Deep ocean long range underwater navigation with ocean circulation model corrections.

An underwater navigation algorithm that provides a "cold start" (CSA) geographic position, geo-position, underwater while submerged using travel times measured from a constellation of acoustic sources is described in Mikhalevsky, Sperry, Woolfe, Dzieciuch, and Worcester [J. Acoust. Soc. Am. 147(4), 2365 - 2382 (2020)]. The CSA geo-position is used as the receive position in the ocean for acoustic modeling runs using an ocean general circulation model (GCM). A different geo-position is calculated using adjusted ranges from the travel time offsets between the data and modeled arrival times for each source. Because the CSA geo-position is close to the true position, the source to CSA position propagation model path and the source to true vehicle position data path of the acoustic arrivals are nearly coincident, enabling accurate measurement of travel time offsets. The cold start with model (CSAM) processing reduced the CSA geo-position errors from a mean of 58 to 25 m. A simulation is developed to estimate CSA and CSAM performances as a function of group speed variability between the source paths. The CSAM geolocation accuracy can be calculated from and is controlled by the accuracy of the GCM.

Acoustic travel-time variability observed on a 150-km radius tomographic array in the Canada Basin during 2016-2017.

The Arctic Ocean is undergoing dramatic changes in response to increasing atmospheric concentrations of greenhouse gases. The 2016-2017 Canada Basin Acoustic Propagation Experiment was conducted to assess the effects of the changes in the sea ice and ocean structure in the Beaufort Gyre on low-frequency underwater acoustic propagation and ambient sound. An ocean acoustic tomography array with a radius of 150 km that consisted of six acoustic transceivers and a long vertical receiving array measured the impulse responses of the ocean at a variety of ranges every four hours using broadband signals centered at about 250 Hz. The peak-to-peak low-frequency travel-time variability of the early, resolved ray arrivals that turn deep in the ocean was only a few tens of milliseconds, roughly an order of magnitude smaller than observed in previous tomographic experiments at similar ranges, reflecting the small spatial scale and relative sparseness of mesoscale eddies in the Canada Basin. The high-frequency travel-time fluctuations were approximately 2 ms root-mean-square, roughly comparable to the expected measurement uncertainty, reflecting the low internal-wave energy level. The travel-time spectra show increasing energy at lower frequencies and enhanced semidiurnal variability, presumably due to some combination of the semidiurnal tides and inertial variability.

Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

Observations and simulations of caustic formation due to oceanographic fine structure.

An at-sea experiment in deep water was conducted to explore the impact of small-scale sound-speed variability on mid-frequency (1-10 kHz) acoustic propagation. Short-range (1-5 km) acoustic transmissions were sent through the upper ocean (0-200 m) while oceanographic instruments simultaneously measured the ocean environment within 2 km of the single upper turning points of the acoustic transmissions. During these transmissions, acoustic receptions over a 7.875 m vertical line array show closely spaced, sometimes interfering arrivals. Ray and full-wave simulations of the transmissions using nearby sound-speed profiles are compared deterministically to the received acoustic signals. The sensitivity of the acoustic arrivals to the vertical scales of ocean sound speed is tested by comparing the observed and simulated arrival intensity where the sound-speed profile used by the simulation is smoothed to varying scales. Observations and modeling both suggest that vertical fine-scale structures (1-10 m) embedded in the sound-speed profile have strong second derivatives which allow for the formation of acoustic caustics as well as potentially interfering acoustic propagation multipaths.

A Broadband View of the Sea Surface Height Wavenumber Spectrum.

Airborne lidar altimetry can measure the sea surface height (SSH) over scales ranging from hundreds of kilometers to a few meters. Here, we analyze the spectrum of SSH observations collected during an airborne lidar campaign conducted off the California coast. We show that the variance in the surface wave band can be over 20 times larger than the variance at submesoscales and that the observed SSH variability is sensitive to the directionality of surface waves. Our results support the hypothesis that there is a spectral gap between meso-to-submesoscale motions and small-scale surface waves and also indicate that aliasing of surface waves into lower wavenumbers may complicate the interpretation of SSH spectra. These results highlight the importance of better understanding the contributions of different physics to the SSH variability and considering the SSH spectrum as a continuum in the context of future satellite altimetry missions.

Peak-time sensitivity kernels for noise cross-correlation envelopes.

The envelope of the time-lagged cross-correlation of an underwater noise field between two hydrophones can under certain conditions be used as a proxy for active acoustic receptions between the two locations enabling the study of ocean variability. Previous work looked at the sensitivity of cross-correlation peak amplitudes with respect to the distribution of the noise sources. The present study examines the sensitivity of the cross-correlation envelope peak times with respect to changes in the sound-speed distribution. A wave-theoretic scheme allowing for finite-frequency calculations in two and three dimensions, combined with the Born approximation for perturbations of the Green's function and the peak arrival approach, is used to obtain sensitivity kernels with respect to environmental (sound-speed) changes. These kernels provide a way to infer ocean structure from the cross-correlation peaks, considered as observables on their own and valid even in cases where the cross-correlation function does not approximate the time-domain Green's function between the two receivers. The sensitivity behavior is studied for different propagation conditions and noise-source distributions, ranging from spatially distributed uncorrelated noise sources to point sources, such as individual ships. Deviations from linearity are addressed and discussed.

Moving source ocean acoustic tomography with uncertainty quantification using controlled source-tow observations.

Ocean sound speed and its uncertainty are estimated using travel-time tomography at ranges up to 2 km using a moving source in ∼600 m water depth. The experiment included two 32-element vertical line arrays deployed about 1 km apart and a towed source at ∼10 m depth transmitting a linear frequency modulated waveform. The inversion accounts for uncertainties in the positions and velocities of the source and receivers in addition to the background sound speed state. At these short ranges, the sound speed effects are small and the representational error of the candidate forward models must be carefully evaluated and minimized. This is tested stringently by a separate position parameter inversion and by cross-validating the estimates of sound speed and arrival time, including uncertainties. In addition, simulations are used to explore the effects of adding additional constraints to the inversion and to compare the performance of moving to fixed source tomography. The results suggest that the ray diversity available from the moving source reduces the posterior sound speed uncertainty compared to the fixed source case.

Using a regional ocean model to understand the structure and variability of acoustic arrivals in Fram Strait.

A regional ocean model for Fram Strait provides a framework for interpretation of the variability and structure of acoustic tomography arrivals. The eddy-permitting model (52 vertical levels and 4.5 km horizontal resolution) was evaluated using long-term moored hydrography data and time series of depth-range averaged temperature obtained from the inversion of acoustic tomography measurements. Geometric ray modeling using the ocean model fields reproduces the measured arrival structure of the acoustic tomography experiment. The combination of ocean and acoustic models gives insights into acoustic propagation during winter and spring. Moreover, overlapping arrivals coming from different vertical angles can be resolved and explained. The overlapping arrival of purely refracted rays and surface-reflected/bottom-reflected (SRBR) rays has implications for the inversion of tomography data in Fram Strait. The increased knowledge about the ray-length variations of SRBR rays is valuable for choosing appropriate observation kernels for the data assimilation of acoustic tomography data in Fram Strait.

Observations of phase and intensity fluctuations for low-frequency, long-range transmissions in the Philippine Sea and comparisons to path-integral theory.

In the Philippine Sea, from April 2010 to March 2011, a 330-km radius pentagonal acoustic transceiver array with a sixth transceiver in the center transmitted broadband signals with center frequencies between 172 and 275 Hz and 100 Hz bandwidth eight times a day every other day. The signals were recorded on a large-aperture vertical-line array located near the center of the pentagon at ranges of 129, 210, 224, 379, 396, and 450 km. The acoustic arrival structures are interpretable in terms of ray paths. Depth and time variability of the acoustic observations are analyzed for six ray paths (one from each transceiver) with similar vertical sampling properties in the main thermocline. Acoustic-field statistics treated include: (1) variances of phase and intensity, (2) vertical coherence and intensity covariance, (3) glinting and fadeout rates, and (4) intensity probability density functions. Several observed statistics are compared to predictions using Feynman path-integral theory assuming the Garrett-Munk internal-wave spectrum. In situ oceanographic observations support this assumption and are used to estimate spectral parameters. Data and theory differ at most by a factor of two and reveal the wave propagation regimes of unsaturated, partially saturated, and fully saturated. Improvements to the evaluation of path-integral quantities are discussed.

Estimating relative channel impulse responses from ships of opportunity in a shallow water environment.

The uncertainty of estimating relative channel impulse responses (CIRs) obtained using the radiated signature from a ship of opportunity is investigated. The ship observations were taken during a 1.4 km (11 min) transect in a shallow water environment during the Noise Correlation 2009 (NC09) experiment. Beamforming on the angle associated with the direct ray-path yields an estimate of the ship signature, subsequently used in a matched filter. Relative CIRs are estimated every 2.5 s independently at three vertical line arrays (VLAs). The relative arrival-time uncertainty is inversely proportional to source bandwidth and CIR signal-to-noise ratio, and reached a minimum standard deviation of 5 µs (equivalent to approximately 1 cm spatial displacement). Time-series of direct-path relative arrival-times are constructed for each VLA element across the 11 min observation interval. The overall structure of these time-series compares favorably with that predicted from an array element localization model. The short-term standard deviations calculated on the direct-path (7 µs) and bottom-reflected-path (17 µs) time-series are in agreement with the predicted arrival-time accuracies. The implications of these observed arrival-time accuracies in the context of estimating sound speed perturbations and bottom-depth are discussed.

Resolution, identification, and stability of broadband acoustic arrivals in Fram Strait.

An ocean acoustic tomography system consisting of three moorings with low frequency, broadband transceivers and a moored receiver located approximately in the center of the triangle formed by the transceivers was installed in the central, deep-water part of Fram Strait during 2010-2012. Comparisons of the acoustic receptions with predictions based on hydrographic sections show that the oceanographic conditions in Fram Strait result in complex arrival patterns in which it is difficult to resolve and identify individual arrivals. In addition, the early arrivals are unstable, with the arrival structures changing significantly over time. The stability parameter α suggests that the instability is likely not due to small-scale variability, but rather points toward strong mesoscale variability in the presence of a relatively weak sound channel as being largely responsible. The estimator-correlator [Dzieciuch, J. Acoust. Soc. Am. 136, 2512-2522 (2014)] is shown to provide an objective formalism for generating travel-time series given the complex propagation conditions. Because travel times obtained from the estimator-correlator are not associated with resolved, identified ray arrivals, inverse methods are needed that do not use sampling kernels constructed from geometric ray paths. One possible approach would be to use travel-time sensitivity kernels constructed for the estimator-correlator outputs.

Numerical investigation of shipping noise in the Red Sea.

Underwater noise pollution is a significant environmental issue that can have detrimental effects on marine ecosystems. One of the main sources of underwater noise pollution is ship traffic, which has been shown to negatively impact marine animals by masking communication signals and altering their behaviors. This study represents the first comprehensive analysis of underwater ship noise in the Red Sea, wherein noise maps of ships sailing through the main shipping lane in the Red Sea were simulated by integrating both anthropogenic and environmental variables. These maps offer valuable insights for policymakers, enabling them to make informed decisions and implement targeted mitigation efforts.

Response of sea surface temperature to atmospheric rivers.

Atmospheric rivers (ARs), responsible for extreme weather conditions, are mid-latitude systems that can cause significant damage to coastal areas. While forecasting ARs beyond two weeks remains a challenge, past research suggests potential benefits may come from properly accounting for the changes in sea surface temperature (SST) through air-sea interactions. In this paper, we investigate the impact of ARs on SST over the North Pacific by analyzing 25 years of ocean reanalysis data using an SST budget equation. We show that in the region of strong ocean modification, ocean dynamics can offset over 100% of the anomalous SST warming that would otherwise arise from atmospheric forcing. Among all ocean processes, ageostrophic advection and vertical mixing (diffusion and entrainment) are the most important factors in modifying the SST tendency response. The SST tendency response to ARs varies spatially. For example, in coastal California, the driver of enhanced SST warming is the reduction in ageostrophic advection due to anomalous southerly winds. Moreover, there is a large region where the SST shows a warming response to ARs due to the overall reduction in the total clouds and subsequent increase in total incoming shortwave radiation.

Using a numerical model to understand the connection between the ocean and acoustic travel-time measurements.

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea using the adjoint of a numerical model. A one year series of five day backward integrations of the adjoint model quantify the sensitivity of travel-times to varying dynamics that can alter the travel-time of a 611 km ray by 200 ms. The early evolution of the sensitivities reveals high-mode internal waves that dissipate quickly, leaving the lowest three modes, providing a connection to variations in the internal tide generation prior to the sample time. They are also strongly sensitive to advective effects that alter density along the ray path. These sensitivities reveal how travel-time measurements are affected by both nearby and distant waters. Temporal nonlinearity of the sensitivities suggests that prior knowledge of the ocean state is necessary to exploit the travel-time observations.

Structure and stability of wave-theoretic kernels in the ocean.

Wave-theoretic modeling can be applied to obtain travel-time sensitivity kernels (TSKs) representing the amount ray travel times are affected by sound-speed variations anywhere in the medium. This work explores the spatial frequency content of the TSK compared to expected ocean variability. It also examines the stability of the TSK in environments that produce strong sensitivity of ray paths to initial conditions. The conclusion is that the linear TSK model is an effective predictor of travel-time changes and that the rays perform nearly as well as the full-wave kernel. The TSK is examined in physical space and in wavenumber space, and it is found that this is the key to understanding how the travel time reacts to ocean perturbations. There are minimum vertical and horizontal length scales of ocean perturbations that are required for the travel time to be affected. The result is that the correspondence between true travel times and those calculated from the kernel is high for large-scale perturbations and somewhat less for the small scales. This demonstrates the validity of ray-based inversion of travel time observations for the cases under study.

Analyzing sound speed fluctuations in shallow water from group-velocity versus phase-velocity data representation.

Data collected over more than eight consecutive hours between two source-receiver arrays in a shallow water environment are analyzed through the physics of the waveguide invariant. In particular, the use of vertical arrays on both the source and receiver sides provides source and receiver angles in addition to travel-times associated with a set of eigenray paths in the waveguide. From the travel-times and the source-receiver angles, the eigenrays are projected into a group-velocity versus phase-velocity (Vg-Vp) plot for each acquisition. The time evolution of the Vg-Vp representation over the 8.5-h long experiment is discussed. Group speed fluctuations observed for a set of eigenrays with turning points at different depths in the water column are compared to the Brunt-Väisälä frequency.

Observations of sound-speed fluctuations in the western Philippine Sea in the spring of 2009.

As an aid to understanding long-range acoustic propagation in the Philippine Sea, statistical and phenomenological descriptions of sound-speed variations were developed. Two moorings of oceanographic sensors located in the western Philippine Sea in the spring of 2009 were used to track constant potential-density surfaces (isopycnals) and constant potential-temperature surfaces (isotherms) in the depth range 120-2000 m. The vertical displacements of these surfaces are used to estimate sound-speed fluctuations from internal waves, while temperature/salinity variability along isopycnals are used to estimate sound-speed fluctuations from intrusive structure often termed spice. Frequency spectra and vertical covariance functions are used to describe the space-time scales of the displacements and spiciness. Internal-wave contributions from diurnal and semi-diurnal internal tides and the diffuse internal-wave field [related to the Garrett-Munk (GM) spectrum] are found to dominate the sound-speed variability. Spice fluctuations are weak in comparison. The internal wave and spice frequency spectra have similar form in the upper ocean but are markedly different below 170-m depth. Diffuse internal-wave mode spectra show a form similar to the GM model, while internal-tide mode spectra scale as mode number to the minus two power. Spice decorrelates rapidly with depth, with a typical correlation scale of tens of meters.

Sensitivity kernel for surface scattering in a waveguide.

Using the Born approximation, a linearized sensitivity kernel is derived to describe the relationship between a local change at the free surface and its effect on the acoustic propagation in the water column. The structure of the surface scattering kernel is investigated numerically and experimentally for the case of a waveguide at the ultrasonic scale. To better demonstrate the sensitivity of the multipath propagation to the introduction of a localized perturbation at the air-water interface, the kernel is formulated both in terms of point-to-point and beam-to-beam representations. Agreement between theory and experiment suggests applications to sensitivity analysis of the wavefield for sea surface perturbations.

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.

Information and linearity of time-domain complex demodulated amplitude and phase data in shallow water.

Wave-theoretic ocean acoustic propagation modeling is used to derive the sensitivity of pressure, and complex demodulated amplitude and phase, at a receiver to the sound speed of the medium using the Born-Fréchet derivative. Although the procedure can be applied for pressure as a function of frequency instead of time, the time domain has advantages in practical problems, as linearity and signal-to-noise are more easily assigned in the time domain. The linearity and information content of these sensitivity kernels is explored for an example of a 3-4 kHz broadband pulse transmission in a 1 km shallow water Pekeris waveguide. Full-wave observations (pressure as a function of time) are seen to be too nonlinear for use in most practical cases, whereas envelope and phase data have a wider range of validity and provide complementary information. These results are used in simulated inversions with a more realistic sound speed profile, comparing the performance of amplitude and phase observations.