internal tidal energy fluxes in the south china sea from density and velocity measurements by

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Internal tidal energy fluxes in the South China Sea from density

and velocity measurements by gliders

T. M. Shaun Johnston1, Daniel L. Rudnick1, Matthew H. Alford2,

Andy Pickering2, and Harper Simmons3

Abstract. Internal tidal energy fluxes were obtained from June–August 2011 using un-derwater gliders in the South China Sea. Spray gliders profiled every ∼2 hours to 500m, which is deep enough given the shallow thermocline to compute mode-1 fluxes fromvertical mode fits to tidal displacements and currents. Westward, mode-1 diurnal andsemidiurnal fluxes exceeded 40 and 30 kW m−1. To our knowledge, these flux observa-tions are the first from both velocity and density measurements by gliders. Fluxes com-pare well with a mooring near a generation site in southern Luzon Strait and a regionalmodel. Furthermore, the zonal-depth structure of the internal tide is obtained by bin-ning measurements, which cover four spring-neap cycles and over 100 km along 20◦ 39′N.Westward phase propagation is found for currents and displacements, while roughly con-stant phase is found along beams. Both these features of the phase suggest a narrow-banded internal tide. Semidiurnal energy density is largest along a ray path which co-incides with generation sites on both the eastern and western ridges in Luzon Strait. Di-urnal energy density is surface-intensified consistent with relatively shallower diurnal raypaths emanating from the eastern ridge.

1. Introduction

Some of the largest internal tides in the ocean, withdepth-integrated energy fluxes >60 kW m−1, are gener-ated at two parallel ridges in Luzon Strait (Figure 1)[Alford et al., 2011; Simmons et al., 2011]. Averagingover many glider missions, considerable asymmetry isfound between eastward and westward propagation intothe Pacific Ocean or South China Sea [Rainville et al.,2012; Rudnick et al., 2013]. Here we focus on the waves,which propagate westward into the South China Sea,steepen, produce large-amplitude internal waves on theshallow thermocline, and ultimately shoal on the conti-nental slope [Duda et al., 2004; Ramp et al., 2004; Zhaoet al., 2004; Alford et al., 2010; Zhang et al., 2011; Rud-nick et al., 2013].

Tidal currents encountering topography heave strati-fied water vertically to produce internal tides, the magni-tude of which depends on the flow strength, topographicslope, and their three-dimensional details [Baines, 1982;Merrifield and Holloway , 2002]. Further spatial and tem-poral variability of internal tidal generation and prop-agation may arise due to either changing backgroundconditions (i.e., stratification, vorticity, mesoscale cur-rents, and the Kuroshio Current) or interference patternsfrom multiple generation sites on the complex topography[Kunze, 1985; Holloway and Merrifield , 1999; Rainvilleand Pinkel , 2006; Rainville et al., 2010; Buijsman et al.,2010; Zhang et al., 2011; Zilberman et al., 2011; Jan et al.,2012; Nash et al., 2012a, b].

1Scripps Institution of Oceanography, University ofCalifornia, San Diego, La Jolla, California, USA

2Applied Physics Laboratory and School of Oceanography,University of Washington, Seattle, Washington, USA

3University of Alaska Fairbanks, Fairbanks, Alaska, USA

Copyright 2013 by the American Geophysical Union.0148-0227/13/$9.00

1

X - 2 JOHNSTON ET AL.: INTERNAL TIDAL ENERGY FLUXES IN THE SOUTH CHINA SEA

In the face of such variability, extensive spatial cov-erage in the South China Sea and temporal coverageover spring-neap cycles is required to assess the gen-eration and propagation of internal tides away fromLuzon Strait (Figure 1). Our work is a componentof the Internal Waves in Straits Experiment (IWISE),an initiative funded by the Office of Naval Research.Two Spray underwater gliders, each equipped with aconductivity-temperature-depth instrument (CTD) andacoustic Doppler profiler (ADP), obtained internal tidalenergy flux from tidally-resolving density and velocitymeasurements in the South China Sea. To our knowl-edge, this work is the first such calculation of energy fluxfrom underwater gliders.

2. Methods

Two gliders observed the internal tide over four spring-neap cycles (13 June–8 August 2011) in the South ChinaSea. At 5 sites along ∼20◦39′N, time series were obtainedwith each covering a spring-neap cycle (Figure 1). Oneglider took advantage of strong northward mean currentsand surveyed the northern South China Sea. This capa-bility to relocate during a mission allows for coverage inspace and time.

For this project, Spray sampled every 6 s (or verti-cally <1 m) during ascents [Sherman et al., 2001]. Thepayload included: (a) a pumped Sea-Bird Electronics(SBE) 41CP CTD to obtain temperature and salinity(S), from which potential temperature (θ) and potentialdensity (σθ) are calculated and (b) a Sontek 750 kHzADP aligned to measure horizontal velocities (u and vwhich are positive east- and northward, x and y) in five4-m vertical range bins. Over 2 months, a total of 1312profiles were completed. Data and times are averaged in10-m bins centered from 10–500 m (Figure 2). To resolvetides, the gliders dove at an angle of 30◦ from 0–500 min depth every ∼2 hours on average. The time betweendives increased from 1.6 hours at the start of the missionto 2.6–2.8 hours at the end due to increased drag frombiofouling [e.g., Rudnick et al., 2013].

Velocity profiles are made similar to lowered profilesfrom ships [Visbeck , 2002]. Vertically-averaged currentsare calculated from Global Positioning System fixes andthe glider’s measured attitude [Todd et al., 2009]. Thedepth-mean current is combined with ADP-measured,glider-relative velocities in a linear system of equations,which is solved by a least squares method for water veloc-ities [Todd et al., 2011]. Similar results are obtained byreferencing objectively-mapped and vertically-integratedADP-measured shear to the depth-mean current [Davis,2010].

A glider can hold station if current speeds are lessthan its speed through the water, 0.25 m s−1. Here, thedepth-mean current and its standard deviation are ∼0.25± 0.15 m s−1, which is a combination of strong Kuroshio,mesoscale, and internal tides (Figures 2c, e). Spray cal-culates its next course based on currents encountered onits previous dive, which is not ideal for oscillating cur-rents with periods comparable to a dive cycle. Neverthe-less, both gliders held their 5 stations (i.e., excluding theSpray 33’s transit north of 21◦N) located along a meanlatitude of 20◦ 39′N from 119◦ 40′E to 120◦ 27′E within aroot-mean-squared distance of 3–15 km.

Four spring tides were observed over 2 months and aredenoted spring tides 1–4. Spray 35 occupied 3 stationsfurther west from the ridge, while Spray 33 occupied 2stations further east and nearer the ridge before survey-ing to the north (Figure 1). To provide a visual refer-

JOHNSTON ET AL.: INTERNAL TIDAL ENERGY FLUXES IN THE SOUTH CHINA SEA X - 3

ence between temporal and spatial views of the results,alternating light/dark glider bars denote a time seriesduration and increasingly darker blue dots are spaced atweekly intervals (Figures 2a–b and similarly in later fig-ures).

At the same time as the glider operations, a mooring atstation S9 (19◦ 20′N, 121◦ 2′N) was near a generation siteat 2300-m water depth on the eastern ridge in southernLuzon Strait [Alford et al., 2011; Pickering and Alford ,2013]. Two stacked McLane Moored Profilers profileddepths of 330–1260 and 1300–2230 m every ∼1.5 hours.Each was equipped with an acoustic current meter andCTD to measure u, v, θ, and S. A subsurface float at300 m contained an upward looking 75 kHz RDI acousticDoppler current profiler, measuring velocity from 40–300m. Temperature in the upper 300 m was obtained fromSBE-56 temperature loggers at 15-m spacing. An SBE-37MicroCAT at 80 m measured θ, S, and pressure. Inter-nal tidal energy flux was calculated from velocity anddisplacement using standard methods [Nash and Moum,2005; Pickering and Alford , 2013], which are similar butnot identical to glider flux calculations (Sections 3 and5).

Further below, we compare the spatial pattern ofthe glider-based mode-1 flux measurements with a re-gional tidal model. The Regional Hallberg IsopycnalTide Model (RHIMT) model is an isopycnal coordinatemodel, which is similar to one used previously to studyinternal tidal generation and propagation both regionallynear Luzon Strait and globally [Simmons, 2008; Simmonset al., 2011]. The model is configured to cover the north-west South China Sea over the region from 17◦ to 25◦N,115◦ to 127.5◦W including Luzon Strait; is forced at theboundaries with M2, K1, O1, and S2 constituents fromthe TPXO6.2 barotropic tidal analysis [Egbert and Ero-feeva, 2002]; uses uniform stratification from the General-ized Digital Environmental Model hydrographic database[Teague et al., 1990]; uses bathymetry from merged ship-based soundings and satellite data [Smith and Sandwell ,1997]; has a horizontal grid resolution of 0.025◦; and has40 vertical layers with their extents optimized for thestudy of internal waves. Three model runs each of ∼1month duration are used to examine temporal variabilityin the glider results. Even though model runs overlapover 5 days, edge effects may occur from spin-up tran-sients and making flux averages over 3 days similar tothe glider data (Sections 3 and 6).

3. Harmonic Analysis

Mode-1 energy fluxes are calculated by fitting one ver-tical mode to harmonic tidal fits of baroclinic pressureand velocities. Here, we present the method used forthe glider data, which is equivalent to the treatment ofthe model and mooring results, although some details arenecessarily different due to the gliders’ lack of full-depthcoverage. First, vertical displacements are obtained fromdensity changes as follows:

η(z, t) =g∆σθ

σθ〈〈N2〉3 d〉100m(1)

where 〈·〉 denotes a running mean over the subscriptedintervals- in this case 100 m in depth and three days, ∆σθ(= σθ − 〈σθ〉3 d) is the density deviation from the three-day lowpassed mean, N2 is the buoyancy frequency, andg is the gravitational acceleration (Figures 2d, f).

Next, harmonic analysis using inertial, M2, andK1 fre-quencies is applied over a moving 3-day window to η, u,and v. Phases are calculated relative to 9 July 2011, the


midpoint of the time series. More details of the fittingand windowing are in Appendix A. With a 3-day window,frequency resolution is sufficient to identify but not dis-criminate amongst diurnal and semidiurnal constituents,which are collectively denoted D1 and D2. Tidal periodsare: T = 12, 12.42, 23.93, and 25.82 hours for S2, M2,K1, and O1. The inertial period is 34 hours and so the fitwindow covers 2 inertial periods. Tidal time series (η′,u′, and v′) are constructed from these D1 and D2 fits andthe reconstructed time series explain 55, 54, and 44% ofthe variance in η, u, and v (Figures 2g–j). Additionalharmonic fits are made using moving 15-day windows todistinguish amongst M2, K1, O1, and S2 constituents(Section 6.4).

4. Zonal and Vertical Structure

To describe the zonal-depth structure of the internaltide propagating westward from Luzon Strait, we bin theglider data south of 21◦N in 0.05◦ zonal and 10-m depthbins (Figure 3). Data cover 4 spring-neap cycles, extend1◦ zonally, and have a mean latitude of 20◦39′N. The twogliders cover the upper 500 m (orange, Figures 3a–b) nearthe first surface reflection of the D1 rays emanating fromthe two ridges in Luzon Strait, while D2 rays reflect fromboth the sea surface and the top of the western ridge.

There are some suggestions of constant phase alongray paths, but the main feature is westward phase prop-agation for both φu and φη (Figures 3i–l). The changeof the depth-mean phase (〈φ〉z) over ∼100 km is roughlyconsistent with the ∼250- and 130-km wavelength of theD1 and D2 internal tides in the South China Sea (Figures3m–n). 〈φ〉z for u′ and η′ are similar as is expected for apropagating internal wave [Gill , 1982].

Energy density is obtained using the tidal amplitudes(A) of u′, v′, η′ (Appendix A):

E(z, t) = 〈ρ〉t(A2u +A2

v + 〈N2〉tA2η)/2 (2)

from which bin means are calculated. Tidal ray pathssuggest possible trajectories from generation sites at theridges in Luzon Strait to observed features in E.

For D1, E is strongest in the upper 200 m (Figure 3c)consistent with the shallow ray paths emanating fromthe topography in Luzon Strait (Figure 3a). While Eis dominated by the kinetic energy as evidenced by thesimilarity of E and Au (Figures 3c and e), the poten-tial energy also suggests energy is concentrated along raypaths. Aη is larger along the ray path from the easternridge, which we observed slightly westward of its surfacereflection (white line, Figure 3g). There is a suggestionof constant phase along this ray path (white line, Figure3k).

For D2, E and Au are strongest up to the first surfacereflection of the ray path from the western ridge and thenabruptly disappear (Figures 3d and f). Aη is strongestin the east and possibly along the upward ray path fromthe western ridge (Figure 3h). Even though the ampli-tudes decrease substantially, phases still show a westwardincrease (Figures 3j and l).

There are at least two possible explanations for thesudden disappearance of the D2 beam after the first sur-face bounce: either (a) turbulence dissipates the beam or(b) the beam propagates out of the study area. Shears arelarger in the upward beam, which could lead to greatermixing. Although application of shear-based mixing esti-mates is questionable in a region of internal tide genera-tion, large-amplitude internal waves, and generally coher-ent waves, we nevertheless attempt estimates of depth-mean turbulent dissipation and diffusivity between 100


and 500 m as [Gregg , 1989; MacKinnon et al., 2013]:

ε = εo〈N2〉3 dN2o

E2L(Rω, α) (3)

Kρ =Γε

〈N2〉3 d(4)

where εo = 6.73 × 10−10 W kg−1 is the background dissi-pation due to a typical Garrett-Munk (GM) internal wavefield, No = 5.24 × 10−3 rad s−1 is the reference buoy-ancy frequency, Γ = 0.2 is a typical value of the mixingefficiency, and L is a correction for the shear-strain ratio(Rω) of the internal waves at a latitude of α. Here we useRω = 3, which is typical for an open ocean, GM internalwave field, and yields L ∼ 1 at this latitude. Rω mightbe different in this region of strong D1 or D2 motions.Since this method is suspect anyhow in a region with co-herent internal waves and since a change by this factormakes little difference as we will find below, we avoid thisadditional detail. Shear is normalized as:

S2 =U2z + V 2

z

〈N2〉3 d(5)

where the shear variance is computed from verticalwavenumber spectra of observed and GM S2 from 100-500 m, over a range of wavenumbers from 1/(200 m) to1/(50 m), and then averaged over 3 days. The ratio ofobserved to GM shear variance is:

E2 =〈S2〉23 d〈S2GM 〉23 d

1 + 1/Rω4/3

(6)

After applying this parameterization to the Spray 33data, we find a mean value of Kρ of O(10−5) m2 s−1,which is a typical open-ocean value. Therefore, it is un-likely that the sudden disappearance of the beam is dueto turbulent dissipation. The more likely explanation isthat the beam bypassed the western portion of our studyarea.

5. Mode Fits

Vertical mode 1 is calculated from a merged N2 pro-file. θ and S observations from 0-500 m are combinedwith those from the World Ocean Atlas 2009 analysisfor depths greater than 500 m (Figures 2a–b, Figure 2d,and insets in Figures 4b and d) [Antonov et al., 2010;Locarnini et al., 2010]. Water depth is predicted fromaltimeter measurements and constrained by soundings[Smith and Sandwell , 1997]. Mode 1 is fit to η′, u′, andv′ to yield mode-1, tidal motions (η′, u′, and v′), wherethe tilde denotes a modal fit (Figures 4a–d). η′, u′, andv′ explain 40, 38, and 29% of the variance in η, u, and v.Mode-1 baroclinic pressure perturbation, p′, is calculatedfrom η′ (Figures 4e–f) and has a zero depth mean [Nashet al., 2005]:

p′(z, t) = psurf + ρ

∫ 0

z

η′〈N2〉t dz (7)

p′surf (z, t) =ρ

H

∫ 0

−Hη′〈N2〉t dz (8)

where p′surf is the unmeasured barotropic or surface pres-sure perturbation, ρ is the in situ density and 〈N2〉t de-notes the time mean from the merged N2 profile.

Lastly, mode-1 tidal energy fluxes are obtained basedon both density and velocity measurements as (Figures4g–h):


[Fx(z, t), Fy(z, t)] = 〈p′u′, p′v′〉3 d (9)

for either D1 or D2 tides with averages over t = 3 days.Pressures, velocities, and fluxes vary in space and time(Figure 4).

Our modal decomposition is limited by depth cover-age. The mode fit is performed over a 500-m depthrange, even though modes are orthogonal only over thefull water depth. When the depth is stretched relative tothe mean stratification (which includes a shallow thermo-cline), 55% of the mean 3200-m water depth is covered(insets in Figures 4b and d) [Nash et al., 2005]. Thisstrong stratification in the upper ocean permits a fit tomode 1 (Figure 2d), which has a zero crossing for u anda maximum for η near 900 m (insets in Figures 4b andd). u (η) has a surface maximum (zero).

Nash et al. [2005] estimate energy flux errors fromMonte Carlo simulations using synthetic data with largegaps in vertical coverage. For a two-mode fit with a 2600-m gap in 3100 m of water, errors are 30–40% of the full-depth values. Fitting only one mode will reduce this errorand, in our particular case, mode 1 dominates. Since suchenergy flux estimates are unbiased, our 3-day harmonicfitting interval will further reduce errors.

6. Mode-1 Fluxes

6.1. Overview

To demonstrate our capability to measure mode-1 tidalfluxes from gliders, we discuss details of the tidal andmodal fits before moving on to a description of the fluxes,their variation in space and time, and a comparison tothe mooring and model.

Considerable tidal variation is evident in the data fromSpray 35 (Figures 2a–c and e). Similar results are foundfor Spray 33, but are not shown. Mesoscale changes in uand v are similar in magnitude to the tidal oscillations.Tidal displacements of ∼40 m (Figure 2f) have similaramplitudes to mesoscale changes, which are evident in θand S (Figures 2a–b).D1 u

′ shows 4 spring tides and has surface-intensifiedvalues consistent with mode 1 (Figure 2g), while theD2 component is weaker, does not display as clear aspring-neap cycle, and is not surface-intensified (Figure2i). D2 η

′ has a larger magnitude near 500 m which re-sembles mode 1, while the D1 fit displays more verticalstructure. The modal and tidal fits are stronger at depthfor η′ and near the surface for u′ (Figures 4a–d). Suchstructures produce surface-intensified p′ and fluxes (e.g.,p′u′) with four spring-neap cycles (Figures 4e–h). Fluxesare westward.

Depth-integrated D1 and D2 fluxes are strongest near20◦ 30′N in both the observations and model (Figure 5).Fluxes are almost always westward and propagating awayfrom Luzon Strait. While some of what appears to bespatial variability is due to sampling over spring and neaptides (Figure 6), weaker fluxes are generally found in thenorthern portion of the study area (Figure 5).

Glider fluxes display a combination of spatial and tem-poral variability. Model results include a spring-neap cy-cle driven by 4 tidal constituents and can help distinguishspatial from temporal variability. In Figure 6, model re-sults are sampled along the glider tracks. Comparisonof glider and moored fluxes gives some idea of temporalvariability from generation versus propagation.

6.2. Spray 35

First, we consider Spray 35 results against those from


the model and mooring. Over much of the time series,D2 fluxes are about 10 kW m−1 for Spray 35 and themooring, but for the last spring tide the mooring flux in-creases (Figure 6b). For the rest of the time, it is difficultto identify 4 spring tides except in the model, which issubsampled along the glider’s track. They are roughlyequal around 25 kW m−1 in the glider’s area of opera-tion.

For D1, Spray 35 shows stronger spring tides 2–3 at 40kW m−1 (orange line, Figure 6a), weaker spring tides 1and 4, and a similar pattern to the model’s Fx (red line)and the mooring’s northward flux (dashed blue line is -Fy). Fx from the mooring displays roughly equal springmagnitudes of 15–20 kW m−1. The propagation direc-tion of moored fluxes (Figure 5) and similarity of fluxmagnitudes between the mooring and Spray 35 (Figure6a) indicate waves from the southeast corner of LuzonStrait reach the glider in the South China Sea.

6.3. Spray 33

Next, fluxes from Spray 33 are compared with thosefrom the model and Spray 35. D1 fluxes measured bySpray 33 increase from spring tide 1 to 2, similar to Spray35 (Figures 6a and c). Spring tides 3 and 4 are smallerfor Spray 33 as it moves out of the main D1 beam aroundspring tide 3 and then transits northward for spring tide4 (Figures 5a and 6c). D2 fluxes for spring tides 1–3 are25–30 kW m−1 with a drastic decrease for spring tide 4in the northern half of the South China Sea (Figures 5cand 6d). The modelled fluxes along the glider’s trackdecrease from ∼30 kW m−1 at spring tides 1–2 to ∼20kW m−1 at spring tides 3–4.D1 fluxes appear to increase with distance west-

ward from Luzon Strait (Figures 5a, 6a, and 6c), whileD2 fluxes decrease (Figures 5b, 6b, and 6d). This increasein D1 flux is found with the model and indicates a su-perposition of energy from various generation sites (Fig-ure 5b). Glider-measured D2 fluxes along 120◦ 18′W arewest-northwestward and stations further to the south orwest may be out of the main beam, which appears nar-rower than in the model (Figure 5b). D2 fluxes closer tothe ridge are comparable in magnitude to model predic-tions (spring tides 1–2, Figure 6d), but the observed fluxdirection is west-northwestward rather than westward asin the model (Figure 5b). The modelled westward fluxbeam has a larger meridional extent, which suggests thegliders should have been in the beam even if the beamwas moved 50 km or oriented west-northwestward (Fig-ure 5c).

6.4. Individual Tidal Constituents

To distinguish between K1, M2, O1, and S2 con-stituents in the data, a 15-day window for harmonic fitsprovides sufficient frequency resolution. The dominantconstituents are K1 and M2 (figures not shown). Themean fluxes over a spring/neap cycle for both K1 andM2 are 15–20 kW m−1 near the ridge from Spray 33 (fig-ures not shown), which are similar to mean fluxes fromRainville et al. [2012]. Mean M2 fluxes decrease to 5kW m−1 further west from the ridge at Spray 35. O1 andS2 fluxes are negligible closer to the ridge, while O1 isabout 5 kW m−1 further west.

6.5. Model-Data Comparison

Root-mean-squared (rms) differences are calculatedbetween model and glider D1 and D2 mode-1 fluxes(Table 1). Mission-mean fluxes, 〈Fx〉t, are within 6–7kW m−1 excluding the D2 estimate from Spray 35, which


seems to be out of the main flux beam. These differencesof 33–64% of 〈Fx〉t are equal or larger than what is ex-pected because of the data gap below 500 m (Section 3).The rms differences are (again excluding D2 fluxes fromSpray 35) about 20% of the peak Fx values which are2-3× larger than 〈Fx〉t.

It seems D1 fluxes increase westward likely due to su-perposition of waves from different sources, as evidencedby the similar spring-neap patterns and magnitudes be-tween Spray 35 and the mooring. D2 fluxes decrease tothe west. Greater D2 variability is seen in the gliderdata than expected from the model (i.e., stronger/weakerD2 flux in the east/west at Spray 33/35 than expectedfrom the model).

However, the comparison of D1 fluxes from gliderswith model and mooring fluxes still suffers from confu-sion of space and time [Rudnick and Cole, 2011]. On onehand, the similar temporal pattern in fluxes from Spray35 and the mooring suggests the glider is sampling wavesgenerated near the mooring and show temporal variationin generation- there seems to be little effect on mode-1propagation. On the other hand, similar model results(which is driven by TPXO currents with similar springmagnitudes) suggest the gliders are seeing mostly spatialvariability in fluxes (before Spray 33 transits northward).

7. Conclusion

As our primary technical result, we calculate mode-1fluxes from velocity and density measurements by glid-ers which profiled rapidly enough to resolve the tides inthe upper 500 m. Time series at fixed locations and evenwhile moving provide regional coverage over the northernhalf of the South China Sea using two gliders. The mainlimitation in our method is the lack of glider data below500 m, which is mitigated by both the shallow thermo-cline and fitting mode 1 to tidal currents and displace-ments. During spring tides, westward D1 and D2 mode-1fluxes exceed 40 and 30 kW m−1. As long as the ther-mocline is shallow enough to permit mode-1 fits, gliderscan survey regional areas for internal tides with mode-1flux estimates once every few days for ∼2 months.D1 fluxes from the model and observations show a

beam of westward flux along ∼20◦ 39′N and decreasingfluxes in the northern half of the South China Sea (Figure5). While the model shows roughly uniform, westwardD2 fluxes near 20◦ 39′N, our observations indicate themain D2 flux beam was west-northwestward near Spray33 and bypassed Spray 35 in the west. The model indi-cates that the beam should be of sufficient meridional ex-tent that this orientation should not matter much. How-ever, the mesoscale or Kuroshio may affect the gener-ation or propagation of internal waves. Such possibili-ties can be investigated with models which include bothmesoscale and tides [Ko et al., 2009].

The middle two D1 spring tides observed by Spray 35show 60 and 10% stronger fluxes than spring tides 1 and4, which is a similar to the pattern of moored fluxes (Fig-ure 6a). The range of spring magnitudes in the glider,mooring, and model fluxes is similar, although the modeldoes not replicate the largest spring tides 2–3 since it issolely forced by TPXO tidal currents with a horizontallyuniform stratification. Over these 2 months, the TPXOD1 and D2 tidal currents show little variation betweenspring tides. While the good comparison between gliderfluxes and model fluxes along glider tracks suggests spa-tial variation, the similar pattern of spring tide magni-tudes at the mooring and Spray 35 suggests internal tidegeneration is varying in time (Figures 5–6). Mesoscale or


Kuroshio influences on internal tidal generation might ac-count for the variable spring tide magnitudes. However,given the similarity between mooring fluxes and gliderfluxes at a distant location, propagation effects on mode1 seem small.

Despite the similar patterns in the westward fluxes,model-data rms differences are ∼20%/50% of thepeak/mean westward glider fluxes from 3-day harmonicfits. Some of this disagreement is likely due to our largedata gap below 500 m, while some arises from real spa-tial and temporal variability in the observations of inter-nal tidal generation and/or propagation, which are notincluded in the model.

Perhaps the most interesting scientific result is thatour phase estimates appear stable across 100 km and 2months. The zonal and vertical structure of the inter-nal tide is obtained by binning our measurements, whichcover four spring-neap cycles and over 100 km along20◦ 39′N. This result is somewhat surprising given thevigourous mesoscale flows in this area and other processesaffecting internal tidal generation and propagation, whichgenerally produce a broad-banded internal tide [Section1; Nash et al., 2012a, b]. Consistent phase propagationover a 2-month mission highlights the narrow-banded na-ture of the internal tide in time, which also makes someof the calculations here and in Rainville et al. [2012] pos-sible. Another interesting feature is the roughly constantphase along some ray paths emanating from likely gener-ation sites on both ridges in Luzon Strait even after one(three) reflection(s) for the D1 (D2) rays. Energy densitycan be intensified along these ray paths, which are thencalled internal tidal beams to emphasize the larger dis-placement and velocity amplitudes [Holloway and Merri-field , 1999; Martin et al., 2006; Cole et al., 2009; John-ston et al., 2011]. While constant phase (i.e., a wavecrest) defines a ray path [Mowbray and Rarity , 1967],constant phase along a beam has been infrequently ob-served. Previous observations in other locations showconstant phase along ray paths either over smaller hor-izontal distances, with less resolution, or closer to gen-eration sites [Torgrimson and Hickey , 1979; Pingree andNew , 1991; Petruncio et al., 1998; Lam et al., 2004].

Overall, our results build on the successful approachof the Hawaii Ocean Mixing Experiment in using modelpredictions to focus field work [Merrifield et al., 2001;Rudnick et al., 2003], a method which is applied againin IWISE and other field work in the South China Sea[Simmons et al., 2011]. This simultaneous spatial andtemporal coverage by the gliders, mooring, and modelnot only provides increased confidence in our flux cal-culations from gliders, but allows us to make some in-roads separating temporal from spatial variability. Evenwith these substantial observational and modelling ef-forts, some confusion of space and time variability re-mains.

While mode-1 carries most of the energy flux, consid-erable variance is found at smaller scales, which can beinvestigated with the <1-m vertical resolution of gliders.Recent measurements of high-frequency internal wavesby gliders shows the vertical velocity variance is highnear the Luzon Strait and decays away from it [Rudnicket al., 2013], a similar pattern to the mode-1 energy flux[Rainville et al., 2012]. Our next step is is to examinepossible energy transfer from the large-scale propagatinginternal tides to energetic high-frequency internal waves.Both aspects of this problem are now amenable to inves-tigation with gliders.


Appendix A: Window for the HarmonicFit

We choose window sizes of nw = 3 and 15 days forthe harmonic fits here to resolve spring-neap variabilityand distinguish amongst D1 and D2 constituents. Toassess this choice of window length, a synthetic spring-neap cycle is constructed from K1 and O1 constituents(red line in Figure 7a): h(t) = AK1 cos(ωK1t − φK1) +AO1 cos(ωO1t−φO1), where subscripts identify tidal con-stituents (K1, O1), A is the amplitude (2, 1), ω is theradial frequency, and φ is the phase (0 in both cases). Asin Section 3, a harmonic fit for K1 only is applied overa running 3-day window. Since the window length is in-sufficient to distinguish between the D1 constituents, theamplitude and phase of the D1 tide through the spring-neap cycle is reproduced well (orange line in Figure 7a).The 13-day window extracts the correct phase (φK1 = 0)and amplitude (AK1 = 2), but for shorter windows phaseand amplitude varies over a spring-neap cycle. The phasedifference between the harmonic fit and the K1 signalat various window lengths (nw = 1–13 days) is greatestbetween spring and neap tides, while it reaches zero atspring and neap tides when the K1 and O1 signals areperfectly in and out of phase (Figure 7b). The amplitudefrom the harmonic fit is minimum at neap tide and maxi-mum at spring tide (Figure 7c). If there is sufficient datadistributed in phase through a spring-neap cycle, correctamplitudes and phases can be obtained by averaging thephases or amplitudes obtained from harmonic fits usingshorter windows (i.e., an average along a line of constantnw in Figures 7b–c yields AK1 ∼ 2 and φK1 ∼ 0). With-out averaging, phase will vary from its true value.

Acknowledgments. This work was supported by the Of-fice of Naval Research grants # N00014-09-1-0273, N00014-09-1-0219, N00014-10-0315, and N00014-05-1-0360 as compo-nents of IWISE. Spray was developed and is operated by theInstrument Development Group at SIO. We thank the masterand crew of R/V Roger Revelle; D. Black and A. Waterhouse(SIO); and E. Boget, K. Magness, J. Mickett, Z. Parsons, andL. Rainville (APL, UW) for deploying and recovering the glid-ers and mooring. We are grateful for logistical assistancefrom our colleagues, T. Y. Tang (Institute of Oceanography,National Taiwan University), Y. J. Yang (Naval Academy, Tai-wan) and M.-H. Chang (National Taiwan Ocean University).

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Table 1. D1 and D2 mission-mean glider fluxes (〈Fx〉t) androot-mean-squared (rms) differences with the model in unitsof kW m−1 for both Spray 35 and Spray 33.

Tide Spray 35 Spray 33

〈Fx〉t rms 〈Fx〉t rms

D1 -21 7 -11 7

D2 -6 11 -13 6

20 kW m−1model

mooring

(a) D1

18o

19o

20o

21o

22oN

120o 121oE

Spr

ay 3

5

Spray 33

(b) D2

120o 121oE

SouthChinaSea

LuzonStrait

50Depth [km]

Figure 1. Time-averaged, depth-integrated, mode-1 en-ergy fluxes of 20–30 kW m−1 are generated at the ridgesin Luzon Strait and propagate into the South China Seafor (a) D1 and (b) D2 constituents from the model (red)and mooring (blue). Glider tracks (orange and black forSpray 33 and 35), mooring location (cross), and the re-gion (yellow) in Figure 5 are also indicated. Bathymetry(grey shading), land (brown shading), and a scale vectorare shown.


(a)

0

200

400

θ

[oC]

10

20

30

(b)

S[psu]

33.8

34.8

(c)

0

200

400

v

[m s−1

]

−0.7

0

0.7

(d)

N

2

[s−2

]

10−5

10−3

(e)Depth

[m

]

0

200

400

u

[m s−1

]

−0.7

0

0.7

(f)

η

[m]

−40

0

40

(g)

D1

0

200

400

u′

[m s−1

]

−0.5

0

0.5

(h)

D1

η′

[m]

−30

0

30

(i)

2011

D2

19 Jun 03 Jul 17 Jul 31 Jul

0

200

400

u′

[m s−1

]

−0.25

0

0.25

(j)

2011

D2


η′

[m]

−20

0

20

Figure 2. Observations from Spray 35 of: (a) θ, (b) S,(c) v, (d) N2, (e) u, (f) η with isopycnals (black lines,σθ = 22, 24, and 26 kg m−3), (g) D1 u

′, (h) D1 η′, (i)

D2 u′, and (j) D2 η

′. Note the changes in colour shadingintervals. Blue dots plotted at 7-day intervals and thealternating lighter and darker colours on the upper axesallow comparison with the glider locations in Figure 5.


120o 121

o 122

oE

(a) D1

0

1000

2000

3000

120o 121

o 122

oE

(b) D2

(c) D1

0

200

400

E

[J m−3

]

0

5

(d) D2

E

[J m−3

]

0123

(e) D1

Depth

[m

]

0

200

400

Au

[m s−1

]

0

0.5

(f) D2

A

u

[m s−1

]

0

0.5

(g) D1

0

200

400

Aη [m]

0300

(h) D2

Aη [m]

0300

(i) D1

0

200

400

φu [

o ]

90

270

(j) D2

φu [

o ]

0

180

(k) D1

0

200

400

φη [

o ]

0

180

360

(l) D2

φη [

o ]

0

180

(m) u η

D1

120oE 120

o 30’

⟨ φ ⟩

z [

o ]

120

180

(n)

D2

120oE 120

o 30’

0

90

180

Figure 3. The vertical-zonal structure of the internaltide for D1 (left column) and D2 (right column) con-stituents is displayed. (a–b) Ray paths are traced to to-pography in Luzon Strait and are shown in the upper500 m in the subsequent panels. Orange boxes (upperleft) indicate the location of the glider data in subsequentpanels. We calculate vertical-zonal bin means for (c–d)baroclinic energy density, tidal amplitudes from the har-monic fits of (e–f) u′ and (g–h) η′, and tidal phases for(i–j) u′ and (k–l) η′. (m–n) Depth-mean phases for u′

and η′ are calculated from data in Figures 3i–l.


(a)

D1

0

200

400

u′

[m s−1

]

∼

−0.5

0

0.5

(b)

D2

u′

[m s−1

]

∼

−0.2

0

0.2

00

3200

(c)

D1

0

200

400

η′

[m]

∼

−20

0

20

(d)

D2

η′

[m]

∼

−20

0

20

00

3200

(e)

De

pth

[m

]

D1

0

200

400

p′

[kPa]

∼

−0.7

0

0.7

(f)

D2

p′

[kPa]

∼

−0.4

0

0.4

(g)

2011

D1


0

200

400

p′u′

[W m−2

]

∼ ∼

−200

0

200

(h)

2011

D2


p′u′

[W m−2

]

∼ ∼

−60

0

60

Figure 4. Mode-1 reconstructions for Spray 35 fromD1 (left column) and D2 (right column) harmonics (Fig-ure 2g–j) yield (a–b) u′ and (c–d) η′. (e–f) p′ is calculatedfrom η′, which allows calculation of (g–h) zonal mode-1fluxes, p′u′. Blue dots plotted at 7-day intervals andthe alternating lighter and darker colours on the upperaxes allow comparison with the glider locations in Figure5. Insets in Figures 4b and 4d show the vertical mode-1 structure for pressure and displacement over the fulldepth (yellow) and in the upper 500 m sampled by thegliders (orange) with the mean stratification at the meanwater depth of 3200 m for the glider missions.


20 kW m−1

glidermodel

mooring

(a) D1

20o

30’

21oN

21o

30’

Spray 35

Spray 33

121o 2

’E

19o 20’N

(b) D2

20o

30’

21oN

21o

30’

119o 30’ 120oE 120o 30’Figure 5. Depth-integrated, mode-1, baroclinic energyfluxes in the South China Sea are measured over springand neap cycles by the gliders (orange) and are time-averaged from the model (red) and mooring (blue) for(a) D1 and (b) D2 constituents. Glider fluxes are plot-ted at 1-day intervals. The glider tracks are plotted withalternating lighter and darker colours correspond to al-ternating colours on the time axes in Figures 6–4. Themooring lies further south and the vector is inset (lowerright). Blue dots are plotted at 7-day intervals (here andin Figures 6–4) and get darker with increasing time.


(a) D11 2 3

4 Spray 35−50

0 (b) D2glidermodelmooring Spray 35

(c) D1

F[k

W m

−1]

Spray 33

201119 Jun 03 Jul 17 Jul 31 Jul

−50

0 (d) D2

Spray 33

201119 Jun 03 Jul 17 Jul 31 Jul

Figure 6. Depth-integrated, zonal, mode-1 energy flux(Fx) from (a–b) Spray 35 and (c–d) Spray 33 for D1 (left)and D2 (right) exceed 40 and 30 kW m−1 westward.Solid lines indicate Fx from the gliders (orange), model(red), and mooring (blue). The dashed blue line is -Fyfrom the mooring (i.e., this flux is northward). Springtides are labelled 1–4 (Figure 6a). Blue dots plotted at7-day intervals and the alternating lighter and darkercolours on the upper axes allow comparison with theglider locations in Figure 5. Areas of model overlap (lightred) may suffer from edge effects.

−2

0

2

h

(a)

(b)

2

6

10∆φ

−30o

0o

30o

n

w

[da

ys]

t [days]

(c)

0 2 4 6 8 10 12

2

6

10A

1

3

Figure 7. (a) A synthetic spring-neap cycle (dottedblue) is constructed from K1 (black) and O1 (grey) sig-nals with constant amplitudes of 2 and 1, to which aharmonic fit for K1 only is applied over a running 3-daywindow (red). (b) The phase difference between the har-monic fit and the K1 signal at various window lengths(nw = 1–13 days) is greatest between spring and neaptides, while it reaches zero at spring and neap tides whenthe K1 and O1 signals are perfectly in and out of phase.(c) The amplitude from the harmonic fit is minimum atneap tide and maximum at spring tide.

internal tidal energy fluxes in the south china sea from density and velocity measurements by

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