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 semidi-urnal variability, presumably due to some combination of the semidiurnal tides and inertial variability. V C 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC

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 carbon dioxide and other greenhouse gases (McLaughlin et al., 2011;Jeffries et al., 2013;Wood et al., 2015).Sea ice extent and thickness have declined (Kwok, 2018;Stroeve and Notz, 2018;Serreze and Meier, 2019).Multiyear ice that has survived one or more summer melt seasons has largely disappeared (Kwok, 2018).Ocean stratification is also changing as warmer waters have entered the Arctic Ocean from the North Atlantic and North Pacific Oceans (Polyakov et al., 2012;Timmermans et al., 2014).The 2016-2017 Canada Basin Acoustic Propagation Experiment (CANAPE) was conducted to assess the effects of the changes in the Canada Basin north of Alaska on underwater acoustic propagation and ambient sound, as the extensive underwater acoustic measurements made during the Cold War (e.g., Mikhalevsky, 2001) no longer reflect current conditions.During CANAPE, 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, combining measurements of acoustic propagation and ambient sound with the use of acoustic remote sensing methods to help characterize the large-scale sound-speed field in this difficult to measure region.The one-year deployment provided measurements in largely open water during summer, in the marginal ice zone (MIZ) as it transitioned across the array during the autumn and spring, and under complete ice cover during winter.In this paper, the variability in the travel times of the early resolved acoustic arrivals with the shortest travel times will be described.These arrivals are from steep ray paths that reflect from the surface and have lower turning depths between 500 and 3500 m.
Changes in the characteristics of the ice are important for ocean acoustics because the Arctic sound-speed profile is largely upward refracting, and sound interacts repeatedly with the ice as it propagates.The characteristics of first-year sea ice are quite different from those of multiyear ice.In addition to different physical properties, multiyear ice has larger pressure ridges than first-year ice, with associated ice keels that can extend down tens of meters.These deep keels are disappearing together with the multiyear ice.First-year ice is not featureless, however, as it is weaker and more easily deformed than multiyear ice, leading to pressure ridges and unconsolidated keels extending down 10 m or so (Strub-Klein and Sudom, 2012).Changes in ocean stratification are a) Electronic mail: pworcester@ucsd.edualso important, particularly in the western Arctic (McLaughlin et al., 2011).Changes in waters entering through the shallow Bering Strait between Russia and Alaska have resulted in the strengthening of a subsurface sound-speed duct formed by a layer of relatively warm, high sound-speed Pacific Summer Water (PSW), called the Beaufort Lens, that lies above the colder, more saline, and lower sound-speed Pacific Winter Water (PWW), creating a sound-speed minimum at a depth of roughly 175 m (Litvak, 2015).The sound-speed duct is referred to here as the Beaufort Duct.Signals transmitted from sources within the duct can be trapped and propagate to long ranges without interacting with the surface or bottom (Freitag et al., 2015;Webster et al., 2015;Duda, 2017).The CANAPE sources were located within the duct, and arrivals from acoustic energy trapped in the duct were observed during the 2016-2017 CANAPE experiment.However, interpreting these arrivals is complex and better suited to an acoustic normal mode analysis than the ray analysis used here (Kucukosmanoglu et al., 2021).This analysis will therefore be done in a subsequent paper.
Section II describes the 2016-2017 CANAPE experiment.Section III summarizes the oceanographic environment in the Canada Basin during 2016-2017.Section IV describes how time series of travel times were generated for the resolved acoustic ray paths.Section V discusses the observed travel-time variability.Some concluding remarks are made in Sec.VI.Finally, an Appendix briefly describes the ocean stratification, mesoscale variability, internal waves, and barotropic tides in the Beaufort Gyre.

II. 2016-2017 CANAPE EXPERIMENT
The 2016-2017 CANAPE experiment is described in the following subsections, including the geometry, signal processing, and environmental measurements.A short-term pilot study during summer 2015 preceded the 2016-2017 CANAPE experiment.One of the principal goals of the pilot study was to determine the appropriate spatial scale for the 2016-2017 experiment, i.e., the ranges at which the signalto-noise ratios of the receptions would be expected to be adequate.The environmental measurements from the pilot study have been reported by DiMaggio et al. (2018).

A. Acoustic transceivers
Six Teledyne Webb Research (TWR) swept-frequency acoustic sources (Morozov et al., 2016) with integrated Distributed Vertical Line Array (DVLA) receiving systems (Worcester et al., 2009;Worcester et al., 2013) were deployed in the Canada Basin during August-September 2016 and recovered during September-October 2017.The acoustic transceiver array was in the form of a pentagon with a radius of 150 km (Fig. 1).
The sixth transceiver was in the center at about 74.5 N, 149 W (Table I).The median source depths (as a proxy for the depths when the moorings were vertical) were 173-182 m, approximately on the axis of the sound-speed minimum formed by the PWW (Table I).
The array was located on the Canada Abyssal Plain with relatively featureless bathymetry.Five sources transmitted 135-s linear frequency modulated (LFM) signals with bandwidths of 100 Hz and center frequencies of approximately 250 Hz (Table II).One source (T2) transmitted a 135-s, 140-205 Hz LFM signal.The source beam patterns are cylindrically symmetric in the horizontal and have an approximate dipole antenna pattern in the vertical.The average measured source levels in the horizontal varied from 183.8 to 185.2 dB re 1 lPa at 1 m root-mean-square (rms) (Table II).
The sources transmitted every 4 h beginning at 0000, 0400, …, 2000 universal time coordinated (UTC).To avoid interference, transmissions from the six sources were sequenced at 6-min intervals during each transmission cycle, with source T1 transmitting on the hour (Table II).Sources T1 through T5 transmitted throughout the year, but source T6 failed shortly after deployment.Each source began transmitting shortly after it was deployed.The last transmission cycle occurred at 2000 UTC on 31 August 2017, after which  the transmissions were programmed to stop in preparation for the mooring recoveries.
Each acoustic transceiver recorded the transmissions from the other transceivers at ranges varying from approximately 150 to 285 km (Table III).The DVLA recorded the transmissions from T1 to T5 at ranges from approximately 110 to 207 km (Table III).
A DVLA receiver with 15 Hydrophone Modules spaced 9.0 m apart (i.e., $ 3/2 k at 250 Hz) was located above each source to record the transmissions from the other sources.The top Hydrophone Modules were located 6.5 m below the subsurface floats, which had a design depth of 40 m (although the actual depths when the moorings were vertical varied by a few meters).The DVLA array above each source and the mooring wire extending below each source to a depth of about 580 m had four-sided hairy fairing overbraid to reduce mooring strum.Although the source at T6 failed prematurely, the transceiver continued to record the transmissions from the other sources for the remainder of the experiment.The receivers recorded for 175 s beginning 20 s prior to the nominal arrival times of the transmissions from the moored sources to provide approximately 20-s buffer periods before and after the receptions.The sample rate was 1953.125 Hz.
Long-baseline acoustic navigation systems with three acoustic transponders (Teledyne Benthos XT-6001-13, Teledyne Benthos, North Falmouth, MA) on the seafloor were used to determine the source and Hydrophone Module positions.The transponder locations were surveyed following deployment using interrogations from a shipboard acoustic transducer whose position was determined using the Global Navigation Satellite System (Kongsberg Seapath V R 330þ dual-frequency GNSS receiver and inertial system, Kongsberg, Buskerud, Norway).The ship's heading was used to correct for the offset between the locations of the GNSS antenna and the shipboard transducer on the USCGC Healy.The estimated absolute accuracy of the transponder positions (WGS84) was 3 m rms.The transponders were interrogated once per hour throughout the experiment by the DSTAR controllers located in each source, and the replies were recorded by the DSTAR and the Hydrophone Modules.In addition to a bias in the instrument positions at each mooring due to the uncertainty in the transponder positions, there is an uncertainty of about 1 m that is uncorrelated from measurement to measurement (see Sec. V B).The mooring displacements used to correct the acoustic travel times were computed relative to reference locations that were close to, but not identical to, the mooring anchor locations (Table I).The reference and mooring anchor locations are not the same because the reference locations were selected prior to the acoustic surveys used to determine the transponder positions.The precise positions of the acoustic releases near the bottom of each mooring were also determined during the transponder surveys.Ocean currents displaced the moorings horizontally and vertically at times throughout the year (Fig. 2).The displacements were quite large at times, with mooring T4 showing a maximum vertical excursion in excess of 250 m.

B. DVLA
A DVLA receiving array located at the intersection of the T1-T4 and T3-T5 paths recorded the transmissions from the moored sources throughout the year (Fig. 1).The DVLA had two subarrays of 30 Hydrophone Modules each, giving a combined total of 60 Hydrophone Modules, with DSTAR controllers located at the bottom of each subarray.The Hydrophone Modules were spaced 9.0 m apart except for a gap of 18.0 m spanning the DSTAR controller at the bottom of the top subarray (i.e., effectively one missing hydrophone).The DVLA subarrays had four-sided hairy fairing overbraid to reduce strum.As was the case for the transceiver moorings, the top Hydrophone Module was located 6.5 m below the subsurface float, which had a design depth of 40 m, and the DVLA recorded for 175 s beginning 20 s prior to the nominal arrival times of the transmissions from the moored sources at a sample rate of 1953.125 Hz.A long-baseline acoustic navigation system identical to those used to track the motions of the transceiver moorings (except with four instead of three acoustic transponders) determined the Hydrophone Module and DSTAR positions once per hour.The DSTAR controller for each subarray independently interrogated the bottom transponders.

C. Signal processing and beamforming
The received signals were processed by correlating with idealized replicas of the transmitted signals.The replicas had constant amplitude throughout the linear frequency sweeps (unlike the actual transmitted signals).This "phasematched only" filter yields narrower output pulses than a true matched filter but at the expense of some decrease in signal-to-noise ratio (Birdsall, 1976).The replicas were also adjusted based on measurements made at the U.S. Navy Seneca Lake Acoustic Test Facility to partially account for the non-linear phase responses of the sources caused by resonances in the transducer matching circuitry.It was found empirically that assuming the transmission durations differed slightly from the actual 135.000 s partially compensates for the non-linear phase responses and gives improved pulse shapes after processing (Table IV).
The resulting processed output pulses were close to the ideal shape with main lobes that had full widths of 20 ms between the first zeroes.Figure 3 shows a time front recorded on the DVLA for a transmission from source T3 at a range of 176 km together with a predicted time front.The soundspeed field used to make the parabolic equation prediction was constructed using temperature and salinity profiles from the National Center for Environmental Information (NCEI) Arctic Regional Climatology (1/4 Â 1/4 degree, annual average) (Boyer et al., 2015;Seidov et al., 2015).The observed and simulated time fronts show common features.There are early-arriving, high-angle, well-separated time front branches coming in groups of four, followed later by many closely spaced branches with shallower lower turning depths.The last several hundreds of milliseconds of the receptions show a reverse dispersion pattern in which the travel times decrease rather than increase as the vertical arrival angle approaches the horizontal (see also Fig. 9).This paper focuses on the travel times of the earliest arrivals shown in Fig. 3, namely, the first three groups of four.
After pulse compression, the receptions on the vertical arrays were beamformed using a turning point filter, which is an extension of linear beamforming that accounts for ray curvature (Dzieciuch et al., 2001).

D. Environmental measurements
Conductivity-Temperature-Depth (CTD) casts were made during the mooring deployment and recovery cruises.Casts were made near each mooring location in both 2016 and 2017.In 2017, casts were also made at approximately the mid-points of the paths on the periphery of the pentagonal array.
Extensive oceanographic instrumentation was deployed on the seven moorings to provide environmental information throughout the year, as described in detail in Kucukosmanoglu et al. (2021) and Kucukosmanoglu et al. (2023).The DVLA mooring included 28 Sea-Bird MicroCATs (Sea-Bird Scientific, Bellevue, WA, SBE 37-SMP/SM) that spanned the depth range of 50-425 m to measure the thermohaline structure in the upper ocean.The instruments had a typical separation of 13.5 m and sampled at 5-min intervals.In addition, the 60 Hydrophone Modules in the DVLA made temperature measurements (60.005C) at 20-min intervals.The subsurface floats for moorings T1-T6 had 420-kHz ASL Environmental Sciences IPS-5 (ASL, Saanichton, Canada) ice profiling sonars to determine ice draft (using the procedures described in Krishfield et al., 2014) and upward-looking RDI Workhorse Sentinel 600-kHz ADCPs (Teledyne RD Instruments, Poway, CA) to measure upper ocean currents and sea ice velocities.Mooring overshoots during anchor-last deployments in the open water present during the deployment cruise damaged the precision pressure sensors in the IPS-5 ice profiling sonars.The pressure sensors in Sea-Bird MicroCATs located 4.1 m below the subsurface floats were instead used to compute ice drafts, slightly degrading the accuracy.The 15 Hydrophone Modules in the receiving arrays above the sources made temperature measurements (60.005C) at 12-min intervals.In addition, ten temperature sensors located below the sources made measurements at 10-s (Sea-Bird SBE 56) or 5-s (RBRsolo T) intervals.The temperature sensors below the sources had design depths from 180 m to 570 m.Finally, a Bottom Pressure Recorder (BPR) was located at each transceiver anchor.

III. OCEANOGRAPHIC ENVIRONMENT IN THE CANADA BASIN DURING 2016-2017
The transceiver array was located in the anticyclonic (clockwise) Beaufort Gyre.The gyre centroid, which drifted slowly to the northwest during the 2000s, was at approximately 76 N, 150 W in 2014 two years before the CANAPE experiment (Armitage et al., 2017).Mooring T6 at the center of the acoustic array at 74.5 N, 149 W was slightly south of the Gyre center.The atmospheric circulation during winter (January through March) of 2017 was, however, anomalous (Moore et al., 2018).The quasistationary region of high atmospheric pressure known as the Beaufort High collapsed, leading to a reversal of the normally anticyclonic surface winds and sea ice motion.
The Beaufort Gyre has been studied extensively, and a brief overview of the oceanographic environment is given in the Appendix.This section will focus primarily on the environmental measurements made during the 2016-2017 CANAPE experiment, although some information necessary for understanding the acoustic observations will also be provided.Kucukosmanoglu et al. (2021) and Kucukosmanoglu et al. (2023) also report on the oceanographic environment in the Canada Basin during 2016-2017 using data collected during the CANAPE experiment.

A. Ocean stratification
The temperature and salinity structure in the Canada Basin is made up of five principal layers: a strongly seasonally varying surface layer, Pacific Summer Water (PSW), Pacific Winter Water (PWW), Atlantic Water (AW), and deep ocean layers (see the Appendix; McLaughlin et al., 2011;Proshutinsky et al., 2020).Figure 4 shows the top 1000 m of each CTD cast made during the mooring deployment and recovery cruises.The temperature maximum at a depth of roughly 80 m is associated with the PSW.The temperature minimum between approximately 140 and 250 m is associated with the PWW.Below the PWW is the AW, which is associated with another temperature maximum at about 400 m.
Sound speed depends mostly on temperature, and the sound-speed profile in the upper ocean, therefore, displays a similar structure with a minimum in sound speed associated with the PWW.This is the Beaufort Duct (Litvak, 2015;Duda, 2017;Duda et al., 2021).The temperatures in the upper 600 m at the DVLA constructed by combining the Sea-Bird MicroCAT and Hydrophone Module data show the structure of the Beaufort Duct at that location throughout the year (Fig. 5; see also Kucukosmanoglu et al., 2021).
The PWW and AW show relatively little temporal variability over the year.There are some fluctuations in the PSW FIG. 4. Temperature, salinity, and sound speed from CTD casts made during the mooring deployment and recovery cruises (light gray) and the mean of the casts (black).The CTD cast with an anomalously high temperature of about 2 C near 100 m depth was between moorings T3 and T4 on the southwest side of the array during the 2017 mooring recovery cruise.associated with mesoscale variability (Kucukosmanoglu et al., 2021), but the Beaufort Duct at the DVLA is nonetheless relatively stable throughout the CANAPE experiment.There is no apparent seasonal variability in the PSW, as expected (Timmermans et al., 2014).The PSW (and therefore the Beaufort Duct) displays more variability across the CANAPE array, as can be seen in temperature measurements made at moorings T1-T6 (see Supplementary Material from Kucukosmanoglu et al., 2023).The PSW is relatively stable at moorings DVLA, T1, T5, and T6 in the northern part of the CANAPE array but displays significantly more temporal variability at T2, T3, and T4, which are closer to the shelf where the eddy density is higher.
As discussed previously, the formation and strengthening of the Beaufort Duct in recent years due to the warming of the PSW are of particular importance for acoustic propagation (Litvak, 2015;Freitag et al., 2015;Webster et al., 2015;Duda, 2017;Ballard et al., 2020;Duda et al., 2021;Baggeroer and Collis, 2022;Bhatt et al., 2022).The structure of the Beaufort Duct has relatively little effect on the travel times of the steep ray paths with deep lower turning depths discussed here, however.These ray paths are more sensitive to variability near their lower turning depths.The deep ocean below the AW is remarkably stable in the Canada Basin, slowly warming in response to geothermal heating.
B. Mesoscale variability Manley and Hunkins (1985) estimated that mesoscale eddies occupy up to one quarter of the surface area of the Beaufort Sea.A variety of eddy types have been identified (see the Appendix).Eddies are presumably responsible for the mooring pulldowns evident in Fig. 2. Most of the mooring pulldowns are relatively brief, but T2 and T4 experienced lengthy pulldowns, suggesting that the eddies causing those pulldowns were quasi-stationary for extended periods.The eddy field is spatially and temporally variable (Zhao et al., 2016).The southern and western portions of the Canada Basin (where the CANAPE array was located) have higher eddy densities.The number of lower halocline eddies increased from 2005 at least through 2014.
Mesoscale eddies are evident in the profiles of temperature vs time at the DVLA (Fig. 5).Kucukosmanoglu et al. (2021) show in detail an eddy near year day 300.There is a particularly strong eddy near the end of the record.Several mesoscale eddies are evident in the temperature records at the transceiver moorings (Kucukosmanoglu et al., 2023).The near-surface ADCP observations on the transceiver moorings, combined with the deep ADCP data from the DVLA mooring, also show energetic but isolated eddies (Kucukosmanoglu et al., 2021).

C. Internal waves
Consistent with previous observations (see the Appendix), Kucukosmanoglu et al. (2021) found low internal wave energy levels in the Canada Basin that averaged roughly 5% of the Garrett-Munk reference level.They also found that the spectral energy and spectral shape varied significantly over the year.The implication of the low internalwave energy levels for acoustic propagation is that much less acoustic scattering due to internal-wave-induced soundspeed fluctuations is expected than in midlatitudes (e.g., Colosi, 2016).

D. Tides
Barotropic tidal amplitudes and currents in the Canada Basin are small, with the largest amplitudes associated with the semidiurnal component M 2 (see the Appendix).The critical latitude for M 2, where the tidal and inertial frequencies are identical, is 74.48 N, which is nearly the latitude of mooring T6 in the center of the CANAPE array.The S 2 critical latitude is 85.77 N, which is well north of the CANAPE moorings.However, numerical tidal models do not seem to show unusual spatial structure for the M 2 tide near the critical latitude (Kowalik and Proshutinsky, 1994;Padman and Erofeeva, 2004;Chen et al., 2009).

E. Sea ice
During 2016, the sea ice extent in the Arctic reached its summer minimum (4.14 Â 10 6 km 2 ) on 10 September 2016, around the time that the CANAPE moorings were being deployed (National Snow and Ice Data Center, NSIDC).The subsequent winter maximum (14.42 Â 10 6 km 2 ) occurred on 7 March 2017.The 2017 summer minimum (4.64 Â 10 6 km 2 ) was reached on 13 September 2017, around the time that the moorings were being recovered.Sea ice concentration derived from the AMSR2 satellite (Spreen et al., 2008) shows that the ice began to reach the northeastern part of the CANAPE array on about 20 October 2016 and advanced to the southwest, covering the entire array by around 10 November 2016 (Fig. 6).The array remained largely ice-covered until around 20 July 2017, when the ice began retreating from southwest to northeast across the array.The array was largely ice-free by 1 August 2017 (Fig. 6).
The ice profiling sonars on the transceiver moorings all show a gradual increase in ice draft over the winter, with the daily median ice drafts reaching maxima of about 1.5 m around the beginning of June 2017 before rapidly decreasing to zero by about 1 August 2017 (Fig. 7).The implication is that the CANAPE array was entirely covered by first-year ice.
The daily maximum ice drafts occasionally reached 15 m but rarely exceeded 20 m (not shown).The maximum ice drafts are associated with ice keels formed when the first-year ice deforms in response to winds and currents.For comparison, Strub-Klein and Sudom (2012) report that the maximum keel depth for first-year ice in the Beaufort Sea has a mean of 12.6 m based on the analysis of 58 keels.First-year keels have a consolidated layer that lies above rubble made up of loose ice blocks with water trapped in between.The degree of consolidation of first-year ridges is almost always much less advanced than that of older multiyear ridges.

IV. TRACKED AND CORRECTED TRAVEL TIMES
The generation of time series of travel times for the ray arrivals in the acoustic receptions involves several steps (Munk et al., 1995).The procedure is not new but is nonetheless described here in some detail because the variability in the resulting time series is extraordinarily low.It is therefore important to document the quality of the data and the various corrections that have been applied.First, the receptions on the vertical receiving arrays are beamformed using the turning point filter (Dzieciuch, 2001).Dot plots that display travel times as a function of year day are then constructed by plotting each peak in the beamformed receptions that exceeds a specified signal-to-noise ratio (SNR) as a dot whose size depends on the SNR and whose color depends on the vertical arrival angle at the receiver (Fig. 8).Dot plots for the acoustic paths T5-T6, T1-T5, and T3-T5 show the arrival patterns at ranges of approximately 150 km, 175 km, and 285 km, respectively, corresponding to the three basic ranges between the acoustic transceivers in the array (Table III).These dot plots have been corrected for clock drifts in the source and receiver (Munk et al., 1995).They have also been corrected to first order for travel-time changes due to horizontal mooring motion, assuming the rays are horizontal.
Ray paths are evident in these plots from their continuity from reception to reception.One immediately apparent feature is the stability of the travel times of the resolved ray paths throughout the year.Another striking feature is the disappearance of arrivals in wintertime, particularly as the range increases.This is most likely due to acoustic scattering as the signals reflect from the ice as they propagate from the source to the receiver, increasing the transmission loss.The earliest arrivals have fewer surface reflections and so experience less loss.
The next step is identifying the ray arrivals evident in the dot plot with specific ray paths by comparing measured and predicted arrival patterns.Figure 9 makes this comparison in travel-time-arrival-angle space for the acoustic paths shown in Fig. 8.The early, resolved ray arrivals appear as peaks in histograms constructed for the receptions throughout the year.Also, evident in the plots are grating lobes at an angle above and below the main peaks because the hydrophones in the vertical receiving arrays were separated by 9 m (i.e., $ 3/2 k at 250 Hz).The predicted ray arrivals for sound-speed fields computed using the NCEI Arctic Regional Climatology (1/4Â 1/4 degree, annual average) (Boyer et al., 2015;Seidov et al., 2015), which uses the Arctic area data available in the World Ocean Database through 2010, are close to the peaks for the early arrivals in the histogram.The ray predictions were range-dependent, using sound-speed fields that were linearly interpolated in the horizontal.The focus here is on the early arrivals for which there is a one-to-one correspondence between the measured and predicted arrivals.The agreement is poor for the late arrivals because the Beaufort Duct is not well represented in the NCEI Climatology.
The arrivals come in groups of four in which all four ray paths have the same number of lower turning points.The subsequent analysis will be confined to the first three groups of arrivals for each source-receiver pair, corresponding to the three sets of four ray paths with the deepest turning points.The ray paths for these arrivals for the acoustic paths shown in Fig. 8 are shown in Fig. 10.Time series of travel times for each resolved ray path are then generated by tracking the arrivals from one reception to the next using the Viterbi algorithm with a metric that accounts for the travel time, vertical arrival angle, and amplitude of each peak (Dzieciuch, 2014).Ellipses that surround each of the arrival clusters of interest in the histogram are defined, and the tracked peaks are required to lie in these regions (Fig. 9).In this case, the travel time variability over the year is sufficiently small that tracking the arrivals is relatively straightforward except for times when the moorings are displaced substantial amounts in the vertical by ocean currents, affecting the measured travel times.
Finally, the time series of travel times for the identified ray paths are corrected for travel-time changes caused by the vertical displacements of the source and receiver.The corrections are made assuming that the ray wave fronts are local plane waves normal to the ray path, using the vertical angles at the source and receiver for the predicted ray path (Munk et al., 1995).

V. TRAVEL TIME VARIABILITY
The time series of corrected travel times for the earliest and deepest turning tracked arrivals for the three acoustic paths for which dot plots are shown in Fig. 8 (T5-T6, T1-T5, and T3-T5) are shown in Fig. 11.The ray IDs are -5 for T5-T6, -7 for T1-T5, and -11 for T3-T5.The mean travel time for each path has been subtracted to emphasize the variability.These arrivals were selected for display because they have the most complete time series (i.e., the fewest missing arrivals).The variability over the year for these paths is slightly less than 20 ms peak-to-peak.For comparison, the full width of the main lobes of the ideal output pulses for the transmitted signals after signal processing is 20 ms.Although the variability is roughly similar for most other paths, peak-to-peak variabilities of up to about 50 ms do occur (not shown).The peak-to-peak variability is sensitive to errors in the tracking, however.
The variability is extraordinarily small compared to that seen in previous ocean acoustic tomography experiments at similar ranges (Munk et al., 1995).The variability, as quantified by computing the standard deviations of the travel-time series, has values of a few ms rms at all ranges (Fig. 12).There is considerable scatter at each range, but somewhat surprisingly, the variability does not show an obvious dependence on range.

A. Travel-time spectra
The gaps in the travel-time series, particularly the larger gaps in wintertime for the arrivals at longer ranges that experience more surface reflections, complicate the task of computing spectra to characterize the travel-time variability.Here, spectral estimates are made using a weighted least squares harmonic analysis that does not require interpolation of the time series.The technique is fundamentally the same as that described in Kachelein et al. (2022), where conventional tidal harmonic analysis was extended using Maximum a Posteriori (MAP) estimation to allow for irregularly spaced observations and uncertainty in the observations.Here, however, the basic functions for the harmonic analysis do not include sinusoids at tidal frequencies but instead are sinusoids evenly spaced in frequency at intervals of 1=T, where T is the length of the time series.This approach emulates the results that could be obtained using a standard Fourier transform if the time series did not have gaps, except that it explicitly allows for data error and weights the least squares fit in accord with a prior estimate of the spectra.The result is somewhat similar to a periodogram rather than a power spectral estimate, as the procedure in Kachelein et al. (2022) is designed to characterize dominant tidal peaks.
The prior estimate of the spectra was obtained by computing the average of the squares of the individual fast Fourier transforms of the linearly interpolated travel-time time series for all the identified rays.This yields a red spectrum with a slope of approximately -1 and a peak at the inertial/semidiurnal tidal band.An uncertainty of 2 ms was assumed for all travel times, which is approximately the expected travel-time measurement uncertainty (see Sec. V B).As a by-product of estimating the harmonic components, estimates of the low-and high-frequency components of the travel-time time series can be constructed using the harmonic components with periods longer and shorter than two days, respectively.
The spectra for the three acoustic paths for which dot plots are shown in Fig. 8 (T5-T6, T1-T5, and T3-T5) are shown in Fig. 13.The spectra for all of the tracked ray paths for each of the three acoustic paths are included on the plots.
All three spectra are red at low frequencies.There is no obvious dependence on range, consistent with Fig. 9, in which the standard deviations of the time series are independent of range.All three spectra have a small peak at 2 cycles/ d, i.e., the inertial/semidiurnal tidal frequency, with a peak harmonic variance of about 7 Â 10 À8 s 2 (0.26 ms rms).It is not possible to separate the inertial and semidiurnal tidal contributions because the M 2 critical latitude runs through the center of the CANAPE array, as noted previously.

B. Low-frequency and high-frequency travel-time series
The low-frequency travel-time series can be used to study the variability in the mesoscale eddy field, the Beaufort Gyre, and other oceanographic phenomena that vary on time scales of days and longer, either by dataoriented inverse methods or by assimilation into ocean models (Munk et al., 1995).From this perspective, the highfrequency travel-times series represent the noise in the data.The inversion and/or assimilation of the low-frequency travel times is beyond the scope of this paper.Here, the dependence of the variability of the low-frequency and high-frequency travel times on range and the number of surface reflections will be explored.Range and the number of surface reflections are not fully independent, of course, because the number of possible surface reflections increases with range.Nonetheless, there are multiple rays at each range with differing numbers of surface reflections.
The variability in the low-frequency travel times is quite small (Fig. 14).It has no obvious dependence on range and is quite similar to the variability for the overall time series shown in Fig. 12 (Fig. 14).
The low-frequency variability might have been expected to increase with range as the ray paths encounter increasing numbers of eddies and the large-scale variability within the Beaufort Gyre.The lack of such dependence is rather surprising.There is perhaps a weak dependence on the number of surface reflections (Fig. 14).Travel times are most sensitive to sound-speed perturbations at the turning points of the rays, which are in the deep ocean for the ray paths considered here (Cornuelle et al., 1993).There is, nonetheless, some sensitivity to perturbations throughout the water column.One might speculate that ray paths with more surface reflections traverse the variable upper ocean more times and therefore show somewhat more variability than those with fewer surface reflections.However, the effect is not significant because of the relatively low sensitivity of the travel times to upper ocean variability.
The variability in the high-frequency travel-time series is uniformly small (roughly 1-3 ms rms) and shows no dependence on either range or the number of surface reflections.One might have expected scattering from the ice to cause the variability to increase with the number of surface reflections.However, redoing the calculation on a monthby-month basis still shows no increase in the variability of the high-frequency travel-time series with the number of surface reflections even when the ice is thickest (not shown).
The precision with which travel times can be measured is limited by (i) ambient acoustic noise, (ii) interference between unresolved arrivals, (iii) scattering from internalwave-induced sound-speed fluctuations and other smallscale sound-speed variability, (iv) errors in the corrections for the positions of the sources and receivers as the moorings move in response to ocean currents, and (v) clock error (Munk et al., 1995).Surface scattering might also be expected to limit the travel-time precision of the deepturning, surface-reflected rays discussed here when ice is present.
The SNR fundamentally limits the accuracy with which arrival times can be measured.The rms arrival-time uncertainty for a single, resolved arrival embedded in white Gaussian noise after matched filter processing is where Dx ð Þ rms ¼ 2p Df ð Þ rms is the rms bandwidth of the signal, ðDf Þ rms is in Hz, E is the energy in the received signal, N 0 is the spectral density of the ambient noise (single-sided), and 2E=N 0 is the SNR (e.g., Helstrom, 1968;Munk et al., 1995).The sources on T1, T3, T4, and T5 had LFM bandwidths of 100 Hz; the source on T2 had a lower center frequency and a narrower LFM bandwidth of 65 Hz.If the transmitted signal power were constant across the LFM bands, the rms signal bandwidths would be 28.9 and 18.8 Hz, respectively.The actual rms signal bandwidths are somewhat less because the transmitted power decreases toward the ends of the LFM bands (Table II).The average of the rms bandwidths for T1, T3, T4, and T5 is 20.4 Hz; the rms bandwidth for T2 is 12.4 Hz.The nominal rms traveltime uncertainties assuming a SNR of 20 dB (2E=N 0 ¼ 100) are then 0.8 ms and 1.3 ms, respectively.
The observed high-frequency travel-time variability is roughly 1-3 ms rms, with minimum values of about 1 ms rms, which is comparable to the theoretical travel-time precision for a 20 dB SNR (Fig. 14).The appropriate SNR to use in this calculation is uncertain, however.As is evident from the dot plots (Fig. 8), the SNR changes substantially over the year, with minimum values during the time that the ice is thickest.The appropriate SNR to use is also uncertain because the ambient noise level before the signals arrive is substantially lower than during the receptions (not shown).This is partly because the received signals have sidelobes in travel time and vertical arrival angle after pulse compression and beamforming.These sidelobes are a form of self-noise that interferes with determining travel times even for arrivals that do not overlap directly with other nearby arrivals.In addition, reverberation resulting from in-plane and out-ofplane scattering from the underside of the ice is another form of self-noise that interferes with determining travel times.Assuming a SNR of 20 dB, therefore, provides only rough guidance on the expected travel-time precision.
Errors in the measurements of the instrument locations also limit the accuracy with which travel times can be measured.The mooring motion corrections contain a small bias because the accuracies of the absolute positions of the acoustic bottom transponders are limited by the accuracy of the Global Navigation Satellite System (GNSS) ship positions during the survey of the transponder positions after deployment.The estimated accuracy of the transponder positions is approximately 3 m rms.There is, in addition, a component of mooring motion error that is uncorrelated from measurement to measurement.The acoustic longbaseline systems employed here can measure instrument positions with an accuracy of about 1 m, contributing roughly 1 ms rms to the observed high-frequency traveltime variability (e.g., Munk et al., 1995).
Clock error is not expected to contribute significantly to the high-frequency fluctuations in the travel-time measurements.The instruments used a two-oscillator system to maintain precise time (e.g., Munk et al., 1995).When combined with pre-and post-cruise clock checks, the clock error reaches a maximum value of roughly 1-2 ms in the middle of the experiment and varies smoothly over the year.
The conclusion is that the observed high-frequency travel-time variability of 1-3 ms rms is roughly consistent with the expected variability due to ambient acoustic noise and errors in the mooring motion corrections.Travel-time fluctuations due to scattering from internal-wave-induced sound-speed fluctuations and other small-scale sound-speed variability are apparently comparable to or less than the instrumental precision with which travel times can be measured, consistent with the low internal-wave energy levels in the Canada Basin.

VI. DISCUSSION
The low-frequency and high-frequency travel-time variabilities were both extraordinarily small in the Canada Basin during 2016-2017 compared with those observed in previous ocean acoustic tomography experiments (Munk et al., 1995).Even with the dramatic changes occurring in the Arctic, the Beaufort Sea still provides a highly stable acoustic environment.The ice cover is still present throughout much of the year, albeit thin and with reduced areal extent, insulating the Arctic Ocean from wind and solar forcing.The implication is that long temporal processing and near-optimal pulse compression gains should be possible.Internal-wave energy levels may well increase in the future, however, as the ice extent continues to decrease and allows additional wind forcing, decreasing the stability of the Arctic acoustic channel.
The temporal stability of the Arctic channel is only one of the factors important in designing future acoustic monitoring, positioning, and communication systems in the Arctic (Mikhalevsky et al., 2015).Subsequent papers are planned to characterize the transmission loss and ambient sound during the CANAPE experiment.

ACKNOWLEDGMENTS
The success of the CANAPE experiment is the result of the efforts of many people, including the officers and crew of the USCGC Healy and individuals at the Scripps Institution of Oceanography (S.Carey, L. Green, D. Horwitt, M. Norenberg, K. Scott), the Naval Postgraduate School (C.Miller, M. Stone), and Woods Hole Oceanographic Institution (F.Bahr, J. Dunn).This material is based upon work supported by the Office of Naval Research under Award No. N00014-15-1-2068.Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the Office of Naval Research.

APPENDIX: THE BEAUFORT GYRE
Much of the information in this appendix is derived from the Beaufort Gyre Observing System (BGOS), which was initiated in 2003 to collect measurements and analyze atmospheric, sea ice, oceanic, and geochemical parameters in the region (e.g., Proshutinsky et al., 2020), and from Ice Tethered Profilers (ITP) deployed in the region (e.g., Krishfield et al., 2008).The combination of the BGOS observations and modeling done in the Forum for Arctic Modeling and Observational Synthesis (FAMOS) project form the Beaufort Gyre Exploration Program (BGEP).BGOS mooring A is nominally located at 75 N, 150 W, roughly in the center of the Beaufort Gyre and not far from CANAPE moorings T6 and DVLA.

Ocean stratification
The surface layer structure varies depending mainly on sea ice conditions and wind forcing (Proshutinsky et al., 2020).It includes a surface mixed layer but, depending on the season, can also include a Near-Surface Temperature Maximum (NSTM) and a remnant Winter Mixed Layer (rWML).The surface mixed layer, with an average depth of 16 m in summer and 24 m in winter (Toole et al., 2010), overlies the NSTM, whose heat is derived from incoming solar radiation in the summer.The NSTM appeared in the 2000s as the ice thinned and/or disappeared.The NSTM often overlies a weakly stratified rWML remaining from the previous winter's mixed layer after seasonal restratification.
Below the surface layer are waters of largely Pacific origin that entered through the Bering Strait.The PSW is characterized by a relative temperature maximum (McLaughlin et al., 2011).Relatively fresh and warm PSW is modified within the Chukchi Sea during summer, while the more saline and colder PWW has its properties set in the Chukchi Sea during winter (Timmermans et al., 2014;Timmermans et al., 2017).The PSW showed a general freshening and warming trend in the 2000s, with the maximum potential temperature (relative to the surface) increasing to around 0 C in recent years, although with considerable spatial and interannual variability (with the maximum temperature varying by up to 1 C from year to year).The depth of the temperature maximum is in the range of 40-90 m with a mean of about 60 6 10 m.There does not appear to be significant seasonal variability in the properties of the temperature maximum.The thickness of the PSW layer also increased in the 2000s, from about 90 to 120 m, primarily because the depth of the bottom of the PSW layer has increased.The freshwater and heat contents of the PSW increased during the 2000s due to the freshening, warming, and thickening of the layer.
The PWW is characterized by a temperature minimum.The temperature and thickness of the PWW near the center of the Beaufort Gyre have been relatively stable, with the average potential temperature increasing by $0.1 C during the 2000s and the thickness remaining around 110 m (Zhong et al., 2019).The depth of the PWW has increased by $3.3 m/year during the 2000s, however (i.e., $50 m in 15 years from 2002 to 2016) and now extends from $140 m to $250 m.
Below the PWW is the AW, with an upper component of Fram Strait Branch Water (FSBW) characterized by a relative temperature maximum near 400 m depth and a colder, lower component of Barents Sea Branch Water (BSBW) found from roughly 700-2000700- -m depth (McLaughlin et al., 2011;;Dosser and Timmermans, 2018).The AW began warming in the late 1970s and is now warmer in all Arctic Ocean regions than in the 1970s (Polyakov et al., 2012).The increase in temperature has not been monotonic, however.The first decade of the 2000s was dominated by a warm anomaly in the FSBW with maximum temperatures increasing from $ 0.45 C to > 0.7 C in the Canada Basin by 2010 (McLaughlin et al., 2011;Polyakov et al., 2012;Dosser and Timmermans, 2018).
Beneath the BSBW, the deep waters consist of the deep temperature minimum layer (DTML) centered around roughly 2500-m depth and the Canada Basin Deep Water (CBDW) found below $2700 m (Dosser and Timmermans, 2018;Carmack et al., 2012).The CBDW is near-homogeneous in both temperature and salinity.The DTML and CBDW are slowly warming at about 0.004 C per decade, consistent with geothermal heating from below.

Mesoscale variability
Various eddy types have been identified in the Beaufort Sea (see, e.g., Carpenter and Timmermans, 2012;Zhao et al., 2014;Zhao et al., 2016;Zhao and Timmermans, 2015;Bebieva and Timmermans, 2016; and the references therein).Most of the eddies in the Canada Basin are in the halocline with core depths between 30 and 300 m, azimuthal velocities in the range of 0.1-0.3m/s, diameters consistent with first baroclinic deformation radius ($12 km in this region), and lifetimes of months to years.Almost all eddies are anticyclonic, and the majority have a cold core.These eddies can be divided into upper halocline eddies (salinities Շ32 and core depths $ 80 m) in the PSW and lower halocline eddies (salinities տ 32 and core depths $ 200 m) in the PWW.There are also eddies with vertically aligned double cores (anomalously cold and anomalously warm), with one core at the base of the halocline (around 200 m) and the other at the depth of the Atlantic Water (around 400 m) (Zhao and Timmermans, 2015).Below the halocline, a small number of anticyclonic eddies have been observed confined to the Atlantic Water with core depths deeper than 300 m (Bebieva and Timmermans, 2016).Finally, anticyclonic deep eddies with a core depth of $ 1200 m have been observed at BGOS mooring B (78 N, 150 W) close to the northern region of the Northwind Ridge (Carpenter and Timmermans, 2012).These deep eddies are likely not present in the region of the CANAPE array, however, which was located further to the south.

Internal waves
The internal wave energy level under the ice in the Canada Basin (as in the Arctic as a whole) is an order of magnitude or more below that at lower latitudes (e.g., Levine et al., 1987;Dosser et al., 2014;Dosser and Rainville, 2016;DiMaggio et al., 2018;Kucukosmanoglu et al., 2021).It is also spatially and temporally variable.Using data from Ice-Tethered Profilers, Dosser and Rainville (2016) found that near-inertial internal wave amplitudes in the Canada Basin decrease with increasing latitude and that there is a seasonal cycle.The internal wave field is most energetic during summer when the sea ice extent is at a minimum, and there is a second, smaller energy maximum in early winter when there are strong winter storms.They also found that the average near-inertial internal-wave amplitude has increased only slightly in recent years but the variability has increased substantially.The implication is that unusually large near-inertial internal waves are generated more frequently.

Tides
Bottom pressure measurements in the Canada Basin made as part of BGOS show that barotropic tidal amplitudes are small (Chen et al., 2009).At 75 N, 150 W (BGOS Mooring A), the semidiurnal component M 2 is the largest, with an amplitude of 4.5 cm.Tidal components S 2 , K 1 , and O 1 are smaller and have amplitudes of 2.2, 1.6, and 2.3 cm, respectively.Measured tidal currents are correspondingly small (Baumann et al., 2020).M 2 is again the largest, but tidal currents for all four constituents are less than 1 cm s À1 .

FIG. 1
FIG. 1. (Color online) Geometry of the 2016-2017 CANAPE experiment.Broadband acoustic transceivers were moored at T1-T6.A DVLA receiver was moored at DVLA.The bathymetry is from the International Bathymetric Chart of the Arctic Ocean (Jakobsson et al., 2012).
FIG. 3. (Color online) Measured (top) and predicted (bottom) acoustic time fronts on the DVLA for a transmission from mooring T3.The plots are scaled to display the transmission loss (TL).The recording was made on 23 September 2016 (year day 267) at 04:12:00 UTC.The predicted time front does not include the bottom-reflected arrivals that are evident in the measured time front at about 122.9 s.

FIG. 5
FIG. 5. (Color online) In situ temperature vs year day 2016 in the upper 600 m at the DVLA.

FIG. 6
FIG. 6. (Color online) Sea ice concentration derived from AMSR2 satellite data (Spreen et al., 2008) for the times that the ice was advancing (top) and retreating (bottom) across the CANAPE moorings.The top plots are at weekly intervals: 27 October-10 November 2016.The bottom plots are at four-day intervals: 24 July-1 August 2017.
FIG. 8. (Color online) Travel times vs year day 2016 for transmissions from T5 to T6 (top), T1 to T5 (middle), and T3 to T5 (bottom).The size of the dots is proportional to the signal-to-noise ratio, and the color indicates the vertical arrival angle at the receiver.The arrows on the right-hand axis indicate the groups of early, resolved acoustic arrivals analyzed here.Each group contains four ray paths (Fig. 9).
FIG. 9. (Color online) Histograms of the measured peak positions in travel-time-arrival-angle space for the acoustic paths shown in Fig. 8 (T5-T6, top; T1-T5, middle; and T3-T5, bottom).The predicted ray arrivals are marked in red.The green ellipses were used when tracking the arrivals from reception to reception.

FIG. 10 .
FIG.10.Predicted ray paths for the first three groups of four arrivals for the acoustic paths shown in Fig.8(T5-T6, top; T1-T5, middle; and T3-T5, bottom).Ray paths that have shallower turning depths and longer travel times are not shown.
FIG. 13. (Color online) Spectra for the three acoustic paths for which dot plots are shown in Fig. 8 (T5-T6, T1-T5, and T3-T5).The variance of each harmonic component is plotted as a function of frequency.The ray IDs for the tracked travel-time series are color coded.

FIG. 14 .
FIG. 14.Standard deviations of the travel-times vs range (left) and the number of surface reflections (right) for the low-frequency (top) and high-frequency (bottom) travel-time series.

TABLE I .
Mooring motion reference locations, median source depths, and water depths.Water depths are true depths determined from acoustic surveys of the acoustic release locations, which were 3.25 m above the seafloor.

TABLE II .
Moored acoustic source characteristics and transmission times.Transmission times are in minutes after the hour.

TABLE IV .
Parameters of the replica signals used to process the receptions.