In order to assess the mechanisms behind AABW transformation and circulation variability, a fully closed WMT budget is desirable. To calculate this, we must first close the temperature and salinity budgets. WMT volume budget analysis was conducted using Estimating the Circulation and Climate of the Ocean (ECCO), Southern Ocean State Estimate (SOSE), and Simple Ocean Data Assimilation (SODA) reanalysis data. In all of these cases, the ocean is divided into discrete layers σ̃n, and each of the relevant terms is calculated inside these discrete layers. The discrete analog of the cumulative volume integral (Eq. ) is 10V(σ̃n,t)=∑i,j,kΔVH(σ̃n-σ), where the summation is over each model grid cell within the region of interest and ΔV is the finite volume of each cell. Henceforth, we use the shorthand V=cumsumσ(ΔV) to denote this operation.

The time rate of volume change was computed and balanced by the calculated σ total tendency (Ωtottend) and a residual (R1) due to the discretization of isopycnal layers: 11∂V∂t=Ωtottend+R1, where 12Ωtottend=-∂∂σ̃cumsumσ(Gtottendσ) and where Gtottendσ=(∂σ/∂θ)Gtottendθ+(∂σ/∂S)GtottendS is the model's total tendency for potential density, a weighted sum of total tendencies for temperature and salinity. This term is the sum of conservative tendencies due to horizontal and vertical advection, non-conservative tendencies due to horizontal and vertical diffusion and surface forcings (including shortwave penetration for the potential temperature component). It is helpful to calculate R1 explicitly in order to determine if the chosen σ bin size is appropriate. We found that the budgets were not sensitive to changing σ bin sizes. Smaller bin sizes meant higher resolution; however, that did not significantly change R1 and increased computational costs.

Next, the total advection tendency term (Ψadv) is decomposed to σ's velocity component (Ψvel) and a residual term (R2) attributed by a yet-to-be-determined combination of numerical mixing and numerical cabbeling effects: 13Ψadv=Ψvel+R2. The term 14Ψadv=-∂∂σ̃cumsumσ∂σ∂θGadvθ+∂σ∂SGadvS represents the direct effect, as output from the models, of the advection of temperature and salinity on the total tendency of potential density in each grid cell, while 15Ψvel=-cumsumσ(u⋅n^δA) is the net transport across the region boundary, accumulated in σ̃n bins; this is the conventional overturning streamfunction. In the continuous world, Ψadv and Ψvel can be shown to be mathematically identical. However, numerical discretization of the advection operator yields a residual term representing non-advective affects of the advection scheme. This residual has in fact been used to quantify numerical mixing in other studies . Separating out the numerical residual allows us to explicitly see the volume transport of certain densities by purely physical inflow/outflow mechanisms and by a mixing term.

Water mass transformation, Ωtf, was computed by summing the rest of the tendency terms due to non-conservative, thermodynamic processes such as diffusion, shortwave radiation and surface forcings of heat and freshwater: 16Ωtf=-∂∂σ̃cumsumσ[∂σ∂θ(Ghdiffθ+Gvdiffθ+Gsurfθ+Gswθ)+∂σ∂S(GhdiffS+GvdiffS+GsurfS)].

By defining residuals in this way, we arrive at a numerical form of Eq. () below, which is closed by construction: 17∂V∂t=Ψvel+R2+Ωtf+R1.

Since R2 represents numerical mixing, we can more concisely write Eq. () to be 18∂V∂t=Ψvel+Ω∗+R1, where 19Ω∗=Ωtf+R2.

We can even further decompose the various Gsurf terms by breaking them into different sub-components. One such analysis we do here is to separate GsurfS into a component directly related to sea ice and a component due to direct exchange of freshwater with the atmosphere and land, as done also by . We found a minimal contribution of E–P–R to surface salt fluxes and a dominant role from sea ice activity. Specifically, we saw brine rejection activity throughout most of the season until summer when there were spikes in ice melt during a few summer months (amplitude usually matching the highest brine rejection spike). SODA does not provide any tendency diagnostics; however, it does provide the velocity field. Thus, in SODA we simply define Ω∗ via the residual: Ω∗=∂V/∂t-Ψvel.

Equation () represents the WMT volume budget expressed by explicit terms due to physical and thermodynamic processes captured by the model. Now we can see the time rate of volume change is balanced by the physical transport into and out of the WG, plus the residual mixing term, the transformation term and the numerical discretization residual. Subsequent plots in Sects. , and display each term's contribution to the total WMT volume budget.

We used observational temperature and salinity as a baseline for validating the use of each model. The evaluation of each model compared with observations is in Sect. . The observational temperature and salinity data are from the World Ocean Atlas 2013 (WOA) . WOA is a set of objectively analyzed 1∘ gridded climatological fields of in situ temperature and salinity. The 1∘ climatological fields averaged over 2005–2012 are presented in this paper as a means for model validation assessment.

Temperature and salinity profile data were obtained from bottled samples; ship-deployed conductivity–temperature–depth (CTD); mechanical, digital and expendable bathythermographs (XBT); profiling floats; moored and drifting buoys; gliders; undulating oceanographic recorder (UOR); and pinniped mounted CTD sensors. WOA contains both observed-level profile data and standard depth profile data with various quality control flags applied. In most regions with sparse data coverage, such as the WG region, flagged data seen as outliers were not removed because they may still represent legitimate values, and they are therefore, included in the climatological periods used here .

ECCO version 4 release 3 state estimate is a reconstruction of the 3-D time-varying ocean and sea ice state . Produced from MITgcm, ECCO has an approximately 1∘ horizontal grid resolution and 50 vertical levels of varying thickness. It provides monthly-averaged 3-D ocean, sea ice and air–sea flux fields; 2-D daily-averaged ocean and sea ice fields; and 6-hourly atmosphere fields, all covering the period 1 January 1992 to 31 December 2015.

The ECCO state estimate provides a statistical best fit to observational data; however, unlike other ocean reanalyses that directly adjust the model state to fit the data, such as SODA, described in Sect. , ECCO is a free-running model that simulates what is observed in the ocean based on the governing equations of motions, a set of initial conditions, parameters and atmospheric boundary conditions. Some observational data ECCO uses are from Argo floats, shipboard CTD and XBT measurements, marine mammals, mooring data, the Radar Altimeter Database System, satellite products from the National Snow and Ice Data Center (NSIDC), and programs such as SSM/I DMSP-F11 and SSM/I DMSP-F13 and SSMIS DMSP-F17 .

The ECCO state estimate satisfies physical conservation laws, with no unidentified sources of heat and buoyancy. Due to the model's dynamically consistent nature, it conserves heat, salt, volume and momentum ; the state estimate can be used to explore the origins of ocean heat, salt, mass, sea ice and regional sea level variability . It uses a nonlinear free surface combined with real freshwater flux forcing and the scaled height coordinate, and users of ECCO are able to assess model–data misfits . Known issues of the state estimate are mentioned for the first release in . For example, ECCO has residual systematic errors, especially in regions with sparse data .

SOSE is a model-generated best fit for Southern Ocean observations . It is a solution to the MITgcm, constructed in spherical coordinates with 42 vertical levels of varying depth (m) and a C-gridded dataset at a 1/6∘ horizontal resolution, available at timestamps daily and annually . Its iteration runs at 5 d averages starting from 1–5 January 2005 and ending on 31 December 2010.

SOSE is also a data-assimilating model. It uses similar observation data as ECCO. Observations of daily sea ice concentration have been attained from the NSIDC. Some limitations are similar to that of reanalyses with regard to regions and variables being more reliable, with more observations covered in those areas, and the opposite being true for regions with sparse data. SOSE provides a self-consistent state estimate that satisfies momentum, volume, heat and freshwater conservation. Some of its key strengths are that SOSE has a better spatial and temporal resolution than most state estimate models and is the highest-resolution model used in this study. It is dynamically consistent and best-fit to the available 190 observations, and its biases are well-documented .

This study examines the Weddell Sea region, and so far one major bias has been found during our analysis: SOSE produces an open-ocean polynya in the first year of its run (2005) which was not observed in the real ocean; therefore, this year is removed from the time mean and climatology, but the anomalous interannual variability still includes the year 2005.

SODA ocean/sea ice reanalysis is the third numerical model used for our water mass transformation analysis. The SODA3 reanalyses are built on the Modular Ocean Model, version 5, ocean component of the Geophysical Fluid Dynamics Laboratory CM2.5 coupled model , with fully interactive sea ice at a 0.25∘ × 0.25∘ horizontal and 50-level vertical resolution . The sea ice data are taken from the Geophysical Fluid Dynamics Lab's Sea Ice Simulator model . They do not include flow of ice from continental regions into the ocean, including ice shelves and their interaction with the ocean. Improvements have been made in SODA3 such as upgrades to the sea surface temperature (SST) datasets and a 40 % increase in hydrographic data from the latest release of the World Ocean Database. Earlier generations of ocean reanalysis have contained systematic errors that have several sources, including measurement bias, inaccurate model physics and numerical resolution, and biases in fluxes and initial conditions. The release of SODA3 was an effort to address these broad issues; for example, the adoption of the iterative flux correction procedure of addresses the bias in surface forcing in which flux error is estimated from the misfits obtained from an initial ocean reanalysis to alter fluxes for a revised ocean reanalysis. SODA3 was also upgraded to be an ensemble reanalysis, for which the ensemble spread provides an estimate of uncertainty. A comparison to ORAS5 and ECCO is provided in .

SODA3 is included with finer eddy-permitting spatial resolution, active sea ice and bias adjustment. The version this study uses is SODA3.4.2 (SODA henceforth), which means that the assimilated data are restricted to the basic hydrographic data and SST with meteorological forcing derived from the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) daily average surface radiative and state variables and the COARE4 bulk formula with flux bias correction applied. The ocean and ice data run every 5 d from 4 January 1993 to 19 December 2019 and the transport files every 10 d from 7 January 1993 to 17 December 2019. There were jumps in the salt field from the ocean files occurring before 1997 that we suspect are the result of the reanalysis's nudging technique. For this reason, we have used SODA running from 15 February 1997 to 17 December 2019.

The biggest difference between SODA, ECCO and SOSE is their method of data assimilation. ECCO and SOSE use the adjoint data assimilation method, which optimizes the initial conditions and model parameters by incorporating observation data to a physics-based numerical simulation. The SODA experiment uses an optimal interpolation method for their data assimilation, in which the ocean state is constructed from a forecast using a linear deterministic sequential filter and based on the difference between observations and the forecast mapped onto the observation variable and its location . Due to the method of data assimilation, it is not possible to diagnose a closed heat budget in SODA, and therefore we cannot explicitly calculate Ω. However, we can calculate ∂V/∂t and Ψ. So in the following analysis, we infer Ω as a residual.

It is well known that numerical models struggle to capture the complex physics on the Antarctic shelves that determine AABW properties and circulation . Although these models assimilate data, they are still constrained by their resolution and physical parameterizations. In this section we assess each model against the World Ocean Atlas data. This step gives a base for assessing each model's reliability in simulating ocean physics in a region with limited observational data, such as the Weddell Sea region. Such validation was assessed by comparing bottom temperature and salinity spatial distributions, as well as time-averaged temperature–salinity (TS) distributions, in the WG region between ECCO/SOSE/SODA and WOA. ECCO and SODA were averaged over the same time period as the WOA product (2005–2012) except for SOSE, whose time period only spans 2005–2010. Noting that the time period between SOSE and observation is different, we still execute the comparison with what is available but recognize that this introduces unknown biases to our comparison. The boundaries of the WG region are defined here to be from 65∘ W to 30∘ E and from 78 to 57∘ S .

Figure a, c, f and i show the time mean bottom temperatures in the WG region for WOA (2005–2012), ECCO (2005–2012), SOSE (2006–2010) and SODA (2005–2012), respectively. The coldest temperatures in each model are located near the coast of Antarctica and gradually become warmer equatorward, with signatures of the Antarctic Circumpolar Current (ACC) present in the upper left. However, in ECCO there appears to be a strip of relatively warmer water enclosing the coldest temperatures before the more gradual equatorward warming is displayed. Showing the temporal standard deviation of temperature, which we use as a proxy for the (unknown) reanalyses uncertainties, in Fig. d, g and j from ECCO, SOSE and SODA, respectively, we can see that in ECCO and SODA (Fig. d and j) there is little spatial variability in bottom temperature, whereas in SOSE (Fig. g), there is a lot of variability in the open region of the Weddell Sea. Furthermore, looking at the difference in temperature between each model and WOA (Fig. e, h and k), we also see that ECCO and SODA are overall warmer than observations (Fig. e and k). From ECCO and SODA, the difference is as high as 2 ∘C; however, in SODA, the model on average simulates colder bottom temperatures along the Antarctic Peninsula (Fig. k). In SOSE, however, there is less of a difference between simulated and observed temperature (Fig. h). The hatched region denotes the places where the difference between modeled and observed temperatures is less than the standard error of the observational estimates; and as we can see in SOSE (Fig. h), the model's bottom temperature agrees with WOA in the open ocean.

Following a similar assessment for bottom salinity, the spatial distribution of salinity in all three models and WOA appears to be more uniform than their respective temperature fields. The distribution in SOSE (Fig. f) indicates that the model is on average fresher than the others. Another distinction that stands out is the more variable spatial distribution in ECCO and SODA's salinity field (Fig. c and i, respectively), with fresher water located closest to the coast of the continent. In ECCO, however, there are saltier plumes around 40∘ W (Fig. c), just north of where the Filchner–Ronne Ice Shelf would be, indicating that ECCO is reproducing High Salinity Shelf Water (HSSW) in around the same areas present in the observational data (Fig. a). Looking at the temporal deviations, we see in ECCO and SODA little variability overall in bottom salinity (Fig. d and j). In SODA, however, there is a significant sliver of variability in the eastern part of the region along the coast. In SOSE (Fig. g), there are strong temporal deviations from the average salinity field along the coast of the peninsula. In Fig. e and k, there is very little difference between model and observational bottom salinity, as is indicated by black hatching. The biggest difference we see between model and observed salinity is between SOSE and WOA. As we saw from Fig. f, SOSE is much fresher than what is observed and simulated in the other models by about 0.5 psu.

To further test the validity of model representation of real-world processes, volume-weighted TS distributions were compared between model and observations (Fig. ). Once again, ECCO and SODA were averaged over the same climatological period as WOA (2005–2012), and SOSE was averaged over 2005–2010. The difference between each model's TS distribution and observation is shown in Fig. . The approximate temperature and salinity profile ranges of AABW are as follows: -0.2 ∘C < θ < -0.7 ∘C and 34.6 psu < S < 34.7 psu , and this is delineated by the cyan box in both figures.

Looking at Fig. , an obvious observation is that all three models' TS distributions have a similar shape and have more spread over the lighter density ranges than in WOA. WOA's spread across density contour 1037.0 kg m-3 and lighter, however, is unlike any of the models' TS distribution. Observation and models show that the most voluminous waters in the WG are Circumpolar Deep Water (CDW) and AABW since their densities and temperature–salinity ranges exist in those regions (darkest blue). One notable feature of Fig.  is the strong peak in the SODA TS histogram around T=0. This feature does not appear in the hydrography or the other models. We investigated the peak extensively by isolating the values close to 0 and plotting the geography and spatial variability. There was no apparent pattern to these values which we could discern; they are a real feature of the SODA temperature output.

We took the difference between each model's TS distribution and the observed one and viewed the difference on a semi-logarithmic scale (Fig. ). This allows us to see a wider range of data. All models underrepresent the coldest, densest HSSW in TS space. This suggests biases in the AABW formation processes. In the CDW range, we observe that the models generally have a more spread-out TS distribution, in contrast to WOA, where CDW has a tighter relationship. We speculate that this bias may be related to a misrepresentation of interior mixing processes.

Overall, ECCO and SODA appear to reproduce bottom salinity where the difference between modeled and observed values is less than the observation's standard error (as denoted by hatching). SOSE reproduces bottom temperature with the difference also being less than WOA's standard error. Simulated bottom temperature in ECCO and SODA, however, is warmer than what is observed, and SOSE has a fresher tendency than what is observed. These are important biases to note in each model as we continue our analysis of AABW variability using all three models.

We first examine the annual mean WMT budget, which represents the long-term mean transformation and overturning structure of the WG, averaging over all spatial and temporal variability. Figure a, b and c show the annual mean budget from ECCO, SOSE and SODA, respectively. The black line represents the time evolution of the cumulative water mass volume distribution, ∂V/∂t, in the WG region during each model's respective time period. It is balanced by the total inflow/outflow transports (Ψ, red line) and mean transformation (Ω∗, purple line), which includes the residual due to numerical mixing. Conceptual models usually assume that the system is in a steady-state balance between overturning and transformation (∂V/∂t=0), but that is clearly not the case for any of the models examined here. The existence of a tendency indicates a model drift and/or low-frequency variability over the climatological period.

In σ2 coordinates the water masses that are the Weddell Sea's recipe for AABW are distinguished as follows by their densities: CDW/WDW (Warm Deep Water) (1037.13<σ2<1037.24 kg m-3) and WSBW/HSSW/ISW (WSBW: Weddell Sea Bottom Water; ISW: Ice Shelf Water) (σ2≥1037.2 kg m-3). Our budget coarsely separates all water into two classes, which are delineated by a boundary σ†: bottom water (denser than σ†) and deep water (by volume, mostly CDW and its regional variants). Due to volume conservation, in this construction, the transport of bottom water across the basin boundary is equal and opposite to the transport of deep water. The dividing isopycnal σ† is defined for each model via the minimum of the overturning streamfunction (Ψ). Because the streamfunction is a cumulative integral quantity, the framework defines AABW transport as the flow across the boundary of all water denser than σ†. So one single transport value represents both the deep outflow and the equal-and-opposite bottom water inflow. Recapitulating, here we define AABW's density (σ†) specific to each model based on where each Ψ reaches its extreme (minimum value) after crossing 0. The values of σ† are 1037.155 kg m-3 for ECCO, 1037.145 kg m-3 for SOSE and 1037.175 kg m-3 for SODA. On average, as shown by the negative extremum of Ψ, AABW is exported from the region at the rate of 7.9 Sv (Sv = 106 m3 s-1) in ECCO, 4.9 Sv in SOSE and 1.9 Sv in SODA. The export is countered by thermodynamic transformation (Ω) by 3.6 Sv in ECCO and 0.4 Sv in SODA and paired by Ω in SOSE by 1 Sv. This leads to a total volume loss of the bottom water class of 2.8 Sv in ECCO, 6.6 Sv in SOSE and 1.5 Sv in SODA. The export value from ECCO is similar to the mean outflow value of , who found the mean outflow of AABW to be 10.6±3.1 Sv using a 1/12∘ 20-year global ocean simulation. We note that though obtained this value from a transect at the tip of the Antarctic Peninsula, they do attempt to capture the dominant outflow of the Weddell Sea AABW. Similar transport values of AABW have been reported by , who determined 8.5 Sv of AABW traveling northward in the Atlantic sector of the Southern Ocean Meridional Overturning Circulation.

We now examine the thermodynamic processes driving transformation in more detail. AABW transformation in ECCO (Fig. a) is mainly due to brine rejection at the surface (orange dashed line). We categorize the transformation from surface salt fluxes as influence only from sea ice since our analysis showed an almost negligible role for the atmosphere. Therefore, positive transformation values are associated with brine rejection and negative values with ice melt. The effects of surface cooling and mixing are generally confined to lighter water masses in the region and tend to cancel each other out. However, mixing does have a stronger tendency to lighten bottom water (by about 4.5 Sv) than surface-cooling-induced positive transformation (0.6 Sv). In ECCO, the dominant impact of brine rejection on transformation (7.4 Sv) is similar to , who found brine rejection dominating the transformation of bottom water by ∼ 5 Sv. In SOSE (Fig. b) the effect of transformation on bottom water shows the opposite behavior to ECCO. SOSE's Ω is driven by mixing (2.8 Sv) and is countered by an equal combination of surface cooling and brine rejection (both 0.9 Sv). Overall, the ECCO and SOSE models are in qualitative agreement with the literature of what is known about bottom water circulation in the Weddell Sea . The two models show that brine rejection and surface cooling drive positive bottom water transformation, while mixing with warmer WDW and fresher AAIW (Antarctic Intermediate Water) acts to decrease AABW. Because we cannot explicitly calculate WMT in SODA but rather infer it as a residual, it is not possible to further decompose SODA's transformation into different components.

While the long-term annual mean shown above is what matters most for the global-scale overturning and climate, the annual mean masks a huge amount of seasonality in WMT. Exploring this seasonality is important for understanding the mechanisms behind WMT. Here we examine the monthly climatology of the transformation budget in the three models (Figs.  and ). The climatology of each term was calculated as a monthly average. Figure  shows this climatology via contour plot and for a wider range of densities to illustrate the seasonality across multiple water masses. For ECCO and SOSE, we also decomposed Ω into transformation from mixing, surface cooling/warming and surface freshwater fluxes in Fig. .

We switch to focus on a single time series that best represents AABW transformation and overturning, rather than the entire range of densities in Figs.  and . We do this by moving from a transformation budget to a formation budget. Again, for each model, we define the boundary between CDW (inflowing water) and AABW (outflowing water) as the density σ† where Ψ reaches its extreme (minimum value). As stated before, the values of σ† are 1037.155 kg m-3 for ECCO, 1037.145 kg m-3 for SOSE and 1037.175 kg m-3 for SODA. By sampling Ψ, Ω and ∂V/∂t at σ†, we obtain a single value or time series representing the net export rate, formation rate and volume tendency of AABW.

In summary, the monthly view reveals that the overturning Ψ is relatively steady over the year in ECCO and SODA; in SOSE, transport shows more seasonality (Figs.  and ). Next, Ω exhibits a seasonal cycle an order of magnitude larger than their annual mean. Moreover, the seasonal cycle in ∂V/∂t and Ω is largely compensatory; excess dense water is created by WMT in winter and then destroyed in summer, and a residual is left over for export from the basin via Ψ. However, in ECCO the destruction is caused by less contribution from transformation and the influence of outflow becomes compensatory.

Going into more detail with Fig. , we see from all three models that bottom water gains volume during the austral winter months and loses volume during the rest of the year. However, in SODA (Fig. c), bottom water volume gain occurs over a longer time range: for three-quarters of the year. SOSE reveals a slight imbalance between the formation rate of AABW and its export; more water is being exported over the year than is being formed. This leads to a continuous decrease in AABW volume, which we will see is the case in Sect.  (also visible in Fig. b). However, superimposed upon this overall trend is a strong seasonal cycle, with excess AABW production and a corresponding volume tendency in winter.

One immediately notices in SODA (Fig. c) the overall larger monthly variability. There was also a dramatic switch between volume gain in January to significant volume loss in February (>25 Sv). SODA, as it was detailed in Sect. , differs from the other two data-assimilating models in that SODA nudges the data to fit the observations it is trying to match. Such a data-assimilating technique commonly causes jumps in the data and produces unphysically large magnitudes in our budget terms, which is consequently evident in our water mass transformation budgets. For this reason, we inserted averaged salt and temperature values from the day before and day after some of the spikes we observed in our preliminary analyses. It would help to remind the reader that the Ω* term shown here is not quite the same as the transformation terms shown for ECCO and SOSE. The transformation term in SODA implicitly carries the residuals that were explicitly calculated in ECCO and SOSE (R1 and R2). In SODA, the advective transport of bottom water is almost insignificant compared to the large magnitude of inferred transformation. SODA still concurs with ECCO and SOSE in showing that volume gain occurs during the winter months; however, bottom water volume grows over half a year as opposed to only a few months centered in the year in ECCO and SOSE.

Looking at ∂V/∂t over a wider density range in Fig. , we can see in all three models that densification acts upon the lighter densities at the beginning of winter, and as the season progresses the thermodynamic process moves down to transform the denser range of the ocean. This pattern can be derived from the surface cooling component of transformation in ECCO and SOSE. This is in agreement with the general understanding that AABW in the Weddell Sea is created when sea ice forms during the winter season, and during the warmer months the production of AABW decreases (Fig. a) or is even destroyed (Fig. b and c). There is year-round export of bottom water in all three models, with the intensity of outflow peaking and varying in the middle of the year. Peak export happens at ∼10 Sv in June in ECCO, ∼12 Sv April–July in SOSE and ∼3 Sv in March in SODA. Both ECCO and SOSE values are within the error bars of the maximum monthly mean outflow value of 12.2±3.0 Sv.

Breaking down the components of Ω (Fig. ), we can see some significant differences between ECCO and SOSE; however, note how both models exhibit a broadly similar σ-temporal structure in these terms (Fig. a and b) but with a different magnitude and position within σ space. In ECCO (Fig. a), the contribution of Ωsurfθ is negligible, and ΩsurfS is positive throughout the winter; this indicates that brine rejection is the dominant process behind AABW formation, as was seen in the annual mean budget (Fig. a), with little impact from ice melt, runoff or precipitation. All the while, throughout the year, transformation due to mixing is trying to homogenize the waters; therefore, bottom water is essentially being destroyed throughout the year on the order of 4 Sv.

In SOSE (Fig. b), AABW production during the winter months is also mainly due to brine rejection. Unlike ECCO, surface cooling provides an additional source for AABW formation in SOSE. Mixing, though more variable throughout the year in SOSE than in ECCO, still works to homogenize (destroy) bottom water. Towards the end of the winter season, ΩsurfS is negative, corresponding to ice melt.