Global Assessment of Semidiurnal Internal Tide Aliasing in Argo Proﬁles

OCTOBER 2019 H E N N O N E T A L . 2523

TYLER D. HENNON AND MATTHEW H. ALFORD Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

ZHONGXIANG ZHAO Applied Physics Laboratory, University of Washington, Seattle, Washington

(Manuscript received 16 May 2019, in ﬁnal form 17 July 2019)

ABSTRACT

Though unresolved by Argo floats, internal waves still impart an aliased signal onto their profile measurements. Recent studies have yielded nearly global characterization of several constituents of the stationary internal tides. Using this new information in conjunction with thousands of floats, we quantify the influence of

the stationary, mode-1 M2 and S2 internal tides on Argo-observed temperature. We calculate the in situ temperature anomaly observed by Argo ﬂoats (usually on the order of 0.18C) and compare it to the anomaly expected from the stationary internal tides derived from altimetry. Globally, there is a small, positive correlation between the expected and in situ signals. There is a stronger relationship in regions with more intense internal waves, as well as at depths near the nominal mode-1 maximum. However, we are unable to use this relationship to remove signiﬁcant variance from the in situ observations. This is somewhat surprising, given that the magnitude of the altimetry-derived signal is often on a similar scale to the in situ signal, and points toward a greater importance of the nonstationary internal tides than previously assumed.

1. Introduction within internal tide or near inertial frequency bands. Inertial waves are intermittent and generated by spo- The array of Argo floats, which reached quasi-global radic storm events (D’Asaro 1985; Alford 2001), mak- coverage in 2004 (Roemmich and Gilson 2009), has been ing them naturally irregular. The forcings for internal transformative for the in situ study of a wide variety of tides are astronomical (Munk and Wunsch 1998)and oceanographic phenomena. Argo floats are well suited therefore they have a much higher degree of predict- to capture processes that occur on time scales from ability. A moored profiler near the Hawaiian ridge months to years, such as large-scale changes in oceanic shows that temperature in the thermocline can fluctu- heat content (Sutton and Roemmich 2011; Trenberth ate by 1.58–2.08C at tidal frequencies (Figs. 1a,c). In this et al. 2016), salinity properties (Anderson and Riser region, at least, it would be valuable to disentangle 2014; Wilson and Riser 2016; von Schuckmann et al. the strong internal tide signal from nontidal processes 2009), and biogeochemical tracers (Martz et al. 2008; measured by Argo floats, as a signal of .18Ccould Hennon et al. 2016; Bushinsky et al. 2017). potentially obscure these nontidal processes and, for Internal waves, on the other hand, are a phenomenon example, add noise to heat content estimates. not well resolved by Argo float measurements. The Recent studies have characterized the semidiurnal floats nominally profile the upper 2000 dbar of the ocean internal tide from satellite observations (Zhao et al. once every 10 days, which is far below the sampling 2016; Ray and Zaron 2016; Zhao 2017). Using this new frequency required to resolve most internal waves. information, Zaron and Ray (2017) investigated 1497 However, their signal is still aliased onto Argo profile Argo float profiles near Hawaii and found that the M measurements, as internal waves vertically heave gra- 2 internal tide only accounted for a small fraction of the dients of temperature, salinity, and tracers. This acts to overall steric height variability. To build upon this add variability to Argo observations that are generally analysis and expand it to the global domain, here we use considered ‘‘noise.’’ Most baroclinic energy is often characterizations of the stationary mode-1 M2 and S2 internal tides (Zhao et al. 2016; Zhao 2017) alongside Corresponding author: T. Hennon, [email protected] measurements from 4251 Argo floats to construct a

DOI: 10.1175/JPO-D-19-0121.1 Ó 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/28/21 08:56 AM UTC 2524 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 49

0 FIG. 1. (a) The full record of temperature anomaly from the moored profiler TMP. (b) The expected temperature anomaly based on 0 0 0 altimetric estimates of the semidiurnal tide Ttide. (c) The time series of TMP (gray) and Ttide (red) at 300 m [indicated by the dashed line in 0 (a) and (b)]. A harmonic fit of the stationary M2 and S2 signal Tfit is also included (blue). The cutout shows the period from 30 Apr to 4 May in more detail. The dashed line in the cutout alternates between black/gray every 24 h in order to highlight the diurnal peaks. (d) A map of the amplitude of the stationary, mode-1 M2 internal tide (mm), with the white ‘‘3’’ showing the MP location. (e) The correlation 0 0 0 0 0 r profile between TMP and Ttide. (f) A profile of the RMS of TMP (gray), RMS when Ttide is subtracted from TMP (red), and the RMS when 0 0 Tfit is subtracted from TMP (blue). global survey of the impact of internal waves on Argo collected CTD measurements in the upper 1400 m of the profile observations, with the purpose of identifying water column once every 1.75 h. regions where the semidiurnal internal tide may be a While the 40-day record of the MP is much shorter significant contributor to Argo-observed variability and than the typical Argo float lifespan (up to 6 years), the investigating the feasibility of a correction. sampling frequency is adequate to resolve semidiurnal tidal signals. The vertical range is also comparable to Argo floats (upper 2000 m). The MP is deployed in a 2. Method examined on moored profiler data region of strong internal tides and low mesoscale vari- a. Methods ability (Shum et al. 1990; Chelton et al. 2007), which are ideal conditions for observing clear tidal signatures in The primary objective of this work is to establish how temperature. Combined, these factors allow us to de- effectively we can use altimetric observations of the velop a rough sense of the ‘‘best case’’ scenario for our stationary semidiurnal internal tide (M and S ) to es- 2 2 methods, which are detailed hereafter. timate the influence of internal waves on Argo profile We focus our analysis on the temperature anomaly observations. To demonstrate and validate the methods observed by the MP T0 , which is defined as we use when analyzing Argo float data (section 3), we MP first turn to mooring data. Mooring data provide the 0 5 2 TMP(z, t) TMP(z, t) TMP(z), (1) temporal resolution to explicitly resolve internal waves, whereas the ;10-day periods of Argo cycles do not. where TMP is the temperature recorded by the MP in Here, we examine data from a moored profiler (MP) pressure z and time t coordinates, and TMP is the mean deployed as part of the IWAP experiment (Alford et al. temperature profile (calculated on isobars over the full 0 2007). The MP was fixed to a mooring deployed at temporal record). Temperature anomaly TMP is then 25.498N, 165.158W, from 25 April to 4 June 2006, and high-pass filtered along isobars with a fourth-order

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC OCTOBER 2019 H E N N O N E T A L . 2525

Butterworth filter using a cutoff period of 30 days. Since multiplying the vertical displacement by the vertical the record is only 40 days, this makes very little dif- temperature gradient dT/dz, 0 ference to TMP, but is done to be consistent with the dT T0 (z, t) 5 h(z, t) (z, t), (4) procedure we subsequently use on Argo data, where tide dz low-pass filtering is used to reduce signals induced by the lateral migration of floats (section 3b). where dT/dz is calculated from the MP tempera- Since the semidiurnal tides are well resolved within ture record, which is low-pass filtered (fourth-order 0 TMP, it is straightforward to estimate the contribu- Butterworth) in time and pressure (2 days and 100 dbar, 0 tions of the M2 and S2 constituents through, for ex- respectively). Naturally, Ttide will be large where in- ample, spectral analysis or harmonic fitting. However, ternal waves are big, and in the thermocline where the end goal of this work is to demonstrate how well vertical temperature gradients are strong. altimetric estimates of the internal tides can be used b. MP results to predict, and potentially correct, observed variability. Therefore, we use the M2 and S2 sea surface height In the main thermocline the observed temperature 0 (SSH) signals to estimate the expected temperature anomaly TMP is generally similar in structure to the ex- 0 anomaly within the MP record due to the semidiurnal pected temperature anomaly Ttide (Fig. 1). There is good internal tides. phase agreement, and fortnightly modulation of the 0 0 First, we calculate the predicted SSH time series for spring–neap cycle is present in both TMP and Ttide. 0 the record of the MP deployment, However, Ttide significantly underestimates the largest 0 ; peaks of TMP (up to a factor of 4), likely because it only 5 å v 1 u SSH(t) Ai(x, y) cos[ it i(x, y)], (2) includes the first mode of the stationary M2 and S2 sig- 5 i M2,S2 0 0 nals. Subtracting Ttide from TMP reduces the variance by at least 20% from 250 to 750 m, and by up to 40% where A is the SSH amplitude of the tidal signal, while from 500 to 750 m. Below 750 m, dT/dz and T0 are very v and u are the corresponding frequency and phase, MP weak, and subtracting T0 does not appreciably change respectively. Variables A and u are both obtained from tide the overall variance. Likewise, below 750 m the corre- data in Zhao et al. (2016) and Zhao (2017), for the M 2 lation between T0 and T0 (calculated on each pres- and S constituents, respectively. Here, x and y denote MP tide 2 sure surface) decreases substantially (Fig. 1e). For longitude and latitude, respectively, and are set to the comparison, on each pressure surface we find the best coordinates of the mooring. M and S fits to T0 using harmonic analysis. The M Next, we estimate the internal wave vertical dis- 2 2 MP 2 h and S2 fits are added together, creating an estimate for placement 0 the combined stationary semidiurnal signal, Tfit (Fig. 1c, 0 h(z, t) 5 SSH(t)R(x, y)F(x, y, z). (3) blue line), which serves as a useful comparison to Ttide. 0 0 The amplitudes of Ttide and Tfit are roughly the same Here, SSH is as in Eq. (2), R is the ratio of SSH to the magnitude and very similar in phase, consistent with maximum internal wave vertical displacement (which results found by Zhao et al. (2010). 0 0 have scales of millimeters and meters, respectively), and By subtracting Tfit from TMP, we can slightly improve F 0 is the mode-1 vertical structure of vertical displace- upon the variance reduction compared to that of Ttide ment (normalized so the maximum is one). Parameters (Fig. 1f). However, the variance reduction when using F 0 R and are longitudinally and latitudinally dependent Ttide only marginally underperforms the variance re- u F 0 (as with A and ), and has the additional dimension of duction from Tfit, indicating that the majority of the depth (z). The R and F are derived from the polarization semidiurnal signal is mode-1 and coherent, and the relation for a mode-1 internal tide and are computed methods in section 2a work well for this location. Al- from climatological stratification, as elucidated in Zhao though the stationary, mode-1 M2 and S2 signals do not et al. (2016). While it would be optimal to use in situ account for even half of the overall variance, there are stratification to calculate the mode-1 structure, Argo many other tidal constituents that are neglected. For floats often sample less than half the water column (only example, from 30 April to 4 May, there is a very strong down to 2000 m). Moderate deviations between clima- diurnal signal (over 18C peak to trough), which is not tological and in situ stratification do not strongly impact included in our analysis. The diurnal signal adds signif- the mode-1 vertical structure, so the use of climatology icant variance near Hawaii (Dushaw et al. 2011), and by for F does not severely alter our results. Finally, we using eight total tidal constituents, Dushaw et al. (2011) calculate the expected temperature anomaly from the generally find higher fractions of variance explained 0 stationary, mode-1 semidiurnal internal tide Ttide by than we do here.

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC 2526 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 49

FIG. 2. A map of the global coverage of floats in group A and B (see section 3a). The color in the 28328 bins denotes the presence of profile data from group A (light blue), group B (teal), or both A and B (dark blue). Bins with no profile data are white.

3. Argo data and methods this coarse pressure time series to estimate the timing of each CTD measurement. For the floats included in a. Argo float data group A, the coarse pressure time series have a mini- We now turn our analysis to Argo floats, where we use mum of five points during the vertical profiles, though very similar methods to examine how the semidiurnal 78% have between 10 and 25 (inclusive). tide influences Argo profile observations in a global The second is a set of 2939 floats that use Iridium te- context. Estimating the expected temperature anomaly lemetry and whose only time stamp is at the surface of due to the semidiurnal internal tide for Argo float data is their profiles, hereafter referred to as group B floats. not as straightforward as for continuous data from These floats do not have any temporal information as- mooring records (section 2). The MP records the precise sociated with their vertical profile measurements, but, sample time associated with each CTD measurement unlike floats that use ARGOS telemetry, the reported collected during profiling, which makes calculating the surface time is generally accurate to within 5–15 min of concurrent SSH signal [Eq. (2)] for any MP measure- the true end (top) of the profile (J. Gilson 2018, personal ment trivial. Because Argo floats must transmit their communication). Therefore, we can estimate the timing information via satellite, most do not include the precise of each CTD sample by using the surface time of the time of each sample point for profile measurements. profile and extrapolating backward in time, assuming a 2 Instead, in order to reduce the size of the transmitted constant 10 cm s 1 accent rate (roughly consistent with data package, frequently only the surface time (when the ascent rate observed in group A floats). While less the float breaches the water to transmit data) is included. accurate than the methods for group A floats, modest Argo floats sample only on the upcast, and with an differences between the assumed and true ascent rate 2 ascent rate of roughly 10 cm s 1, the duration of the full will result in errors of roughly 0.5 h at the bottom of the 2000-m profile spans roughly 6 h. Thus, over the course profile (with less error at shallower depths). This is an of a vertical profile the semidiurnal phase changes acceptably small fraction of the semidiurnal period nearly 1808, so the surface time alone is insufficient to (;12 h). characterize semidiurnal signals over the entire profile. Both sets of floats offer coverage over large swaths To apply Eq. (2) to Argo float data and calculate the (Fig. 2). Group A floats have a significant gap in cov- state of the semidiurnal internal tide SSH signal, we erage in the North Pacific and eastern Indian Oceans, must accurately estimate the timing of all profile mea- while group B floats are relatively sparse in the central surements. Two types of Argo floats allow us to over- South Pacific. Together, the two sets of floats offer come this obstacle (float data are retrieved from http:// nearly comprehensive spatial coverage of the world’s www.usgodae.org/ftp/outgoing/argo/dac/). oceans. The first is a set of 1312 floats that return coarse time b. Argo temperature anomaly series of pressure during the floats’ vertical profiles, hereafter referred to as group A floats. Using linear in- We proceed to analyze the Argo data in a similar terpolation (and extrapolation when necessary), we use manner as in section 2. We linearly interpolate profile

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC OCTOBER 2019 H E N N O N E T A L . 2527

FIG. 3. (a) The trajectory of float 5904055 (black line) from its first (green ‘‘3’’) to last profile (red ‘‘3’’), with the 0 color indicating the magnitude of the stationary, mode-1 M2 SSH amplitude (mm). (b) The time series of Targo 0 (gray) and Ttide (red) at 950 m over the multiyear deployment of float 5904055. Note: the temperature anomaly range is significantly lower than in Fig. 1c, primarily due to the different depths highlighted. (c) The correlation 0 0 profile r (computed from Targo and Ttide on pressure surfaces), where the thick line is the correlation, thin lines show the range of the 95% confidence interval, and the dashed line delineates between positive and negative correlations. data to a pressure grid from the surface to 2050 dbar, exercises. Thus, the 30-day cutoff period should not spaced by 5 dbar. As in Eq. (1), we calculate the Argo appreciably diminish the internal wave signal in our 0 temperature anomaly Targo by subtracting the average observations. The correlations presented here are not temperature (from the full float record) along isobars. very sensitive to the filter cutoff period used. A signifi- 0 We high-pass filter Targo with a 30-day cutoff period cantly longer cutoff (100 days) was also tested, with along isobars. Although this makes little difference to negligible quantitative differences to the correlations 0 0 the MP data because it was only deployed about between Targo and Ttide. 6 weeks, Argo floats can remain active for up to 6 years, To compute the predicted temperature anomaly from 0 and over that time can be advected across different the internal tides Ttide we again use Eqs. (2)–(4), with water masses that cause large signals in temperature. only two notable changes. First, for the MP data we took The high-pass filter largely removes these migration- A(x, y), u(x, y), R(x, y), and F(x, y, z) to be constant in induced changes, so instead we can focus on the profile- x and y, reflecting the fixed position of the mooring. Now to-profile variability that internal waves are most likely these variables are allowed to evolve with the lateral to impact. Here it is important to note that if the Argo migration of the Argo floats (Fig. 3a). Second, dT/dz is floats remained at a fixed location like a mooring (and only low-pass filtered in depth (again a 100-dbar continued to profile every 10 days), the stationary in- cutoff), not time, as the cycling frequency of Argo 2 ternal tidal signal is assumed constant. High-pass filter- floats (;0.1 days 1) is not high enough to make the ing with a 30-day cutoff could remove nearly all of the same temporal filtering used in section 2 useful. 0 0 semidiurnal signal, as it is aliased to frequencies not in Using Targo and Ttide (Fig. 3b), we calculate the cor- the pass band. However, the floats do migrate (often relation r to estimate the relationship between in situ rapidly) through the phase space of the M2 and S2 in- temperature anomaly and the anomaly expected from ternal tides, so there is no single stationary signal that is the semidiurnal tide. This correlation is calculated along aliased in a manner familiar to simple signal processing isobars for the full deployment of each float that met two

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC 2528 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 49 conditions. First, the float acquired at least 20 profiles of data, and second, at least 75% of those profiles occur where there are valid estimates of SSH from altimetry. This yields one vertical profile of r per float (Fig. 3c). Profiles occurring in regions without valid estimates of the mode-1 M2 (Zhao et al. 2016) and S2 (Zhao 2017) 0 SSH signals, and consequently Ttide, are not included in our calculations of r. While it is possible to break data into smaller blocks (e.g., year-long segments) we opt to keep the longest record possible, as shorter blocks do not change the qualitative results in sections 4 and 5, but add considerable scatter.

4. Argo results Combining groups A and B, there are initially 4251 floats available for analysis. Due to a combination of spatial gaps in the altimetric SSH data used (Zhao et al. 2016; Zhao 2017) and because some floats have de- ployments too short for useful analysis, the number of floats with usable data is significantly reduced (section 0 3b). At 950 m, 2668 floats have sufficient data to use Targo 0 FIG. 4. The distribution of correlation coefficients for the entirety and Ttide to calculate r (the exact number varies slightly of all float data. The color indicates the number of estimates N that by depth because of variable profiling schemes used by fall in each bin (in log10 scale). Bins are separated by 5 dbar in the floats). pressure and 0.01 in r. The dashed line delineates between positive Among all the floats used to calculate r, the average is and negative correlations. The solid black line shows the average r weakly positive at all depths (Fig. 4). The mean value of as a function of pressure. r as a function of depth has a mode-1 resemblance, be- ginning at zero near the surface, reaching a maximum of r broadly resembles that of the SSH amplitude of the

(;0.08) at 1125 m, and then decaying gradually with stationary mode-1 M2 (Zhao et al. 2016) and S2 (Zhao increasing depth. Many estimates of r are negative. Of 2017) constituents of the internal tides. Using the tem- the 772 floats where r , 0 at 950 m, only 37 are significant poral average of A [SSH amplitude from Eq. (2)] along at the 95% confidence level (4.8% of total), implying each float’s drift path as a proxy, we observe a clear that these negative correlations likely arise simply from relationship between r and the strength of the semi- statistical variation due to nontidal signal. For compar- diurnal tide (Fig. 6). ison, of the 1896 floats where r . 0 at 950 m, 438 are The use of correlation coefficients is a helpful metric 0 significant at the 95% confidence level (23.1% of to- to characterize the phase agreement between Ttide and 0 tal), far exceeding the number expected from random Targo, but it does not give insight on their comparative processes. magnitudes. To quantify this, we calculate the standard 0 d The global patterns of r also illustrate several broad deviation of Ttide ( tide) along isobars. This provides an trends (Fig. 5). Most apparently, r is generally positive estimate of the temperature variability expected from (red in Fig. 5), but with significant variability. There are the stationary, mode-1 semidiurnal tide. To compare regions where the correlation is noticeably stronger, this to the total temperature anomaly observed by Argo 0 d such as the north and southwest Pacific, while other re- floats, we also take the standard deviation of Targo ( argo) gions are weaker or negligible, such as near the equator. along isobars. Naturally, dtide is largest close to the sur- The low correlations at the equator are due to the almost face (where thermal gradients are stronger), but is also nonexistent stationary tide there, as equatorial jets and larger near regions of strong internal waves (Fig. 7, left changes in stratification decohere the internal tides panels). The ratio of dtide and dargo (dtide/dargo) similarly (Zhao et al. 2016; Buijsman et al. 2017). As with the is large around regions where the stationary internal global aggregate of data (Fig. 4), the maximum corre- tides are more intense, but does not have the same decay lations appear to be near 1000 m over much of the globe, with depth as dtide (Fig. 7, right panels). The highest but the correlation is not strongly depth dependent be- values of dtide/dargo are generally near the mode-1 max- low the first few hundred meters. The spatial structure imum (;1000 m).

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC OCTOBER 2019 H E N N O N E T A L . 2529

0 0 FIG. 5. A global plot of the correlation coefﬁcient between Targo and Ttide at 950 m. (top) The trajectory of all ﬂoats (both groups A and B), where the color represents the value of r calculated over the full record of data. (bottom) As in the top panel, but averaged in 48348 bins so that regional trends are more apparent. Red hues represent positive correlations, while blues are negative correlations. The coverage of data here is less than in Fig. 2 because altimetric observations used for Eq. (2) are absent in regions of high mesoscale activity (e.g., the Antarctic Circumpolar Current and western boundary currents) and poleward of 608.

The methods described in sections 2 and 3 use tem- (dtide/dargo) represents a lower bound on the total vari- perature as the primary variable of interest. When ability contributed by semidiurnal internal tides. The temperature in Eqs. (1) and (4) is replaced with po- fraction dtide/dargo is generally higher where the corre- tential density it only very slightly improves the correlation r is higher (Fig. 5), which leads to the fairly in- lations between variability observed by Argo floats tuitive conclusion that Argo float measurements are and that expected from the stationary semidiurnal more likely to be affected by internal waves where sta- tides. Given the marginal difference, we choose to keep tionary internal waves are strong. 0 0 analysis in terms of temperature because it is somewhat Ideally, we would subtract Ttide from Targo in order to more intuitive, as well as more applicable to efforts to disentangle the fraction of variance accounted for by the characterize changes to ocean heat content (Fahrbach mode-1 semidiurnal tides and the remaining signal et al. 2004; Purkey and Johnson 2010; Lyman and (nontidal and other tidal constituents). However, given 0 Johnson 2014). the low correlations and the noise within both Ttide and 0 Targo, such analysis is generally ineffective for these purposes. Even if we isolate analysis to just the floats 5. Discussion with r . 0 significant to the 95% level (438 floats at 0 The magnitude of the temperature variability ex- 950 m, 16% of the total available), Ttide generally only ; 0 pected from the stationary mode-1 M2 and S2 internal explains 5% of the total variance in Targo. tides is often a considerable fraction of the total high- This is somewhat surprising, given the relatively passed signal observed by Argo floats, exceeding 0.25 in strong semidiurnal internal tidal signal present over roughly half the world’s oceans at 950 m (Fig. 7). Be- much of the globe. Yet these results are consistent with cause the nonstationary tide is neglected, this fraction the findings of Zaron and Ray (2017), who observed that

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC 2530 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 49

record their surface times, so we are forced to estimate the timing of the CTD measurements during their profiles by using an assumed ascent rate and extrapolating backward. Since a profile spans roughly 6 h, moderate discrepancies between the assumed ascent rate and true ascent rate could contribute to significant phase differences (most pronounced at the bottom of the profile). To address this potential issue, we took all group A floats and used only the surface time to estimate the timing of the CTD samples (as done with group B floats), and recalculated r. There is a tight relationship between the recalculated values of r and the original values of r, as the correlation between the original and recalculated values is 0.96. The original estimates of r have a marginally higher average at 950 m (0.080) than the recalculated values (0.075), likely arising from the slightly better time estimates. However, these differences are minimal, suggesting that the lack of timing FIG. 6. The correlation coefficient r at 950 m plotted against the average amplitude A of SSH estimated from altimetry along each information within profiles is not a significant hindrance float path. Each gray circle is representative of one full Argo de- for group B floats. ployment. The dashed line delineates between positive and nega- Other parameters in Eqs. (2)–(4) require brief scru- tive correlations. The thick line is the average correlation tinization. Parameters R and F are computed using cli- coefficient calculated over bins spaced by 2 mm (minimum 20 matological datasets. Neither are particularly sensitive values per bin), and the vertical ranges show the standard deviation within each bin. to small perturbations, so large errors arising from differences between climatology and in situ conditions are unlikely. The temperature gradient dT/dz is computed even near a strong source of internal waves (the Hawaiian directly from Argo profile data, and the step between

Ridge) the M2 internal tide only explained a small per- vertical internal wave displacement h and temperature 0 centage of the total variance of steric height. There are anomaly Ttide is straightforward [Eq. (4)]. The rela- many factors that could hinder the ability to observe a tionship between the satellite-estimated SSH ampli- stronger relationship between Argo profile variability tude A used in Eq. (2) and the in situ amplitude observed and the expected internal wave signal. by moorings is roughly linear, but with a moderate de- Some are methodical in nature. Small differences gree of scatter (Zhao et al. 2016). While the error in between the in situ phase and the satellite-estimated altimetric-derived phase and amplitude for weak in- phase used in Eq. (2) could cause misalignment and ternal wave signals could be high enough to adversely 0 0 0 0 reductionincorrelationbetweenTargo and Ttide.In affect Ttide, estimates of Ttide in regions of strong internal 0 section 2 we find good phase agreement between TMP waves should be reasonably accurate. So our question 0 and Ttide. More generally, when internal tide signals are stands, why do we not observe a stronger correlation . 0 0 at least moderately strong (SSH amplitude 5mm), between Ttide and Targo in regions with prominent in- Zhao et al. (2016) find a fairly tight coupling between ternal wave signals? the mooring-observed and satellite-estimated phase, so Although a detailed analysis is beyond the scope of inaccuracies with the satellite-estimated phase are un- this work, it is important to note several prominent likely to be too severe near regions with strong tidal phenomena that can decohere internal tides. Meso- signals. However, when SSH amplitudes are ,5mm scale eddies are a nearly ubiquitous phenomenon in Zhao et al. (2016) find much more scatter between the ocean everywhere but the equator (Chelton et al. mooring-observed and satellite-estimated phase. This 2011) and can refract internal tidal beams. Rainville and is likely an important factor in the negligible correla- Pinkel (2006) find that the path of the mode-1 internal tions associated with floats in regions of weak SSH tide emanating from Hawaii can be significantly altered tidal signals (Fig. 6). depending on the state of the mesoscale field. Buijsman Given multiple time stamps per profile, the timing of et al. (2017) observe that changes in stratification and measurements in group A floats is accurate to well under equatorial jets can erode the stationary tide such that 1 h, minimizing any deleterious effects from timing- it is nearly nonexistent at the equator. Other fronts, related phase offsets. However, group B floats only such as the Kuroshio, have strong shear gradients that

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC OCTOBER 2019 H E N N O N E T A L . 2531

0 d 83 8 FIG. 7. (left) Logarithmic scale of the standard deviation of Ttide ( tide) averaged into 4 4 bins. (right) The ratio 0 d 0 d 83 8 of the standard deviation of Ttide ( tide) and the standard deviation of Targo ( argo) averaged into 4 4 bins. Gray contours are at 0.25. manifest as potential vorticity barriers capable of re- variance explained). Since Argo floats undersample flecting internal tides (Rainville and Pinkel 2004), so semidiurnal signals, can migrate considerable distances variability in front paths can alter internal wave trajec- between profiles, and are often in regions of relatively tories and weaken the stationary tide. Internal tides are weak internal tides, perhaps it is unsurprising that the 0 0 capable of propagating thousands of kilometers (Ray correlations between Targo and Ttide are mostly small. and Mitchum 1997; Alford and Zhao 2007), and any combination of the aforementioned processes can act to 6. Summary decohere internal tides, which in turn can obscure the altimetric signal used to characterize their stationary We aim to quantify the impact of the stationary,

SSH signature. mode-1 M2 and S2 internal tides on the vertical profile Finally, internal tides are clearly not the only signal measurements of .2500 Argo floats. There is a weak, 0 within Targo. There can be nontidal frequencies that add but positive correlation between the in situ temperature considerable variance to the internal wave spectrum anomaly observed by floats and the temperature anom- (Hennon et al. 2014). Additionally, the same processes aly expected from the heaving induced by the stationary that refract internal waves can also add variability to semidiurnal internal tide. Although this correlation 0 Targo, as features such as mesoscale eddies and fronts tends to be stronger in regions where the internal tides create uneven gradients in temperature as the floats drift are prominent as well as near the mode-1 maximum, it is laterally through the ocean (Gould 1985; Chaigneau and still somewhat weaker than expected given the of the Pizarro 2005; Chaigneau et al. 2011). The MP examined relative strength of the expected temperature anomaly (section 2) was at a fixed location in a strongly tidal re- compared to the observed temperature anomaly 0 gion, yet the correlation coefficient between Ttide and (Fig. 7). The inclusion of additional tidal constitu- 0 ; ; TMP peaked at 0.6 (representing a maximum of 40% ents would almost certainly improve the correlations

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC 2532 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 49 between the observed and expected temperature Chelton, D. B., M. G. Schlax, R. M. Samelson, and R. A. de Szoeke, anomaly, but this does not fully address the cause of 2007: Global observations of large oceanic eddies. Geophys. the low correlations found. Res. Lett., 34, L15606, https://doi.org/10.1029/2007GL030812. ——, ——, and ——, 2011: Global observations of nonlinear me- We scrutinize our methods and find that the errors in soscale eddies. Prog. Oceanogr., 91, 167–216, https://doi.org/ methodology are unlikely to account for the low corre- 10.1016/j.pocean.2011.01.002. lations between expected and observed temperature D’Asaro, E., 1985: The energy flux from the wind to near- anomalies in regions of strong internal tides. However in inertial motions in the mixed layer. J. Phys. Oceanogr., 15, , regions of weak internal tides perhaps error in the alti- 1043–1059, https://doi.org/10.1175/1520-0485(1985)015 1043: TEFFTW.2.0.CO;2. metric estimates (particularly phase) contribute to low Dushaw, B. D., P. F. Worcester, and M. A. Dzieciuch, 2011: On the correlations. A variety of phenomena decohere internal predictability of mode-1 internal tides. Deep-Sea Res. I, 58, tides as they propagate, such as mesoscale eddies and 677–698, https://doi.org/10.1016/j.dsr.2011.04.002. fronts, weakening the stationary internal tides. Addi- Fahrbach, E., M. Hoppema, G. Rohard, M. Schröder, and tionally, the lateral migration of the floats presents an A. Wisotzki, 2004: Decadal-scale variations of water mass properties in the deep Weddell Sea. Ocean Dyn., 54, 77–91, additional obstacle in capturing internal wave signatures https://doi.org/10.1007/s10236-003-0082-3. as signals from other processes add to the temperature Gould, W. J., 1985: Physical oceanography of the Azores front. variability measured by Argo floats. Prog. Oceanogr., 14, 167–190, https://doi.org/10.1016/0079- 6611(85)90010-2. Acknowledgments. We thank John Gilson for his Hennon, T. D., S. C. Riser, and M. H. Alford, 2014: Observations of internal gravity waves by Argo floats. J. Phys. Oceanogr., 44, expertise and guidance in the use of the Argo data used 2370–2386, https://doi.org/10.1175/JPO-D-13-0222.1. here. Madeleine Hamann and Arnaud Le Boyer gave ——, ——, and S. Mecking, 2016: Profiling float-based observa- helpful feedback that significantly improved the man- tions of net respiration beneath the mixed layer. Global uscript, as did two anonymous reviewers. This work Biogeochem. Cycles, 30, 920–932, https://doi.org/10.1002/ was funded by NASA under Grant NNX13AD90G 2016GB005380. and by the Office of Naval Research under Grant Lyman, J. M., and G. Johnson, 2014: Estimating global ocean heat content changes in the upper 1800 m since 1950 and the in- N00014-17-1-2112. fluence of climatology choice. J. Climate, 27, 1945–1947, https://doi.org/10.1175/JCLI-D-12-00752.1. REFERENCES Martz, T. R., K. S. Johnson, and S. C. Riser, 2008: Ocean meta- bolism observed with oxygen sensors on profiling floats in the Alford, M. H., 2001: Internal swell generation: The spatial distri- South Pacific. Limnol. Oceanogr., 53, 2094–2111, https:// bution of energy flux from the wind to mixed-layer near-inertial doi.org/10.4319/LO.2008.53.5_PART_2.2094. motions. J. Phys. Oceanogr., 31, 2359–2368, https://doi.org/ Munk, W., and C. Wunsch, 1998: Abyssal recipes II: Energetics of 10.1175/1520-0485(2001)031,2359:ISGTSD.2.0.CO;2. tidal and wind mixing. Deep-Sea Res. I, 45, 1977–2010, https:// ——, and Z. Zhao, 2007: Global patterns of low-mode internal- doi.org/10.1016/S0967-0637(98)00070-3. wave propagation. Part I: Energy and energy flux. J. Phys. Purkey, S. G., and G. C. Johnson, 2010: Warming of global Oceanogr., 37, 1829–1848, https://doi.org/10.1175/JPO3085.1. abyssal and deep Southern Ocean waters between the 1990s ——, J. A. MacKinnon, Z. Zhao, R. Pinkel, J. Klymak, and and 2000s: Contributions to global heat and sea level rise T. Peacock, 2007: Internal waves across the Pacific. Geophys. budgets. J. Climate, 23, 6336–6351, https://doi.org/10.1175/ Res. Lett., 34, L24601, https://doi.org/10.1029/2007GL031566. 2010JCLI3682.1. Anderson, J. E., and S. C. Riser, 2014: Near-surface variability of Rainville, L., and R. Pinkel, 2004: Observations of energetic high- temperature and salinity in the near-tropical ocean: Obser- wavenumber internal waves in the Kuroshio. J. Phys. Ocean- vations from profiling floats. J. Geophys. Res. Oceans, 119, ogr., 34, 1495–1505, https://doi.org/10.1175/1520-0485(2004) 7433–7448, https://doi.org/10.1002/2014JC010112. 034,1495:OOEHIW.2.0.CO;2. Buijsman, M. C., B. K. Arbic, J. G. Richman, J. F. Shriver, A. J. ——, and ——, 2006: Propagation of low-mode internal waves Wallcraft, and L. Zamudio, 2017: Semidiurnal internal tide through the ocean. J. Phys. Oceanogr., 36, 1220–1236, https:// incoherence in the equatorial Pacific. J. Geophys. Res. Oceans, doi.org/10.1175/JPO2889.1. 122, 5286–5305, https://doi.org/10.1002/2016JC012590. Ray, R. D., and G. T. Mitchum, 1997: Surface manifestations of Bushinsky, S. M., A. R. Gray, K. S. Johnson, and J. L. Sarmiento, internal tides in the deep ocean: Observations from altimetry 2017: Oxygen in the Southern Ocean from Argo floats: De- and island gauges. Prog. Oceanogr., 40, 135–162, https:// termination of processes driving air-sea fluxes. J. Geophys. Res. doi.org/10.1016/S0079-6611(97)00025-6.

Oceans, 122, 8661–8682, https://doi.org/10.1002/2017JC012923. ——, and E. Zaron, 2016: M2 internal tides and their observed Chaigneau, A., and O. Pizarro, 2005: Eddy characteristics in the wavenumber spectra from satellite altimetry. J. Phys. Ocean- eastern South Pacific. J. Geophys. Res., 110, C06005, https:// ogr., 46, 3–22, https://doi.org/10.1175/JPO-D-15-0065.1. doi.org/10.1029/2004JC002815. Roemmich, D., and J. Gilson, 2009: The 2004-2008 mean and an- ——, M. Le Texier, G. Eldin, C. Grados, and O. Pizarro, 2011: nual cycle of temperature, salinity, and steric height in the Vertical structure of mesoscale eddies in the eastern South global ocean from the Argo program. Prog. Oceanogr., 82, 81– Pacific Ocean: A composite analysis from altimetry and Argo 100, https://doi.org/10.1016/j.pocean.2009.03.004. profiling floats. J. Geophys. Res., 116, C11025, https://doi.org/ Shum, C. K., R. A. Werner, D. T. Sandwell, B. H. Zhang, R. S. Nerem, 10.1029/2011JC007134. and B. D. Tapley, 1990: Variations of global mesoscale eddy

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC OCTOBER 2019 H E N N O N E T A L . 2533

energy observed from Geosat. J. Geophys. Res., 95,17865– J. Phys. Oceanogr., 46, 1361–1376, https://doi.org/10.1175/ 17 876, https://doi.org/10.1029/JC095iC10p17865. JPO-D-15-0147.1. Sutton, P., and D. Roemmich, 2011: Decadal steric and sea surface Zaron, E. D., and R. D. Ray, 2017: Using an altimeter-derived in- height changes in the Southern Hemisphere. Geophys. Res. ternal tide model to remove tides from in situ data. Geophys. Lett., 38, L08604, https://doi.org/10.1029/2011GL046802. Res. Lett., 44, 4241–4245, https://doi.org/10.1002/2017GL072950.

Trenberth, K. E., J. T. Fasullo, K. von Schuckman, and L. Cheng, Zhao, Z., 2017: The global mode-1 S2 internal tide. J. Geophys. Res. 2016: Insights into Earth’s energy imbalance from multiple Oceans, 122, 8794–8812, https://doi.org/10.1002/2017JC013112. sources. J. Climate, 29, 7495–7505, https://doi.org/10.1175/ ——, M. H. Alford, J. A. MacKinnon, and R. Pinkel, 2010: Long- JCLI-D-16-0339.1. range propagation of the semidiurnal internal tide from the von Schuckmann, K., F. Gaillard, and P.-Y. Le Traon, 2009: Hawaiian Ridge. J. Phys. Oceanogr., 40, 713–736, https:// Global hydrographic variability patterns during 2003–2008. doi.org/10.1175/2009JPO4207.1. J. Geophys. Res., 114, C09007, https://doi.org/10.1029/ ——, ——, H. L. Simmons, and L. Rainville, 2016: Global ob- 2008JC005237. servations of open-ocean mode-1 M2 internal tides. J. Phys. Wilson, E. A., and S. C. Riser, 2016: An assessment of the Oceanogr., 46, 1657–1684, https://doi.org/10.1175/JPO-D-15- seasonal salinity budget for the upper Bay of Bengal. 0105.1.

Unauthenticated | Downloaded 09/28/21 08:56 AM UTC