The Danish National Space Center data set DNSC08 mean sea surface (MSS) is a new enhanced mapping of the mean sea surface height of the worlds oceans, derived from a combination of 12 years of satellite altimetry from a total of eight different satellites covering the period 1993–2004. It is the first global MSS without a polar gap including all of the Arctic Ocean by including laser altimetry from the ICESat mission. The mean dynamic topography (MDT) is the quantity that bridges the geoid and the mean sea surface constraining large-scale ocean circulation. Here we present a new high-resolution 1 min global MDT called DNSC08 MDT derived from the slightly smoothed difference between the DNSC08 MSS and the EGM2008 geoid. The derivation and quality control of the new DNSC08 MSS and DNSC08 MDT is presented in this paper along with suggestions for time period standardization of the MSS and MDT models. This way a consistent modeling of the interannual sea level variability is carried out before different MSS and MDT models are compared. Altimetric derived physical MSS can be converted into an “inverse barometer corrected MSS” by correcting the altimeter range for the inverse barometer effect of the atmosphere on the sea surface height. It is demonstrated that it is important to choose the right version of the MSS when comparing with hydrodynamic models and GPS measured tide gauges.
 The mean sea surface (MSS) is an important parameter in geodesy and physical oceanography. It is the time-averaged physical height of the oceans surface. In principle, a complete separation of the oceans mean and variable part requires uninterrupted infinite sampling in both time and space. The challenge in MSS mapping is to achieve the most accurate filtering of the temporal sea surface variability with a limited time span and simultaneously obtaining the highest spatial resolution. This is normally achieved by combining data from the highly accurate exact repeat mission (ERM), with data from the older nonrepeating geodetic mission (GM) like ERS-1 and GEOSAT.
 The MSS is the sum of the geoid height G and the temporal mean of the ocean dynamic topography (MDT)
where the MDT is the quantity bridging the geoid and the MSS and the quantity constraining large-scale ocean circulation. Consequently, a better estimation of the geoid and altimetric MSS is, in particular, expected to improve the determination of the mean ocean circulation [Wunsch, 1993; Wunsch and Gaposchkin, 1980].
 Whereas the MSS and the geoid vary up to ±100 m relative to the reference ellipsoid, the MDT only varies up to a few meters reflecting the steady state ocean circulation as well as and the oceans response to thermohaline expansion [Wunsch, 1993]. The ocean contains signals at nearly all timescales, and consequently any altimetric MSS will contain a small unwanted effect due to the incomplete temporal averaging. One example is the large El Nino signal in 1997–1998 which will affect altimetric MSS averaged across these data. Consequently, different MDT and MSS will be different, particularly, because of various temporal averaging of large ocean signals.
 Over the past decade several MSS models have been published. A summary of these is presented in Table 1. All of these MSS models are based on GM data from the ERS-1 and GEOSAT mission combined with ERM data from, i.e., T/P. Temporal averaging are based on less than one decade of altimetry, and spatially the models are limited to the south by Antarctica and to the north by the 80°N or the 82°N parallel, so none of these have complete global coverage. Most MSS have been derived using a remove-restore technique with respect to a global geoid model like, e.g., EGM96 [Lemoine et al., 1998].
 The Danish National Space Center data set DNSC08 MSS is derived independently of any geoid model except for the region north of 86°N where no altimetry is available. DNSC08 MSS is the first MSS to extend the temporal averaging to more than a decade and to extend the spatial coverage all the way to the North Pole and to include Jason-1 and Envisat radar altimetry as well as ICESat laser altimetry. The DNSC08 MSS and the associated DNSC08 MDT are derived on a global common 1 min resolution grid along with the DNSC08ERR interpolation error file reflecting the accuracy of the MSS. Altimetry does not support 1 min or 2 km spatial resolution with the densest cross-track and along-track spacing between observations being 6 km. Furthermore the interpolation suppresses wavelength shorter than roughly 15 km and a better proxy for the resolution of the MSS is 15–20 km. The 1 min grid is chosen to limit the loss of information in the interpolation and to ease the joint use of the suite of global DNSC08 fields (gravity, bathymetry, error, MSS, and MDT) by giving all on a common global grid.
2. DNSC08 Mean Sea Surface
 High-resolution MSS models are derived by merging several years of repeated observations from, e.g., TOPEX/Poseidon measured along widely spaced ground tracks with dense nonrepeating data from the GM. The MSS is generally derived by direct interpolation of the averaged sea surface height (SSH) observations or the along track SSH gradients using various sophisticated interpolation techniques [Andersen and Knudsen, 1998; Hwang et al., 2002; Hernandez and Schaeffer, 2000]. When interpolating SSH observations one must ensure consistency between ascending and descending tracks and between different satellites and missions. Any insufficient removal of these inconsistencies will lead to ground track related striation in the resulting MSS also called the orange skin effect [Knudsen, 1993].
 The DNSC08 MSS is based on data from a total of nine satellite missions (Jason-1, T/P, T/P interleaved mission, ERS-1 GM, ERS-2 ERM, Geosat GM, Geosat Follow On (GFO)-ERM, Envisat ERM, and ICESat). The various data sets along with their accuracy, spatial coverage and ground track spacing are shown in Table 2. The accuracy is determined from crossover inspection of the ERM tracks and from the 1 s standard deviation of the individual observations for the GM tracks. All altimetric data have been processed using, what is believed to be the best set of range and geophysical corrections. One is a slightly modified version of the GOT00.2 ocean tide model by Ray  called GOT00.2X. This model is spatially extended toward and onto the coast to avoid coastal observations being erroneous or edited out because of a lack of the ocean tide correction close to the shore.
Table 2. Summary of All the Data Sets Used to Compute the DNSC08 MSSa
Number of Years
Number of Repeats
Ground Track Spacing/Coverage
The accuracy reflects the a priori error used for the estimation. The ground track spacing is the distance between parallel tracks at the Equator and the coverage represent the maximum latitude reached by the satellite. EAPRS, Earth and Planetary Remote Sensing Laboratory.
 After the tidal effects, the next most rapid variations are due to the ocean reacting as a huge inverted barometer, coming up when atmospheric pressure is low, and down when pressure rise. The physical MSS measured by the satellite, can be corrected to reflect the mean pressure of the atmosphere creating an inverse barometer corrected MSS. The DNSC08 MSS is available as both a DNSC08 MSS-no inversion barometer (NIB) (true physical sea surface not corrected for inversion barometer (IB)), and as a DNSC08 MSS-IB (corrected using a global mean pressure of 1013 mbar [Dorandeu and Le Traon, 1999]).
 Depending on the application it is very important to choose the right MSS, as the difference ranges up to several decimeters, particularly in the Southern Ocean close to Antarctica. For most oceanographic purposes (like determination of geostrophic currents) the IB corrected MSS is preferred, but for comparisons with SSH determined from tide gauges or GPS heights, the NIB version of the MSS should be used.
2.1. Merging Various Satellite Missions
 The DNSC08 MSS has been derived using a two-step procedure in which the long-wavelength MSS is initially mapped from the temporally averaged ERM data. The long-wavelength MSS is subsequently used in a remove-restore way in order to map the shorter wavelength of the MSS from mainly the GM data. For the development of DNSC08 MSS we have deliberately chosen to avoid using a geoid model for the remove/restore process as this might constrain the MSS to the geoid. The two-step approach is important to handle the GM data and to limit the effect of unmodeled ocean signal adding to the “orange skin” effect [Rapp and Yi, 1997] as mentioned above. Finally, the two contributions are added to create the final MSS.
 The long-wavelength part of the MSS is based on the 12 years uninterrupted joint T/P+Jason-1 mean profile (NASA Pathfinder, version 13.1) to which all other satellites are referenced. Before merging the T/P+Jason-1 and the ERS-2 mean profiles systematic differences between the two data sets must be removed. This is caused by the sum of reference frame offsets, different orbits, different applied range and geophysical corrections and different time averaging periods and epochs [Fu and Cazenave, 2001; Andersen and Scharroo, 2009]. The differences were found by computing crossover differences between the two data set and the correction was computed by expanding the residuals to spherical harmonic degree and order 2–4 and adding this surface to the ERS-2 data set, hereby fitting ERS-2 to T/P+Jason1. The choice of harmonic degree and order 2–4 gave the best adjustment as shown in Figure 1. The 4 year GFO and 2.5 year mean T/P interleaved mission profiles were considered too have too short averaging period and hence not used as profile information at this stage, but were used as data between the mean profiles as described later.
 In order to provide uniform data coverage globally, additional data had to be added close to the Equator, where the cross-track distance between the ERM data is largest (Table 2), and at high latitude where the coverage of satellite data decreases (T/P+Jason-1 are absent above the 66° parallel and ERS-2 are absent above the 82° parallel).
2.1.1. Creating Uniform Data Coverage Close to the Equator
 Toward the Equator the satellite ground tracks are oriented increasingly north-south creating elongated diamond structures between the ground tracks without data (i.e., 80 km east west by 500 km north-south for ERS-2). Data have to be added into these diamonds in order to create uniform data coverage. This is particularly important in the Pacific Ocean where numerous sea mounts are found, as they contribute with amplitudes up to one meter to the MSS, and on so short spatial scale, that they might fall within the diamond structures.
 Data within the diamonds were obtained in the following way: A smooth MSS was created from T/P + Jason-1 and adjusted ERS-2 data. The GFO and T/P interleaved mission mean profiles along with GM data were adjusted to this surface by removing linear signals longer than 500 km and then averaged in quarter degree boxes. These where then added to the joint T/P and ERS-2 ERM data set but only within the diamonds structures.
2.1.2. Complimenting With Envisat Data at High Latitudes
 High latitudes are the most difficult regions for any MSS determination. The number of satellites decreases, as does the quality and spatial and temporal coverage of the data due to the presence of permanent and/or seasonal sea ice. Similarly, any mean sea surface will be biased toward the summer as seasonal coverage in sea ice limits data availability in winter.
Figure 2 shows the difference between the ERS-2 (left) and Envisat (right) mean profiles and the PGM04 geoid model in the Arctic Ocean. PGM04 is an unpublished precursor to the EGM2008 geoid model (N. Pavlis, personal communication, 2008). Large differences are seen in the Canadian Basin between the ERS-2 mean tracks and the preliminary PGM04 geoid. These differences are gone in the comparison with Envisat due to a better editing of these data. Consequently, the spatial extend of the MSS can be improved by adding in Envisat data. ERS-2 data are still preferred due to its longer time span, and Envisat data are only added in where ERS-2 data are considered problematic or missing. The improved spatial coverage is partly a consequence of the recession of the ice cover in the Arctic Ocean (i.e., 73°–75°N, 165°–180°E) during the last decade. Before substituting the Envisat data into the ERS-2 data set, a reference frame offset between the two satellites of 13 cm was added to the Envisat data. Envisat was primarily added in the Canadian Basin and east of Greenland, but also on the southern hemisphere around, i.e., the Ross Ice Shelf close to Antarctica.
2.1.3. ICESat in the Arctic Ocean
 ICESat laser altimetry is a new and complimentary data source to conventional radar altimetry [Zwally et al., 2002]. These data were used in the partly ice-covered parts of the Arctic Ocean (between 70°N–86°N, 100°E–270°E) and at latitudes above 80°N in all of the Arctic Ocean in order to extend the MSS toward the North Pole. The ICESat data were only used in partly ice-covered regions due to the short averaging period. Six repeats of each one month were taken from version 28 of the NESDIS data archive. All standard corrections including the saturation correction was applied to the data.
 For radar altimetry the 1 s average of all individual 18 SSH observations are used, but for ICESat a three point lowest-level mean value was implemented in order to take advantage of the narrow 70 m footprint of the laser and its ability to range to the oceans surface within open leads in the ice. Within each 1 s the 40 individual SSH observations were inspected and edited for outliers and the lowest-level mean was subsequently estimated as the mean of the three lowest values.
 Investigating the use of the 1 s mean observations within each second revealed a considerable height increase toward the northwest coast of Greenland compared with the lowest-level mean value. This corresponds to the well-known thickening of the sea ice in this region [Forsberg et al., 2007], which gives confidence that the lowest-level mean is a better proxy for the sea surface height and hence the MSS, than the 1 s mean values. In order to correct ICESat data for possible seasonal effects and pointing offsets each individual ICESat epoch was compared with the ERS-2/Envisat mean profiles. The mean of the six ICESat monthly epochs range between 10 and 40 cm below the corresponding Envisat mean height, and this offset was corrected as shown in Figure 3. Finally all six epochs were combined and quarter degree mean heights were computed and added to complete the data coverage up to 86°N.
2.1.4. Closing the Polar Gap
 The final step to close the Polar Gap is to fill-in MSS proxy data north of 86°N where no altimetry is available. This was done by feathering in the most recent Arctic geoid model (ArcGP.06) [Kenyon and Forsberg, 2008] in the following way. A preliminary MSS was calculated up to 86°N using the satellite altimetry data alone. Subsequently the difference between the MSS and the Arctic geoid was computed and the mean offset of 18 cm was removed. The residual grid was transformed into a regular grid in Polar stereographic projection enabling interpolation across the North Pole using a second-order Gauss Markov covariance function with a correlation length of 800 km. These residuals were then transformed back into geographical coordinates and quarter degree mean values were computed and added to the data set north of 86°N. These data were assigned a relatively low accuracy (20 cm) in order to ensure a smooth interpolation across the 86°N parallel (N. Pavlis, personal communication, 2008).
2.1.5. Computing the MSS and MDT
 Before merging the T/P+Jason-1 data with data from other satellite missions, the mean value were computed using a 4 parameter fit to the individual T/P+Jason-1 time series like
where ωann is the annual cycle. This simultaneous fits the mean height and the largest contributions to sea level variations, namely the linear sea level change over the 12 years (h1) and the annual cycle. For ERS-2 data only the mean value (h0) was fitted. This step is important in order to enable standardization of the time period for MSS models by accounting for different interannual ocean variability (section 2.3).
 The T/P+Jason-1, ERS-2 ERM mean profiles were merged with the 1/4° mean fill-in values and the long-wavelength MSS was computed on a 1/8° grid by interpolating the data using a second-order Gauss Markov covariance function with an correlation length of 200 km using the a priori standard deviations given in Table 1.
 The long-wavelength MSS is then used in a remove-restore way to introduce the ERS-1 and GEOSAT GM data. The ERS-1 GM data were double retracked using the rule-based expert retracking system by Berry et al. . Double retracking enhances the number of data by nearly 10%, particularly in ice-covered and coastal regions, by using multiple tolerant retrackers. The double retracking system and its importance to the quality of the geodetic mission data is described in more detail by Andersen et al. . The Geosat GM data were reprocessed and retracked by NOAA [Lillibridge et al., 2004]. Each 1 Hz GM data point was assigned an error corresponding to the 1 s standard deviation of the 18 or 10 Hz individual SSH observations for ERS-1 and Geosat, respectively.
 All available 1 s mean ERM and GM data were used to compute the high-resolution part of the MSS. Long-wavelength residual signal were initially removed by analyzing the data in 2° latitude by 10° longitude blocks with an overlay of 1° increasing the computational block size to 4° latitude by 12° longitude. In each block a crossover adjustment were carried out and each track was fitted to the long-wavelength MSS by applying a minimum variance criterion to avoid problems with rank deficiency. This procedure removes seasonal, orbital and all other long-wavelength signals. Subsequently, all data are interpolated onto a regular grid with a resolution of 1/60° using a refined second-order Gauss Markov interpolation technique with a correlation length of 12 km and a modified covariance function to account for small remaining correlated along track errors as described by Andersen and Knudsen .
 Finally the long-wavelength MSS were restored to complete the derivation of the DNSC08 MSS as shown in Figure 4 (top). It should be noted, that DNSC08 MSS is identical to DNSC07 MSS which was used for the computation of the EGM2008 global geoid model and the associated mean dynamic topography DOT08A to spherical harmonic degree and order 70 [Pavlis et al., 2008]. The correction for the inverse barometer effect was derived from the mean of the inverse barometer correction on T/P+Jason-1 and ERS-2 supplemented with IRI07 [Bilitza and Reinisch, 2008] values outside the 82° parallel and interpolated onto a similar 1 min as the MSS.
 The MDT is normally defined as the difference between the IB corrected MSS and the geoid (derived using equation (1)). An initial DNSC08 MDT was derived by differencing the DNSC08 MSS and the EGM2008 geoid. This grid was subsequently inspected for MSS or geoid outliers by inspecting all data within each 1 degree region using a mean and 3 times standard deviation of the local difference. The final DNSC08 MDT was finally created reinterpolating the edited data onto the same 1 min grid using a correlation length of 75 km in order to smooth the DNSC08 MDT slightly. DNSC08 MDT is shown in Figure 4 (bottom).
2.2. MSS and MDT Error Field
 The estimated DNSC08 MSS interpolation error is shown in Figure 5. The interpolation error is the combined error from the two steps in the development of the DNSC08 MSS. The global map shows the spatial variation of the error estimate with zones of higher and lower error correlated with the sea state. The interpolation error is on average around 6 cm globally. The error shows latitudinal variation with lowest values around the 65°parallel, where the density of the T/P + Jason-1 observations are highest.
 The actual MSS error is potentially somewhat larger than the interpolation error, as the actual error is a complicated combination of orbit errors and errors in various range corrections as well as interpolation errors. However, the validation with independent GPS leveled tide gauge data (described in section 3.2), shows agreement within the magnitude of the interpolation error indicating that this is a reasonably proxy. In the Arctic Ocean the presence of sea ice and shorter time spans of data will cause the error estimate to be somewhat larger.
 The error of the DNSC08 MDT can be combined from the error on DNSC08 MSS and the error associated with EGM2008. There is no actual error associated with EGM2008 geoid, but the error is believed to be better than 7–10 cm in the ocean [Pavlis et al., 2008], Therefore, the error estimate for the DNSC08 MDT will be around 9–12 as a rule of thumb.
2.3. Interannual Sea Level Variability
 Interannual sea level anomalies are computed by averaging all residual T/P+Jason-1 observations to DNSC08 MSS, within each year as shown in Figure 6 and interpolating these to a regular grid. The El Nino-La Nina pulsing of the central Pacific Ocean can be clearly seen in almost every year, but the strong El Nino in 1997–1998 is particularly striking.
 The sum of all twelve years interannual sea level anomalies adds up to zero. The mapping of the interannual sea level variability on annual scale is important to ensure that the differences between various MSS and MDT models do not reflect the different mapping of interannual sea level variability. This is, i.e., important when the altimetric MSS are compared with hydrographic and other MDT models which might be computed over shorter or longer periods (more in section 3.4).
3. Comparison and Validation
 Altimetric MSS models are very difficult to validate. This is because altimetry provides the most accurate SSH determination, and because nearly all available altimetric data have already been used in the derivation of the MSS. Consequently, altimetry does not provide independent validation, and comparison between MSS models and the mean profiles used to determine it, essentially only gives the reliability level of the estimation technique.
 We propose to validate the DNSC08 MSS in several independent ways. First, by inspecting the difference with another MSS model, second, by comparing the MSS model against MSS height estimates from tide gauges positioned using GPS and finally by comparing with independent altimetry data from the recently launched Jason-2 satellite as well as ERM data from the old ERS-1 satellite.
 MDT models, on the other hand, are easier to validate as these can be compared with hydrodynamic derived MDT models. The DNSC08 MDT will be compared with two different MDT models. One based on averaging a hydrodynamic model and one based on a combination of various oceanographic, geodetic and hydrographic data.
3.1. DNSC08 MSS Comparison With the CLS01 MSS
 One of the presently most widely used global MSS models is the CLS01 MSS model [Hernandez and Schaeffer, 2000]. This MSS model is based on 7 years of satellite altimetry covering the period 1993–1999. In evaluating the DNSC08 MSS it is interesting to examine the differences between these two independently derived MSS models. Scrutinizing the differences between the DNSC08 MSS and the CLS01 MSS in Figure 7 yields the following four dominating factors.
 1. A global bias between DNSC08 and CLS01 has been corrected using an inverse barometer correction with an average pressure of 1011 mbar (global ocean average pressure), instead of a constant pressure of 1013 mbar (global averaged pressure) [Dorandeu and Le Traon, 1999], for DNSC08 MSS. This generates a ∼2 cm height bias between the two MSS. This bias has been removed prior to creating Figure 7.
 2. Large-scale differences of the order of ±5 cm from east to west in the Pacific Ocean reflect interannual ocean variability that is averaged differently. The east-west dipole in the Pacific Ocean is largely caused by the influence of the large 1997–1998 El Nino on the 7 years CLS01 mean period (1993–1999) and on the 12 year DNSC08 MSS mean period (1993–2004). For more detail see Andersen et al. . This signal will also show up by summing the annual variability of the 1993–1999 period from Figure 6.
 3. Close to Antarctica and in the Arctic Ocean large white regions represent voids in the CLS01 MSS due to lack of data. In the DNSC08 MSS careful data editing and inclusion of Envisat and ICESat means that DNSC08 MSS has no significant voids.
 4. Altimetric related striation originates from a combination of different range corrections, different averaging periods and different interpolation techniques used. The difference between the two MSS models and the EGM08 geoid is shown along a west-east going profile in the Pacific Ocean at 10°N in Figure 8. Removing a 2° running mean to account for the smooth MDT signal yields a residual signal of 5.1cm for the CLS01 MSS and 2.8 cm for the DNSC08 MSS, which indicate, that the DNSC08 MSS is significantly smoother and closer to EGM2008. Recent investigation has shown that the striation is most likely due the way that sun-synchronous range corrections applied to ERS-2 data are averaged [Andersen and Scharroo, 2009].
3.2. Comparison With GPS Leveled Tide Gauges
 An independent validation of the DNSC08 MSS was made by comparing the DNSC08 MSS-NIB (No inverse barometer corrected MSS) with a large set of GPS leveled tide gauges around Britain. The NIB version of the DNC08MSS is chosen as the tide gauges measure the average of the physical sea surface in the presence of the atmosphere. A total of 320 GPS leveled tide gauges with more than one year of data were compared with the height interpolated or extrapolated from DNSC08 MSS. The mean height difference between tide gauges and DNSC08 MSS is 1.24 cm with a standard deviation of 6.3 cm. The differences are shown in Figure 9 as color coded dots.
 The height comparison between the MSS and the GPS leveled tide gauges had to be adjusted for the difference in the tidal system used to derive the two MSS height quantities. GPS data are processed in the tide-free system whereas the DNSC08 MSS is given in the mean tide system. The adjustment is given as closed formulas [Lemoine et al., 1998] and it ranges up to several decimeters from pole to pole. The MSS interpolation error given in Figure 5 is roughly of the same magnitude as the standard deviation with the tide gauge heights, which leads us to conclude, that the interpolation error is most likely a good proxy for the accuracy of the MSS.
 The largest height differences with GPS data are found in the Bristol Channel and in the Irish Sea where the differences range up to 80 cm. These differences can originate from both the tide gauges or from the DNSC08 MSS. It is most likely that they originate from the DNSC08 MSS, as several obvious reasons might explain these differences: First, the accuracy of the tide model will degrade close to the coast and unmodeled shallow water constituents might contribute up to several decimeter [Andersen, 1999]. Second, the altimetric observations close to the coast might be missing or heavily degraded and no altimetric data is generally available closer than roughly 5–10 km to the coast, which means that the comparison is generally based on extrapolated MSS values.
3.3. Comparison With Altimeter Data
 Whereas tide gauge data can be used to validate the MSS close to the coast, altimeter data still provide the most accurate SSH observations for global validation. In all comparisons we strived to use recent data from 2005 and onward, which are not included in the DNSC08 MSS determination. Furthermore, independent data from the ERS-1 ERM and the very recent Jason-2 missions have also been introduced for independent validation. A comparison with 10 random tracks each containing 3000 observations was used from each of the following satellite missions: T/P (7 years, 1993–1999), T/P interlaced (2 years, 2003–2005), Jason-1 (5 years, 2004–2008), Jason-2 (0.8 year, 2008), Envisat (5 years, 2004–2008), ERS-1 (4 years, 1995–1998), and GFO (4 years, 2004–2007). State of the art range and geophysical corrections have been applied to the observations as provided in the Radar Altimeter Database System (RADS) archive [Scharroo, 2003].
 The MSS are compared with both individual SSH observations as well as with mean profiles both in terms of height differences but also in terms of along-track slope differences. The results are summarized in Table 3 for the DNSC08 MSS with the value for CLS01 MSS given in brackets.
Table 3. Comparison Between the DNSC08 MSS and CLS01 MSS for Individual Sea Surface Observations, for Along Track Slopes of Individual SSH Observations, for Mean Profiles, and for Slopes of Mean Profilesa
SSH Observations SD (mm)
Slope of SSH Observations SD (mm/km)
Mean Profile Height SD (mm)
Slope of Mean Profile SD (mm/km)
Here SD is standard deviation and the values in parentheses are the comparisons between the DNSC08 MSS and CLS01 MSS.
T/P (7 years, 1993–1999)
T/P Interlaced (2.5 years, 2003–2005)
Jason-1 (5 years, 2004–2008)
Jason-2 (0.8 years, 2008)
Envisat (4 years, 2005–2008)
ERS-1 (3 years, 1992–1994)
GFO (4 years, 2004–2007)
 The difference with individual SSH observations describes the overall reduction of the observed SSH signal and the assumption is, that the lower the standard deviation of the difference, the more the SSH signal is reduced, and the more accurate the MSS model is. The comparison with mean profiles gives an estimate of the accuracy of the MSS interpolation procedure itself, but also the accuracy of the MSS model when compared with independent data like the Jason-2 and ERS-1 mean profiles.
 For nearly all comparison the DNSC08 MSS gives lower standard deviation than the CLS01 mean sea surface, indicating that it generates less residual, which is an indication of higher accuracy. The only exception is the comparison with the 7 years (1993–1999) of T/P data which shows better comparison with CLS01 with height differences of around 15 mm and better than 1 mm/km slope estimation. However, this period is exactly the averaging period of the CLS01 model and so it indicates that CLS01 was most likely fitted tighter to the T/P observations than the DNSC08 MSS. The comparison with Jason-2 shows nearly identical fits for both models with around 40 mm height difference and 1.5 mm/km along track slope difference. This is surprisingly good, as less than one year of Jason-2 data were available to derive the mean profile. The comparisons with Envisat, ERS-1 and GFO clearly favor the DNSC08 MSS. These discrepancies are significantly higher than the T/P and Jason-1 discrepancies, due to the fact, that many inaccurate high-latitude data are involved in this comparison due to the higher inclination of these satellites.
3.4. MDT Comparisons
 Several global MDT model are available for comparison with the DNSC08 MDT [Bingham and Haines, 2006]. Here we have chosen to compare three MDT models, which are very different in their origin and development.
 DNSC08 MDT is derived from 12 years satellite altimetry alone. The Ocean Circulation and Climate Advanced Modeling Project (OCCAM) MDT is derived from a three year (1993–1995) average run of the OCCAM hydrodynamic model [Fox and Haines, 2003] forced with wind stresses from the European Centre for Medium-Range Weather Forecasts (ECMWF), hydrographic data, and surface temperature relaxed to the Reynolds and Smith  climatology. RIO05 is a combined MDT derived from inverse methods combining the EIGEN-GRACE02S geoid, the CLS01 MSS, drifter and other hydrographic data [Rio et al., 2006] covering the seven years period 1993–1999.
 In order to ensure that the MDT models are referenced to the same period we use the fact that the temporal changes in the geoid heights are small [Chambers et al., 2004]. Consequently, changes in the MSS must be due to temporal changes in the MDT [Bingham and Haines, 2006] due to interannual ocean variability. Using equation 1 one get
Letting period 2 represent the 1993–2004 DNSC08 MSS period, and period 1 the period for OCCAM or RIO5, respectively, the interannual ocean variability in Figure 6 can be used to standardize the time period so the various MDT models represent the same temporal period and interannual variability.
 The OCCAM MDT adjusted to the 1993–2004 period computed like OCCAM (93–04) = OCCAM (93–95) + ΔDNSC08 MSS (96–04). ΔDNSC08 MSS(96–04) is the sum of the interannual sea level anomalies for the years (1996–2004) and the contribution/correction is shown in Figure 10.
 The difference between DNSC08 MDT and the OCCAM MDT referenced to 1993–2004 is shown in Figure 11. The difference seems to be a combination of long-wavelength errors, with a latitudinal pattern of highs in the western Pacific and Indian Oceans and lows at midlatitudes. The differences seem to be real oceanographic signal rather than random noise and indicate signal mismodeled by one or the two MDT models. The differences between RIO05 and DNSC08 MDT (not shown) also show real oceanographic signal, though slightly larger in the RMS. The fact that the differences seem to be caused by real oceanographic signal can be used to update and calibrate future MDT models. The differences are generally a little larger than the error estimate of DNSC08 MDT; however OCCAM and most other hydrodynamic MDT models are not provided with error estimates so it is difficult to judge exactly, how accurate the hydrodynamic models are. Comparing Figures 10 and 11 reveals that the differences between the MDT models are generally significantly larger than the corrections required to standardize the time period, so this correction will only affect the result slightly. However, in all comparisons the standardization of the time period improves the comparison.
 This can also be seen from Table 4 summarizing the comparison between the three models. The standard deviations with and without time period standardization) is shown above the diagonal, and below the diagonal the offset between the three models are shown. All comparisons presented in Table 4 were confined to regions with ocean depth greater than 1 km and all models were smoothed to a common 1 degree smoothing. The constant offset between the various models reflects the way these have been developed. The standard deviation between DNSC08 and OCCAM is only 11 cm which is believed to be very good and the difference is smaller than the differences between both DNSC08 MSS and OCCAM and the RIO05MDT which are around 14–17 cm. Similar numbers have recently been quoted in a comparison between 12 MDT models in the Atlantic Ocean by Bingham and Haines .
Table 4. Comparison Between the DNSC08 MDT, OCCAM, and RIO5 MDT Modelsa
Values above the diagonal show the standard deviation with and without time period standardization to the 1993–2004 reference period (without standardization is shown in parentheses). The globally computed offsets between the models are shown below the diagonal. All values are given in cm.
 In this paper the DNSC08 MSS mean sea surface and the DNSC08 MDT mean dynamic topography have been presented and their development described. The DNSC08 MSS is a new altimetric description of the averaged height of the oceans surface derived from a combination of 12 years of satellite radar altimetry from a total of 8 different satellites covering the period 1993–2004. The DNSC08 MSS is delivered on a 1 min grid and is the first MSS to includes all of the Arctic Ocean by including ICESat laser altimetry data and data from the Arctic Gravity Field project.
 A procedure was presented to standardize different MSS or MDT models to the same averaging period. This way the MDT from satellite altimetry can be compared with hydrodynamic derived MDT with consistent modeling of the interannual ocean variability. In all case the time period standardization improved the comparison slightly.
 A comparison between the DNSC08 MSS and 320 GPS leveled tide gauges along the coast of Britain showed a mean difference of 1.24 cm and a standard deviation of 6.3 cm. This comparison indicates, that the interpolation error ranging between 4 and 10 cm is a reasonably proxy for the accuracy of the DNSC08 MSS.
 Future improvements in altimetric derived MSS and MDT await longer time series and improved data quality, particularly in coastal and Polar Regions, which will be the key elements to future improvement. Data from a new geodetic mission satellite or from a satellite in a near repeat orbit [Smith and Scharroo, 2009] would also significantly improve MSS and MDT determination in the future.
 The authors would like to thank B. Beckley (NASA Goddard) for providing the NASA Pathfinder altimetry data, R. Scharroo (altimetrics.com) for maintaining the RADS archive and providing data, and P. Berry and J. Freeman (De Montfort University) for providing retracked ERS-1 GM data. The authors are also thankful to J. Lillibridge, W. Smith, and D. Sandwell (NOAA) for providing the reprocessed and retracked GEOSAT altimetry. N. Pavlis (NGA) and S. Homes (SGT) provided the PGM04 geoid model and the comparison with the CLS01 MSS. The comparison with 320 GPS tide gauges was kindly provided by J. Illiffe and M. Ziebert (UCL, London). The entire suite of DNSC08 fields (MSS, MDT, gravity, bathymetry, and interpolation error) can be downloaded from http://www.space.dtu.dk/ or mailed on DVD by request to the authors (firstname.lastname@example.org).