3.1. Structure of the Deep Waters
 A schematic of the deep Canada Basin and the processes affecting the water there is shown in Figure 2a. CBDW appears as a thick, near-homogenous bottom layer extending from ∼2700 m to the bottom (Figure 2b). Above lies an ∼300-m-thick deep transitional layer (DTL) that is characterized by a temperature–salinity step structure, and the top of this layer is marked by a temperature minimum (Tmin) at ∼2400 m, the sill depth at Cooperation Gap on the Alpha-Mendeleyev Ridge complex. The staircase structure, through which both the mean temperature and mean salinity increase with depth, is observed at all stations across the entire basin and has been a persistent feature for at least two decades and is shown in Figure 2c for 2003 and 2010. The step structure is typically characterized by three to four mixed layers that are 10–60 m thick and are separated by 2–20 m-thick interfaces over which changes are δθ ∼ 0.003°C and δS ∼ 0.0007 [see Timmermans et al., 2003]. The θ/S properties of the deep basin (Figure 2d) show that stratification below the Tmin is marginally stable with respect to density calculated at 3000 m and that those of the Tmin itself closely match those of the Makarov Basin at sill depth, pointing to this as the likely source maintaining the Tmin layer [Timmermans et al., 2003]. For any given year the θ of CBDW within the deep basin is laterally near-uniform, varying by less than 0.0007°C across the full study area, reflecting the isolation of the basin and also the ubiquity of geothermal heating. The θ of the Tmin, however, shows greater spatial variability, as discussed below within contexts of circulation and renewal.
Figure 2. (a) Schematic of Canada Basin Bottom Water (CBDW) structure and processes; MB is the Makarov Basin, A/M is the Alpha Mendeleyev Ridge, CB is the Canada Basin, Slope is the continental slope in the south and east. E and D are entrainment and detrainment associated with a hypothetical descending plume of cold salty water from the shelf. (b–d) Changes in potential temperature (red), salinity (blue) and density in the central Canada Basin at JOIS station CB-15 at 77N, 140W (see Figure 1b, green dot) in 2003 (thin lines) and 2010 (thick lines). The profile from 2000 m to the bottom is shown in Figure 2b, the deep transitional layer (DTL) from 2450 to 2750 m is shown in Figure 2c and potential temperature vs. salinity is shown in Figure 2d with contours of potential density referenced to 3000 db.
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3.2. Temporal Trends and Spatial Variation
 The time sequence of potential temperature (θ) profiles in the deep Canada Basin from 2002 to 2010 reveals the steady increase in temperature of the CBDW (Figure 3). As shown below, this rate of warming is consistent with, but slightly less than, the geothermal heat flux. A least-squares fit to all available CBDW temperature data from 1993–2010 for stations deeper than 3000 m gives a rate of warming of ∼0.0004°C/yr; a similar rate of warming is observed in the Tmin, although there is a much larger spatial variation (Figure 4a). A least-squares fit to the associated salinity data from 1993 to 2010 shows no discernable trend for either the CDBW or the Tmin (Figure 4b).
Figure 3. Time series from 2002 to 2010 of potential temperature (θ) profiles in the deep Canada Basin showing the increase in temperature of CBDW over time. The profile plotted for each year is the average profile for all JOIS stations in that year that have water depths greater than 3000 m.
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Figure 4. Times series from 1993 to 2010 for average values of (a) potential temperature and (b) salinity for the CBDW and Tmin. The average for each year is the average of all JOIS data for casts with bottom depths greater than 3500 m. The error bars denote 2x the standard deviation of the station to station variation rather than the accuracy of the data. The accuracy of the data is discussed in the text.
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 Stations above the slope in the south and east of the Canada Basin show CBDW temperatures warmer than those in the deep basin (Figure 5). In this plot temperatures have been normalized by removing the temporal trend and are shown as an anomaly referenced to temperatures below 3500 m. This analysis shows that stations with bottom depths of 3000 m are ∼0.0020°C warmer than the deep basin and stations with bottom depths of 2700 m are ∼0.0032°C warmer. This is because, for a uniform heat flux, a shallower bottom layer will warm faster. The key point here is that heat from the deep basin will not diffuse laterally into the shallower, warmer water over the slope.
Figure 5. A plot of bottom depth versus CBDW temperature for JOIS cruises 2003–2010 showing the increase in CBDW temperatures with decreasing bottom depth. Each profile is normalized such that the average CBDW temperature for each year, for stations with bottom depths greater than 3500 m, has been subtracted from the profile to remove the warming trend.
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3.3. Heat Budget Considerations
 The homogeneity of CBDW suggests a relatively short time-scale for vertical convection. Wüest and Carmack  give a rotating convective vertical velocity scale w* = 2.4(gαFg/ρcpf)0.5, where g is acceleration due to gravity, α is the thermal expansion coefficient, cp is the specific heat capacity, ρ is density, and f is the Coriolis parameter. Applying this formula yields a w* of 0.8 mm s−1; thus for the 1000 m-thick CBDW the time-scale for convection is calculated to be ∼15 days. This value suggests rapid mixing of the CBDW, particularly in relation to its isolation age.
 If geothermal heat were to remain trapped within the bottom layer, the layer would either become thicker or the temperature of the layer would increase. Examination of data from 2002 to 2010 (not shown) reveals no significant change in CBDW thickness. This is to be expected as the overlying DTL is primarily salt-stratified. If an input of geothermal heat Fg ∼ 50 mWm−2 [Langseth et al., 1990] remains in the bottom layer, the potential temperature of this layer θB with a thickness HB ∼ 1000 m (the volume-weighted mean thickness [see, e.g., Aagaard et al., 1985]), will increase according to dθB/dt = Fg/ρcpHB, where ρ = 1040 kg m−3 is the density and cp = 3900 J kg−1 °C−1 is the specific heat capacity. Applying this equation, and using the estimated geothermal heat flux of 50 mWm−2, suggests that θB will increase by ∼0.0004°C yr−1, or about 0.0032°C between 2003 and 2010. This rate of warming is consistent with the best fit of temperature data in CBDW shown in Figure 4, implying that the substantial fraction of geothermal heat remains in the deep layer. The potential temperatures at Tmin (θM) and within the DTL also increase by a similar amount, and thus the same potential temperature difference is maintained between θB and θM from year to year (Figure 4). Applying the above equation to the ∼300 m thick DTL we find that an additional heat flux of 10–15 mWm−2 is required to explain the observed warming. Thus, by these calculations, a total geothermal heat flux of 60–65 mWm−2 is needed, and this is within the range of 40–60 mWm−2 given by Langseth et al. . Hence, we can conclude that the reported geothermal heat flux can be accounted for by warming of the bottom and deep transitional layers.
3.4. Double Diffusive and Thermobaric Convection
 The temperature and salinity structure of the deep transitional layer (DTL), with cool fresher water above warmer and more saline water is conducive to double diffusive convection and thus to the formation of the observed staircase structure [Turner, 1968; Timmermans et al., 2003]. The stability of double-diffusive interfaces is defined in terms of the density ratio Rρ = βδS/αδθ; where α = −ρ−1 δρ/δT, β = −ρ−1 δρ/δS and ρ is density [Turner, 1973]. As noted by Timmermans et al.  the mean Rρ value for interfaces within the deep transitional layer is ∼1.6, a value conducive to strong double diffusive convection. Values of Rρ at the base of the DTL are smaller yet and thus conducive to even larger double diffusive fluxes.
 In the absence of direct, microstructure-based heat flux measurements, heat flux FH through a diffusive layer interface may be estimated using laboratory-derived flux laws [e.g., see Kelley, 1990; Polyakov et al., 2012] in which heat flux is given by the product of an empirically derived function of Rρ and the change of potential temperature across the diffusive interface δθ to the 4/3 power. Kelley  proposed the following relationship , where Pr = ν/κ is the Prandtl number, ν = 1.89 × 10−6 m2 s−1 is the kinematic viscosity, κ = 1.28 × 10−7 m2 s−1 is the thermal diffusivity, and g = 9.8 m s−2. From over 200 profiles collected between 2003–2010 in the Canada Basin the interface thickness through the DTL ranged from between 2 and 20 m, over which δθ averages ∼0.003°C and δS averages ∼0.0007 psu, while mixed-layer thicknesses are between 10 and 60 m. This yields average double diffusive heat fluxes through the multiple layers of the DTL of FH ∼ 45 mWm−2, which supports the argument that some of the vertical heat loss from the geothermally heated CBDW escapes by double diffusion. However, these values are even larger than required to match the observed warming rate of the DTL, being almost equivalent to the full geothermal heat flux estimate and more three times that which is observed in terms of DTL warming. They arise from the relatively low values of Rρ used above. However, as noted above and by Timmermans et al. , the observed values of interface thickness are much greater than typical values reported from microstructure profiles through active DL interfaces, raising some doubt that the diffusive instability is continuously active [cf. Padman and Dillon, 1987; Howard et al., 2004]. We thus assume that the double diffusion is intermittent or is influenced by additional processes such as shear instabilities or differential diffusion [Polyakov et al., 2012; Gargett and Ferron, 1996] .
 Nonetheless, the step structure is robust, as steps are found in nearly every profile, and so they are being maintained in spite of the tendency of diffusion to smooth them. If the processes creating the steps were not active, the steps would be eradicated by diffusion over a time scale τ = (H/2)2/2κ, where H is the step thickness. Using H = 40 m, and the molecular value for thermal diffusivity given above, yields a time scale of 50 years. However, the thermal diffusivity may be higher than molecular in the deep basin. For example 14C data lead to a diffusivity estimate of 4 × 10−5 m2s−1 [Macdonald et al., 1993], which gives a time scale of 2 months to eradicate the steps.
 Because the temperatures of CBDW and the DTL are increasing at approximately the same rate and salinities are remaining constant, the δθ/δS slope through the DTL has remained near-constant throughout the period of observation. This could be either coincidence or could signal a feedback mechanism that regulates vertical heat flux. Also, because the δθ/δS slope is very weakly stable for densities referenced to 3000 m, the potential exists for a convective process arising from the differential compressibility of water [Fofonoff, 1961; McDougall, 1987]. Since cold water is more compressible than warm water, a conditional instability (the thermobaric instability) occurs when a temperature interface where colder water overlying warmer water is displaced to a depth where the density of the underlying warm water is less dense than the cold water above [cf. Carmack and Weiss, 1991; Adkins et al., 2005]. Further, an interface can be preconditioned for the onset of thermobaric instability by either cooling from above or heating from below. In the present case, a two stage process may be required to trigger the thermobaric instability: first, steady warming of the CBDW end member relative to the base of the overlying DTL to decrease its density (referenced to local pressure) relative to that of the overlying water; and second, a descending motion of the interface to compress the overlying cold water more than the underlying warm water, thus making it denser and triggering thermobaric instability.
 Are geothermal heating rates and vertical displacements within the DTL sufficient to trigger the thermobaric instability? Figure 2d shows that a warming of ∼0.001°C of CBDW, requiring only 2 to 3 years of geothermal heating, would be required to trigger the thermobaric instability, assuming that the DTL remained unchanged. Vertical displacements within the DTL were measured by Timmermans et al.  using recording thermometers deployed within the deep transitional layer and they found typical vertical excursions at near-inertial frequency of 10–20 m, which they attributed to the very weak stratification. Timmermans et al.  noted larger excursions of up to 1040 m associated with topographic Rossby waves. Thus as temperatures within the bottom layer increase, and tilt the deep δθ/δS slopes closer to the critical gradient for instability, these vertical motions may be sufficient to trigger intermittent thermobaric overturning cells. The thermobaric overturning mechanism may also sharpen interface gradients, and may thus enhance conditions for double diffusive transfer.