a. ADCP measurements

Each of the three moorings included two upward-looking ADCPs installed on floats at different depths. The top float of each mooring, a DeepWater Buoyancy StableMoor (see Harding et al. 2017), housed a Nortek Signature-500 (hereafter SIG500) 5-beam ADCP. A syntactic foam float ∼45–50 m deeper contained a Teledyne Workhorse-300 (hereafter WH300) ADCP (Fig. 1b). The depths of each of the top floats were ∼45 m for SODA-A, 42 m for SODA-B, and 27 m for SODA-C (a float depth of 45 m was targeted for all three moorings, but logistical constraints during deployment resulted in a shallower depth at SODA-C). The distance between the upper and lower instruments was fixed except for small adjustments due to line creep through the year, and when currents inclined the moorings. During strong currents, the top float at SODA-B had a maximum vertical deviation of ∼14 m from its resting position; vertical deviations were even smaller at the other moorings. Data from the SIG500 ADCPs were previously presented by Brenner et al. (2021), and the concurrent sampling schemes used with those instruments are described in that paper. Velocity measurements from both ADCPs were merged together to create a continuous product within the top ∼80 m of the water column, with a 2 m vertical bin spacing and a temporal resolution of 1 h.

To focus on vertical shear only at the base of the ML, we consider the shear corresponding specifically with inertial oscillations, which are associated with “slab-like” motion of the ML (e.g., Pollard and Millard 1970). Horizontal velocities (u, υ) were filtered to retain the clockwise-rotating near-inertial frequency band using complex demodulation (Tukey 1961) with a fourth-order low-pass Butterworth filter applied with a frequency with a cutoff of 0.1f. The inertial frequencies (periods) at each of the three moorings were: 1.395 × 10⁻⁴ rad s⁻¹ (12.51 h), 1.412 × 10⁻⁴ rad s⁻¹ (12.36 h), and 1.412 × 10⁻⁴ rad s⁻¹ (12.25 h), for SODA-A to SODA-C, respectively, so the filter bandwidth was ∼2.5 h. The inertial shear magnitude is $S_I={[{(\partial u_I/\partial z)}^2+{(\partial {\upsilon }_I/\partial z)}^2]}^{1/2}$, where subscript I refers to the inertially filtered velocities.

The echo intensity/amplitude recorded from each of the ADCPs were treated separately (i.e., the Signature500 and WH300 echo data on each mooring were not merged). For each record, the relative acoustic backscatter (SV) was found from the recorded echo data by accounting for acoustic transmission loss and beam spreading following Gostiaux and van Haren (2010), which is based on Deines (1999) but with empirical fits of the scale factor k_c and a more careful accounting for signal-to-noise ratios near the noise floor. The relative backscatter is calculated as

$\text{SV}=I_{\text{dB}}-A+20\log R+2\alpha R,$(1)

where R is a distance from the instrument, A is an empirical constant value that incorporates transmit power and geometric factors, α is a frequency-dependent attenuation coefficient [taken as 0.069 for the WH300s (Deines 1999) and 0.146 for the SIG500s, calculated from Francois and Garrison (1982)], and I_dB is a relative acoustic intensity (in dB) derived from the recorded echo intensity, E after scaling and subtracting noise:

$I_{\text{dB}}=10\log ({10}^{k_{c}E/10}-{10}^{k_c{E}_{\text{noise}}/10}).$(2)

The fitted values of A, k_c, and E_noise for each of the instruments are shown in Table 1. Note that while the values of SV will vary somewhat if calculated for different accepted values of these parameters [e.g., using the constant value of k_c = 0.45 from Deines (1999) for WH300 instruments], the overall results of this study—which are based just on identifiable peaks in SV profiles—are relatively insensitive [e.g., in a similar procedure, Macrander et al. (2007) simply use the echo amplitude E after removing an exponential fit]. Acoustic reflections of other mooring components were frequently seen in the echo data from the deeper WH300 ADCPs, so contaminated bins were removed, as identified based on the magnitude of the annually averaged error velocity (using a threshold of 1.5 × 10⁻³ m s⁻¹). In addition to reflections from the pycnocline that are used to determine ML depth (section 3), the acoustic backscatter also recorded signals of biological activity in the water column including both the diel vertical migration of zooplankton (e.g., Dmitrenko et al. 2020, 2021), and seasonal differences that might be associated with the phytoplankton bloom (e.g., Ardyna et al. 2014). The signal associated with diel vertical migration produced peaks in backscatter that competed with the pycnocline reflection, so to minimize this impact we averaged the acoustic backscatter in daily time bins. This smears out the signal of the diel migration while leaving the peak associated with the ML depth relatively intact.

Table 1

Acoustic parameters used for determining the relative backscatter, SV for each instrument and mooring, based on the fitting procedure described by Gostiaux and van Haren (2010).

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Altimeter distances from the vertical beam of the SIG500 were corrected for ADCP tilt, speed of sound (measured at the instrument), and atmospheric pressure variations (Brenner et al. 2021). Sea ice draft was calculated as the difference between the instrument depth H (based on pressure measurements; instrument accuracy 10% of pressure range) and the altimeter distance D. Altimeter burst measurements were categorized as being either sea ice or open water based on their spectral properties following Shcherbina et al. (2016; also see Kirillov et al. 2020; Brenner et al. 2021). In sea ice cover, the difference between the instrument depth H (based on pressure measurements) and the altimeter distance D was used to calculate sea ice draft: d = H − D. For bursts identified as being in open water (based on spectral characteristics), erroneous nonzero values of d (i.e., nonzero values of ice draft) indicate water column sound speed variations due to shallow stratification (section 4).

b. Temperature and salinity measurements

On each of the moorings, the ∼45 m distance between the two ADCPs was instrumented with a set of Seabird SBE37 MicroCAT conductivity–temperature–depth (CTD) sensors and SBE56 temperature (T) sensors (Fig. 1b). A total of 10 of sensors (6 SBE37 and 4 SBE56) were installed with a spacing of ∼4–5 m between instruments, and instrument types alternating. At all three of the moorings, the uppermost SBE37 (positioned directly underneath the topmost float) failed sometime during the summer season (between late May and early July), but pressure and temperature measurements made by the SIG500 ADCP itself continued to provide a record at that float throughout the full data record, albeit with a decreased temporal resolution and accuracy (prior to failure, the uppermost SBE37 was used to correct and calibrate the SIG500 temperature measurements).

In addition, a 40-m-long, buoyant “breakaway chain” of high-spatial-resolution (0.25 m spacing) temperature sensors was attached to the tail of the StableMoor (the topmost float) in order to measure temperatures shallower than the float depth. These sensors measured with a 3-h sampling period. The chain was built up of 8 sections that were each 5 m long (a total length of 40 m) and connected with a set of weak links of progressively increasing strength. All data collected by the sensors along the chain were recorded by a datalogger housed in the StableMoor float. This allowed for sections of the chain to break off without the loss of data as they were raked by passing sea ice keels. The breakaway chains were successfully deployed for SODA-A and SODA-C. At SODA-B, a rough sea state during (anchor-last) mooring deployment resulted in the chain fouling with the main mooring line and no data above the StableMoor. At SODA-C, which was located in perennial sea ice cover, the shallower top float depth (∼27 m) resulted in some chain sections being initially against the ice at the surface, so most of the chain broke away shortly after deployment. Of the eight chain sections, five of them (the top 25 m) had broken off by 12 October 2018 (less than 1 week after deployment). An additional 5 m section broke off on 11 March 2019, leaving only two sections (10 m) for the remainder of the deployment. At SODA-A, one section broke away on 18 December 2018, and a second section was lost 19 February 2019; the other six sections (30 m) of the chain remained intact. Pressure sensors located at distances of 5, 20, and 35 m along each of the chains allowed for reconstruction of their positions in the water column and the depths of each of the temperature sensors. This was done using a quadratic model fit to the available pod distances and pressures (which decreased in number as chain sections broke away) including the pressure measured by the Signature500 ADCPs at distance 0. The pressure measurements show that the strong ocean currents at SODA-A (up to 0.5 m s⁻¹) resulted in significant movement and frequent “blow down” of the chain (in extreme cases, the vertical extent measured by the chain was <5 m even when the chain was 30 m long). At SODA-C, which was more quiescent, the chain was usually fairly vertical. There were occasional data spikes or dropouts along some sections of the breakaway chain. These were more prominent at SODA-A (possibly due to chain movement which may have disrupted internal cabling), with sections 1 and 3 missing data for most of the year. Though less frequent at SODA-C, similar spikes and dropouts still occurred. Data spikes were most apparent as unphysically high temperatures. To account for these issues, all temperatures above 6.5°C were removed from the record of both moorings, and temperatures were interpolated across data gaps and dropouts. Measurements were then bin averaged in 2-m along-chain (8 sensor) bins. Some noise and horizontal banding remaining in the final data record shows some calibration offsets/errors associated with individual sensors that could not be resolved.

Temperatures and salinity measurements made by the Seabird sensors on the mooring line and by the breakaway chains were both temporally averaged into 1-day bins (note that inspection of temperature sections from the breakaway chains prior to averaging did not reveal significant subdaily variations in the apparent ML depth). Measured temperatures and salinities were converted to Conservative Temperature and Absolute Salinity using the Gibbs Seawater Oceanographic toolbox (IOC et al. 2010); references to temperature and salinity made in section 4 refer to those quantities.

In addition to the mooring measurements, an autonomous Seaglider (SG229) sampled temperature and salinity from 16 August to 30 September 2019 in a 20 km “bow-tie” pattern around SODA-A, with a mean distance from the mooring of ∼12 km (Fig. 1a). The Seaglider is a small, reusable, long-range autonomous underwater vehicle designed to glide from the ocean surface to 1000 m and back while collecting profiles of temperature, salinity, and other oceanic variables. Gliders steer through the water by controlling attitude (pitch and roll) and can thus navigate between waypoints to execute survey patterns, in this case with successive dives separated by ∼4 km, and ∼6.5 h. Temperature and salinity were measured by SG229 were averaged into 1 m vertical bins and temporally averaged into 1-day bins for consistency with the other data sources. It is not possible to completely separate the effects of temporal and spatial variability measured by the Seaglider. Nonetheless, ML properties measured by the Seaglider did not vary considerably across the bow-tie pattern. Over any individual bow-tie track, ML-averaged temperature anomalies (relative to a linear trendline over the whole record) had a maximum standard deviation of 0.29°C, and there was no correlation of those anomalies with position. Below the ML, there are some minor differences in the “patchiness” of the temperature profiles between the Seaglider and the mooring data (not shown), which suggest some spatial variability in subsurface eddy features over the sampling area. This subsurface spatial variability is unlikely to impact any of the conclusions of the present study.

In situ measurements were supplemented with satellite-derived sea ice concentrations (A) and sea surface temperatures (SSTs) provided by the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) data product (Donlon et al. 2012). These are provided at daily intervals at 0.05° resolution. Data were interpolated to provide time series of A and SST at SODA-A.

a. Approach

Sharp temperature and salinity gradients cause reflections of acoustic signals due to changes in acoustic impedance (e.g., Ross and Lavery 2012), so peaks in measured acoustic reflectance (backscatter) can be related to stratification (e.g., Shibley et al. 2020). Furthermore, particles (e.g., plankton) can accumulate at the ML boundary (e.g., Möller et al. 2012), which can further enhance backscatter there. These principles have been used to identify oceanic structures from acoustic echo sounder or seismic data (e.g., Penrose and Beer 1981; Holbrook and Fer 2005; Stranne et al. 2017; and others; including of the Arctic ML; Stranne et al. 2018).

Peaks in stratification are also often a location of strong vertical shear of horizontal velocity. The ocean ML responds directly to wind forcing (e.g., Price et al. 1987; Randelhoff et al. 2014; Chaudhuri et al. 2021). Particularly for inertial oscillations, which are rotational motions of the ML at the local Coriolis frequency, the velocity profile is generally more or less uniform in the ML (the “slab” models of Pollard and Millard 1970; D’Asaro 1985), with strong inertial shear at the ML base. Because of the slab-like structure of inertial oscillations, inertial shear will be relatively weak within the ML and have a strong signal at the ML base. As such, inertial-band shear is likely a better indicator of the ML depth than broadband shear (which would likely include other signals within the ML; e.g., due to mixing layer development).

Macrander et al. (2007) previously showed that a seafloor mounted ADCP could be used to identify the interface depth of a deep exchange flow: the Denmark Strait Overflow. Those authors considered both echo intensity (a measure of acoustic backscatter) and shear separately to construct and compare different time series of Denmark Strait Overflow interfacial depth. As both shear and backscatter in the surface ML can be impacted by a variety of processes absent in deeper overflow water, we adapt and build on the ideas presented by Macrander et al. (2007) in order to develop a methodology for identify the ML depth from moored (uplooking) subsurface ADCPs.

Here, the ML depth is identified using ADCP measurements of inertial shear and acoustic backscatter together. An overview of the procedure is as follows:

1. 1) For each of the data sources (WH300 backscatter, SIG500 backscatter, inertial shear), identify ML depth at each time step from local maxima, subject to constraints on “peak prominence” and the depth range considered (see below).
2. 2) Combine individual ML depth measurements for separate sources into a single time series for each season.
3. 3) Perform a weighted-moving average.

Steps are described below in more detail. These steps were performed separately for “winter” and “summer” seasons to account for different ML characteristics: deeper MLs throughout the ice-covered period of the year, with a shift to shallow MLs with the injection of freshwater from melting sea ice (Peralta-Ferriz and Woodgate 2015). Different constraints on the depth range considered were used for each season. The delineation between these seasons was chosen manually based on visual inspection of backscatter and shear, in which we looked for the time at which both shear and backscatter showed a developing and coherent near-surface signal. Winter/summer boundaries were identified as 12 June, 4 July, and 18 July 2019 for SODA-A, SODA-B, and SODA-C, respectively; before these dates was considered “winter,” and afterward was considered “summer.” The method for ML depth identification would be improved by a more objective identification of the onset of the shallow summer stratification, but we were unable to identify a satisfactory approach for this that was robust to measurement noise/variability. At all three moorings these dates correspond to sea ice concentrations of A ∼ 68%. It is likely that summer freshwater layers were present earlier than these dates, but were too shallow to be identified (the shallowest resolvable ADCP measurements were ∼6 m deep due to surface sidelobe reflection).

• Step 1. Rather than identifying the ML as the absolute maximum values of shear or backscatter for a given time step (as in Macrander et al. 2007), we searched for local maxima. At each time step, we associated the ML with the shallowest local maxima whose peak extends above background values by some minimum threshold, and is within a specified depth range (with different depth bounds for the search algorithm for winter and summer seasons, and for different data sources; Table 2). This was done separately for each of the three data sources, using the MATLAB findpeaks function with a “minimum peak prominence.” Peak thresholds were chosen ad hoc after inspecting the data fields (Table 2). ML depths were only identified for times when there were peaks that met the threshold value. For each of the identified peaks, a three-point quadratic stencil was applied to points centered on the peak, with the ML depth taken as depth of the maximum of the quadratic fit (Figs. 2d,e). The three-point stencil allows for the determination of ML depth values between ADCP measurement bins. The inertial shear magnitude often showed multiple additional peaks below the ML (Fig. 2a). For this reason, variability in the strength of inertial shear peaks relative to the assigned threshold can lead to “jumps” in the identified ML depth (e.g., in late February Fig. 2a); this is why both shear and backscatter signals are used together (step 2) and subsequently smoothed (step 3) to create the final ML product.

• Step 2. For each season, individual ML depth points from the different sources (backscatter and shear) were combined into a single time series. Due to instrument limitations (depth and range) and environmental differences, the blended data included different data from different data sources during different times of the year. In particular, elevated midwater column backscatter during sea ice breakup and open water (possibly due to seasonal phytoplankton bloom) partly obfuscated WH300 backscatter measurements, and lead to the divergence of peaks found in backscatter and inertial shear. As inertial shear is more representative of ML dynamics, we took this divergence as an indication that those backscatter data were not reflective of ML depth. For this reason, backscatter-derived ML depth points from the WH300 were included during winter only. While these effects were also present in the SIG500 backscatter, they were minimized by the shallower depths of those instruments. Depths from the SIG500 backscatter were included during summer only, when MLs would be consistently above those instruments. Inertial shear data were included throughout the full year, as summarized in Table 2.

  Table 2

  ML depth algorithm parameters for each of the data sources. Threshold identifies the minimum peak prominence used for identifying local maxima. Depth range identifies the vertical bounds of the search algorithm for each of the two seasons. Date range shows when data from each instrument were considered. R.S. = record start; R.E. = record end; F.R. = full record.

  

  

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• Step 3. A smoothed daily ML depth time series was constructed by taking the weighted averages of depths in centered moving 7-day windows. Weights were calculated as the prominence of each peak (from the peak detection algorithm) normalized by the minimum threshold for each data type; this gives higher weights to peaks associated with strong acoustic reflection or shear. The distribution of weights associated with the different data sources were generally similar: weight values for shear and SIG500 backscatter were mostly between 1 and 5, with means of ∼2–2.5, while for WH300 the range was slightly higher with means ∼4–5. For windows containing 3 or fewer measurements, no calculation was performed. Finally, days in which no averages were reported due to lack of data were filled in with linear interpolation. At SODA-B and SODA-C, linear interpolation accounted for a minimal amount of the record, filling in 10 and 6 days total, respectively, and with the longest gap at either mooring being 4 days. At SODA-A, ML detection was more challenging (ocean conditions there were more variable) and required longer periods of interpolation. This record contained a number of gaps up to 1 week long (e.g., during the passage of a large eddy in early November) and a total of 46 days of interpolated ML depths.

Figure 2 provides an example of the ML depth identification procedure from a 3-month period in winter at SODA-C (including a view of the diel variations of acoustic backscatter). The figure demonstrates the variability in the signals of both backscatter and shear.

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Example of ML depth identification from a 3-month period in winter/spring 2019 at SODA-C, showing time series of (a) inertial shear magnitude (S_I) and (b) daily averaged relative acoustic backscatter (SV). Points in (a) and (b) show identified ML depths. (c) An inset from (b) demonstrating the effects of diel migration on backscatter and showing (top panel) the daily averaged backscatter used for identifying the ML and (bottom) the same data before averaging. (d),(e) The peak identification for individual profiles of (d) backscatter and (e) shear, including the subgrid three-point stencil [inset in (e)] for the times identified by vertical dashed lines in (a) and (b).

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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b. Results

Figure 3 shows time series of the ML depths found for each mooring. At all moorings, the method produced ML depths similar to recent measurements in the same region (Cole et al. 2017), with winter mean ML depths of 42.7, 40.0, and 39.7 m, for SODA-A to SODA-C, respectively, and mean summer depths of 20.2, 16.2, and 14.4 m. Cole et al. (2017) found ML depths of 40 m in winter and depths 10–15 m at the beginning of summer, which deepened through September.

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Time series of upper-ocean temperatures at each of the three moorings (as labeled from north to south). (c) SODA-A, with temperatures from mooring measurements prior to 16 Aug 2019 and from the Seaglider after that date [(c) delineated by a vertical dash–dotted line]. (b) SODA-B and (a) SODA-C, with temperature measurements are only from the mooring. Black lines in each panel show the final ML depth time series identified through shear and backscatter (i.e., independent of temperature measurements). White contours in (a) and (c) show the ML depth based on the −1°^-C isotherm (through winter) or from the peak N from Seaglider measurements [(c); summer].

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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The ML depths determined from ADCP shear and backscatter (black line in Fig. 3) followed variations in the measured upper-ocean temperature from the moorings and Seaglider. Wintertime variability in ADCP-derived ML depth corresponded to vertical displacement of isotherms, and tracked the depth of a strong vertical temperature gradient. To quantify the fit, the −1° isotherm was taken as representative of the winter ML depth from SODA-A and SODA-C mooring sections (since the surface water was at the freezing temperature during winter ice cover, this corresponds to a ΔT threshold of ∼0.5°–0.6°). The −1° isotherm was chosen as it generally tracks local peaks of dT/dz (which are likely collocated with peaks in buoyancy frequency), but calculation/identification was less impacted by measurement noise in the breakaway chain (which is amplified when taking gradients). From August–September at SODA-A, a ML depth was defined based on the depth of the maximum buoyancy frequency, N, from the Seaglider measurements. These ML depths are shown as white contours in Fig. 3.

There is good correspondence between the ADCP-estimated ML and that determined from the mooring/Seaglider sections (Fig. 4). Correlation coefficients and root-mean-square errors were r = 0.60, RMSE = 8.28 m for SODA-A, and r = 0.88, RMSE = 2.67 m for SODA-C. The approach used to identify ML depths from the ADCP measurements is entirely independent of the temperature–salinity data, so the ML depths determined using those measurements corroborate this method.

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ML depths based on the −1°C isotherm (SODA-A and SODA-C; winter) or from the peak N in Seaglider measurements (SODA-A; summer) vs ML depths estimated from ADCP-measured shear and backscatter. The black dashed line shows the 1:1 slope.

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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At SODA-B, where shallower temperature data were less available, direct comparisons or validation of the estimated ML depths was not possible. Nonetheless, some of the temporal variations in the ML depth during winter at that mooring match with the heaving of isotherms deeper in the water column (Fig. 3b).

Aside from when the Seaglider measurements were available, temperature data were too deep in the water column to compare ML depth measurements during the summer shallow ML period. This highlights the limitations of using those data to investigate summer MLs, and the value of being able to derive those measurements from ADCPs.

a. Approach

The advent of vertical altimeter beams on some ADCP models allows for measurements of sea ice draft or surface gravity waves (e.g., Magnell et al. 2010; Thomson and Rogers 2014; Kirillov et al. 2020; Brenner et al. 2021; Cooper et al. 2022; Thomson 2022). However, the presence of surface stratification, such as shallow MLs, leads to small offsets in these altimeter measurements, primarily due to changes in acoustic travel time as a result of vertically varying sound-speed profiles. As such, offsets between the pressure-derived instrument depth H and the altimeter-derived instrument depth D measured in open water have been used to make empirical sound speed corrections to these measurements (e.g., Kirillov et al. 2020; Brenner et al. 2021). Here, we instead make use of those erroneous measurements from a SIG500 ADCP to infer the summertime ML temperature using an inverse sound speed model. As this method requires sufficient sound speed differences between the ML and deeper water and some amount of identifiable open water, it is applicable to summer conditions only. This limitation is not prohibitive as wintertime ML temperatures can already be assumed to be near the local freezing temperature, so it is in the summer conditions when we would be most interested.

We focus only on summer measurements from SODA-A as a demonstrative example. At SODA-A, measurements of H − D in open water reached as high as ∼0.5 m (Fig. 5). Shallow stratification can cause errors in these measurements due to both sound speed changes (which impact the altimeter distance, D) and density changes (which impact the conversion from pressure to instrument depth, H). Thus, open-water depth offsets d = H − D can be expressed as d = ε_H + ε_D, where ε_H and ε_D are the separate errors associated with H and D. While in general these effects cannot be separated, Arctic waters exist in a temperature–salinity regime in which density, and hence ε_H, is set almost entirely by salinity. So ε_H can be estimated separately given an appropriate model of salinity. For the small salinity differences (and thus small salinity-derived ML density variation) predicted here, ε_H is small and most of the error can be attributed to ε_D.

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Distance offset (H − D) measurements for burst data at SODA-A identified as open water (left axis), and sea ice concentration (right axis). Points show individual measurements, while the solid line show daily averages. Note that open-water bursts occur for nonzero ice concentration due to measurements between sea ice floes. Blue points at the beginning of the record show times when the ML depth was below the depth of the instrument.

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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The speed of sound in water is a strong function of temperature. Inverse sound speed models provide a measure of integrated ocean heat content based on observed travel times of acoustic signals (Watts and Rossby 1977). Together with a model for the water column structure, these measurements have been leveraged to determine details of the vertical temperature distribution. For example, Sanchez et al. (2021) use acoustic travel times measured by pressure-sensor-equipped inverted echo sounders (PIES; Meinen and Watts 1998) to investigate temperature and thickness of Atlantic Water inflow to a glacial fjord. Knowing upper- and lower-layer temperatures, Macrander et al. (2007) also makes use of travel time measurements from PIES to estimate the depth interface of the Denmark Strait Overflow (for comparison to the backscatter and shear methods; section 3).

Prior to the onset of the shallow summer stratification, the ML was at the local freezing temperature (Fig. 3). As sea ice concentration decreases and shallow summer stratification sets in, the ML is expected to rapidly warm (e.g., Peralta-Ferriz and Woodgate 2015) while the ocean below the ML remains approximately the same temperature. As a first-order approximation, we model the upper ocean as a two-layer system with a homogeneous surface ML of depth h₁ overlying a lower layer of depth h₂ which has linear temperature and salinity gradients (Fig. 6). The lower-layer gradients dT/dz and dS/dz are assumed to be constant in time. We find these gradients by making linear fits to the average of measurements from the mooring line between July and August 2019 (using only measurements deeper than the SIG500 ADCP); those gradients are extrapolated upward to the base of the ML (at depth h₁). In this way, the profiles of T₂ and S₂ are given as T₂(z) = T(H) + (dT/dz)(H − z), where T(H) is the temperature at the ADCP, taken from the mooring measurements, and equivalently S₂(z) = S(H) + (dS/dz)(H − z).

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Schematic of the two-layer model showing profiles of Conservative Temperature (T), Absolute Salinity (S), and sound speed (c) with depth.

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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Equation (4) was applied to calculate c₁ with daily averaged values of ε_D, using h₁ from section 3 (and h₂ = H − h₁) and sound speeds c(H) and 〈c₂〉 calculated from the modeled lower-layer profiles T₂(z), S₂(z) using functions provided in the Gibbs Seawater Oceanographic toolbox (IOC et al. 2010). Then, c₁ values were numerically inverted using the estimated ML salinity, S₁, to find the ML temperature, T₁. As sound speed is only weakly dependent on salinity, estimates of T₁ were insensitive to the modeled ML salinity (differences of ≤0.1°C compared to simply extending the S₂ profile to the surface). To assess the effect of uncertainties of the ML depth, and of the distance offset measurements, T₁ were recalculated while varying h₁ by ±3 m (corresponding with the summertime RMSE of h₁, cf. section 3), and d by ±0.05 m (roughly corresponding with the uncertainty of the ADCP pressure sensor).

b. Results

The sound speed model produces realistic ML temperatures (Fig. 7). Modeled temperatures exceeded satellite SSTs by up to ∼3°C when temperatures peaked in mid-July, though satellite SSTs roughly overlapped with the lower uncertainty bound on temperature. From mid-August onward, the modeled ML temperature matched with both satellite SST and the ML temperature observed by Seagliders (Fig. 7). Correlation coefficients and root-mean-square errors between the ADCP-derived ML temperatures and the satellite SST product were r = 0.89 and RMSE = 1.46°C. For the Seaglider, they were r = 0.79 and RMSE = 0.85°C.

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ML temperatures (T₁) as determined using the ADCP with the sound speed model (black line) and from satellite SST (from OSTIA; green line) and the Seaglider measurements (pink line). The gray shaded area indicates the estimated uncertainty of T₁, obtained by simultaneously varying h₁ by ±3 m and d by ±0.05 m.

Citation: Journal of Atmospheric and Oceanic Technology 40, 1; 10.1175/JTECH-D-22-0055.1

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Uncertainties in T₁ resulting from simultaneously varying h₁ and d translated to a relatively large uncertainty range of +5°C to −3°C in ML temperature when h₁ was shallow (∼15 m, in mid-July; Fig. 3), but had minimal impact on T₁ estimates for deeper MLs (±1°C in mid-August–October when h₁ ∼ 25–30 m). When taken separately, the uncertainties in T₁ associated with varying either h₁ or d individually both have similar patterns, with peaks in mid-July (not shown). At the peak, h₁ variations of ±3 m result in an uncertainty in T₁ of +3°C to −2°C while d variations of ±0.05 m result in ±1.5°C differences in T₁ (the uncertainty varying them simultaneously is a nonlinear combination of the two). Later in the record (mid-August–October), the range of d gives an uncertainty in T₁ of ±0.7°C, and h₁ gives an uncertainty of ±0.3°C. The larger uncertainties in T₁ early in the record are the result of both the uncertainty being inversely proportional to h₁, and the fact that when h₁ is shallow, variations of ±3 m reflect a larger relative difference. The largest overestimates of T₁ relative to the satellite SST occur when the ML depth is not constrained by Seaglider measurements, and might suggest an underestimate of the ML depth. That the lower uncertainty bound of T₁ overlaps with the satellite SST during this period (Fig. 7) indicates that an increase of the estimated ML depth by ∼3 m (from ∼15 to ∼18 m) would be sufficient to approximately recreate the observed SST.

Aside from uncertainty in the ML depth, the mismatch between satellite SST and ADCP-derived estimates of the ML temperature in July might be partly attributed to the simplicity of the two-layer model being applied here (Fig. 6), and partly to larger-scale (smoother) satellite SST estimates underestimating values relative to point measurements. Heat within some transition layer underneath the homogeneous ML (e.g., Price et al. 1986) would be misattributed here to higher ML temperatures. In applying a sound speed model to find the temperatures in Sermilik Fjord, Sanchez et al. (2021) fits hyperbolic-tangent profiles for temperature and salinity with some constant known interfacial thickness. A similar model might improve these results, though it is unlikely that the interfacial thickness would remain constant through the summer. There are also a variety of other reasons why in situ ML temperature measurements with satellite SST might disagree. There are challenges in determining SST from satellite measurements in the Beaufort Sea, and variability between different data products (Castro et al. 2016). Additionally, skin effects lead to temperature offsets between SST and the underlying ocean temperature (Minnett et al. 2019). Crews et al. (2022) found differences between in situ observations of surface temperature and satellite SST of ∼1°C in the same study region (though of the opposite sign than suggested here, and using a different SST product). While further work is needed to address potential mismatches, the strong correlation between the satellite SST and ADCP-derived ML temperatures (r = 0.89) indicates the viability for prediction of ML temperatures from ADCP altimeter measurements.