1. Introduction

Satellite altimeters have transformed our view of the ocean. Analysis of global sea surface height (SSH) has quantified spatial and temporal scales, and the spectral distribution of energy associated with large- and mesoscale ocean circulation. Together with complementary in situ and satellite observations, the 20 year altimeter SSH record led to a greater understanding of many aspects of ocean dynamics, such as the ocean’s response to large-scale forcing, wave propagation, and heat storage. Readily available SSH products delivered by government agencies have been transformative regarding their global coverage and convenient access to the public. Altimetric sea surface height estimates are not without their limitations and uncertainties. Intercomparisons with open-ocean observations have been limited owing to sparse in situ measurements of sea surface height. Studies have focused on the consequences of the satellite altimeter temporal and spatial sampling, their ramifications for mapped products, and the relative contributions of steric versus mass-loading variability.

Aliasing of high-frequency SSH signals has been assessed with observations in a limited number of studies. Gille and Hughes (2001) used 23 bottom pressure records, primarily from the Atlantic and Southern Oceans, to evaluate the 10-day sampling of the TOPEX, Jason-1, and Jason-2 missions and found that aliased energy was substantial for frequencies higher than 1/100 cpd. Neglected in Gille and Hughes (2001) is the steric contribution to SSH. Focusing on the Agulhas region, Byrne and McClean’s (2008) joint analysis of an ocean circulation model and in situ SSH found that aliasing effects were mainly restricted to frequencies higher than 1/70 cpd. Strategies to compensate for aliased energy due to high-frequency signals typically employ a barotropic model driven by atmospheric pressure and wind forcing. A recent study by Quinn and Ponte (2011) evaluated high-frequency bottom pressure variability at frequencies above 1/60 cpd because of their specific interest in aliasing associated with the Gravity Recovery and Climate Experiment (GRACE) mission with 1/30 cpd sampling. They evaluated two ocean circulation models—the Ocean Model for Circulation and Tides (OMCT; Thomas 2002), which is the current operational model used to dealias GRACE data, and the data-constrained Estimating the Circulation and Climate of the Ocean (ECCO) model (Wunsch et al. 2009)—and nearly 40 bottom pressure records. They found that only 15%–25% of the observed high-frequency bottom pressure variance was captured by the OMCT and ECCO solutions, respectively. Furthermore, differences between model solutions were ascribed to details of the specification of bathymetry in the models, highlighting the dependence of the bottom pressure signal on bathymetry.

Pressure recording inverted echo sounders (PIES) have been successfully employed to compare altimeter and in situ SSH, mainly in strong jet regions, that is, western boundary current systems and the Antarctic Circumpolar Current (ACC; Hendry et al. 2002; Baker-Yeboah et al. 2009; Park et al. 2012; Behnisch et al. 2013). The PIES measurements of bottom pressure and round-trip travel time converted to geopotential height anomaly allow separation of the mass and steric contributions to SSH. Following Baker-Yeboah et al. (2009), sea surface height anomaly (SSHA) can be decomposed as

where the prime indicates an anomaly from the time mean, is bottom pressure anomaly, g is gravity, and is geopotential height anomaly relative to the bottom. The first term on the right-hand side of Eq. (1) represents the contribution of mass loading and in this work it is denoted by SSHA_ref. The second term on the right-hand side of Eq. (1) results from density variability in the water column and we term it SSHA_bcb, where is shorthand for baroclinic referenced to the bottom. In the North Atlantic Current, Hendry et al. (2002) found good comparisons, correlation coefficients greater than 0.82, between along-track TOPEX and PIES SSHA for sites located within 15–30 km of the altimeter track. SSHA_bcb and SSHA_ref both contributed to SSHA and they could not easily be separated spectrally. Similarly in the Agulhas region, Baker-Yeboah et al. (2009) found that SSHA_ref made up about 20% of SSHA variance and could be much larger in single events. Moreover, they found that correlations between SSHA_bcb and SSHA_ref were site specific. In the Kuroshio Extension, Park et al. (2012) found mean correlations greater than 0.92 with mapped SSHA products and low correlations were found in regions with high energy at frequencies above 1/20 cpd, while in the ACC, Behnisch et al. (2013) report a range of correlations (0.33–0.92) with lowest correlations in regions of high SSHA_ref variability.

In this study, current and pressure recording inverted echo sounders (CPIES) from the cDrake experiment are compared with the recent AVISO Data Unification and Altimeter Combination System (DUACS) 2014 global, delayed-time, gridded, two-satellite-merged product. cDrake was designed to study the ACC over a 4-yr period (2008–11). The CPIES array consisted of a transport line spanning Drake Passage and a local dynamics array, located between the Subantarctic Front (SAF) and the Polar Front (PF), composed of a grid of CPIES centered on the eddy kinetic energy maximum in the passage around 57°S, 63°W (Fig. 1). The cDrake dataset (Tracey and University of Rhode Island 2015) offers a unique opportunity to examine the constituents of SSHA and compare satellite SSHA with in situ measurements in the Southern Ocean. The dataset is unprecedented in its spatial and temporal coverage as well as spatial and temporal resolution. Specifically, the instrumentation spanned multiple dynamic regions: northern and southern boundaries, the energetic mesoscale midpassage region, and the relatively quiescent region in the southern passage. Drake Passage was well sampled with a horizontal resolution between 45 and 65 km and a temporal resolution on the order of hours over a span of 4 years. Because both Park et al. (2012) and Behnisch et al. (2013) found better correlations and smaller RMS differences with gridded products compared to along-track products, we restrict our comparison to one mapped product.

• Download Figure
• Download figure as PowerPoint slide

cDrake CPIES site locations. Triangle color denotes record length in years (red: 4, orange: 3, green: 2, and blue: 1). Sites with a continuous 4-yr record from one instrument are A03, B02, C06, C07, C10, C11, C13, C14, C15, C17, C19, D03, E03, F02, and G01. Bathymetry derives from Smith and Sandwell (1997), contoured every 1000-m depth: Colors transition from tan, which represents land, to pinks, which represent shallow depths, to light and darker blues, which represent successively greater depths. Multiple satellite altimeters operated during the cDrake measurement period (November 2007–December 2011): Jason (dashed dark gray) and Envisat (solid light gray). Mean positions of the three major ACC fronts inferred from altimetry data as in Lenn et al. (2008) shown with green lines.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

Section 2 introduces our CPIES and altimeter SSHA datasets. Observed SSHA, SSHA_bcb, and SSHA_ref variance are provided in section 3, followed by the comparison between mapped-satellite and in situ SSHA in section 4. The discussion and conclusions are given in section 5.

2. Data

a. CPIES

The cDrake array (Fig. 1) deployed in November 2007 in Drake Passage operated continuously until late 2011. The array consisted of a transport line (C line) spanning 800 km across the passage and a local dynamics array (LDA). The spatial resolution between CPIES sites ranged between 45 and 65 km, with tighter spatial resolution north of 57.5°S, near topography and within the LDA. Details about deployment duration, location, and bottom depths of all cDrake CPIES moorings can be found in Tracey et al. (2013). The site designations shown in Fig. 1 refer to a specific location. At many sites, over the course of the experiment, individual instruments were recovered and redeployed as necessary. Fifteen sites have full 4-yr records from a single CPIES (sites noted in the caption of Fig. 1). Here, 43 time series of CPIES SSHA were analyzed (triangles in Fig. 1). Thirty-one sites provided records for the full 4-yr period (Fig. 1, red triangles).

CPIES measured round-trip acoustic travel time (τ), bottom pressure , and currents 50 m above the bottom using an Aanderaa acoustic Doppler current sensor. Tracey et al. (2013) and Firing et al. (2014) provide detailed data processing procedures. Here we briefly describe how the measured τ pings, pressure, and currents were processed. The data are available through Tracey and University of Rhode Island (2015). The 24 pings transmitted each hour were windowed and sorted to find the first quartile point (Kennelly et al. 2007). Bottom pressure, also averaged hourly, was detided using response analysis (Munk and Cartwright 1966), and leveled and dedrifted using geostrophic streamfunction from geostrophic objective mapping of bottom velocity (Donohue et al. 2010). The lunar monthly and fortnightly tides were removed using the Global Inverse Tide Model TPXO7.1 (Egbert and Erofeeva 2002; available from https://www.esr.org/polar_tide_models/Model_TPXO71.html). At each site and for each variable, a single time series was constructed. For instruments that were replaced during the experiment, a single time series was created from the site’s multiple deployments. All data were low-pass filtered using a 72-h fourth-order Butterworth filter, run forward and backward, and then subsampled to half-daily values.

Standard τ and bottom pressure processing was used (see, e.g., Baker-Yeboah et al. 2009). Here τ was adjusted for pathlength changes due to mass loading (calculated with bottom pressure), the estimated inverted barometer effect of atmospheric pressure (using ERA-Interim product; Dee et al. 2011), the effect of latitude on gravity in converting between geometric height and pressure, and the seasonal cycle. Cutting (2010) showed that, in Drake Passage, the main seasonal signal was contained in the upper 150 m and had a τ signal amplitude of 0.6 ms. Measured τ together with a gravest empirical mode (GEM; Meinen and Watts 2000) allowed measured τ to be used as a proxy for hydrographic profiles of temperature, salinity, and specific volume anomaly (δ). The GEM is an empirically derived lookup table constructed from historical hydrography. Each measured τ was converted to the GEM index , which was τ between the surface and a deep index level: τ was scaled to using the polynomial , where the coefficients A and B were calculated from historical hydrography. CTDs taken at each CPIES site determined the offset C. For the cDrake experiment, the index level was 2000 dbar except at the southernmost site, C17, where the index level was 1000 dbar.

Four independent sources of error for 72-h low-pass-filtered τ were identified (Baker-Yeboah et al. 2009; Donohue et al. 2010): (i) the scatter in τ due to sea surface roughness of 0.07 ms; (ii) the conversion to a purely steric τ by removal of mass-loading pathlength change had an error of 0.02 ms (mostly associated with uncertainty on the pressure drift); (iii) the error associated with the conversion from measured τ to a τ independent of a latitudinal dependence of gravity of 0.03 ms; and (iv) the conversion of the τ to of 0.15 ms. Thus, the total error in was 0.17 ms.

The GEM technique has been successfully used in many studies of the ACC region, including Sun and Watts (2001), Swart et al. (2010), and Behnisch et al. (2013). For the cDrake experiment, the detailed accounting of the construction of the GEM is discussed in Cutting (2010), Firing et al. (2014), and Chidichimo et al. (2014). For this work, we converted to geopotential anomaly ϕ. A specific volume anomaly GEM was used to create . Geopotential anomaly was determined by integrating between two pressure surfaces:

The quality of the GEM can be expressed by how much of the signal variance is captured by the GEM (Meinen and Watts 2000; Sun and Watts 2001). Firing et al. (2014) and Chidichimo et al. (2014) showed that the , relative to 4000 dbar, explained 98% and 70% of the variance at the surface and 3800 dbar, respectively.

In this work, we assumed that the ocean response to a change in atmospheric pressure was purely the inverted barometer and that bottom pressure was unaffected. Our treatment of τ removed the pathlength changes associated with atmospheric pressure. Note that for SSHA calculated from the CPIES, the seasonal signal was removed from τ. Following Donohue et al. (2010), a seasonal ϕ cycle, which had an amplitude of about 0.1 m² s⁻² in the upper 150 m, was added back into the CPIES data.

The total error in SSHA_bcb derived from two sources, scatter in the ϕ_GEM and error, and was determined by

where was the root-mean-square (RMS) scatter about the fit between ϕ at the surface relative to ϕ at the bottom. Here we used a representative estimate from Chidichimo et al. (2014): 0.52 m² s⁻² was the RMS scatter about the fit between ϕ at the surface relative to ϕ at 4000 m. The relationship between ϕ and was approximately linear with an average slope of −680 m² s⁻³. The total error was 0.53 m² s⁻². Dividing by gravity yielded a total error of 0.0544 m in SSHA_bcb. Error in SSHA_ref was derived from measurement error and uncertainty in the determination of the pressure drift. Based upon values determined in the Kuroshio Extension System Study (Donohue et al. 2010), an estimate of 0.0072 m was used here. Total error in SSHA due to the combined contributions of error in SSHA_bcb and SSHA_ref was 0.0549 m. This error estimate is comparable to SSHA errors determined from PIES: 0.056 m in the Agulhas Retroflection region (Baker-Yeboah et al. 2009), 0.045 m error in the ACC region south of Africa (Behnisch et al. 2013), and 0.06–0.076 m in the Kuroshio Extension region (Park et al. 2012).

b. Satellite altimetry

Satellite altimeter products were produced by SSALTO/DUACS and distributed by AVISO with support from CNES (http://www.aviso.altimetry.fr). For this study the DUACS 2014 global, delayed-time, gridded, two-satellite-merged product was used. Grid resolution was 1/4° Cartesian and the temporal resolution was daily. The two-satellite-merged dataset was based on two missions and replaces the earlier “ref” product. For the cDrake time period, the platforms were either Jason-1/Envisat or Jason-2/Envisat. The Jason satellites have ground tracks with a between-track spacing of 315 km at the equator and a 10-day repeat cycle. Envisat has much higher spatial between-track resolution, 90 km at the equator, but the repeat interval is longer, occurring once every 35 days. The satellite tracks superimposed on the regional topography and cDrake array are shown in Fig. 1. The transport line was purposely placed along an Envisat line; C02 and C03 were deployed slightly to the east of this line to avoid a steep topographic depression. Several sites were located along or very close to the Jason-1/2 lines, notably A01, C04, C05, C08, and C09. Two sites, C15 and E02, were located at Jason-1/2 crossovers.

For the DUACS 2014 version, a formal mapping error was included in the product. Further details are available in Le Traon et al. (1998) and Ducet et al. (2000). The mean mapping error for the period of the cDrake field program is shown in Fig. 2. At the CPIES sites, the mean mapping error ranged from 0.16 to 0.66 m, with the largest errors found between Jason-1 and Jason-2 tracks.

• Download Figure
• Download figure as PowerPoint slide

Mean AVISO mapping error (m) for the cDrake period. Contour interval is 0.01 m. CPIES locations are shown by black circles. Mean positions of the three major ACC fronts inferred from altimetry data as in Lenn et al. (2008) shown with green lines. Multiple satellite altimeters operated during the cDrake measurement period (November 2007–December 2011): Jason (dashed dark gray) and Envisat (solid light gray).

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

For the CPIES and altimeter SSHA comparisons, the two-satellite gridded AVISO product was interpolated to each CPIES site. An ice mask, based on AMSR-E ice concentration (Spreen et al. 2008), was applied to the C-line sites south of and including C11. AMSR-E Arctic and Antarctic sea ice concentration (ASI) 6.25-km data, version 5.6 (downloaded from ftp://ftp-projects.zmaw.de/seaice/AMSR-E_ASI_IceConc/) were used to construct the ice mask. The longest data gaps due to ice coverage occurred during austral winter 2011, ranging from 4 days at C11 to 73 days at site C15. Table 1 provides the length of gaps for each instrument year.

Table 1.

Length of data gaps due to ice coverage (days) during the austral winters of the cDrake field program. Austral winter was defined as 21 Jun–21 Sep ± 45 days. A gap is defined as a day with AMSR-E (Spreen et al. 2008) percent ice concentration greater than 0.

AVISO SSHA processing partially compensated for aliased energy due to signals with frequencies higher than the sampling rate of the Jason-1/2 altimeters by subtracting a predicted sea level response to high-frequency atmospheric wind and pressure forcing. Note, the Nyquist frequency is 1/20 cpd for Jason-1/2 and 1/70 cpd for Envisat. This high-frequency adjustment, greater than 1/20 cpd, consisted of model output from the barotropic tidal model Modèle aux Ondes de Gravité 2D (Mog2D; Carrère and Lyard 2003) forced by 6-h ECMWF wind and pressure. The adjustment was bundled with an inverted barometer correction determined by 6-h ECMWF atmospheric pressure and delivered in what AVISO termed the dynamic atmospheric correction (DAC). Formally, the DAC was produced by the Collecte Localisation Satellites (CLS) Space Oceanography Division distributed by AVISO, with support from CNES and LEGOS. The CPIES bottom pressure measurements resolved the high-frequency barotropic response to atmospheric forcing; therefore, to compare the CPIES SSHA to the altimeter product, the high-frequency adjustment should be subtracted from the CPIES SSHA. Following, Park et al. (2012), we determined high-frequency adjustment in the following manner. The inverted barometer correction, estimated from ECMWF atmospheric surface pressure, was subtracted from the DAC. The resulting time series was high-pass filtered with a 1/20 cpd cutoff, termed here (DAC-ECMWF_ib)_hf and was the high-frequency adjustment subtracted from the CPIES SSHA. Correlations between SSHA_{ref_hf} and (DAC-ECMWF_ib)_hf were positive and increased southward across Drake Passage (not shown). North of the Shackleton Fracture Zone and C10, the mean correlation squared () was 0.12; south of the Shackleton Fracture Zone, mean was 0.50 with a maximum value of 0.72 at site C16. Overall, this correction led to a 2.4% and 10% reduction in SSHA_ref variance north and south of the Shackleton Fracture Zone, respectively.

3. Distribution of SSH variance

Meandering ACC fronts created elevated SSHA variance in northern Drake Passage (Figs. 3a,b). Within the LDA, variance was highest in the west at sites close to the Shackleton Fracture Zone: the mean LDA CPIES SSHA variance was 0.038 m², the maximum CPIES SSHA variance of 0.047 m² occurred at A02, and the minimum variance of 0.017 m² occurred at G02. Statistics for individual sites are provided in Table 2. Along the northern boundary, at C02, and south of 59°S, variability was weak, about 10% of the average LDA variance. AVISO and CPIES SSHA showed a similar variance distribution; section 4 focuses on the intercomparison between the two measurement systems.

• Download Figure
• Download figure as PowerPoint slide

SSHA variance (m²) for (a) AVISO SSHA, (b) CPIES total SSHA, (d) SSHA_bcb, (e) SSHA_ref, and (f) CPIES covariance between SSHA_bcb and SSHA_ref plotted as 2cov. (c) CPIES SSHA variance along the C line for total SSHA (black), SSHA_bcb (red), SSHA_ref (cyan), and 2cov(SSHA_bcb, SSHA_ref) (blue). (g) Contribution of high-frequency ( cpd) SSHA variance to total SSHA variance expressed as a percentage and (h) its variance (m²). (i) High-frequency SSHA variance along the C line for total SSHA (black) and its constituents SSHA_bcb (red) and SSHA_ref (cyan), and 2cov(SSHA_bcb, SSHA_ref) (blue) along the C line. The (DAC-ECMWF_ib)_hf variance (orange line). CPIES sites with record lengths of 2 years or longer (red and orange triangles in Fig. 1) are shown. ACC fronts are green lines in (a). The Shackleton Fracture Zone (brown line) is shown in (b)–(i).

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

Table 2.

Percent variance captured by SSHA_bcb, SSHA_ref, 2 × covariance of SSHA_bcb and SSHA_ref, total variance, and percent variance of SSHA_hf relative to total SSHA. Here refers to frequencies higher than 1/20 cpd.

The relative contributions of SSHA_bcb and SSHA_ref to total SSHA variance was determined by

and is shown in Figs. 3c–f and provided in Table 2. The pattern of both SSHA_bcb and SSHA_ref variance mirrored that of total SSHA variance; the highest variance was located within or near the LDA associated with the meandering baroclinic ACC fronts (Figs. 3c–e). Overall, SSHA_bcb made a larger contribution to total SSHA variance compared to SSHA_ref; averaging over all cDrake sites, = 73% and = 19%. The relative contribution of SSHA_ref to total SSHA was slightly larger south of the Shackleton Fracture Zone and along the northern boundary: sites with are southern sites C12, C13, C16, and C17 and the northern slope site C02. The covariance contribution, SSHA_bcb, SSHA_ref, ranged from −0.51 to 0.31 with typical values about 0.20. Sites with statistically significant correlations at the 95% level between SSHA_bcb and SSHA_ref were LDA sites A03, B03, C08, C09, C18, D01, E01, and F02. Degrees of freedom were determined from autocorrelations of the measurements following the methodology discussed in Bendat and Piersol (2000, p. 173).

The time series of CPIES SSHA and its two constituents, SSHA_bcb and SSHA_ref, are shown in Fig. 4 to illustrate several characteristics of SSHA_bcb and SSHA_ref variability. Sites were chosen for northern Drake Passage (C02 and C03), the LDA (C08), and the southern end of the C line (C14–C17). In the LDA, although SSHA variability was mainly composed of SSHA_bcb, at certain times SSHA_ref (cyan) contributed a sizable fraction to SSHA. For example, note the mid-2011 event at C08 (Fig. 4e), where SSHA_ref was nearly a third of the signal. This was typical of periods of cyclogenesis (Chereskin et al. 2009). Furthermore, this upper-deep coupling during baroclinic instability led to the high covariance values in the LDA (Figs. 3c,f). Yet, relatively large pulses of SSHA_ref did not always covary with SSHA_bcb. For example, two large SSHA_ref events occurred at C02 in early 2008 and late 2010 when SSHA_bcb variability was weak. These were likely due to remotely forced signals that propagated along Drake Passage’s northern boundary. Southern SSHA_bcb and SSHA_ref were not correlated with one another.

• Download Figure
• Download figure as PowerPoint slide

Time series of SSHA: (left) CPIES SSHA total (black), SSHA_bcb (red), and SSHA_ref (cyan); (right) CPIES total SSHA (black) and AVISO SSHA (gray). Periods of ice coverage appear as gaps in the AVISO data. The correlation (upper right) and RMS difference (lower right) between CPIES and AVISO are included in each panel. Note the y-axis range is larger for sites C03 and C08.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

To address how much of the SSHA_bcb signal can be captured by upper-ocean profiling floats, Fig. 5 shows the variance of SSHA_bcb and the variance of SSHA_bc referenced to 2000 and 1000 dbar for sites along the C line in water depths greater than 1000 m. SSHA_bc referenced to 1000 dbar (2000 dbar) explained 25% (60%) of the SSHA_bcb variance. Therefore, using the profiling floats in combination with the satellite altimetry to infer SSHA_ref will misappropriate 40%–75% of the variance depending upon the profiling range of the float.

• Download Figure
• Download figure as PowerPoint slide

CPIES SSHA_bc variance along the C line for sites located in water depths greater than 2000 m. SSHA_bc has been referenced to the bottom (black), 2000 dbar (dark gray), and 1000 dbar (light gray). The location of the Shackleton Fracture Zone (thin gray vertical line) along the C line is shown.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

The high-frequency component (signals with frequency > 1/20 cpd) of SSHA warrants attention because these signals are aliased by the sampling frequency of the Jason-1/2 altimeter. As mentioned previously, the (DAC_ECMWF_ib)_hf adjustment (shown along the C line in Fig. 3i) was subtracted from the CPIES SSHA, yet a high-frequency signal persisted within the water column, as evidenced in the CPIES SSHA. Here several aspects of the high-frequency SSHA_hf signal, shown in Figs. 3g–i, are noted. First, the high-frequency signal variance was typically 10% (ranging between 3% and 20%) of the total SSHA variance (Fig. 3g; Table 2), exceeding 15% of the total SSHA variance only at a handful of sites: the northernmost sites, C02 and C03, and the three southern sites, C12, C23, and C16. Second, SSHA_hf variance was largest in the LDA (Fig. 3h). Third, as mentioned previously, the (DAC_ECMWF_ib)_hf adjustment only partially reduced the SSHA_{ref_hf} signal. Fourth, for most of the sites, SSHA_{bcb_hf} dominated the high-frequency signal (Fig. 3i). It is only south of 60°S and away from the southern ACC front where SSHA_{ref_hf} and SSHA_{bcb_hf} had comparable variances.

We assessed the impact of aliased signals by determining how much energy is aliased by the 10-day repeat of the Jason-1/2 altimeter. The Nyquist theorem shows that energy with periods shorter than twice the sampling period are aliased to different, lower frequencies, making those lower frequencies appear on average more energetic. Following Gille and Hughes (2001), CPIES hourly SSHA time series were subsampled at 10-day intervals, and the spectrum was computed. This process was iterated, offsetting the starting point by one data point each time, until the spectrum had been computed for all data points in the 10-day interval. The average of all individual spectra in the set was computed. The fraction of aliased energy can be quantified at each frequency by

Figure 6 shows for the nine 4-yr records along the C line. First, consider sites at or north of the Shackleton Fracture Zone (red lines in Fig. 6). The fraction of aliased energy for SSHA and SSHA_bcb is less than 0.25 for frequencies longer than 1/50 cpd. This reflects the red spectra (not shown) associated with these sites. Aliased energy associated with SSHA_ref for frequencies longer than 1/50 cpd was slightly elevated compared to SSHA and SSHA_bcb yet remained close to 0.25 for most northern sites. In contrast, at the southern sites (cyan and black lines in Fig. 6) a larger portion of SSHA low-frequency variance was aliased energy. The southernmost site, C17, had the highest values: greater than ~0.5 for frequencies between 1/100 and 1/20 cpd. Moreover, both SSH_bcb and SSHA_ref contributed to aliased energy.

• Download Figure
• Download figure as PowerPoint slide

Fraction of aliased energy as a function of frequency (cpd) for (top) SSHA, (middle) SSHA_bcb, and (bottom) SSHA_ref. Term color-coded by region: at and north of the Shackleton Fracture Zone: C19, C06, C07, and C10 (red); southern sites: C11, C13, C14, and C15 (cyan); and the southernmost site, C17 (black). In the top panel, corresponding periods (days) are provided above the lower x axis of the plot.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

4. AVISO CPIES SSHA comparison

As noted earlier, the AVISO and CPIES SSHA presented similar patterns of variability (Figs. 3a,b). Correlation coefficients (Figs. 7a,d) were high for most sites: correlations were greater than 0.74 for 93% (37/43) of the sites. The six relatively low correlations, ( 0.53) were found at C02 along the northern boundary and at southern sites C12 and south. The maximum correlation of 0.94 occurred at LDA site C08; the minimum correlation of 0.35 was found at site C16. Figure 7d shows that the low correlation between CPIES and AVISO occurred for sites with low variance, reflecting a decrease in the signal-to-noise ratio. C15 and its close neighbor C23 stood out among the southern low-variance sites with correlations of 0.83 and 0.81, respectively. Their proximity to the Jason-1/2 crossover likely contributed to their relatively high correlations. All correlations are significant at the 95% level except for the boundary sites, C02 and C17.

• Download Figure
• Download figure as PowerPoint slide

AVISO/CPIES SSHA comparisons. (a) Correlation coefficient, (b) RMS difference (m), (c) RMS difference as a function of predicted error (m) with circles color-coded by CPIES SSHA high-frequency variance. (d) Correlation coefficient as a function of 3-day low-passed CPIES SSHA variance, (e) RMS difference as a function of 3-day low-passed CPIES SSHA variance, and (f) as a function of high-frequency CPIES SSHA variance. (g) Taylor diagram (Taylor 2001) for the comparison of CPIES-derived SSHA with AVISO product. RMS difference to the standard deviation of the total CPIES SSHA (cyan circles). The reference point (filled black circle) marks the perfect agreement. Colors denote the CPIES record length as in Fig. 1. The Shackleton Fracture Zone (brown line) is shown in (a) and (b).

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

CPIES SSHA are plotted together with AVISO SSHA (Fig. 4, right panels). At the energetic northern sites (C03 and C08), CPIES and AVISO tracked each other well. Although C14 and C15 had comparable variances to each other, 0.049 and 0.062 m², respectively, their CPIES/AVISO correlations differed. As mentioned in the previous paragraph, the higher correlation at C15 was likely due to its positioning at a Jason-1/2 crossover. At C14, which sat beneath an Envisat track, the AVISO record generally followed the CPIES time series yet occasionally strong events were missed, for example, the strong negative pulses in late 2010 and late 2011. In contrast to C16, where the low signal-to-noise ratio likely explained the low correlation, at C17, the AVISO time series missed the apparent 4-yr trend of increasing SSHA revealed in the CPIES record. The C02 records compared well over portions of the record; however, several large events were missed in the AVISO time series, for example, the decrease in SSHA in late 2010. We return to the C02 and C17 records in the discussion section.

The RMS differences between AVISO and CPIES SSHA ranged from 0.035 m at C16 to 0.106 m at LDA site A01 (Figs. 7b,c). The RMS differences were lower along the southern end of the transport line than in the LDA. The cDrake mean RMS difference was 0.075 m. We found no systematic relationship between the RMS difference and the distance to the closest altimeter track. To explore this relationship, for each CPIES site we calculated the minimum distance to a Jason track () and the minimum distance to an Envisat track (), and created a weighted distance with weighting factor w. We calculated the correlation coefficient between d and the RMS difference. We considered weighting factors from 0 to 1 and subsets of CPIES sites based on their variance. The highest correlation found was 0.31 for a weighting factor of 0.45 using only CPIES sites with individual variances greater than the mean variance of the combined 43 sites. This correlation is not statistically significant. The RMS difference increased with increasing variance (Fig. 7e)—and in particular, increases with high-frequency variance (Fig. 7f). The predicted RMS error was determined by

where was 0.0549 m and was the time mean of the AVISO error (Fig. 2) interpolated to the CPIES sites. The predicted error spanned a smaller range than the RMS difference—0.057–0.086 m compared to 0.032–0.106 m, respectively—although the mean RMS difference of 0.074 m was comparable to the mean predicted error of 0.072 m. Figure 7c shows that the predicted error was an overestimate for sites with weak high-frequency signals, and conversely, an underestimate for sites with strong high-frequency signals. An explanation for the underestimated errors is that the high-frequency signals were not resolved by the mapped product and likely not included in the estimated mapping error produced by AVISO.

A Taylor diagram provides a summary of the comparison statistics (Fig. 7g): A perfect agreement between CPIES and AVISO would be located at the reference point along the x axis; most sites are clustered together; normalized RMS differences are near 0.5 (cyan lines); and the ratios of the AVISO and CPIES standard deviations (y axis) are between 0.54 and 1.1 and the correlations (gray lines) are between 0.7 and 0.95. Sites outside the central cluster consisted of low-variance southern sites and the northernmost site, C02. These sites had weaker correlations ( 0.6) and normalized RMS differences near 1.

As a final comment on the CPIES and AVISO SSHA comparisons, we calculated the magnitude-squared coherence for the nine sites with 4-yr ice-free records (not shown). These AVISO and CPIES SSHA time series were coherent at the 95% confidence level for frequencies lower than 1/33 cpd. Coherence dropped sharply to values that were not statistically significant for frequencies higher than 1/20 cpd, the Nyquist frequency of the Jason-1/2 sampling. This is because the AVISO mapped products, although provided at daily resolution, did not contain accurate variance above the Nyquist of the Jason-1/2 sampling (not shown).

5. Discussion and conclusions

The cDrake project provided an unprecedented dataset to analyze SSHA in Drake Passage. In the passage interior, meandering ACC fronts elevated SSHA variance; south of the Shackleton Fracture Zone and along the northern continental slope, SSHA variance decreased by a factor between 6 and 10. In situ analysis focused on the two constituents of SSHA, SSHA_ref determined from bottom pressure anomalies and SSHA_bcb calculated from geopotential height referenced to the bottom. Nowhere in Drake Passage can the SSHA signal be considered either purely steric or mass loading. Both SSHA_bcb and SSHA_ref peak variance occurred in the energetic region between the SAF and PF. The contribution of SSHA_bcb to total SSHA variance was greater than 40% at all sites and it was 73% averaged over all cDrake sites. Behnisch et al. (2013) found SSHA_ref contributions of up to 60% of the total SSHA (equivalent to our SSHA_bc referenced to 2000 dbar) between the jets of the ACC. In Drake Passage, it was only the sites located away from the meandering deep-reaching ACC fronts where the contribution of SSHA_ref to total SSHA variance exceeded 30%. These sites were found along the northern continental slope and south of the Shackleton Fracture Zone away from the southern ACC front. For short periods of time, on the order of weeks, SSHA_ref made a sizable contribution to SSHA, notably in the LDA, where upper meanders jointly developed with deep eddies. This is consistent with similar regions of meandering strong jets, such as the Agulhas (Baker-Yeboah et al. 2009) and the Kuroshio Extension (Park et al. 2012).

We characterized signals with frequencies above 1/20 cpd because these high-frequency signals are not resolved by the Jason-1/2 altimeter sampling. Our estimate of the AVISO dynamic atmospheric adjustment employed to lessen the aliasing effects of high-frequency variability correlated well with SSHA_ref, particularly in southern Drake Passage, and led to a 2.4% and 10% reduction of SSHA_ref variance north and south of the Shackleton Fracture Zone, respectively. Nevertheless, high-frequency signals persisted in the CPIES SSHA after applying the adjustment. Moreover, for most sites, high-frequency SSHA_bcb signals dominated the high-frequency SSHA signal. It is only south of 60°S where high-frequency SSHA_bcb and SSHA_ref had comparable variances. Therefore, improvements to a wind- and atmospheric-pressure-driven barotropic model alone will not lessen the impacts of aliased signals; high-frequency processes within Drake Passage include large-scale barotropic waves generated by cyclogenesis and wind stress or wind stress curl variations. Following Gille and Hughes (2001), we assessed the aliasing of high-frequency signals by Jason-1/2 sampling. Gille and Hughes (2001) used bottom pressure data, with the underlying assumption that bottom pressure variability would be a proxy for SSHA. They found that with a few exceptions, the fraction of energy due to aliasing for frequencies longer than 1/50 cpd was less than 0.5. Results here suggested that the outlook for total SSHA was slightly better in Drake Passage away from the southern boundary; the fraction of energy due to aliasing at frequencies longer than 1/50 cpd for sites at and north of the Shackleton Fracture Zone was less than 0.25. Nevertheless, significant aliasing occurs for frequencies higher than 1/50 cpd.

During the cDrake period, CPIES SSHA agreed well with the mapped two-satellite AVISO SSHA product in the cDrake region. The mean correlation coefficient was 0.82 and mean RMS difference was 0.075 m. Comparison was best in regions of high SSHA variance in central Drake Passage, presumably because in these regions variability was dominated by low-frequency long-wavenumber signals that were well resolved by the altimeter sampling. RMS differences increased as a function of CPIES high-frequency SSHA variance because the mapped product does not resolve these frequencies. Estimated errors associated with the measurement systems agreed fairly well with RMS differences except for sites with large high-frequency variability where predicted error underestimated RMS difference.

Correlations between CPIES and AVISO were notably poorer at the northern and southern boundaries. Hughes and Meredith (2006) showed that altimeter SSH signals were highly correlated all along the South American continental slope, revealing a waveguide that extends southward from the tropical Pacific along the Chilean coast, bends around the tip of South America, and reaches into the Atlantic along the wide Patagonian shelf. Figure 8a shows correlations between the C02 CPIES SSHA and regional AVISO SSHA, and Fig. 8b shows correlations between AVISO SSHA interpolated to the location of the C02 site and the regional AVISO SSHA. The CPIES C02 record shows high correlations with the regional AVISO product along the Hughes and Meredith (2006) waveguide, while the AVISO product interpolated to the C02 site does not. The northernmost site, C02, was not collocated with either a Jason-1/2 track or an Envisat track; it is possible that the two-satellite AVISO mapped product has degraded quality at the C02 site, or perhaps the cross-passage scales of remotely forced waves are shorter in this region.

• Download Figure
• Download figure as PowerPoint slide

Correlation coefficients between AVISO SSHA and (a) CPIES C02 SSHA and (b) AVISO SSHA interpolated to C02. C02 location indicated by black diamond.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

The comparison at the southernmost CPIES SSHA record, C17, stood out from other southern-site comparisons because the AVISO record had half the observed variance, 0.48 (Fig. 7g). In particular, the AVISO record did not reproduce the apparent 4-yr trend of increasing SSHA that derived from both SSHA constituents (Fig. 4n). To estimate their magnitudes, linear fits to SSHA, SSHA_bcb, and SSHA_ref produced estimates of 0.031, 0.017, and 0.014 m yr⁻¹, respectively. Bottom currents at C17 were nearly stable over the 4 years but at C16 westward currents increased in magnitude by 0.01857 m s^–1 yr^–1. Holding C16 pressures constant, a simple geostrophic calculation yields a C17 SSHA_ref trend of 0.0073 m yr⁻¹, about half the SSHA_ref trend. Therefore, while uncertainty in pressure drift must be considered as a possible contribution to the SSHA_ref trend, a portion of the signal is physical. Figure 9 shows hydrocasts taken during the cDrake experiment, color-coded by year. Over the 4 years, geopotential referenced to 1000 dbar increased nearly 0.28 m² s⁻² (0.0071 m yr⁻¹), a larger increase than seen in SSHA_bcb. A clear water-mass transition took place between 2009 and 2010. Hydrocasts taken after 2009 had a temperature maximum indicative of Upper Circumpolar Deep Water (UCDW; near 27.75 kg m³; Orsi et al. 1995). The mapped altimeter product does not resolve this sharp water-mass transition. Note that we do not intend to imply secular changes in the southern boundary of the ACC; more likely, our 4-yr record indicated interannual migrations of the water-mass boundary. Results here emphasize that baroclinic contributions to SSHA along the Drake Passage’s southern boundary can be sizable.

• Download Figure
• Download figure as PowerPoint slide

(a) Potential temperature–salinity plot of hydrocasts taken at C17 during the cDrake field program and potential density (kg m⁻³) (dotted lines). Casts are color-coded by year noted in the legend (upper right) along with their geopotential height anomaly value at the surface relative to 1000 dbar, (m² s⁻²). (b) Term as a function of year.

Citation: Journal of Atmospheric and Oceanic Technology 33, 4; 10.1175/JTECH-D-15-0249.1

Overall, there was very good agreement between CPIES and AVISO two-satellite SSHA: r between 0.74 and 0.94, north of Shackleton Fracture Zone and away from the northern boundary. Predicted errors that include contributions from both measurement systems agreed with RMS differences. The short-scale variability along both Drake Passage’s northern and southern boundaries was not well represented in the mapped altimeter product; a natural next step would be to evaluate along-track SSHA products near the passage boundaries. Finally, we note that even a perfect barotropic model will not solve the aliasing problem because substantial high-frequency variance is due to baroclinic instability.