Acoustic arrival predictions using oceanographic measurements and models in the Beaufort Sea

Over the past few decades, there have been significant changes to the Arctic environment. Observational data collected between 1979 and 2021 show atmospheric temperatures rising in the Arctic nearly four times as fast as the global average,¹ between 1987 and 2017 the heat content in the ocean between 50- and 150-meters depth has approximately doubled,² and sea ice thickness and extent have both decreased.³ These changes highlight the importance of collecting oceanographic measurements of temperature and salinity in the Arctic Ocean to track changes in this continually-evolving environment. These measurements can be incorporated into ocean models to better understand ocean dynamics and changes in temperature structure, which affect underwater acoustic propagation, ocean circulation,⁴ and marine mammal habitats.⁵ As ocean temperature dictates how sound propagates through the ocean, this also has implications for underwater communication, tracking, and sound source identification. In 1994, the Transarctic Propagation (TAP) experiment utilized signals transmitted across the Arctic Ocean to study the use of long-range acoustics for Arctic temperature and ice cover monitoring.⁶ From October 1998 to December 1999, a vertical receiver array received signals across the Arctic to analyze changes in net heat flux as part of the joint US–Russian Arctic Climate Observations using the Underwater Sound (ACOUS) project.⁷ Decades later in 2019, acoustic signals were transmitted across the Arctic Ocean as part of the Coordinated Arctic Acoustic Thermometry EXperiment (CAATEX) to measure heat content and ice cover and for comparison to the results of the TAP and ACOUS experiments.⁸ 

Over the past few decades, significant changes in the stratification of the Beaufort Sea in particular have led to the formation of an acoustic duct, referred to as the Beaufort duct, enabling sound transmission to long ranges.⁹ Oceanographic data in the Beaufort Sea were collected by two Seagliders in late summer 2017 in the Canada Basin Acoustic Glider Experiment (CABAGE), part of the larger Canada Basin Acoustic Propagation Experiment (CANAPE).¹⁰ This work highlights the importance of obtaining measurements of the upper ocean sound-speed structure by examining the effect of the sound-speed profile defining the Beaufort duct on the resulting acoustic time-front arrival structure.

Water masses that make up the water column in this region are apparent in a representative sound-speed profile of the Beaufort Sea (Fig. 1). Below the surface layer is a layer of warm, salty Pacific Summer Water (PSW) which enters through the Bering Strait due to sea level difference between the Pacific and Arctic Oceans and wind forcing.¹¹ Between 1987 and 2017, the heat content in this layer has approximately doubled.² A layer of cool Pacific Winter Water (PWW) also enters through the Bering Strait and lies below the PSW. The warmer, saltier Atlantic Water that enters through the Nordic Seas lies between the PWW and the cold Arctic Deep Water.^11,12 The Beaufort duct is created by the PSW, PWW, and Atlantic Water.

Just as the Sound Fixing Ranging (SOFAR) channel enables long-distance acoustic propagation for sources placed within the channel at the sound-speed minimum, the local sound-speed minimum in the Beaufort duct enables propagation of sound to long ranges. The final cutoff of the acoustic arrivals, or the finale, in a SOFAR-like propagation environment, is comprised of the low-order modes. Similarly, an idealized Arctic sound-speed profile, in which the sound speed increases linearly with depth, results in energy being refracted upward towards the ocean surface. The low-order modes are trapped at the surface and arrive at the receiver last. Unlike theoretical Arctic propagation or SOFAR propagation, acoustic propagation in the Beaufort Sea results in the most intense arrivals, corresponding with low-order modes, arriving before the final cutoff (Fig. 2). We refer to this as the Reverse Geometric Dispersion (RGD) of the time front, where “geometric” is included as the reverse in dispersion discussed here is solely due to the geometry of the waveguide.¹³ The RGD is apparent beginning around second 208 in the lower panel of Fig. 2. This feature begins with an intense peak corresponding to the lowest order mode trapped within the duct and continues with increasing mode numbers until the final cutoff. This RGD feature overlays the more typical progression of arrivals of modes of decreasing order until they meet at the final cutoff. This is observed in the acoustic predictions as well as recorded acoustic time series from the region.¹⁴ The RGD contains information about the minimum sound speed in the subsurface duct from the peak arrival, as well as information about the bottom of the duct from the final arrivals. This could potentially be used to extract underlying information about the ocean environment through which the sound travels. Here, it is used as an indicator of the effect of environmental inputs on the acoustic predictions.

The CANAPE array, deployed from summer 2016 to summer 2017 in the Beaufort Sea, consisted of five moored tomography sources in the shape of a pentagon with the sixth source placed at the center (Fig. 1). These sources were deployed within the Beaufort duct near 180-meters depth and transmitted 135-s linear frequency modulated (LFM) sweeps with center frequencies varying between 172.5 and 275 Hz. These sources had a bandwidth of 100 Hz except for the lowest-frequency source (T2 in Fig. 1), which had a bandwidth of 65 Hz. The area considered in this analysis encompasses the six moored sources, T1–T6, and the Seaglider tracks above the mooring labeled T3 (roughly between 73- and 76-degrees North and 154- and 144-degrees West). The time frame considered is August and September of 2017, to reflect the 2017 data collected by the Seagliders during CABAGE. During this time there was no ice cover present and the Seagliders surfaced between dives.

Sound-speed profiles from environmental measurements collected on the Seagliders are used as inputs to range-dependent acoustic predictions. Comparing these predictions to acoustic time front predictions for sound-speed environments based on existing oceanographic datasets and models of the region demonstrates the sensitivity of the ducted acoustic arrivals to the sound speed of the upper ocean and the importance of collecting in situ measurements for accurate acoustic predictions.

Estimates of range-dependent sound-speed environments were made using CABAGE data as well as the Navy Global Hybrid Coordinate Oceanographic model (HYCOM),^15,16 the Arctic Subpolar gyre sTate Estimate (ASTE),¹⁷ and the World Ocean Atlas (WOA)¹⁸ to serve as inputs for broadband acoustic predictions (Fig. 3).

This work focuses on the section from T3 to T4 (Fig. 1) as a Seaglider transited that path during the summer of 2017. The Seagliders were within the study area between August 20th and September 23rd, so this is the time frame analyzed here. Temperature and salinity profiles obtained from each of these four sources were used to calculate range-dependent sound speed for the range and depth slice using the Thermodynamic Equation of Seawater–2010 (TEOS–10).¹⁹ Each sound-speed slice was constructed using linear interpolation resulting in 40 profiles along the transect with a range spacing of approximately 4.5 km. The variability in profile spacing between the datasets resulted in some repeated datapoints in the HYCOM and WOA sound-speed slices.

Two Seagliders equipped with conductivity-temperature-depth (CTD) sensors traversed between the moored sources collecting environmental data down to an average depth of 582 meters as they moved through the water in a sawtooth pattern. They were also equipped with a passive acoustic monitor receiving acoustic transmissions from five of the tomography sources deployed as part of CANAPE.¹⁴ Sound-speed profiles were calculated using the environmental data collected by the Seagliders. The temperature and salinity profiles collected on the Seagliders were extended in depth using CTD cast data collected during CANAPE.

The sound speed calculated from the CABAGE measurements have a standard deviation of 3.03 m/s at 10-meter depth. Below approximately 50-meter depth, the profiles are fairly consistent throughout the study area, with a horizontal standard deviation of 0.28 m/s at 200-meter depth. There are two subsurface ducts, one between the surface and 100-meters depth as well as the Beaufort duct between 100-and 300-meter depth with a minimum sound speed of around 165 meters (Fig. 1).

HYCOM is a global ocean model that provides ocean temperature, salinity, currents, and sea-surface height predictions. The model inputs include satellite surface data and in situ temperature and salinity profiles from instruments such as expendable bathythermographs (XBTs), Argo floats, and moored buoys that are incorporated using the Navy Coupled Ocean Data Assimilation (NCODA) system developed by the Naval Research Laboratory (NRL).²⁰ The model output has a longitudinal resolution of 0.08 degrees and the latitudinal resolution is 0.04 degrees in this region. It provides values at 3-h time intervals and 40 depth layers from the surface down to 5000 meters with layer thicknesses ranging from 2 to 1000 meters. The HYCOM values used in this analysis are for the study area and dates described previously.

Sound-speed profiles computed from the HYCOM model have one large subsurface duct between 50- and 350-meter depth with a minimum sound speed at an approximately 100-meter depth as well as a surface duct that varies in strength throughout the region (Fig. 3). Below 73.5 degrees latitude the surface temperature is warmer, resulting in a stronger surface duct towards the southern end of the study area. The surface sound speed, computed at a 10-meter depth, has a standard deviation of 4.3 m/s, which is significantly higher than at deeper depths such as 200 meters, which has a standard deviation of 1.2 m/s.

ASTE is a data-constrained Arctic Sea ice and oceanographic model covering the years 2002–2017. ASTE incorporates data from ice-tethered profilers (ITP), other CTD instrumentation, and satellite data. The model is fit to the observed data using linear least square minimization of a misfit function constrained by the model conservation laws.¹⁷ The boundaries of this model are 47.6 degrees north in the northern Pacific Ocean and 32.5 degrees south in the southern Atlantic Ocean and excludes the Mediterranean Sea with a boundary at the Strait of Gibraltar. The resolution ranges from 30 km in the mid-Atlantic Ocean to 13 km towards the pole resulting in an average spacing of 15.7 km in the study area. It has 50 depth layers ranging in thickness from 10 to 500 meters. This analysis uses the ASTE daily averaged fields during the study time frame.

The ASTE model produces sound-speed profiles that contain a subsurface duct between 80- and 300-meter depth with a minimum sound speed of around 170 meters. Like the HYCOM model, the ASTE model has warmer surface temperatures at the southern end of the study area resulting in a subsurface duct between the surface and an 80-meter depth which is stronger at lower latitudes. ASTE has the highest standard deviation in sound speed at a 10-meter depth of 4.36 m/s throughout the study area. Below the surface, the horizontal variability in the ASTE sound-speed profiles is very small. The standard deviation at 200-meters depth is 0.17 m/s.

The WOA is a collection of oceanographic data at gridded latitude, longitude, and depth intervals. The WOA consists of in situ data from the World Ocean Database (WOD), managed by the National Oceanographic and Atmospheric Administration (NOAA) National Centers for Environmental Information (NCEI), and includes measurements from ship deployed CTDs, profiling floats, pinniped-mounted CTD sensors, and other measurement tools.^21,22 The data used in this analysis are summer seasonal data from the WOA18 dataset, comprised of measurements from 2005 to 2017. The temperature and salinity data are gridded with resolutions of one-fourth degree at 102 depths down to 5500 meters with layer thickness ranging from 5 to 100 meters.

The WOA data are sparser than the HYCOM and ASTE models since it is a collection of in situ data. Just under two-thirds of the latitude-longitude points in the study area grid have no data at any depth step. The surface values are even more sparse with only five percent of the study area having data points at a 5-meter depth. These data do, however, result in sound-speed profiles with the Beaufort duct visible between 80- and 300-meter depth with a minimum sound speed of around 125 meters and a strong surface duct above it. Seven out of the 24 data points scattered throughout the study area have warmer surface temperatures producing a subsurface duct instead of a surface duct. The horizontal standard deviation in sound speed at a 10-meter depth is less than both HYCOM and ASTE at 3.29 m/s, but similar to CABAGE, HYCOM, and ASTE, this decreases with depth with a horizontal standard deviation at 200 meters of 0.45 m/s.

Each of these models and datasets shows at least one subsurface duct in the sound-speed profile in the study area. However, the depth and shape of the duct varies, and sometimes the profile includes two subsurface ducts. The sound-speed profile transect from T3 to T4 created using HYCOM differs the most from the representative CABAGE profile (Fig. 3). The subsurface duct present in the HYCOM model lies at a depth between the two subsurface ducts present in the CABAGE data. The mean difference in sound speed in HYCOM between a 200- and 400-meter depth throughout the study area is 10.8 m/s. This is substantially lower than CABAGE, ASTE, and WOA which are 15.2, 15.8, and 15.5 m/s, respectively.

The range-dependent sound speed from each of these sources was used to calculate acoustic time front predictions from a source placed at T3 to a receiver at T4 (Fig. 4). Broadband predictions of acoustic arrivals were obtained using Fourier synthesis of the split-step Padé solution to the parabolic equation.²³ The source was placed at a 180-meter depth and source characteristics emulated the T3 CANAPE source which transmitted a broadband signal centered at 275 Hz with a bandwidth of 100 Hz. The model did not include ice cover to reflect the conditions in which CABAGE took place. The model was run with four Padé coefficients, a depth resolution of 0.2 meters, a range resolution of 50 meters, and a frequency resolution of 0.2 Hz. The ocean depth between the two moored sources is relatively flat, ranging from a 3777- to 3872-meter depth. Bathymetry was from the International Bathymetric Chart of the Arctic Ocean (IBCAO).²⁴ Sediment density, sound speed, and attenuation used in the model have previously been used in sediment acoustic modeling in the Beaufort Sea.²⁵ These parameters were used down to 300 meters into the sediment.

One of the most notable differences between these predictions is the travel time of the final ducted arrival. The predicted final RGD arrivals for both CABAGE and WOA occur around 122.7 s. However, in the CABAGE prediction, some later arrivals at depths corresponding with the depth of the upper subsurface duct arrive out to 122.8 s. The ASTE and CABAGE predictions have strong peak arrivals in the RGD at 122.3 s at the depth of the slowest sound speed in the Beaufort duct. The HYCOM time front has the earliest final acoustic arrivals, around 122.3 s. This approximately lines up with the beginning of the RGD in the other time fronts.

Although the HYCOM model has the best horizontal resolution, it differs the most from the measured CABAGE data both in terms of the sound-speed environment and the resulting predicted acoustic arrivals. The CABAGE data and ASTE model produce very similar sound-speed environments, although ASTE has warmer temperatures between a 50- and 100-meter depth resulting in stronger acoustic arrivals close to the surface later in the time front. WOA matches the measured sound-speed environment from CABAGE within the Beaufort duct most closely, which may be expected given that both result from in situ datasets collected in the Beaufort Sea in the summer months.

The top few hundred meters of the sound-speed fields considered here, including the Beaufort duct, have significantly slower sound speeds than the depths below. This region channels sound and results in the RGD in the predicted acoustic arrivals. The depth span of the RGD is consistent with that of the Beaufort duct in the corresponding sound-speed profile, visible in Fig. 3 down to approximately 300 meters depth in the CABAGE, ASTE, and WOA sound-speed profiles. The HYCOM model differs significantly from the CABAGE data at these depths, although it does exhibit an upper duct with a local minimum of around 60 meters. The more consistent gradient below the subsurface duct in the HYCOM model results in a more traditional Arctic arrival pattern, where the final arrival corresponds with the depth of the minimum sound speed (Fig. 2, middle panel).

In the CABAGE profile, the duct above the Beaufort duct has a sharper sound speed gradient, and mode 1 at 275 Hz is trapped within this upper duct; however, this mode is only weakly excited as the source is in the Beaufort duct at a 180-meter depth. The WOA data has a very similar Beaufort duct structure to CABAGE so the RGD portion of the time front looks very similar; however, this dataset does not capture the shape of the upper duct seen in CABAGE. The separation between the upper duct and the Beaufort duct, particularly at the beginning of the transect, is less well-defined as is apparent in Fig. 3 in the darker blue section between 50- and 100-meters depth. The WOA time front does not show ducted acoustic energy past the RGD (Fig. 4). The ASTE subsurface duct is similar to that seen in the CABAGE data, but does not follow the shape of the CABAGE Beaufort duct as closely as the WOA profile does; however, these similarities in sound speed structure result in similar acoustic arrival structures with strong RGD features.

The acoustic predictions presented here, or the “forward problem,” show the RGD is particularly sensitive to the upper-ocean sound-speed profile. Characteristics of this feature could offer valuable information for the inverse problem, providing information about the profile of sound-speed over long ranges. The RGD has been observed in the recorded acoustic data from CABAGE and CANAPE,²⁶ and could be used as a tool to extract information about the sound-speed channel through which the acoustic signal travels.

Although differences between the four different data sources in the later arrivals of the acoustic time front, specifically the RGD, are apparent in Fig. 4, predictions of the early acoustic arrivals are quite consistent. These early arrivals are more influenced by sound speed in the deep ocean. Measurements of these early arrivals on the CANAPE moorings have shown consistency with predictions based on existing ocean models, whereas predictions of the later arrivals omit significant acoustic energy transported within the Beaufort duct.²⁶ Bottom bounce arrivals, which are also strongly impacted by the deep ocean sound-speed, were also consistently predicted by the four different sound-speed environments considered here, with similar arrival times.

It is important to note that the four sound-speed environments analyzed here were not created the same way. CABAGE and WOA are in situ measurements and HYCOM and ASTE are oceanographic models that use in situ surface and vertical measurements from Argo floats, XBTs, CTDs, ITPs, as well as other measurement platforms, and satellite observations as inputs.

The results presented here assume a synoptic sound-speed field, that is the sound-speed input data represent an instant in time, which is the case for the HYCOM and ASTE models, but the CABAGE and WOA sound-speed profiles are computed using in situ measurements taken over a range of time. The WOA in situ data is a collection of measurements throughout the summers from 2005 to 2017, and due to the sparseness of available data, the T3 to T4 transect is made up of only five data points based on what was available in the WOD. The in situ CABAGE data are treated as synoptic, however, the Seaglider took ten days to traverse between moored sources T3 and T4 to collect the environmental measurements used in this analysis.

The measurements collected on Seagliders during the CABAGE experiment offer a unique dataset of in situ environmental data including important measurements in the upper ocean that strongly impact acoustic arrivals in the Beaufort Sea. These data provide insight into the acoustic propagation in this region where both surface and subsurface sound channels, or ducts, are often present in the top few hundred meters of the ocean.

Propagation within the duct leads to an RGD, which is present in the predicted acoustic time fronts generated using sound-speed data from CABAGE, ASTE, and WOA. Both the shape and duration of this feature are highly sensitive to the sound speed of the upper ocean. The HYCOM acoustic time front for the section of the Beaufort Sea in Summer 2017 modeled here does not display an RGD, illustrating the sensitivity of predicted acoustic arrival structure on upper ocean sound speed.

The Arctic regions are remote environments where it is difficult to obtain in situ measurements, as evident by the scarcity of the WOA data available in the study area, so we often need to rely on ocean models. The results presented here, however, highlight the importance of having measurements of the upper ocean sound speed to understand acoustic propagation in the Beaufort Sea in particular and the Arctic Ocean in general.

This work was performed as part of the Ph.D. work of Jessica B. Desrochers funded by the Naval Undersea Warfare Center, Division Newport. This work was performed at the University of Rhode Island with support from the Office of Naval Research (ONR) Ocean Acoustics Program (Award No. N00014-22-1-2034, PI: Dr. Lora Van Uffelen). Funding for the CABAGE deployment was provided by the ONR through the Ocean Acoustics Program (Award No. N00014-17-1-2228, PI: Dr. Lora Van Uffelen, URI) and the Arctic and Global Predictions Program (Award No. N00014- 16-2596, PI: Dr. Sarah Webster, APL-UW) as well as Defense Research and Development Canada (DRDC) (Contract No. W7707-175902/001/HAL, PI: Dr. Sarah Webster, APL-UW). Funding for the development of HYCOM has been provided by the National Ocean Partnership Program and the Office of Naval Research. Data assimilative products using HYCOM are funded by the U.S. Navy. Computer time was made available by the DoD High Performance Computing Modernization Program. The output is publicly available at https://hycom.org. The authors would like to acknowledge the scientists, captain, and crew on the USCGC Healy and the R/V Ukpik who enabled the data collection during CABAGE and to Peter Worcester and Matthew Dzieciuch from Scripps Institution of Oceanography who provided the CTD profiles from CANAPE. Additionally, the authors are grateful to Peter Worcester for his valuable insight and input on this work. Distribution A: Unclassified, approved for public release by the Naval Undersea Warfare Center, Division Newport. Distribution Unlimited.

The authors have no conflicts of interest.

The data that support the findings of this study are available from the corresponding author upon reasonable request.