The dynamics of the wind-generated near-inertial internal wave field in the Canada Basin of the Arctic Ocean are investigated using the drifting Ice-Tethered Profiler dataset for the years 2005 to 2014, during a decade when sea ice extent and thickness decreased dramatically. This time series, with nearly 10 years of measurements and broad spatial coverage, is used to quantify a seasonal cycle and interannual trend for internal waves in the Arctic, using estimates of the amplitude of near-inertial waves derived from isopycnal displacements. The internal wave field is found to be most energetic in summer when sea ice is at a minimum, with a second maximum in early winter during the period of maximum wind speed. Amplitude distributions for the near-inertial waves are quantifiably different during summer and winter, due primarily to seasonal changes in sea ice properties that affect how the ice responds to the wind, which can be expressed through the “wind factor”—the ratio of sea ice drift speed to wind speed. A small positive interannual trend in near-inertial wave energy is linked to pronounced sea ice decline during the last decade. Overall variability in the internal wave field increases significantly over the second half of the record, with an increased probability of larger-than-average waves in both summer and winter. This change is linked to an overall increase in variability in the wind factor and sea ice drift speeds, and reflects a shift in year-round sea ice characteristics in the Arctic, with potential implications for dissipation and mixing associated with internal waves.
The standard picture of Arctic internal waves derives from observations made during the 1980s and 1990s [e.g., the Arctic Internal Waves Experiment (AIWEX) in spring of 1985 (Levine et al. 1987; D’Asaro and Morehead 1991; Merrifield and Pinkel 1996) and the Surface Heat Budget of the Arctic Experiment (SHEBA) in 1997 to 1998 (Pinkel 2005)], which found a quiescent Arctic Ocean with an internal wave field energy level an order of magnitude or more below that at lower latitudes (Levine et al. 1985, 1987).
Low internal wave energy levels in the Arctic are attributed to the presence of sea ice, which causes dissipation of internal waves in the under-ice surface boundary layer, limiting energy propagation across the Arctic (Morison et al. 1985; Pinkel 2005; Fer 2014). It has been suggested that sea ice impedes momentum transfer from the wind to the water column (Plueddemann et al. 1998), with ice deformation being of more importance to internal wave generation (Halle and Pinkel 2003).
At lower latitudes, internal waves carrying wind energy through the water column are associated with significant diapycnal mixing, resulting in water mass modification and redistribution of ocean properties (Munk and Wunsch 1998). The impact of rapid Arctic sea ice decline and changing sea ice properties on internal wave generation, propagation, and energy is largely unknown. This paper presents long-term estimates of the internal wave climate in the Canada Basin, and seeks to address the question of changes in internal wave energy in the Arctic by quantifying the relationship between sea ice properties and the amplitude of near-inertial internal waves, both spatially and temporally.
a. Near-inertial waves in the Arctic
Most of the energy in the internal wave field is contained in the near-inertial frequency band, from roughly f–1.1f, where f is the local Coriolis or inertial frequency (Garrett and Munk 1972; Garrett 2001). In the Arctic Ocean, observations of the internal wave spectrum show the expected peak at the inertial frequency (Halle and Pinkel 2003; Fer 2014; Cole et al. 2014). Near-inertial internal waves can be generated whenever wind stress resonantly forces the air–ice or air–water interface at or near the inertial frequency. In the Northern Hemisphere, anticyclonic or clockwise inertial oscillations are set up in the sea ice and mixed layer. These purely horizontal oscillations create disturbances at the base of the mixed layer, generating a freely propagating near-inertial wave in the stratified water column below (D’Asaro 1985). The result is vertical propagation of energy through the water column to depths at which the internal waves can become unstable and break (Gregg et al. 1986; Hebert and Moum 1994).
Near-inertial internal waves can also be generated as a result of the motion of drifting sea ice. The rough bottom of the ice impulsively forces the water column, or there may be horizontal variations in bottom roughness that cause vertical motion of the fluid below. This results in a pattern of forcing related to ice roughness and ice–ocean drag that is moving at the velocity of the sea ice, which can generate internal waves (McPhee and Kantha 1989) with horizontal and spatial scales consistent with observations of near-inertial waves in the Arctic Ocean (D’Asaro and Morehead 1991).
In the presence of sea ice, the transfer of momentum from the wind to internal waves is also sensitive to variations in the air–ice drag coefficient. The drag coefficient for thick, rigid multiyear ice, rafted into peaks and ridges and possibly covered in deep snow, is very different from that for thin, patchy first-year ice, with large melt ponds and surrounded by areas of open water. Yet the ice concentration as measured by satellite can be the same for both. Martin et al. (2014) found that modeled momentum transfer to low-frequency currents was at a maximum for ~80% ice concentration, since sea ice provides a rougher surface than open water. Andreas et al. (2010) considered changes in sea ice form drag associated with leads and melt ponds in the marginal ice zone and found maximum momentum transfer for ~50% ice cover. These studies were not considering ice motion at the inertial frequency or the generation of internal waves by sea ice. Nevertheless, energy in the internal wave field is expected to be closely linked to sea ice characteristics that affect the drift speeds or deformation of the ice.
In most of the world’s oceans, internal waves at tidal frequencies are a dominant contributor to the oceanic variance (Garrett and Kunze 2007). These “internal tides” are generated when the barotropic tide sloshes back and forth over topographic features such as the Northwind Ridge or the Yermak Plateau, launching upward propagating internal wave beams at the tidal frequency. In the Arctic Ocean, the M2 and S2 tidal frequencies fall within the near-inertial frequency band. However, because the majority of the Arctic Ocean lies north of the critical latitude for the dominant semidiurnal lunar M2 tide (74.5°N), topographically generated internal tides are evanescent and must dissipate locally (Simmons et al. 2004). Localized topographic mixing associated with the internal tides may therefore be important (D’Asaro and Morison 1992; Plueddemann 1992; Fer et al. 2010; Lenn et al. 2011; Rippeth et al. 2015), but a significant internal tide within the central Canada Basin, away from the basin boundaries, is not expected.
b. Changes in the Arctic
In recent decades, the Arctic Ocean has undergone rapid changes. Sea ice decline has accelerated over the last decade, with significant decreases in summer sea ice extent (Serreze et al. 2007; Stroeve et al. 2012) and thickness (Rothrock et al. 2008; Lindsay and Schweiger 2015), and less multiyear ice overall (Comiso 2002). Winter storms may be increasing in frequency and intensity (Serreze et al. 1997; McCabe et al. 2001; Zhang et al. 2004) with an associated increase in sea ice drift speeds (Hakkinen et al. 2008).
Sea ice speed varies roughly linearly with wind speed, and is influenced by internal ice stress and air–ice and ice–ocean drag, which are in turn related to the concentration, thickness, and deformation of the ice cover (Hakkinen et al. 2008). Spreen et al. (2011) and Rampal et al. (2009) both reported increased sea ice drift speeds in recent decades, as well as a sharp increase in ice deformation rate (Rampal et al. 2009). The magnitude of inertial oscillations in the sea ice has also increased during the last 30 years (Gimbert et al. 2012b), due to the changing characteristics of the sea ice (Gimbert et al. 2012a). It has been suggested that these changes could cause an increase in the energy of the Arctic internal wave field, particularly during the summer months, but this has not been readily apparent (Gimbert et al. 2012a; Rainville et al. 2011).
Previous measurements of the internal wave field in the Arctic Ocean have shown indications of a seasonal cycle related to sea ice cover (Plueddemann et al. 1998; Halle and Pinkel 2003; Rainville and Woodgate 2009). Martini et al. (2014) observed a seasonal cycle in near-inertial wave energy using a mooring array on the Beaufort continental slope, and found a peak in internal wave energy during ice formation in the fall, corresponding to <90% ice concentration. Cole et al. (2014) found elevated near-inertial wave energy in the Canada Basin in the fall and early winter of 2009 relative to that in late winter. Dosser et al. (2014) found indications of a seasonal cycle in near-inertial vertical displacement wave amplitude, with larger waves during periods of <100% sea ice concentration. However, comparisons of historic data with recent expendable current profiler (XCP) and CTD measurements by Guthrie et al. (2013) found no trend in internal wave energy in the Beaufort Sea over the last 30 years, which they attribute to an increase in the strength of the near-surface stratification.
c. Estimating the internal wave field in the western Arctic
This paper presents a unique year-round, multiyear record of internal waves in the Arctic Ocean, with spatial coverage over much of the Canada Basin. Observations of Arctic internal waves have typically been spatially and temporally limited, due to the difficulty of making wintertime measurements and the battery power required to obtain the necessary time resolution from a mooring or profiler. Ice-Tethered Profiler (ITP) data provides a nearly decade-long record, from 2005 to 2014, with year-round measurements from just below the mixed layer to ~750-m depth. Spatially, the ITPs provide coverage over much of the study region: the Beaufort Gyre region of the Canada Basin, from roughly 72° to 82°N and from roughly 130° to 160°W (Fig. 1).
The paper is organized as follows: In section 2, the data products used are described. The methods used to calculate the near-inertial wave field are explained in section 3. A clear spatial trend in near-inertial wave amplitude with latitude is investigated in section 4a. Seasonal variations in the wave field are quantified and compared to changes in the wind factor, which relates to wind speed and ice speed, in section 4b, and increasing interannual trends in near-inertial wave energy and variability are shown to correspond to trends in sea ice properties in section 4c. In section 5, air–ice–ocean dynamics pertaining to wave generation are discussed and connected to the observed seasonal and interannual variations.
a. Ice-Tethered Profiler
The data used herein were collected by 27 ITPs that drifted in the Beaufort Gyre region of the Canada Basin between fall 2005 and fall 2014 (see the appendix), completing a total of just over 30 000 density profiles. This represents a subset of the total ITP dataset, but includes the majority of profiles in the Canada Basin. ITPs that stopped profiling after a month or two were excluded to minimize a seasonal bias in number of measurements, as were those with drift tracks outside of the chosen study region.
ITPs are anchored in a perennial ice floe by a surface buoy, and report temperature and conductivity at 1 Hz, corresponding to roughly every 0.25 m in the vertical, from ~7 m below the surface to ~750-m depth. The data are transmitted by an inductive link to a surface unit, where they are relayed to shore by the Iridium satellite system (Krishfield et al. 2008). Typically ITPs sample the water column twice per day, with one-way vertical profiles beginning at 0000 and 0600 UTC. Other sampling schedules used in this analysis include three or at most four profiles per day (see the appendix). The profiling instrument moves vertically at ~0.25 m s−1, so that a 750-m profile takes about 1 h to complete. Each surface unit also reports hourly GPS position data.
Raw temperature, conductivity, and pressure profiles from all 27 ITPs are processed following similar techniques to those used by the ITP group at the Woods Hole Oceanographic Institution (www.whoi.edu/itp; Krishfield et al. 2006). Processing steps include identification and removal of unphysical data, corrections for the sensor response behavior (including thermistor lag, temperature and conductivity sensor physical separation, and conductivity thermal mass). As noted in Krishfield et al. (2006), a pressure correction is needed because of geometry, and because the CTD sensors are in the wake of the instrument during down profiling. However, here that correction is chosen to be a pressure offset that can only vary linearly with time (calculated over the length of each deployment, to allow for sensor drift). In contrast to the WHOI processing, the correction used here is independent of drift speed, as no solid correlation between ice speed and pressure offset was found for the entire ITP dataset. The processing also ensures that the time-mean density profiles from all up and down profiles match. The spatial and temporal patterns and conclusions discussed herein are not changed if the WHOI correction (empirically relating pressure offset to ice drift speed) is applied instead.
b. Wind velocity
Wind velocity was obtained from ERA-Interim 10-m winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (Dee et al. 2011), which is calculated on a 0.75° × 0.75° grid. Comparisons (not shown) with 10-m winds from the National Centers for Environmental Prediction (NCEP) reanalysis project (Kalnay et al. 1996; Kanamitsu et al. 2002), calculated on a 2.5° × 2.5° grid, did not significantly alter the results presented herein. The wind velocity data currently available from reanalysis products are gridded every 6 h, and so cannot resolve the inertial frequency band partially responsible for wave generation (Alford 2003; Martini et al. 2014).
c. Sea ice concentration
SSM/I satellite passive microwave data (Cavalieri et al. 1996) provide 25 km × 25 km gridded sea ice concentration. Sea ice concentration in a 125 km × 125 km box around the ITP was selected for the analysis herein, as 125 km is of the same order as the horizontal resolution of the wind velocity data, is a reasonable horizontal scale for wind forcing by storms, and is comparable to the expected horizontal extent of the internal waves themselves (a typical horizontal wavelength for a near-inertial wave with vertical wavelength between 10 and 100 m would be roughly 5–50 km). Average sea ice concentration is generally not very sensitive to the choice of box size, from 25 km up to values of several hundred kilometers. The average values of sea ice concentration reported herein are not necessarily representative of the overall Canada Basin average as ITPs do not sample uniformly; regions of open water, for example, are very rarely sampled.
d. Sea ice velocity
The motion of the ITP surface unit provides the velocity of the ice floe in which the instrument is anchored. Each ITP track is determined from hourly GPS measurements, and frequently shows the ITP moving in inertial circles and/or traveling rapidly in a given direction. Sea ice velocity is separated into subinertial (<0.9f, herein referred to as “ice drift speed” or “subinertial ice drift speed”) and near-inertial (0.9f–1.1f) bands, with the near-inertial band further separated into the clockwise (CW) and counterclockwise (CCW) components of motion using rotary spectral analysis. The inertial CW component of sea ice velocity dominates over CCW for most time periods.
e. Barotropic tide
The Arctic Ocean Dynamics-based Tide Model (AODTM-5) barotropic forward tide model for the Arctic Ocean (Padman and Erofeeva 2004) is used to determine the tidal current velocity associated with the semidiurnal tidal components (M2, S2, N2, K2) in the Canada Basin. The model provides values on a 5-km regular grid based on solving the shallow water equations following Egbert and Erofeeva (2002). Tidal current speeds are determined along each ITP track for the full semidiurnal tidal signal, and for specific components of interest.
The typical ITP sampling scheme poorly resolves isopycnal displacements associated with near-inertial waves. Each day, a pair of profiles separated by ~6 h is collected, an interval chosen to minimize “potential biases” associated with inertial waves in daily averages. The near-inertial signal can be extracted from the data by taking advantage of the coherence of near-inertial waves over a few days, and the fact that the inertial period is not exactly 12 h. Dosser et al. (2014) describes how complex demodulation can be used to estimate the vertical displacement amplitude of near-inertial internal waves from ITP data. This procedure is briefly summarized here.
Instantaneous depths for isopycnals initially separated by ~25 cm in the vertical are determined for each ITP, and a daily mean is subtracted to retain higher-frequency vertical isopycnal displacements. A sinusoid with a specified frequency (chosen to be ω = 1.05f) is least squares fit to 4-day segments of vertical displacement data. Sliding the sinusoid in 1-day increments provides daily vertical displacement amplitude estimates Aη, which vary on a time scale of 4 days. To reduce the effect of instrument noise, data points from five adjacent isopycnals above and below each fit (spanning ~3–9 m in the vertical) are combined to provide 10 times as many data points. This procedure assumes a typical wave is coherent over roughly eight inertial periods and about 5 m in the vertical.
In the analysis described herein, near-inertial wave amplitude estimates have been restricted to the upper water column, from just below the near-surface mixed layer, between ~10- and ~50-m depth (Toole et al. 2010), to the top of the Atlantic Water layer at roughly 200-m depth (Fig. 2). This near-surface depth range is most relevant to an investigation of the interactions between wind, sea ice, and ocean dynamics. The deepest density level included in the analysis corresponds to the 1027.1 kg m−3 isopycnal, chosen since it is consistently above the Atlantic Water layer.
The significance of each amplitude estimate is characterized by the R2 value of the least squares fit; amplitudes from fits explaining 25% or less of the variance in the data are excluded. Uncertainty in the remaining estimates (95% confidence interval) is determined from ensemble Monte Carlo simulations, which account for instrument noise and uncertainty in isopycnal depth, aliasing of high-frequency motions associated with the internal wave continuum, and the effect of specifying a particular frequency for the fit. The wave frequency ω = 1.05f explains the most variance in the measured isopycnal displacements. However, the results are fairly insensitive to this choice, with a reduction in variance explained of 5% or less for ω in the range 0.9f–1.1f. The energy in a near-inertial wave is proportional to the vertical displacement amplitude squared, but highly dependent on intrinsic wave frequency. While an increase in the average wave amplitude indicates an increase in the overall energy of the wave field, values of energy cannot be precisely quantified using ITP data since exact wave frequencies cannot be determined.
The total uncertainty in a given amplitude estimate Aη is the sum of a relative uncertainty of ±25%–40% Aη, which varies with latitude because of the changing Coriolis frequency, and an absolute uncertainty of between ±0.5 and 1.5 m, with 95% of amplitudes accurate to within ±1 m or better. The majority of wave amplitude estimates are statistically significant and explain on average 60% of the variance in the data points. Amplitude estimates for a given time are not independent over the depth range considered, and are also dependent over the 4-day segment used for the fit. Accounting for this, the total number of amplitude estimates included in (for example) a monthly average (Fig. 3a) results in negligible total uncertainty.
The distribution of calculated wave amplitudes over the upper water column is nonnormal, with a long tail, as expected for internal waves (Fig. 3c). Since the distribution is not Gaussian, the mean and the median differ, with the mean being skewed high. The median of the distribution is used for the analysis herein for any calculation of “depth average” or “time average” to characterize a “typical” wave amplitude. As a result, most average values reported will be slightly lower than if the mean were used. The key findings of this paper hold regardless of whether the median or mean is used.
To provide an uncertainty estimate for a calculated median wave amplitude, bootstrapping is used (Efron and Tibshirani 1994). This method provides an estimate of the standard error of the median for a nonnormal distribution, and is typically very small [O(10−3) m] for the near-inertial wave field due to the well-sampled wave amplitude distribution. When the standard deviation is reported below, it serves as a measure of the variability in the wave field about the average value, equal to the square root of the variance. The standard deviation is often large (0.7 m in Fig. 3c), owing to the high variability in wave amplitude on a range of temporal and spatial scales and to the long tail of the amplitude distribution.
The complex demodulation technique applied to the ITP dataset allows for an unprecedented assessment of the near-inertial wave field in the Arctic Ocean, spanning nearly 10 years and all seasons (Fig. 3a). As a result of the drift of the sea ice in which the ITPs are anchored, measurements of the near-inertial internal wave field capture variations in both time and space. During the time period analyzed, the ITPs transited a significant fraction of the Beaufort Gyre (Fig. 1). If the entire data record is viewed as a spatial map (Fig. 3b), bearing in mind that every measurement corresponds to a different time, sometimes separated by years, then spatial patterns in the near-inertial wave field can be investigated across a large fraction of the Canada Basin. If the entire data record is treated as a time series, both seasonal and interannual variations in the wave field can be quantified and compared to changes in wind forcing and sea ice characteristics, providing insight into internal wave evolution in the Arctic over the last decade. With over 106 individual estimates of near-inertial wave vertical displacement, the resulting distribution of wave amplitudes (Fig. 3c) provides a robust statistical basis for analysis.
a. Spatial pattern
The dominant spatial pattern in the depth-averaged near-inertial wave field is a decrease in wave amplitude with increasing latitude (Fig. 3b), with larger waves near the south of the Beaufort Gyre. To ensure that this pattern is not a result of the stratification in the region, which varies spatially, seasonally, and with depth, the amplitude estimates need to be normalized by a function of the stratification (following the so-called Wentzel–Kramers–Brillouin approximation; e.g., Pedlosky 2003). Stronger stratification suppresses isopycnal displacement and results in waves of smaller vertical displacement amplitude, Aη. To account for the effect of variations in stratification on the measured near-inertial wave field, a scaled wave amplitude, As, is calculated: , where N(z) is the buoyancy frequency at each depth of each ITP profile and No is a constant reference buoyancy frequency, calculated as the dataset average. The scaled wave amplitude is used for all analysis hereinafter.
The scaled wave amplitude displays a roughly linear decreasing trend with latitude (Fig. 4), with only a slight increase below the critical latitude of the M2 semidiurnal tide (74.5°N). The standard deviation of the wave amplitude estimates also decreases with latitude. Assuming a linear trend, average wave amplitude decreases from 1.85 to 0.75 m between 72° and 82°N, a change of 12% per degree latitude (relative to the average wave amplitude). The rms subdaily (high frequency) vertical displacements of isopycnals in the water column also show a latitudinal trend (Fig. 4), confirming that this spatial pattern is not an artifact of the complex demodulation technique described in section 3.
Guthrie et al. (2013) hypothesized that the relatively weak internal wave signal in the Canada Basin was a result of the strength of the near-surface stratification. The scaled wave amplitude accounts for variations in the buoyancy frequency with depth and with latitude across the basin (Fig. 5a). Note, however, that this scaling cannot account for the potential interactions between stratification features and the generation or propagation of individual internal waves. For example, inertial wind energy may result in mixed-layer deepening as opposed to near-inertial wave generation, or internal waves may reflect from double-diffusive layers in the Atlantic Water. While interesting, such impacts are outside the scope of the current work.
The observed isopycnal displacements could also be associated with a semidiurnal internal tide. Freely propagating internal tides are possible south of the critical latitude for the M2 tide (74.5°N), and across the whole basin for the weaker S2 tide. Some large wave amplitudes are observed south of 74.5°N (Fig. 3b). This area has a potential spatial/temporal bias caused by many ITP profiles taken near the shelf in the southwest corner of the basin during the summer of 2013 (Fig. 1; appendix). Data very close to the shelf typically have more gaps and incomplete profiles due to the ITPs’ rapid transit along the shelf, making it impossible to determine if the wave field has a spring–neap cycle. A trapped (evanescent) internal tide could cause elevated displacements near the Northwind Ridge and the Canadian Arctic Archipelago, where tidal current speeds are high. The central Canada Basin is smooth and far from rough topography, with small barotropic tidal currents (Fig. 5b). In fact, the semidiurnal barotropic tidal current strength increases with latitude, which would result in larger internal tides to the north. Thus tidal forcing cannot explain the latitudinal trend in internal wave amplitude in the central basin.
Internal waves generated at the inertial frequency are restricted to propagate equatorward, suggesting a possible accumulation of wave energy in the southern basin. However, the “one-bounce” hypothesis of Pinkel (2005) predicts significant if not total wave dissipation in the under-ice boundary layer following a single reflection from the sea floor. If a significant fraction of near-inertial wave energy in the Canada Basin were to survive a single bounce, the wave field in the southern basin would contain a combination of locally and remotely generated waves—with frequencies above the local inertial frequency. Further investigation would require determining if the peak in the internal wave spectrum around the local inertial frequency f is broader to the south in the Arctic, which is not possible using ITP data.
Comparison with the spatial distribution of wind speed, sea ice concentration, and CW inertial and subinertial sea ice drift speed shows no comparable latitudinal trend (Figs. 5c–f) that can fully explain the trend in wave amplitude. However, both wind and sea ice show variations with latitude that could potentially result in more energetic internal waves to the south. Slightly higher measured average wind forcing to the south, combined with increased open water, explains the more rapid ice drift and prevalence of inertial motions in the ice. These in turn could result in the generation of more energetic near-inertial waves, as could direct wind forcing on the open ocean. Changes in wind and ice concentration are only 1% per degree latitude toward the south, compared to the 18% increase per degree latitude for wave amplitude. Sea ice CW inertial and subinertial drift speed increase by 7% and 5% per degree respectively, and so partially explain the variation with latitude in the near-inertial wave field. Other possible contributions to the spatial pattern in the wave field include the presence of older, thicker, more rigid sea ice to the north and east of the Canada Basin, and potential wave interactions with the eddy field. Further study is needed to determine the exact combination of causes.
The primary goal of this study is to examine the relationship between local sea ice conditions and wind forcing and the near-inertial internal wave field. To better understand the relationship between the wind, the sea ice, and the internal waves, it is necessary to examine temporal as well as spatial variations. The presence of the large-scale spatial pattern acts to bias temporal measurements. To ensure that temporal variability is biased as minimally as possible by the decrease in wave amplitude with latitude, a linear fit to the latitudinal trend (Fig. 4) is removed from the wave amplitude estimates. The results presented in the following Sections do not change significantly if this adjustment is not made. However temporal correlations are slightly higher when the large-scale north–south spatial pattern has been accounted for.
b. Temporal variations: Seasonal
The dynamics of the near-inertial wave field are influenced seasonally by both sea ice properties and wind forcing. Unlike ice concentration and CW inertial ice speed, which are dominated by an obvious seasonal cycle, the seasonal cycle in the near-inertial wave field is small, and not immediately apparent (Fig. 6). The near-inertial wave field is highly variable on both short (days to weeks) and long (seasonal to interannual) time scales, as are the wind and sea ice drift speed.
Based on monthly average vertical displacement amplitude for all years from 2005 to 2014, the seasonal cycle in the near-inertial wave field is quantified (Fig. 7a). The magnitude of the seasonal cycle in the near-inertial wave field is on the order of ¼ the average wave amplitude, at 0.25 m. The ITPs may be underestimating the magnitude of the seasonal cycle, due to their infrequent sampling of open water and low-ice conditions.
While the uncertainty in the calculated monthly averages for wave amplitude is nearly negligible, the interannual variability in the seasonal cycle for near-inertial waves is high, as indicated by the standard deviation (Fig. 7a). To determine the statistical significance of seasonal differences, the median amplitude of waves during summer (June–November) is compared to that during winter (December–May) and found to be 16% higher, indicating larger, more energetic waves overall during the summer (Fig. 7b). While the summer and winter distributions of wave amplitude estimates have notably different medians, their variances are similar.
1) Near-inertial waves and sea ice
The seasonal cycle in the near-inertial internal wave field (Fig. 7a) has a maximum during the summer sea ice melt period (1 August–1 October) when ice concentration (Fig. 8b) and thickness are at their lowest, and a minimum in early spring when sea ice is at its thickest and most rigid (1 March–1 May). Wave amplitudes decrease through the fall during ice formation, then increase slightly in early winter (1 December–1 February), during a period of near-total sea ice cover, when wind speeds are rising and strong winter storms occur frequently (Fig. 8a).
Seasonal variations in the near-inertial internal wave field do not match those in CW inertial ice speed. However, the seasonal cycle for CW inertial ice speed (Fig. 8d) has a sharp peak in summer matching the decrease in ice concentration during melt (Fig. 8b), when near-inertial wave amplitudes are largest. Gimbert et al. (2012b) observed a small secondary peak in CW inertial oscillations in sea ice drifter motion during the winter months, similar to that in the near-inertial wave seasonal cycle, which is not seen in CW inertial ice speed from ITPs. The ITPs may be underestimating CW inertial oscillations in the ice, and their impact on the near-inertial wave field (particularly in summer), as the instruments are typically deployed in large, thick ice floes that are less likely to regularly enter a state of rapid free drift.
The seasonal cycle for the subinertial ice drift speed (Fig. 8c) agrees fairly well with that for the near-inertial waves. Subinertial ice drift speed does not have a second peak in early winter, and increases more gradually than near-inertial wave amplitude through the summer. The near-inertial wave field is more energetic during early summer than during late fall, despite similar values of monthly subinertial ice drift speed for the two periods. The seasonal cycle in subinertial ice drift speed does not match that in wind speed, although wind forcing is the primary driver of sea ice motion and is highly correlated with ice drift speed on daily time scales (Hakkinen et al. 2008). In late winter, for example, increased internal ice stress prevents high monthly ice drift speed, despite strong wind forcing.
Comparing seasonal variations in wind to those of the near-inertial waves shows relatively low wind speeds in summer when the wave field is most energetic and the highest wind speeds in winter when the wave field is at a minimum (Figs. 7a and 8a). This is in contrast to the seasonal cycle for near-inertial waves at lower latitudes, which matches that of the wind forcing, emphasizing the impact of sea ice on the near-inertial wave field.
2) Near-inertial waves and wind factor
The amplitude of the near-inertial waves should be strongly affected by the ease of momentum transfer from the wind through the sea ice to the stratified ocean below. Many properties of the ice that impact momentum transfer are not available for this analysis, but their effect on ice motion is simplistically represented by the “wind factor,” the ratio of the ice drift speed to the wind speed. Martini et al. (2014) found that the wind factor had some agreement with the near-inertial internal wave field near the continental slope of the southern Canada Basin on weekly time scales.
The wind factor is calculated as
assuming ocean current speeds are low relative to sea ice drift speed (Wadhams 2000). For consistency with the available four-times-daily reanalysis data for wind speed, subinertial ice drift speed is used. This excludes the inertial component of wind forcing and sea ice motion from the calculated wind factor values. If the ice is in free drift, the wind factor can be related to the ratio of the air–ice to ice–ocean drag coefficients. If the ice is not in free drift, internal ice stresses will affect the ice speed, which in turn modifies the wind factor.
A high wind factor indicates that the wind can move the ice easily. This may be because the ice–ocean drag is low, because the ice surface is rough, so that the air–ice drag is high, or because internal ice stresses are weak. Ice cover that is patchy and in free drift will increase the air–ice drag due to increased form drag. On the other hand, a low wind factor indicates sea ice resistance to wind-driven motion. For example, the surface of the ice may be smooth, so that air–ice drag is low; the bottom of the ice may be rough, so that ice–ocean drag dominates; or internal ice stresses may limit the ice response to the wind forcing.
Comparing seasonal variations in the wind factor with those in the near-inertial internal wave field shows very good agreement (Fig. 9). During summer, even relatively weak wind forcing can easily accelerate the ice, leading to a peak in ice speed and thus in wind factor. The strength of the ice response decreases to a minimum in March, matching the minimum in the near-inertial wave field. The wind factor plateaus in early winter but does not show a second peak like that in the near-inertial wave field. During this time period, wind forcing is increasing but the sea ice response decreases. This is caused by variations in air–ice and ice–ocean drag, and/or by changes in the rigidity and internal stresses of the ice pack. The close agreement between the near-inertial wave field and the wind factor implies that seasonal variations in the energy of the Arctic internal wave field are caused by sea ice properties that determine how readily the ice responds to wind forcing.
c. Temporal variations: Interannual
Interannual variability in the monthly-average vertical displacement amplitude of the near-inertial internal waves (Fig. 10) is significantly correlated with the wind factor (r = 0.6). Neither the wind speed nor sea ice concentration alone can explain the variations in near-inertial wave amplitude on these time scales. Note that the peak in near-inertial wave amplitude during the summer of 2013 may be partially caused by a spatial bias due to an unusually high number of ITPs drifting near the continental slope in the southwest corner of the basin, south of the critical latitude for the M2 tide. The high correlation with the wind factor should not be construed as an indication of a linear relationship between wind factor and wave amplitude, but rather as an indication that seasonally varying sea ice properties (that impact ice speed) affect the average energy of the wind-generated near-inertial wave field.
Compared to pre-2008 values, the median near-inertial wave amplitude (Fig. 11) is slightly higher for the periods 2008–11 and 2012–14, increasing by 5% overall. The variance in the distribution of near-inertial wave amplitude estimates doubles between the early part of the record (pre-2007 sea ice minimum) and the later part of the record (post-2012 sea ice minimum). This increase in variance in later years indicates an overall broadening in the distribution of wave amplitudes, with a higher probability of larger-than-average waves. Results are significant at the 95% confidence level based on a Kolmogorov–Smirnov significance test for the difference between distributions.
Interannual trends in near-inertial internal wave vertical displacement amplitude are small but significant, increasing during both the summer (Fig. 12a) and the winter (Fig. 12b) seasons, with 1.0% per year and 2.5% per year increases respectively (Table 1). The trend in winter is influenced by unusually large waves associated with the 2012 sea ice minimum. In fact, the highest average wave amplitude for both summer and winter occurs during 2012. The variance of the wave field (Table 1) increases dramatically by 11% per year (based on a linear trend) for wave amplitude estimates during summer (Fig. 12c) and by 15% per year for winter (Fig. 12d).
Sea ice concentration (Table 1) declines during the summer at a rate of −1.4% per year, consistent with previous observations of total Arctic sea ice extent (Comiso et al. 2008), with a 17% per year rise in variance associated with the increased frequency of low ice concentrations. Although wind speed only marginally increases over the course of the record and does not show any significant increase in variance along the ITP tracks, both CW inertial and subinertial ice speed have positive interannual trends in magnitude and variance (Table 1), with a 26% per year increase in the variance of CW inertial ice speed during the winter months. The percent increases per year in wind and ice drift speed are comparable to Arctic-wide trends from Spreen et al. (2011) for the period 2004–09.
These results follow the trajectories of the ITPs, and do not provide overall Canada Basin averages. Despite the purposeful deployment of ITPs in large ice floes, the overall change in observed sea ice characteristics during the last decade as the Canada Basin transitioned from a thicker, multiyear ice pack to relatively younger, thinner ice cover is still apparent. Accompanying a slight increase in the overall energy of the near-inertial wave field, evidence suggests that the evolving sea ice is driving an increase in the frequency of unusually energetic near-inertial waves. The episodic generation of these large-amplitude waves would cause intermittent spikes in the energy of the wave field.
5. Discussion: Dynamics of the near-inertial wave field
Key results for the near-inertial internal wave field include 1) the presence of a latitudinal trend in wave amplitude, with larger waves in the south of the Canada Basin; 2) a seasonal cycle in wave amplitude, with monthly variations closely matching those in wind factor, and summer sea ice conditions associated with more ice motion and a more energetic wave field; 3) a slight interannual trend in wave amplitude linked to decreased sea ice concentration and increased ice speeds; and 4) a large interannual trend in variance suggesting that the generation of highly energetic near-inertial internal waves is on the rise, linked to increased variability in the ice cover.
a. Near-inertial wave generation and ice properties
The agreement between the average amplitude of the near-inertial waves and the wind factor on a seasonal time scale (Figs. 9 and 10) is closely tied to variations in subinertial ice drift speed (Fig. 8c), with the wind factor (ratio of ice speed to wind speed) acting as a proxy for sea ice properties, such as ice thickness, age, roughness, internal stress, and amount of open water or ice in free drift, that change the relative response of the sea ice to wind forcing.
Interpretation of the agreement between near-inertial wave amplitude, wind factor, and changes in ice properties on seasonal to interannual time scales must necessarily consider how wind-forced sea ice results in wave generation. The seasonal increase in near-inertial wave amplitude for waves generated during the summer months (Fig. 7) is likely driven primarily by two factors. First, summer sea ice is thin and patchy, providing maximum area for direct contact between the wind and the ocean’s surface (Fig. 8b). Second, sea ice is in free drift during summer, which can increase wave generation through resonant inertial responses in the sea ice to wind forcing, with the resulting clockwise oscillations in ice motion (Fig. 8d) translating into inertial oscillations in the mixed layer and water column below.
Outside of the summer months, when the sea ice is a coherent pack with ~100% concentration (Fig. 8b) and low CW inertial ice speeds (Fig. 8d), an alternate mechanism for wave generation largely explains the variations in the near-inertial wave field. Subinertial ice motion (Fig. 8c) can generate near-inertial waves when horizontal gradients in ice drift speed or bottom roughness induce a vertical velocity perturbation of the stratified water column at the resonant inertial frequency (McPhee and Kantha 1989), referred to as “inertial pumping.” The minimum in subinertial ice drift speed occurs in March, when near-inertial wave energy is lowest, presumably because the ice is at its thickest and most rigid, with high internal stress limiting ice motion and deformation.
In terms of interannual variations, the wind factor has somewhat larger interannual trends than the near-inertial wave field (Table 1) during both summer and winter, but comparable increases in variance. This reflects increased variance in sea ice speed during both summer and winter (Table 1) and increased variability in sea ice properties (including ice concentration, and potentially air–ice drag, ice–ocean drag, and internal ice stresses), caused in part by large amounts of multiyear ice melting out of the Canada Basin during this decade.
During summer, increases in the median and variance of the distribution of near-inertial wave amplitudes (Table 1, Figs. 12a,c) are related to increasing and more variable sea ice speed and higher likelihood of open water in the vicinity of the ITPs (Table 1). In winter, the interannual increase in variance in the wave field (Table 1, Fig. 12d) is largely driven by changes occurring around the time of the second peak in the seasonal cycle (Fig. 7a), and may be related to the timing of sea ice freeze-up. The increasing trend in median wave amplitude is comparable with increases in clockwise inertial and subinertial ice drift speed (Table 1). The increasingly variable sea ice cover in later years could also be reducing near-inertial wave dissipation in the under-ice boundary layer, so that larger than average waves are able to exist longer prior to dissipating.
Exactly how individual sea ice properties affect near-inertial wave generation remains an open question that cannot be addressed by the ITP dataset at present. Internal wave generation is not directly captured by the ITPs, and the uncertainty in individual wave amplitude estimates can be up to ±1 m, as discussed in section 3. A complete understanding would require detailed information on not only local sea ice characteristics, but also inertial current speeds in the mixed layer, on both daily to weekly and seasonal time scales.
b. Case study—ITP 41
To qualitatively connect the statistical results for seasonal and interannual changes to individual wave generation events and wave amplitude estimates from individual instrument records, ITP 41 is used as a case study (Fig. 13). This record begins in October 2010 and runs through July 2012.
During the summer melt, near-inertial wave amplitudes from ITP 41 are consistently elevated on daily to monthly time scales (Figs. 13c–e). There is a rapid decrease in ice concentration and increase in CW inertial ice speed (Fig. 13a). Daily-averaged sea ice concentration and CW inertial ice speed are not significantly correlated with near-inertial wave amplitude over the full 2005–14 record; however, correlations between wave amplitude and CW inertial ice speed during the summer melt are significant for most years (r = 0.3 for ITP 41 at the 95% level).
In fall and early winter, near-inertial wave amplitude increases sharply during several significant storm events (Fig. 13c), in which wind speeds exceed 10 m s−1 (Fig. 13b). Ice concentration is close to 100%, although it sometimes drops slightly during a storm as wind forcing perturbs the newly formed ice (Fig. 13a). Storms cause subinertial ice speed to rise sharply and sometimes drive an increase in inertial ice speed (Figs. 13a–c), presumably depending on ice characteristics. Daily-averaged near-inertial wave amplitude has low correlations with wind speed (r = 0.2) and ice drift speed (r = 0.3 at the 95% level) over the entire ITP dataset. During fall and winter, the correlations between daily-averaged wave amplitude and wind or subinertial ice speed are slightly higher for most years when lagged by 1–3 days, suggesting a finite amount of time for wind momentum to transfer through the sea ice and mixed layer into internal wave generation.
During late winter (March and April), the near-inertial internal wave field is at a minimum (Fig. 13), although waves continue to be generated. Wind speeds are elevated, but sea ice is at 100% concentration. Both inertial and subinertial ice speeds are low and less variable, indicating that the wind is unable to transfer momentum effectively to the ice, even during storms. This record is from recent years, when more first-year ice was present in the Canada Basin. Momentum transfer from wind forcing to sea ice motion in winter could have been further reduced by the lower drag coefficient for first-year ice compared to multiyear ice (Wadhams 2000).
In all seasons, the timing of energetic wave generation events is tied to storms driving rapid increases in sea ice speed. Daily wind speed correlates strongly with sea ice drift speed over the full 2005–14 record (r = 0.6), indicating that sea ice motion is closely tied to changes in the wind on short time scales. This matches findings from Thorndike and Colony (1982), who found that geostrophic winds accounted for over 70% of the variance in daily sea ice motion, a result that was corroborated by Rigor et al. (2002). It is this daily wind-driven sea ice motion that forces near-inertial wave generation, either through variations in horizontal subinertial drift speed or through inertial oscillations in the ice.
The low correlation values reported for the full record for daily near-inertial wave amplitude estimates and wind or ice speed are partially due to a mismatch between the strength of the wind forcing and the strength of the sea ice and thus wave response during different ice conditions. (The limitations of the ITPs, including large uncertainties in individual wave amplitudes, also no doubt play a role, as does an internal wave field composed of both locally and remotely generated waves.) The effect of seasonally and interannually varying sea ice properties on the average energy in the near-inertial wave field is simplistically captured by the wind factor. As expected, the wind factor does not correlate with the near-inertial internal wave field on daily time scales, but rather varies with the near-inertial waves on longer (weekly to monthly) time scales (Fig. 13d).
The near-inertial internal wave field is quantified using nearly a decade (2005–14) of observations from drifting Ice-Tethered Profilers in the Beaufort Gyre region of the Canada Basin. Vertical displacement amplitude for near-inertial waves is compared to wind speed, sea ice concentration, and ice drift speed to determine how wind–ice–ocean dynamics have affected Arctic internal waves over the last decade, both spatially and on seasonal and interannual time scales.
The near-inertial wave field displays a spatial pattern consistent with a linear decrease in vertical displacement wave amplitude of 12% per degree latitude to the north, decreasing by over 1m on average between 72° and 82°N. This pattern is partially explained by slightly elevated wind and ice speeds, and lower sea ice concentration in the south of the Canada Basin. The latitudinal trend in wave amplitude could also be caused by the strictly southward propagation of internal waves generated at the inertial frequency. This is inconsistent with the idea that internal waves are dissipated in the under-ice boundary layer following a single reflection from the sea floor (Pinkel 2005), although it is possible that the under-ice boundary layer (Morison et al. 1985) is becoming less dissipative. Further investigation is necessary to determine the exact cause or causes of this spatial pattern.
On a seasonal time scale, near-inertial internal waves are largest during the summer months, with a second peak in late fall as wind forcing increases, and a minimum in late winter. Median wave amplitude is 16% larger during summer and fall (June–November) than during winter and spring (December–May). Both seasonal and interannual variations in the near-inertial internal wave field are found to match changes in the wind factor, the ratio of subinertial ice drift speed to wind speed. Momentum transfer varies based on the characteristics of the sea ice, such as ice concentration, thickness, roughness, form drag, and internal ice stresses. Many of these properties are reflected in how readily the wind is able to accelerate the sea ice, which is simplistically captured by the wind factor.
There is a small but significant interannual trend during both the summer and winter months, with a 5% increase in the median amplitude of the near-inertial waves between the years 2005–07 and 2010–14, paralleling the decline in sea ice cover during the summer and the increase in sea ice speed during both summer and winter. More importantly, the variance in the distribution of near-inertial wave amplitudes doubles between the years 2005–07 and 2012–14, with an 11% increase in variance per year during summer and a 15% increase in variance per year during winter. Therefore, while the average amplitude of near-inertial waves is only slightly larger in recent years, unusually large waves are generated much more frequently. Variability in the wave field is linked to more variable sea ice cover, with increases in variance for ice concentration and speed during both summer and winter. Sea ice changes could increase the generation of energetic internal waves and/or reduce the dissipation of such waves in the under-ice boundary layer.
Near-inertial internal wave generation in is known to occur due to horizontal variations in sea ice velocity (or wind velocity over open water) driving vertical inertial pumping at the base of the mixed layer. Alternately, during summer free drift or a strong winter storm, the wind can excite a clockwise inertial response in the sea ice. Variations in sea ice speed cannot fully explain the seasonal cycle in the near-inertial internal waves. Instead, the results indicate that the average energy in the wave field on seasonal and interannual time scales is linked to both the wind forcing and the ice response, as determined by the sea ice properties. Changing, and increasingly variable, ice characteristics—such as the continued dramatic reduction in multiyear sea ice in the Canada Basin—appear to be directly affecting the energetics of the Arctic internal wave field.
The ITPs do not directly measure internal wave generation, and cannot be used to distinguish between locally generated downward propagating waves, and remotely generated upward propagating waves. They lack sufficient time resolution to measure the internal wave frequency spectrum, so do not provide accurate estimates of internal wave energy. Despite these limitations, the ITP dataset has provided unique information about the spatial, seasonal, and long-term evolution of the near-inertial wave field in the Arctic, and brought to light connections between wind forcing, local sea ice properties, and the resulting internal waves.
The near-inertial internal wave field in the Canada Basin has become increasingly energetic and variable over the last decade, reflecting a fundamental shift in year-round sea ice characteristics in the Arctic Ocean. As the properties of the sea ice continue to change, the internal wave field will continue to evolve as well. This has important implications for mixing in the upper ocean due to wave overturning and dissipation, as the most energetic waves are those most likely to become unstable and break. Any resulting increase in mixing would influence the vertical flux of heat and nutrients, and weaken the stratification of the upper halocline.
We acknowledge the support of the Office of Naval Research (Grant N00014-11-1-0454) for this study. We gratefully acknowledge the Ice-Tethered Profiler Program and Beaufort Gyre Exploration Program based at the Woods Hole Oceanographic Institution (in collaboration with researchers from Fisheries and Oceans Canada at the Institute of Ocean Sciences) for deploying and maintaining the ITPs (http://www.whoi.edu/itp, http://www.whoi.edu/beaufortgyre). We thank J. Toole, S. Cole, and K. Martini for useful discussions.
Details and Biases of ITP Sampling
The analysis herein uses data from 27 ITPs that completed density profiles and recorded hourly GPS position between August 2005 and October 2014 (Fig. A1) in the Beaufort Gyre region of the Canada Basin (72°–82°N, 130°–160°W). Measurements were made during all months of the year for all years within that time span. ITPs that profiled for only a month or two before failing were excluded from the analysis, as were those ITPs whose drift tracks were outside the study region. The 30 364 profiles used in the analysis represent 85% of the total number of ITP profiles recorded in the Canada Basin. As such, the information in Fig. A1 is for those ITPs and time periods used in this analysis, and does not represent all profiles currently available for all ITPs.
Note that out of the 27 ITPs used, 14 sampled more frequently than the typical twice-daily profiling schedule. Alternate sampling schedules had either 3 or 4 profiles per day, from below the mixed layer to ~750-m depth. Several ITPs completed additional shallow profiles to roughly 250-m depth; these were not used in the analysis. The complex demodulation technique (section 3) is applied to all available deep profiles from each instrument (never more than 4 times daily). Comparisons (not shown) between the resulting near-inertial vertical displacement wave amplitude estimates and amplitude estimates for which the data was subsampled to the typical twice-daily schedule show agreement well within the stated error bounds, and negligible differences on seasonal time scales. For an individual ITP, the year-long median wave amplitude when subsampling profiles differs by O(0.1) m or less from that found using all available profiles, with differences in the variance of the near-inertial wave amplitude distribution on the same order. There is a tendency for the wave amplitude variance to be higher with twice-daily sampling, as infrequent sampling does not constrain wave amplitudes as precisely. Since many ITPs in the later part of the record sampled more than twice per day, the reported interannual increase in variance in wave amplitude may actually be a slight underestimate.
ITPs are typically deployed in late summer in the northern portion of the Canada Basin, in the thickest ice floes available, and drift south during the following winter and summer. There is therefore a slight spatial bias in the distribution for month of the year profiles were taken, as a function of latitude (Fig. A2a). However, the variability in this average latitude of measurement is very high, and the associated spatial pattern in month of year of measurement (Fig. A2b) does not match that for the near-inertial wave amplitude estimates (Fig. 3b). This slight temporal measurement bias in ITP sampling may partially explain the latitudinal trend in wave amplitude, although this is largely due to its connection to sea ice concentration and speed, which are considered separately. Note that numerous measurements were made during the summer of 2013 in the southeast corner of the basin, in a region south of the M2 critical latitude and therefore permitting generation of a semidiurnal internal tide. A temporal/spatial bias for that time period is discussed further in the text.