On the Predictability of Sea Surface Height around Palau

a. Inverted echo sounders

As part of the FLEAT program, nine pressure-sensor equipped inverted echo sounders (PIESs) were deployed from the Research Vessel (R/V) Roger Revelle in May 2016 surrounding Velasco Reef off the northern tip of Palau (Table 1). Two PIESs were able to sample in “rapid mode” (RPIESs), and four of the PIESs were further equipped with near-bottom current sensors (CPIESs). The four CPIESs, two RPIESs, and two of the three standard PIESs were successfully recovered 10 months later, in April 2017, giving 314-day duration records at eight sites.

Table 1.

PIES array details.

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The four CPIESs were deployed underlying two repeat tracks maintained during October 2015–January 2018 with Spray underwater gliders (Zeiden et al. 2019) on either side of the meridional ridge that extends north from Velasco Reef, which is part of the larger Kyushu–Palau Ridge system (Fig. 1). Minimum spacing between neighboring instruments varied from 42 km between sites F5 and F6 to 102 km between sites F8 and F9. Some of the instruments were deployed on the satellite tracks for direct comparison of satellite-measured SSH and PIES-inferred SSH (Fig. 1b).

The C/R/PIESs (collectively referred to as PIESs hereafter, Fig. 3), were programed to obtain hourly measures of 1) bottom-to-surface, round-trip acoustic travel time τ(t); 2) bottom pressure p(t); and 3) in the case of each of the four CPIESs, hourly near-bottom horizontal currents u(t) and υ(t). The currents are not considered here for our analysis of SSH but are reported elsewhere in a study of the deep structure of mesoscale eddies (Andres et al. 2019). For our study, PIESs’ bottom pressure and acoustic travel time signals provide information about mass-loading and steric changes in the overlying water column. Processing of these p and τ measurements follows established procedures and is outlined in the appendix.

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Schematic of a CPIES (left side) and a PIES (right side). A C/PIES detects each 12-kHz ping’s echo off the sea surface (heavy black curve), which is at η(t). It does not detect the weaker echoes from the pycnocline (thin black curve); however, pycnocline displacements d(t) do influence echoes’ round-trip travel time τ via the dependence of the sound speed profile c(z, t) on temperature and salinity profiles. Figure not to scale (i.e., η is typically tens of centimeters while d is tens of meters; e.g., Gill and Niiler 1973). The total (time varying) distance between the C/PIES and the sea surface is $\mathit{D}\left(\mathit{t}\right)=\overline{\mathit{D}}+\eta \left(\mathit{t}\right)$.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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2) Acoustic travel time records

The hourly measured τ depends both on the time-varying pathlength D(t) between the fixed PIES and the free sea surface η (Fig. 3) and on the intervening sound speed profile c(z, t). For a vertically averaged sound speed ⟨c⟩ this dependence is

$\tau \left(t\right)=2{\displaystyle {\int }_{-\overline{D}}^{\eta \left(t\right)}1/c\left(z,t\right)\hspace{0.17em}dz}=2\mathit{D}\left(\mathit{t}\right)/\langle c\rangle ,$(3)

where the factor of 2 arises because the measured time interval is a round-trip travel time. Typically, most τ variability is due to changes in the sound speed profile, which in turn is sensitive to temperature (and to a lesser extent, salinity) in the water column overlying the instrument. Because of the strong temperature dependence of c, τ often serves as an excellent proxy for thermocline and pycnocline displacement in many regions. However, pathlength changes can also measurably influence τ, and in conjunction with bottom pressure measurements can be used to infer mass-loading changes in the overlying waters.

Spectral analysis of the hourly τ measurements from the FLEAT PIES array shows that most of the variance is at tidal periods (Fig. 4a). Much of this is coherent with bottom pressure variability, indicating that pathlength changes associated with barotropic tides dominate the τ signal here. However, the phase of individual tidal constituents in the τ records is nonstationary, with this variability arising from internal tides. The barotropic (τ_BT) and internal (or “baroclinic,” τ_BC) tidal signals can be separated from the full τ signal using the method described in the appendix that capitalizes on the PIESs’ collocated measures of travel time and bottom pressure.

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Example spectra of acoustic travel times from site F8. (a) Variance preserving spectrum of τ (i.e., the full hourly acoustic-travel-time record) at site F8. (b) Variance preserving spectrum of τ_BT (i.e., the “detided” acoustic-travel-time record, which is the hourly record with the contribution from the barotropic tide removed). (c) Variance preserving spectra for 3-day low-pass-filtered ${\tau }_{\mathrm{LP}}^{\prime }$). In each panel, the local inertial frequency is denoted with the red dashed line; the frequencies used in the response method detiding (Munk and Cartwright 1966) are shown with solid red lines (from low to high frequency, these are diurnal: Q1, O1, P1, K1, and semidiurnal: N2, M2, S2, K2). The gray shaded bands are the frequency bands used here to bandpass filter the internal tide’s contribution to acoustic travel time. The mesoscale band (green) and a superinertial band (pink) are also indicated. Note the different vertical scales in the panels.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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Spectra of the barotropically detided hourly records τ − τ_BT still have tidal energy at diurnal and semidiurnal periods (e.g., Fig. 4b). This internal tidal signal τ_BC manifests in τ because the first mode internal tide can cause vertical isopycnal motions that affect τ via changes in the vertically averaged sound speed [i.e., via ⟨c⟩ in Eq. (3)] rather than due to changes in pathlength. There may also be higher mode internal tides, however, these likely do not manifest so clearly in τ, since isopycnal shoaling—and decreases in sound speed—at some depths may be compensated by isopycnal deepening—and increases in sound speed—at other depths (e.g., Li et al. 2009). To isolate τ_BC, we apply bandpass filters to the barotropically detided records τ_BT at 23.0–26.8 h for the diurnal internal tide τ_D1 and at 11.50–12.92 h for the semidiurnal internal tide τ_D2 following Park and Watts (2006). The amplitudes of the diurnal and the semidiurnal internal tides identified in this way each vary independently (e.g., Fig. A2 and Table 2), both over time and from site to site, and are considered further in section 3a.

Table 2.

Acoustic travel time variance (ms²).

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With these barotropic and internal tide contributions to the hourly acoustic travel time records quantified, we are able to calculate a residual hourly record τ′, that captures temporal perturbations to travel time arising from nontidal processes (e.g., Fig. A2, red curve):

${\tau }^{\prime }\left(t\right)=\tau \left(t\right)-{\tau }_{\text{BT}}\left(t\right)-{\tau }_{\text{BC}}\left(t\right)-\overline{\tau }.$(4)

The $\overline{\tau }$ at each site depends on $\overline{D}$ and on the time-averaged, vertically averaged sound speed at the site $\hspace{0.17em}\overline{c}$:

$\overline{\tau }=2\overline{D}/\overline{c}.$(5)

A low-pass-filtered record τ_LP is formed from the hourly τ using a fourth-order Butterworth filter run forwards and backward with a 3-day cutoff period. From this, $\overline{\tau }$ is removed to obtain a low-passed, demeaned record ${\tau }_{\mathrm{LP}}^{\prime }$ at each site (e.g., Fig. A2, gray curve). Variance preserving spectra of ${\tau }_{\mathrm{LP}}^{\prime }$ (Fig. 4c) show that most of the variance in ${\tau }_{\mathrm{LP}}^{\prime }$ occurs at periods between about 20 and 100 days; based on the spectra, this range is used here to isolate the “mesoscale band” with 10 days used as a cutoff period for further filtering to obtain ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$. To explore the mesoscale band, these low-pass-filtered records are examined in section 3c with lagged-correlation analysis and complex empirical orthogonal function (CEOF) analysis (Horel 1984). Separately, the hourly records are detided and then bandpass filtered between 1 and 10 days to isolate nontidal, high-frequency variability ${\tau }_{\mathrm{BP}}^{\prime }$, including a superinertial signal, using lagged correlations and CEOF analysis (section 3d).

b. Other data

Additional datasets and model output are used to help interpret the PIES observations and to provide spatial and temporal context for the FLEAT experiment.

3) Tide gauge data

Due to strong interannual variability in the tropical North Pacific associated with El Niño events (Wang et al. 2019; Andres et al. 2019), long-term tide gauge data are used here to provide temporal context for the 2016–17 FLEAT experiment period. Sea level observations since 1969 are available from a tide station maintained at Malakal on Palau (7.333°N, 134.467°E, GLOSS ID 120). Both the annual-mean and the monthly mean Revised Local Reference (RLR) sea levels were obtained from the Permanent Service for Mean Sea Level (PSMSL 2018; Holgate et al. 2013) for the period from 1980 through 2018 (Fig. 5, black curve).

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Monthly mean sea level anomalies measured by the tide station at Malakal, Palau (black) and an ENSO indicator (plotted as the inverse of the Niño-3.4 index) showing El Niño (red) and La Niña (blue) periods. Depth of the 1024.5 kg m⁻³ isopycnal (i.e., the thermocline), calculated from Argo profiles in the region of Palau, is plotted in green from 2002 onward. Transitions at the ends of “very strong” El Niño events (1982/83, 1997/98, and 2014/16) are shaded; these correspond to large sea level increases at Palau. The minimum sea levels associated with the “strong” and “moderate” El Niño events (1986/87, 1987/88, 1991/92, 1994/95, 2002/03, and 2009/10) are denoted with dashed lines; as with the very strong events, these El Niño events are also followed by marked sea level increases at Malakal.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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6) Satellite SSH

Measures from satellite altimetry of SSH across the North Pacific spanning 5°–20°N from 2013 through the second half of 2017 were obtained from the mapped absolute dynamic topography (MADT) daily product, which is available at ¼° resolution from the Copernicus Marine Environment Monitoring Service (CMEMS 2017). Though the product is provided at daily intervals, the individual satellite reference tracks (Fig. 1b) are only repeat sampled at about 10-day intervals.

SSH from altimetry is used here to compare directly with the in situ measurements during the FLEAT experiment (section 3c) and further to provide spatial context for the region around Palau by highlighting westward-propagating signals.

To identify these large-scale propagating signals, we meridionally averaged MADT over the latitude band 8°15′–8°45′N to obtain SSH_sat. A Hovmöller plot of SSH_sat, shows variability superimposed on a general east–west gradient, with lower SSH_sat toward the eastern half of the basin (Fig. 6a). Slopes of the phase lines on this plot indicate that some of this variability is either propagating very rapidly across the entire basin (e.g., as barotropic Rossby waves; Andres et al. 2012) or it is associated with large-scale zonal processes like seasonal heating and cooling. One particularly striking feature that stretches across much of the western basin, is a broadscale SSH_sat increase by about 30 cm in early 2016. As discussed in section 3b, this is associated with a rapid transition from El Niño to La Niña, which occurred just before the FLEAT PIES array deployment; the transition was already complete by May 2016 when the PIESs were deployed (Schönau et al. 2019).

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(a) Time vs SSH_sat (meridionally averaged over 8°15′–8°45′N). The longitude of Palau is indicated with the solid black line, and the time period during which the array was deployed (2016–17) is highlighted in magenta on this line. Topography along the Pacific is indicated in the lower subpanel. (b) Time series of SSH_sat zonally averaged between the black dashed lines shown in (a). (c) Time vs $\mathrm{SS}{\mathrm{H}}_{\mathrm{sat}}^{\prime }$; black phase lines show westward propagation at 15 km day⁻¹; several other propagation speeds are shown for comparison (white lines). Topography along the Pacific is indicated in the lower subpanel.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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To highlight that part of SSH_sat that may be associated with slow westward-propagating mesoscale eddies, we filter SSH_sat as follows. At each time, SSH_sat is averaged over a zonal band stretching from 130° to 170°E (Fig. 6b). This zonally uniform SSH time series is subtracted from the full SSH_sat at each longitude and time to give a residual $\mathrm{SS}{\mathrm{H}}_{\mathrm{sat}}^{\prime }$ (Fig. 6c). The sloped phase lines of signals that approach the longitude of Palau suggest signal propagations of about 15 km day⁻¹ toward the west. During the instrument deployment period (2016–17), a series of about five sea surface highs and lows reaches Palau. Their amplitude in $\mathrm{SS}{\mathrm{H}}_{\mathrm{sat}}^{\prime }$ spans from about −11 to +5 cm.

a. Tidal variability

We determine the amplitudes and phases of eight tidal constituents of the barotropic tide by applying the response method to the observed pressure records p from each PIES site (Table 3). With this, we then identify the internal tides from p and τ as described in section 2a(2).

Table 3.

Barotropic tide amplitude (first number) and phase (second number).

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1) Barotropic tides

The largest tidal constituent, the M2 tide, has amplitude and phase that each increase slightly from east to west across the array (by about 4 cm and 1°). For the K1 tide, which is the most energetic of the diurnal constituents, amplitude varies little within the array (~1 cm) and the phase increases by about 3° from east to west. As an example, the total barotropic tide at F8 leads to a standard deviation in η_BT of about ±42 cm and a maximum range at spring tide of about ±1 m (Fig. A1a); this translates to a variance in travel time (i.e., in τ_BT) of about 0.31 ms² due to pathlength changes as the sea surface rises and falls. The standard deviation of η_BT is similar at the other sites (Table 2).

The observed tides from the FLEAT PIES sites generally compare well with the amplitudes and phases modeled by the TPXO7.2 global inverse barotropic tidal solution (Egbert and Erofeeva 2002), though amplitude is slightly larger in the observations than in the model output, both for the K1 tide (Fig. 7a) and for the M2 tide (Fig. 7c). For the K1 tide, the phasing around the complicated bathymetry surrounding Palau is reproduced well by the model (Fig. 7b) and for the M2 tide, the model suggests some structure in the phase that is not borne out by the observations (Fig. 7d). We note that the model bathymetry is relatively coarse at the scales of the island, with a shallowest point of around 100 m—thus the island of Palau is represented in this model as a seamount. These small discrepancies between modeled and PIES-observed barotropic tides, suggest that it is necessary to have local measures of barotropic tides to properly isolate the internal tides in the acoustic travel time records.

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(a),(c) Amplitude and (b),(d) phase of the (left) diurnal K1 tide and (right) semidiurnal M2 tide as calculated with the response method (Munk and Cartwright 1966) applied to the in situ pressure records from the PIES sites (colored dots) and as estimated in the region (shading) from a global tidal model (Egbert and Erofeeva 2002). Bathymetric contours are shown with a 1000-m interval from 500- to 5500-m depth.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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2) Internal tides

Using thermistor data and a numerical model, Wolanski et al. (2004) inferred that internal tides are generated on the slope of the island and radiate outwards into the ocean interior. Observations from the PIES array confirm the presence of internal tides around the island, and show that, in general, the semidiurnal internal tides near Palau reach larger amplitudes than do the diurnal tides (Fig. 8, cf. the left and right columns), with the exception of site F5 where the diurnal tide is particularly enhanced. The diurnal internal tides observed by the FLEAT PIESs are relatively strong compared to the diurnal signals observed in other PIES experiments; this is consistent with recent high-resolution HYCOM model runs that incorporate tidal forcing (e.g., Arbic et al. 2012). The 1/25° HYCOM simulations suggests that Palau in the western tropical North Pacific, sits in a region of particularly strong diurnal internal tides, in addition to strong semidiurnal internal tides there (Savage et al. 2017, see their Figs. 14 and 15).

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Time series of (a) the semidiurnal τ_D2 and (b) the diurnal components τ_D1 of τ_BC extracted from the PIES records (black axis). Right axes (red) show the associated thermocline displacements d for the sites (F3, F5, F7, and F8) for which it is possible to calibrate the travel time measurements due to the nearby glider profiles [see section 3a(2)].

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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The pycnocline (or thermocline) displacements d associated with internal tides at sites F3, F5, F7, and F8 are inferred here using both the GEM and a direct empirical relation between τ and thermocline depth (Fig. 8, red y axes on the right), with negligible differences from each method. The vertical structure of the internal tide contributing to the travel time variability cannot be unambiguously identified using these data, but the structure of the GEM suggests that they are dominantly mode 1 (Fig. A6). We note that the contributions of higher modes to travel time variability (discussed by Li et al. 2009) are sensitive to both the amplitudes of the modes and their structure (derived from the stratification profile), but they are expected to be small, perhaps contributing to the scatter in these estimates. Internal tides are estimated here to have pycnocline (thermocline) displacement amplitudes of around 5 m at the eastern sites (F7 and F8) and 10 m at each of the western sites (F3 and F5).

An estimate of the SSH anomaly associated with these pycnocline displacements can be made by assuming the vertical structure of the internal tide is that of a mode 1 wave over a flat bottom. Full depth CTD casts from the PIES deployments and recoveries are used to form stratification profiles at each of the sites, which are then used to numerically solve the linear internal wave eigenvalue problem for waves at tidal frequencies. By varying the amplitude of the computed mode 1 structure, a relation between travel time anomalies associated with the modes and their SSH is derived, with a 1-ms anomaly in travel time being associated with around 5-cm SSH anomaly at each of the sites. As such, internal tide SSH anomalies are estimated to lie in the range of 2–5 cm at each location, covarying in time with the amplitudes of isotherm (and isopycnal) displacements.

Overall, τ_D1 and τ_D2 amplitudes are smaller on the eastern side of the island compared to the west, though at the uncalibrated instrument sites this should be interpreted with some caution. Nevertheless, if the uncalibrated travel time amplitudes do represent the amplitude of the internal tide, it suggests the presence of relatively stronger diurnal tides to the north and west of the island compared to the east.

Temporal variability in τ_D1 and τ_D2 amplitude is evident at each of the sites in both tidal bands. Though some of this variability in amplitude can be attributed to local changes in internal tide forcing associated with the spring-neap cycle, there is considerable variability of a more intermittent nature. This intermittency is characteristic of internal tide measurements, which are a sum of locally generated internal tides and internal tides generated remotely, the latter having traveled long distances from their generation point (Nash et al. 2012). Variability in remotely incident waves can arise from processes that influence the paths and speeds of waves as they transit from their source. In particular, mesoscale changes in stratification and currents can refract internal waves toward and away from the measurement location (Rainville and Pinkel 2006). At Palau, we likely see manifestations of both local (from the Kyushu–Palau Ridge) and remote sources. The relatively larger internal tides to the west of the island insinuate the Luzon Strait or Sangihe Ridge as potential remote source regions, with the strong mesoscale variability of the western Pacific then contributing to the observed internal tide variability of signals that arrive at Palau. The lack of consistent time variability in internal tide amplitudes across the array illustrates the lack of spatial coherence of the internal tide in this region. For example, relatively larger internal tides were observed around mid-September 2016 at site F5, but not at F6, only 40 km away.

b. El Niño

While the barotropic tide causes the largest amplitude SSH variability observed around Palau, SSH variability on interannual time scales also has large amplitudes here, a manifestation of the dominance of ENSO. Increases in sea level of up to 40 cm are observed at island tide gauges, with these changes associated with transitions from El Niño to La Niña (Fig. 5, gray bands and dashed lines). In general, sea level around Palau is anomalously low throughout El Niño periods (Figs. 5 and 9a), but the extrema in sea level and in Niño-3.4 index are not perfectly synchronous. For the nine El Niño events that occurred between 1980 and 2016, sea level reached a minimum at the tide gauge in Malakal on average about 2 months after the maximum in Niño-3.4 index; the lags range from 0 to 5 months. Further, the correlation between the strength of each of the nine El Niño events and the minimum sea level experienced at Malakal during that event is relatively weak (correlation r = −0.31). In contrast, the sea level rise experienced after each El Niño event is strongly positively correlated with the strength of the preceding El Niño event (r = 0.88, p = 0.002 and Fig. 9b) where strength is quantified by the maximum in Niño-3.4 index reached during the El Niño. This high correlation suggests that the Niño-3.4 index is an excellent predictor of the subsequent sea level rise that will be experienced in Palau over the following 3–7-month period. For every unit strength of a given El Niño event (i.e., as quantified by the maximum Niño-3.4 index reached during the event), there will be a 22-cm (±3-cm standard deviation) increase in sea level at Malakal (relative to the minimum attained during the El Niño, typically ~2 months after the maximum in Niño-3.4 index) as the conditions around Palau relax toward the La Niña state.

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(a) Monthly mean sea level anomalies from the Malakal tide station vs the contemporaneous Niño-3.4 index from 1980 through mid-2016 (gray). The minimum sea level anomalies and peak Niño-3.4 index values recorded during each El Niño event are shown by red circles (note these are usually not quite synchronous as the sea level extrema generally lag the Niño-3.4 maxima by ~2 months). (b) Sea level increase experienced at Malakal after each of the nine El Niño events (calculated as the first maximum sea level attained after the Niño-3.4 index begins to fall minus the minimum sea level experienced during the El Niño event).

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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The details of the processes underpinning the correlations and the observed lags remain to be investigated in a future study. In the meantime, to examine whether this striking ENSO SSH signal has a corresponding expression in the pycnocline (or thermocline) around Palau, we turn to the Argo profiles from the region. With these temperature and salinity profiles, we calculate an area-averaged time series of the depth d of the 1024.5 kg m⁻³ isopycnal since 2002 in the region surrounding Palau (Fig. 5, green line). Over periods of months to years, d varies by tens of meters, with the largest shoaling of more than 100 m associated with El Niño 2014/16. During this same period, sea level at the island tide gauge drops by 50 cm. A linear regression between SSH from the tide gauge and d from the (area-averaged) Argo floats (figure not shown) has an R² value of 0.51, indicating that around 50% of pycnocline variance is explained by variance in surface height, with an average of 1-cm SSH displacement at Palau corresponding to a 2.5-m pycnocline displacement (in the opposite direction) in the region.

c. Mesoscale variability

On the backdrop of the region’s strong interannual SSH variability associated with ENSO, we next consider the influence on SSH of mesoscale eddies around Palau during the FLEAT experiment period. The 10-month duration PIES ${\tau }_{\mathrm{LP}}^{\prime }$ records show strong mesoscale variably at periods from 20 to 100 days (see the green shaded band in Fig. 4c). As expected, to first order, this ${\tau }_{\mathrm{LP}}^{\prime }$ is anticorrelated with the mapped SSH_sat interpolated to each instrument site (Fig. 10a), particularly during the first half of the deployment period from April to October. This sense of correlation is consistent with the η inferred at the four CPIES sites from τ, p, and the GEM lookup tables (Fig. 11) and is as expected since sea surface highs (anticyclones) are accompanied by a depressed pycnocline and thermocline and higher vertically averaged sound speed, while sea surface lows (cyclones) are accompanied by a shoaled thermocline and lower vertically averaged sound speed (e.g., Ramp et al. 2017).

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(a) ${\tau }_{\mathrm{LP}}^{\prime }$ (red) for each PIES site superimposed on the mapped SSH_sat interpolated to each instrument location and demeaned (black). The interval between ${\tau }_{\mathrm{LP}}^{\prime }$ tick marks is 0.5 ms, and the interval between (demeaned) SSH_sat tick marks is 5 cm, where the SSH scale is reversed (increasing downward) to better highlight the negative correlation. (b) ${\tau }_{\mathrm{BP}}^{\prime }$ for each site (1–10-day band). The interval between tick marks is 0.05 ms. In both panels, the green line highlights 15 Oct 2016 when the correlation between SSH and acoustic travel times deteriorates.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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Sea surface height anomaly η′ and pycnocline depth d inferred from the CPIES records at sites (b) F3, (a) F5, (c) F7, and (d) F8 where Spray glider dives are available for calibrations. In the upper panel of each set, the steric contribution η_ST inferred from τ_LP is red, the mass-loading contribution η_ML inferred from p_LP is blue. These contributions sum to give the total sea surface anomaly η′ at each site (heavy black curve). In the lower panels in each set, the red line shows the record-mean pycnocline depth. Correlations between η′ and d in (a)–(d) are 0.92, 0.88, 0.87, and 0.93, respectively.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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For the calibrated CPIES sites, we can quantify variability in the sea surface height η and the pycnocline depth d. Mesoscale variability in the total sea surface height (η_TOT =η_ST + η_ML, which excludes any tidal contributions) arises primarily from variability in the steric component η_ST, which is determined from τ_LP [in conjunction with the GEM lookup table and Eq. (8)]. The time series of η_TOT and η_ST anomalies track one another very closely at all sites (see the red and heavy black curves in the upper panels in Fig. 11). While variability in the mass-loading component η_ML, which is determined from p_LP and Eq. (9), does contribute to the overall sea surface height variability, its variance is less half that of the steric contribution.

At site F5, where the range in η_TOT is largest (20-cm range), the range in pycnocline depth is also largest, with d varying between 110- and 150-m depth during the deployment record (Fig. 11a). Errors in pycnocline depth estimated using the PIESs are around 15 m, constituting a significant fraction of the total variability in pycnocline depth at this location. Consistent with expectations (e.g., Gill and Niiler 1973), changes in d mirror and amplify changes in η_TOT: for these sites near Palau, an increase in sea surface height of 1 cm is accompanied by a deepening of the pycnocline by about 1.6 m.

The most striking events in the ${\tau }_{\mathrm{LP}}^{\prime }$ and SSH_sat records (Fig. 10a) occur early during the deployment period when two anomalies, in mid-June and in mid-July, each manifested as a depressed sea surface and an elevated pycnocline (Fig. 11). At site F5, for example, the sea surface height anomaly η′ reached −11 cm and d reached 110-m depth, which is 17 m above the record’s time mean. These signals are due to the arrival of two strong cyclonic eddies. The details of their effects on the vertical structure and bottom currents at the CPIES sites and on moored FLEAT instruments deployed closer to the tip of Velasco Reef are reported in Andres et al. (2019).

Hovmöller plots of pycnocline depth anomaly to the east and west of Palau obtained with objectively mapped Spray glider data [see section 2b(2)] corroborate that the mesoscale pycnocline depth typically varies by tens of meters over time scales of weeks (Fig. 12) with arrival of strong mesoscale eddies leading to rapid changes in pycnocline depth. For example, early in the record in the region southwest of the ridge (July–August in the bottom panel of Fig. 12), the pycnocline is depressed at a rate of 3 m day⁻¹ to a depth anomaly of −30 m. The latitude-mean depth of the pycnocline is highly correlated across the ridge (r = 0.89), indicating that the zonal length scale of these incident mesoscale features exceeds the 80-km scale of the array. This is consistent with the interpretation that the pycnocline variability on time scales of 20–100 days is due to the westward propagation of mesoscale eddies that by definition have length scales on the order of the first baroclinic Rossby radius, which is about 100 km near Palau (Chelton et al. 1998).

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Objectively mapped anomalies in pycnocline depth (taken as the 1024.5 kg m⁻³ surface) from the Spray glider sections taken along a meridional line (top) east and (bottom) west of the ridge (shaded; times with no data are blank). The latitudes of the nearby CPIESs are indicated with the dashed black lines.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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The quality of the correlation between SSH_sat and τ_LP drops markedly and suddenly across the entire array starting in mid-October and lasting for the duration of each record (Fig. 10a see the green line, Table 4). This drop in correlation is observed both for those instruments that fall directly along a satellite repeat track (F1, F5, F7, and F9) and for those that sites are off-track (F3, F4, F6, and F8) and is accompanied by a marked increase of τ′ variance in the band between the local inertial period and the diurnal tide (Figs. 13 and 10b). The aliasing of this high-frequency variability into the satellite record could lead to the degradation of the observed correlation. Also, a known “hump artifact error” can lead to poorer than expected correlation between satellite and in situ observations (Jeon et al. 2018).

Table 4.

Correlation and regression for τ_LP vs SSH_sat.

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Example for F7 of the degraded correlation between τ_LP and SSH_sat from mid-October onward. (a) Time series of τ_LP (red and green curve) and SSH_sat (gray curve, inverse scale on right). (b) τ_LP vs SSH_sat before 15 Oct (red circles; r = −0.76) and thereafter (green circles, r = −0.38). To correspond with the altimeter sampling interval, values in (b) are shown for each time series subsampled to 10-day intervals. The correlation coefficients are both significant (at the 99% and 95% levels, respectively) treating each value subsampled at 10-day intervals as independent.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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Based on the tilted phase lines observed on the $\mathrm{SS}{\mathrm{H}}_{\mathrm{sat}}^{\prime }$ Hovmöller plot (thin black lines in Fig. 6c), mesoscale eddies in this latitude band are expected to propagate westward across the northern tip of Palau at about 15 km day⁻¹ (0.17 m s⁻¹). To investigate in further detail the propagation of these mesoscale eddies through the PIES array and across the Ridge, which sits in a “hole” between satellite repeat tracks (Fig. 1b), the lagged correlations of acoustic travel time records are examined using the records from all of the sites (not just the calibrated CPIES records). Since ${\tau }_{\mathrm{LP}}^{\prime }$ (which is 3-day low-pass filtered) contains a component of variability that is unrelated to mesoscale eddies and whose phase propagation direction is southeastward through the array (section 3d), we further filter the acoustic travel time records with a 10-day cutoff period ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ to isolate the mesoscale signals.

Lagged correlations of ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ between sites confirm that the mesoscale signals arrive first at F9 (east of Palau) and then propagate westward across the ridge and finally arrive at F4 about 9 days later (Fig. 14a). F9 is 190 km east of F4 (and 120 km south, but the eddies have a large meridional extent relative to the array and propagate primarily westward). This suggests that the eddies propagate westward across the array at about 21 km day⁻¹ (0.24 m s⁻¹), about 25% faster than suggested by the phase lines from altimetry at this latitude (Fig. 6c). Whether this is a real local acceleration warrants further study (perhaps with numerical model output) to test whether there is 1) local acceleration of the eddies as they are advected by the NEC and/or 2) local acceleration of the eddies as they encounter the shallow ridge north of Palau. The sense of phase propagation found by the lagged-correlation analysis is confirmed by CEOF analysis of ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$. The CEOF phase structure (Fig. 14b) also shows westward propagation across the array of the first mode (which explains about 76% of the variance).

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(a) Time series of ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ at F9 (blue), at F4 (gray), and at F4 lagged by 9 days (red). (b) Spatial functions of mode 1 phase (shading) and amplitude (represented by the area of the circles) for CEOF analysis of ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$. For comparison, the annotation indicates the lag (in days) of each site’s ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ relative to that at F9.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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To test how far in advance one can predict the arrival of a mesoscale eddy on the eastern edge of Palau, we compare ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ at F7 with altimetry to make lagged-correlation maps. At each time step and for each latitude/longitude, the zonally averaged MADT from 130° to 170°E is subtracted from the local total MADT [to remove the effect of large-scale zonal processes and rapid barotropic waves as in section 2b(5) and Fig. 6c]. This filtered MADT is then compared to ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ at F7 at zero lag (Fig. 15a) and at progressively longer leads (Figs. 15b–d). At zero lag there is a large region of strong negative correlation near F7 (as expected, see Figs. 11 and 13a). As the lead (of SSH relative to ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$) increases, this patch of negative correlation is progressively farther east. At 60-day lead, the distance between the correlated patch and F7 is 870 km, which suggests that the eddies move westward at about 14.5 km day⁻¹ consistent with the slope of the phase lines in Fig. 6c and consistent with the phasing suggested by the CEOF analysis (Fig. 14b). Beyond 60-day lag it is difficult to definitively track this patch of negative correlation farther east as there seem to be regions of spurious correlation in the maps. This may suggest that eddies that reach Palau are generated near 145°E (at least during the 2016/17 FLEAT experiment) or it may simply reflect the noisy eddy field. Regardless, it does seem possible to predict the eddy-related SSH variations near Palau (and the associated subsurface pycnocline displacements) with several month lead time using the filtered MADT. The arrival at Palau of westward-propagating eddies is consistent with the analysis of global satellite altimetry, which shows that these coherent mesoscale features are ubiquitous in the open ocean (Chelton et al. 2011).

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Maps of correlation between ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$ at F7 and filtered MADT at different leads (with the filtered SSH leading ${\tau }_{\mathrm{10-d\_LP}}^{\prime }$). Altimetry repeat tracks are indicated (black) as is the location F7 (yellow dot). Red arrow indicates region of negative correlation that propagates from about 143°E toward Palau.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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d. Superinertial signal

Spectra of τ′ [hourly records from which the barotropic and internal tides have been removed according to Eq. (4) and the methods described in section 2a(2)] show that there is a band that contains comparable variance to the mesoscale with the energy falling primarily between 1.1 and 3 days (Fig. 16, pink shading). Energy in this band is present at all sites, though the variance peaks in this band are strongest at sites F1, F3, and F6 and are relatively weak at F9 (this does not define relative amplitudes since these are not calibrated to a common reference pressure, but it is suggestive). Notably, the spectrum for each site has only a very small (or no) peak in the local near-inertial band (from f to 1.2f, where f is the local Coriolis parameter). This lack of a local near-inertial peak is as expected since these waves—if present—are associated with very small isopycnal displacements (and hence little impact on τ). The frequency band of the 1.1–3-day signal indicates that these waves cannot be due to locally generated near-inertial waves. Here we suggest that the energy in this “superinertial” band may be from near-inertial waves that are generated at a higher latitude and propagate southward toward Palau.

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Spectra of τ′ with each site’s local near-inertial band (from f to 1.2f, Alford et al. 2016) indicated (red dashed lines). Green shading highlights the mesoscale band (20–100-day period) and pink highlights the superinertial band (1.1–3-day period). For reference, the black dotted lines indicate the inertial peak at a latitude near the Philippines (16.2°N, 43 h).

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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To isolate the superinertial signal, the τ′ records are bandpass filtered with a long-period cutoff at 10 days to remove the strong mesoscale variability and a short-period cutoff at 1 day. Time series of these bandpassed records ${\tau }_{\mathrm{BP}}^{\prime }$ show a marked increase in amplitude at each site after 15 October 2016 (Fig. 10b) with “packets” of high-amplitude signal apparent across multiple sites. Due to the difficulties in interpreting the amplitude of the uncalibrated travel time measurements, we focus instead on the phase relations between the ${\tau }_{\mathrm{BP}}^{\prime }$ time series at each site. Lagged correlations of ${\tau }_{\mathrm{BP}}^{\prime }$ between sites calculated for the records after 15 October 2016 show strong (lagged) correlations between sites: F5 leads all other sites and F9 lags all other sites suggesting southeastward phase propagation of the superinertial signal across the array (Table 5). ${\tau }_{\mathrm{BP}}^{\prime }$ at F9 (which is 129 km east and 162 km south of F5) lags that at F5 by 16 h. The slowest propagation speed between sites is observed between F5 and F6 (separated by 41 km) where the strongest correlation occurs at 4-h lag. This suggests the superinertial signals are propagating as plane waves with roughly 10.2 km h⁻¹ (2.8 m s⁻¹) phase speed toward the southeast with a bearing of −32.8° (relative to east).

Table 5.

Results from CEOF and lagged-correlation analyses of ${\tau }_{\mathrm{BP}}^{\prime }$.

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Results from CEOF analysis of the ${\tau }_{\mathrm{BP}}^{\prime }$ records plotted in Fig. 10b are consistent with the lagged-correlation analysis. The first CEOF mode explains about 60% of the variance in this 1–10-day band (Table 5); the second and third modes explain 13% and 9%, respectively. The phase of this first CEOF mode also suggests southeastward propagation across the array (see the shaded dots in Fig. 17a). As suggested by the time series in Fig. 10b, the amplitude time series of this mode increases in mid-October (Fig. 17b, blue curve) hinting at a seasonal component in the forcing of these waves.

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First empirical mode calculated from CEOF analysis of ${\tau }_{\mathrm{BP}}^{\prime }$. (a) The spatial functions of first mode CEOF phase (shading) and amplitude (represented by the area of the circles). (b) The corresponding temporal amplitude time series for the first mode (blue curve). For comparison, in (a) the lags (in hours relative to ${\tau }_{\mathrm{HP}}^{\prime }$ at site F5) are annotated; these lags are calculated by finding the maximum correlation between each site and site F5 for ${\tau }_{\mathrm{BP}}^{\prime }$ from mid-October onward [i.e., after the time denoted by the green line in (b)]. In (b) the red curve shows the standard deviation of the temporal amplitude time series in a moving 120-h window (which is used in section 3d as a measure of the time-varying strength of the superinertial waves).

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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To obtain an estimate of the time-varying amplitude of the superinertial waves, the standard deviation of the CEOF’s temporal amplitude function for the first CEOF mode in a moving 120-h (5 day) window is calculated (Fig. 17b, red curve). The correlation between this amplitude time series and the magnitude of the NCEP wind stress is calculated at each latitude/longitude over the North Pacific to generate a correlation map (Fig. 18). This map shows two features of interest. First, there is relatively low correlation between the amplitude of the superinertial waves and the wind stress magnitude at the location of Palau, indicating that these waves are not locally forced. This is consistent with the waves’ spectra in which the peak at the local inertial period is small or absent (Fig. 16). Second, there is a region of strong positive correlation at zero lag between the amplitude of superinertial waves and the wind stress magnitude near the Philippines. The patch of highest correlation (r > 0.425) stretches northward to about 16°N where the local inertial period is 43 h (a shorter period than the local inertial period at the PIES array). The horizontal group velocities of internal gravity waves peak at slightly superinertial frequencies, with a reasonable value being around 1.5 m s⁻¹, giving a transit time from the Philippines to Palau (700 km) of around 5 days. For the 5-day moving window used to filter the CEOF amplitude function, this is consistent with our finding of maximum correlation at zero lag.

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Correlation map showing 0-lag correlation between wind stress magnitude (calculated from NCEP wind stress) and the strength of the superinertial waves at Palau (i.e., as quantified by the red time series in Fig. 17b). Palau is indicated with the magenta dot.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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A preliminary analysis of 3-h interval output from a data-assimilative numerical model, HYCOM (Chassignet et al. 2007), shows a feature constituent with that revealed in Fig. 18. Using the temperature and salinity profiles from HYCOM, we first calculate the time varying round-trip acoustic travel time between 1000 m and the surface (τ₁₀₀₀) in the western Pacific. The model’s performance is evaluated by comparing at the PIES sites the calculated τ₁₀₀₀ (modeled) with τ_LP (observed). The variability captured by the model compares favorably to that measured by the FLEAT PIESs (e.g., that for site F5 is shown in Fig. 19a). Correlation coefficients between τ₁₀₀₀ and τ_LP at the eight PIES sites show statistically significant values, ranging from 0.35 at F8 to 0.53 at F3.

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(a) Time series of observed acoustic echo time anomaly (black) and calculated (red) using output from HYCOM model. The correlation coefficient between them is 0.52. (b) Amplitude and (c) phase of the first-mode CEOF for the calculated acoustic echo time τ₁₀₀₀. The CEOF was applied after filtering the 3-h interval model output at bands between 1 and 4 days.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-19-0310.1

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CEOF analysis applied to the model’s τ₁₀₀₀ field results in a first mode (which explains 22.1% of total variance at 1–4-day periods) with high amplitude east of the Philippines (Fig. 19b). This coincides with the region where the windstress shows a good correlation with the superinertial waves observed at Palau (Fig. 18). The phase of the first-mode CEOF (Fig. 19c) suggests a southeastward propagation for this mode, which is consistent with the observed propagation of these feature through the array (Fig. 17a). These numerical model results strongly support the hypothesis that the superinertial waves at Palau originate from the region east of Philippines. Further evaluation of the model output and analysis of the superinertial signal within the model framework is the subject of ongoing research.

a. Variability in the sea surface and pycnocline

The observations discussed in section 3 demonstrate that SSH near Palau is subject to variability that occurs over a wide range of temporal scales associated with different oceanic processes, some of which are accompanied by substantial displacements of the pycnocline (Fig. 2). How SSH and d are related is strongly process dependent, reflecting the relative contribution of the steric versus the mass-loading contribution to the total SSH associated with each of these processes. For example, sea surface displacements associated with the barotropic tide η_BT can reach ±1 m during spring tide around Palau (e.g., Fig. A2a) and have little expression in the pycnocline, since, by definition, η_BT contains only a mass-loading signature and no steric component. Signals associated with the internal tide, on the other hand, are mostly subsurface, with pycnocline displacements reaching 5–10 m amplitude for both the diurnal and the semidiurnal bands around Palau (Fig. 8). Sea surface displacements associated with these internal tides are estimated to be between 2 and 5 cm. Variability associated with cyclonic and anticyclonic mesoscale eddies near Palau manifests strongly both in the sea surface and in the pycnocline (Fig. 11). For the mesoscale eddies observed during the FLEAT experiment, the SSH:d ratio is about 1:160 (inferred from p, τ, and the GEM lookup table) and the eddies’ SSH signals are mostly steric with η_ST reaching 10-cm amplitude and η_ML reaching only 1-cm amplitude around Palau. As with mesoscale eddies, variability near Palau associated with ENSO events is also strongly expressed both in the sea surface and in the pycnocline (Fig. 5) but the SSH:d ratio is about 1:250 for the 2003–17 period (inferred from tide gauge measurements and Argo profiles), reflecting larger pycnocline displacements for a given SSH displacement than is observed for the eddies. Also, the amplitude of the ENSO signal in SSH is about 20 cm, twice that associated with mesoscale eddies. The differing ratios of SSH:d associated with each of these processes reflect their different steric/mass-loading fractions on SSH.

Table 6 summarizes our results from the PIES observations, showing the contributions to η and d for those processes and sites where these can be inferred from the site’s p and τ measurements. These include standard deviations and ranges for η_BT [comprising the total sea surface displacement from 8 constituents of the barotropic tide, section 2a(1) and 3a(1)], d_tide [the pycnocline displacements for the total semidiurnal plus diurnal internal tide at sites where we have sufficient calibration casts from gliders, and also assuming a mode 1 structure for these internal tides, section 2a(2) and 3a(2)], η_TOT [the total sea surface displacement in the mesoscale band comprising the steric η_ST and mass-loading contributions η_ML, section 2a(4) and 3c], and d_eddy (the mesoscale’s contribution to pycnocline displacements) where η_ST (and hence η_TOT) and d_eddy are inferred using the lookup tables—but only at the sites where we have the glider calibration casts. We do not know the vertical structure of the variability in the superinertial band (as it may not be well represented by the gravest mode that is captured in the lookup tables), so we do not estimate the superinertial η and d here nor the relative steric/mass-loading contributions to total η in this band. Nevertheless, we note that τ variance in this band is quite tiny compared to that in the other bands (Table 2), so the superinertial η and d signals are likely small as well.

Table 6.

Summary of results from the PIES observations.

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b. Propagation and predictability

As discussed in section 3, how signals in these frequency bands move across the FLEAT PIES array is process specific, as is the predictability of the associated SSH variations north of Palau. Notably, as mesoscale eddies move westward through the array across the Kyushu-Palau Ridge, their phase speed is 0.24 m s⁻¹, about 25% faster than observed with altimetry at this latitude east of Palau, suggesting a local acceleration of the eddies, perhaps related to the topography of the ridge. An analytical study suggests that mesoscale eddies can speed up in the presence of closed potential vorticity contours (f/H, where f is the Coriolis parameter and H is the water depth) due to the “Rossby wormhole” effect (Marshall 2011). Despite this slight local speedup, SSH anomalies are quite coherent as they move westward, and lagged correlations suggest it is possible to use altimetry to predict an eddy’s SSH (and d) signal near Palau with about 60-day lead.

In contrast to the eddies, signals in the superinertial band have southeastward phase propagation across the FLEAT array, with 2.6 m s⁻¹ phase speed. If these are wind forced, the amplitude of packets of these waves arriving at Palau may be tied to seasonal variations in the remote winds and it may be possible to predict when they will be energetic. This remains speculative, however, as we only have a 10-month record in which they manifest starting around October and last through the following April (which is the end of our record). The inferred group speed for these waves (assuming they are generated by the winds near the Philippines) is consistent with that of internal gravity waves (about 1.5 m s⁻¹).

The largest contributors to SSH variations around Palau are the barotropic tide (which is regular and predictable and fairly well represented by tidal models in this region with the M2 tide amplitudes reaching 50 cm) and the SSH variability associated with ENSO events. Though the timing of the SSH increase on Palau after an El Niño peaks and relaxes back to a La Niña state is not well constrained (and varies from about 3 to 7 months), the magnitude of this sea level increase is predictable and is well correlated with the Niño-3.4 index’s peak value during the El Niño event.

The internal tides (which have only small expression in SSH but a significant expression in d) have a regular component that seems tied to the local spring-neap cycle (and is hence predictable), but this is overlaid with large intermittent variability suggesting local and remote sources that are challenging to predict.