A gravest empirical mode (GEM) projection of temperature and salinity fields over the circumpolar Southern Ocean is presented and is used in combination with satellite altimetry to produce gridded, full-depth, time-evolving temperature, salinity, and velocity fields. Optimal interpolation of historical hydrography, including Argo floats, is used to produce GEM projections of the circumpolar temperature and salinity fields. Parameterizing these fields by dynamic height allows the use of altimetric SSH values from 1992–2006 to create synoptic temperature and salinity fields at weekly intervals on a ⅓° grid at 36 depth levels. The satellite-derived temperature and salinity fields generally capture over 90% of the property variance below the thermocline, with RMS residuals of 1.16°C and 0.132 in salinity at the surface, decreasing to less than 0.45°C and 0.05 below 500 dbar. The combination of altimetry with the GEM fields allows the resolution of the subsurface structure of the filamentary fronts and eddy features. Velocity fields derived from the time-evolving temperature and salinity fields reproduce the Antarctic Circumpolar Current (ACC) velocity structure well, and are strongly correlated (r > 0.7) with in situ measurements from current meters and drifters, with RMS velocity residuals of 4.8–14.8 cm−1 in the Subantarctic Front.
Observations of the Antarctic Circumpolar Current (ACC) and Southern Ocean are in general extremely sparse in time and space. While the Argo program has dramatically improved the in situ coverage of the Southern Ocean, this dataset only exists from 2002 onward, and the spatial resolution at any instant remains relatively low. This low resolution at depth restricts the observational analysis of subsurface ACC variability to hydrographic sections, and basin- or circumpolar-scale studies of subsurface variability are largely model based. In contrast, surface variables, notably temperature and sea surface height (SSH), have been well observed in space and time through the use of satellite observations. It is possible, however, to extract substantial information on the subsurface structure by taking advantage of the close relation between subsurface density profiles and surface proxies, such as dynamic height, that exists in the Southern Ocean (Rintoul et al. 2002; Sokolov et al. 2004) due to its strong vertical coherence and equivalent barotropic nature (Killworth 1992).
The gravest empirical mode (GEM) technique exploits this relationship to parameterize vertical temperature and salinity structures as a function of integrated water column density (e.g., dynamic height or acoustic travel time) and to assign a unique T–S profile to each vertical integral value (Meinen and Watts 2000). This parameterization works particularly well in regions of strong horizontal density gradients, and has been applied in the North Atlantic current (Meinen 2001; Perez-Brunius et al. 2004), the southwestern Japan/East Sea region (Mitchell et al. (2004), and the North Pacific (Nardelli and Santoleri 2005). The strong meridional density gradient and baroclinic variability of the ACC make it ideal for GEM applications (Sun and Watts 2001), and the GEM relation has previously been utilized near the World Ocean Circulation Experiment (WOCE) SR3 section to produce time series of vertical T–S profiles based on acoustic travel time data (Watts et al. 2001). The present study shows that it is possible to use the GEM relation to couple ACC temperature and salinity vertical profiles to altimetric SSH values, and therefore use SSH as a proxy to observe the time evolution of the subsurface T–S variability over the whole Southern Ocean domain, where altimetric records exist.
We describe the creation of circumpolar Southern Ocean GEM temperature and salinity fields that have a much higher longitudinal resolution than any previous study in sections 2 and 3, and we demonstrate that these fields may be combined with altimetric SSH measurements to create, for the first time, observational, gridded, four-dimensional fields of temperature and salinity around the ACC (section 4). We show that these fields have considerable predictive skill and accurately re-create in situ observations and may be used to estimate full-depth synoptic geostrophic velocity fields, which agree with in situ drifter and current meter velocity data (section 5). The results of the study as well as limitations and potential uses for this product, dubbed satGEM, are discussed in section 6.
a. The hydrographic data
The hydrographic profile data used in this study were obtained from the WOCE Southern Ocean Atlas Database (Orsi and Whitworth 2001) and the Argo Global Data Assembly Center. This atlas consists of measurements by ships of over 93 000 hydrographic bottle and CTD stations south of 25°S that have been quality controlled by comparison with nearby WOCE observations. From these data, profiles that extended from shallower than 100 dbar to deeper than 2000 dbar with at least 20 measurements in this range were selected and linearly interpolated onto 5-dbar intervals. The quality control process removed obvious outliers, leaving 16 432 complete profiles of both temperature and salinity.
There were 946 Argo floats found between 35° and 66°S from 2002 to 2006, with a total of 58 877 profiles. Only those profiles that had adequate vertical resolution in both T and S, had QC flags of 1, and reached a depth of at least 1900 dbar were used. The resulting 14 413 Argo profiles were interpolated onto 5-dbar intervals. XBT data were not included in the study, despite the potential to dramatically increase the number of temperature profiles in the upper ocean. This exclusion was made due to the lack of corresponding salinity observations to calculate dynamic heights, as well as potential biases in XBT records (Gouretski and Koltermann 2007).
The GEM projection in dynamic height space is ambiguous where different hydrographic profiles have the same dynamic height (Watts et al. 2001). This often occurs when significantly different water masses converge together or are in close proximity. For example, the water masses north of the Subtropical Front (STF) have significantly higher temperatures and salinities in the upper ocean than south of the front, but have overlapping dynamic height ranges relative to 2000 dbar. To avoid these ambiguities, all profiles north of the STF were excluded using the Belkin and Gordon (1996) definition of STF water (temperature and salinity at 200 dbar greater than 12°C and 35, respectively) reducing the total number of profiles available to 24 571.
As is typical for Southern Ocean observations, there is a substantial summertime bias in the historical hydrography. The data were therefore subsampled to include an equal number of observations in each month, leaving a total of 15 912 profiles, the distribution of which is shown in Fig. 1. The profiles that were not used to create the GEM fields (approximately 8600) were used as independent data for subsequent testing.
b. Altimetric data
The altimetric data used to create the satGEM (see section 4) was the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) updated delayed time map of sea level anomaly (MSLA; SSALTO/DUACS 2007). This product combines the gridded output of SLA from along-track altimetry from four satellite missions, significantly improving the mesoscale structure recovery from the data (Le Traon et al. 2003; Pascaul et al. 2006). The data are gridded onto a ⅓° Mercator grid and contain 728 weekly “snapshots” from 14 October 1992 to 20 September 2006. This dataset resolves 100-km wavelengths in the Southern Ocean and has variability at the 50-km scale, although with a reduced level of energy (Ducet et al. 2000; Morrow et al. 2004).
Because the MSLA only gives an anomaly, a mean dynamic topography (MDT) must be added to it to produce SSHs suitable for comparison with dynamic heights (Robinson 2004). The 2006 Commonwealth Scientific and Industrial Research Organisation (CSIRO) Atlas of Regional Seas (CARS; Ridgway et al. 2002) is used to create an MDT at 100 dbar relative to 2000 dbar. CARS is based on several datasets including Argo, the World Ocean Database 2001, WOCE Hydrographic Programme version 3 (WHP 3.0), and CSIRO data holdings, and was produced using a modified loess filter to map these data onto a regular ½° × ½° grid. This was in turn linearly interpolated onto the ⅓° Mercator grid of the AVISO altimetric data described above and added to the MSLA anomalies to produce a time-evolving dynamic topography over the domain. The monthly gridded 1° × 1° NOAA World Ocean Atlas 2005 (WOA05) temperature and salinity climatology was used along with the CARS atlas to compare with the satGEM fields (section 4d).
During the calculation of geostrophic velocities the, Rio05 MDT produced by the Collecte Localisation Satellite’s (CLS) Space Oceanography Division (Rio and Hernandez 2004) was used as an MDT rather than the CARS, which only includes steric influences on SSH. Rio05 was constructed by combining the EIGEN-GRACE 03S geoid with the Levitus climatological MDT as a first guess and was successively improved by adding barotropic influences diagnosed using inverse methods to combine the mean field with in situ hydrographic measurements and drifter velocities. The Rio05 MDT has been shown to be a significant improvement over other MDT solutions when compared to in situ observations, particularly in regions of high variability such as the ACC (Rio and Hernandez (2004). The Rio05 MDT (½° resolution) was interpolated onto the ⅓° MSLA grid and added to the MSLA anomalies.
3. Circumpolar GEM creation
To create the time-invariant GEM fields, objective mapping techniques (Betherton et al. 1976) were used to map the hydrographic temperature and salinities onto regular grids in longitude and dynamic height space on 36 depth levels, from the surface to 5400 dbar. This produces T–S profiles associated with a unique dynamic height at each longitude. The dynamic height (ϕ) was chosen relative to 2000 dbar such that
where δ is the specific volume anomaly (m3 kg−1) at some pressure p (dbar). This depth range captures much of the observed steric change (Morrow et al. 2008), allows for the use of Argo data and reduces the influence of the seasonal thermocline. A grid spacing of 0.01 dynamic meters (dyn m) and ⅓° of longitude was chosen to resolve the zones between the frontal features and to match the AVISO MSLA altimetric grid.
Due to the irregular distribution of data over the domain (Fig. 1), the objective mapping was carried out individually for each grid point and depth. This allowed the use of data-density-dependent length scales, to improve resolution in data-rich areas and to smooth data-sparse regions. The length scales would grow until either 150 data points were included in the objective mapping or a maximum longitudinal scale (15°) was reached. Length scales were strongly anisotropic, growing at a rate of 1° of longitude for every 0.01 dyn m, as the longitudinal covariance is much greater than in the dynamic height (approximately meridional) direction. The mean data value was then removed and a Gaussian optimal interpolation was performed on the data, using the data variance and a priori noise to establish a signal-to-noise ratio. The optimal interpolation was performed independently for temperature and salinity.
The maximum length scales and degree of anisotropy were chosen such that the RMS error of the total mapping to the original data points approached the global domain a priori error resulting from spatiotemporal aliasing of observations (Watts et al. 2001). The a priori noise was calculated assuming that the oceanic noise is uncorrelated and the minimum distance between stations is less than the signal correlation length (Bindoff and Wunsch 1992). The a priori error is then estimated as
where ϕ is the distance between stations i and j, and Ti and Tj are the temperatures at the respective stations. Distance in this case is the dimensionless value between two points in a normalized longitude, dynamic height space. The global a priori errors at 150 dbar for temperature and salinity are 0.46°C and 0.075, decreasing to less than 0.2°C and 0.028 below 500 dbar.
b. Correcting for the seasonal signal in surface waters
In the upper 200–300 dbar the residuals between the optimally interpolated GEM and the original data have strongly seasonal periodicity in both temperature and salinity. This was removed using the method of Watts et al. (2001). At each depth level down to 300 dbar the mean residual was calculated for each month and a seasonal curve fitted to the resulting values using a low-pass Butterworth filter (Fig. 2). This seasonal value was then subtracted from each observation and the GEM optimal interpolation was repeated, reducing the RMS residuals in the surface layer in temperature and salinity from 1.34°C and 0.108 to 0.90°C and 0.103, respectively. Parameterizing the seasonal cycle by dynamic height or latitude as well as time of year produced no significant improvement over this method.
c. The structure and residuals of GEM
A selection of meridional slices of the time-invariant GEM temperature and salinity fields is shown in Fig. 3. The GEM fields clearly re-create the important large-scale features of the ACC. For example, the circumpolar deep water progressively becomes cooler and fresher eastward from Drake Passage, and there is a strong Antarctic Intermediate Water (AAIW) freshwater tongue extending northward. Additionally, a temperature inversion exists south of the northern Polar Front (n-PF), and east of around 70°E there are regions of mode water extending to depth on the northern side of the Subantarctic Front (SAF). An important distinction of the GEM projection is that the dynamically interesting frontal regions of the ACC are stretched in this coordinate system, and therefore do not appear as sharp features.
The deviation from zero of the mean residual at each depth between the quality-controlled hydrographic data not used in the GEM creation (section 2a), and the collocated GEM temperature and salinity profiles, is very small, indicating that there is no mean bias between the GEM field and the independent hydrographic data (Fig. 4). While there are some extreme outliers, the RMS temperature residuals in the upper 300 dbar are small: between 0.25 and 0.90°C, dropping to less than 0.2°C below 500 dbar, and less than 0.1°C below 1000 dbar. These values are very close to the global a priori error. The RMS salinity errors range from 0.045 to 0.103 above 300 dbar, and from 0.025 to less than 0.015 below 500 dbar.
The percentage of the in situ variance of T and S captured by the GEM fields is defined here, as in Watts et al. (2001), as
where is the variance of residuals to the GEM and is the total variance of the hydrography. These variances were calculated on data binned by 5° latitude intervals and for each depth levels. The choice of zonal bins reduces the by reducing the strong meridional temperature and salinity gradients. For temperature, over 90% of the total variance is captured by the GEM fields near the surface, while below about 500–1000 dbar the value is close to 99% (Fig. 5). Less variances is captured near the northern and southern boundaries, but still remain typically over 90%. Slightly less of the salinity variance is captured, particularly at the surface, where less than 90% of the total variance is explained by the GEM, although 90%–99% is captured over the remainder of the depth range.
d. GEM agreement with hydrography and temporal coherence
Around the ACC, frontal positions (defined as high SSH gradient regions) are very closely associated with particular dynamic heights (Sokolov and Rintoul 2002, 2007, 2009a,b). We find that south of Australia (130°–160°E) fronts identified by their SSH gradient may be matched through the GEM to their traditional hydrographic definitions, and that this relationship is stable over the period of altimetric observations. We define fronts as local maxima in the altimetric SSH gradient (section 2b) of greater than 0.3 dyn m (100 km)−1. The frequency distribution of these steep gradients by altimetric dynamic height shows a distinctly peaked spectrum (Fig. 6a). The clearest of these peaks extends from 1.60 to 1.8 dyn m, with a maxima near 1.75 dyn m. In the GEM temperature field at the corresponding height range (Fig. 6b), we see the temperature increasing from 7° to over 8.5°C at 400 dbar. These values correspond to the hydrographic definition of the northern Subantarctic Front (n-SAF, 6°–8°C at 400 dbar) at the WOCE SR3 section given by Sokolov and Rintoul (2002). The other peaks in the distribution also occur at dynamic heights where the GEM temperature field matches the Sokolov and Rintoul (2002) hydrographic definitions of major fronts [from the north; northern Polar Front (n-PF): northern extent of the θmin = 2°C layer, central SAF (c-SAF), southern SAF (s-SAF): 3°C < θ < 6°C at 400 dbar, southern PF: southern extent of θmax = 2.2°C]. The presence of some steep gradients at points between these peaks is caused by eddies between fronts and periods or regions where multiple frontal filaments merge, such as is commonly observed between the s-SAF and c-SAF at the WOCE SR3 section (Sokolov and Rintoul 2002).
The clear correspondence between hydrographic features in the GEM fields and frontal peaks in the frequency distribution, despite the 14-yr time series and transitory, filamentary nature of the fronts south of Australia, indicates that hydrographic features are indeed strongly and persistently associated with a narrow range of dynamic heights. It also shows that the GEM fields accurately re-create the subsurface properties associated with these fronts as defined by high-resolution WOCE hydrographic sections.
4. Combining the GEM with satellite altimetry
In this section we combine the GEM fields with the altimetrically observed SSHs to produce time-evolving three-dimensional T–S fields. This is achieved by using the GEM fields as lookup tables for the vertical T–S profiles associated with the altimetric SSH observed at each latitude, longitude, and time in the altimetric record. We dub these time-evolving fields in latitude and longitude satGEM fields, to distinguish them from the static GEM fields in longitude–dynamic height space.
a. GEM baroclinicity and its application to the Southern Ocean
For the GEM fields to give meaningful estimates of subsurface properties when combined with altimetry, the changes in observed SSH in an Eulerian reference frame must be strongly correlated to steric changes in the water column. We define baroclinic (steric) changes to SSH as those resulting from density changes in the water column, as in Guinehut et al. (2006). In contrast, barotropic SSH variability is caused by alteration of the total mass of the water column, and does not necessarily modify the vertical T–S structure.
To test the correlation between the SSH and in situ steric anomalies in the Southern Ocean, mean dynamic heights at 100 dbar relative to 2000 dbar were calculated using the CARS climatology and linearly interpolated onto the positions of all available hydrographic T–S profiles from the altimetric period 1992–2006. The resulting CARS values were then subtracted from the in situ hydrographic data to produce steric anomalies and were compared with the AVISO altimetric SSH anomalies observed at the same position and time (Fig. 7). The fitted linear regression has the value
where error bars give 99% confidence intervals. Here, x is the altimetric SSH anomaly, and y is the in situ steric anomaly. The nearly 2:1 gradient is due in part to the limited range of depth integration (100–2000 dbar) of the in situ anomalies, while the satellite observes the anomaly due to the full-depth integration. This relation does not significantly change by region or latitude, and so for simplicity it was used over the whole domain where the GEM is considered to be valid. There is a strong, highly statistically significant correlation between the two datasets (r = 0.68 at greater than 99%) and the RMS residual between the steric anomaly and the SSH anomaly is 0.052 dyn m. This residual value represents the barotropic, or deep baroclinic, contribution to the SSH that is uncorrelated with the steric change in the upper 2000 dbar, as well as ageostrophic effects and errors associated with instrument noise in the altimeter, data processing, resolution, and interpolation of both the altimetry and MDT. Seasonal effects in the top 100 dbar not included in the steric height may also contribute to this difference. The correlation and RMS error are similar to values obtained over the rest of the globe (Guinehut et al. 2006). The strong correlation and relatively small residual, despite the number of possible confounding influences, indicate that baroclinic changes dominate SSH variations in the Southern Ocean. This suggests that altimetric observations may be used in combination with GEM fields to make estimates of in situ T–S profiles.
b. Combining the GEM with altimetry
To create the satGEM, the empirical relation between the collocated altimetry and hydrographic dynamic height anomalies is applied to the entire AVISO SSH time series and added to the CARS MDT, producing a dynamic height value at each altimetric latitude, longitude, and time point. For each geographic point and time then, the observed dynamic height can be referenced against the corresponding dynamic height and longitude of the GEM field (section 3), and the vertical T–S profile from the GEM field “inserted” at the latitude/longitude/time of the altimetric point. These steps are repeated over the full altimetric record, producing time-evolving, three-dimensional T–S satGEM fields. This process effectively uses the time-evolving altimetry to map the GEM fields back to geographic space. As the resulting satGEM T–S fields are seasonless, due to the seasonal signal removal during the original GEM creation process, the seasonal cycle in the surface 300 dbar is added back into the satGEM fields using the simple empirical model described in section 3b.
c. Residual differences to observations
Due to the additional errors associated with using altimetric estimates of dynamic height, the RMS error in the satGEM fields is larger than when using in situ dynamic height, particularly between 200 and 1000 dbar (Fig. 8). However, the RMS error is still relatively small, with values of 0.60° to 1.16°C above 300 dbar, decreasing to 0.45°C at 500 dbar, and to less than 0.11°C below 1500 dbar. Similarly, the salinity RMS is increased by around a third over the in situ GEM residuals, but remains below 0.132 at the surface, decreasing to below 0.03 below 1000 dbar. Despite this increase in residuals, the satellite-based GEM remains significantly more accurate on average than estimates based on the CARS climatology, with RMS residuals that are 10%–50% smaller below 200 dbar. This improvement in residuals over traditional climatologies such as CARS is even greater in regions where there is high mesoscale activity, as well as near fronts (see section 4d). The percentage of the latitude-binned zonal data variance explained by the satGEM fields is also reduced slightly in comparison to the static GEM, particularly on the northern boundary (Fig. 9). However, over all depths south of 52°S the satGEM fields still explain over 90% of the variance of the temperature data in zonal circumpolar bands. Again, less of the salinity field variance is described by the satGEM, but typically greater than 85%–90% is captured south of 55°S. North of this point the percentage variance described by the satGEM drops as low as 65%, perhaps reflecting greater barotropic variability on the northern edge of the ACC.
The spatial distribution of residuals for temperature and salinity at 200 dbar is shown in Fig. 10. Over most of the domain the residual values are small, although they tend to increase in frontal regions and where water masses meet, such as south of western boundary currents. These regions have the highest SSH variance in the domain, changing on short spatial and temporal scales, so part of the residual error is likely to be caused by changes unresolved or oversmoothed by the altimetry or MDT. Dynamic processes associated with eddy mixing or higher vertical modes not captured by the satGEM may be another cause of the larger residuals in these regions (see section 6).
d. Reconstructing synoptic hydrographic sections
We use the satGEM to re-create the T–S sections observed during the January–February 2005 occupation of WOCE section P16S (150°W) south of 48°S by the R/V Roger Revelle (Fig. 11). The satGEM temperature and salinity capture the primary features of the hydrographic section, including the sharp n-SAF and s-SAF at 51° and 53°S, respectively; the temperature inversion (n-PF); the SAMW north of the n-SAF; and the presence of the characteristic AAIW low-salinity tongue.
There are also some parts of the section where the satGEM temperature and salinity reconstruction do not work as well. The warm anomaly around 400 dbar at 55°S is only partially re-created by the satGEM, and the temperature and salinity gradients across the n-SAF are too weak, leading to a warm and fresh anomaly in the difference fields. Additionally, the shallowing of isotherms and isohalines north of 49°S is not well reproduced due to the density compensating water mass anomalies north of the n-SAF (Rintoul and England 2002). Finally, south of the n-PF, the satGEM field does not produce a cool enough Tmin layer. This is due to the inability of the simple seasonal model to reproduce the highly stratified seasonal summer warming south of the PF, resulting in an artificial warming of the Tmin layer.
Overall, however, the satGEM field does a very good job of re-creating the section. Below 200 dbar, the satGEM field explains over 90% of the temperature variance in the section, and below 300 dbar over 96% is captured (not shown). The satGEM salinity field has a lower level of skill in the surface layers but still describes over 90% of the variance below 300 dbar. The errors can be largely attributed to differences between the satellite-estimated dynamic height and the in situ value (Fig. 12). The altimetric dynamic height is generally smoother than the in situ values, and tends to underestimate the height north of 54°S, leading to warm anomalies in Fig. 11, and to overestimate it south of this point (cool anomalies). There is also a warm-core feature at 55°S in the hydrography that is not well resolved in the altimetry. The smoothness of the altimetry also leads to the weaker T–S GEM gradients across the SAF mentioned above.
Despite the oversmoothing, the top-to-bottom RMS residuals in T and S show that the satGEM-based fields capture the important frontal regions with significantly smaller (reduced by 25%–50%) temperature residuals than do either the monthly CARS or WOA05 fields (Fig. 13). As these steep gradients have strongly time-varying positions and occur over small regions, traditional interpolation in geographic space oversmooths fronts, resulting in greater residuals in frontal regions, as occurs here at the SAF and PF (48°–51°S and 53°–55°S, respectively).
5. Creating satGEM-based velocity fields
a. Method of calculating velocities
The time-evolving satGEM temperature and salinity fields result in realistic density fields, suitable for the calculation of geostrophic velocities. At each depth and time step, zonal (u) components of baroclinic velocity were calculated at the halfway point between latitudinal grid points, using the relation
where f is the Coriolis parameter, y is the horizontal distance between meridional grid points, and φ is the geopotential height anomaly referenced to the surface (Pond and Pickard 1983). This calculation was also performed for the meridional (υ) baroclinic velocity referenced to the surface at the longitudinal grid midpoints. The surface absolute geostrophic velocities calculated from the Rio05-referenced dynamic topography gradient were then added to the baroclinic velocities, thus obtaining absolute velocities at all depths. The use of altimetry in this way to obtain surface absolute velocities has been well demonstrated (Wunsch and Stammer (1998); (Leeuwenburgh and Stammer 2002), but by combining the surface velocities with the satGEM-derived baroclinic shear, the time-evolving baroclinic + barotropic geostrophic velocity is estimated for the full water column.
Immediately apparent in the satGEM velocity fields is the highly filamentary nature of the ACC (Fig. 14). High velocity (>0.5 m s−1) jets associated with fronts are found at all longitudes of the domain, extending along the zonal extent of the ACC. This filamentary nature is consistent with high-resolution modeling studies (Hallberg and Gnanadesikan 2006) and recent observational studies (Sokolov and Rintoul 2007). They are extremely variable and oscillate north and south, appearing and disappearing, such that high-velocity jets are not continuous around the globe. The topographic influence on the velocity field is apparent, and around regions such as Campbell Plateau and the Falkland Islands the current jets are persistent in time and space, while over flatter topography, such as east of Kerguelen Plateau, the jets meander considerably. Also obvious in the velocity field is the presence of mesoscale eddies. These rings are clearly observable in the time series and extend to below 1500 dbar.
The mean meridional structure of the ACC velocity field tangent to the local mean dynamic height contour, averaged circumpolarly and in time (Fig. 15), shows that the average velocity is eastward everywhere shallower than 3000 dbar, and there is a clear surface maximum in the central core of the ACC at around 1.35 dyn m. The velocities are similar in magnitude to those observed in model studies in similar coordinate frames (Ivchenko et al. 1996; Best et al. 1999; Treguier et al. 2007), although the fixed contours of integration cause the mean velocity to be substantially smaller than the instantaneous jet velocities shown in Fig. 14. Despite this artifact, the averaging along mean contours still captures the multifrontal nature of the ACC. There are two broad current cores associated with the n-PF (1 dyn m) and the c-SAF core at around 1.35 dyn m, and smaller cores occur at 0.75 m (s-PF), 1.1 m (s-SAF), and 1.6 m (n-SAF). The circumpolar average means that these values do not all exactly match those identified south of Australia in section 3d.
b. Comparison to Argo velocity estimates
To estimate the satGEM skill at estimating synoptic velocities, we compare the satGEM velocity field against the subsurface velocities in the Yoshinari–Maximenko–Hacker 2007 (YoMaHa’07) dataset, inferred using a simple difference method applied to Argo floats (Lebedev et al. 2007). We interpolate the satGEM gridded u and υ velocity field to the position and time of each Argo drift velocity in the Southern Ocean during the altimetric period at the parking depth of the float. This gives 27 323 collocated velocity estimates at parking depths ranging from 400 to 2000 dbar.
There are high degrees of correlation between the inferred Argo u and υ velocity components and the satGEM velocity field (Fig. 16). This is particularly the case in the Indo-Pacific and much of the Atlantic sectors, where the coefficients for the u and υ components are generally greater than r = 0.7. Elsewhere, there is still good agreement, except in the eastern Pacific north of the SAF, where the values are low or not statistically significant. When separated by parking depth (Table 1), the u component correlation coefficient ranges from between 0.50 at 1500 dbar to 0.71 at 400 dbar (0.60 circumpolarly). The υ component is slightly less well correlated and ranges between 0.42 and 0.57 with a circumpolar value of 0.53. There does not appear to be any obvious relationship between the depth of the floats and the degree of correlation. The RMS difference between the satGEM velocities and the Argo floats varies from 15.8 cm−1 at 400 dbar to 6.5 cm−1 at 1000 dbar and these residuals are larger in regions where the correlation coefficient is lower, including Campbell Plateau, the Patagonian Plateau, and around Kerguelen Island (Fig. 16c). All of these areas have fast current jets that are strongly topographically steered.
Up to 60% of the residuals between the satGEM and YoMaHa’07 dataset in the u component of velocity, and slightly less for the υ component (see the appendix). can be attributed to observational aliasing. The Argo data in the Southern Ocean have an average distance between fixes of 58.23 ± 53.78 km. Because this distance is substantially greater than the first baroclinic Rossby radius of deformation in the Southern Ocean [10–20 km; Chelton et al. (1998)], it is likely that the Argo float will not travel in a straight line between the two points, and the actual velocity vector at a point half way between the two surface locations is unlikely to point exactly along the straight line between them. Around Kerguelen Plateau, this aliasing of the velocity fields by the Argo sampling frequency is shown in the appendix to result in RMS residuals of around 4 cm−1 at 1000 dbar. This aliasing increases the residuals and decreases the correlation coefficients between the actual and estimated velocity components in regions of high mesoscale activity, meaning the satGEM is a better estimate of in situ velocities than is implied by comparison with Argo drift.
c. Comparison to SAFDE current meter data
A more precise, but spatially limited, test of the satGEM velocities is against data from three (south, central, and north) current meter moorings deployed south of Australia at approximately 51°S, 144°E during the Subantarctic Flux and Dynamics Experiment (SAFDE), between 1995 and 1997. The velocity data from the current meters have had tides removed, were corrected for mooring motion, and were low-pass filtered for frequencies greater than 14 days, to match the satGEM temporal resolution. At all depths there is good agreement between the satGEM and the current meter u and υ components of velocity (see Fig. 17 for the u components) with coefficients of between 0.68 and 0.89, and velocity magnitude RMS differences of between 4.8 and 14.8 cm−1, decreasing with depth (Table 2).
These values are generally slightly greater than the approximately 5 cm−1 RMS GEM-based residuals at the same array reported by Watts et al. (2001) when using in situ estimates of dynamic height rather than altimetric values. This increased error is due to confounding by barotropic and deep baroclinic effects, as well as the limited altimetric resolution of the array. However, the satGEM RMS error is still small in comparison to the current velocities observed in this region (frequently greater than 25 cm−1), and re-creates the direction and magnitude of the observations at all depths very well, while offering much greater spatial and temporal coverage.
6. Discussion and conclusions
We have presented a new gravest empirical mode projection for the Southern Ocean, constructed at substantially higher resolution than previous approaches. This immediately has useful applications as an alternate climatology, as projections in dynamic height space have much improved resolution in frontal regions, and reduce mapping noise due to frontal meandering and eddy shedding. A much greater amount of information, however, is gained by combining these time-invariant GEM fields with satellite altimetry to create time-evolving, full-depth temperature and salinity fields in geographic space at ⅓° resolution with weekly time steps. By including the synoptic frontal meandering and eddy shedding that dominate Southern Ocean variability, the highly filamented nature of the ACC is re-created in greater detail than in traditional spatially averaged climatologies, which tend to oversmooth fronts. The satGEM fields reproduce the T–S fields observed by hydrography to within 1.16°C RMS error at the surface, and significantly less at depth, and capture over 96% of the global variance in the historical hydrography below the thermocline. These fields are used to calculate geostrophic velocities and are shown to agree well with both localized current meter observations as well as circumpolar velocity estimates.
In addition to the obvious use of observing subsurface T–S properties and variability in regions not often occupied by hydrographic surveys, many other important oceanographic parameters may be calculated from these gridded datasets—notably mass, heat, and freshwater transports and their variability. Additionally, because of the synoptic nature of satGEM, the response of the subsurface ACC to changes in wind stress forcing may also be observed on a circumpolar scale.
Obviously, the satGEM product must be treated with caution, as there are inherent limitations in both the GEM fields and satGEM methodology. Most notable of these is the assumption that the thermohaline structure in dynamic height space is static, the choice of mean dynamic topography and the confounding influence of uncorrelated barotropic variations in the SSH field, such as may arise from ice-melt mass addition. Future work will investigate the degree to which the Southern Ocean GEM varies temporally and the influence this has on the bulk properties of the ACC. The satGEM is also limited by the spatial and temporal resolution of the satellite altimetry, which tends to smooth frontal and eddy features. Additionally, the satGEM requires that each dynamic height be associated with just one T–S profile at each longitude. This means that outside of strongly baroclinic regions with well-defined density gradients, such as the ACC or boundary currents, the usefulness of the satGEM approach is questionable. More subtle limitations also exist, notably the inability of the satGEM to reproduce higher-order vertical modes. These are important in introducing eddy “tilt” or asymmetries that allow net property transport across eddies, and by extension across closed circumpolar streamlines. Without these higher modes, satGEM eddies are strongly symmetrical and exhibit limited transport in a υ’θ’ sense.
Therefore, it seems likely that the GEM and satGEM will find their greatest use as climatologies to be subtracted from in situ observations to produce residuals caused by departures from an equivalent barotropic state, where dynamically interesting higher-order properties may be revealed. For example, the GEM may be subtracted from the historical hydrography to reveal diabatic temperature and salinity trends in dynamic height space, separating the observed warming (Aoki et al. 2003; Gille 2008) into diabatic components (the time evolution of the mean GEM) and the adiabatic change caused by the southward shift of fronts (Sokolov and Rintoul 2009b). The distribution of spatial residuals to satGEM may be used in a similar fashion to diagnose and possibly quantify regions of enhanced isopycnal mixing. The application of the satGEM velocity fields to in situ current meter observations may also reveal the degree and importance of higher baroclinic modes in driving divergent heat transport.
This work is supported by the Australian Governments Cooperative Research Centers Programme, through the Antarctic Climate and Ecosystems CRC. Additionally, we thank Rosemary Morrow and Jean-Baptiste Sallée for their useful comments and critiques. The altimeter products used in this analysis were produced by SSALTO/DUACS and distributed by AVISO, with support from CNES (http://www.aviso.oceanobs.com/en/data/product-information/duacs/index.html). This work was supported in part by the Australian Climate Change Science Program of the Department of Climate Change.
Argo Sampling Errors
To test the hypothesis that the sampling frequency of the Argo floats aliases drift velocities, we create artificial drifter tracks using the satGEM velocity fields around Kerguelen Island. A single snapshot of velocity is used for simplicity, rather than a time-evolving one. The drifter velocities and positions are calculated hourly and therefore closely approximate the “true” paths of Lagrangian particles moving through the laminar velocity field. To simulate the Argo sampling regime, we record the float positions at 9.5-day intervals, representing the float surfacing to communicate its position. These positions are then used to calculate drift tracks and velocities using the same difference method employed in the YoMaHa’07 dataset (Lebedev et al. 2007).
The resulting high- and low-frequency sampling drift tracks (Fig. A1a) clearly show that the lower-frequency sampling regime misses much of the path structure, particularly in regions where there are meanders (such as near 46°S, 76°E) or mesoscale eddies (Fig. A1b) and, consequently, has larger errors. The statistics (Table A1) support this, and we see that the drifter paths in the satGEM velocity field are on average 40.8 km longer than is implied by lower-frequency sampling for drifters at 400 dbar, and 12.1 km longer for floats at 2000 dbar. There are also large RMS differences between the implied velocity fields, and the low-frequency sampling regime has RMS velocity errors of up to 6.3 cm−1. The correlation coefficient between u and υ velocity components is lower for drifter tracks at shallower (faster flowing) depths (0.8), than at 2000 dbar (0.94), indicating that in regions of higher velocities, the disparity between the actual drifter path and the path estimated using the Argo sampling frequency is increased.