Barotropic and deep-referenced baroclinic SSH variability derived from Pressure Inverted Echo Sounders (PIES) south of Africa

Authors


Abstract

[1] The objective of this paper is to evaluate the baroclinic and barotropic components of sea surface height (SSH) anomalies in the Southern Ocean and investigates the causes for the weak correlation between hydrographically derived and satellite measured SSH anomalies. To this end, data obtained by six Pressure Inverted Echo Sounders (PIES) deployed south of Africa were used to derive baroclinic and barotropic SSH anomalies. Our results show that the barotropic component accounts for 30%–60% of the variability between the jets of the Antarctic Circumpolar Current (ACC). In contrast, the jets associated with the major ACC fronts are predominantly baroclinic. The deep baroclinic component is important in the ACC and accounts for the major part of the baroclinic variability. The comparison with along-track satellite altimetry (Jason 1/2) shows correlations coefficients of 0.24–0.92, with low values in regions of high-barotropic variability. The comparison with gridded Aviso satellite altimetry generally shows higher correlation coefficients (0.33–0.92) and lower root mean square (RMS) errors compared to the along-track product. In conclusion the barotropic SSH anomaly plays a major role in this region and has to be accounted for when assimilating SSH into ocean models. Due to their high-baroclinic component, the correct representation of the time and space varying ACC fronts seems to be crucial for the right SSH anomaly partitioning used for assimilation purposes. Gridded products, namely Aviso, seems to be more suitable compared to along-track products (Jason 1/2) in representing the variability of SSH anomalies.

1. Introduction

[2] Sea surface height (SSH) as it is commonly denoted in oceanography or dynamic topography (DT) as it is named in the geodetic community, is an integral property of the ocean's dynamic state. Its evolution in time reflects the interaction of various physical processes that work in the ocean ranging over periods from seconds to millennia and on spatial scales from millimeters to 1000s of kilometers (across ocean basins). The variability of the SSH, or Sea Level Anomaly (SLA), comprises a barotropic component (sea level fluctuations with no immediate density signature, such as additional ocean mass from melting glaciers) and a baroclinic part which is due to changes in temperature and salinity [e.g., Gill and Niiler, 1973; Fukumori et al., 1998]. SSH variability can be derived either from hydrographic data (moored instruments, Lagrangian floats or shipborn measurements) which are limited in time and space or measured directly from space using satellite altimeters like TOPEX/POSEIDON, Jason-1 or Jason-2.

[3] The global coverage of satellite altimetry and the high-temporal (10 days) resolution make altimetric measurements useful for assimilation into global ocean circulation models [e.g., Wunsch and Gaposchkin, 1980; Blayo et al., 1994]. However, space-borne measurements of SSH can not distinguish between the barotropic and the baroclinic components and are also limited in time/space resolution [e.g., Guinehut et al., 2006]. Dhomps et al. [2011] compared SSH anomalies measured from satellites and profiling Argo floats. Argo floats measure temperature and salinity profiles in the upper 2000 m and thus represent only the baroclinic SSH anomaly of the upper ocean. Dhomps et al. [2011] derived correlation coefficients in the order of 0.8 between satellite altimetry and Argo derived SSH anomalies throughout most parts of the Indian and Pacific Oceans. South of inline imageS the correlation coefficient decreases below 0.6. The regression coefficient shows a similar trend and decreases from 0.8 in the tropics to 0.3–0.4 in the Southern Ocean. Furthermore, Dhomps et al. [2011] showed that the correlation depends on the reference level used to calculate the SSH anomalies from Argo data. In the Southern Ocean, the correlation coefficients increase locally from 0.3 to 0.6 when the reference level from 700 to 1000 m. A further deepening of the reference level (e.g., to 2000 dbar in this study) is expected to capture more of the deep baroclinic signal.

[4] The discrepancy between the Argo derived SSH anomalies and the satellite altimetry can be explained by the deep baroclinic and the barotropic signals. Deep baroclinic signals can be addressed theoretically by using a deeper reference level, while barotropic signals can be measured by bottom pressure sensors. Baker-Yeboah et al. [2009] used pressure sensor equipped Inverted Echo Sounders (PIES) to investigate the baroclinic and barotropic SSH variability in the South Atlantic's Cape Basin. The correlation between the SSH anomalies derived from PIES and Aviso satellite altimetry products ranges from 0.66 to 0.97 with root mean square (RMS) difference between 5.6 and 9.0 cm. Furthermore, Baker-Yeboah et al. [2009] found that the barotropic SSH component accounts for 20% of the total SSH variance and can increase to 47% during large anomalous events, such as the passing of an Agulhas ring. The study was conducted in a region where Dhomps et al. [2011] found a correlation of 0.8 between Argo (baroclinic component) and satellite altimetry observations, whereas Baker-Yeboah et al. [2009] found correlations larger than 0.9 in most places when correlating the total (baroclinic + barotropic) PIES derived SSH anomalies with satellite altimetry. Thus, the addition of the barotropic component to the SSH anomalies substantially improves the correlations and consequently the understanding of satellite altimetry signals. The barotropic signal is expected to increase further to the South in the regime of the Antarctic Circumpolar Current (ACC) because high-baroclinic signals triggered by steep density gradients are only expected across the ACC fronts [Deacon, 1937; Orsi et al., 1995].

[5] Assimilation schemes [e.g., Fukumori et al., 1999; Cooper and Haines, 1996] use SSH anomalies as an additional constraint for ocean circulation models. Maes [1998] and Wenzel and Schröter [1995, 1998] showed the importance of the correction of the temperature and salinity fields when using SSH as an assimilation parameter. Other methods such as Representers [Bennett et al., 1996] or Kalman Filter e.g., Ensemble Kalman Filter [Evensen and van Leeuwen, 1996] or Singular Evolutive Extended Kalman filter (SEEK; Pham et al. [1998]) have successfully been used in the assimilation of SSH anomalies. Nevertheless, the region of the Southern Ocean remains a problem for common assimilation schemes [Fox et al., 2000; Ferry et al., 2007]. Ferry et al. [2007] separated the SSH anomalies into a baroclinic and a barotropic component by estimating their partitioning from an ocean model. The baroclinic part is then assimilated using the lifting-lowering method from Cooper and Haines [1996] while the barotropic part is assimilated using the approximation of Pinardi et al. [1995]. In the weakly stratified regions of the Antarctic and Arctic oceans, the method fails due to an incorrect partitioning of baroclinic and barotropic component. For this reason, the assimilation scheme projects mostly all SSH anomaly changes into the barotropic component. Fox et al. [2000] used a different approach to deal with this problem. They also use the assimilation scheme of Cooper and Haines [1996] but instead of partitioning the SSH signal into baroclinic and barotropic components they filter out the barotropic signal and assimilate only the baroclinic component. This method still showed weaknesses especially in the Southern Ocean where the density errors increased.

[6] Guinehut et al. [2006] already stated the importance of distinguishing between baroclinic and barotropic to correctly merge altimeter and in situ data in ocean models. They found correlation and regression coefficients between altimetry and in situ data which are as low as found by Dhomps et al. [2011]. Their outlook suggests a deepening of the reference level of the baroclinic mode to 1000 or 2000 m depth to achieve further improvements.

[7] Here time series of ocean bottom pressure and acoustic travel time obtained from PIES are converted into barotropic and baroclinic SSH variability using the Gravest Empirical Mode method [Meinen and Watts, 2000] and the hydrostatic equation. The baroclinic SSH component is calculated relative to a reference level of 2000 dbar. For comparison with the results of Dhomps et al. [2011] the baroclinic component is also calculated relative to 1000 dbar. Furthermore the total SSH anomalies derived from PIES are compared to the SSH anomalies measured by satellite altimetry. Two altimetry products are used for the comparison on the one hand the along-track product of Jason-1 and Jason-2 provided by the OpenADB data base and on the other hand the gridded ( inline image× inline image) multimission product provided by Aviso.

[8] The objective of this paper is to provide a better understanding of the baroclinic and barotropic SSH anomaly components across the ACC south of Africa. The baroclinic SSH anomaly is derived relative to the deep-reference level of 2000 dbar in this study. In previous studies, satellite altimetry is often compared to hydrographicly derived baroclinic SSH anomalies. This study will investigate the difference between correlating only baroclinic or total SSH anomalies derived from Pressure Inverted Echo Sounder with satellite altimetry.

[9] In this study baroclinic SSH anomaly is derived relative to the deep-reference level of 2000 dbar and further stated as baroclinic SSH anomaly without further comments on the reference level.

2. Methods

2.1. Data

[10] Along the Good Hope line [Swart et al., 2008] south of Africa an array of six Pressure Inverted Echo Sounders (PIES) have operated since 2003. Table 1 lists the individual PIES positions and deployment periods. The individual PIES were deployed at cross over points of the satellite altimeter Jason-1. Figure 1 shows the PIES' positions and the main fronts and current systems in the area. The northern end of the array is located in the path of Agulhas rings, while the center of the array is in the vicinity of the South Atlantic Drift [Stramma and Peterson, 1990]. The southern end is placed in the Antarctic Circumpolar Current (ACC). The ACC is defined between the Subtropical Front (STF) and the Southern ACC Front (SACCF) [Orsi et al., 1995]. In the observation area, the southern extent of the ACC is bounded by the Weddell Gyre. Klatt et al. [2005] observed this boundary at approximately inline imageS, about 170 km farther south than the southernmost PIES. The array covers most of the ACC including the Subantarctic Front (SAF) and the Polar Front (PF). These two fronts are associated with the major ACC transport [e.g., Peterson and Whitworth, 1989; García et al., 2002].

Table 1. Deployment Sites and Periods of the PIES
PIESLatitude (°S)Longitude (°W)Deployment Period
ANT 337.0912.764 May 2007–11 Feb. 2008
ANT 541.1309.9427 Jan. 2005–12 Feb. 2008
   13 Oct. 2008–2 Dec. 2010
ANT 744.6607.0828 Nov. 2002–27 Jan. 2005
   29 Jan. 2005–13 Feb. 2008
ANT 947.6604.2630 Jan. 2005–16 Feb. 2008
ANT 1150.2601.4219 Feb. 2008–6 Dec. 2010
ANT 1352.51−1.4025 Oct. 2006–10 Feb. 2008
 53.5200.0021 Feb. 2008–8 Dec. 2010
Figure 1.

Schematic representation of the main current systems in the deployment area of the PIES. Deployment sites of the PIES are marked by black dots. Black lines indicate the major fronts: Subtropic Front (SAF), Subantarctic Front (SAF) and Polar Front (PF) and Southern ACC Front (SACCF) [Orsi et al., 1995]. The gray-shaded area marks the area of the Antarctic Circumpolar Current (ACC) bounded by the STF and the SACCF. Indicated as gray lines are the 0, 1000, and 3000 m isobaths.

[11] PIES are deployed as free fall landers and measure ocean bottom pressure inline image and acoustic travel time inline image at intervals of 10–30 min. Acoustic travel time is the time an acoustic signal needs to get to the sea surface and back to the bottom. The raw data are processed with the PIES processing toolbox from the University of Rhode Island/ Graduate School of Oceanography (URI/GSO; Kennelly et al. [2007]) to remove outliers. The bottom pressure signal drift is corrected by using either a linear or an exponential fit depending on the appearance of the drift. The tides are removed from the bottom pressure signal using the empirical ocean tide model EOT08a [Savcenko and Bosch, 2008]. Furthermore, hourly means are derived for acoustic travel time and bottom pressure. The bottom pressure data are additionally filtered with an 100 h low-pass filter to remove fast barotropic waves other than tides (i.e., forced by the high frequencies of the wind). Hence, no separate correction for the inverse barometer effect is necessary.

Table 2. From the Cruises Below Profiles Deeper Than 2000 dbar and Along the Good Hope Line Are Used to Create the Lookup Tablea
ShipCruiseYearSource
  1. The cruises are conducted during austral spring, summer and autumn.

MeteorM11/51990WOCE Hydrographic Programme [2002a]
PolarsternANT-X/41992WOCE Hydrographic Programme [2002b]
PolarsternANT-XI/21993/1994Fahrbach [2010]
PolarsternANT-XV/41998Fahrbach and Rohardt [2007a]
PolarsternANT-XVI/21998/1999Fahrbach and Rohardt [2007b]
PolarsternANT-XVIII/32000/2001Fütterer and Rohardt [2007a]
PolarsternANT-XX/22002/2003Fütterer and Rohardt [2007b]
PolarsternANT-XXI/32004Arntz and Rohardt [2007]
PolarsternANT-XXII/22004/2005Spindler and Rohardt [2007]
PolarsternANT-XXIII/72006Rohardt [2009a]
PolarsternANT-XXIV/32008Rohardt [2009b]
Figure 2.

Gravest empirical mode lookup table for (a) temperature and (b) salinity. The three major fronts in this region, polar front (PF), subantarctic front (SAF), and subtropic front (STF) are indicated as black lines.

2.2. Gravest Empirical Mode

[12] Following Meinen and Watts [2000] the Gravest Empirical Mode (GEM) method was used to obtain temperature and salinity time series from acoustic travel time measurements. The GEM method projects the first dynamical or ”gravest baroclinic” mode, which is commonly used as a representation of the vertical ocean structure into baroclinic stream function space. The baroclinic stream function is a vertically integrated property like for example the acoustic travel time. The method is limited to regions where this projection is unique. In the Southern Ocean, GEM is feasible as there is a monotonic north-south gradient in temperature, which affects sound speed and acoustic travel time. The key idea behind GEM is to assign a unique temperature/salinity profile to each acoustic travel time measurement. To this end hydrographic profiles from 58 CTD (conductivity, temperature, depth, see Table 2) profiles along the Good Hope line and 126 temperature and salinity profiles from Argo floats (These data were collected and made freely available by the Coriolis project and programs that contribute to it, http://www.coriolis.eu.org) are used to create a temperature/salinity (T/S) look up table (Figure 2). The lookup table assigns a hydrographic profile to each acoustic travel time and is further used to attribute a temperature and salinity profile to each PIES travel time.

[13] Argo profiles cover the upper 2000 dbar only because of the limited profiling depth of the floats and were taken from an inline image wide corridor around the Good Hope line. Because the CTD profiles alone do not provide a suitable coverage of the T/S field below 2000 dbar the lookup table covers only the upper 2000 dbar. The variability of acoustic travel time below 2000 dbar was analyzed using the Finite Element Sea Ice Ocean Model (FESOM). FESOM [Sidorenko et al., 2011] shows a standard deviation of acoustic travel time below 2000 dbar in the order of inline image which is below the detection limit of the PIES ( inline image). Nevertheless, FESOM is a model and possibly underestimates the variability of acoustic travel time below 2000 dbar. Due to a lack of observational data this issue can not be clarified. All profiles were interpolated to pressure levels ranging from the surface to 2000 dbar at 25 dbar intervals. A smoothing spline was fitted to each pressure level of the lookup table to create a unique two-dimensional relation of travel time, temperature/salinity and pressure. Due to the smoothing process the lookup table only represents the gross features of variability in a region. The captured variance is an estimate of how much variance is represented by the lookup table. It is calculated as one minus the fraction of the squared standard deviations of the measurements used to create the lookup table minus the lookup table profiles ( inline image) and the standard deviations of the measurements ( inline image).

display math(1)

[14] The temperature lookup table captures over 90% of the variability (Figure 4) with a root mean square (RMS) error of inline image at the surface decreasing to inline image at 2000 dbar. The salinity look up table captures more than 90% of the variance above 600 dbar (Figure 3). Below 600 m the captured variance decreases to 47% at 1950 dbar. This drop in captured variance may be due to regional differences between profiles of similar acoustic travel time, containing either more saline North Atlantic Water (NADW) or less saline Antarctic Intermediate Water (AAIW) [e.g., Lynn and Reid, 1968]. As salinity has only a minor influence on sound speed (in contrast to temperature), salinity signals independent from temperature changes (NADW and AAIW being both near inline image) cannot be captured by the GEM look up table. The captured variance starts to recover below 1950 m and reaches 50% at the maximum depth (2000 dbar) of the lookup table. To provide an estimation of the lookup table error the RMS errors between the lookup table and the measurements used for its creation are derived. Figure 4 shows the RMS errors for the temperature and salinity lookup table. The RMS error decreases with depth for temperature from inline image to inline image and for salinity from 0.13 PSU at the surface to 0.01 PSU at 2000 dbar. The RMS errors are further used to estimate the SSH uncertainty caused by the lookup table (see Table 3).

Figure 3.

Root mean square (RMS) error of the temperature and salinity lookup table derived from the differences between the lookup tables and the measurements used for its creation.

Figure 4.

Percent variance of temperature (blue) and salinity (red) covered by the lookup table.

Table 3. Error Budget for the PIES Measurements
PIES Error BudgetMeasurement UncertaintyHeight Uncertainty (cm)
IB effect0.13 ms0.46
Travel time (low pass)0.08 ms0.28
Sea state0.05 ms0.18
Lookup table RMS 2,9
Pressure uncertainty0.7 dbar0.7
Pressure drift correction0.01 dbar0.01
Total 4.53

2.3. Sea Surface Height Anomaly

[15] Integrating the hydrostatic equation over depth leads to the following expression for baroclinic SSH anomaly inline image (derivation see Baker-Yeboah et al. [2009]);

display math(2)

[16] The geopotential height inline image is calculated from temperature (T) and salinity (S) profiles. Because the T/S-profiles from the GEM lookup table only reach 2000 dbar, the calculated geopotential height is relative to 2000 dbar ( inline image) in contrast to the study of Baker-Yeboah et al. [2009] who used a reference level of 4500 dbar. Looking at deep CTD stations of this region and the FESOM model it becomes apparent, that below 2000 dbar the variability of sound speed and hence the contribution to the variability of acoustic travel time is negligible. This fact substantiates the assumption that the geopotential height anomaly relative to the bottom ( inline image) is approximately the same as relative to 2000 dbar ( inline image). Furthermore, the geopotential height anomaly is calculated relative to 1000 dbar for comparison with the results of Dhomps et al. [2011].

[17] Concurrently, the barotropic SSH anomalies inline image (derivation see Baker-Yeboah et al. [2009]) are derived as follows:

display math(3)

[18]  inline image is the bottom pressure anomaly. The time mean was removed from the detrended and detided bottom pressure time series. The bottom pressure time series were detided by using the empirical ocean tide model EOT08a. The mean density of the water column inline image is defined as the potential density relative to 2000 dbar of deep water in this region ( inline image).

[19] The total SSH anomaly inline image is the sum of baroclinic inline image and barotropic inline image SSH anomaly (equation (4))

display math(4)

[20] Table 3 lists an estimated error budget for the PIES measurements and the conversion into SSH anomalies. The largest uncertainty is caused by the lookup table RMS (shown in Figure 3) which is consistent with the error budget found by Baker-Yeboah et al. [2009].

[21] The total variance is derived as the sum of the baroclinic and barotropic variance and two times the covariance between the baroclinic and barotropic component. To calculate the contribution (in percent) to the total variance the following equations are used for the baroclinic (Bc, equation (5)) and barotropic (Bt, equation (6)) part:

display math(5)
display math(6)

2.4. Comparison With Satellite Altimetry

[22] The SSH anomalies derived from PIES were correlated with SSH anomalies measured by the satellite altimeters Jason-1 and Jason-2 (in the following denoted by Jason 1/2). The data were downloaded from the OpenADB website (http://openadb.dgfi.badw.de/) provided by the German Geodetic Research Institute (Deutsches Geodätisches Forschungsinstitut, DGFI). The data are available along the satellite track and is provided with all atmospheric corrections (e.g., wet and dry troposphere, ionospheric effect,… Schwatke et al. [2010]). Furthermore, barotropic waves other than tides which are related o atmospheric surface pressure and wind stress forcing have been removed using the MOG2D model [Carrère and Lyard, 2003]. Jason-1 and Jason-2 have a repeat cycle of 10 days, but due to the fact that the PIES had been deployed at cross-over points two measurements are available within the 10 day repeat cycle. The data have been interpolated and resampled at 5 day regular time intervals. The 5 day regular time step allows an intercomparison between the PIES position (not shown in this study) although it holds the risk of aliasing effects. The PIES derived SSH anomalies are furthermore compared to the daily gridded ( inline image× inline image) Aviso data produced by Ssalto/Duacs and distributed by Aviso, with support from CNES (http://www.aviso.oceanobs.com/duacs/). The results of the two comparisons are checked against each other, although they are not performed at the same time step. This comparison gives an indication which data set better represents the variability in this area. It might be unfair with respect to the different time steps (daily along track and 5 day gridded data) but this would be restrictions/problems which arise for assimilation purposes too.

3. Results

[23] Figure 5 shows the measured acoustic travel times relative to a reference level of 2000 dbar. Indicated by black lines are the three major fronts of this region, Subtropical Front (STF), Subantarctic Front (SAF), and Polar Front (PF). The fronts were defined applying the hydrographic criteria of Orsi et al. [1995] to the lookup table. A general increase in travel time is seen from north to south. ANT 3 and ANT 5 are north of the SAF and show high-eddy activity indicated by features of extremely low-travel times. The PIES south of the SAF show lower variability of travel times.

Figure 5.

Acoustic travel time relative to 2000 dbar for all deployments between 2003 and 2010 with fronts indicated as horizontal lines.

3.1. Baroclinic and Barotropic SSH Component

[24] Table 4 lists the contributions to the total variability of the baroclinic (Bc), barotropic (Bt) part of the SSH anomalies and the total variability inline image derived from PIES. The contributions vary strongly not only between positions but also between the two reference levels chosen for calculating the baroclinic SSH anomaly. For all positions except ANT 7, the baroclinic component increases with deepening the reference level. The contribution of the baroclinic SSH anomaly is smallest at the positions ANT 9 and ANT 13 (both ACC) for both reference levels.

Table 4. Percent Variance Captured by the Baroclinic (Bc) and the Barotropic (Bt) Part of the SSH Anomaly and the Total Variance for the 2000 dbar and 1000 dbar Reference Level
 Reference Level (2000 dbar)Reference Level (1000 dbar)
PIESBc [%]Bt [%] inline image [cm inline image]Bc [%]Bt [%] inline image [cm inline image]
ANT 372.3227.6781168.9531.05690
ANT 589.6410.3616270.0329.9757
ANT 766.8633.142370.3329.6726
ANT 952.9047.102954.9845.0231
ANT 1171.7728.237676.8223.1791
ANT 1340.0060.001912.9887.0215

[25] The two longest coherent time series are recorded at the positions ANT 7 and ANT 13. At the position ANT 7 the baroclinic part dominates the variability while at the position ANT 13 the barotropic part is more pronounced. Figure 6 shows the Continuous Wavelet Transformation (CWT, Grinsted et al. [2004]) of the baroclinic (a) and barotropic (b) SSH anomalies at the position ANT 7 using a Morlet wavelet. For the baroclinic part the highest wavelet power can be found on semiannual time scales (90–180 days). The pronounced maximum on semiannual time scales is absent in the year 2005 where the highest significant signal is on monthly time scales.

Figure 6.

Continuous Wavelet Transformation (CWT) of (a) the baroclinic and (b) the barotropic SSH anomalies at the position ANT 7 using the Morlet wavelet. The contours show the power spectrum normalized by the variance. The black line indicates the 95% significance level.

[26] For the barotropic part of the SSH anomalies, significant maxima exists on monthly scales ( inline image days) but are less pronounced. An exception can be found in the year 2004 where the highest observed baroclinic signals are on time scales between 70 and 128 days. This signal vanishes in the ensuing years.

[27] Figure 7 shows the CWT of the baroclinic and barotropic signal at the position ANT 13. The strongest signal is at the annual cycle for both parts. Significant signals are observed on weekly to monthly time scales (8–30 days).

Figure 7.

Continuous Wavelet Transformation (CWT) of (a) the baroclinic and (b) the barotropic SSH anomalies at the position ANT 13 using the Morlet wavelet. The contours show the power spectrum normalized by the variance. The black line indicates the 95% significance level.

[28] In contrast to the CWT analysis of the baroclinic and barotropic PIES component, Figure 8 shows a CWT analysis of the gridded Aviso total SSH anomalies at the positions ANT 7 and ANT 13. The Aviso time series are longer compared to the PIES time series and hence resolve significant strong signal at interannual time scales at both positions. At the position ANT 7 significant variability is found on time scales of 30–1000 days whereas at the position ANT 13 variability is found on time scales of 16–800 days.

Figure 8.

Continuous Wavelet Transformation (CWT) of the gridded Aviso SSH anomalies at the positions ANT 7 (a) and ANT 13 (b) using the Morlet wavelet. The contours show the power spectrum normalized by the variance. The black line indicates the 95% significance level.

3.2. Comparison With Satellite Altimetry

[29] Figure 9 shows the SSH anomalies measured by the satellite altimeters on board Jason-1 and Jason-2 (blue) and the total SSH anomalies inline image derived from PIES. Table 5 lists the correlation coefficients of the total (R), the baroclinic ( inline image) and the barotropic ( inline image) SSH anomalies derived from PIES with total SSH anomalies from satellite altimeters Jason 1/2. All correlation coefficients are significant at a 98% significance level. Furthermore the regression coefficients for the total and baroclinic SSH anomalies and the RMS error are listed.

[30] The highest correlation coefficient between PIES and satellite altimetry is at the position ANT 3. This PIES is the northern most one, recording the highest amplitudes. The lowest correlation coefficient is found at the southern most position ANT 13. Generally, the correlation coefficient decreased with increasing southern latitude. The only exception is position ANT 11, which shows a correlation of similar magnitude to the one observed at the position ANT 5.

Figure 9.

Total SSH anomalies measured by satellite altimeters (Jason-1 and Jason-2, blue) and derived from PIES (red).

Table 5. Correlations Between PIES Derived and Altimetric Along-Track SSH Anomalies (Jason 1/2)a
PIESR inline image inline imageRegression (Total)Regression (bc)RMS Error(cm)
  1. a

    Correlation coefficients are derived for the total R, the baroclinic relative to 2000 dbar inline image and the barotropic inline image SSH anomalies. The regression coefficients were determined by a linear fit between altimetry and PIES derived SSH anomaly on the one hand for the total SSH anomaly and on the other hand for the baroclinic (bc) SSH anomaly. Furthermore the RMS error between the PIES derived total SSH anomaly and satellite altimetry was calculated.

ANT 30.920.960.510.580.4422.2
ANT 50.680.670.230.770.699.6
ANT 70.590.6700.290.37.7
ANT 90.660.630.410.610.384.7
ANT 110.660.700.380.820.627.0
ANT 130.240.080.220.250.065.6

[31] The correlation coefficient between the SSH anomalies measured by altimetry and the baroclinic SSH anomalies derived from PIES is in some cases (ANT 3, ANT 7 and ANT 11) higher than for the correlation between the total SSH anomalies. In contrast, at the southern most position the correlation with the baroclinic SSH anomalies is negligible.

[32] The regression coefficient of the total SSH anomalies varies between 0.25 and 0.82. Total regression coefficients are higher than 0.58 except ANT 7 and ANT 13. The highest value of 0.82 is observed at the position ANT 11 which also shows a high-correlation coefficient compared to the adjacent positions. The regression coefficient of the baroclinic SSH anomalies shows in principle the same characteristics as the regression coefficient of the total SSH anomalies but 0.08 to 0.2 smaller. The RMS error decreased from 22.2 to 5.6 cm from north to south.

[33] Table 6 lists the correlation and regression coefficient between the baroclinic SSH anomalies relative to 1000 dbar derived from PIES and SSH anomalies from Jason 1/2. This table is used for comparison with the study of Dhomps et al. [2011]. Table 7 lists the same parameters as Table 5 but for the comparison with the daily gridded ( inline image× inline image) Aviso products. Except for ANT 3 the correlation and regression coefficients increase while the RMS error decreases. Figure 10 shows the total SSH anomalies derived by Aviso and PIES. Compared to the Jason 1/2 (Figure 9) product the Aviso product appears smoother which is expected due to the gridding process. Figure 11 shows the comparison of the two data sets (Jason 1/2 and Aviso) depicted as a Taylor Diagram [Taylor, 2001]. It can be seen that the standard deviation of Aviso and Jason 1/2 from OpenADB at ANT 7 and ANT 5 is up to twice as high as the standard deviation measured by the PIES. For all other positions, the ratio of standard deviations is close to 1 or slightly below 1. For all positions except ANT 7 and ANT 13 the ratio of RMS error and standard deviation of the PIES measurement is below 1.

Table 6. Correlation and Regression Coefficients Between PIES-Derived Baroclinic SSH Anomalies inline image Relative to 1000 dbar and Altimetric SSH Anomaly (Jason 1/2)
PIES inline imageRegression (bc)
ANT 30.930.39
ANT 50.690.38
ANT 70.740.36
ANT 90.610.38
ANT 110.690.7
ANT 130.050.02
Table 7. Correlations Between PIES Derived and Gridded Aviso SSH Anomalya
PIESR inline image inline imageRegression (Total)Regression (bc)RMS Error (cm)
  1. a

    Correlation coefficients are derived for the total R, the baroclinic relative to 2000 dbar inline image and the barotropic inline image SSH anomaly. The regression coefficients were determined by a linear fit between altimetry and PIES derived SSH anomalies on the one hand for the total SSH anomalies and on the other hand for the baroclinic (bc) SSH anomalies. Furthermore the RMS error between the PIES derived total SSH anomaly and satellite altimetry was calculated.

ANT 30.920.960.520.580.4421.7
ANT 50.870.870.241.050.966.2
ANT 70.580.660.000.320.327.2
ANT 90.740.670.510.820.483.8
ANT 110.900.860.630.890.614.1
ANT 130.330.070.340.410.064.8
Figure 10.

Total SSH anomalies provided by Aviso (blue) and derived from PIES (red).

Figure 11.

Taylor diagram for the comparison of agreement of total SSH anomaly derived from PIES, measured by Jason 1/2 (dots) and the daily gridded SSH anomalies provided by Aviso (triangles). The colors indicate the different positions of the PIES. The green circles indicate the ratio of the RMS error and the standard deviation of the total SSH anomaly derived from PIES. The reference point marks the perfect agreement with PIES observations.

4. Discussion

[34] The PIES array across the ACC enabled us to investigate the baroclinic and barotropic contributions of the total SSH anomalies. Furthermore, a direct comparison with altimetry was performed to investigate if the addition of the barotropic component significantly increases the correlation between PIES's derived SSH anomalies and altimetry. The comparison was performed for two different altimetry data sets on the one hand for the along-track data of Jason 1/2 received from the OpenADB data base and on the other hand for the daily gridded ( inline image× inline image) Aviso product.

[35] Baker-Yeboah et al. [2009] showed that the barotropic component accounts for 20% of the total SSH variability while during extreme events this contribution reaches 47%. In contrast, this study found barotropic contributions of up to 60% farther south in the ACC. The increase of the barotropic component is observed south of the position ANT 7 and is only interrupted at the position ANT 11. This might be due to the ACC being organized in jets along the two major fronts (Polar Front (PF) and Subantarctic Front (SAF), e.g., Sokolov and Rintoul [2006]). The fronts are characterized by step-like density gradients [Orsi et al., 1995]. Hence, high-baroclinic signals are expected across the fronts. By applying the frontal criteria of Orsi et al. [1995] to the lookup table it is possible to assign a travel time to an individual front (black lines Figure 2). Using these travel time criteria it becomes obvious that the PIES ANT 11 is in the vicinity of the Polar Front (PF), explaining the high-baroclinic component at this position. In between the fronts the regime is highly barotropic.

[36] The reference level used to calculate the baroclinic SSH anomalies have a big influence on the contribution of baroclinic and barotropic SSH anomalies, especially in regions of low stratification [Dhomps et al., 2011] such as the regions between the ACC fronts. Dhomps et al. [2011] used a reference level of 1000 dbar whereas this study uses 2000 dbar. Except of ANT 7, the baroclinic component increases with deepening the reference level which implies that baroclinic variability is missing when using the shallower reference level. The strongest impact is seen at the position ANT 13 were the baroclinic component decreases from 40% to 13%. A similar strong decrease is observed at the position ANT 5, indicating that the passing Agulhas rings, which are responsible for most of the baroclinic variability have a pronounced deep baroclinic component. Furthermore, the correlation coefficient between PIES derived and altimetric total SSH anomalies are slightly increased by 0.1 using the deeper reference level. In contrast, the regression coefficient of the baroclinic component is significantly improved (up to 0.33) at all positions except ANT 7 and ANT 9 by deepening the reference level. This suggests that mainly the amplitude of the SSH anomalies are affected by a deeper reference level. An exception of this general behaviour is found at the position ANT 7, where the correlation and regression coefficients at the shallower reference level are higher. ANT 7 is in the vicinity of the South Atlantic Drift which is a region of cross-frontal mixing of Subantarctic and Antarctic Intermediate Water (AAIW) with subtropical waters [Boebel et al., 2003]. This mixing process is probably the reason for the poorly captured variance of the salinity lookup table below 600 m as noted in section 2.2. Hence, the decrease of the correlation and regression coefficient by deepening the reference level is caused by the inability of the lookup table to represent the mixing processes between AAIW and adjacent water masses like (e.g., NADW). This hypothesis is supported by a comparison of independent CTD data (not used for the lookup table) which shows the largest salinity differences below 600 dbar between inline image and inline imageS whereas the temperature difference is very small. Generally the correlation coefficient between the PIES derived baroclinic SSH anomalies (relative to 1000 dbar, Table 6) and Jason 1/2 observations are in the same order as found by Dhomps et al. [2011] but with lower regression coefficients except at position ANT 11.

[37] This study shows that a deepening of the reference level from 1000 to 2000 dbar increases the correlation between PIES and satellite derived SSH anomalies. A further deepening of the reference level of the baroclinic SSH anomalies might lead to a further increase in correlation. Due to the limitation of available deep CTD-data the lookup table can not be extended to greater depths and hence this assumption can not be proven in this study. Furthermore, the high-barotropic components in this region might suggest that a further increase of the correlation is more probable achieved by improving the barotropic signal.

[38] At the northern edge of the ACC (ANT 7), semiannual baroclinic variations were the most prominent signals in CWT analysis, while monthly variations are barotropic. The CWT at position ANT 13 shows the most prominent signal on annual and monthly time scales. The results of the CWT analysis are consistent with the findings of Vinogradova et al. [2007] who investigated the relation between SSH and bottom pressure using the MIT general circulation model. To investigate inter annual variability the time series obtained so far are too short, which might be overcome in future by extending the time series with new data. The CWT showed that the significant time scales of baroclinic and barotropic SSH anomalies vary with time and space. Hence, the partitioning of baroclinic and barotropic SSH anomalies also changes with time and space.

[39] The correlation coefficient of the total SSH anomalies observed by PIES vs. Altimetry decreases from North to South from 0.92 to only 0.24 for the Jason 1/2 product from OpenADB. The only exception in this trend is seen at the position ANT 11 and coincides with a high-baroclinic component compared to the adjacent positions. Interestingly the correlation of the baroclinic part is higher than the correlation with the total SSH anomalies at four positions (out of six, Table 5). This is unexpected because the satellite altimeter measures the total SSH anomalies and hence the correlation of the total SSH anomalies should be higher than the correlation with only the baroclinic part. It possibly indicates a more fundamental problem and could be caused by uncertainties in the correction of altimeter data and the small amplitude of the signal south of the Subantarctic Front which is close to the uncertainty of the method presented here (4.53 cm). That the correction of satellite altimetry plays a major role can be seen when computing the correlation coefficients between along-track Aviso data and PIES. These correlations are not only higher compared to the correlations with OpenADB but also lower than the correlations with the gridded Aviso product (Table 6). Further correlating gridded Aviso data and along-track OpenADB data results correlation coefficients of 0.75–0.89 for the positions ANT 3 to ANT 11 while correlation at the position ANT 13 is only 0.36. To investigate these differences is not an ambition of this paper but it gives a hint on the difficulties of processing satellite altimetry data.

[40] Oceanic tide corrections are applied to both satellite altimetry and ocean bottom pressure in the same way but different filtering methods are applied to remove barotropic waves. A 100 h low-pass filter is used to remove fast barotropic waves from the PIES data whereas for the Jason 1/2 data the MOG2D model [Carrère and Lyard, 2003] was used. Tests showed that using the MOG2D correction from the satellite data to correct the unfiltered PIES data lead to much smaller correlations between the two products. Hence, the filtering method was used also it holds the risk not having the optimal filter length. This probably causes differences in the barotropic components which are essential in the ACC region. Aliasing effects might be another reason for the poor correlation coefficient in the ACC region because variability is reduced by smoothing and filtering the data as reported by Byrne and McClean [2008].

[41] Figure 11 indicates that the PIES derived SSH anomaly is in better agreement with the smoothed Avsio product than the along-track product from OpenADB. The correlation coefficients range from 0.33 to 0.92 and are higher than 0.6 at all positions except ANT 13. Further the gridded Aviso products have a lower RMS error compared to the along-track product. In contrast in four (ANT 5,9,11 and 13) out of six cases, the Aviso product misses variability compared to the PIES derived SSH anomalies (see Figure 11). Comparing the CWT analysis of the gridded Aviso SSH and the PIES it be becomes obvious that the missed variability is at submonthly time scales. This might be caused by the uncertainties of the altimetry measurements which are close to the amplitude of the signal in this region. The uncertainty of the satellite signal depends on many factors, e.g., instrument errors or background model errors. The formal accuracy (globally averaged) of OpenADB along-track data is below 1 cm in the open ocean but might be much larger in the polar regions (personnel communication Roman Savcenko) due to position dependent accuracy of the individual corrections. Gridding the data smooths up variability but also errors which otherwise lead to smaller correlation coefficients and higher RMS errors. The gridding process smoothes out short-term variability which is hard to distinguish from noise in the Southern Ocean. A CWT analysis of the gridded Aviso data shows almost no variability below 1 month, which means that the satellite product would miss nearly the complete barotropic signal. Another issue might be the higher temporal resolution of the gridded data.

[42] It is potentially impossible to measure short-term SSH variability with both methods (PIES and altimetry) presented here because of their uncertainties. For assimilation purposes, it is at least under debate that in the Southern Ocean the along-track SSH product provides more trust able information compared to the gridded SSH product. Further investigations are needed to decide whether along-track or gridded SSH data is better for assimilation purposes. This study suggests that the gridded Aviso might be more suitable for the Southern Ocean because of its better agreement with the in situ measurements from PIES. This statement is only valid for the Southern Ocean and all error sources need to be taken in account judging this question.

[43] Our results show that the barotropic SSH component plays an important role in the Southern Ocean. But the contribution of the barotropic part is not monotonously increasing from north to south. It is interrupted by regions of low-barotropic variability associated with the oceanic fronts. Hence, the partitioning into baroclinic and barotropic SSH anomalies needs to be done in time and space. This should be taken into account when assimilating SSH anomalies into ocean models. But the position and movement of oceanic fronts in the Southern Ocean are not well captured in coarse resolution ocean models (e.g., ORCA2; Ferry et al. [2007]), hence this should be improved first (for example by increasing the models horizontal resolution) before deriving the partitioning of the SSH anomalies as done by Ferry et al. [2007].

5. Conclusion

[44] In the ACC the barotropic contributions can reach up to 60% of the total SSH variance. Highest barotropic contributions are found in between the jets of the SAF and PF whereas at the fronts the baroclinic contribution is dominant with 72%. The comparison with Jason 1/2 satellite altimetry shows high correlations of 92% and 67% in the northern part. Toward the South the correlations decrease to 24%–42%. In four out of six cases, the correlation with just the baroclinic SSH anomalies is higher than the correlation with the total SSH anomalies. This might be due to the different corrections applied to remove barotropic waves and the low signal-to-noise ratio in the Southern Ocean.

[45] The correlation coefficients between the gridded Aviso product and the PIES derived SSH anomalies are higher compared to the along-track product of Jason 1/2 and have lower RMS errors. This suggests that the gridded (rather than along-track) SSH anomalies are more suitable for assimilation purposes in the Southern Ocean, despite the fact the variability and errors in the gridded products are smoothed in the interpolation procedures used to generate these fields which may result in aliasing effects at mesoscale time scales [Xu et al., 2009].

[46] Continuous wavelet transformation shows that baroclinic and barotropic signals appear on different time scales which change with latitude and time. Regarding assimilation schemes our results imply that it is important to include a realistic partitioning into baroclinic and barotropic signals. Ideally information about this partitioning is gained from long-term hydrographic data such as PIES or moorings. The partitioning might vary in time due to the movement of the fronts.

Acknowledgments

[47] The authors wish to thank the three anonymous reviewers for their helpful comments which greatly improved the quality of the manuscript. This study was supported by the German Research Foundation (DFG) under grant SCHR 779/4-3 within the Special Priority Program SPP 1257 Mass Transport and Mass Distribution in the System Earth. Further the authors acknowledge the excellent support of the officers and crews of R.V. Polarstern during deployment and recovering of the PIES.

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