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    Std dev (cm) of 84-month interannual time series of pb from (a) satellite observations and (b) the state estimate. Fields range over the years 2005–11 and have been smoothed spatially using a 750-km Gaussian filter. White stars are shown at 49°S, 98°E in the AAB and 59°S, 251°E in the BB, which are local maxima of pb variability in the ECCO solution and are locations for time series and spectra shown in subsequent figures. Black contours denote smoothed depth values at intervals of 500 m.

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    Comparison of estimated vs observed interannual pb time series over 2005–11 (from Fig. 1). (a) The rms difference (cm) and (b) correlation coefficient between estimated and observed pb. Correlation coefficients are only shown if they are significantly different from zero at the 95% confidence level, which is denoted by the black dashed contours. White stars are as in Fig. 1.

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    Time series (cm) of interannual pb (red) and ζ (blue) over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Also shown is the Antarctic Oscillation index multiplied by a scale factor (gray) and the collocated time series of interannual pb based on GRACE data from Fig. 1 (black). In each panel, all time series are significantly correlated at the 95% confidence level.

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    (a) Std dev (kg m−2 s−1) of 240-month interannual time series of wind stress curl × (τ/f) from the state estimate. Wind curl time series range over the years 1992–2011 and have been smoothed spatially using a 750-km Gaussian filter. (b) Amplitude(s) of the gradient of H/f from the estimate. Prior to taking the amplitude, the vector components (H/f) have been smoothed spatially using a 750-km Gaussian filter. (c) Normalized ratio of std dev of × (τ/f) to |(H/f)| [i.e., (a) divided by (b)]. White stars in both panels are as in Fig. 1.

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    Time series (kg m−2 s−1) of interannual potential vorticity balance terms over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are time series for wind stress curl × (τ/f) (red) and the sum of the Jacobian terms J(pb, H/f) + J(P, 1/f) (blue). Also shown is the residual × (τ/f) + J(pb, H/f) + J(P, 1/f) (black).

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    Time series (kg m−2 s−1) over 1992–2011 of interannual Jacobian terms appearing in the potential vorticity balance, from the ECCO solution, at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are time series for the topographic term J(pb, H)/f (green), the β effect HJ(pb, 1/f) (magenta), and the baroclinic term J(P, 1/f) (gold). The sum of Jacobians J(pb, H/f) + J(P, 1/f) from Fig. 5 is reproduced in pale blue for reference. In both panels, the green, magenta, and gold curves sum up to the pale blue curve.

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    Power spectral densities of potential vorticity balance terms, based on Welch’s method using a Hamming window, and computed from detrended monthly time series over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are spectra for wind stress curl × (τ/f) (red), the sum of Jacobian terms J(pb, H/f) + J(P, 1/f) (blue), the baroclinic term J(P, 1/f) (gold), the topographic term J(pb, H)/f (green), the β effect HJ(pb, 1/f) (magenta), and the residual × (τ/f) + J(pb, H/f) + J(P, 1/f) (black). The 90% confidence interval of the spectral estimates is shown in the upper left. Gray vertical dashed lines mark the annual and semiannual periods.

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    (a) Smoothed H/f contours shown from H/f = −3 × 107 to −4 × 107 m s−1 (thin light gray curves); at intervals of 1 × 106 m s−1. Thick black curves emphasize the H/f = −3.3 × 107 and −3.6 × 107 m s−1 contours, which are the H/f bounds of integration for estimating bottom pressure; thick dark gray vertical bars are shown at 98° and 134°E as well as 251° and 271°E, which are the lon bounds of integration. Time series (cm) of interannual pb over 1992–2011 averaged along (b) 47°–52°S, 98°E (AAB) and (c) 45°–64°S, 251°E (BB) generated by the ECCO solution (red), estimated by integrating the wind stress curl between lon and H/f contours shown in the panel above (black) and by integrating the wind stress curl and adding the eastern boundary condition (blue).

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Interannual Bottom Pressure Signals in the Australian–Antarctic and Bellingshausen Basins

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  • 1 Atmospheric and Environmental Research, Inc., Lexington, Massachusetts
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Abstract

Analyses of large-scale (>750 km) ocean bottom pressure pb fields, derived from the Gravity Recovery and Climate Experiment (GRACE) and from an Estimating the Circulation & Climate of the Ocean (ECCO) state estimate, reveal enhanced interannual variability, partially connected to the Antarctic Oscillation, in regions of the Australian–Antarctic Basin and the Bellingshausen Basin, with pb magnitudes comparable to those of sea level and good correlation between the GRACE and ECCO pb series. Consistent with the theory of Gill and Niiler, the patterns of stronger pb variability are partly related to enhanced local wind curl forcing and weakened gradients in H/f, where H is ocean depth and f is the Coriolis parameter. Despite weaker H/f gradients, motions against them are sufficiently strong to play a role in balancing the local wind input. Topographic effects are as or more important than changes in f. Additionally, and contrary to the dominance of barotropic processes at subannual time scales, baroclinic effects are not negligible when balancing wind input at periods of a few years. Results highlight the emerging capability to accurately observe and estimate interannual changes in large-scale pb over the Southern Ocean, with implications for the interpretation of low-frequency variability in sea level in terms of steric height and heat content.

Corresponding author address: Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421. E-mail: rponte@aer.com

Abstract

Analyses of large-scale (>750 km) ocean bottom pressure pb fields, derived from the Gravity Recovery and Climate Experiment (GRACE) and from an Estimating the Circulation & Climate of the Ocean (ECCO) state estimate, reveal enhanced interannual variability, partially connected to the Antarctic Oscillation, in regions of the Australian–Antarctic Basin and the Bellingshausen Basin, with pb magnitudes comparable to those of sea level and good correlation between the GRACE and ECCO pb series. Consistent with the theory of Gill and Niiler, the patterns of stronger pb variability are partly related to enhanced local wind curl forcing and weakened gradients in H/f, where H is ocean depth and f is the Coriolis parameter. Despite weaker H/f gradients, motions against them are sufficiently strong to play a role in balancing the local wind input. Topographic effects are as or more important than changes in f. Additionally, and contrary to the dominance of barotropic processes at subannual time scales, baroclinic effects are not negligible when balancing wind input at periods of a few years. Results highlight the emerging capability to accurately observe and estimate interannual changes in large-scale pb over the Southern Ocean, with implications for the interpretation of low-frequency variability in sea level in terms of steric height and heat content.

Corresponding author address: Rui M. Ponte, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421. E-mail: rponte@aer.com

1. Introduction

Since its first orbit cycles in 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has been collecting gravity field data from which variations in the ocean mass field, or equivalently bottom pressure pb, can be derived at scales of a few hundred kilometers and nominal monthly sampling. The accumulating GRACE record, now more than a decade long, provides an unprecedented view of low-frequency pb variability on a global scale. Observed pb trends and interannual variability have been examined in the North Pacific (Song and Zlotnicki 2008; Chambers 2011; Cheng et al. 2013), the Mediterranean (Tsimplis et al. 2013), and globally (Johnson and Chambers 2013). The basic pb dynamics seem to involve wind forcing, as with the earlier analysis of the seasonal cycle by Gill and Niiler (1973) and Ponte (1999), and correlations with major climate modes such as the Pacific decadal oscillation and the El Niño–Southern Oscillation (ENSO) in the Pacific and the North Atlantic Oscillation in the Mediterranean. Similar conclusions are drawn by Boening et al. (2011) regarding a large pb anomaly observed over a period of a few months in the South Pacific.

In a recent comparison of GRACE and satellite altimetry strictly focusing on interannual periods, Piecuch et al. (2013) found that many extratropical regions contain pb fluctuations that are comparable in magnitude and correlated with variations in sea level ζ. Several such examples occur in the Southern Ocean, more specifically in extensive regions over the Australian–Antarctic Basin (AAB), southwest of Australia, and in the southeast Pacific sector or Bellingshausen Basin (BB), where elevated pb signals are observed (Fig. 1a). The reasons for the spatial structure of pb variability in the Southern Ocean and its relation to ζ remain an interesting issue, particularly in light of current efforts to understand what controls regional ζ fluctuations at low frequencies and to simulate and predict such variations.

Fig. 1.
Fig. 1.

Std dev (cm) of 84-month interannual time series of pb from (a) satellite observations and (b) the state estimate. Fields range over the years 2005–11 and have been smoothed spatially using a 750-km Gaussian filter. White stars are shown at 49°S, 98°E in the AAB and 59°S, 251°E in the BB, which are local maxima of pb variability in the ECCO solution and are locations for time series and spectra shown in subsequent figures. Black contours denote smoothed depth values at intervals of 500 m.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

In this regard, similar enhanced large-scale variability in ζ at intraseasonal periods (<6 months), of a strong barotropic nature, had been observed over some of these regions (Fu and Smith 1996), and a large literature exploring the relevant dynamics exists. Ponte and Gaspar (1999) discuss the weakened gradients in ambient potential vorticity (i.e., f/H with f being the Coriolis parameter and H the ocean depth), as well as the presence of closed f/H contours in both AAB and BB. Apart from the possibility of special, localized vorticity wave resonances (Fukumori et al. 1998), such conditions can allow for the amplification of the Sverdrup response (Koblinsky 1990). Webb and de Cuevas (2002a,b, 2003) and Fu (2003) favor an explanation of the enhanced intraseasonal variability that requires the neglect of f/H gradients in the dynamics, implying that wind curl fluctuations are dominantly balanced by changes in the relative vorticity of the flow or strong dissipation, but Vivier et al. (2005) still indicate a nonnegligible role of motions against the ambient vorticity gradient. Weijer (2010) discusses how topographic features of the AAB lead to an “almost-free” mode response, with mode leakage accounting for a good deal of the observed damping at intraseasonal periods.

Whether such dynamic regimes control the patterns of interannual pb variability seen by GRACE is a hypothesis worth investigating. As periods get longer, gradients in f/H, albeit weak but not zero, can become more efficient at controlling the dynamics. Possible modification of the low-frequency dynamics by baroclinic effects is also an issue (Gill and Niiler 1973). Such effects are typically neglected in potential vorticity equations of large-scale motions in the Southern Ocean (Fu 2003; Vivier et al. 2005). More generally, the relevance of the simplified pb dynamics discussed by Gill and Niiler (1973) and the ability of general circulation models to simulate the newly observed interannual pb fluctuations have not been investigated in detail.

In this paper, we examine the interannual pb signals in AAB and BB in the context of the overall pb variability in the Southern Ocean, using both GRACE data and a 20-yr state estimate produced by the Estimating the Circulation & Climate of the Ocean (ECCO) consortium (Wunsch et al. 2009). Details of the data and ECCO solution and the analysis methods used are described in section 2. A comparison of the GRACE and ECCO fields is carried out in section 3 to assess current capabilities for observing and simulating interannual pb signals. In section 4, we use the 20-yr-long ECCO fields to explore dynamics and mechanisms responsible for the enhanced pb variability at interannual periods present in AAB and BB. Results are summarized and discussed in section 5.

2. Basic methods and analyses

The primary data considered in this work are the latest Release-05 GRACE set of gravity field spherical harmonic coefficients, as provided by the three main processing centers at the GeoForschungsZentrum, the Jet Propulsion Laboratory, and the Center for Space Research (University of Texas). We confine our GRACE analysis to the period from 2005 to 2011 to avoid extended gaps and other issues affecting the quality of the data in the early years of the mission and to be concurrent with the ECCO state estimate described below. The monthly pb grids are derived from GRACE data using the postprocessing methods detailed in Quinn and Ponte (2008). Only a brief summary of the procedures is provided here. Values of the (2, 0) spherical harmonic coefficients are derived from the satellite laser ranging data and the geocenter motion not sensed by GRACE is taken from Swenson et al. (2008). Spatial filtering in terms of common destriping (Chambers 2006; Swenson and Wahr 2006) and 750-km Gaussian smoothing is applied. Analysis done with less smoothing (500 km) did not lead to any different results. Reduction of leakage from land hydrology signals is attempted based on the method of Wahr et al. (1998). Linear interpolation in time is used to fill any missing months and to adjust for some slight temporal irregularities in the GRACE nominal monthly sampling. As in Piecuch et al. (2013), we use the average of all three products for noise reduction.

For comparison with the observations and for the exploration of the dynamics underlying the observed pb variability in the Southern Ocean, we use the new-generation ECCO Central Production state estimate (ECCO, version 4, or ECCO.v4 for short) produced by Gael Forget at the Massachusetts Institute of Technology. A summary of the various solutions and corresponding methodologies pursued under the ECCO project is given by Wunsch et al. (2009), and recent analyses of version 4 output in other contexts have been pursued by Speer and Forget (2013) and Wunsch and Heimbach (2013a,b). The ECCO.v4 estimate examined here involves several improvements over previous versions, such as the full treatment of sea ice, a global grid that includes the Arctic, and representation of atmospheric forcing based on bulk formulae. As in previous efforts, the present solution is obtained by fitting the Massachusetts Institute of Technology General Circulation Model (MITgcm) (Marshall et al. 1997) to most available satellite and in situ datasets, as summarized in Wunsch and Heimbach (2013a), in an optimization procedure based on the method of Lagrange multipliers (Wunsch and Heimbach 2007). Closer fits to the observations are obtained iteratively by adjusting initial conditions (temperature and salinity), surface atmospheric parameters defining forcing boundary conditions (wind stress, precipitation, radiation, etc.), and internal model parameters as well (e.g., diffusion coefficients). As such, the optimized estimates represent true solutions to the primitive equations, as coded in the MITgcm, and obey exactly all implicit conservation principles of momentum, vorticity, and so on.

The ECCO.v4 estimate is provided on a grid with nominal 1° × 1° spacing but variable in latitude and decreasing to ⅓° near the equator. For comparison with the GRACE fields, ECCO.v4 pb fields are smoothed with the same 750-km Gaussian filter applied to the data. Two other important considerations are that 1) no pb GRACE data were used to constrain the solution examined here, which provides for an independent comparison between the two estimates, and 2) global means of both GRACE and ECCO.v4 pb smoothed fields are calculated and removed for each month, as these do not have any dynamical relevance and can also be corrupted by the assumption of a Boussinesq ocean implicit in the MITgcm formulation used in ECCO.v4. Throughout the paper, we work with pb values scaled by a constant factor = 10 000 kg m−2 s−2 (g is acceleration of gravity and ρ is water density), and results are given in units of equivalent centimeters of water. Basic time series are calculated monthly, but as the focus is on interannual periods, we remove a linear trend and use a low-pass, sharp cutoff Fourier filter to include only periods >1 yr.

3. Interannual pb signals in GRACE and ECCO

Estimates of interannual variability in the low-pass-filtered series of pb for the Southern Ocean are shown in Fig. 1 for both ECCO and GRACE based on the period 2005–11. Standard deviations range from a few millimeters to more than 1 cm, with close agreement in the spatial patterns and magnitudes displayed by GRACE and ECCO. As discussed in the introduction, there are two clear centers of enhanced energy in the AAB (approximately confined to the east of the Kerguelen Plateau and south of the Southeast Indian Rise) and BB (mainly to the east of the East Pacific Rise).1 Two other regions of higher variability are also seen in the Weddell–Enderby Basin (Piecuch et al. 2013). Besides having slightly higher “background” values in general, the GRACE fields show another spot of elevated energy east of Patagonia, in the area of the Zapiola Rise, which is missing in the ECCO solution. Although not the focus of our discussion here, this area is known to have strong high-frequency variability and complex dynamics involving eddy-driven circulations (Hughes et al. 2007; Weijer et al. 2007). Such variability is thus likely missing in the coarse-resolution ECCO estimate. In addition, it is also possible that some of the energy observed by GRACE is due to aliasing, as the model used by data processing centers to mitigate the effects of rapid (submonthly) pb variability is likely not able to capture the relevant eddy-driven dynamics of this region.

A more quantitative examination of the agreement between GRACE and ECCO pb interannual variability is provided by the root-mean-square (rms) differences and correlation coefficients shown in Fig. 2. The rms differences can be taken as representing the combined rms error in GRACE and ECCO, assuming their respective errors are weakly correlated. Compared with the standard deviations in Fig. 1, good signal-to-noise levels are particularly noticeable in the AAB and BB regions of enhanced pb variability, as well as in the Enderby Abyssal Plain, but weaker in the Weddell Sea. Significant correlations are present over broad segments of the Pacific and Indian sectors, and high values (~0.9) occur near the regions of largest variability in the AAB and BB. Consistent with the rms differences and inferred signal-to-noise ratios, poor correlation is found in the Weddell Sea and also in the Zapiola Rise region, and thus these regions are not discussed any further. Results in Figs. 1 and 2 provide confidence on the ability of GRACE and ECCO to observe and (independently) estimate interannual pb signals in places with enhanced signal amplitudes such as AAB and BB, which are the focus of analysis here.2

Fig. 2.
Fig. 2.

Comparison of estimated vs observed interannual pb time series over 2005–11 (from Fig. 1). (a) The rms difference (cm) and (b) correlation coefficient between estimated and observed pb. Correlation coefficients are only shown if they are significantly different from zero at the 95% confidence level, which is denoted by the black dashed contours. White stars are as in Fig. 1.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

To examine the relationship between interannual pb and ζ variability in the state estimate, Fig. 3 shows the respective 20-yr time series from ECCO for points with the largest variability in AAB (49°S, 98°E) and BB (59°S, 251°E). Fluctuations around ±3–5 cm are seen in both pb and ζ, with the series very well correlated. Although slightly smaller in magnitude, pb changes can account for a large part of the variance in ζ, as found also in the data analysis of Piecuch et al. (2013). Such relation between pb and ζ points to a mixture of barotropic and baroclinic dynamics acting in the regions of interest. Admittance calculations (not shown) indicate that differences in pb and ζ behavior get accentuated as frequency decreases, indicating progressively more important baroclinic effects at the longest time scales (e.g., Vinogradova et al. 2007).

Fig. 3.
Fig. 3.

Time series (cm) of interannual pb (red) and ζ (blue) over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Also shown is the Antarctic Oscillation index multiplied by a scale factor (gray) and the collocated time series of interannual pb based on GRACE data from Fig. 1 (black). In each panel, all time series are significantly correlated at the 95% confidence level.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

Also plotted in Fig. 3 are the GRACE pb series for the same AAB and BB locations, which show interannual variability consistent with the ECCO time series in the overlapping period. Given the similar behavior found between GRACE and ECCO pb fields in Figs. 13, in the remainder of the paper, we focus for the most part on analyzing the longer pb ECCO fields, which extend to 1992 and come with a complete state estimate that permits an exploration of the relevant dynamics.

4. Exploring the nature of pb signals

a. Relation to climate modes

The pb series shown in Fig. 3 for AAB and BB are significantly correlated, with a coefficient of −0.42. Such anticorrelation suggests a possible relation to large-scale climate modes of variability affecting the Southern Ocean. At higher frequencies, pb signals in the Southern Ocean have been tied to both the Antarctic Oscillation (AAO) (Hughes et al. 2003) and ENSO (Boening et al. 2011). Figure 3 includes time series of the AAO index (available at www.esrl.noaa.gov/psd/data/correlation/aao.data) as defined by Thompson and Wallace (2000). Correlation coefficients between the AAO index and pb are 0.49 and −0.63 for the AAB and BB series, respectively. The opposite sign of these correlations is consistent with the spatial structure of the AAO, which tends to show opposite polarity between the BB and AAB sites (Thompson and Wallace 2000) and could result in the anticorrelation of the respective pb series.

Similar analyses based on the multivariate ENSO index (MEI), obtained from the NOAA website (available at www.esrl.noaa.gov/psd/data/correlation/mei.data), yield statistically significant correlations for BB, but not for AAB. Partial correlation analysis shows that, for the BB region, the relation of pb fluctuations to the AAO is slightly stronger than with ENSO. In any case, although statistically significant, correlations with the AAO index or MEI are not near 1. Thus, a considerable part of the pb variability at interannual time scales seen in Figs. 13 is not simply related to either the AAO or ENSO, and other influences are also likely to be important.

b. Basic forcing and dynamics

The AAB and BB regions highlighted in Figs. 1 and 2 correspond approximately to those studied by Webb and de Cuevas (2002a,b), Fu (2003), Weijer (2010), and others regarding enhanced intraseasonal barotropic variability. Higher annual amplitudes in pb were also noted by Ponte (1999) and Vivier et al. (2005). The importance of wind stress curl forcing and bottom topography in shaping the annual and intraseasonal variability in AAB and BB has been stressed in these previous studies, and such factors are likely to play a role in the structure of interannual pb signals in Figs. 1 and 2.

To explore the dynamics quantitatively, we use the approximate equation originally derived by Gill and Niiler (1973) to describe large-scale seasonal pb variability in a stratified, variable depth ocean:
e1
Here J denotes the Jacobian, H is ocean depth, f is the Coriolis parameter, τ is wind stress, and
e2
is the potential energy, with g being the acceleration of gravity and ρ denoting density.

The dynamics in (1) and (2) represent a main balance between wind vorticity input and motions along gradients of H/f, with effects of baroclinicity represented parametrically by the term involving P. Similar equations are discussed in Ponte (1999) and Hughes (2008). Approximations in (1) involve neglecting several transient terms of order ω/f, where ω is frequency, as well as forcing by atmospheric pressure and freshwater flux, which is typically negligible compared to wind curl forcing at the scales of interest here. Ignoring for the moment the role of baroclinicity (P), at the local level (1) essentially represents a topographic Sverdrup balance as discussed by Koblinsky (1990) and many others in the context of barotropic vorticity dynamics. One expects pb variability to scale roughly with the magnitude of the wind curl. In addition, the importance of the J(pb, H/f) term is dependent on the magnitude of (H/f). Such a gradient can change substantially because of variable topography and act as a modifying factor on the pb response; for a given wind curl magnitude, locally driven pb variability will be amplified where (H/f) is small and vice versa.

Values of the standard deviation of the wind curl (only accounting for interannual time scales) and the amplitude of |(H/f)| are shown in Figs. 4a and 4b. Wind curl fields are based on ECCO-adjusted wind stresses, which are constrained to be close to both the original Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) fields and monthly scatterometer fields within expected uncertainties. Wind curl variability exhibits peak values in two broad regions generally overlapping the AAB and BB,3 thus suggesting that the more vigorous pb signals in those regions can be locally forced. In addition, these regions have relatively weaker values of |(H/f)| (Fig. 4b). The ratio of wind curl on |(H/f)| (Fig. 4c) indicates that AAB and BB regions are particularly prone to enhanced pb variability. However, not all regions with a large ratio in Fig. 4c have enhanced pb variability and vice versa (cf. Fig. 1), and actual pb behavior is dependent on other factors, including nonlocal forcing, spatial structure of wind curl variability, and baroclinicity, as implicit in (1) and illustrated in section 4d for the regions of interest in Fig. 3.

Fig. 4.
Fig. 4.

(a) Std dev (kg m−2 s−1) of 240-month interannual time series of wind stress curl × (τ/f) from the state estimate. Wind curl time series range over the years 1992–2011 and have been smoothed spatially using a 750-km Gaussian filter. (b) Amplitude(s) of the gradient of H/f from the estimate. Prior to taking the amplitude, the vector components (H/f) have been smoothed spatially using a 750-km Gaussian filter. (c) Normalized ratio of std dev of × (τ/f) to |(H/f)| [i.e., (a) divided by (b)]. White stars in both panels are as in Fig. 1.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

c. Local dynamical balances

Using the full 3D output from the ECCO estimate, one can calculate all the terms in (1) and assess how well the balance holds locally for the AAB and BB regions of focus here. Figure 5 shows time series of the wind curl and the sum of the Jacobian terms for the AAB and BB locations examined in Fig. 3. There is a very good balance over the full 20 yr examined, with the residuals being small compared to the variability in either term. Thus, for both sites, local wind vorticity input is for the most part balanced by motions against gradients of topography and planetary rotation and possibly by baroclinic effects represented in J(P, 1/f). These findings generally hold for broad areas surrounding the examined sites.

Fig. 5.
Fig. 5.

Time series (kg m−2 s−1) of interannual potential vorticity balance terms over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are time series for wind stress curl × (τ/f) (red) and the sum of the Jacobian terms J(pb, H/f) + J(P, 1/f) (blue). Also shown is the residual × (τ/f) + J(pb, H/f) + J(P, 1/f) (black).

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

The different Jacobian terms, associated with the effects of topography [J(pb, H)/f], planetary rotation or β effect [HJ(pb, 1/f)], and baroclinicity [J(P, 1/f)], are all important in contributing to the balance in (1), judging from the respective time series in Fig. 6. Topographic gradients play a major role, with J(pb, H)/f exhibiting the largest magnitudes in general and matching some of the largest fluctuations in the total Jacobian term (correlations of 0.89 and 0.87 for AAB and BB, respectively). Effects of β are generally smaller and at times opposite to the topographic effects, but correlations between those time series are weak and not statistically different from zero. The tendency for balancing behavior in β and topographic terms indicates that “free” oscillatory motions along H/f contours are part of the response and can become more apparent in periods of weaker local forcing (e.g., BB region for the period 2003–08).

Fig. 6.
Fig. 6.

Time series (kg m−2 s−1) over 1992–2011 of interannual Jacobian terms appearing in the potential vorticity balance, from the ECCO solution, at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are time series for the topographic term J(pb, H)/f (green), the β effect HJ(pb, 1/f) (magenta), and the baroclinic term J(P, 1/f) (gold). The sum of Jacobians J(pb, H/f) + J(P, 1/f) from Fig. 5 is reproduced in pale blue for reference. In both panels, the green, magenta, and gold curves sum up to the pale blue curve.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

Nonnegligible baroclinic effects are also apparent at the longest time scales in Fig. 6. In addition, there is a noticeable tendency for the P Jacobian term to lag the total Jacobian term for both AAB and BB sites. In fact, calculations of coherence between the J(P, 1/f) and J(pb, H/f) time series (not shown) yield high, statistically significant amplitudes at interannual periods with the baroclinic term lagging by ~90°. The coherence indicates a coupling of the two Jacobian terms in (1), and the quadrature phase relation is suggestive of a damping role for the baroclinic term in the topographic Sverdrup balance represented by (1).

For an assessment of the relevance of all terms as a function of frequency, Fig. 7 shows spectra of the time series in Figs. 5 and 6, using the full monthly resolution and covering periods from ~8 yr to 2 months. Wind curl forcing in both regions is close to white in frequency with an annual peak. Most other spectra are similarly flat, with the exception of the J(P, 1/f) spectra, which are clearly red and negligible at subannual periods. For the AAB series, the main balance implicit in (1) basically holds at scales from seasonal to interannual; the wind curl and the sum of the Jacobian terms have virtually identical spectra and are generally an order of magnitude above the residual spectrum, also shown in Fig. 7. The baroclinic term is the largest term balancing the wind at periods longer than approximately 4 yr, although there is considerable uncertainty in this cutoff period given the spectral uncertainties. Similar considerations apply to BB region, but worth noting is the lesser role played by the β effect relative to the topographic term at the longest periods, in comparison with AAB. In addition, at some frequencies (e.g., near annual) the topographic term is actually larger than the total Jacobian term, reflecting the tendency for compensation by the β term, as already noted in Fig. 6.

Fig. 7.
Fig. 7.

Power spectral densities of potential vorticity balance terms, based on Welch’s method using a Hamming window, and computed from detrended monthly time series over 1992–2011 from the ECCO solution at (a) 49°S, 98°E (AAB) and (b) 59°S, 251°E (BB). Shown are spectra for wind stress curl × (τ/f) (red), the sum of Jacobian terms J(pb, H/f) + J(P, 1/f) (blue), the baroclinic term J(P, 1/f) (gold), the topographic term J(pb, H)/f (green), the β effect HJ(pb, 1/f) (magenta), and the residual × (τ/f) + J(pb, H/f) + J(P, 1/f) (black). The 90% confidence interval of the spectral estimates is shown in the upper left. Gray vertical dashed lines mark the annual and semiannual periods.

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

d. Determining pb

Large-scale variability in pb can be diagnosed from (1) or, neglecting baroclinic contributions likely to be relevant only at the longest time scales as suggested by Fig. 7, from
e3
as done originally by Gill and Niiler (1973) for the North Pacific and North Atlantic. We assess how well (3) can approximate the full estimate of pb at AAB and BB sites by integrating over an area defined by relevant longitudes and H/f contours, as shown in Fig. 8a. As in Gill and Niiler (1973), integration is performed westward, from a longitude λe where local pb variability is relatively weaker, to the longitude of the sites with maximum pb variability analyzed in Figs. 6 and 7. Choice of H/f contours is somewhat arbitrary but consistent with the focus on large scales. The method provides estimates of average pb over the range of latitudes between the chosen H/f contours. The derived pb time series are shown in Figs. 8b and 8c together with respective ECCO estimates based on the full model dynamics.
Fig. 8.
Fig. 8.

(a) Smoothed H/f contours shown from H/f = −3 × 107 to −4 × 107 m s−1 (thin light gray curves); at intervals of 1 × 106 m s−1. Thick black curves emphasize the H/f = −3.3 × 107 and −3.6 × 107 m s−1 contours, which are the H/f bounds of integration for estimating bottom pressure; thick dark gray vertical bars are shown at 98° and 134°E as well as 251° and 271°E, which are the lon bounds of integration. Time series (cm) of interannual pb over 1992–2011 averaged along (b) 47°–52°S, 98°E (AAB) and (c) 45°–64°S, 251°E (BB) generated by the ECCO solution (red), estimated by integrating the wind stress curl between lon and H/f contours shown in the panel above (black) and by integrating the wind stress curl and adding the eastern boundary condition (blue).

Citation: Journal of Physical Oceanography 44, 5; 10.1175/JPO-D-13-0223.1

The pb series based in (3) are well correlated with full model estimates (0.8 for AAB and 0.96 for BB) and account for a good percentage of their variance (63% for AAB and 90% for BB). Considering only effects of “local” winds, that is, removing contributions from the boundary condition at λe, results in only slightly weaker correlations (0.78 for AAB and 0.92 for BB) and explained variances of 60% for AAB and 62% for BB. Thus, with just good knowledge of the wind fields, more than half of the variance in pb can be diagnosed using (3).

Despite the noted qualitative agreement, discrepancies between estimated and “true” pb series in Fig. 8 are clear. A number of factors can be involved. For example, evaluation of the local balance in (3) over the area considered in the AAB integral (not shown) reveals residuals at some places that are larger than those calculated for the specific site analyzed in Fig. 5. Even if the balance in (3) holds perfectly over the area of integration, in practice calculations may not be straightforward because of the convoluted nature of the H/f contours as in the BB (Fig. 8a) or because there is poor knowledge of the eastern boundary condition (Fig. 8c). The corollary is that either dynamical processes excluded in (3) are not negligibly small at least in some regions or the calculations of terms in (3) are uncertain and sensitive to detail, and thus only qualitative knowledge of pb can be obtained by the simplified diagnostics in Fig. 8.

5. Summary and discussion

The length and quality of GRACE measurements have begun to provide an unprecedented view of the large-scale pb variability at interannual scales. In particular, the observed pb fluctuations in various regions of the Southern Ocean are in good agreement with estimates derived from a recent ECCO solution that is not constrained by the time-dependent gravity observations (Figs. 1, 2). Convergence of these separately derived pb estimates provides new ground for improved knowledge of low-frequency pb fields in the future through the use of formal constrained optimization procedures, as initially attempted by Köhl et al. (2012) based on a previous GRACE data release of considerably lower quality.

Although formal data uncertainties, as derived by Quinn and Ponte (2008) and Siegismund et al. (2011) for earlier GRACE releases, have not been discussed here, the present results indicate that there is useful information in the most recent GRACE data at interannual time scales important for climate. Assimilation of GRACE data should thus lead to better understanding of processes contributing to low-frequency variability in ζ and steric height, with consequences for the determination of changes in ocean heat content and its vertical distribution, from near the surface to abyssal depths (Jayne et al. 2003; Piecuch et al. 2013). The availability of GRACE data in the Southern Ocean and other high-latitude regions covered by ice should prove particularly useful, given the lack of routine observations from satellite altimetry and Argo floats.

Both GRACE and ECCO pb fields show enhanced variability over several areas of the Southern Ocean. Exploration of the basic dynamics in the AAB and BB regions with particularly good signal-to-noise ratios confirms the expected role of local wind curl forcing and topography implicit in the simplified theory of Gill and Niiler (1973). The prevalent low-frequency dynamics in these regions follow a basic balance between wind input (partly connected with the Antarctic Oscillation) and motions along gradients of H/f, consistent with the findings of Vivier et al. (2005) based on vorticity analysis of a barotropic ocean, and does not seem to be dominated by transient dynamics and strong dissipation invoked to explain large intraseasonal barotropic variability in the Southern Ocean (e.g., Webb and de Cuevas 2003; Fu 2003).4 Also in contrast with intraseasonal variability analysis, baroclinic effects are found to become nonnegligible at interannual periods, pointing to the need for a full treatment of stratified dynamics if one wants good quantitative estimates of pb fluctuations at those time scales.

Although not the focus of analysis here, for the subseasonal periods shown in Fig. 7 baroclinic effects are clearly negligible and the term J(pb, H/f) retains its importance consistent with Vivier et al. (2005). The topographic Sverdrup balance between winds and J(pb, H/f) is, however, not as good, and other processes as considered by Webb and de Cuevas (2003), Fu (2003), and Vivier et al. (2005) are likely involved.

Besides dependence on time scale, the nature of dynamical balances can also depend on location. In other places of enhanced interannual pb variability, such as in the Enderby Basin, attempts to assess the balance in (1) yielded nonnegligible residuals (not shown). The results may indicate just noisy calculations of some of the terms in (1) or, more fundamentally, the presence of other important dynamics. Analysis of these regions requires careful evaluation of a full pb diagnostic equation (e.g., Hughes 2008), consistent with the dynamics and numerics of the model used in the ECCO solution, to ensure that all relevant terms in the budget are computed accurately and that the overall residual is comparatively small. Such analysis is left for future study.

Acknowledgments

This research has been funded by NASA’s Solid Earth Natural Hazards program through GRACE Grant NNX12AJ93G and by NSF Grant OCE-0961507. Main support for the ECCO project is provided by NASA’s Physical Oceanography program. We thank K. Quinn (AER) for postprocessing the GRACE data and two anonymous reviewers for helpful comments.

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1

As pointed out by a reviewer, these areas of enhanced interannual variability are not exactly coincident with those of elevated intraseasonal ζ variability, particularly for AAB (Webb and de Cuevas 2002b; Fu 2003; Quinn and Ponte 2012), which suggests that the influence of bathymetry, forcing, and other factors is dependent on time scale.

2

Agreement between GRACE and ECCO is also good in the Enderby Abyssal Plain, but further analysis of this region is deferred here until a more complete vorticity analysis is developed (see discussion in section 5).

3

These peaks are also present in the original ERA-Interim fields and are thus not a product of the optimization. An explanation for these regions of enhanced curl forcing is not immediately obvious, but air–sea coupling is a possibility. Further exploration of this issue is beyond our scope here.

4

Attempts at finding a local response to winds that increases with decreasing frequency, as expected for transient dynamics, were inconclusive.

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