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FEATURE ARTICLE
HOW DO TIDES AFFECT
UNDERWATER ACOUSTIC PROPAGATION?
A COLLABORATIVE APPROACH TO IMPROVE INTERNAL WAVE MODELING
AT BASIN TO GLOBAL SCALES
By Martha C. Schönau, Luna Hiron, John Ragland, Keshav J. Raja, Joseph Skitka, Miguel S. Solano, Xiaobiao Xu,
Brian K. Arbic, Maarten C. Buijsman, Eric P. Chassignet, Emanuel Coelho, Robert W. Helber, William Peria, Jay F. Shriver,
Jason E. Summers, Kathryn L. Verlinden, and Alan J. Wallcraft
INTRODUCTION
Te underwater soundscape encompasses a range of ambi-
ent, anthropogenic, and biological sound, with research span-
ning acoustic communications to passive acoustic monitoring.
Te density of water allows sound, which is a pressure wave,
to travel short distances and across ocean basins. Te speed of
sound is set by water temperature and salinity, and pressure.
As it travels, sound scatters from the bathymetry, the surface,
animals, or other objects. Sound refracts when it encounters a
diference in sound speed, which can be introduced by fronts,
eddies, currents, vertical stratifcation, internal tides, and gravity
waves and mixing.
Soundscape modeling, such as that used to trace the impacts
of anthropogenic noise on marine mammals, is dependent on
the sound speed structure employed in the ocean model. Te
vertical motions of internal tides and internal gravity waves
(IGWs) bring cold water up and push warm water down, chang-
ing the sound speed (Gill, 1982). Internal tides and IGWs dissi-
pate energy to both smaller and larger scales. Te sound speed
in tidally forced simulations may difer drastically from simula-
tions without tidal forcing. Simulations are also highly sensitive
to grid spacing, mixing parameterizations, and boundary condi-
tions. Identifying the diferences of tidally driven ocean models
from their non-tidal counterparts and the actual ocean, and the
length scales that resolve IGW processes, may in turn inform
how internal wave models should be used for diverse acoustic
and biological studies.
Tis paper presents progress in the modeling of internal tides
and IGWs, the efect of these advances on modeling sound speed
and sound propagation in underwater ray-tracing acoustic mod-
els, and the use of deep learning (DL) to predict the ocean state.
Te research stems from a coordinated project funded under the
Ofce of Naval Research (ONR) Task Force Ocean (TFO) initia-
tive designed to train early career scientists in cross- disciplinary
oceanography, underwater acoustics, and machine learning
techniques. Te project was dubbed “TFO-HYCOM” afer
the US Navy’s operational HYbrid Coordinate Ocean Model
(HYCOM), which featured prominently in the research project.
BACKGROUND AND APPROACH
Internal Gravity Waves
Internal gravity waves exist as undulations along constant den-
sity ocean surfaces (isopycnals) with a restoring force of grav-
ity. As IGWs displace isopycnals, they create a profle of depth-
dependent velocities. Internal tides, a special type of IGWs,
exist at tidal frequencies and are generated by tidal fow over
ABSTRACT. Accurate prediction of underwater sound speed and acoustic propagation is dependent on realistic representation
of the ocean state and its underlying dynamics within ocean models. Stratifed, high-resolution global ocean models that include
tidal forcing better capture the ocean state by introducing internal tides that generate higher frequency (supertidal) internal waves.
Trough the disciplines of internal wave modeling, acoustics, and machine learning, we examined how internal wave energy moves
through numerical simulations, how this energy alters the ocean state and sound speed, and how machine learning could aid the
modeling of these impacts. Te project used global, basin-scale, and idealized HYbrid Coordinate Ocean Model (HYCOM) simu-
lations as well as regional Massachusetts Institute of Technology general circulation model (MITgcm) simulations to examine how
tidal inclusion afects sea surface height variability, the propagation and dissipation of internal wave energy, and the sensitivity of
internal wave modeling to vertical and horizontal grid spacing. Sound speed, acoustic parameters, and modeled acoustic propaga-
tion were compared between simulations with and without tidal forcing, and deep learning algorithms were used to examine how a
tidally forced ocean state could be generated while reducing computational costs.
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bathymetric features (e.g., Bell, 1975). Tey difer from near-
inertial IGWs that are generated by high-frequency wind forc-
ing that have frequencies near the Coriolis frequency (Pollard
and Millard, 1970). Aside from internal tides and near-inertial
waves, there is a spread of internal wave energy known as the
IGW continuum spectrum (Garrett and Munk, 1975), which
can be shaped by mesoscale eddies (Barkan et al., 2017) and
nonlinear interactions. Nonlinear interactions can bring IGW
scales down to 1 m or less and can cause IGWs to overturn and
break, a dominant process in the mixing of the ocean interior
(MacKinnon et al., 2017).
IGWs can be discussed in terms of their vertical structures, or
“modes” (Gill, 1982). Tese modes approximate IGW dynamics
as a linear superposition of standing waves in the vertical direc-
tion and propagating waves in the horizontal direction. Tis is
reasonable in a buoyancy-driven fow where the horizontal scale
is much greater than that of the vertical. Each wave mode has
a characteristic length, phase speed, and vertical structure that
depends on the frequency of the IGW, the Coriolis frequency,
and the vertical density gradient. Te lowest baroclinic mode
has a singular, two-layer horizontal structure (i.e., the veloci-
ties are out of phase above and below the thermocline); higher
modes have greater vertical structure. Waves in the IGW spec-
trum at frequencies greater than tidal frequency, called super-
tidal, are thought to arise from nonlinear interactions between
internal tides and near-inertial IGWs (Müller et al., 1986).
IGW variability has not been well captured by global ocean
simulations. Simulations may lack certain forcing (e.g., tidal)
or may parameterize, rather than resolve, fner-scale processes.
Barotropic tidal models, where water movement is uniform with
depth, have been available since the 1970s (e.g., Hendershott,
1981), but they do not allow stratifed fow. In the last two
decades, increases in computational power have made it possi-
ble to accurately model internal tides in a stratifed ocean. Tese
models have evolved from using horizontally uniform two-layer
(Arbic et al., 2004) or multilayer (Simmons et al., 2004) stratif-
cation to embedding tidal forcing in ocean general circulation
simulations with stratifcation that varies geographically in a
realistic manner (Arbic et al., 2012).
Tis study focused on the modeling of internal tides and
IGWs in HYCOM, the backbone of the operational forecasting
system of the US Navy (Metzger et al., 2014). Te Navy HYCOM
simulations use a hybrid vertical coordinate system: isopycnal
coordinates in the stratifed ocean interior, a dynamic transi-
tion to pressure (p) coordinates in the surface mixed layer, and
bathymetry-following (σ) coordinates in shallow shelf water
(Bleck, 2002; Chassignet et al., 2006). Te simulations use real-
istic atmospheric forcing from the Navy Global Environmental
Model (NAVGEM; Hogan et al., 2014) and can be run with or
without data assimilation and with or without tidal forcing.
Sophisticated methods from the data-assimilation literature
have also been applied to bring the tidal simulations closer to
observations (Ngodock et al., 2016).
For this study, HYCOM was primarily utilized without data
assimilation. Data assimilation can create “shocks” as it brings
the model closer to observations, disrupting the geostrophic
balance between horizontal pressure gradients and rotation.
Raja et al. (2024) found that as the modeled ocean tries to restore
geostrophic balance, spurious low-mode internal waves are gen-
erated. Tese waves have frequencies that overlap with the tidal
and inertial bands, complicating the analysis of naturally occur-
ring tidal and near-inertial waves. Te interaction of these spuri-
ous IGWs with other internal waves or eddies and their eventual
dissipation can also alter the ocean energetics. For this reason,
most of our HYCOM internal tide and IGW studies (e.g., Raja
et al., 2022), and subsequent acoustics research for this project,
have used HYCOM simulations without data assimilation.
Te HYCOM model was used in this study with a variety of
vertical, horizontal, and bathymetric grid spacings. Te most-
used model setups were regional and global versions of tidally
forced HYCOM with a horizontal grid spacing of 1/25° to 1/50°,
typically the highest resolution spacing at which Global HYCOM
can be run. Tis is fner than the 1/12° grid spacing available in
most of today’s publicly available global ocean models. Idealized
versions of the model, such as using a single temperature-
salinity profle in a two-dimensional feld, were used to isolate
the efects of internal tides on stratifcation and energy trans-
fer. Regional simulations using the Massachusetts Institute of
Technology general circulation model (MITgcm) were com-
pared to HYCOM simulations because of MITgcm’s diferent
boundary conditions and, for this study, its fner grid spacing.
Sound Propagation
Internal tides and IGWs have long been associated with under-
water acoustics. Te infuence of internal tides and IGWs on
sound speed variability has been at the core of many observa-
tional (e.g., Flatté et al., 1979; Tang et al. 2007; Worcester et al.,
2013) and modeling (e.g., Colosi and Flatté, 1996) studies.
Alternatively, acoustic tomography, an inverse method that uses
long-range acoustic propagations to infer ocean structure, has
been used to study the barotropic and baroclinic tides themselves
(Dushaw, 2022). In addition to the tilt of density surfaces caused
by internal waves, temperature and salinity fuctuations along a
constant density surface, called “spice,” can have a similarly large
impact on sound speed and its gradients (Dzieciuch et al., 2004).
“Spiciness,” caused by ocean stirring by mesoscale eddies, could
difer between tidal and non-tidally forced ocean simulations.
Tis study focused on upper ocean acoustic structure and
propagation. In the uniform temperature and salinity layer found
at the ocean surface in many regions, pressure causes sound
speed to increase with depth, ofen creating a local subsurface
maximum in sound speed (Helber et al., 2008). Tis subsur-
face sound-speed maximum, called the sonic layer depth (SLD),
has the potential to form a surface-layer duct where sound is
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refracted upward from the SLD and refected downward by the
surface, allowing acoustic energy to travel long distances. Te
sound speed gradient below the SLD, called the below-layer gra-
dient (BLG), can infuence the potential of this surface-layer duct
to trap energy.
For this project, sound speed, its variability, the SLD, and
the BLG were compared between simulations with and with-
out tidal forcing. Acoustic transmission loss (TL), an estimate
of acoustic pressure, was calculated from a virtual source using
a three-dimensional ray-tracing acoustic model, Bellhop 3D
(Porter, 2011). TL exemplifes how the diferences in sound
speed between diferently forced ocean simulations can afect
acoustic propagation models.
PROGRESS IN IGW MODELING
Bringing Models Closer to Observations
Realistically capturing ocean variability at diferent length scales,
from large-scale eddies to smaller coastal features, is a central
goal of global ocean models. Sea surface height (SSH) variability
is a useful proxy for mesoscale ocean variability. Te SSH wave-
number spectrum was used as a single descriptor of the rela-
tive strength of ocean variability as a function of length scale.
Wavenumber, defned as one divided by wavelength, is large
where spatial scales are small. Figure 1f shows an example of
the wavenumber spectra and the spectral slope of the mesoscale
variability (the steepness of the spectrum from 250 km to 70 km
wavelength). Te SSH spectral slope varies greatly by location
(Figure 1e; Zhou et al., 2015). Te slope is steepest (–5) along
the western boundary current (Gulf Stream), which has large-
scale currents and high mesoscale eddy variability. Te slopes
are fatter (close to –3) in the mid-latitude interior, such as the
eastern North Atlantic, and much fatter (close to –1) in the
equatorial region.
Te inclusion of tidal forcing in ocean models is paramount
to bringing SSH variability in simulations closer to observations.
Figure 1 compares a series of high-resolution regional 1/50°
North Atlantic HYCOM simulations to satellite altimetry obser-
vations. Without tidal forcing, high-resolution models could not
replicate this spatial SSH variability (e.g., Figure 1a,b; Chassignet
and Xu, 2017). With tidal forcing (Figure 1c,d), the SSH spec-
tral slope in the equatorial Atlantic and the eastern subtropi-
cal North Atlantic began to match observations. Here, there are
strong barotropic tides and strong stratifcation in the upper layer
of the water column. In these regions, SSH variability at length
scales of 70–120 km increased, fattening the spectral slope in the
70–250 km mesoscale range (Figure 1f). High-resolution bathym-
etry (Figure 1b) and high-frequency wind variability (Figure 7b
in Xu et al., 2022) had comparably minor impacts on the spec-
tral slope, except at local scales where internal tides are generated
along topography, such as near the shelf break (Xu et al., 2022).
NEATL
NEATL-T-HB
Zhou et al. (2015)
Wavenumber Spectra
NEATL-HB
NEATL-T
FIGURE 1. (a–e) Mesoscale sea surface height (SSH) wavenumber spectral slope in the
Atlantic Ocean based on a series of 1/50° numerical simulations and observations: (a) NEATL
(no tides), (b) NEATL-HB (no tides, with high-resolution bathymetry), (c) NEATL-T (with tides),
(d) NEATL-T-HB (with tides, high-resolution bathymetry), and (e) satellite observations from
Zhou et al. (2015). (f) Example of the wavenumber spectra averaged from 10°S–10°N and
35°–15ºW from observations and four model configurations. The mesoscale spectral slope
in panels a–e was calculated between 70 km and 250 km. Modified from Xu et al. (2022;
their Figures 7 and 11)
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From Global to Regional: Supertidal Energy
Tidal energy is mainly concentrated at the diurnal and semi-
diurnal astronomical forcing frequencies, and some of this
energy is transferred to higher (and lower) frequencies. Band-
pass fltering can separate the energy between that at semi-
diurnal tidal frequencies (Figure 2a) and that at higher, super-
tidal frequencies (Figure 2b). Diurnal and semidiurnal energy
dominate most of the internal tide spectrum, except along the
path of large amplitude internal tides near the equator. Most of
the research on IGW-IGW interactions in the open ocean has
focused on “subharmonic resonance,” a transfer of tidal energy
to lower frequencies (e.g., Ansong et al., 2018). For this project,
Solano et al. (2023) evaluated the decay of the low-mode inter-
nal tide due to superharmonic wave-wave interactions, leading
to the transfer of tidal energy to higher, supertidal frequencies.
Globally, supertidal kinetic energy (KE) accounts for about 5%
of the total IGW energy. Supertidal energy is greatest at low
latitudes. Equatorward of 25°, 9% of the total tidal energy is
transferred to supertidal KE. At generation sites of large ampli-
tude internal tides or “hotspots,” such as the Bay of Bengal,
the Amazon Shelf, and the Mascarene Ridge, 25%–50% of the
IGW KE is found at supertidal frequencies (Solano et al., 2023;
Buijsman et al., 2025).
Here, we focus on two regions with high supertidal KE: the
Amazon Shelf and the Mascarene Ridge (Figure 3). Te nonlin-
ear IGW KE transfer from primary to supertidal frequencies has
a banding pattern (Figure 3a,b) that is also present in the hor-
izontal divergence of the supertidal energy fux (Figure 3c,d),
suggesting a common mechanism for the nonlinear energy trans-
fer between length scales. Decomposing the energy into separate
modes (Figure 3e,f), the banding pattern appears when the low-
est modes (1+2) are superimposed but not for individual modes.
FIGURE 2. Time-mean and depth-integrated internal wave
kinetic energy (J m–2) band-passed at (a) semidiurnal, and
(b) supertidal frequencies. Regions with relatively high
supertidal energy indicated by the black rectangles are:
(1) the Amazon Shelf, (2) the Mascarene Ridge, and (3) the
Luzon Strait. (c) Zonal mean (averaged over seafloor depths
>2,000 m and 10° latitude bins) of the maximum number of
modes (vertical structures) resolved for various internal tide
frequency resolution criteria. K1, M2, M4 represent the domi-
nant diurnal, semidiurnal, and supertidal constituents of inter-
nal tides with decreasing wavelengths, respectively. For the
horizontal (vertical) resolution, the dark-colored polygons
(dashed lines) mark the range of the number of resolved
modes for the zonal mean, and the light-colored polygons
±1 standard deviation from this mean.
Zonal mean of the maximum
number of modes resolved
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Tus, it is likely that the mode-1 and mode-2 internal tides inter-
fere constructively at the locations of the patches where their
velocities are in phase and increase the tidal amplitude, steepen
the internal tide, and enhance the energy transfer to higher har-
monics. Te locations of these patches are modulated by the
slowly varying subtidal current and the spring-neap cycle, with
greater energy available to transfer to higher- harmonics during
spring tides (Solano et al., 2023).
Impacts of Horizontal and Vertical Grid Spacing
on IGWs in Global Models
Ocean model grid spacing, both horizontal and vertical, deter-
mines how bathymetry and the wavelengths of IGW modes are
resolved. For example, a decrease in HYCOM horizontal grid size
from 8 km to 4 km can increase the IGW generation and energy
density by about 50%, largely because it increases the number of
internal wave modes resolved (Buijsman et al., 2020).
We examined what diurnal, semidiurnal, and supertidal ver-
tical wave modes could be resolved in a global, 1/25° tidally
forced global HYCOM simulation with 41 layers (Figure 2c).
Horizontal spacing and IGW wavelengths vary spatially in global
ocean models. Earth’s sphericity causes grid spacing to decrease
poleward, while wavelengths of tidally generated IGWs increase
poleward with the increase of the Coriolis frequency (Buijsman
et al., 2025). We used the criterion that a vertical mode could be
resolved if there were at least six to eight horizontal grid spac-
ings per wavelength (Stewart et al., 2017). A similar criterion was
applied for the vertical resolution, called vertical criterion CZA.
However, this criterion was designed for z-coordinate models,
whereas HYCOM is an isopycnal model below the mixed layer.
Terefore, an additional criterion was developed to account for
the changes in vertical and horizontal velocity structure caused
by isopycnals, called vertical criterion CZB.
In the horizontal, internal wave modes with lower frequen-
cies (longer wavelength) were better resolved. For example, K1
had eight modes resolved at the equator and 20 modes near the
K1 turning latitude of about 30° (Figure 2c). (Poleward of this
latitude, the tidal frequency is lower than the Coriolis frequency,
and diurnal IGWs cannot exist.) Te shorter wavelength, M2,
had fewer modes resolved, with only about four modes resolved
at the equator. For supertidal waves, M4, which has the most
energy globally (Buijsman et al., 2025), only two modes were
resolved. Te number of resolved modes was sensitive to the ver-
tical resolution criteria. CZB appeared to be a more appropriate
FIGURE 3. At the Amazon Shelf and the Mascarene Ridge: (a,b) time-mean and depth-integrated kinetic energy transfer (‹Π(τ=9hr)›); (c,d) time-mean,
depth-integrated divergence of supertidal energy flux ( ∙‹FHH›); (e,f) time-mean surface kinetic energy (KE) for the superposition of modes 1 and 2.
Panels (a–f) were modified from Solano et al. (2023). (g) Mean sound speed and (h) standard deviation of sound speed for each the tidally and non-tid-
ally forced HYCOM simulations from May 20–29, 2019, in the Amazon region, plotted by latitude along the dotted line shown in (a). The star and radial
(dashed black line) in (a) are noted for reference in Figure 6. In (b), a short, dashed line indicates the transect used in Figure 5b,c.
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criterion than CZA. Accounting for the isopycnal layering in
HYCOM, as in CZB, a maximum of 12 diurnal modes could be
resolved at the equator.
Vertical Grid Spacing in Idealized Models
Recent discussions among the oceanography community
resolve that global models can achieve a more accurate ocean
state if they include tidal forcing and have a horizontal grid spac-
ing on the order of 1/50° or fner (the most up-to-date global
HYCOM has 1/25° grid spacing). However, the optimal num-
ber of vertical layers needed in submesoscale resolving mod-
els to resolve internal tides and their energetics is unknown.
To explore this question, we used an idealized HYCOM con-
fguration with 1/100° horizontal grid spacing (~1 km), forced
only by the semidiurnal (M2) tides over a centrally spaced
ridge, and varied the number of layers in the simulations from
8 to 128 (Figure 4; Hiron et al., 2025). Te idealized confgu-
ration allowed the problem to be isolated from contamination
by ocean eddies and currents while resolving all the physics
allowed in HYCOM.
Each idealized simulation was initialized with a climatologi-
cal temperature profle averaged over the Cape Verde area and
constant salinity. Te domain size, approximately 8,000 km in
the zonal direction, was large enough to prevent the refection
of internal tides at the boundaries. Te vertical grid discretiza-
tion was chosen based on characteristic wavelengths of difer-
ent IGW modes. To generate internal tides, a steep ridge with a
Gaussian shape was added in the center of the domain. Te crit-
icality of the slope, which is a measure of the ridge steepness
normalized by the ray slope of the internal waves, was larger
than one, allowing for nonlinear waves and wave beams to be
generated (Garrett and Kunze, 2007).
Te wave beams were the strongest near the ridge (Figure 4a).
Te depth-integrated vertical KE of the 8- and 16-layer sim-
ulations difered from the others in amplitude and phase
(Figure 4b). As the number of layers increased, the simulations
became more similar. For the 48- to the 128-layer simulations,
amplitude and phase were similar across simulations. When
integrated from 0–2,000 km, the tidal barotropic-to-baroclinic
energy conversion, the vertical kinetic energy, and the turbu-
lent dissipation were greatest in the 128-layer simulation and
decreased with coarser vertical grid spacing (Hiron et al., 2025).
Tese variables converged for the simulations with greater than
48 layers, showing that the number of vertical layers can deter-
mine the IGW energy transfer; however, these results may difer
at other horizontal grid spacings.
A Final Word on Grid Spacing: Interaction of
IGWs and Eddies
Te IGW spectrum covers the transfer of energy between IGWs
and the transfer of KE from its injection at large scales in eddies,
near-inertial waves, and tides to the smallest scales. It is applica-
ble globally but uses free parameters to account for regional and
seasonal variations of the ocean state, such as the slowly varying
background circulation and surface forcing. Ongoing research
focuses on what determines these parameters and any devia-
tion from this spectral form; nonlinear interactions involving
IGWs, such as those on display in the Amazon basin and near
Mascarene Ridge, are thought to be of particular importance.
Previous work on IGW-IGW interactions has identifed
some important processes that move energy to smaller scales
(McComas and Bretherton, 1977; Dematteis et al., 2022). Tese
FIGURE 4. (a) Snapshot of the vertical velocity for the 128-layer simulation, zoomed in to the ridge centered at 40°W, where the domain is symmetric
about the ridge. The black triangles indicate the location of the sound speed profiles in (c,d). (b) Time-averaged, depth-integrated vertical kinetic energy
(½ ∫w2dz), where w is the vertical velocity, for diferent vertical discretization: 8, 16, 32, 48, 64, 96, and 128 layers. (c) Mean and (d) standard deviation
of sound speed 83 km from the ridge for the 8-, 16-, 32-, 48-, and 96-layer simulations.
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studies considered IGW-IGW interactions to be the dominant
processes. One mechanism, called “induced difusion,” involves
the interaction of near-inertial and tidal IGWs. Induced difu-
sion is thought to be very important in transferring KE across
length scales. However, most studies have not considered
IGW-eddy interactions in the same manner.
Skitka et al. (2024) used a framework to diagnose IGW-eddy
interactions with IGW-IGW interactions in a regional MITgcm
(1/48°) ocean simulation of the North Pacifc. Tey found that
IGW-eddy interactions induce a downscale KE fux in a man-
ner analogous to IGW-IGW interactions. At this grid spacing,
the “eddy-induced difusion” was the dominant mechanism of
energy exchange within the IGW supertidal continuum, and
comparable to the wave-induced difusion achieved by regional
models with 250 m (1/192°) horizontal grid spacing. Tus, fner
vertical and horizontal grid spacing is expected to change the
details of the IGW cascade in simulations, including the mecha-
nisms and rate of energy transfer and its dissipation.
ACOUSTICS
Tidally Forced Simulations and Sound Speed
We frst examined how tidal forcing afects sound speed and
acoustic properties using a series of global HYCOM (1/25°)
simulations with or without tidal (T) forcing and with or with-
out data assimilation (DA), four simulations in all. Each simu-
lation was forced by wind and had 41 layers. Hourly output was
recorded from May to June 2019. Temperature and salinity were
interpolated from the native grid to a uniform 2 m vertical grid
and then used to compute sound speed.
As an initial comparison, the sound speed variability in each
of the four simulations was compared to glider observations
over a small geographic area in the North Pacifc (Figure 5a;
Rudnick, 2016). A mean and standard deviation of sound speed
was computed from May 20 to May 26, using three-hour out-
put from the simulation and averaged over the region covered
by the glider track. Te glider profled from the surface to 500 m
depth roughly every three hours. Although this is not a region
of large tidal energy, the simulations with tidal forcing still had
FIGURE 5. (a) Standard deviation of sound speed for May 20–26, 2019, from Global HYCOM simulations with and without tides and with and without
data assimilation (DA) at the location indicated on the map of the coast of California. Simulations were compared to standard deviation computed from
glider observations over the same week and location. (b,c) The depth of the 1,510 m s–1 sound speed along 20°N, extending from the coast of Hainan
Island eastward (111.16°E–160°E) for global HYCOM simulations. Bathymetry is overlaid on each, with the Luzon Strait located at 1,000 km distance from
the coast. (d,e) SLD and BLG for global HYCOM simulation with tides (Exp 19.0) and for a nonhydrostatic regional MITgcm simulation at the Mascarene
Ridge near the island of Madagascar (see Figure 3b).
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greater sound speed variability. A simulation with tidal forcing
undulates the thermocline leading to greater temperature and
salinity (and thus sound speed) variability at a given depth. Data
assimilation brought the simulations closer to observations;
however, it can also abruptly alter the temperature and salin-
ity during an assimilation window, causing implausible jumps
in sound speed. Te elevated sound speed variability in the DA
simulations could be caused by natural ocean variability or this
“shock.” For these reasons, and those discussed in the earlier sec-
tion, Internal Gravity Waves, we chose to use ocean simulations
without DA while studying the sensitivity of acoustics to IGWs.
Acoustic Case Studies at IGW Hotspots
At IGW hotspots, such as the Luzon Strait, the Amazon Shelf,
and the Mascarene Ridge, tidal forcing strongly undulates the
upper ocean, and there is IGW energy transfer among modes
(see the section, From Global to Regional: Supertidal Energy).
Across the Luzon Strait, we compared the depth variability of
a single sound speed surface between the tidally forced and
non-tidally forced global HYCOM simulations (Figure 5b,c). In
the tidally forced simulation, depth striations radiated from the
Luzon Ridge, located at 1,000 km distance, and other ridges with
steep topography (e.g., 4,800 km) as tides propagated in both
directions (Figure 5b). Tese were largely absent in the simula-
tion without tides (Figure 5c).
We hypothesized that such diferences in sound speed between
the tidal and non-tidally forced simulations would cause notable
diferences in acoustic propagation. To test this idea, we turned
to the Amazon region, where semidiurnal internal tides propa-
gate northeastward away from the coast (Figure 3). Te mean
sound speed along the transect was similar between the tides
and no-tides simulations (Figure 3g), but they difered in sound
speed variability (Figure 3h). Te tidal simulation had peri-
odic “banding” in sound speed variability in the thermocline
(~150 m depth) at locations near where there was greater IGW
energy transfer (Figure 3a).
A 1,500 Hz virtual acoustic source was placed at 20 m depth
at 4.1°N, 44.8°W, a location of enhanced sound speed variabil-
ity and IGW energy transfer (yellow star in Figure 3a). Te
sound speed, vertical sound speed gradient, and transmission
loss were examined along the 30° radial (clockwise from north).
In the tidal case, there were undulations in sound speed and
SLD (Figure 6a). Without tidal forcing, the sound speed was
more uniform, and SLD was deeper. A deeper SLD will also
typically improve transmission in the surface layer. Tidal forc-
ing also introduced changes to vertical sound speed gradients
(Figure 6a,b) and can be inferred to introduce them in the hori-
zontal as well. Surface layer transmission occurred in both cases
but was stronger in the simulation without tidal forcing. Turning
to time series (Figure 6c), TL tended to be greater in simulations
with tidal forcing than without and ofen fuctuated at semidiur-
nal timescales (i.e., every 12 hours), such as from May 20 to 23.
Te semidiurnal variability extended to both SLD and BLG. In
the nontidal case, TL varied with eddies and currents but not at
semidiurnal frequencies (Figure 6c).
Because the horizontal and vertical structures of the sound
speed determine the path of the sound, the introduction of ver-
tical and horizontal gradients in sound speed in the simulation
with tides could have resulted in more scattering and refraction
of sound throughout the waveguide. However, the mesoscale
diferences between the tidal and non-tidal simulations made it
difcult to directly compare their acoustic properties. Some of
the simulation variability was caused by tidal interaction with
the mesoscale feld and atmospheric forcing. Correlation coef-
fcients between wind and mixed layer depths in the Amazon
region were similar between the tidally forced and non-tidal
simulations, but with greater diferences near the coast where
currents and tidal variability were strongest.
Sound Speed and Grid Spacing
Like IGWs, sound speed is also afected by simulation grid spac-
ing. A fner grid may resolve more processes and have difer-
ent temperature and salinity gradients. As an example, we com-
pared two tidally forced simulations with diferent model setups
to see how model grid-spacing and boundary conditions may
afect sound speed structure: the hydrostatic tidally forced
global HYCOM simulation (Experiment [Exp.] 19.0; 1/25° res-
olution; Figure 5d) and a two-dimensional nonhydrostatic sim-
ulation of the MITgcm (Figure 5e), with a horizontal grid spac-
ing of 100 m. Te Mascarene Ridge, where the simulations are
compared, is known for nonlinear wave interactions; solitons are
generated and propagate away from the ridge (Figure 3b,d,f).
Because the simulations were initialized with an ofset in tem-
perature, they couldn’t be compared directly; however, a rela-
tive comparison of SLD and BLG was insightful. Te HYCOM
simulation had organized semidiurnal fuctuations of the SLD
and BLG, each oscillating twice a day (Figure 5d). In contrast,
the MITgcm simulation had a periodic signal, but it appeared
disorganized, with a more variable SLD and BLG (Figure 5e).
Te fner grid spacing of the MITgcm simulation likely allowed
for nonlinear interactions to occur, which in turn impacted
the sound speed structure. Tis structure is likely closer to real
ocean variability, showing the difculties of predicting sound
speed using coarser-resolution ocean models.
To address the confounding challenges of the divergent meso-
scale eddy felds and initialization states, we turned to the ide-
alized model (section on Vertical Grid Spacing in Idealized
Models) to isolate the impact of vertical grid spacing on sound
speed. Hourly output from each of the idealized simulations
with 8, 16, 32, 48, and 96 isopycnal layers was interpolated to
a uniform depth coordinate for a 72-hour period. From this
we calculated the sound speed means and standard deviations
(Figure 4c,d). Te mean sound speeds were greater in simu-
lations with 32 or fewer layers (Figure 4c) and did not resolve
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the depth of greatest sound speed variability (Figure 4d). As the
number of layers increased, the mean and standard deviation of
the sound-speed profles converged, with very little diference
between the 48- and 96-layer simulations. Tese results parallel
the fndings that, for a 1 km horizontal grid spacing, a minimum
of 48 isopycnal layers is necessary to resolve displacement of iso-
pycnals by internal tides.
A DEEP LEARNING APPROACH TO INCLUDING
IGW IN OCEAN MODELS
Te fner grid spacing and the inclusion of tidal forcing in ocean
simulations improves the realism of the ocean state. However,
these improvements in a global ocean model are computationally
expensive. To reduce computational cost, we investigated using a
generative adversarial network (GAN; Goodfellow et al., 2014) to
generate a tidally forced ocean state without solving the physical
forcing equations. GANs are a deep learning technique that learn
a transformation from one statistical distribution to another
instead of learning an exact distribution. In a GAN, a “generator,”
which generates new data, is trained alongside a “discriminator,”
which is a classifer that diferentiates between actual data and
generated data. Te GAN works through iteration, with the gen-
erator learning a distribution transformation and the discrimina-
tor learning to distinguish between real data and generated data.
We trained two pairs of generators and discriminators using
Global HYCOM (1/25°) with (Exp. 19.0) and without (Exp. 19.2)
FIGURE 6. Comparison of acoustic propagation and properties between HYCOM simulations with and without tidal forcing at the Amazon Shelf, starting
at 4.1°N, 44.8°W and extending 30° (clockwise from north) as indicated in Figure 3a. (a) A snapshot from May 20, 2019, 18:00:00 of sound speed (m s–1),
vertical gradient of sound speed (s–1), and transmission loss (TL; dB) for each simulation. (b) A single sound speed profile at 100 km distance along the
radial for the tidal (red) and non-tidal simulation. (c) TL at 20 m depth, sonic layer depth (SLD) and below-layer gradient (BLG). TL is calculated from a
1,500 Hz source at 4.1°N and 44.8°W at 20 m depth.
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tidal forcing as the initialization states. One generator, GNT→T(·),
translated from the non-tidal to the tidal domain, and the other
generator, GT→NT(·), translated from the tidal to non-tidal
domain. To address the issue of the chaotic, turbulent nature of
the ocean, we considered the simulations to be unpaired (i.e., not
a direct translation between one state and the other). Instead,
the GAN used “cycle-consistency loss,” the mean-squared difer-
ence between the original data sample and the doubly translated
data (Zhu et al., 2017). Te cycle-consistency loss was combined
with the traditional GAN losses (i.e., the diference between the
generator and the discriminator output) to train the networks.
Te Atlantic Ocean was used as a test-case region; one week of
hourly HYCOM data was split into 90% training data and 10%
validation data.
Te GAN results retained the general structure of the tem-
perature and salinity profles from HYCOM while adding or
removing a semidiurnal tide (Figure 7). Te GAN performed
well in the relatively quiescent region of the tropical mid-
Atlantic (Figure 7b). Tere, periodic signatures in HYCOM with
tides matched the periodicity of the outputs of GNT→T(·). Te
semidiurnal signature was also removed in GT→NT(·) to match
the non-tidally forced HYCOM. It was more difcult to separate
the tidal structure from mesoscale variability in more energetic
regions, such as near the Gulf Stream (Figure 7c,d). For example,
just north of the Gulf Stream (Figure 7c), the GNT→T(·) repro-
duced semidiurnal periodicity of the tidally forced HYCOM,
but there was also periodicity in the nontidal felds. In the Gulf
Stream extension (Figure 7d), the GAN imposed a periodicity to
make the sample like other tidally forced results, but this was a
region dominated by mesoscale variability.
Because the HYCOM output used to train the GAN was sam-
pled from the same region of the globe during the same time of
year, no two samples were completely independent. Tis intro-
duces the risk of overftting. Using unpaired data made the
model more robust to overftting but did not remove the risk
entirely. Additionally, the sound speed structure had a persistent
ofset of about 5 m s–1 greater in the GAN-generated results than
the original HYCOM simulations (not shown). Tus, although
this work provides a good starting point, further work will help
revise this approach.
FIGURE 7. Temporal out-
puts of the deep learn-
ing GAN model at the
locations mapped in (a).
For each panel, the first
column shows the non-
tidal (NT) HYCOM results
(Exp 19.2); the second
column shows the NT
results translated into
the tidal domain using
the GAN model; the
third column shows the
tidal (T) HYCOM results
(Exp 19.0); and the fourth
column shows the T
results translated into
the NT domain using a
GAN model. From top
to bottom, rows in (b–d)
show water tempera-
ture, salinity, eastward
velocity, and northward
velocity, respectively.