Observations of the space/time scales of Beaufort sea acoustic duct variability and their impact on transmission loss via the mode interaction parameter.

The Beaufort duct (BD) is a subsurface sound channel in the western Arctic Ocean formed by cold Pacific Winter Water (PWW) sandwiched between warmer Pacific Summer Water (PSW) and Atlantic Water (AW). Sound waves can be trapped in this duct and travel long distances without experiencing lossy surface/ice interactions. This study analyzes BD vertical and temporal variability using moored oceanographic measurements from two yearlong acoustic transmission experiments (2016-2017 and 2019-2020). The focus is on BD normal mode propagation through observed ocean features, such as eddies and spicy intrusions, where direct numerical simulations and the mode interaction parameter (MIP) are used to quantify ducted mode coupling strength. The observations show strong PSW sound speed variability, weak variability in the PWW, and moderate variability in the AW, with typical time scales from days to weeks. For several hundreds Hertz propagation, the BD modes are relatively stable, except for rare episodes of strong sound speed perturbations. The MIP identifies a resonance condition such that the likelihood of coupling is greatest when there is significant sound speed variability in the horizontal wave number band 1/11

Effects of Pacific Summer Water layer variations and ice cover on Beaufort Sea underwater sound ducting.

A one-year fixed-path observation of seasonally varying subsurface ducted sound propagation in the Beaufort Sea is presented. The ducted and surface-interacting sounds have different time behaviors. To understand this, a surface-forced computational model of the Chukchi and Beaufort Seas with ice cover is used to simulate local conditions, which are then used to computationally simulate sound propagation. A sea ice module is employed to grow/melt ice and to transfer heat and momentum through the ice. The model produces a time- and space-variable duct as observed, with Pacific Winter Water (PWW) beneath a layer of Pacific Summer Water (PSW) and above warm Atlantic water. In the model, PSW moves northward from the Alaskan coastal area in late summer to strengthen the sound duct, and then mean PSW temperature decreases during winter and spring, reducing the duct effectiveness, one cause of a duct annual cycle. Spatially, the modeled PSW is strained and filamentary, with horizontally structured temperature. Sound simulations (order 200 Hz) suggest that ducting is interrupted by the intermittency of the PSW (duct gaps), with gaps enabling loss from ice cover (set constant in the sound model). The gaps and ducted sound show seasonal tendencies but also exhibit random process behavior.

A coupled mode model for omnidirectional three-dimensional underwater sound propagation.

A fully three-dimensional (3D) omnidirectional numerical coupled mode model of acoustic propagation is detailed. A combination of normal mode and finite element computational methods is applied to produce the numerical results. The technique is tested in a strongly range-dependent ocean environment modeled after the Hudson Canyon. Modeled sound from three source locations selected over different bathymetric depths is examined to determine capabilities and difficulties associated with varying numbers of propagating vertical modes across the horizontal domain, and variable amounts of mode coupling. Model results are compared to those from a unidirectional Cartesian 3D parabolic equation simulation, and from adiabatic (uncoupled) simulations to illustrate the capabilities of the techniques to study the influences of coupling, strong refraction, and reflection.

Multiscale multiphysics data-informed modeling for three-dimensional ocean acoustic simulation and prediction.

Three-dimensional (3D) underwater sound field computations have been used for a few decades to understand sound propagation effects above sloped seabeds and in areas with strong 3D temperature and salinity variations. For an approximate simulation of effects in nature, the necessary 3D sound-speed field can be made from snapshots of temperature and salinity from an operational data-driven regional ocean model. However, these models invariably have resolution constraints and physics approximations that exclude features that can have strong effects on acoustics, example features being strong submesoscale fronts and nonhydrostatic nonlinear internal waves (NNIWs). Here, work to predict NNIW fields to improve 3D acoustic forecasts using an NNIW model nested in a tide-inclusive data-assimilating regional model is reported. The work was initiated under the Integrated Ocean Dynamics and Acoustics project. The project investigated ocean dynamical processes that affect important details of sound-propagation, with a focus on those with strong intermittency (high kurtosis) that are challenging to predict deterministically. Strong internal tides and NNIW are two such phenomena, with the former being precursors to NNIW, often feeding energy to them. Successful aspects of the modeling are reported along with weaknesses and unresolved issues identified in the course of the work.

Acoustic signal and noise changes in the Beaufort Sea Pacific Water duct under anticipated future acidification of Arctic Ocean waters.

It is predicted that Arctic Ocean acidity will increase during the next century as a result of carbon dioxide accumulation in the atmosphere and migration into ocean waters. This change has implications for sound transmission because low-pH seawater absorbs less sound than high-pH water. Altered pH will affect sound in the 0.3-10 kHz range if the criterion is met that absorption is the primary cause of attenuation, rather than the alternatives of loss in the ice or seabed. Recent work has exploited sound that meets the criterion, sound trapped in a Beaufort Sea duct composed of Pacific Winter Water underlying Pacific Summer Water. Arctic pH is expected to drop from 8.1 to 7.9 (approximately) over the next 30-50 yr, and effects of this chemical alteration on the intensity levels of this ducted sound, and on noise, are examined here. Sound near 900 Hz is predicted to undergo the greatest change, traveling up to 38% further. At ranges of 100-300 km, sound levels from a source in the duct may increase by 7 dB or more. Noise would also increase, but noise is ducted less efficiently, with the result that 1 kHz noise is predicted to rise approximately 0.5 dB.

Weakly dispersive modal pulse propagation in the North Pacific Ocean.

The propagation of weakly dispersive modal pulses is investigated using data collected during the 2004 long-range ocean acoustic propagation experiment (LOAPEX). Weakly dispersive modal pulses are characterized by weak dispersion- and scattering-induced pulse broadening; such modal pulses experience minimal propagation-induced distortion and are thus well suited to communications applications. In the LOAPEX environment modes 1, 2, and 3 are approximately weakly dispersive. Using LOAPEX observations it is shown that, by extracting the energy carried by a weakly dispersive modal pulse, a transmitted communications signal can be recovered without performing channel equalization at ranges as long as 500 km; at that range a majority of mode 1 receptions have bit error rates (BERs) less than 10%, and 6.5% of mode 1 receptions have no errors. BERs are estimated for low order modes and compared with measurements of signal-to-noise ratio (SNR) and modal pulse spread. Generally, it is observed that larger modal pulse spread and lower SNR result in larger BERs.

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

Bottom interacting sound at 50 km range in a deep ocean environment.

Data collected during the 2004 Long-range Ocean Acoustic Propagation Experiment provide absolute intensities and travel times of acoustic pulses at ranges varying from 50 to 3200 km. In this paper a subset of these data is analyzed, focusing on the effects of seafloor reflections at the shortest transmission range of approximately 50 km. At this range bottom-reflected (BR) and surface-reflected, bottom-reflected energy interferes with refracted arrivals. For a finite vertical receiving array spanning the sound channel axis, a high mode number energy in the BR arrivals aliases into low mode numbers because of the vertical spacing between hydrophones. Therefore, knowledge of the BR paths is necessary to fully understand even low mode number processes. Acoustic modeling using the parabolic equation method shows that inclusion of range-dependent bathymetry is necessary to get an acceptable model-data fit. The bottom is modeled as a fluid layer without rigidity, without three dimensional effects, and without scattering from wavelength-scale features. Nonetheless, a good model-data fit is obtained for sub-bottom properties estimated from the data.

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.

Modal analysis of the range evolution of broadband wavefields in the North Pacific Ocean: low mode numbers.

The results of mode-processing measurements of broadband acoustic wavefields made in the fall of 2004 as part of the Long-Range Ocean Acoustic Propagation Experiment (LOAPEX) in the eastern North Pacific Ocean are reported here. Transient wavefields in the 50-90 Hz band that were recorded on a 1400-m long 40 element vertical array centered near the sound channel axis are analyzed. This array was designed to resolve low-order modes. The wavefields were excited by a ship-suspended source at seven ranges, between approximately 50 and 3200 km, from the receiving array. The range evolution of broadband modal arrival patterns corresponding to fixed mode numbers ("modal group arrivals") is analyzed with an emphasis on the second (variance) and third (skewness) moments. A theory of modal group time spreads is described, emphasizing complexities associated with energy scattering among low-order modes. The temporal structure of measured modal group arrivals is compared to theoretical predictions and numerical simulations. Theory, simulations, and observations generally agree. In cases where disagreement is observed, the reasons for the disagreement are discussed in terms of the underlying physical processes and data limitations.

Piecewise coherent mode processing of acoustic data recorded on two horizontally separated vertical line arrays.

Motivated by measurements made in the 2004 Long-Range Ocean Acoustic Propagation Experiment (LOAPEX), the problem of mode processing transient acoustic signals collected on two nearby vertical line arrays is considered. The first three moments (centroid, variance, and skewness) of broadband distributions of acoustic energy with fixed mode number (referred to as modal group arrivals) are estimated. It is shown that despite the absence of signal coherence between the two arrays and poor high mode number energy resolution, the centroid and variance of these distributions can be estimated with tolerable errors using piecewise coherent mode processing as described in this paper.

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: shallow-water environments.

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.

Observations of sound-speed fluctuations on the New Jersey continental shelf in the summer of 2006.

Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the -1.81 power, whereas the spice spectrum shows a -1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three.

On whether azimuthal isotropy and alongshelf translational invariance are present in low-frequency acoustic propagation along the New Jersey shelfbreak.

To understand the issues associated with the presence (or lack) of azimuthal isotropy and horizontal (along isobath) invariance of low-frequency (center frequencies of 600 Hz and 900 Hz) acoustic propagation in a shelfbreak environment, a series of experiments were conducted under the Autonomous Wide-Aperture Cluster for Surveillance component of the Shallow Water 2006 experiment. Transmission loss data reported here were from two mobile acoustic sources executing (nearly) circular tracks transmitting to sonobuoy receivers in the circle centers, and from one 12.5 km alongshelf acoustic track. The circle radii were 7.5 km. Data are from September 8, 2006. Details of the acoustic and environmental measurements are presented. Simple analytic and computer models are used to assess the variability expected due to the ocean and seabed conditions encountered. A comparison of model results and data is made, which shows preliminary consistency between the data and the models, but also points towards further work that should be undertaken specifically in enlarging the range and frequency parameter space, and in looking at integrated transmission loss.

Horizontal coherence of low-frequency fixed-path sound in a continental shelf region with internal-wave activity.

Sound at 85 to 450 Hz propagating in approximately 80-m depth water from fixed sources to a joint horizontal/vertical line array (HLA/VLA) is analyzed. The data are from a continental shelf area east of Delaware Bay (USA) populated with tidally generated long- and short-wavelength internal waves. Sound paths are 19 km in the along-shore (along internal-wave crest) direction and 30 km in the cross-shore direction. Spatial statistics of HLA arrivals are computed as functions of beam steering angle and time. These include array gain, horizontally lagged spatial correlation function, and coherent beam power. These quantities vary widely in magnitude, and vary over a broad range of time scales. For example, correlation scale can change rapidly from forty to five wavelengths, and correlation-scale behavior is anisotropic. In addition, the vertical array can be used to predict correlation expected for adiabatic propagation with cylindrical symmetry, forming a benchmark. Observed variations are in concert with internal-wave activity. Temporal variations of three coherence measures, horizontal correlation length, array gain, and ratio of actual correlation length to predicted adiabatic-mode correlation length, are very strong, varying by almost a factor of ten as internal waves pass.

Observationally constrained modeling of sound in curved ocean internal waves: examination of deep ducting and surface ducting at short range.

A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones).

Focused sound from three-dimensional sound propagation effects over a submarine canyon.

Ship noise data reveal an intensification of the near-surface sound field over a submarine canyon. Numerical modeling of sound propagation is used to study the effect. The noise data were collected during an ocean acoustic and physical oceanography experiment northeast of Taiwan in 2009. In situ measurements of water sound-speed profiles and a database of high-resolution bathymetry are used in the modeling study. The model results suggest that the intensification is caused by three-dimensional sound focusing by the concave canyon seafloor. Uncertainties in the model results from unsampled aspects of the environment are discussed.

Modeling deep ocean shipping noise in varying acidity conditions.

Possible future changes of ambient shipping noise at 0.1-1 kHz in the North Pacific caused by changing seawater chemistry conditions are analyzed with a simplified propagation model. Probable decreases of pH would cause meaningful reduction of the sound absorption coefficient in near-surface ocean water for these frequencies. The results show that a few decibels of increase may occur in 100 years in some very quiet areas very far from noise sources, with small effects closer to noise sources. The use of ray physics allows sound energy attenuated via volume absorption and by the seafloor to be compared.

Acoustic mode radiation from the termination of a truncated nonlinear internal gravity wave duct in a shallow ocean area.

Horizontal ducting of sound between short-wavelength nonlinear internal gravity waves in coastal environments has been reported in many theoretical and experimental studies. Important consequences arising at the open end of an internal wave duct (the termination) are examined in this paper with three-dimensional normal mode theory and parabolic approximation modeling. For an acoustic source located in such a duct and sufficiently far from the termination, some of the propagating sound may exit the duct by penetrating the waves at high grazing angles, but a fair amount of the sound energy is still trapped in the duct and propagates toward the termination. Analysis here shows that the across-duct sound energy distribution at the termination is unique for each acoustic vertical mode, and as a result the sound radiating from the termination of the duct forms horizontal beams that are different for each mode. In addition to narrowband analysis, a broadband simulation is made for water depths of order 80 m and propagation distances of 24 km. Situations occur with one or more modes absent in the radiated field and with mode multipath in the impulse response. These are both consistent with field observations.

Revisiting experimental methods for studies of acidity-dependent ocean sound absorption.

The practical usefulness of long-range acoustic measurements of ocean acidity-linked sound absorption is analyzed. There are two applications: Determining spatially-averaged pH via absorption measurement and verifying absorption effects in an area of known pH. The method is a differential-attenuation technique, with the difference taken across frequency. Measurement performance versus mean frequency and range is examined. It is found that frequencies below 500 Hz are optimal. These are lower than the frequency where the measurement would be most sensitive in the absence of noise and signal fluctuation (scintillation). However, attenuation serves to reduce signal-to-noise ratio with increasing distance and frequency, improving performance potential at lower frequencies. Use of low frequency allows longer paths to be used, with potentially better spatial averaging. Averaging intervals required for detection of fluctuations or trends with the required precision are computed.