1. Introduction
Throughout the ice-covered polar oceans, the transfer of momentum from the wind into the ocean is mediated by the presence of sea ice. Sea ice itself is highly dynamic, moving, deforming, and fracturing in response to both winds and ocean currents. A portion of the momentum and energy that would be transferred into the ocean is instead borne by internal stresses in the ice. Consequently, the total surface stress into the ocean depends on the mechanics and dynamics of the sea ice, which in turn depend on the ocean currents in a highly coupled system. This complexity has led to challenges in understanding the extent to which the sea ice might suppress atmosphere–ocean momentum transfer. In the Arctic Ocean, other lines of evidence, such as low interior mixing rates (D’Asaro and Morison 1992; Rainville and Winsor 2008; Fer 2009; Dosser et al. 2021), provide ancillary support for the notion that the ice there is an effective barrier to wind-driven motions. Though other factors like the strong halocline might also be important in setting those differences (Guthrie and Morison 2021), the degree to which ice impacts ocean surface stress remains unclear.
Wind is one of the primary drivers of ocean circulation, and by mediating this process sea ice impacts circulation across a range of spatiotemporal scales. The Beaufort Gyre—the dominant mean ocean circulation pattern in the western Arctic—is controlled by a balance of Ekman pumping, from large-scale gradients in wind-driven Ekman transport and ice–ocean stress (e.g., Dewey et al. 2018; Doddridge et al. 2019; Armitage et al. 2020; Meneghello et al. 2020), with important contributions from lateral eddy fluxes (e.g., Manucharyan and Spall 2016). Low internal wave energy in the Arctic interior relative to lower latitudes (D’Asaro and Morehead 1991; Levine et al. 1985, 1987) may be a result of the presence of sea ice impacting surface stress transfer (e.g., Rainville and Woodgate 2009; Martini et al. 2014; Kawaguchi et al. 2019). Shear-driven mixing at the base of the surface mixed layer (ML) arising from wind-forced ocean surface currents (including inertial oscillations; e.g., Lenn et al. 2011; Fer 2014) can entrain warmer subsurface water (e.g., Meyer et al. 2017; Peterson et al. 2017) and can lead to sea ice melt (Jackson et al. 2012; Peterson et al. 2017; Smith et al. 2018; Graham et al. 2019). Efforts to predict or interpret any of these dynamics rely on accurate understanding and descriptions of the transfer of momentum and energy through the atmosphere–ice–ocean system.
Inertial oscillations, which are rotational motions that are a natural resonant response to wind forcing, are useful for understanding the role of sea ice in local atmosphere–ocean momentum flux. Both the sea ice and the ocean ML exhibit inertial oscillatory motions. Early field campaigns recognized that the seasonal cycle in the sea ice inertial motion was linked to the internal mechanical strength of the ice (e.g., McPhee 1978; Colony and Thorndike 1980): oscillations are weak in the winter pack ice and increase in magnitude as ice concentration drops (Thorndike and Colony 1980; Leppäranta and Omstedt 1990; Kwok et al. 2003; Geiger and Perovich 2008; Gimbert et al. 2012). In the ocean, the seasonality of ML inertial oscillations and the increase in oscillation strength in marginal ice and open water (Plueddemann et al. 1998; Hyatt 2006; Rainville and Woodgate 2009; Martini et al. 2014; Dosser and Rainville 2016; Kawaguchi et al. 2019) is taken as an indicator that sea ice suppresses wind-driven currents (e.g., Rainville and Woodgate 2009; Martini et al. 2014). Due to their fairly simple physics (e.g., Pollard and Millard 1970; D’Asaro 1985), ML inertial oscillations provide an ideal test case for the potential of sea ice to impede the transfer of momentum and energy from the wind. Though, as the oscillations of sea ice and the upper ocean are strongly coupled (McPhee 1978, 1980; Colony and Thorndike 1980; Leppäranta et al. 2012), it is important to consider both systems together when investigating the implications for momentum and energy transfer.
Arctic sea ice loss in recent decades adds an additional layer of uncertainty to atmosphere–ocean momentum flux. As sea ice in some Arctic regions shifts to a more dominantly seasonal regime (Thomson et al. 2016; Onarheim et al. 2018), the greater extent of open water will allow direct connection between the wind and the ocean. It is thought that this may lead to a change in the dominant physical processes in the upper ocean, and a shift to an increasingly wind-forced regime (Rainville et al. 2011). While some focus has been placed on the impacts of changing ice concentration (Guthrie et al. 2013; Dosser et al. 2021), associated decreases in thick, multiyear ice (e.g., Kwok 2018) might also lead to mechanical weakening of the sea ice pack. This is supported by studies showing increasing sea ice deformation and drift speeds (Rampal et al. 2009) and changes in the scale of sea ice inertial oscillations (Gimbert et al. 2012). Furthermore, the shift to younger sea ice may also be associated with a decrease in sea ice surface roughness, impacting ice–ocean coupling (Cole et al. 2017; Brenner et al. 2021). A weaker and less rough ice pack could have an influence on the efficiency of atmosphere–ocean momentum transfer, even during winter sea ice cover.
In this study we seek to better characterize and understand the impact of sea ice on wind-driven motions in the ocean surface ML.
2. Observations and data
a. Field measurements
This study is based on in situ measurements from a set of three subsurface moorings installed across the Beaufort Sea as part of the Stratified Ocean Dynamics of the Arctic (SODA) experiment (Lee et al. 2016; Brenner et al. 2021). The moorings recorded data over one full annual cycle from fall of 2018 to fall 2019. They were roughly aligned along the axis of the Canadian Basin of the Beaufort Sea and spanned different sea ice regimes and different parts of the Beaufort Gyre. The southern moorings, designated SODA-A and SODA-B, were both located in the seasonal ice zone with SODA-B being near the September minimum sea ice edge during the deployment season, while the northern mooring, SODA-C, was located in perennial sea ice (Fig. 1a).
Maps showing the locations of the moorings in the context of (a) the sea ice concentration from 18 Sep 2018 (the 2018 sea ice minimum), with the inset showing the map location, and (b) the September 2018–October 2019 mean Beaufort Gyre circulation from smoothed Dynamic Ocean Topography (DOT; shaded in yellows and blues) with corresponding geostrophic velocity (black arrows), and from the mooring measured average ML current velocities (current roses, shaded in reds). Gray contours show 1000-m isobaths.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
This study applies sea ice and ocean velocity measurements, as well as measurements of the sea ice draft made by upward looking acoustic Doppler current profilers (ADCPs) installed on the moorings. Brenner et al. (2021, 2023) previously reported data from these moorings and describe data processing and sampling schemes in more detail.
Additionally, we use time series of ML depth at each mooring derived from a combination of ADCP backscatter and near-inertial velocity shear (Brenner et al. 2023). ML depths exhibited a strong seasonal cycle, consistent with recent measurements from the same region (Cole et al. 2017) and with the expected seasonal variability (Peralta-Ferriz and Woodgate 2015). Wintertime average ML depths were ∼40 m at all moorings and transitioned abruptly to shallow summer MLs of ∼14–20 m (from SODA-C to SODA-A, respectively) during the ice melt season. While mean winter ML depths were similar across all the moorings, the ML depths at SODA-A had a deeper maximum (62 m, as compared with ∼54 m at SODA-B and -C) and significant variability driven by apparent isopycnal heave from passing subsurface eddies. Time series of ML depth at each mooring are shown in Brenner et al. (2023, see their Fig. 3).
The analysis of the ocean velocity primarily makes use of depth-averaged velocity within the mixed layer. Because of sidelobe reflections from the surface or from the ice–ocean interface, the shallowest usable ADCP measurements were at ∼6-m depth. Unresolved near-surface shear (i.e., in the shallow “inner boundary layer” under the sea ice) could impact the depth averages. To quantify that impact, we consider—as an upper bound—extrapolation of the profile assuming that the velocity matches that of the sea ice at the ice–ocean interface, and a linear variation to shallowest measured ADCP bin. Including this linear extrapolation resulted in an average difference in the depth-averaged velocities of ∼3%–8% (by mooring); though larger errors (∼15%) occur at SODA-C when the ML was shallow (during the summer).
When describing velocities in the “near-inertial” range we consider a frequency band from 0.9f to 1.1f, where f is the Coriolis frequency, and selected only the component rotating clockwise (CW) in time. Time series of the “slowly varying” magnitude and phase of the CW inertial signal are extracted using complex demodulation: velocities are frequency-shifted by a factor f (by multiplying the complex velocities by eif) and then low-pass filtered using a fourth-order Butterworth filter with a cutoff of 0.1f.
b. Atmospheric forcing
As the moorings had no surface expression, reanalysis data were used for atmospheric measurements. For consistency with Brenner et al. (2021), we used the fifth major global reanalysis produced by the European Center for Medium-Range Weather Forecasts (ECMWF) (ERA5; Hersbach et al. 2020), which provides hourly measurements at a 0.25° × 0.25° grid resolution.
The use of reanalysis wind forcing for this study provides some challenges. Reanalysis wind has been shown to underrepresent energy in the superinertial frequency band (Fine et al. 2021). Furthermore, reanalysis can miss events in the marginal ice zone (Brenner et al. 2020). However, Cooper et al. (2022) show that inferred wind speeds using wave measurements from these moorings and others (following Thomson et al. 2013; Voermans et al. 2020) provide a reasonable match with reanalysis, including for fetch-limited waves in the marginal ice zone (those authors compare with a different reanalysis product, but repeating their analysis for ERA5 produces similar statistical matches). Brenner et al. (2021) also showed high correlations between ERA5 wind speeds and observed sea ice drift speeds from the SODA moorings. These results give some confidence that the reanalysis data can be cautiously used for evaluating near-inertial and subinertial signals here.
c. Sea ice concentration
While there are a variety of sea ice concentration products available, we use the ice concentration that is included as part of the ERA5 reanalysis. As the atmosphere–ice drag coefficient in ERA5 [and also used here and in Brenner et al. (2021)] is parameterized as a function of ice concentration (see section 3a), this choice is then self-consistent with the wind forcing used. Sea ice concentration in ERA5 is based on the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) data product (Donlon et al. 2012), resampled to the reanalysis model grid, effectively spatially smoothing the satellite estimates (ECMWF 2019a). The OSTIA product uses SSM/I passive microwave satellite measurements of ice concentration from the Ocean and Sea Ice Satellite Applications Facility (OSI-SAF; Breivik et al. 2001). Ice concentration data are provided with a daily resolution.
Throughout this study, the marginal ice zone (MIZ) is defined as having fractional ice concentration from 0.15 to 0.85; concentrations lower than 0.15 are defined as open water, and higher than 0.85 as pack ice (values of both 0.8 and 0.85 have been used as an upper-bound concentration on the MIZ in previous literature; e.g., Strong and Rigor 2013; Heorton et al. 2019). While a variety of different metrics exist for defining the MIZ (e.g., Horvat 2021), a transition between marginal ice and pack ice at A ∼ 0.8–0.85 is reflective of a dynamical shift in the sea ice internal stress and is evident in our observations.
3. Modeling framework
To interpret the observations, we used a simplified vertical one-dimensional model of the coupled sea ice and upper-ocean velocities. A range of one-dimensional models exist for the upper ocean with differing approaches and complexities in the their treatment of turbulent fluxes. Significant insight has been gained through the application of simplified one-dimensional models in sea ice covered regions. In particular, versions of the Price–Weller–Pinkel (PWP) model (Price et al. 1986) and the Local Turbulence Closure (LTC) model (McPhee 1987, 1999, 2008) have been used to investigate upper-ocean mixing under sea ice [PWP: Toole et al. (2010), Dewey et al. (2017), Wilson et al. (2019), including from inertial oscillations, Hyatt (2006); LTC: Gallaher et al. (2017) and Gallaher (2019)], and the LTC model has been further used to understand inertial oscillations (McPhee 2008, chapter 8). These models include the evolution of momentum, temperature, and salinity profiles and require some prescription of the surface heat and salt fluxes in addition to surface stress.
This work focuses on the wind-forced dynamics of the upper ocean, which are sensitive to the ML depth. The surface heat and salt fluxes required for accurate prediction of ML depth in one-dimensional models are poorly constrained in our observations. Indeed, even when those fluxes are known, it can be difficult to correctly reproduce observed ML depths with such models (Toole et al. 2010), possibly due to lateral restratification processes (e.g., Timmermans et al. 2012). To remove the uncertainty associated with modeling the vertical temperature and salinity profiles and the associated ML depth and instead focus on the dynamical response to wind, we opt to use the damped “slab-ocean” model from Pollard and Millard (1970) which models only the upper-ocean momentum and impose the ML depth taken from observations. The modeled physics in the slab-ocean model are less realistic than other (even simplified) one-dimensional models, but it has been used extensively for investigations of ML inertial oscillations in the open ocean (e.g., D’Asaro 1985; Alford 2003), and has also been employed under sea ice (Gimbert et al. 2012; Martini et al. 2014; Kawaguchi et al. 2019).
The slab-ocean model simulates the response of the depth-averaged ML velocity to surface wind stress; specifically capturing inertial oscillations and Ekman transport. To account explicitly for the presence of sea ice, we include the sea ice momentum equation and couple the two through ice–ocean stress (similar to Gimbert et al. 2012).
In practice, we found that the strong ice–ocean coupling present at inertial time scales (see section 4c) meant that the modeled (Zi)NI was approximately equal to α(Zo)NI for any value of α chosen (where the subscript []NI denotes inertially filtered motions). The observations show that (Zi)NI/(Zo)NI is broadly centered around ∼0.78 (Fig. 2), thus a value of α ∼ 0.78 + 0i was chosen for the model to reproduce the observed behavior. This value of α implies minimal shear and turning in the ML. While that is not generally true for the broadbanded ocean response, it does approximately hold for velocities in the inertial frequency band [and is part of the basis for ML depth identification in Brenner et al. (2023)]. Example profiles show that the average inertial response has a “slab-like” structure (Fig. 3a) consistent with the model description, although upper-ocean shear is observed outside of the inertial band (Figs. 3b,c), so this choice of α may be insufficient to fully resolve aspects of the low-frequency variation. Generally, the qualitative results of this study were insensitive to the specific value of α chosen.
Histograms of the ratio of inertially filtered sea ice velocity to inertially filtered ML-averaged ocean velocity, (Zi)NI/(Zo)NI, from (a) observations and (b) the damped slab model when applied with α = 0.78 + 0i. Purple and green colors show ratios of the real and imaginary parts of each signal. Vertical lines show the medians of the real and imaginary components.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
Profiles of upper-ocean velocity: (a) 3-day average of inertially filtered velocities after rotation into the frame of reference of sea ice motion, (b) 3-day average of broadbanded velocities after rotation into the frame of reference of sea ice motion, relative to the velocity level at the ML depth [thick black lines are observations, and thin gray lines are a theoretical Ekman spiral fit, following Cole et al. (2017)], and (c) example of an instantaneous velocity profile. Averages in (a) and (b) are taken from 10 to 13 Feb 2019 at SODA-C, and the profile in (c) is from 11 Feb 2019. Horizontal dash–dotted lines in each panel show the averaged ML depth during this time frame.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
Linear damping terms model stress at the ML base (roZo) and internal stress in the sea ice (riZi). The use of linear damping for both of these effects is a significant simplification of the true physical processes, providing a crude but useful tool for investigating their respective roles in the momentum balance. These terms are discussed in more detail in section 3b.
This model is closely related to the damped ice–ocean coupled slab model used by Gimbert et al. (2012). While our approach and goals differ somewhat from those authors (particularly by our explicit inclusion and evaluation of measured ocean ML velocities and depth), their previous use of a similar model provides precedent for our application here.
a. Implementation
The sea ice and ML velocities, Zi and Zo were found by integrating Eqs. (1a) and (1b) forward numerically. For numerical stability of the coupled equations, integration was performed with a time step of 2 min (all model inputs/parameters were interpolated to this resolution). Additionally, for A > 0, a minimum sea ice draft d of 0.10 m was permitted to avoid model blow-up (i.e., all d < 0.10 m were set to the value of 0.10 m). The modeled near-inertial components of the velocities (Zi)NI and (Zo)NI were determined through complex demodulation of the broadbanded results (see section 2a). Note that this is distinct from the version of the ocean slab model by D’Asaro (1985), which models the ML inertial motions directly.
The drag coefficients in the surface stresses for each of the interfaces [Eqs. (3) and (4)] all vary in time. The atmosphere–ice drag coefficient, Cai was parameterized as a function of sea ice concentration, A, following ECMWF (2019b), and varied between ∼2 × 10−3 and 3 × 10−3 (also see the supporting information for Brenner et al. 2021). The atmosphere–ocean drag coefficient, Cao was parameterized as a function of wind speed, Za following Large and Yeager (2004), with an average value of ∼1.3 × 10−3. We used the ice–ocean drag coefficients Cio determined by Brenner et al. (2021) for these mooring data, which varied between ∼1 × 10−3 and 12 × 10−3 in response to seasonal changes in sea ice geometry (Tsamados et al. 2014; Lu et al. 2011). In calculating Cio, Brenner et al. (2021) used the same definitions and parameterizations of Cai and Cao as we used here, so the values are all self-consistent.
The factor βw in Eq. (2) relates to surface gravity wave growth: βw = Twaves/Tao, where Twaves is the momentum flux from the wind into the waves. Steele et al. (1989) use a constant value of βw ∼ 0.14. As the moorings measured the surface gravity wave spectra (Cooper et al. 2022), we calculate Twaves following Zippel et al. (2022, adapted for scalar spectra). In our measurements, βw values were always ≤ 0.06, with the highest values during strong wind events in open water.
b. Linear damping parameters
Momentum is removed from the system through the sea ice and ML linear damping terms: riZi and roZo. The damping coefficients ri and ro are the only tunable parameters for fitting the model to observations. These coefficients can alternatively be discussed in terms of their damping time scales:
The damping coefficient for the ML, ro, has been the subject of a number of previous studies in the open ocean, in which it nominally represents the radiation of near-inertial internal waves from the ML (e.g., Alford 2001, 2003; Park et al. 2009). In practice, shear-driven mixing and entrainment at the ML base also results in the loss of energy from ML inertial oscillations (Plueddemann and Farrar 2006; Johnston et al. 2016; Alford 2020) and mesoscale/submesoscale activity can influence the ML inertial oscillations through a variety of mechanisms (Johnston et al. 2016). As such, it would be expected that ro has both spatial and temporal variability that might depend on physical properties such as stratification or ML depth. Nonetheless, it is common to take either ro or rof−1 as a fixed value. For example, Voelker et al. (2020) finds that a damping time scale of
Because the sea ice damping term (riZi) parameterizes internal ice stresses, we follow Gimbert et al. (2012) in interpreting the damping coefficient ri as a proxy for sea ice mechanical strength. At a bulk scale, sea ice strength is known to vary with both ice thickness and concentration, and this is reflected in the damping coefficient values Gimbert et al. (2012) found across a number of ice conditions. A common representation of the thickness and concentration dependence in sea ice rheological models is through an ice strength formulation of the form: P = P*de−20(1−A), where P* is a tunable strength parameter (Hibler 1979). While the usage of P in sea ice models is much more complicated than the linear damping parameterization used here, we adopt this ice strength formulation and make the damping coefficient
We chose the tuning parameters ro and
Damping parameter values and fit statistics for the slab model. Linear damping coefficients are shown in terms of their equivalent damping time scales (values of
4. Annual patterns of wind-driven motion
a. Observed patterns of sea ice and upper-ocean velocities
The moorings measured a background flow that is consistent with the large-scale Beaufort Gyre circulation as determined by satellite altimetry (Armitage et al. 2016, 2017). This is shown by the current-roses in Fig. 1b, and lines in Fig. 4. The annual DOT-derived geostrophic velocities were 69%, 62%, and 125% of the annually averaged ML velocities for SODA-A, SODA-B, and SODA-C, respectively, and were directed at angles < 30° offset from the in situ observations.
Time series of (a),(c),(e) observed ML-averaged current speeds |Zo| and (b),(d),(f) observed sea ice drift speeds |Zi| from each of the moorings: (top) SODA-C, (middle) SODA-B, and (bottom) SODA-A. Lighter-colored, thin lines in all panels show the broadbanded speeds, and thicker, darker lines show the inertially filtered signals (|Zo|NI and |Zi|NI). Dash–dotted lines in (a), (c), and (e) show the gyre-scale geostrophic current speed from dynamic ocean topography (see Fig. 1). Colored bars along the top of each panel show the sea ice concentration.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
Superimposed on the gyre circulation, the measured velocities of both sea ice and upper-ocean show considerable seasonal modulation, particularly in the magnitude of near-inertial frequency motions (Fig. 4). At all three moorings, inertial ice drift and current speeds were enhanced in periods of marginal ice and open water (A ≤ 85%), and relatively quiescent under pack ice. This seasonality is consistent with prior studies (e.g., Plueddemann et al. 1998; Rainville and Woodgate 2009; Dosser and Rainville 2016; Kawaguchi et al. 2019; Polyakov et al. 2020a).
Across the moorings, the near-inertial sea ice and ML-averaged velocities are nearly identical during the pack-ice-covered period (cf. Figs. 4a–c with Figs. 4d–f), clearly demonstrating that inertial oscillations of the sea ice and ocean ML are highly coupled throughout the year. This matches with past studies (McPhee 1978; Leppäranta and Omstedt 1990). In our observations, this strong coupling is generally maintained through the marginal ice period, though there are some noticeable discrepancies. In particular, there is a strong peak in the ML inertial oscillations during the marginal ice-covered period at SODA-B (∼21 July 2019) that is not matched by the sea ice. The decoupling of ice and ocean velocities during this event is not predicted by the model (see sections 4b and 4c), suggesting the possibility of a separate surface velocity layer shallower than resolvable by the ADCPs (e.g., such as the shallow layers seen by Cole et al. 2017).
Aggregating the measurements from the three moorings reinforces that the seasonality of ML inertial oscillations is linked to sea ice concentration. ML inertial oscillation strength, binned by ice concentration, shows a significant decrease in average momentum for pack-ice-covered conditions (Fig. 5a). This is also reflected in the near-inertial ML horizontal kinetic energy (HKE) per unit area [
The (top) ML inertial oscillation strength |Zo|NI, (middle) inertial horizontal kinetic energy HKENI, and (bottom) Ekman transport magnitude |MEk|, all bin-averaged by sea ice concentration (aggregate for all moorings), for (a),(c),(e) observed values and (b),(d),(f) modeled values. Horizontal gray lines in each panel show the means for fractional sea ice concentrations above/below 0.85.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
In contrast to the patterns of inertial oscillation, there was no strong seasonal modulation of the calculated net Ekman transport: MEk = TS(if)−1 (where the ice–ocean stress, Tio in TS was calculated using observed sea ice and ocean ML velocities). There was no significant ice concentration dependence on bin-averaged Ekman transport magnitudes, |MEk| (Fig. 5e), and if anything |MEk| was slightly elevated for A > 0.85 (e.g., see gray lines Fig. 5e). Stratification can compress the Ekman spiral into shallow MLs (e.g., Price et al. 1987; Schudlich and Price 1998; Randelhoff et al. 2014; Chaudhuri et al. 2021). Averaging velocity profiles in a rotated frame of reference aligned with the sea ice velocity show similar Ekman spirals constrained within the ML (Fig. 3b). So the ML average velocity associated with the Ekman transport ZEk = MEkD−1 will have seasonality associated with ML depth and makes up some of the broadbanded velocity signal seen in Fig. 4.
Rotary spectra of sea ice and ML velocities reveal additional features of the broadbanded response. Spectra of the complex sea ice and ML velocities (Zi and Zo) were created with Welch’s method (Welch 1967), using 512-point (∼21.3 day) Hamming windows overlapped by 50%, for a total of ∼32 degrees of freedom. For additional context, similar spectra are also created for the wind velocity Za. Observed spectra of both the sea ice and ML velocities show a “red” spectral shape and a strong peak in the clockwise rotating signal at the inertial frequency (Figs. 6d–i). The observed spectra of the sea ice velocity are similar across the three moorings (Figs. 6d–f), while those of the ocean ML velocity have differing shapes at low frequencies (Figs. 6g–i). At SODA-A there is a roughly constant power-law slope of the observed spectra for
Rotary spectra of (a)–(c) reanalysis wind velocity, (d)–(f) sea ice velocity, and (g)–(i) ML velocity for moorings (left) SODA-A, (center) SODA-B, and (right) SODA-C. In all panels, thick lines are clockwise-rotating velocities and thin lines are counterclockwise-rotating velocities. Error bars in the corner of each panel show the 95% confidence interval (label CI).
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
b. Modeled near-inertial and broadbanded response
The model broadly captured the observed seasonal variations of sea ice and ocean ML inertial oscillation strength (Fig. 7). The oscillations were small during the pack-ice-covered period and increased as the moorings shifted into marginal ice and open water (also Fig. 5b). Many of the peaks in oscillation strength associated with storm events are faithfully represented both during pack ice covered and marginal ice/open water periods. While some peaks in oscillation strength were weaker in the model than in the observations (including the strong peak in the MIZ at SODA-B when observed ML and sea ice inertial oscillations diverge), the model–observation correlations are high (Table 1). When aggregated, the ML inertial current speed and HKENI have ice-concentration dependence that match observations (cf. Figs. 5b and 5d to Figs. 5a and 5c). As such, we deem the model sufficient for further investigating the dynamics associated with inertial oscillations.
Comparison of observed and modeled inertial oscillation strength for each of the moorings (as labeled), for (a),(c),(e) the ML and (b),(d),(f) sea ice. Gray lines show observations, and colored lines show modeled results (colors follow Fig. 1a). Colored bars along the top of each panel show the sea ice classification.
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
The model has mixed success in representing the variability outside of the inertial response, as seen by a comparison of model and observed rotary spectra (Fig. 6). For sea ice, the model reproduces the CW inertial and subinertial spectra at all moorings. For the ML, the match differs between the moorings. At SODA-C, the model reproduces the observed spectra in the subinertial range, while at the other two moorings there is more subinertial energy and a different spectral shape in the observations than in the model (particularly at SODA-A). The mismatch at high frequencies for both sea ice and the ML is not surprising given the underrepresentation of superinertial wind forcing in reanalyses, and the simplifications inherent in the model (i.e., the slab nature of the ML and the representation of internal stress).
Spectral matches/mismatches between the model and the observations at subinertial frequencies suggest other details of the sea ice and ocean dynamics. Low-frequency sea ice motions are primarily wind-driven and, to a good approximation, can be described as moving at a fixed percentage of the wind speed (e.g., Brunette et al. 2022). This explains the similar spectral shape of low-frequency wind and sea ice velocity spectra (which both roll off below
As with the observations, the Ekman transport (MEk) is roughly independent of sea ice concentration (Fig. 5f), with only a small decrease in the median transport in the bin centered at A = 1 that is more pronounced than the observations. While the difference may not be statistically significant, it does hint that the linear damping term used for internal ice stress may not faithfully reflect all aspects of the stress transfer (which is not surprising given its simplicity).
c. Ice–ocean inertial coupling
A feature of both the present study and of past observations (McPhee 1978; Leppäranta and Omstedt 1990) is the strong coupling between sea ice and ocean ML inertial oscillations: both mediums oscillate in unison. McPhee (1978) previously explained this coupling with a model of the total vertically integrated momentum transport, M, of both the sea ice and the ocean boundary layer together (roughly equivalent to M = ρodZi + ρoDZo). In his formulation, there is no stress at the base of the boundary layer so momentum is only removed from the system by sea ice internal stress, which he also models as a linear damping term (with a slightly different form than used here). With that model, McPhee (1978) showed that observed sea ice inertial oscillations are only reproduced when the ocean inertial is included in the formulation.
If the ice and ocean ML are not allowed to coevolve (due to either imposed ocean currents in an ice model or imposed ice velocity in an ocean model), it can be shown that the evolution equation for Zrel will still include a similar quadratic damping term. The effect of this is that an imposed ice drift velocity or ocean ML velocity provides a strong constraint on ice–ocean coupling—particularly at the inertial time scale. For example, in our experiments, application of the slab model for the ML alone [Eq. (1b)] using observed sea ice velocities in Eq. (4) (similar to the approach by Kawaguchi et al. 2019) reproduced observations with high accuracy even for unrealistic choices of model inputs/parameters (Cio, ro, and D). Moreover, modeling the ocean boundary layer with a fixed sea ice velocity (such as in Morison et al. 1985, and others) may lead to excess dissipation in the ice–ocean boundary layer relative to ice that is allowed to move; though, such a scenario may be reflective of the role of internal stress within the sea ice and therefore somewhat realistic. Similarly, choosing to set the ocean velocity to zero, either explicitly or by considering a form of the ice–ocean stress [Eq. (4)] that only includes ice velocity will lead to excess damping of sea ice inertial oscillations.
An additional corollary of the nonlinear damping in the relative ice–ocean velocity is that inertial oscillations of the upper-ocean decay more quickly for a constant nonzero sea ice velocity than when the ice is held stationary. Thus, decoupling of the sea ice motion from the ocean currents while still allowing large-scale coherent motion of the ice pack [e.g., through constant wind forcing or ice internal stress, as expressed by
d. Drivers of inertial current seasonality
The model provides insight into the observed seasonal cycle of sea ice and ML inertial oscillations. This seasonal cycle provides some evidence that sea ice partly inhibits momentum transfer from the atmosphere into the ocean (Fig. 5), as has been previously suggested. Though, as seen in the model equations [Eqs. (1)–(4)], there are a variety of parameters and inputs that have temporal variations and could contribute to a seasonal response. Of particular note are the significant seasonal variations in the ML depth at each mooring (Brenner et al. 2023). As the input forcing is distributed over the ML [Eq. (1b)], it is expected that ML velocities will scale directly with ML depth.
Model parameter tests can be used to further investigate the drivers of inertial seasonality. To perform these tests, we considered a number of candidate model parameters and inputs that each have underlying seasonal variations which could contribute to the overall seasonal cycle of the inertial oscillations. For each of those variables, the model was rerun while setting the selected variable to a set of different constant values (and leaving all other variables as seasonally varying). A comparison of the model runs with both the observations and with a reference model provides information about each variables’ relative importance in controlling the seasonal cycle. Candidate variables that we tested were
-
the ice–ocean drag coefficient Cio,
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the atmosphere–ice drag coefficient Cai,
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the ML depth H, and
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the sea ice damping coefficient (sea ice strength parameter) ri.
For each of these variables, tests set the input values to the 0.01, 0.1, 0.25, 0.5, 0.75, 0.9, and 0.99 percentiles of their full range at each of the moorings (Table 2).
Range of parameter input values used in sensitivity tests at each mooring.
Horizontal kinetic energy ratios
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
As expected, tests showed that the ML depth and the sea ice internal strength (as represented by the damping coefficient ri) both have important contributions to the seasonality of the inertial oscillations. For both of these parameters, tests in which values are held constant have
The tests further show different degrees of sensitivity of the ice–ocean and atmosphere–ice drag coefficients: Cio and Cai, respectively. Removing variability in Cai slightly impacted the seasonality of the inertial response (
The lack of sensitivity to Cio in the inertial frequency band is reflective of the highly coupled nature of the sea ice and ML oscillations. If the sea ice velocity were fixed (e.g., in a model forced by observed ice motion), then increasing the drag coefficient also increases the stress transfer into the ocean because Tio ∝ Cio [Eq. (4)]. But because the ice and ocean are coupled, changes to Cio can also be compensated by changes to the sea ice velocity Zi, with a minimal change to Tio [because of the ice–ocean relative velocity in Eq. (4)]. This adjustment is reflected by the damping of ice–ocean relative velocity in section 4c. For any physically reasonable values of Cio that would match past observations, the damping time scale for ice–ocean relative velocity will be less than the inertial time scale (section 4c), and so sea ice and ocean velocities react to changing Cio and they oscillate together.
While this study shows a minimal role of Cio in setting the strength of inertial oscillations, Cole et al. (2018) found that elevated sea ice roughness (represented by high Cio) was linked to more energetic near-inertial wave generation within pack ice covered areas. This contrast does not represent a discrepancy between our results and those of Cole et al. (2018); instead it highlights that near-inertial internal wave generation is multifaceted. While ML inertial oscillations are a starting point for understanding sea ice impacts on near-inertial wave generation in the Arctic (e.g., Martini et al. 2014; Kawaguchi et al. 2019), there may be other ways that ice affects wave generation. For example, Jutras (2016) identifies that in high ice concentrations, differential internal ice stresses can lead to sea ice convergence/divergence that drives inertial pumping and wave generation. Furthermore, the drag coefficients in Cole et al. (2017, which are used in Cole et al. 2018) are derived from drifting point measurements of Reynold’s stress and capture intermittent, short time scale, highly localized variability, while those used here (from Brenner et al. 2021) are from data fits over week-long periods and reflect larger-scale averages that could be used in models (such as in the present context). These differences in definitions of Cio may relate to the generation mechanism for internal waves (i.e., if they are predominantly associated only with the largest roughness elements). In any case, the mechanisms by which sea ice roughness may separately impact inertial oscillations and internal wave generation provides an opportunity for further study.
5. The net impact of sea ice on ML inertial velocity
The modeling framework used here allows us to investigate idealized scenarios, namely a complete absence of ice [A = d = 0 in Eqs. (1b) and (2)], or the presence of ice without internal strength (ri = 0). In both cases, the term involving surface waves (βw) is set to zero to avoid introducing seasonal biases.
Differences between these two cases arise because there are a number of ways that sea ice impacts momentum transfer from the wind. While internal stress can act as a sink for momentum, increased surface roughness over sea ice relative to open water (Cai > Cao) results in more momentum flux out of the atmosphere for the same wind speed, and amplification of ocean surface stress (e.g., Martin et al. 2014; Brenner et al. 2021). In a pan-Arctic sea ice modeling study with imposed wind and ocean currents, Martin et al. (2014) suggest that these competing effects lead to a maximum momentum transfer from the wind to the ocean at some intermediate sea ice concentration. Further, sea ice acceleration/deceleration may lead to phase mismatches between wind stress and inertial oscillations, impacting the resonant response.
Figure 9 shows histograms of
Stacked histograms of the ratio of the ML inertial oscillation strength in the full reference model to (a) the “no ice” test and (b) the “no stress” test. Colors correspond to the different moorings following Fig. 1a (SODA-A: blue; SODA-B: red; SODA-C: yellow), with darker-shaded colors being measurements in pack ice conditions (A > 0.85) and lighter-shaded colors being marginal ice (0.15 < A < 0.85).
Citation: Journal of Physical Oceanography 53, 7; 10.1175/JPO-D-22-0112.1
Despite the broad range of
In the “no stress” test,
6. Summary and conclusions
In this study we investigated wind-driven sea ice and surface ML velocities, with a particular focus on the ML inertial-frequency response. Using a simplified one-dimensional ice–ocean coupled model to interpret observations across the Beaufort Sea, we identified drivers of the seasonality in sea ice and ocean ML inertial velocities. The results provide insight into the role of sea ice in mediating momentum transfer across the atmosphere–ice–ocean system. Our findings reinforce and build on previous understanding of the seasonal variations of sea ice drift speeds and ocean ML current speeds. The increased understanding gained from measurements of the combined sea ice and upper-ocean inertial response over a full annual cycle and across widely varying ice conditions provides an important contribution to the literature.
Observed seasonality in ML inertial signals has long been linked to sea ice cover (Plueddemann et al. 1998; Rainville and Woodgate 2009; Martini et al. 2014; Dosser and Rainville 2016; Lincoln et al. 2016; Kawaguchi et al. 2019). In this work, we see similar patterns, with a marked difference in inertial ML horizontal kinetic energy above and below an ice concentration of A ∼ 0.85. Whereas past studies have primarily attributed this seasonal response to sea ice internal stress (e.g., Plueddemann et al. 1998; Rainville and Woodgate 2009), we compare a variety of factors that could influence the strength of the inertial currents. Our simplified model shows that the seasonal variation of the ML depth is also important for controlling the strength of the oscillations. The fact that ML depth variations are a salient contribution to the response is not frequently discussed in modern literature of inertial current strength in sea ice covered regions (e.g., Rainville and Woodgate 2009; Kawaguchi et al. 2019; Polyakov et al. 2020a), and may be overlooked. Because of the strong coupling between sea ice and ocean ML inertial velocities, ongoing trends in ML depth (e.g., Peralta-Ferriz and Woodgate 2015) and potential changes in surface mixing regimes as sea ice conditions change (e.g., Polyakov et al. 2020b) will imprint themselves on sea ice inertial motion so caution should be used when interpreting observed trends in sea ice drift. The strong seasonal differences in ML depth in the Arctic imply that even in the absence of internal ice stress, seasonal differences in inertial oscillation strength will persist.
A comparison between moorings further showed variations in the degree to which sea ice mechanical strength impacted the inertial response. While sea ice internal stress (in its simplified representation in the model) caused strong damping of inertial oscillations at the northern moorings, it had only a modest impact on oscillation strength at the southern mooring. Using a different methodology in assessing the same set of moorings, Brenner et al. (2021) also suggested a minimal role of sea ice internal stress in the ice drift at the southern mooring. Insofar as the southern mooring in the seasonal ice zone is representative of future sea ice conditions, this comparison suggests a weakening of the sea ice as Arctic sea ice continues to decline (consistent with Gimbert et al. 2012).
Importantly, we show that the paradigm that sea ice reduces the transfer of momentum in to the ocean surface layer is more nuanced than has previously been discussed in the literature. In these measurements, sea ice internal stresses decreased inertial oscillation strength in pack ice. However, local ice–ocean coupled-model results suggested that weak ice could increase inertial oscillation strength relative to open water conditions, in broad agreement with previous pan-Arctic modeling using imposed ocean currents (Martin et al. 2014). The net Ekman transport, meanwhile, had no ice concentration dependence. This suggests that in the Beaufort Sea, sea ice may act as a filter, reducing higher-frequency motions while transmitting momentum at low (subinertial) frequencies. This lack of concentration dependence on the net Ekman transport may be an emerging feature of the Beaufort Sea as the ice pack shifts to a younger and more seasonal regime, and has implications for the large-scale equilibration of the gyre (e.g., through mechanisms such as the “ice–ocean governor” Dewey et al. 2018; Meneghello et al. 2018). Differences in the subinertial rotary spectra between moorings do support that sea ice stresses play a role in damping nonlocal motions (as in, e.g., Manucharyan and Thompson 2022).
In summary:
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In addition to sea ice internal strength, ML depth is an important—and possibly overlooked—control on Arctic inertial oscillation seasonality and trends.
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Sea ice mechanical strength may be playing a decreasing role in the dynamics of younger, thinner sea ice, leading to increasing wintertime atmosphere–ocean inertial coupling.
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The net Ekman transport was minimally impacted by the presence of sea ice, suggesting that modern sea ice does not limit momentum transfer from the wind to the ocean at subinertial frequencies.
Research continues to explore how changing sea ice conditions impact the efficiency of Arctic atmosphere–ocean momentum flux across spatiotemporal scales. The Eulerian in situ measurements presented in this study capture sea ice and ocean behaviors across a broad range of environmental conditions and give a complementary view to prior measurements from Lagrangian ice camps and from pan-Arctic numerical models. These measurements support earlier results on the seasonality of inertial oscillatory motions while also highlighting important drivers of those behaviors (beyond just the presence of sea ice) and giving an expanded view of total atmosphere–ocean momentum flux. In particular, the apparent frequency dependence of the momentum transfer implied by the results of this study (summary point 3) is a novel result that bears further research. In addition, the improved understanding of the drivers of the inertial-frequency ML response provides context for ongoing research in evolving internal wave conditions in the Arctic (e.g., Dosser et al. 2021; Fine and Cole 2022). Although, we caution future researchers interested in those topics to take care in their treatment of both sea ice and ML depth when applying slab-ocean models.
Acknowledgments.
Financial support for this work was provided by Office of Naval Research (authors Brenner, Thomson, Rainville, Crews, and Lee) and the National Science Foundation (Crews). Funding from Office of Naval Research was part of the Stratified Ocean Dynamics of the Arctic (SODA) research project and was provided through Grants N00014-18-1-2687 (Brenner), N00014-16-1-2349 (Thomson), and N00014-14-1-2377 (Rainville, Crews, and Lee). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant DGE-1762114 (LC). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The authors thank Captain Greg Tlapa and Captain MaryEllen Durley, along with the rest of the command team and crew of USCGC Healy for operational support in 2018 and 2019. We additionally thank Joe Talbert, Jason Gobat, Eric Boget, and Ben Jokinen (University of Washington, Applied Physics Laboratory) for mooring deployment/recovery and engineering support. This work has benefited from ideas and feedback from Tim Stanton and Bill Shaw, Shawn Gallaher, and three anonymous reviewers.
Data availability statement.
Arctic dynamic topography/geostrophic currents data were provided by the Centre for Polar Observation and Modelling, University College London (https://www.cpom.ucl.ac.uk/dynamic_topography) (Armitage et al. 2016, 2017). Data files containing the time series of measurements used to produce this study can be accessed at http://hdl.handle.net/1773/46919 and http://hdl.handle.net/1773/49495. More information about the project can be found online (https://www.apl.washington.edu/soda).
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