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J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

Spatial variability of the Arctic Ocean’s double-diffusive staircase

NICOLE SHIBLEY∗ AND MARY-LOUISE TIMMERMANS†

Department of Geology and Geophysics, Yale University, 210 Whitney Ave, New Haven CT 06511, USA.

JEFFREY R. CARPENTERInstitute for Coastal Research at Helmholtz Zentrum Geesthacht, Geesthacht, Germany

JOHN TOOLEWoods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA

ABSTRACT

The Arctic Ocean thermohaline stratification frequently exhibits a staircase structure that has been attributedto the diffusive form of double-diffusive convection, overlying the Atlantic Water Layer. The staircase consistsof multiple mixed layers of order 1-m in thickness separated by sharp interfaces, across which temperatureand salinity change abruptly. Through a detailed analysis of Ice-Tethered Profiler measurements acquired be-tween 2004 and 2013, the double-diffusive staircase structure is characterized across the entire Arctic Ocean.Staircase properties (mixed-layer thicknesses and temperature and salinity jumps across interfaces) are ex-amined in relation to a bulk vertical density ratio spanning the staircase stratification. It is shown that theLomonosov Ridge serves as an approximate boundary between regions of low density ratio (approximately3 to 4) on the Eurasian side and higher density ratio (approximately 6 to 7) on the Canadian side. We findthat the Eurasian Basin staircase is characterized by fewer, thinner mixed layers than that in the CanadianBasin, although the margins of all basins are characterized by relatively thin mixed layers. A double-diffusive4/3-flux law parametrization is used to estimate vertical heat fluxes in the Canadian Basin to be O(0.1) Wm−2.It is shown that the 4/3-flux law is not an appropriate representation of heat fluxes through the Eurasian Basinstaircase. In this region, molecular heat fluxes are computed where interfaces between mixed layers can beresolved; they are found to be O(0.01) Wm−2. However, many uncertainties remain about the exact nature ofthese fluxes.

1. Introduction

Arctic climate processes are strongly influenced by theexistence and persistence of Arctic sea ice (Perovich et al.2013), which is influenced by ocean heat. Water enteringthe Arctic from the Atlantic Ocean is a significant sourceof this heat (e.g., Rudels et al. 2004). The distribution andfluxes of Atlantic Water Layer (AWL) heat is a central el-ement of the Arctic Ocean heat budget. This study ex-amines the temperature and salinity structure at the topboundary of the AWL (the Arctic Ocean’s thermocline),from which inferences about vertical ocean heat fluxes,and their spatial distribution, can be made.

The heat transfer from the AWL to the upper ocean (andthen to the sea ice) could have a substantial effect on seaice thickness (e.g., Aagaard et al. 1981; Rudels et al. 2004;Carmack et al. 2015). In fact, there is sufficient heat con-

∗Corresponding author address: Department of Geology and Geo-physics, Yale University, 210 Whitney Ave., New Haven, CTE-mail: nicole.shibley@yale.edu†Yale University, New Haven, CT

tained in the AWL that if it could be fluxed to the sur-face ocean in contact with sea ice, it would melt the en-tire sea-ice pack (Maykut and Untersteiner 1971). How-ever, at present, a strong density stratification (primarilydue to salinity – the Arctic halocline) effectively insulatesthe surface ocean from AWL heat in the central basins ofthe Arctic (e.g., Aagaard et al. 1981; Padman and Dillon1987; Timmermans et al. 2008; Fer 2009). In the Arctic’scentral Canada Basin, vertical heat fluxes from the AWLare negligible compared to typical summer ocean-to-iceheat fluxes at the surface (e.g., Timmermans et al. 2008).In the Eurasian Basin on the other hand, AWL heat fluxesare believed to be an important factor in contributing tosea ice decline (Lenn et al. 2009; Polyakov et al. 2012).

Atlantic Waters have a general cyclonic circulationaround the Arctic Basin from where they enter throughFram Strait and the Barents Sea opening. Where theLomonosov Ridge reaches the edge of the Russian con-tinental shelf, the Atlantic inflow splits into two cyclonicflows: one with waters circulating the entire CanadianBasin, and the other with waters circulating the Eurasian

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Basin along the Lomonosov Ridge, and back towardsFram Strait (e.g., Rudels et al. 1994; McLaughlin et al.2004). The AWL maximum potential temperature θmaxin the Eurasian Basin is around 1.3 ◦C (where the depthof the θmax is approximately 280 m), and in the CanadianBasin θmax ≈ 0.7 ◦C (where the depth of the θmax is ap-proximately 390 m) (Fig. 1).

Above the depth of the AWL θmax, both temperature andsalinity increase with depth and the water column is proneto the diffusive form of double-diffusive convection (e.g.,Turner and Stommel 1964; Schmitt 1994; Radko 2013);throughout much of the central Arctic basin, there exists adouble-diffusive staircase at the top boundary of the AWL,which has been well studied (Melling et al. 1984; Padmanand Dillon 1987, 1988; Timmermans et al. 2008; Polyakovet al. 2012). The double-diffusive staircase can be charac-terized by a density ratio, which is a measure of the changein density due to salinity across the staircase to the changein density due to temperature (e.g., Turner 1965). If thestabilizing effect of salinity is larger than the destabilizingeffect of temperature (i.e., the density ratio is larger than1 and the ocean is statically stable), double-diffusive stair-cases are often found in the ocean for density ratios up to≈ 10 (e.g., Kelley et al. 2003).

The AWL staircase is characterized by well-mixed ho-mogeneous layers generally between about 0.5 and 3.5 mthick, separated by high gradient interfaces across whichpotential temperature and salinity change by δθ ≈ 0.04 ◦Cand δS ≈ 0.01, respectively. The double-diffusive heatflux through the staircase may be estimated by comput-ing the fluxes through individual interfaces, employinga parametrization (a 4/3 flux law which is proportionalto δθ 4/3) that depends on the potential temperature andsalinity jumps across them (Kelley 1990). Reported AWLdouble-diffusive heat flux estimates range from 0.02-0.3Wm−2 in the Canada Basin (Padman and Dillon 1987;Timmermans et al. 2008), to approximately 8 Wm−2 inthe Laptev Sea (Polyakov et al. 2012) and 0.16 Wm−2

in the Amundsen Basin (Guthrie et al. 2015). These es-timates are based on both direct microstructure measure-ments as well as on double-diffusive heat flux parametriza-tions. Recent work has shown, however, that in some re-gions of the Arctic Ocean, the use of a double-diffusiveflux parametrization may not be appropriate (e.g., Carpen-ter and Timmermans 2014). Planetary rotation, for exam-ple, which is not accounted for in double-diffusive fluxparametrizations, can reduce double-diffusive heat fluxesexpected if the Ekman boundary layer is sufficiently thin-ner than the interface (Kelley 1987; Carpenter and Tim-mermans 2014). If the 4/3 flux parametrization (e.g., Kel-ley 1990) is appropriate, the parametrized heat flux shouldequal the molecular heat flux through an interface in thestaircase for density ratios approximately larger than 2(Carpenter et al. 2012; Sommer et al. 2013; Carpenter and

Timmermans 2014). Timmermans et al. (2008) and Pad-man and Dillon (1987) find that this is the case in theCanada Basin. Here, calculated molecular fluxes fromtemperature measurements that resolve interfaces were es-timated to be approximately 0.2 Wm−2, while the parame-terization returned comparable values: 0.22± 0.10 Wm−2(Timmermans et al. 2008).

In this paper, we present the first Arctic-wide character-ization of the properties of the AWL thermocline and stair-case. We take advantage of the high-resolution tempera-ture and salinity data from Ice-Tethered Profilers (ITPs)(Krishfield et al. 2008a; Toole et al. 2011) that sampledover the entire central Eurasian and Canadian basins; weanalyze data from the 2004–2013 period. The next sectiondescribes the ITP data and analysis methods. In section 3,we characterize the AWL across the basin by its potentialtemperature maximum (and salinity and depth at this max-imum) and evaluate a bulk vertical density ratio across thedepth range of the staircase. In section 4, we examine thedetails of the staircase structure (mixed layer thicknessesand vertical density ratios across individual mixed layersin the staircase), and identify regions across the Arcticbasin where a staircase structure is present or absent. Thevalidity of a 4/3 flux law parametrization for different re-gions is examined in section 5, where heat fluxes are alsodiscussed. Finally, in section 6, we summarize and discussthe results.

2. Data and Methods

a. Ice-Tethered Profiler Measurements

ITPs measure conductivity, temperature, and pressurein the Arctic water column from several meters below seaice through the core of the AWL (Krishfield et al. 2008a;Toole et al. 2011). ITPs consist of a surface buoy typicallydeployed in multi-year sea ice and a wire rope that hangsbelow to a depth of about 750 m. A CTD (conductivity-temperature-depth) profiling unit is attached to the wire,and the CTD crawls up and down through the water col-umn (at ≈ 25 cm s−1). The data (including GPS infor-mation) are transmitted by satellite in near real time. Atotal of approximately 15,800 up-going profiles from 52ITPs deployed throughout the Arctic Ocean between 2004and 2013 are used in the analysis (Fig. 2). Note theCTD sensors are located at the top of the profiling unitand measurements made during down-going profiles areinfluenced by the wake of the profiler; for the finescalestructures being examined here, only up-going profiles areused. Full vertical resolution measurements (≈ 25 cm fora 1 Hz sampling rate) are used.

The temporal lag between CTD channels is cor-rected during processing through examination of thetemperature-salinity finestructure of the double-diffusivestaircase. Temporal lags can often be exhibited by spikesin salinity at the staircase interfaces. Here, both the final

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processed data (Level III) as well as full-resolution LevelI data are used, for which accuracies of temperature andpressure are ± 0.001 ◦C and ±1 dbar, respectively. Salin-ity accuracy is < 0.005 for the Level III data, and likelyworse for the Level I data; however, absolute accuracydoes not factor in the vertical salinity gradients consid-ered here. Profiles which exhibited salinity spikes fromuncorrected sensor response were excluded from the anal-ysis. Full data processing details are in Krishfield et al.(2008a,b); Johnson et al. (2007) and at www.whoi.edu/itp.

b. Characterizing the Thermocline and Double-DiffusiveStaircase

We characterize the AWL by its prominent potentialtemperature maximum, θmax. Salinity and depth values atthe θmax for each profile were also determined. To avoidthe selection of spurious maxima (or potential temperaturemaxima associated with warm Pacific Water intrusions inthe Canadian sector), θmax estimates are restricted to pres-sures≥ 100 dbar and < 500 dbar, and salinities≥ 34. Pro-files where θmax > 6 ◦ C or < -1 ◦C were also excludedfrom the data set. These criteria were confirmed to excludeonly spurious values; further, they are consistent with pre-vious studies indicating θmax ≈ 1-3 ◦C, and the depth atthese potential temperature maxima range from ≈ 200-400 m (Rudels et al. 1999; Timmermans et al. 2008; Lennet al. 2009; Polyakov et al. 2012).

A bulk density ratio, Rρ , specifies the relative contribu-tions of the bulk salinity gradient to density and the bulkpotential temperature gradient to density as

Rρ =(β∆S)(α∆θ)

, (1)

where ∆θ and ∆S are vertical potential temperatureand salinity changes respectively across some specifieddepth interval (chosen to be much larger than a typicalmixed layer thickness), and α = −ρ−1∂ρ/∂θ and β =ρ−1∂ρ/∂S are the coefficients of thermal expansion andsaline contraction, respectively. Another characterizationof the staircase is via the interface density ratio, Rρ , whichquantifies the relative contributions of the salinity gradi-ent on density and the potential temperature gradient ondensity across each interface in the staircase:

Rρ =(βδS)(αδθ)

. (2)

Both the small-scale Rρ characterizing individual steps,and the larger-scale bulk Rρ , have been calculated in thisstudy.

The depth of the θmax provides a reference point for thechoice of an appropriate depth range across which to char-acterize the staircase. A specified depth above the AWLθmax that indicated a deep bound on the staircase region

was visually identified for each ITP (with the exception ofITP 56 drifting in the Eurasian Basin, where two boundswere determined on either side of warm fronts). The deepbound was selected to avoid the interleaving intrusionsthat are generally found in depths around the core of theAWL. For ITPs that drifted in the Eurasian Basin, thisbound was 106 ± 23 m above the AWL θmax, and in theCanadian Basin was 142± 13 m above the AWL θmax. Aninterval of 50 m above the deep bound was considered forthe determination of bulk water-column properties in thestaircase region.

Four representative profiles from (1) the centralEurasian Basin, (2) the boundary of the Eurasian Basin,(3) the central Canada Basin, and (4) the boundary of theCanada Basin indicate how the appropriate depth rangechanges from region to region (Fig. 3). The bulk densityratio, Rρ , was computed based on bulk potential temper-ature and salinity gradients (from end-point differences)over these 50 m depth intervals; α and β were computedat the mid-depth of the interval.

Any value of Rρ greater than 10 or less than 1 was ex-cluded. Close inspection of the profiles indicated that val-ues in these ranges were associated with spurious temper-ature and/or salinity measurements or isolated mischarac-terization of the double-diffusive staircase interval.

The lower 25 m of each 50 m depth segment for agiven profile was taken as the depth interval to charac-terize individual mixed layers and interfaces in the stair-case. Mixed layers are consistently most prominent inthis range (mixed layer thickness tends to increase withdepth). While the depth interval of 50 m is best for thecalculation of Rρ (a smaller depth interval may be influ-enced by individual mixed layers), we find that Rρ calcu-lated over the lower 25 m differs by less than 15% fromRρ calculated over 50 m. Mixed layers in the staircase aretaken to lie where the potential temperature difference be-tween two adjacent data points in a profile was less thana threshold value (between 0.001 and 0.006 ◦C), whichwas determined to be most appropriate (by trial and visualinspection) for each ITP. The potential temperature gradi-ent ∂θ/∂ z in a mixed layer was required to be less than asecond threshold value (between 0.001 and 0.009 ◦Cm−1)which was also determined for each ITP. The detectionof at least three mixed layers, not including the first andlast mixed layer (that may have been only partially sam-pled) and a sum of mixed layer depths of at least 6.25 m,were required to mark a staircase as present in that pro-file. The minimum requirement of 6.25 m ensures that asignificant portion (at least 25%) of the depth interval isoccupied by mixed layers. Mean mixed layer thickness,h, was calculated by averaging the thicknesses of mixedlayers in each profile, excluding the first and last mixedlayers in the 25 m segment. We compare our method fordetermining mixed layer thickness with that described byPolyakov et al. (2012), again excluding the first and last

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mixed layers from the mean. Polyakov et al. (2012) findthe anomaly between potential temperature and potentialtemperature averaged over 3-m depth, and take mixed lay-ers to be located between the local minima and maxima ofthe anomaly with respect to depth (see their Fig. 3). Usingthe profile set from ITP 1 as representative of the CanadianBasin, we find h = 2.20± 0.52 m, while the method de-scribed by Polyakov et al. (2012) gives h = 1.83±0.39 m.Using the profile set from ITP 38 as representative of theEurasian Basin, we find h = 2.18± 0.78 m, while themethod of Polyakov et al. (2012) gives h = 1.18±0.31 m.Although we appreciate that neither method is perfect, thegenerally smaller values of the method of Polyakov et al.(2012) appear to be related in some cases to spurious de-tection of very small “mixed layers.” The density ratio, Rρ ,was computed over individual interfaces using the valuesof δθ and δS between adjacent mixed layers.

AWL staircase interface thicknesses, δh, have beendescribed previously in various sectors of the ArcticBasin using microstructure measurements. Polyakov et al.(2012) estimate interface thicknesses in the Laptev Seaof 1 < δh < 5 m, and Padman and Dillon (1989) findδh≈ 0.15 m in the Canada Basin. Interface thicknesses inthe Amundsen Basin were found to be, on average, 0.1 m(Guthrie et al. 2015). Given these measurements and esti-mates, and the limiting vertical ITP resolution of 0.25 m,interfaces generally tend to be too thin in the Canadiansector to be resolved with the ITP measurements. ITPs canresolve interface thicknesses in parts of the Eurasian Basinwhere interfaces are thicker (Fig. 4). Where interfaces aretoo thin to be resolved by ITP measurements, it remainspossible to infer heat fluxes using a double-diffusive fluxlaw parametrization, provided we can rely on the verifica-tion of past studies that such a flux law is appropriate inthe region in question.

For the thicker interfaces in the Eurasian Basin, that canbe resolved in ITP data, interfaces were identified as theregions between adjacent mixed layers (the thickness be-tween the top of one mixed layer and the bottom of that ad-jacent). If the interface was thicker than a threshold value,which was determined by inspection for each ITP (andtaken to be between 1.75 and 2.5 m), it was excluded fromthe analysis of interfaces. If at least two interfaces werepresent in a staircase region, the mean interface thickness,δh, was calculated for the profile. We again compare ourmethod for determining interface thickness with that de-scribed by Polyakov et al. (2012), where inflection pointsin a vertical profile of potential temperature anomaly (po-tential temperature compared to 3-m vertically-averagedpotential temperature) define the depths of mixed lay-ers/interfaces. Using the profile set from ITP 38 (in theEurasian Basin), we find δh = 1.12 ± 0.31 m, whilethe method of Polyakov et al. (2012) gives δh = 0.64 ±0.17 m. While there is uncertainty in both methods, we

corroborate our interface thickness calculations by com-paring the mean interface thickness for a profile to the me-dian interface thickness for a profile. Across the EurasianBasin, these values vary by less than 5% (i.e., spuriousanomalously thick interfaces are not significantly biasingthe values).

c. Heat fluxes

The main motivation for investigating the double-diffusive staircase is for its relevance to vertical heat fluxesfrom the AWL to the overlying water layers. Typically,heat fluxes through double-diffusive staircases are com-puted using parametrizations formulated by empirical fitsto laboratory and oceanographic data. One of the mostcommonly used double-diffusive parametrizations for theheat flux (in Wm−2) is given by Kelley (1990):

FH = 0.0032e4.8/R0.72ρ ρcp(

αgκPr

)1/3(δθ)4/3, (3)

where cp is the specific heat of water, κ is the moleculardiffusivity of heat, g is gravity, and Pr = ν/κ is the Prandtlnumber, where ν is the kinematic viscosity. The value ofthis formalism is that only the temperature jump across adouble-diffusive interface must be resolved, and not theinterface thickness (which is often too thin to be resolvedwithout microstructure measurements). In regions whereinterfaces can be resolved, a molecular heat flux FM canbe computed across an interface, FM = ρcpκ ∂θ∂ z . A reason-able check as to the validity of the 4/3 flux parametrizationin this region can be made by comparing the magnitudesof FM and FH ; we discuss this further in Section 5.

3. Bulk Properties of the AWL

The AWL θmax, salinity of the θmax, depth of the θmax,Rρ , and h show significant spatial variability across theArctic Basin over the study period. In contrast, tempo-ral variability in AWL properties appears to be negligible.The AWL typically exhibits much smaller seasonal andinterannual variability than surface waters more directlyinfluenced by seasonally-varying surface buoyancy fluxesand wind-driven variability. We observe that in the Cana-dian Basin, the θmax changes at a rate of -0.02 ± 0.16 ◦Cper year (over 2004-13), and in the Eurasian Basin, theθmax changes at a rate of -0.01 ± 0.30 ◦C per year (i.e.,there is no statistically significant trend in either of thetwo main basins over the decade of ITP measurements).The spatial difference in θmax over a section from ≈ 44◦E,85◦N to ≈ 135◦W, 72◦N is around 2◦C. Therefore, the in-fluence of temporal variability may be neglected comparedto basin-wide spatial variability, and we consider the large-scale spatial patterns presented here to be effectively syn-optic.

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a. Properties of the AWL θmax

As the Atlantic Water enters the Arctic Basin and circu-lates eastward, heat is lost through turbulent ocean mixingwith cooler waters (as well as surface buoyancy fluxes)and also through double-diffusive heat fluxes. The AWLis appreciably cooler in the Canadian sector, where θmax≈ 0.73 ◦C, whereas in the Eurasian Basin, θmax ≈ 1.30 ◦C(Fig. 5a). The AWL θmax is coldest in the northeast Cana-dian Basin off the coast of Ellesmere Island. Here, thewaters have propagated cyclonically over the full extent ofthe Arctic Basin. Maximum and minimum observed θmaxare 4.10 ◦C and -0.68 ◦C, respectively (Fig. 5a). A sec-ondary cyclonic circulation of Atlantic Water occurs in theEurasian Basin along the Lomonosov Ridge, as evidencedby the temperature distribution of θmax.

The AWL salinity at θmax is highest closest to the inflowregion and freshens following the decrease in θmax, againbecause of turbulent mixing with overlying fresher watersand double-diffusive salt fluxes as the AWL circulates thebasin (Fig. 5b). The AWL core is shallowest near FramStrait (approximately 200 m deep) and increases (by mix-ing processes and downwelling) along the cyclonic path-way with maximum depths found in the central BeaufortGyre region (approximately 440 m deep), where deepen-ing of isopycnals arises as a result of the large-scale anti-cyclonic wind forcing (Proshutinsky et al. 2009) (Fig. 5c).

b. The bulk density ratio Rρ

The bulk density ratio, Rρ , is lowest in boundary re-gions of the Eurasian Basin, where the AWL core iswarmest (Fig. 5d). In the Eurasian Basin, Rρ = 4.0 ±1.3. Rρ increases along the cyclonic pathway of the AWLaround the Arctic Basin, and takes values of Rρ = 6.3 ±1.4 in the Canadian Basin. Low values of Rρ near the At-lantic Water inflow region are best described by larger ver-tical potential temperature gradients than in other regions;the temperature gradient overlying θmax is proportional toθmax. The largest values of Rρ are found in the regionsof coolest AWL θmax, where potential temperature gradi-ents are smallest (Fig. 6a). Although for all values thereis a near-linear relationship between θmax and the salinityat θmax (not shown), there is no clear relationship betweenbulk salinity gradients and the salinity at θmax.

Values of Rρ show a bimodal distribution, with peaksat approximately 3 and 6, corresponding to values in theEurasian and Canadian Basins, respectively (Fig. 6b). Thesecond, smaller peak around Rρ ≈ 6 appears to be as-sociated with the slightly higher values in the northeast-ern Canadian Basin. These differences in Rρ are manifestin the differing slopes of θ -S plots (in the region of thestaircase) of representative profiles in the respective basins(Fig. 1c).

4. Staircase Properties

a. Presence or Absence of Mixed Layers

A well-defined staircase exists throughout most of thecentral Arctic Basin but is generally not observed alongthe boundaries of the Eurasian Basin, including near theAtlantic Water inflow (Fig. 7a). It is unclear whether thisis due to the dominance of turbulent mixing over doublediffusion. In the Eurasian Basin, the AWL thermoclineis closer to the surface and less sheltered by the overly-ing stratification from winds and surface buoyancy forc-ing. It is likely that turbulent diffusivities are higher in theshallower Eurasian Basin thermocline, inhibiting double-diffusive convection (e.g., Rippeth et al. 2015). The dis-tribution of a staircase structure (Fig. 7a) provides a con-servative estimate with profiles marked as having no stair-case if the criterion described in Section 2b is not satis-fied. The boundary regions are generally characterizedby fewer, thinner mixed layers, and the 25-m region overwhich mixed layers were calculated often does not exhibita staircase structure over the entire interval. Rather, onlya few, isolated mixed layers are found in the 25-m depthinterval.

b. Mixed Layer Thicknesses & Interface Properties

Mean mixed layer thicknesses, h, are generally in therange 0.5 to 3.5 m, with similar values between the Cana-dian Basin and Eurasian Basin (Figs. 7b, 8). Across theentire Arctic Ocean, mean mixed layer thicknesses do notexhibit a spatial pattern. In the Eurasian Basin, where in-terfaces are resolved by ITP profiles, values of mean inter-face thicknesses, δh, generally fall between 0.5 and 2 m(Figs. 7c, 8). δh does not appear to be correlated with h.

δθ across interfaces is, on average, higher in theEurasian Basin than in the Canadian Basin, following asimilar pattern to θmax and ∆θ across the 50-m staircaseregion. δS across interfaces takes similar values in theEurasian and Canadian Basins, though several high val-ues are found in the eastern Canadian Basin, where θmaxis smallest (Figs. 8, 9). Comparably, Rρ and Rρ exhibitsimilar patterns around the basin, although with slight dif-ferences that could be due to curvature in the thermo-cline gradient over the depth interval of interest, or tomixed layers not being precisely resolved. Timmermanset al. (2008) find similar results between Rρ and Rρ in theCanada Basin, with Rρ calculated over individual mixedlayers varying between 2 and 7 and bulk Rρ values in thesame region varying between 3 and 6.

Finally, it is of interest to compute the Rayleigh num-ber, Ra ≡ gαδθh3/νκ . The term (δθ)4/3 in the 4/3 fluxlaw (e.g., Kelley’s parametrization used here) originatesfrom the relationship between the Rayleigh number andthe ratio of convective to conductive heat flux. Here, Ra

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describes the relative effects of the thermal buoyancy forc-ing to viscosity and diffusion across an interface. We findvalues of Ra in the Eurasian Basin are higher than those inthe Canadian Basin, suggesting that buoyancy effects arestronger there than in the Canadian Basin (Fig. 8). Thisis discussed in context with heat fluxes in the next sec-tion. The distributions of h, Rρ , and Ra (Fig. 8) found inthe Eurasian Basin are comparable to those described byGuthrie et al. (2015).

5. Heat Fluxes

Previous studies have shown that Kelley’s 4/3-fluxparametrization agrees with observed heat fluxes in theCanadian Basin (Padman and Dillon 1987; Timmermanset al. 2008). Applying the parametrization (3) to the ITPdata, we derive heat fluxes of O(0.1 Wm−2) for this re-gion. Highest fluxes are found near the western boundaryof the Lomonosov Ridge, consistent with where the AWLis warmest in the Canadian Basin where it enters from theEurasian Basin (Fig. 10a). It is of note that heat fluxes inthe Canadian Basin cannot be predicted from a cyclonicpathway around the periphery of the basin; high valuesof heat flux found in the central Beaufort Gyre are con-sistent with the separation of the AWL from the vicinityof the Northwind Ridge and eastward penetration (possi-bly by double-diffusive intrusions) into the central basin(McLaughlin et al. 2004).

In the Eurasian Basin, the validity of the 4/3 flux lawremains to be examined; for this we can compare the mag-nitudes of FM and FH . For example, for values of δθ in theEurasian Basin, application of Kelley’s 4/3 flux law yieldsa heat flux of 0.73 Wm−2. To support a molecular heat fluxof this magnitude, interfaces would need to be as thin as0.05 m. However, ITP measurements indicate they are typ-ically a little more than 1 m thick (Fig. 4b). It is possiblethat due to the thicker interfaces, rotation plays an impor-tant role in double-diffusive convection here, which is notaccounted for in Kelley’s 4/3 flux parametrization (Kelley1987; Carpenter and Timmermans 2014). This could bethe case since the Ekman layer thickness of a laminar in-terface (≈ 0.1 m for the Eurasian Basin) is significantlysmaller than the interface thickness (Carpenter and Tim-mermans 2014). On the other hand, we cannot rule out thepresence of small mixed layers within what we are takingto be the thicker Eurasian Basin interfaces given the rela-tively coarse resolution of the profiles, in which case a 4/3flux parametrization may apply. In the absence of betterresolved interfaces, we restrict application of the 4/3 fluxlaw to the Canada Basin.

By computing the molecular heat flux through each in-terface using the change in potential temperature acrosseach interface and the resolved interface thickness, av-eraged per profile, we find molecular heat fluxes ofO(0.01 Wm−2) in the Eurasian Basin (Fig. 10b). The

lower heat fluxes in the Eurasian Basin compared to theCanadian Basin are not consistent with the expectationthat higher Ra in the Eurasian Basin would yield largerheat fluxes (due to the relationship between Ra and a con-vective heat flux, although this exact relationship is un-clear). It is also important to note that the low values ofRρ in the Eurasian Basin could indicate that actual fluxesare larger than the FM estimates (based on molecular diffu-sion acting on the resolved gradients) due to the increasingdisturbance of the interfaces by turbulence.

6. Summary and Discussion

Properties of the AWL and double-diffusive staircase atits top boundary have been analyzed using ITP data fromacross the Arctic Basin collected between 2004 and 2013.For the first time, this study takes advantage of the highvertical resolution ITP data sampling the detailed struc-ture of the thermohaline staircase laterally across the en-tire Arctic. As Atlantic Water circulates around the Arc-tic Basin, its maximum core potential temperature andsalinity decrease, as expected. The bulk density ratio,Rρ , is lowest in boundary regions of the Eurasian Basinwhere the AWL is warmest, and increases along the cy-clonic pathway of the AWL around the Arctic Basin.There is no apparent relationship between Rρ and staircasemixed layer thicknesses across the basin. Well-definedmixed layers exist throughout the majority of the centralArctic Basin, while an absence of mixed layers is mostpronounced along boundaries and in the interior of theEurasian Basin. It is not known whether the lack of a stair-case structure is due to the dominance of turbulent mixingover double diffusion. Furthermore, in the absence of adouble-diffusive flux to maintain the staircase structure,staircases would not persist very long: an interface wouldincrease in thickness by molecular conduction alone byabout 20 cm in 1 day, thereby smoothing out the profileand reducing the distinct staircase structure.

In the Canadian Basin, using a double-diffusive 4/3 fluxlaw parametrization, the distribution of vertical heat fluxesthrough the staircase is estimated to be O(0.1) Wm−2.Interfaces appear to be approximately resolved in theEurasian Basin, where we conclude that the 4/3 flux lawdoes not yield an appropriate representation of heat fluxes.Molecular heat fluxes in the Eurasian Basin are estimatedto be O(0.01) Wm−2, which are at least one order of mag-nitude smaller than heat fluxes reported by Polyakov et al.(2012) and Guthrie et al. (2015) for the region. How-ever, it is unclear if Eurasian Basin heat fluxes are well-represented by a laminar molecular heat flux calculationat such low Rρ . The discrepancy in heat fluxes betweenthe two basins is counterintuitive, as fluxes in the EurasianBasin are smaller where the source water is warmer. Fu-ture work will investigate possible explanations for thisdiscrepancy.

J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 7

Further questions remain as to the transition from lami-nar to turbulent interfaces. Future work will examine DNSresults of heat fluxes for interfaces at low Rρ in relationwith measured heat fluxes to determine the limitations of4/3 flux parametrizations in an ocean setting. Additionaldata at higher vertical resolution are necessary for closerinspection of interfaces in the Eurasian Basin.

Acknowledgments. The Ice-Tethered Profiler data werecollected and made available by the Ice-Tethered Pro-filer Program (Toole et al. 2011; Krishfield et al. 2008a)based at the Woods Hole Oceanographic Institution(http://www.whoi.edu/itp). Funding was provided by theNational Science Foundation Division of Polar Programs.

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Carmack, E., and Coauthors, 2015: Toward quantifying the increasingrole of oceanic heat in sea ice loss in the new Arctic. Bull. Amer.Meteor. Soc., 96 (12), 2079–2105, doi:10.1175/BAMS-D-13-00177.1.

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Padman, L., and T. M. Dillon, 1987: Vertical heat fluxes throughthe Beaufort Sea thermohaline staircase. J. Geophys. Res.: Oceans,92 (C10), 10 799–10 806, doi:10.1029/JC092iC10p10799.

Padman, L., and T. M. Dillon, 1988: On the horizontal extent of theCanada Basin thermohaline steps. J. Phys. Oceanogr., 18 (10), 1458–1462, doi:10.1175/1520-0485(1988)018〈1458:OTHEOT〉2.0.CO;2.

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J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 9

30 31 32 33 34 35Salinity

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

θ (�C

)

25 26 27

-2 -1.5 -1 -0.5 0 0.5 1 1.5θ

0

100

200

300

400

500

600

700

800

Dep

th (m

)

30 31 32 33 34 35Salinity

0

100

200

300

400

500

600

700

800

Dep

th (m

)

(a) (b)

(c)

(�C )

FIG. 1. (a) Potential temperature θ (◦C) and (b) salinity profiles in the central Eurasian Basin (red), where the θmax of the AWL is around 300 mdepth, and central Canadian Basin (blue), where the θmax of the AWL is around 400 m. (c) The same representative profiles in θ −S space from theEurasian Basin (red) and Canadian Basin (blue). Isopycnals are labelled, and the dashed red line is the freezing line. Profiles are from Ice-TetheredProfiler measurements in spring 2008.

10 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

70˚N

75˚N

80˚N

85˚N

180W̊

90˚W

0˚

90E̊

A

B

C

D

2004 2006 2008 2010 2012Year

0

500

1000

1500

2000

2500

3000N

umbe

r of p

rofil

es (u

pcas

ts o

nly)

(a) (b)

FIG. 2. (a) Locations (black dots) and (b) temporal distribution (in bins of 1 year) of ITP profiles used in this study. ITP up-going profilesreturned between 2004 and 2013 are analyzed here (a total of ≈ 15,800 ITP profiles with a vertical resolution of ≈ 25 cm). Red letters (A, B, C,D) in (a) correspond to the profiles shown in Fig. 3.

J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 11

-2 -1.5 -1 -0.5 0 0.5 1 1.5θ (° C )

0

100

200

300

400

500

600

700

800

Dep

th (m

)

-0.2 0 0.2 0.4 0.6

140

150

160

-2 -1 0 1 2θ (° C )

0

100

200

300

400

500

600

700

800D

epth

(m)

-0.5 0 0.5 1

150

160

170

-2 -1.5 -1 -0.5 0 0.5 1θ (° C )

0

100

200

300

400

500

600

700

800

Dep

th (m

)

-1 -0.5 0

240

250

260

-2 -1.5 -1 -0.5 0 0.5 1θ (° C )

0

100

200

300

400

500

600

700

800

Dep

th (m

)

-0.8 -0.6 -0.4 -0.2

210

220

230

(a) (b)

(c) (d)

FIG. 3. Four potential temperature (◦C) representative profiles (locations marked in Figure 3(a)): (a) in the central Eurasian Basin (A: ITP 56,29 May 2012), (b) at the boundary of the Eurasian Basin (B: ITP 7, 29 Sep 2007), (c) at the boundary of the Canadian Basin (C: ITP 8, 23 May2009), and (d) from the central Canadian Basin (D: ITP 1, 26 Jun 2006), indicate the appropriate thermocline region in various areas of the ArcticBasin. Given these differences, in order to properly quantify the double-diffusive staircase, a unique “lower depth” of the 50-m staircase interval(marked by green stars from the profiles shown) was determined for each ITP. Blue stars delineate the shallow bound. The red star indicates theAWL θmax in each profile. Insets in each panel show a zoom-in of the potential temperature profile in the 50-m depth interval.

12 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

-0.65 -0.6 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3θ (° C )

210

215

220

225

230

Dep

th (m

)

0 0.1 0.2 0.3 0.4θ (

145

150

155

160

165

170

Dep

th (m

)

(a) (b) ° C )

FIG. 4. (a) Potential temperature, θ (◦C), profiles in the staircase region in (a) the Canadian Basin and (b) the Eurasian Basin. Interfaces aretoo thin to be resolved in the Canadian Sector. Interfaces can be resolved with ITP measurements in the Eurasian sector, as more data points arereturned between mixed layers than in the Canadian Basin. Blue dots indicate ITP data points approximately every 25 cm. Green stars indicate thebeginning and end of the staircase region, while red stars indicate the beginning and end of respective mixed layers.

J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 13

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.5

0.75

1

1.25

1.5

1.75

2

θm

ax (ºC)

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

34.8

34.82

34.84

34.86

34.88

34.9

Salinity at θ

max

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

250

300

350

400

450

500

Depth (m

) at θm

ax

70˚N

75˚N

80˚N

85˚N

180˚W

0˚

90˚E

2

3

4

5

6

7

8

9

90˚W

Rρ

(a) (b)

(c) (d)

FIG. 5. (a) Map of θmax (◦C) across the Arctic Basin. (b) Map of salinity at θmax. (c) Map of depth (m) at θmax. (d) Map of Rρ . As AtlanticWater circulates around the basin, its core θmax and salinity at core θmax decreases, while its depth at core θmax and Rρ increases. Changes in theproperties of θmax are due to both downwelling and mixing.

14 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

β∆S ×10-4

0

0.5

1

1.5

α∆θ

×10-4

0 2 4 6 8 10Rρ

0

0.05

0.1

0.15

0.2

0.25

0.3

PD

F

1 2

4

7

10

0 1 2 3 4 5 6(a) (b)

FIG. 6. (a) Scatter plot of α∆θ vs. β∆S with contours of Rρ overlain. Large values of Rρ (appearing as a lower branch in the plot) are found inthe Canadian Basin, while low values of Rρ (upper branch) are found in the Eurasian Basin. Values of Rρ > 10 have been excluded. (b) PDF of Rρfor all profiles. The two main peaks (with Rρ ≈ 3 and Rρ ≈ 6) generally correspond to the Eurasian Basin and the Canadian Basin, respectively.The greater density of Rρ ≈ 6 observations (compared to those with Rρ ≈ 3) is a result of more ITP profiles in the Canadian Basin. The bin widthis 0.1.

J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 15

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

70˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.5

1

1.5

2

2.5

3

75˚N

h (m)

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.6

0.8

1

1.2

1.4

δh (m)

(a) (b)

(c)

FIG. 7. (a) Map indicating presence (blue) or absence (yellow) of a well-defined double-diffusive staircase. Well-defined mixed layers existthroughout the majority of the central Arctic Basin, with an absence of mixed layers most pronounced along boundaries of the Eurasian Basin.(b) Map of mean mixed layer thickness, h (m). There is no apparent spatial pattern in h. (c) Map of mean interface thickness, δh (m). Interfacethicknesses in the Eurasian Basin do not exhibit a distinctive pattern.

16 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y

0 0.1 0.2δθ (°C)

0

50

PD

F

0 0.02 0.04δS

0

50

100

150

PD

F

0 2 4h (m)

0

0.5

1

PD

F

0 5 10 15Mean Rρ

0

0.2

0.4P

DF

6 8 10log10Ra

0

0.5

PD

F

0 0.1 0.2δθ ( °C)

0

10

20

30

PD

F

0 0.02 0.04δS

0

50

100

PD

F

0 2 4δh (m)

0

0.5

1

1.5

PD

F

0 2 4h (m)

0

0.5

PD

F

0 5 10 15Mean Rρ

0

0.5

PD

F

6 8 10log10Ra

0

0.5

1

PD

F

(a) (b)

0.04 ± 0.01

1.9 ± 0.7

8.6 ± 0.6

5.4 ± 1.7

0.01 ± 0.003 0.06 ± 0.02

2.3 ± 0.7

8.9 ± 0.5

0.01 ± 0.006

4.1 ± 1.5

1.1 ± 0.3

FIG. 8. PDFs of δθ (◦C), δS, δh (m), h (m), mean interface Rρ over a profile (distinct from Rρ ), and Ra in (a) the Canadian Basin and (b) theEurasian Basin. Bin sizes are 0.01 ◦C, 0.003, 0.25 m, 0.25 m, 0.5, and 0.5, respectively. The mean value (± 1 standard deviation) is given on eachpanel.

70˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

75˚N

δθ (˚C)

70˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.006

0.008

0.01

0.012

0.014

0.01675˚N

δS

(a) (b)

FIG. 9. (a) Map of mean potential temperature difference across interfaces, δθ (◦C). (b) Map of mean salinity difference across interfaces, δS.

J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y 17

70˚N

75˚N

80˚N

85˚N

180˚W

90˚W

0˚

90˚E

0.01

0.015

0.02

0.025

0.03

0.035

0.04

FM (W

m-2)

70˚N

75˚N

80˚N

85˚N

180˚W90˚W

0˚

90˚E

0

0.05

0.1

0.15

0.2

0.25

0.3

FH (W

m-2)

(a) (b)

FIG. 10. Heat fluxes (Wm−2) in (a) the Canadian Basin (computed using the 4/3 flux law) and (b) the Eurasian Basin (computed as a molecularflux across interfaces). Heat fluxes in the Canadian Basin are O[(0.1) Wm−2], with the highest values near the eastern Lomonosov Ridge. Heatfluxes in the Eurasian Basin are O[(0.01) Wm−2].