. However, none of the similar validation studies known to the authors has focused on the northern subpolar regions. Recent advances in the processing of satellite altimetry geophysical data records [Dorandeu et al., 2010; Faugere et al., 2006; Faugere et al., 2010] are making available more SSH measurements in high-latitude areas for the periods free of sea ice. In this paper we present a comparison between a state-of-the-art gridded satellite altimetry product and available tide gauge and surface drifter measurements in the Nordic (Greenland, Icelandic, and Norwegian), Barents, and Kara seas. The domain of our study covers an area from 40°W to 100°E and from 60°N to 80°N (Figure 1). We thus aim to complement previous studies by extending the validation of altimetry data further north and provide the first objective assessment of the quality and performance of satellite altimetry in this important region.
 The choice of the regional domain for this study is dictated by the availability of observational records (discussed in the next section) and its particular importance in the regional and global climate system. The Nordic seas connect the Atlantic and the Arctic oceans and play a prominent role in the Earth's climate system. This region is particularly important for deep-water formation and the meridional overturning circulation. Here, warm Atlantic waters lose heat to atmosphere, subduct to intermediate depths, and transport residual heat further into the Arctic Ocean. Multidecadal variability in the temperature of the Atlantic Water core affecting the upper layers of the Arctic Ocean has been reported by Polyakov et al. [2003, 2005]. As a result of global warming, long-term decline in the Arctic sea-ice cover has been observed over the last 30 years [Comiso et al., 2008] with a record minimum seen in 2007 [Stroeve et al., 2008]. Because of this, the study region, in particular, the Kara Sea is experiencing an increase in open water area during summer-early fall and thus more altimeter observations are becoming available.
2. Data and Methods
2.1. Altimetry Data
 In this paper we assess the quality of the maps of sea level anomaly (MSLA) from 14 October 1992 to 1 December 2010, produced by SSALTO/DUACS and distributed by AVISO with support from Centre National d'Etudes Spaciales (CNES; http://www.aviso.oceanobs.com/duacs/). We use the state-of-the-art delayed-time global “reference” MSLA product, generated by merging SSH measurements from two satellites at a time: TP/ERS-1/2, Jason-1/Envisat, and Jason-2/Envisat. This means that SSH data over most of the domain of our study (above 66°N) originates from either the ERS-1/2 or Envisat mission.
 Prior to the production of MSLA, the along-track SSH data are corrected for instrumental noise, orbit determination error, atmospheric attenuation (wet and dry tropospheric and ionospheric effects), sea state bias, and tidal influence. A global crossover adjustment using the TP/Jason-1/Jason-2 orbit as a reference is performed to correct for ERS-1/2 and Envisat orbit errors [Le Traon and Ogor, 1998]. The adjustment uses cubic spline functions that reduce SSH differences at crossovers. Le Traon et al.  and Ducet et al.  have demonstrated the efficiency of this method in the open ocean. A mean profile calculated for the 1993–1999 period is subtracted from SSH measurements to obtain sea level anomalies (SLA).
 A dynamic atmospheric correction is applied to account for the dynamic response of the ocean to atmospheric pressure and wind forcing [Carrere and Lyard, 2003]. This correction combines the high frequencies of the Modèle d'Onde de Gravité à 2 Dimensions (MOG2D) barotropic model [Lynch and Gray, 1979], forced by the ERA-Interim pressure and wind reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), with the low frequencies of the inverted barometer correction. This significantly reduces the aliasing of the high-frequency sea level variability in altimetry data, especially in coastal regions [Carrere and Lyard, 2003; Volkov et al., 2007].
 The mapping procedure to produce MSLA relies on optimal interpolation with realistic correlation functions [Le Traon et al., 1998, 2003]. The optimal interpolation scheme is designed to reduce long wavelength errors. These errors are seen as a bias between neighboring tracks, induced by geographically correlated residual errors (e.g., residual orbit error, instrumental errors) and residual aliasing from large-scale high-frequency signals (tides and high-frequency response to atmospheric forcing). Maps are produced every week on a 1/3° Mercator projection grid. Thus there are 947 maps for the period of study (14 October 1992 to 1 December 2010).
 The maps of absolute dynamic topography (MADT) are obtained by adding the MSLA referenced to the 1993–1999 time period to the MDT_CNES-CLS09 mean dynamic topography (MDT) product for the 1993–1999 period, based on 4.5 years of GRACE data, and 15 years of altimetry and in situ (hydrography and drifter) measurements [Rio et al., 2011]. An alternative MDT can also be used, e.g., DNSC08 MDT by Andersen and Knudsen . The MADT (MSLA+MDT) are used to compute the absolute geostrophic velocity components (Ug and Vg) that will be used for comparison with surface drifter velocities: Ug = −(g/f)(∂η/∂y) and Vg = (g/f)(∂η/∂x), where g is gravity, f is the Coriolis parameter, and η is the SSH.
 Typical mapping errors as a percentage of signal variance given by the optimal interpolation scheme are displayed in Figure 2a (for details on mapping error estimation, see Le Traon et al.  and Ducet et al. ). The errors are relatively small (typically below 10% of the signal variance) south of 66°N due to the combination of two satellites. The ERS-1/2 and Envisat error patterns are more complex than those of TP, Jason-1, and Jason-2/OSTM, showing both space and time variability [Ducet et al., 2000]. North of 66°N, where the sampling is carried out by one satellite at a time, error estimation fields exhibit a typical “diamond structure” with maxima occurring at the centers of intertrack spaces and often reaching 40–50% of the signal variance (Figure 2a). The mapping error is large along the eastern coast of Greenland, in the Fram Strait, northeast of Spitsbergen, and in the eastern part of the Kara Sea. On the other hand, the mapping error in the western and central parts of the Kara Sea is rather low, generally below 20%.
 Because of the seasonal presence of sea ice, the altimetry data in the study region have gaps. The ice flag in ERS/Envisat data is set if one of the following criteria is true: (1) the number of valid 20 Hz data is less than 17, (2) the absolute value of the difference between the radiometer and the ECMWF model wet tropospheric correction is greater than 10 cm, and (3) the waveform peakiness parameter [Laxon, 1994] exceeds a 2.0 threshold (for details on ice detection, see Faugere et al. ).
 The portion of missing data relative to the total number of maps is displayed in Figure 2b. There are either no missing data or missing data constitutes less than 10% in the areas that are free of sea ice all year round. In these areas some data are missing in January–March 1994 when the ERS-1 satellite was flying on a 3-day repeat orbit for calibration and sea ice observation. The percentage of missing data due to sea ice exceeds 20% along the eastern coast of Greenland and in the northeastern part of the Barents Sea. In the Kara Sea the percentage of missing data increases from about 20% in the southwest to about 80% in the northeast, so that over most parts of the sea only SSH data from 3 to 5 summer-autumn months (July through November) are available.
2.2. Tide Gauge Data
 The tide gauge data, used in this study, have been distributed by the Permanent Service for Mean Sea Level (PSMSL, www.psmsl.org). We used the monthly averaged sea level records from 23 tide gauges located along the Eurasian coast and on islands (Figure 1). Many tide gauges in the study region were closed in 1990s and only a few remained operational through 1990s and 2000s [Proshutisky et al., 2007]. The list of the tide gauges with the record intervals used in this study and the number of gaps in the monthly records are summarized in Table 1. The records from the majority of tide gauges have substantial gaps. Several tide gauges (Bugrino, Malye Karmakuly, Morzhovaia, Isachenko, Uedinenia, and Russkii) have no or a very few records overlapping with altimetry measurements. In order to validate the seasonal cycle of the altimetry SSH at these locations, we considered longer tide gauge records starting from January 1958 (January 1965 for Bugrino).
Table 1. The List of Tide Gauges, Their Locations, Record Intervals Used in This Study, and the Number of Gaps in Monthly Data
Tide Gauge Station
Record Interval Used in the Study
Number of Gaps in Monthly Data
Jan 1992 to Dec 2006
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1992 to Dec 2009
Jan 1965 to Dec 1990
Jan 1958 to Dec 1980
Jan 1992 to Feb 1996
Jan 1992 to Oct 1993
Jan 1992 to Dec 2009
Jan 1958 to Sep 1994
Jan 1958 to Feb 1997
Jan 1992 to Dec 2009
Jan 1958 to Nov 1993
Jan 1958 to Mar 1995
Jan 1958 to Jul 1989
Jan 1992 to Dec 2009
Jan 1992 to Jul 2009
 The monthly tide gauge records were corrected for the inverted barometer effect. The inverted barometer correction (IB) is given by IB = (Pa − Pref)/ρg, where Pa is the sea level pressure (SLP), Pref is the SLP averaged over the entire ocean, ρ is the seawater density, and g is gravity. A change of Pa by 1 mbar corresponds to approximately 1 cm change in sea level. For the tide gauges with the record intervals (shown in Table 1) starting in January 1992 we used the monthly averages of ERA-Interim SLP (available from January 1989 onwards), while for those with the record intervals starting in January 1958 (January 1965 for Bugrino) we used the monthly averages of ERA-40 SLP (available from September 1957 to August 2002). The average reference pressure Pref is time varying with a standard deviation of about 0.5 mbar in the ERA-Interim and 0.6 mbar in the ERA-40 data. Because we used monthly averaged tide gauge data, the high-frequency sea level fluctuations (tides, storm surges, etc.) had been filtered out.
2.3. Glacial Isostatic Adjustment
 To account for the vertical crustal motions due to postglacial rebound, the tide gauge records were also corrected for glacial isostatic adjustment (GIA) using the ICE5G_VM4_L90 GIA model by R. Peltier obtained from the PSMSL (www.psmsl.org/train_and_info/geo_signals/gia/peltier) (for details about previous versions, see Peltier [1998, 2004]). This model provides the present-day rate of change of relative sea level, that is the sea surface relative to a nearby benchmark connected to the solid Earth (Figure 3). The tide gauge records are thus corrected by subtracting a linear trend with a slope inferred from the GIA model. Although Scandinavia is experiencing a rather strong postglacial rebound accompanied with a decrease in relative sea level at the maximum rate of about 1 mm/year centered in the Gulf of Bothnia in the Baltic Sea, it appears that the absolute value of the relative sea level change at most tide gauges in the Norwegian, Barents, and Kara seas is an order of magnitude smaller (Figure 3).
 It should be noted that ideally satellite altimetry data must also be corrected for GIA. Crustal deformations due to postglacial rebound are increasing the volume of the ocean basins [Tamisiea and Mitrovica, 2011]. Assuming that the volume of water remains the same, the global average SSH relative to a reference ellipsoid (as measured by space-borne altimeters) must decrease. The associated change of the globally averaged SSH is −0.3 mm/year [Peltier, 2001]. Recently, Tamisiea and Mitrovica  derived a close value of −0.25 mm/year. This means that this correction must be subtracted from the altimetric globally averaged trend of SSH to account for crustal deformations over the ocean.
 When analyzing local (regional) measurements of SSH, the application of the globally averaged GIA correction is not appropriate, because the impact of GIA on the ocean is not uniform due to a nonuniform associated change in gravity. The geographical distribution of the GIA correction over the ocean, presented by Tamisiea and Mitrovica  (their Figure 3b), shows that the absolute value of the GIA impact on SSH along the Norwegian and Russian coasts is close to zero and does not exceed 0.1 mm/year. Unfortunately, these data are not available to us, and therefore we do not correct altimetry data for GIA. As will be shown later in the manuscript, the potential GIA impact on the local SSH is very small and absolutely not sufficient to explain the differences in SSH trends inferred from tide gauges and altimetry.
2.4. Surface Drifter Data
 Satellite-tracked drifters have proven to provide valuable observations for validating altimetry velocities in the open sea [e.g., Ducet et al., 2000; Pascual et al., 2006, 2009]. The drifter data are provided by the Global Drifter Program Data Assembly Center of the Atlantic Oceanographic and Meteorological Laboratory (http://www.aoml.noaa.gov/phod/dac/). The raw data are optimally interpolated to uniform 6-h intervals. The zonal and meridional components of velocity are calculated via centered finite differencing over 1/2-day displacements. The high-frequency ageostrophic phenomena, such as inertial oscillations, tidal currents, internal waves, coastal upwelling, cyclostropic waves, and others, are reduced by applying a 3-day low-pass filter [Rio and Hernandez, 2004]. To obtain the near-surface geostrophic currents, the wind-driven ageostrophic flow (Ekman currents) must be subtracted from the drifter velocities. The estimation of Ekman currents is performed by fitting a two-parameter (angle and amplitude) model to wind stress data and high-frequency ageostrophic currents derived from drifting buoys (for details, see Rio and Hernandez ).
 We used information from 252 drifters that were present in the study region from January 1993 to December 2010. Displayed in Figure 4 are the trajectories of these drifters and the density of drifter data in 1° × 1° bins. One can see that most of drifter records, sometimes exceeding 500 per 1° × 1° bin, are concentrated southwest of Iceland and in the Norwegian Sea (Figure 4b). In these areas the drifter trajectories are highly variable. Poleward from about 70°N some drifters were carried toward the Fram Strait, while some were advected into the Barents Sea (Figure 4a). From the first group, a few drifters reached the interior of the Greenland Sea around 5°W and 75°N. The East Greenland Current carried one drifter all the way south toward the Denmark Strait. From the second group, relatively large number of drifters reached the interior of the Barents Sea. The others followed the coastal current with one drifter entering the Kara Sea through the Karskie Vorota Strait.
3. Quality Assessment
3.1. Comparison With Tide Gauge Records
 For comparison with tide gauge records the data from MSLA were bilinearly interpolated to the locations of the tide gauges. The errors that might be introduced by the interpolation are small because the spatial scales resolved by the MSLA are larger than the grid resolution [e.g., Pascual et al., 2009]. For example, the standard deviation of the difference between SLA averaged over 0.5° × 0.5° around Andenes tide gauge and SLA interpolated at Andenes is 0.3 cm, which is much smaller than about 7 cm standard deviation of SLA near Andenes.
 The time means, computed over the overlapping records, were subtracted from both the altimetry and tide gauge time series. The time series of four characteristic tide gauge records corrected for IB and GIA and the corresponding time series of altimetry data interpolated to the locations of tide gauges are presented in Figure 5. The degree of consistency between the altimetry and tide gauge data is summarized in Table 2, which presents the standard deviations of the time series and root-mean-square (RMS) differences between the records. The comparison is presented only for the tide gauges that have overlapping records with altimetry. In general, the application of the IB correction reduces the standard deviation of the tide gauge data bringing it closer to the standard deviation of the altimetry data, and it reduces the RMS difference between the tide gauge and altimetry data. The static effect of the atmospheric pressure (IB effect) is thus an important contributor to the sea level variability in the region and needs to be corrected for before carrying out the comparison with altimetry data. The impact of the GIA correction on the RMS difference is much smaller, on the order of 1 mm. At some locations, the application of the GIA correction reduces, at some increases, while at the majority of locations it has no impact on the RMS difference.
Table 2. Comparison Between the Monthly Tide Gauge Records and Altimeter MSLA Interpolated to the Location of Tide Gauges in Terms of Standard Deviations and Root Mean Square Differencesa
Tide Gauge Station
Number of Overlapping Records
Standard Deviation of SLA
RMS of SLA Differences
The comparison is conducted only for the tide gauges that have overlapping records with altimetry. The IB correction for the tide gauge data was calculated using the ERA-Interim SLP. The time mean sea level, computed over the overlapping records, was subtracted from both the tide gauge and altimeter data. Abbreviations: ALT is altimeter data, TG is raw tide gauge records, (TG-IB) is tide gauge records corrected for IB, (TG-IB-GIA) is tide gauge records corrected for IB and GIA.
Only data from 2002 to 2009 inclusive are considered.
The 1992–2010 linear trend has been removed from the tide gauge data.
 The lowest RMS difference between the tide gauge and altimetry data down to about 2 cm is estimated at Torshavn and Lerwick, where the altimetry data are based on the combination of two satellites. The tide gauge and altimetry records in the Norwegian and Barents seas are also close (Table 2). The number of overlapping monthly records here is sufficiently large (around 200). The average RMS difference at the Norwegian tide gauges (Andenes, Hammerfest, Honningsvag, Vardo), located in the areas where either ERS-1/2 or Envisat data are available, is about 3 cm. Displayed in Figure 5 (top left) are the time series of the tide gauge and altimetry sea level at Andenes manifesting a good agreement between the data sets in terms of the seasonal and interannual variability. The RMS difference between them is 3.1 cm when GIA correction is applied and 2.9 cm without GIA.
 The agreement between the altimetry and tide gauge data deteriorates in the Barents and Kara seas (Table 2). Here, at most tide gauges the RMS difference is between 5 and 7 cm. At Murmansk tide gauge the RMS difference exceeds 6 cm. This is expected because the tide gauge is located inland in a fjord and altimetry data near Murmansk are more representative of the nearby open sea region. At Zhelania and Dikson tide gauges the agreement is poor with the RMS difference of nearly 11 cm. It should be noted that at several locations (Bolvanskii Nos, Morzhovaia, Isachenko, Uedinenia) the relatively low RMS difference is calculated from a small number of overlaps. Neglecting errors in the tide gauge records, the greater RMS difference in the Kara Sea is probably because the altimetry signal is contaminated by the presence of sea ice, it is more influenced by land, and the residual aliasing from high-frequency signals is large in the shallow areas.
 The reliability of records obtained from two tide gauges, used in this study, is suspect. Namely, by analyzing the time series of the Barentsburg tide gauge (Figure 5), one can notice a contrast between the measurements prior and after 2002. Prior to 2002, the tide gauge record poorly agrees with altimetry. During this time it is considerably more variable than after 2002 and has gaps. If only the period after 2002 is considered, the RMS difference between the tide gauge and altimetry data at Barentsburg is reduced to 4 cm as opposed to 8 cm for the 1992–2009 period (Table 2). On the basis of this comparison and on the station documentation provided by the PSMSL (www.psmsl.org), we conclude that the quality of the Barentsburg tide gauge data between 1992 and 2002 is uncertain. Although Amderma is one of the oldest and key observatories on the Russian Arctic coast, its time series from 1992 to 2009 even after applying the GIA correction have a strong positive linear trend of 1.2 cm/year (Figure 5). The trend estimated from available altimetry data at Amderma is only 0.28 cm/year. We doubt that the trend observed at the tide gauge is realistic and will discuss this issue in more detail in a section dedicated to linear trends. By removing the 1.2 cm/year linear trend from the Amderma tide gauge record, the RMS of the difference between the tide gauge and altimetry data is reduced from 7.5 cm to 5.8 cm.
 As has been mentioned earlier, residual aliasing of tidal and other high-frequency signals in altimetry data remains one of the concerns for the time series analysis [Volkov et al., 2007]. The ERS-1/2 and Envisat altimeters due to their 35-day repeat cycles have problematic alias periods and they are not suitable for recovering shallow-water tides [Andersen, 1994, 1999]. In addition, this imposes the aliasing of K1 and P1 tidal constituents at 365.24 days period, which is not separable from the seasonal cycle [Andersen, 1999; Le Provost, 2001]. Unfortunately, because of substantial data gaps, we are not able to analyze the spectrum of the tide gauge and altimetry records at all locations in order to understand to what degree the aliasing affects the altimetry data. Therefore, here we estimated the power spectral densities (PSD) only at three stations that have continuous records (no gaps) with sufficient duration: Andenes in the Norwegian Sea and Honningsvag and Bugrino in the Barents Sea. At Andenes and Honningsvag, the tide gauge (altimetry) records are from January 1992 to December 2009 (from April 1994 to November 2010). Since there are no overlapping records at Bugrino, we used the tide gauge data from the earlier June 1977 to May 1986 time interval and the altimetry data from April 2001 to February 2010.
 The PSD estimates for both the tide gauge (black curves) and the altimetry data (red curves) are presented in Figure 6. The strongest signal is due to the seasonal cycle (frequency = 1 cpy (cycle/year)). Note that the PSD estimates of the seasonal cycle from the tide gauge and altimetry data are almost of the same power at Andenes and Honningsvag (Figures 6a and 6b). This means that the seasonal cycle at these locations is well observed by altimetry and it is not strongly corrupted by possible aliasing of K1 and P1 tidal constituents. At Bugrino, the seasonal cycle observed by altimetry has more power than the one observed by the tide gauge (Figure 6c). Assuming that the seasonal cycle has been stationary over the period of observations, the PSD offset at the annual frequency is probably due to the quality of altimetry measurements at this location. The Bugrino tide gauge is situated in the southern part of Kolguyev Island on the shelf of the Barents Sea (Figure 1). It is a shallow region subject to shallow water tides and storm surges. The amplitude of the most energetic diurnal constituent K1 here exceeds 10 cm [e.g., Killett et al., 2011; Kowalik and Proshutinsky, 1993]. Thus, in the southeastern part of the Barents Sea the aliasing from the residual tidal and other high-frequency signals can represent a bigger problem than for the two former locations.
 At higher frequencies the altimetry data appear to underestimate the variability. The PSD of the altimetry data is systematically lower than the PSD of the tide gauge data. The tide gauge records at the three locations have PSD maxima at a semiannual periodicity (2 cpy). The altimetry data also show a semiannual periodicity at Bugrino, but it is not as well observed at Andenes and Honningsvag.
3.2. Assessment of the Seasonal Variability
 As we have shown, the seasonal cycle is the major sea level signal in the monthly tide gauge and altimetry records. Therefore, comparing the seasonal variability of sea level observed by tide gauges and altimeters can be regarded as a diagnostic of altimetry products. In this section we estimate the amplitude and phase of the seasonal cycle by fitting a harmonic function (in a least squares sense) with an annual frequency to the monthly averages of the MSLA and tide gauge records.
 The amplitude and phase of the seasonal cycle estimated from the MSLA (Figures 7a and 7b) are possibly influenced by bottom topography. In the Norwegian and Greenland seas, there are two open-sea seasonal amplitude maxima located in the deep parts (depths exceed 3000 m) of the Lofoten Basin around 2°E and 70°N (amplitudes up to 10 cm) and Greenland Basin around 5°W and 75°N (amplitudes about 7 cm). The amplitude is also large, sometimes exceeding 10 cm, along the Norwegian and Russian coasts. In the Barents Sea, the maximum amplitude is concentrated in the southeastern part over the area with depths less than 250 m. The maximum amplitude in the Kara Sea is observed over the coastal area with depths less than 50 m, however, because of gaps in data, the accuracy of these estimates is uncertain and will be discussed below.
 Over the deep parts of the Greenland, Icelandic, and Norwegian seas, the annual maximum of the sea level is observed in September (Figure 7b). In the shallower areas of the study region, where depths are generally less than 1000 m, the maximum sea level occurs later, from October to December. It is observed in October over the Greenland–Iceland and Faeroe–Iceland ridges, along the continental shelf margin, and in the northern parts of the Barents and Kara seas. In the southern part of the Barents Sea and over most of the Kara Sea the annual maximum sea level occurs in November. The December maximum is observed over the shallow southeastern parts of the Barents Sea and along the western coast of Novaya Zemlya archipelago (depths less than 250 m), and in the southwestern and eastern parts of the Kara Sea.
Mork and Skagseth  have analyzed the seasonal variability of SSH in the Nordic seas and found that the steric effect explains only 40% of the total SSH variability and it is primarily caused by the net surface heat fluxes. The seasonal variations in bottom pressure (ocean mass component) have been found dominant. In our study, for the first time we also present the altimetry-based spatial distribution of the seasonal amplitude and phase in the Barents and Kara seas. We have noted that over these relatively shallow seas the seasonal maximum SSH occurs 1–3 months later than over the deep Nordic seas (Figure 7b). In the shallow Barents and Kara seas the steric effect is expected to be smaller than in the deep Nordic seas. Therefore it is reasonable to assume that the bulk of the seasonal SSH variability in these seas, corrected for the static effect of atmospheric pressure, is barotropic and wind-induced. River runoff, which is maximum in June, is influential near estuaries [Proshutisky et al., 2007]. It is likely that wind is also responsible for the phase difference between the deep and shallow parts of the study region, but this suggestion needs to be confirmed in a future study.
 While the estimates of the seasonal amplitude and phase are robust in most areas of the Nordic seas, they may contain significant errors in the Kara Sea and in some areas of the Greenland and Barents seas where sea ice is present in winter. For example, in the areas where the annual maximum and/or minimum sea level occurs at the time when sea ice is present, a least squares fit of the annual harmonic function can be a poor approximation of the seasonal cycle. Substantial river discharge into the Kara Sea may also complicate accurate estimation of the seasonal cycle.
 In order to estimate the associated error, we used the output of a high-resolution global-ocean and sea-ice data synthesis at eddy-permitting resolution from the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) project (www.ecco2.org). An ECCO2 data synthesis is obtained by least squares fit of a global full-depth-ocean and sea-ice configuration of the Massachusetts Institute of Technology general circulation model (for details, see Marshall et al.  and Menemenlis et al. ). Although, the model adequately reproduces the amplitude of the seasonal cycle, the phase of the seasonal cycle (not shown) significantly differs from Figure 7b and does not seem to be realistic. Because the error estimate can be sensitive to the phase information, we combined the high frequencies (periods less than 4 months) of the ECCO2 model sea level, ηhfm(x, y, t), with the seasonal cycle estimated from the altimetry data, ηsca(x, y, t): ηc(x, y, t) = ηhfm(x, y, t) + ηsca(x, y, t). We then imposed the same gaps, as in the altimetry data, to the combined data set, ηc(x, y, t), to generate . After that, the seasonal amplitude and phase were estimated from both ηc(x, y, t) and , and used to reconstruct the seasonal cycle fields ηscrec(x, y, t) and . The error ε(x, y) was then calculated as the percentage of the RMS difference between ηscrec and to the amplitude of the seasonal cycle (asc) computed from ηc: , where N is the number of maps.
 The obtained error estimate is presented in Figure 7c. Over most areas of the Greenland, Icelandic, Norwegian, and Barents seas, where the number of gaps in data is small (Figure 2b), the error is generally below 5%. In the northern part of the Barents Sea the error reaches 20%. As expected, the biggest error is estimated in the Kara Sea. It reaches 50% in some locations in the eastern part of the Kara Sea. Nevertheless, over large areas in the western and central Kara Sea the error is rather low and generally does not exceed 20%.
 The amplitudes and phases of the seasonal cycle estimated from the tide gauge records and from the MSLA interpolated to the locations of the tide gauges are compared in Table 3. At the locations, where there are no or a very few (with gaps) tide gauge records after 1992 (at Bugrino, Malye Karmakuly, Morzhovaia, Dikson, Isachenko, Uedinenia, and Russkii), we also used records prior to 1992 (Table 1), assuming that the seasonal cycle was stationary over the period of observations. One can see that the overall agreement is satisfactory: the amplitudes are similar and the phases are the same at most locations (along the Norwegian coast and at several islands in the Kara Sea); at other locations the phase difference does not exceed 1 month.
Table 3. Comparison of Amplitudes and Phases of the Seasonal Cycle Estimated From the Altimetry and Tide Gauge Dataa
Tide Gauge Station
Amplitude is measured in centimeters and phases are months of the annual maxima.
The amplitude and phase of the seasonal cycle in tide gauge data are computed using the time interval shown in Table 1.
 It should be noted that the semiannual signal is also present in both the altimetry and tide gauge records (not shown). The amplitude of the semiannual signal is relatively small, generally below 2 cm in the Norwegian and Barents seas. However, the semiannual signal is significant at some locations in the Kara Sea due to the impact of summer melt and river runoff. For example, at the Dikson tide gauge, the amplitude of the semiannual signal (5.5 cm) exceeds the amplitude of the seasonal cycle (4 cm). The amplitude of the semiannual signal at the Izvestia CIK tide gauge (4 cm) is already about twice smaller than the amplitude of the seasonal cycle (9 cm). The semiannual signal can thus influence the estimates of the seasonal cycle from available altimetry data, in particular, near estuaries. This is probably why the worst agreement between the amplitudes of the seasonal cycle is observed at Dikson, while the other locations in the Kara Sea are not heavily affected (Table 3). Unfortunately, the data gaps due to seasonal ice cover make the accurate estimation of the semiannual signal in the altimetry data problematic. Therefore, we do not compare the estimates of the semiannual signal in this study.
3.3. Comparison of Linear Trends
 One of the major climate-related concerns for the society is the rise of sea level. Comparisons of linear trends derived from two independent observational systems, i.e., tide gauges and altimetry, may shed some light on the quality of observations. The differences between the trends can be regarded as error bars. The MSLA were used to estimate the linear trends in the Nordic and Barents seas from December 1992 to November 2010 (Figure 8). In the Kara Sea, because of sea ice, the linear trends in altimetry data were estimated using July through September (JAS) averages of MSLA (Figure 9).
 As one can see, the Norwegian and Greenland seas are experiencing the biggest sea level rise in the region reaching 8 mm/year and 5 mm/year, respectively (Figure 8). The sea level is also rising in the southern part of the Barents Sea with a little change in the northern areas. In the Kara Sea, the change of the JAS sea level is much smaller and it is nonuniform, meaning that the error on the determination of trends possibly has a greater relative impact (Figure 9).
 A comparison of trends obtained from tide gauge records and MSLA interpolated to the locations of tide gauges is presented in Table 4. In the Kara Sea, the linear trends in the tide gauge data were estimated using both the entire records from January 1993 and the JAS averages. Only the tide gauges with relatively long records in 1993–2009 (at least 15 years) are considered. Although the trends agree in sign, the difference between them at most locations is substantial. The best agreement is observed at Kristiansund, Hammerfest, and Honningsvag tide gauges in the Norwegian Sea, where the difference between trends does not exceed 1 mm/year. The worst agreement is observed at Barentsburg and Amderma. Although after 2002 the RMS difference between the tide gauge and altimetry data at Barentsburg is reduced to 4 cm (Table 2, Figure 4), the trends from January 2002 to December 2009 differ almost by a factor of 6. The time series of the Amderma tide gauge from January 1993 to December 2009 (corrected for IB and GIA) have a strong positive linear trend of approximately 12 mm/year (Figure 4). The trend estimated for JAS averages from 1993 to 2009 is about 14 mm/year (Table 4). The corresponding trend obtained using JAS averages of MSLA at Amderma is approximately 3 mm/year. Although the latter trend is seasonally biased due to winter ice cover, it is closer to the 1.5 mm/year trend estimated at the Amderma tide gauge from 1954 to 1989 [see Proshutinsky et al., 2004]. It seems to be unlikely that in 1992–2010 the trend increased by almost an order of magnitude, and it raises concerns about the quality of the tide gauge record. The local GIA correction may contain errors and/or the geodetic benchmarks may have been unstable during this period due to possible changes in permafrost.
Table 4. Comparison of Linear Trends Estimated From the Altimetry and Tide Gauge Dataa
Tide Gauge Station
Time Interval Used
Trend in Altimetry Data
Trend in Tide Gauge Data
Linear trends are measured in millimeters per year.
The linear trend is computed using July through September averages.
 In the Kara Sea, the linear trends, estimated from the tide gauges located on islands (Izvestia CIK, Vise, and Golomianyi), are not uniform (Table 4). Sea level was rising at the rate of about 2–3 mm/year in the vicinity of mainland (Izvestia CIK and Golomianyi), but it did not change in the open sea (Vise). The trends inferred from the JAS averages of the altimetry data also show a sea level rise of about 2 mm/year at Izvestia CIK and Golomianyi and no change at Vise. The JAS trends obtained from the tide gauge data significantly differ from those estimated using the entire records. This means that the JAS trends may be not representative.
 The comparison of trends suggests that while the sea level rise by 3–4 mm/year in the Norwegian Sea is probably robust, the present rates of sea level change in the north of the Greenland Sea, and in the coastal areas of the Barents and Kara seas still remain uncertain. It should be noted that the omission of the GIA correction in altimetry data does not explain the differences in trends. The absolute value of the GIA impact on sea level of 0.1 mm/year, documented by Tamisiea and Mitrovica , is at least an order of magnitude smaller than any observed difference (Table 4).
3.4. Comparison With Drifter Trajectories
 In this section we investigate the ability of the high-latitude MADT and MSLA to adequately resolve the ocean circulation, in particular, the mesoscale eddy variability. The mapping errors over the areas sampled by one satellite at a time are not homogeneous (Figure 2a) and this should be taken into account in the interpretation. It has been documented that at lower latitudes the combination of TP and ERS-1/2 reduces the mapping error by a factor of 4 compared to the TP alone and by a factor of 2 compared to ERS-1/2 alone [Le Traon and Morrow, 2001]. Because the computation of the geostrophic velocities involves the differentiation of SLA, the U and V mapping errors are 2 to 4 times larger than the SLA mapping error [Le Traon and Morrow, 2001].
 In this section we compare the drifter velocities corrected for Ekman currents with the absolute geostrophic velocities derived from the MADT by interpolating the altimeter velocity fields to the positions and times of the drifter data. Displayed in Figure 10 are the drifter and altimetry geostrophic velocity observations averaged over all measurements falling into 1° × 1° bins and the difference between them. There is a good agreement in spatial patterns of the velocities (Figure 10, top and middle). One can observe the Norwegian Current that splits into the North Cape Current that enters the Barents Sea and the West Spitsbergen Current that heads toward the Fram Strait following the bottom topography. The East Greenland Current is also resolved by both the altimetry and the drifter observations. In some places altimetry appears to underestimate the velocities (Figure 10, bottom). In particular, the altimetry V velocity is about 10–15 cm/s smaller than the drifter V velocity along the East Greenland Current. The altimetry U velocity is from 5 to 15 cm/s smaller than the drifter U velocity in the southern part of the Barents Sea and in the Karskiye Vorota Strait. The altimetry V velocity is about 5 cm/s smaller than the drifter V velocity along the West Spitsbergen Current.
 The RMS differences between the drifter (corrected for Ekman currents) and altimetry velocities are presented in Figure 11. Depending on local ocean dynamics the values in most areas range between 7 and 15 cm/s. In the areas of low variability the RMS differences usually do not exceed 7 cm/s. In energetic regions, such as the Lofoten Basin in the Norwegian Sea (5°W–10°E, 68°N–72°N) and the East Greenland Current, the RMS differences may reach 20 cm/s. These estimates are comparable to those estimated by Pascual et al. [2006, 2009] at lower latitudes.
 To visualize how well the altimetry data along a particular drifter trajectory matches the drifter measurements, we present the time series of the altimetry and drifter records along four characteristic trajectories (Figure 12). One drifter (SD32531) floated all the way from Iceland to the Barents Sea. Another drifter (SD35368) entered the eddy-rich Lofoten Basin and circulated around the basin for a while, eventually continuing to follow the Norwegian Current. The third drifter (SD63663) was carried by the current from the Lofoten Basin eastward, entered the Kara Sea, and reached the eastern coast of the northern island of Novaya Zemlya archipelago. The forth drifter (SD63945) was circulating around an anticyclonic eddy in the Lofoten Basin for several weeks and then moved northward to the Fram Strait being carried by the West Spitsbergen Current. The time series of the U and V components (Figure 12) demonstrate a rather good agreement between the altimetry data and the drifters. Even the short-term variability is adequately resolved by the altimetry measurements. However, the drifter data manifest stronger variability, probably because they are not as much filtered as the altimetry measurements. The agreement between the time series deteriorates in the southeastern part of the Barents Sea, in the Kara Sea, and in the Greenland Sea (drifters SD63663 and SD63945). The RMS differences for the four considered drifters are on the order of 10 cm/s.
 Displayed in Figure 13 are the trajectories of the drifter SD63945 from 1 August 2009 to 29 August 2009 and the corresponding altimetry MADT and geostrophic velocities in the region between 1.5°W–6°W and 69.2°N–70.6°N. During this time interval the drifter was located in the eddy-rich part of the Norwegian Sea (Lofoten Basin) and, therefore, represents a good example of the relationship between the drifter trajectory and SSH field. The drifter was initially entrained in an anticyclonic eddy located at about 2.6°W and 69.9°W. This eddy is well resolved by the MADT. It was stationary until 12 August and then it started to slowly propagate northwestward. On 26 August the center of the eddy moved to approximately 2°W and 70.2°N. During the considered time interval another anticyclonic eddy entered the region from the east. It is interesting to note how the second eddy eventually entrained the drifter on 22 August. This particular example demonstrates a good agreement between the altimetry and drifter data. Overall, the MADT and MSLA in the Nordic seas seem to provide enough detail to adequately resolve the mesoscale variability.
4. Summary and Conclusions
 The use of altimetry data in the subpolar and polar regions has been challenging due to the persistent sea ice cover. Up to the date, most of the validation studies have been carried out for the low and midlatitudes. Therefore the quality of the high-latitude altimetry records has largely remained uncertain. Recent advances in the processing of geophysical data records, obtained from altimetry satellites, have made available more SSH data at high latitudes. In the work, presented in this paper, we have carried out the first validation of the state-of-the-art gridded satellite altimetry product (distributed by AVISO, www.aviso.oceanobs.com) in the Nordic and Kara seas. We have assessed the quality of the product by comparing altimetry measurements with those collected by tide gauges and surface drifters.
 The comparison with tide gauge records corrected for the IB and GIA has demonstrated that the altimetry data are robust in most coastal areas of the study region. The IB correction has a prominent effect on the variability of the tide gauge time series, bringing them closer to the corresponding SLA time series. The impact of the GIA correction on the RMS difference between the altimetry and tide gauge records is found small.
 In the Norwegian and Barents seas, the RMS difference between the altimetry and tide gauge measurements is generally about 3 cm. This estimate is similar or lower than those reported in the earlier studies focused on lower latitudes [e.g., Pascual et al., 2009]. The discrepancy between the altimetry and tide gauge records increases in the southeast Barents Sea and in the Kara Sea. At the majority of tide gauges located in these seas the RMS difference is about 5–7 cm. Because satellite altimetry is more accurate away from the coast, as expected, the best match in the Kara Sea is usually observed at the tide gauges located on small islands.
 We found that the quality of two tide gauge records is suspect. Namely, the quality of the Barentsburg tide gauge between 1992 and 2002 is probably poor, which is confirmed by the available station documentation. The Amderma tide gauge records from 1992 to 2010 demonstrate an unrealistic rate of sea level rise. Therefore one needs to be cautious when interpreting the tide gauge time series in the region.
 The PSD estimates obtained from the altimetry and tide gauge time series at two locations in the Norwegian (Andenes) and Barents (Honningsvag) seas have shown almost the same power at an annual frequency. This indicates that the seasonal cycle at these locations is well observed by altimetry and it is not strongly corrupted by possible aliasing from the residual tidal and high frequency signals. On the other hand, at Bugrino, located in the shallow part of the southeastern Barents Sea, the altimetry seasonal cycle has a greater power than the tide gauge seasonal cycle. This suggests that the altimetry data in this shallow region can be contaminated by the aliased signals.
 The seasonal cycle is the major signal in the monthly altimetry and tide gauge records. The annual maximum sea level variability with amplitude from about 7 to over 10 cm is observed over the deep parts of the Norwegian and Greenland seas and along the Norwegian and Russian coasts. The annual maximum sea level over most areas of the Greenland, Icelandic, and Norwegian seas occurs mainly in September. In the northern part of the Barents Sea and in the northwestern and central parts of the Kara Seas the annual maximum is observed in October, while in the southern part of the Barents Sea and in the western and eastern parts of the Kara Sea it is observed in November–December. We have compared the amplitudes and phases of the seasonal cycle of sea level estimated from the altimetry and tide gauge data. The amplitudes and phases are found similar at most locations. The difference between the annual phases does not exceed 1 month. Analyzing the seasonal cycle in the altimetry and tide gauge records at lower latitudes, Vinogradov and Ponte  have reported the same difference. Along the Norwegian coast the annual phases are identical.
 The comparison of linear trends has revealed substantial differences at most locations that can be regarded as a measure of uncertainty. On the basis of the results of this study, we conclude that the sea level rise by 3–4 mm/year along the Norwegian coast is probably robust with an uncertainty of about 1–2 mm/year. On the other hand, the present rates of sea level change in the north of the Greenland Sea and in the coastal areas of the Barents and Kara seas remain largely uncertain because the signal-to-noise ratio is often less than 1.
 The comparison with surface drifter data has provided support for the realistic representation of surface circulation by satellite altimetry in the region. The general patterns of circulation observed by altimeters and drifters are similar. In most energetic regions the short-term variability is adequately resolved by the altimetry measurements. However, altimetry appears to somewhat underestimate the surface velocities. This is probably because the drifter data are not as much filtered as the altimetry data. The RMS differences between the drifter and altimetry velocities are comparable to earlier estimates for the World Ocean. They range from about 7 cm/s in the low variability regions to about 15–20 cm/s in energetic regions. We have demonstrated that drifter trajectories are in a good agreement with altimetric SSH and its mesoscale variability.
 In summary, in this paper we have provided a rather strong validation of a modern satellite altimetry gridded product in the Nordic seas. This means that this product can be successfully used to study the variability of sea level and surface circulation in the region. However, some limitations have to be taken into account. We have shown that in some coastal areas of the Kara Sea the agreement between the altimetry and tide gauge data is relatively poor. This can be partly due to the residual aliasing of the high-frequency sea level variability in altimetry data and needs to be further investigated. Caution is also required when analyzing linear trends obtained from both the coastal altimetry and tide gauge data. Regional (Arctic Ocean) tide models, as opposed to the global models used in the AVISO MSLA products, may possibly better correct for the tidal aliasing in altimetry data. Their potential use needs to be explored in the near future.
 This work was carried out at Jet Propulsion Laboratory, California Institute of Technology, within the framework of the project “Investigating the variability of sea level in the sub-Arctic and Arctic seas,” sponsored by the NASA Physical Oceanography program (award NNX11AE27G). The ERA-Interim and ERA-40 sea level pressure data are provided by the European Centre for Medium Range Weather Forecast (www.ecmwf.int). The authors thank C.K. Shum, an anonymous reviewer, and the editor A. Proshutinsky for their comments and suggestions.