[1] In the Agulhas Current and its sources and sinks, variability in steric height derived from the 0.1° POP model is 3–11 times greater than the mass-load signal at periods shorter than 20 days, the approximate limit of temporal resolution for the Jason series of satellite altimeters. Model output is evaluated for realism against in situ SLA data from a suite of moorings deployed in the southeastern South Atlantic Ocean in 2003–2005. The effects of temporal filtering and alongtrack smoothing on output sampled at 10-day intervals is examined. In approximately 14% of the region, including much of the Agulhas Retroflection, aliasing is ≤10% only at periods of ≥120 days. Smoothing reduces that proportion by 40% but also sharply reduces variability at periods of ≤73 days indicating that use of Jason-style altimetry for time series analysis of this current system should be confined to seasonal and longer scales.

[2] Based on model output, Stammer et al. [2000] suggested that high-frequency (HF) barotropic motion in the ocean could be aliased into satellite-sampled sea level records; using in situ bottom pressure gauge data Gille and Hughes [2001] found the potential for up to 63% of barotropic variance to be associated with periods shorter than 20 days. In this paper we investigate the possibility of temporal aliasing of HF motion in altimeter measurements made in the Agulhas Current system (ACS), comprising the Agulhas Current, and its immediate sources and sinks – the Mozambique Channel and East Madagascar Current, and the Agulhas Return Current and Agulhas interocean leakage. The Agulhas Current, the western boundary current of the South Indian subtropical gyre, is an important conduit in the “warm water route” of the Atlantic meridional overturning circulation [Gordon, 1986]. The Agulhas interocean leakage is primarily accomplished by mesoscale rings and eddies [Byrne et al., 2006] and the region is known for its extreme mesoscale variability [Zlotnicki et al., 1989]. Accurate measurements of mesoscale variability (at periods of 20–120 days) are thus a priority in the ACS.

[3] We investigate the strength of HF variability in the sea level anomaly (SLA) signal of the ACS using a suite of in situ records and three years of output from the global 0.1° POP model [Maltrud and McClean, 2005; McClean et al., 2006]. The in situ observations were collected along Jason-1 groundtrack 133 off southwest Africa in 2003–2005. Our focus area in the model encloses 10°W to 50°E and 43°S to 10°S, and comprises waters of 500 m deep or more. For both datasets, we derive the steric height (ϕ) and mass-loading signals (B′) that together constitute the total SLA. We first evaluate the realism of the model SLA constituents by comparing them with the in situ fields. The model output is interpolated to the spatio-temporal sampling pattern of the Topex/POSEIDON and Jason-1 altimeters – ∼7 km alongtrack with a ∼10-day repeat cycle – and used to examine how HF aliasing into the altimeter signal in the ACS might affect our ability to observe events there. The potential utility of temporal filtering and spatial smoothing options to increase the signal-to-noise ratio of measurements made by 10-day repeat altimetry in the ACS are examined.

2. Data and Methods

[4] The twelve in situ moorings, deployed 2003–2005 as part of the Agulhas-South Atlantic Thermohaline Transport Experiment (ASTTEX), were placed along Jason groundtrack 133 between 31°S and 40°S to capture the Agulhas interocean leakage (Figure 1a). None of 41 mesoscale events observed at the ASTTEX mooring line during the 27-month deployment was centered at or north of 33.4°S [see Baker-Yeboah, 2008, Tables 3.4 and 3.5]. Thus we select only the ten ASTTEX moorings south of that for comparison with the Agulhas leakage region in the model. These ten moorings were deployed across the Cape Basin at depths from 4435 m to 5230 m. Nine moorings returned records and are used in this analysis.

[5] The ASTTEX moorings made hourly direct measurements of bottom pressure (P_{B}) and hourly acoustic measurements of the mean temperature. In situP_{B} was processed to remove tides [see Munk and Cartwright, 1966] and a linear estimate of instrumental drift. Using the hydrostatic equation with P_{B}, the variability of the free surface due to mass-loading in the water column (B′) was calculated directly from P_{B} with a root-mean-square (RMS) error of 1 cm [Watts and Kontoyiannis, 1990] using equation (1):

[Baker-Yeboah, 2008], where ρ_{b} is density at the bottom, g is 9.81 m s^{−2}, and is the time-mean pressure at each location. From the acoustic signal, steric height relative to 4500 dbar (ϕ_{4500}) was computed with a RMS error of 5.6 cm [Baker-Yeboah, 2008].

[6] The hourly mooring data were block-filtered to daily averages to match the model output. The power spectral density (PSD) of daily B′ and ϕ values at each of the nine moorings were computed on 365-day segments using a non-parametric multitaper method (with three tapers) [Mann and Lees, 1996], and combined using an adaptive weighting scheme [Thomson, 1982]. The resulting spectra for each site and year were ensemble averaged (Figure 1b).

[7] The ocean simulation used here is a global 0.1-degree, 40-level configuration of the Parallel Ocean Program (POP) [Maltrud and McClean, 2005; McClean et al., 2006]. POP is a z-level coordinate ocean general circulation model with an implicit free surface [Smith et al., 1992; Dukowicz et al., 1993] (see also http://www.climate.lanl.gov/) and largely synoptic forcing except for monthly solar radiation and precipitation [Maltrud and McClean, 2005]. The model uses the Large et al. [1994] mixed layer formulation, K-Profile Parameterization (KPP). The model's portrayal of the large- and meso-scale features of the Agulhas system is realistic in several important aspects, including the level of SLA variability in the Agulhas Retroflection and the frequency of the rings shed from it [Maltrud and McClean, 2005]. Thus we compare model output and in situ results directly. We analyze daily averages of model fields from 1999–2001.

[8] Model P_{B} was calculated by integrating density from the free surface to the bottom. After removing the time-mean at each point, B′ was calculated from the remainder using equation (1). Model steric height was calculated as the difference between the total SLA and B′ (equation (1)) and includes the effects of all changes in seawater density from the surface to the ocean bottom, (ϕ_{B}). The variance of in situϕ_{B} does not differ from that of ϕ_{4500} at the 0.95 confidence level (using Levene's [1960] test of variance applied to ∼330 regional profiles). Hence we compare these quantities directly and drop the subscripts. After derivation, the model SLA components (ϕ and B′) were interpolated to the Jason-1 altimeter groundtrack. The multitaper spectral analysis method described above was applied to year-long segments of model output, and the results for each alongtrack point within the ACS (defined in the next Section) and for each model year were ensemble averaged (Figure 1b). Finally, the model fields were subsampled every 10 days, and the power spectral densities of the subsampled fields (not shown) were computed in the same manner.

3. Results

3.1. High-Frequency SLA Motion

[9] The model and in situ SLA components were divided into their low- and high-frequency constituents using low- and high-pass 4th-order Butterworth filters. The four SLA constituents (ϕ_{LF}, B′_{LF}, ϕ_{HF} and, B′_{HF}) were analyzed for their spatial patterns and relationships to one another. In the vicinity of the modeled Agulhas Current, Agulhas Retroflection and Agulhas Return Current, variability in ϕ_{HF} was elevated with respect to the rest of the region, with a RMS value of ≥1 cm. In fact, this threshold neatly separates the components of the ACS (see Figures 2a and 2b) from surrounding waters and was used to define the geographic limits of the model ACS in the following analysis. Inside the model ACS, RMS(ϕ_{HF}) averages 2.6 cm, ∼10 times higher than outside it. This contrast is also seen in the in situ data, where RMS(ϕ_{HF}) is elevated to over 3.3 cm across the Agulhas leakage, while remaining less than 2.4 cm just outside it.

[10] In both model and observations, ϕ_{HF} is significantly more energetic than B′_{HF} in the ACS, with RMS(B′_{HF}) surpassing RMS(ϕ_{HF}) at less than 1% of model grid points in the entire ACS region. Correspondingly, B′_{HF} within the model ACS describes on average only 15% of the variance in the HF SLA whereas outside the ACS, B′_{HF} describes, on average, 81% of the variance in the HF SLA signal. The ratio, R = RMS(ϕ_{HF})/RMS(B′_{HF}) provides a quantitative indicator of the dominance of ϕ in the HF SLA signal. The in situ data indicate R within the Agulhas leakage has a mean of ∼2.3 and a maximum of ∼3.0; R in the model leakage averages 1.5 and reaches up to 2.25. Over the entire model ACS, R averages over 3.2 and peaks at over 11.5 just north of the mean position of the Retroflection. It is worthwhile noting that outside the ACS, variability in model ϕ is significantly lower at all frequencies than within it (Figure 1b); R < 2.7 everywhere outside the ACS and averages ∼0.5, indicating the dominance of mass-loading in the HF SLA signal.

[11] Zero-lag correlations were computed between select model points in the ACS and all other points in the domain. Weak (∼10%) but significant zero-lag correlations (at the 99% level) in HF SLA were found over large areas of the domain, consistent with a response to large-scale atmospheric forcing. An e-folding length scale, L, was computed from the zero-lag correlations. In the model Retroflection L is ∼150 km, shrinking to ∼135 km at the southern boundary of the Return Current. In contrast, between 23°E and 36°E, where the model Agulhas Current is trapped against the continent and mesoscale variability is low (RMS(ϕ) in the mesoscale band is ∼62% of that found elsewhere in the ACS), L is ∼315 km along-stream, but only ∼78 km across-stream. These scales are significant in choosing spatial smoothing parameters as it is the HF signal we seek to mitigate.

3.2. SLA Spectra

[12] In the model, the annual and semi-annual signals in ϕ are elevated east of 20°E compared to levels found in the Atlantic Ocean, including within the Agulhas leakage where the in situ observations were collected (Figures 1a and 1b). In the modeled Agulhas leakage, power in ϕ at the annual and semi-annual periods (not shown) is less than 25% of the level seen elsewhere in the ACS and within the levels observed in situ at the 95% confidence level. Within the mesoscale band the PSD of model ϕ within the ACS does not differ from that of the in situ observations within the Agulhas leakage at the 95% confidence level (Figure 1b). At periods shorter than ∼10 days, the PSD of model ϕ becomes noticeably less energetic than the observations; the confidence limits of the model and in situ PSD estimates for ϕ cease to overlap at periods shorter than 6 days (Figure 1b). The loss of HF energy in the model relative to observations is due partially to the lack of HF forcing in some fields and partially to the effect of scale-dependent biharmonic mixing in the model formulation. Within the ACS, the overall effect of the energy loss is to reduce ϕ_{HF} by 2.5 cm RMS over the entire HF band and by 2.0 cm RMS at periods between 5 and 2 days. This damping will reduce the apparent amount of aliasing correspondingly and must be taken into account when interpreting model-based results. While the model B′ is everywhere ∼5 times less energetic than observations, the shape of its PSD curve is very similar to that of the observations and should not affect the percent of variance aliased.

3.3. Temporal Aliasing in the ACS

[13] We measured temporal aliasing by the difference in spectral estimates of LF variance between the daily fields of POP model SLA and the 10-day fields. If we assume that the underestimation of ϕ_{HF} in the model is proportional to the HF variance present, and formulate a correction based on the in situ observations of ϕ_{HF}, the additional energy increases temporal aliasing of SLA by 1% at the 90-day period, increasing to 12% at the 20-day period. Applying the in situ-based correction to ϕ_{HF} increases the number of locations with more than 10% of variance aliased by 3–14% between periods of 90 and 20 days. Table 1 summarizes aliasing in SLA+, the augmented SLA signal.

Table 1. Percentage of Alongtrack Sites at Which Aliasing in SLA+ Reaches Over the Specified Percent of Signal Variance in the Given Frequency Band^{a}

Percent Variance Aliased

Outside ACS

ACS

10%

25%

50%

75%

100%

10%

25%

50%

75%

100%

a

Percentages are rounded to the nearest whole number. SLA+ is model output with an in situ-based HF correction.

annual

0

0

0

0

0

1

0

0

0

0

semi-annual

2

0

0

0

0

1

0

0

0

0

120-day period

9

1

0

0

0

6

1

0

0

0

seasonal

21

4

1

0

0

13

1

0

0

0

70-day period

26

7

1

1

0

26

5

1

0

0

60-day period

36

14

4

2

1

37

9

2

0

0

45-day period

49

26

9

5

3

51

19

3

1

0

30-day period

78

68

51

38

27

70

53

28

14

8

20-day period

95

93

89

84

78

92

89

82

72

62

3.4. Damping HF Motion

[14] We experimented with temporal filtering of the model SLA output. Filters tested were simple windows such as boxcar, Hann and Hamming windows, with half-widths varying from 15 to 35 days. Each was applied to the daily model output in the following way: filter input for a given day was limited to 10-day multiples of the central date (e.g., [t − 20, t − 10, t, t + 10, t + 20] where t is the central estimation day). This technique allowed us to examine the effects of a 10-day sampling limitation while still retaining daily resolution for analysis. The effect of the 10-day separation of input dates was dramatic. Virtually all of the original variance was retained at periods of 10, 5, 3.3 and 2.5 days (see Figure 3a). As a result, for all of the filters tested, temporal filtering increased the relative proportion of aliased variance to signal variance rather than reducing it.

[15] We also tested alongtrack spatial smoothing (a distance-squared weighted average). We found a half-width of ∼135 km produced the best results throughout most of the ACS, although a shorter length might be more appropriate for the Agulhas Current itself. Figure 2a shows the amount of variance aliased into the SLA at 10-day sampling resolution as a percent of the total variance in the daily time series. Figure 2b shows the same calculation after alongtrack smoothing has been applied. The most significant improvement is around the Agulhas Retroflection, an area of extreme mesoscale variability. However, alongtrack smoothing also reduced mesoscale variance within the ACS by an average of ∼10% over the 90–120 day band and by ∼25% at the 70-day period (Figure 3a). Overall, alongtrack smoothing reduced the number of sites in which aliasing reached over 10% of signal strength by 15%–35% between the seasonal and annual periods (Figure 3b).

4. Summary and Conclusions

[16] Model and in situ SLA components in the Agulhas Current System were examined for their relative amplitudes and PSDs. Steric height was found to dominate the SLA signal at both low (periods longer than 20 days) and high frequencies, accounting for 85% of the HF variance and 97% of the LF variance in the model ACS. Model output was found to under-represent measured HF SLA by about 2.5 cm RMS. Sampled at 1/10 days, noise from temporal aliasing at 10% of the signal strength is estimated to occur over 13% of the ACS at the seasonal period, increasing to 51% at 45 days and to 92% at the 20-day period.

[17] Temporal filtering and spatial smoothing were applied to reduce the HF component of variability. Filtering increased aliasing in data subsampled at 1/10 days. Smoothing produced an incremental rather than a wholesale reduction in aliasing. We define P_{10} as the period at which aliasing in the SLA signal is limited to less than 10% of the variance. The shorter P_{10}, the smaller the total amount of temporal aliasing in the time series, as aliasing decreases from 10% at all periods longer than P_{10}. In the unsmoothed model output, P_{10} ≤ 90 days over 86% of the ACS. In the spatially smoothed output, P_{10} ≤ 90 days over 91% of the ACS. In general, alongtrack smoothing increases temporal aliasing slightly at those locations where it was low to nonexistent, and decreases it, sometimes significantly, at those locations where it was high. Smoothing shortened the mean value of P_{10} in the ACS by ∼7 days (Table 2), and reduced its standard deviation by ∼10 days.

Table 2. Distribution of the Difference in P_{10}, the Shortest Period at Which Aliasing Remains <10%, Between Smoothed and Unsmoothed SLA Fields in the ACS^{a}

Period (days)

Difference (count)

a

A positive number indicates a larger population for P_{10} in the smoothed SLA than in the unsmoothed.

110

−34

100

−112

90

−136

80

−36

70

−24

60

53

50

65

40

87

30

43

20

124

[18] In the unsmoothed model output along the continental slope (250–1000 m depth), P_{10} averages 121 days, becoming as long as 365 days in some locations. This result is not surprising, because while mesoscale variability of Agulhas Current is low, HF variability is slightly higher than in other parts of the System, resulting in a poor signal-to-noise ratio. Spatial smoothing reduced the mean P_{10} in the Agulhas Current between 25°E and 30°E by 33 days and the maximum P_{10} there by 182.5 days.

[19] In summary, the high level of mesoscale variability present in much of the ACS – including the East Madagascar Current, Agulhas Retroflection, interocean leakage, and Return Current – render it a good prospect for monitoring by 10-day repeat altimetry at periods of ∼70 days and longer. Within the Agulhas Current before it separates from the continent, time series analysis based on 10-day repeat altimetry should be approached with caution and limited to analyses of seasonal or (preferably) longer time scales.

Acknowledgments

[20] This work was supported by NASA/JPL subcontract 1273575 and NSF grants OCE-0099177 (DB), OCE-0549255 (JM) and ONR. The model simulation was conducted at the NAVO MSRC. We thank Victor Zlotnicki for his comments on the work.