The Weddell Gyre heat budget associated with the Warm Deep Water circulation derived from Argo Floats

: The Weddell Gyre plays an important role in the global climate system by supplying heat to underneath the ice shelves, and to the formation of deep and bottom water masses, which have been subject to widespread warming over past 10 decades. In this study, we investigate the redistribution of heat throughout the Weddell Gyre by diagnosing the terms of the heat conservation equation for a 1000 m thick layer of water encompassing the core of Warm Deep Water. The spatial distribution of the different advective and diffusive terms in terms of heat tendencies are estimated using gridded climatologies of temperature and velocity, obtained from Argo floats in the Weddell Gyre from 2002 to 2016. While the results are somewhat noisy on the grid scale, the heat budget (i.e., the sum of all terms) nearly closes when integrated over the southern limb and 15 the interior circulation cell of the Weddell Gyre. There is an overall balance between the mean horizontal advection and horizontal turbulent diffusion of heat, whereas the vertical terms contribute comparatively little to the heat budget. Heat convergence due to mean horizontal advection balances with divergence due to horizontal turbulent diffusion in the southern limb of the Weddell Gyre. In contrast, heat divergence due to mean horizontal advection nearly balances with convergence due to horizontal turbulent diffusion in the interior circulation cell of the Weddell Gyre. Heat is advected into the Weddell 20 Gyre along the southern limb, some of which is turbulently diffused northwards into the interior circulation cell, while some is turbulently diffused southwards towards the shelf seas. This suggests that horizontal turbulent diffusion plays a role in transporting heat both towards the gyre interior where upwelling occurs, as well as towards the ice shelves. Horizontal turbulent diffusion is also a mechanism by which heat can be transported into the Weddell Gyre across the open northern boundary. Plain Language Summary: Ocean currents in the Weddell Sea are governed by a cyclonic gyre circulation, which is 25 connected to the Atlantic sector of the circumpolar Southern Ocean to its north. Cyclonic means that the horizontal circulation is clockwise, and deep waters are brought close to the surface in the centre by upwelling. The eastern limb of this cyclonic gyre transports relatively warm water poleward, where it loses heat to the atmosphere and by contact with the ice shelves. Thereby the water becomes denser, as also by salty brine released during the freezing of sea ice. The densest water masses then sink down the Antarctic continental slope, and after northward transport with western limb of the gyre fill the deepest 30 basins of abyssal global ocean. The main source water mass for these processes and also the main source of heat to the Weddell Sea is the so-called Warm Deep Water. Previous studies have shown the whole water column, especially in the deeper layers, is warming over recent decades in the Weddell Sea. Warm Deep Water, however, varies in its properties too strongly to tease out long-term trends. To better understand how Warm Deep Water redistributes heat throughout the Weddell Gyre, we use hydrography and drift velocity observations from a fleet of Argo floats freely drifting throughout the Weddell Gyre between 35 2002 and 2016. We estimate a heat budget in a 1000 m thick layer, where the upper boundary is defined as the mid-thermocline, which varies typically around 150 m. Thus, we ensure that the core of Warm Deep Water, characterised by a sub-surface temperature maximum, is always included in the 1000 m-thick layer, regardless of its vertical position in the water column. Overall, large uncertainty and variability prevents us from interpreting the results on a local scale, but interesting features emerge when integrating the heat budget over large areas. According to our results heat is advected into the westward-flowing

decades.In this study, we investigate the redistribution of heat throughout the Weddell Gyre by diagnosing the terms of the heat conservation equation for a 1000 m thick layer of water encompassing the core of Warm Deep Water.The spatial distribution of the different advective and diffusive terms in terms of heat tendencies are estimated using gridded climatologies of temperature and velocity, obtained from Argo floats in the Weddell Gyre from 2002 to 2016.While the results are somewhat noisy on the grid scale, the heat budget (i.e., the sum of all terms) nearly closes when integrated over the southern limb and 15 the interior circulation cell of the Weddell Gyre.There is an overall balance between the mean horizontal advection and horizontal turbulent diffusion of heat, whereas the vertical terms contribute comparatively little to the heat budget.Heat convergence due to mean horizontal advection balances with divergence due to horizontal turbulent diffusion in the southern limb of the Weddell Gyre.In contrast, heat divergence due to mean horizontal advection nearly balances with convergence due to horizontal turbulent diffusion in the interior circulation cell of the Weddell Gyre.Heat is advected into the Weddell 20 Gyre along the southern limb, some of which is turbulently diffused northwards into the interior circulation cell, while some is turbulently diffused southwards towards the shelf seas.This suggests that horizontal turbulent diffusion plays a role in transporting heat both towards the gyre interior where upwelling occurs, as well as towards the ice shelves.Horizontal turbulent diffusion is also a mechanism by which heat can be transported into the Weddell Gyre across the open northern boundary.
Plain Language Summary: Ocean currents in the Weddell Sea are governed by a cyclonic gyre circulation, which is 25 connected to the Atlantic sector of the circumpolar Southern Ocean to its north.Cyclonic means that the horizontal circulation is clockwise, and deep waters are brought close to the surface in the centre by upwelling.The eastern limb of this cyclonic gyre transports relatively warm water poleward, where it loses heat to the atmosphere and by contact with the ice shelves.
Thereby the water becomes denser, as also by salty brine released during the freezing of sea ice.The densest water masses then sink down the Antarctic continental slope, and after northward transport with western limb of the gyre fill the deepest 30 basins of abyssal global ocean.The main source water mass for these processes and also the main source of heat to the Weddell Sea is the so-called Warm Deep Water.Previous studies have shown the whole water column, especially in the deeper layers, is warming over recent decades in the Weddell Sea.Warm Deep Water, however, varies in its properties too strongly to tease out long-term trends.To better understand how Warm Deep Water redistributes heat throughout the Weddell Gyre, we use hydrography and drift velocity observations from a fleet of Argo floats freely drifting throughout the Weddell Gyre between 35 2002 and 2016.We estimate a heat budget in a 1000 m thick layer, where the upper boundary is defined as the mid-thermocline, which varies typically around 150 m.Thus, we ensure that the core of Warm Deep Water, characterised by a sub-surface temperature maximum, is always included in the 1000 m-thick layer, regardless of its vertical position in the water column.
Overall, large uncertainty and variability prevents us from interpreting the results on a local scale, but interesting features emerge when integrating the heat budget over large areas.According to our results heat is advected into the westward-flowing https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.

Introduction
Understanding the drivers and pathways of large-scale ocean circulation is a fundamental component of climate science (Rhein et al., 2013).To comprehend the regulatory role of the oceans in the climate system, one can determine the ocean heat budget, which describes the redistribution of heat throughout the ocean by means of horizontal and vertical advection, turbulent diffusion, and surface heat fluxes to the atmosphere (e.g., Tamsitt et al., 2016; an adapted form of the heat budget equation is 50 given in Eq. 1.1).
The Weddell Gyre is located south of 50° S in the Atlantic sector of the Southern Ocean, where Circumpolar Deep Water (CDW) predominantly enters the gyre's southern limb in the east at about 30° E. The CDW that enters the Weddell Gyre is commonly referred to as Warm Deep Water (WDW).WDW circulates the cyclonic gyre, undergoing cooling and freshening on-route, through interaction with the underlying and overlying water masses (e.g., Fahrbach et al., 2004;Klatt et al., 2005;55 Fahrbach et al., 2011;Leach et al., 2011).The core of WDW is identified as the sub-surface temperature maximum (hereon referred to as Θmax), which feeds heat into the Weddell Gyre (Fahrbach et al., 2004(Fahrbach et al., , 2011;;Cisewski et al., 2011;Ryan et al., 2016).The distribution of temperature at the depth of the Θmax is shown in Fig. 1, which is derived from in situ observations from Argo floats (from Reeve et al., 2016Reeve et al., , 2019)).The Weddell Gyre has been ascribed the role of a heat buffer (Fahrbach et al., 2011), in that it acts to store and redistribute heat and salt in the water column, effectively transferring heat to the deeper 60 layers where it is ultimately exported northwards, spreading throughout the abyssal global ocean (e.g., Foster et al., 1987;Naveira Garabato et al., 2002, 2016;Fahrbach et al., 2011).
Warming trends over recent decades have been observed in the WSDW and WSBW (Weddell Sea -Deep and -Bottom Water respectively) (Fahrbach et al., 2011;Meredith et al., 2011;Strass et al., 2020).However, their primary source of heat, WDW, exhibits pronounced decadal variations and shows no significant long-term warming trend (Fahrbach et al., 2011;Kerr et al., 65 2017).While Strass et al. (2020) show that the whole water column below 700 m exhibits a significant long-term warming trend, which would incorporate the lower part of the WDW layer, they also observed significant variability and even areas of cooling in the upper 700 m, which incorporates a significant chunk of the WDW layer.
In this study, we combine observations of the velocity field (Reeve et al., 2019) with the temperature field (Reeve et al., 2016), both derived primarily from Argo floats, to diagnose components of the heat budget of a fixed volume of water fully 70 encompassing the core of WDW within the Weddell Gyre.Given the near-surface seasonal cycle is unresolved throughout, a full basin analysis of the upper 50 m is unfeasible.By analysing the heat budget for a fixed volume encompassing the core of WDW, we can, however, determine the ways in which heat from WDW is redistributed throughout the Weddell Gyre.The rest of this paper is structured as follows.Section 2 describes the data sources used in this study, while Section 3 details the method of applying the heat budget, and its associated estimation of uncertainty.Section 4 presents the individual heat budget 75 terms for the Weddell Gyre for the whole region as well as integrated over specific areas, while Section 5 interprets these results in context of the study limitations and the literature.Lastly, Section 6 provides our final summary.

Data sources
For this study we computed the heat budget of the entire Weddell Gyre using different sets of data from various sources, which 80 will be described in more detail in the following subsections.

Data sources
Table 1 describes the data sources used for determining the heat budget presented in this paper.Each source is then described in further detail in Sections 2 and 3, as well as in the Supplement (S1-4).et al., 2011).We applied objective mapping to the profile data resulting in a climatology of gridded conservative temperature on 41 pressure levels between 50 and 2000 dbar.The grid cell resolution varies slightly with changing latitude (Reeve et al.

90
2019), but is on the order of ~80 x 60 km.This method follows, and is an extension of the objective mapping provided in Reeve et al. (2016), and the reader is referred to that study for further details on the data quality control and mapping method used in this study.The absolute velocity field was derived from Argo float trajectory data at the depth of the float drift ( 800dbar in the Weddell Gyre).This process required careful quality control assessments and surface drift corrections following Park et al. (2005), and, given that under-ice profiles have no geo-located position, all such interpolated trajectories were omitted 95 from the study.Thus, the derived velocity field exhibits considerable bias to summer conditions.The velocities were objectively mapped to provide a grid of absolute velocity at 800 dbar.This process is detailed in Reeve et al. (2019).
Following Reeve et al. (2019), a stream function was fitted to the velocity field at 800 dbar through the application of a cost function.By applying a cost function, the resulting stream function provides a best fit for the entire Weddell Gyre, where the direction of mean flow at the boundaries are assumed to be parallel to the boundaries. .The stream function at 800 dbar 100 provides the reference level for the relative geostrophic velocity, derived from the gridded density field from Reeve et al.
(2016), above.For full details on this methodology, refer to Reeve et al. (2019), which, in addition to Reeve et al. 2016, is the prelude to this study.In Reeve et al. (2019), a careful error analysis and a detailed comparison of volume transports to available estimates in the literature justify the method as a reasonable solution to obtaining a large-scale observation-based estimate of the Weddell Gyre circulation.

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There are, however, important improvements between the stream function provided in Reeve et al. (2019), and the stream function used in this study.The cost function was adapted to allow for a variable coastline, so that the stream function provides a solution which includes the southern ice shelf edge east of the Prime Meridian (though not the shelf edge currents, such as the Antarctic Slope Front, which are not resolved in this study as they are beyond the domain of the Argo floats), which is excluded in Reeve et al. (2019).To better estimate the velocity field along the southern coast of the Weddell Gyre, a few minor 3 Methods

The heat budget
Due to conservation, the heat storage of a certain ocean volume needs to equal the sum of all fluxes comprising advection and 130 turbulent diffusion, both vertical and horizontal.Thus, the heat budget integrated for a volume of water not in contact with the atmosphere is defined as: (1.1) where ∇  is the horizontal divergence operator, U is the horizontal geostrophic velocity,  is the conservative temperature, wE is the vertical velocity (defined as the Ekman pumping velocity; see Supplements S3), z is depth and   and   are the horizontal and vertical diffusivity respectively (adapted from Tamsitt et al. 2016).For the vertical integration in Eq. 1.2, the 135 subscript mT describes the mid-point of the thermocline, which provides the upper boundary, while mT +1000 describes the lower boundary (explanation of the vertical boundaries is provided in the Supplements S1).Each term is multiplied by the specific heat capacity of seawater, Cp (~4000 J K -1 Kg -1 ), and seawater density, (ρ0 = 1027 kg m -3 ), and integrated for a 1000 m thick layer so that units of each component are given in W m -2 .The first term on the right-hand side in Eq. 1.1 describes the mean horizontal geostrophic heat advection, where U is derived from horizontal differentiation of the geostrophic stream 140 function derived from Argo float data (i.e., where u = ψ/y and v = −ψ/x; see Section 2.2 and Reeve et al. 2019).Since we derive velocity from a non-divergent stream function, we assume geostrophic flow conditions and omit ageostrophic advection from the first term.This is a pertinent assumption given that the Ekman Layer is excluded from the analysis.The second term on the right-hand side in Eq. 1.1 describes the mean vertical heat advection.The third and fourth terms in Eq. 1.1 (or, the second part of the first term and the third term in Eq. 1.2) describe the horizontal and vertical turbulent heat diffusion 145 components respectively.The sum of these terms results in an estimate of heat tendency over time (d/dt), which can be used to determine mean temperature change for a column of water, although this method results in an accumulation of associated errors of the individual terms, and should therefore be treated with caution.Maps of the different components are provided in the results section.
There are two unknowns in Eq. 1.These are the horizontal and vertical diffusivities,   and   respectively.For the northern 150 and eastern outskirts of the Weddell Gyre, we define   from the dataset provided by Sevellec et al. (2022).For the rest of the Weddell Gyre, we define   as 400 ± 200 m 2 s -1 , based on the varying values provided in the literature (See Supplements S4 for our reasoning and maps of   ).We define   as 2.6 x 10 -5 ± 2.4x10 -5 m 2 s -1 , again based on values provided in the literature.
The error ranges are to provide a range of reasonable estimates while acknowledging lack of consensus of appropriate values and Cole et al. (2015), of 247 m 2 s -1 , 300 m 2 s -1 and 200-2000 m 2 s -1 respectively.Our chosen baseline   is larger than the first two listed here and more closely aligned with Cole et al. (2015), because we focus on larger length-scales, most similar to the latter study, owing to the resolution and sample density of our data set.The implications of these decisions are discussed 160 in Section 5.

Assessing the uncertainty
The errors for each heat budget term are calculated using the laws of propagation, as detailed in the Supplement to this paper (S7).The main sources of error are from the variables: temperature, horizontal velocity, vertical (Ekman) velocity, and unknown diffusivity, which is assumed constant in the horizontal for the Weddell Gyre interior and southern limb, and 165 throughout the whole Weddell Sea in the vertical.
We used the objective mapping error to represent the error for temperature (Fig. S7), which is provided in Reeve et al. (2016), and assumed to be the dominating source of error for temperature.This means that the error is also representative of the length scales applied in the objective mapping (Reeve et al., 2016).In Reeve et al. (2016), the length scales were assigned based on an investigation which showed that 95 % of the grid points have at least 40 Argo profiles within a distance of 500 km (we were then able to reduce this to 400 km in Reeve et al. 2019), which was thus the length scale applied in the second stage of the objective mapping, along with a fractional scale on the effect of f/H, which alters the shape of the area of influence about a grid point from circular, when the bottom bathymetry is flat, to elongated, when a grid point is in close proximity to bathymetric gradients (Reeve et al. 2016).Since the focus is a climatological mean from 2002 to 2016, the applied length scales are chosen for the mapping to represent the large-scale field of the entire Weddell Gyre (Reeve et al., 2016).The 175 resulting mapping errors are large in regions where bathymetry is complex and data coverage is sparse, and low in regions where the bathymetry is flat or where data density is high.Thus, the regions of largest uncertainty include the northern periphery of the gyre, where data is relatively abundant but the bathymetry is complex, and the eastern edge of the Weddell Gyre, where data is sparse (Fig. S7).
The error for horizontal velocity was provided in Reeve et al. (2019), and is derived from the stream function, where a 180 sensitivity study was implemented, perturbing the velocity field using a combination of factors (mapping errors and drift correction), to provide a range of possible stream function values, from which a standard error was estimated.
Since uncertainty is currently unavailable for the ERA-5 reanalysis data that provided the wind stress field from which Ekman vertical velocity was computed, we took the standard error of the mean of a monthly time series from January 2002 to December 2016 to represent the error for vertical velocity.This represents the natural temporal variability of the vertical 185 velocity, which we assume to be dominating over other possible sources of error, given the large seasonal variability of the wind field.
Lastly, we arbitrarily define an uncertainty range for the diffusivity terms, to be ± 200 m 2 s -1 and 2.4x10 -5 m 2 s -1 for the horizontal  In part one, we provide maps of the vertically integrated heat budget terms (from Eq. 1.2), to obtain an overview of the large-scale heat field of the Weddell Gyre.In part 2, we consider the zonal variation of the heat budget, for two regions: (1) the southern limb (SL), which describes the westward flowing part of the gyre that extends from Gunnerus Ridge (~33°E) to ~45°W (i.e., where the stream function, ψ, is 16 to 30 Sv; the stippled area in Fig. 2b) and ( 2) the interior circulation cell (IC), where streamlines form a fully closed circuit west of Gunnerus Ridge, incorporating both the eastern and western sub-205 gyres, (i.e.ψ >25.9 Sv; the stippled area in Fig. 2d).

Part one: the large-scale investigation of heat within the Weddell Gyre
The heat budget contributions from the different terms in Eq. 1.2 (including the signs of each term, e.g.,−∇   and +  ∇ 2 ) are provided in Fig. 2. While for the gyre at large, the mean horizontal geostrophic heat advection (Fig. 2a) shows a patchwork display of heat transport convergence (positive) and divergence (negative), the southern limb of the gyre is generally dominated 210 by heat transport convergence, of about +20 W m -2 west of the Prime Meridian.A small patch of divergence is found over the western sub-gyre of about -10 to -20 Wm -2 (~35-45°W, ~65°S), and over Maud Rise of about -20 to -30 Wm -2 (~3°W, 65°S).
The whole region east of the Prime Meridian is dominated by particularly strong patches of positive and negative values in excess of ±80 W m -2 .Along the northern limb of the gyre, the pattern is dominated by bands of alternating positive and negative values, of about ±60-80 W m -2 , which are aligned in a manner that appears to follow the complex bathymetry in the region.

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The heat flux due to mean vertical advection (-wE(ΘmT -ΘmT-1000), Fig. 2b) is positive throughout, and considerably weaker than that due to mean horizontal advection, in the range of ~0-3 W m -2 .Vertical advection is weakest west of ~10°W, and strongest over the eastern sub-gyre region between 0 and 30° E. That the entire region shows positive vertical fluxes (with the exception of north of the Weddell Gyre) results from two factors: (1) the mean Ekman pumping velocity is positive (indicating upwelling) throughout the offshore Weddell Gyre (downwelling, i.e. negative Ekman pumping velocity, is found in regions 220 shallower than 2000 m and thus outside of our region of Argo float data availability) (Fig. S3), and (2) the upper boundary displays lower temperatures than the lower boundary (Fig. S1a), which is a consequence of the vertical boundaries applied in this analysis.Positive vertical advection implies that more heat is advected upwards into the core layer of WDW from below than is leaving by advection through the top, implying a convergence of heat within that layer, unless it is removed through other mechanisms such as mean horizontal advection or turbulent diffusion.

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Horizontal turbulent diffusion (Fig. 2c) is characterised by a positive signal of about 0-40 Wm -2 within the IC, and a negative signal along the SL in the range of 20-60 Wm -2 , with the exception of local patches of heat flux convergence such as over Maud Rise and just north of Astrid Ridge at ~10°E (topographic features are marked in Fig. 1).The northern limb of the Weddell Gyre is mostly positive, (40-100 Wm -2 ), though a strip of heat flux divergence sits directly north of this area of heat flux convergence, in the northern boundary zone between the Weddell Gyre and the Antarctic Circumpolar Current.

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As with mean vertical advection, vertical turbulent diffusion (Fig. 2d) exhibits a uniform sign throughout the Weddell Gyre, with negative values in the range of -2 to -7 Wm -2 .The strongest values are found in the southern limb, at about ~20°E (~ -7 Wm -2 ), as well as just west of Maud Rise.There also appears to be slightly enhanced vertical turbulent diffusion along the gyre axis between about 10°E and 20°W.

Results part 2: zonal variation in the heat budget
In this section, we provide an analysis of the zonal variation of the heat budget in the Weddell Gyre of the two regions described at the beginning of Section 4 (highlighted in Figs.2b and d).This is carried out as follows: we integrate meridionally for each zonal band in our data grids, from just west of Gunnerus Ridge (~33° E) in the westward direction towards the Antarctic Peninsula (Figs. 3-4, upper panel).The latitudinal range of the band is defined using the stream function, focusing on the SL 250 and the IC.Lastly, we plot the cumulative zonal integration from east to west (Figs.3-4, lower panel) and provide the zonally integrated heat budget terms in Table 3.We also take the sum of the heat budget terms and divide by the time period to get the temperature change for SL and IC, also listed in Table 3.For both regions, the zonal variation in the heat budget terms (Fig. 3-4, upper panel) show large local imbalances in the overall heat budget, which are physically implausible.However, useful information is provided in the net (zonally integrated) heat budget terms (Fig. 3-4, lower panel).The resulting volume 255 integration describes the heat flux divergence (negative) or convergence (positive), owing to heat fluxes across the boundaries of the volume of water in question.By considering the 4 different heat budget terms with respect to each other, we can build up a picture of how and where heat is redistributed throughout the Weddell Gyre.Table 2 provides a list of the abbreviations for the terms presented in Figs.3-8.The method for computing the associated errors is detailed in Section 3.2 as well as the Supplement (S7).

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Region 1: SL (southern limb) The SL region (Fig. 2b) spans the entire zonal extent of the double gyre system, with the northern boundary being the largest streamline that spans both sub-gyres, from just west of Gunnerus Ridge to ~45° W (30 Sv), and the southern boundary being the southernmost streamline that does not break into the coastline (16 Sv).This enables us to focus on the water that circulates the entire zonal extent of the gyre, thus reaching into the south-western interior.Overall, the primary sources of heat (heat flux convergence) are from the advection terms, mean horizontal advection (AH) and mean vertical advection (AV), whereas the primary heat sinks (heat flux divergence) are from the turbulent diffusion terms, horizontal turbulent diffusion (DH) and vertical turbulent diffusion (DV) (Fig. 3, lower panel).The vertical terms are spatially invariant and contribute to the heat budget to a much lesser extent than the horizontal terms.This compliments the findings in Fig. S2 of the net air-sea heat fluxes, which shows a relatively small heat loss through the surface of the ocean in the SL region.

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The heat flux convergence due to vertical advection is driven by upwelling, which leads to an advection of warm water upwards into the layer, whereas heat flux divergence due to vertical turbulent diffusion removes heat from the layer through the upper boundary (the mid-thermocline).Thus, heat enters the SL primarily through horizontal advection, and to a lesser extent by vertical advection due to upwelling, and is removed from the layer primarily by horizontal turbulent diffusion and vertical turbulent diffusion (a small amount of which may escape through the surface of the ocean).Thus, the turbulent diffusion terms 275 redistribute the heat that is advected into the gyre.
The largest regional fluctuations (Fig. 3, upper panel) in the sum of the terms are caused by large fluctuations in mean horizontal advection, in particular upstream of Maud Rise (i.e., mean horizontal advection increases by ~55 Wm -2 just east of the Maud Rise seamount, from 10° to 7° E, and then sharply decreases by ~80 Wm -2 from 7° E to the Prime Meridian).The effect of Maud Rise is also visible in the net contribution (lower panel of Fig. 3), where it results in an increase in mean 280 horizontal advection of ~7 TW from ~10° to ~5° E, after which a small decrease of ~2 TW occurs from 5° E to the Prime Meridian.This influences the net heat tendency (sum of the heat budget terms), which increases from 0 to ~7 TW, and then decreases to ~4 TW over the same longitudinal range.The perturbation in mean horizontal advection at Maud Rise is an artefact of being unable to resolve the regional circulation around Maud Rise, whereas the gridded temperature captures the presence of the relatively cold Taylor Column situated over Maud Rise (clearly visible in Fig. 1).This creates strong horizontal 285 temperature gradients on the eastern and western flanks of Maud Rise, i.e., in the direction of the dominant flow.This is discussed further in Section 5.2.2.

Region 2: IC (Interior Circulation cell)
The IC region (Fig. 2d) spans the entire zonal extent of the double gyre system, this time forming a fully enclosed circuit to focus on the recirculating waters of the gyre, from just west of Gunnerus Ridge to near the continental shelf edge of the northern 290 tip of the Antarctic Peninsula (~50° W).
Overall, the magnitudes of the heat budget terms are similar in the IC to the SL, with the exception of the mean horizontal advection term, which has a larger magnitude in the SL (10±15 Wm -2 ) than in the IC (-2±24 Wm -2 ) (Table 3).Note the differences in the magnitudes of the net heat budget terms are due to the larger area of the IC (Table 3).As with the SL, vertical terms in the IC remain zonally spatially uniform and are much smaller in total magnitude than the horizontal terms, with heat 295 being vertically advected into the IC domain (via upwelling) and removed from the IC domain by vertical turbulent diffusion.
In contrast, the horizontal terms in IC change sign in comparison to the SL.Horizontal turbulent diffusion (DH) is the primary heat source (i.e., heat flux convergence), whereas horizontal mean advection (AH) is the primary heat sink (i.e., heat flux divergence) (Fig. 4, lower panel).Additionally, in contrast to the SL, the surface heat fluxes in this region (Fig. S2) are positive, implying a positive heat flux into the ocean through the surface.This heat does not appear to cross the thermocline (i.e., the 300 upper boundary of our domain), given the convergence of heat due to vertical advection and the positive vertical velocity values in Fig. S3 imply that, in the vertical, heat is entering the IC domain from below (due to upwelling), and vertical turbulent diffusion provides a heat sink (removal of heat), likely upwards through the thermocline, owing to the strong vertical temperature gradients associated with the thermocline.Thus, the heat entering through the ocean surface is likely to be redistributed by other processes (such as surface transports or ice melt).then to 6 Wm -2 over ~1400 km (from 28 to 12 to 7 °E).We assume these peaks are somewhat an artifact of the mean circulation interacting with strong lateral temperature gradients in the eastern sub-gyre region (i.e., the red and blue ellipses in Fig. 2e over the eastern-sub-gyre coincide with strong temperature gradients in Fig. 1 and S5b), which is further discussed in Section 310 5.2.2.

� 𝐀𝐀𝐀𝐀 ���������
The sum of the heat budget terms in Eq. 1, listed above, where A stands for the horizontal and vertical advection terms and D stands for the horizontal and vertical diffusion terms.

315
In order to learn more about how the heat budget terms act to redistribute heat throughout the IC, we further split the IC into IC-north (Fig. 5) and IC-south (Fig. 7), where the interface between the two regions is defined as the central gyre axis (i.e., the zonal maximum stream function, north of which the flow is predominantly eastward, south of which the flow is predominantly westward).When integrating over these smaller regions, the heat budget does not close.We can, however, learn more about the processes which provide heat sources and sinks to these different regions.The first challenge that emerges is the non-320 objective decision-making required regarding whether to include the easternmost part of the IC, where the horizontal mean advection may be unrealistic.We remove the eastern most values, east of 25°E in the IC-north, and focus only on west of Maud Rise (inclusive of Maud Rise) for the IC-south.We choose these limits in order to remove the anomalous ellipses that extend diagonally north-eastwards from Maud Rise.To further investigate horizontal diffusion, we computed horizontal turbulent diffusion heat fluxes across three zonal boundaries: (1) across the northern boundary of the gyre (defined as the 325 northernmost streamline of the filled region in Fig. 2d i.e., the streamline that, in Fig. 2c, marks the boundary between heat flux convergence within the Weddell Gyre (red) and heat flux divergence to the north (blue)); (2) across the interface between the divergence zone within the SL and the convergence zone in the IC; and (3) across the central gyre axis from IC-south into IC-north, for west of Maud Rise.The zonal variation in heat flux for each boundary is provided in Fig. 5b and 7b-c respectively, whereas the zonal integrations of the fluxes are provided in the Supplements (Fig. S6).

330
Horizontal turbulent diffusion is the dominating heat source to the IC-north, providing a net 78 ± 4 TW of heat, whereas horizontal mean advection is a net heat sink, removing 68 ± 15 TW (Fig. 5a).Half the horizontal turbulent diffusive flux of heat occurs along the northern boundary of the gyre (32 ± 1 TW), with particularly large southward heat fluxes (>200 Wm -2 ) directly downstream of the South Sandwich Trench, and in the region of the southwest Indian Ridge east of 10°E (Fig. 5b), indicating that the rest of this heat flux occurs in the easternmost part of the IC-north.The large fluxes are most likely due to 335 the strong meridional temperature gradients characteristic of the boundary between the warmer ACC to the north and the colder Weddell Gyre to the south.
Overall, when looking at the zonal variation in the heat budget terms in Fig 5a (upper panel), the positive peaks in horizonal turbulent diffusion are synchronous with the troughs in horizontal mean advection, implying that as heat is turbulently diffused across the boundary into the IC-north, horizontal advection "carries" this heat away along the eastward-flowing northern limb 340 of the gyre.We can also demonstrate this by following the evolution of the sub-surface temperature maximum along a single streamline (in this case, Ψ=26 Sv, which is the outer boundary of the IC, as shown in Fig. 2d), which shows an overall increase in temperature along the northern limb of the Weddell Gyre, as well as an overall decrease in temperature along the southern limb of the Weddell Gyre (Fig. 6).

345
Horizontal mean advection provides a heat sink of 3 ± 3 TW in the IC-South directly west of the Prime Meridian, up until ~10°W (Fig. 7a), after which it provides an overall heat source (7 ± 3 TW).The initial heat sink could be indicative of heat advection following the mean circulation about the eastern sub-gyre, as indicated by the streamlines in Fig. 2; west of this, heat is advected into the area that circulates the western sub-gyre.In contrast to the SL, horizontal turbulent diffusion is also a source of heat to this area (3.3 ± 1 TW), which is indicative of a northward diffusive heat flux, which removes heat from the 350 SL, transporting it northwards into the IC-south.This is indeed the case when computing the diffusive heat flux across the northern boundary of the SL in Fig. 7b, which gives a net heat flux of 6.4 ± 0.6 TW, of which 3.4 ± 0.6 TW occurs downstream of Maud Rise (Fig. S6b).Additionally, a net diffusive heat flux of 0.8 ± 0.1 TW occurs northwards from the IC-south across the central gyre axis into the IC-north, mainly occurring 10-28°W, i.e., at the interface between the eastern and western subgyres (Fig. 7c & S6c).The diffusive flux of heat northwards from the SL into the IC occurs at a mean rate of 22 ± 12 W m -2

355
(Fig. 7b), with a maximum at 10° E, of ~50 ± 25 W m -2 , where the streamline along which we are integrating starts to curve northwards to meander around the northern flank of Maud Rise.The streamlines indicate a strong flow in this region, with a sharp meridional gradient between the colder recirculated water close to the central gyre axis, and the relatively warm advected inflow of the southern limb.The main heat sink in the IC-south is the vertical turbulent diffusion term (Fig. 7a), which removes 6 ± 0.3 TW upwards through the thermocline.

Discussion
In this study, velocity and temperature derived from Argo floats were used to determine the heat budget of the Weddell Gyre, for a 1000 m thick layer of water extending from the mid-point of the thermocline, encompassing the core of the WDW layer.

365
In the following section, we provide an in-depth discussion of the study limitations, before ultimately discussing and interpreting the results in Section 5.2.

Study limitations
Before interpreting the results, several limitations of the study require discussion.

Vertical boundary limits 370
The first limitation relates to the omission of the upper 50 dbar from the profiles prior to mapping (Supplements S1), to avoid the highly seasonally varying surface waters.Ideally, we would include the upper ocean layer, in order to explicitly apply the net air-sea heat flux term (Qnet) as a surface boundary condition in the heat budget equation.Since we are interested in the redistribution of heat throughout the Weddell Gyre (with the main heat source being the WDW), we applied boundary conditions which ensure that the Winter Water layer (defined by its temperature-salinity minimum) is not included within the subsurface 375 layer of interest, while the core of WDW (i.e., Θmax) is fully included.The vertical boundary conditions allow us to consider the varying depths of the upper boundary, while also avoiding bias by fixing the thickness of the vertical layer.However, this may introduce some noise into the analysis from grid cell to grid cell, owing to the different depths of the water column the heat budget is integrated over.This may partly explain why there is considerable noise in the maps in Section 4.1, while the noise partially cancels out in Figs. 3 and 4. The implication is that our heat budget analysis is reasonable on large-scales, but 380 would introduce considerable noise when assessed on local-scales.We return to this when discussing regional imbalances in Section 5.2.2, and find that the lateral gradients in the upper boundary depth are unlikely to be a major source of the noise in Fig. 2 (Fig. S5a).

Estimating vertical velocity
Another limitation in the study is a suitable estimate for vertical velocity.Vertical Ekman pumping velocity is used to represent 385 vertical velocity, which is held constant with depth (Supplements S3) throughout the 1000 m thick layer, thus assuming a perfect geostrophic (thus non-divergent) flow.However, reanalysis-based wind products from which wE is computed, are also limited in their accuracy, largely due to lack of in-situ wind measurements in the Southern Ocean.Additionally, vertical velocities resulting from eddies, fronts and along steeply sloping bathymetry are not taken into account in this study, which might be important sources of vertically non-uniform vertical velocities in the upper ocean.
Prime Meridian and the north and eastern peripheries of the gyre.These values vary between 0 and 8000 m 2 s -1 ; and are close to zero around Maud Rise, and can be 4000-8000 m 2 s -1 within the eastern and northern gyre periphery.In this study, we are focused on the large-scale, and have a grid of data representative of the long-term mean from 2002-2016.Our grid cell resolution varies slightly with changing latitude (Reeve et al., 2019), but is on the order of ~80 x 60 km, which is nearly double the station spacing of 55 km in Leach et al. (2011).The length-scales applied in the objective mapping are 800 km in stage 1 420 and 400 km in stage 2, with a skew on the shape of the radius of influence based on the range in potential vorticity (See Section 2.2 in Reeve et al., 2019), and therefore the length scales upon which the analysis falls would actually be considerably greater error propagation computation).A detailed explanation of our method and reasoning regarding the Sevellec et al ( 2022) dataset is provided in the Supplements (S4).
Referring now to the vertical diffusivities, Leach et al. ( 2011) provide particularly small estimates for κv, of 3 x 10 -6 m 2 s -1 for the core of WDW, which they suggest is due to the timing of the survey -having taken place late spring/early summer, when 430 sea-ice had just melted, and the wind had not yet had time to stir up the water column.Other studies provide larger estimates for κv, for various regions throughout the global ocean.Donnelly et al. (2017) estimate κv as 2.4 ± 2.8 x 10 -5 m 2 s -1 .Over rough topography, such as 500 m above abyssal sea mounts on the flanks of the mid-Atlantic Ridge in the Brazil basin, Ledwell et al. (2000) provide an estimate for κv of 3 x 10 -4 m 2 s -1 .Over flat bathymetry of the ocean's abyss, however, Polzin et al. (1997) and Ledwell et al. (1998) estimate κv to be about 1 x 10 -5 m 2 s -1 .Naveira Garabato et al. (2004aGarabato et al. ( , 2004bGarabato et al. ( , 2007) ) provide larger 435 numbers for deep water in the Scotia Seas of 3 x 10 -4 to 1 x 10 -2 m 2 s -1 , which they attribute to breaking internal waves.Also within the Southern Ocean, Cisewski et al. (2005Cisewski et al. ( , 2008) ) acquired 7 x 10 -4 m 2 s -1 in the upper pycnocline of the Antarctic Circumpolar Current at 20° E and Forryan et al. ( 2013) obtained a value of 1.9 x 10 -5 m 2 s -1 based on observations in close proximity to a vigorous frontal system between 60 and 80° E, at the northern edge of the Kerguelen Plateau.
Initially, we attempted to estimate κv through the use of the Richardson Number, following Forryan et al. (2013), defined as 440 the ratio of buoyancy frequency (N) squared to vertical shear squared, and often used to describe the stability of stratified shear flow.For large Richardson Numbers, the resulting diffusivity tends towards a background diffusivity coefficient provided by the authors.In the Weddell Gyre, the circulation is mostly barotropic, and so the vertical shear is small, leading to large Richardson Numbers, especially when one is focused on the long-term mean.Thus, with this method, the resulting diffusivity tends back towards a background diffusivity parameter.Hence, based on the range of values available from the literature, we 445 made the decision to provide a range of potential values for vertical diffusivity, of (2.6 ± 2.4) x10 -5 m 2 s -1 (the "uncertainty" is incorporated into the error propagation computation).
A final consideration regarding uncertainty is related to using a simple differencing scheme at the grid cell resolution in order to compute spatial gradients in the heat budget equation (Eq.1.2).Alternatively, we could have extracted curves from the grid from which to determine the gradients.However, this is dependent on further length scales, which could introduce additional 450 uncertainty, and may also result in additional smoothing of the observed fields.Thus, we applied the former method, which extracts the gradients directly from the gridded datasets at the grid cell resolution, with the expectation that this would result in large regional fluctuations owing to the coarse grid resolution.

5.2
The Weddell Gyre heat budget 455

Overall findings
While the heat budget does not close on regional scales, it does approximately close when integrating over large areas, thus, important and useful information can be provided from comparing the four resulting heat budget terms.
In most regions of the Weddell Gyre, for the core of WDW, the terms dominating the heat budget are mean horizontal geostrophic advection (Fig. 2a), and horizontal turbulent diffusion (Fig. 2c).Horizontal mean advection appears patchy, though 460 generally implying warming (convergence) in the southern limb of the gyre (Fig. 2a).Horizontal turbulent diffusion (Fig. 2c)  Additionally, the sum of the heat budget terms in Fig. 2e imply a general cooling in the SL, and a general warming in the IC, synchronous with the surface heat fluxes in Fig. S2, where the IC experiences a net heat flux into the ocean from the atmosphere, while in the SL the ocean loses heat to the atmosphere.
The spatial patterns in the heat budget terms become distinct when integrating over large areas, namely, the SL and IC (Section 470 4.2).While the vertical terms are spatially uniform throughout, providing a heat source (mean vertical advection) and a heat sink (vertical turbulent diffusion) throughout both regions, the horizontal terms "switch roles" in the SL versus the IC.
Horizontal mean advection is a mechanism which brings heat into the SL, while horizontal turbulent diffusion removes much of that heat from the SL.In contrast, horizontal turbulent diffusion brings heat into the IC, whereas mean horizontal advection provides a heat sink in the IC.Thus, while both mean horizontal and vertical advection are responsible for bringing heat into 475 the core of the WDW layer of the Weddell Gyre, turbulent diffusion is the mechanism which then redistributes that heat throughout the gyre interior.Surface heat fluxes (Fig. S2) also imply that the upward diffusive heat flux through the top of the layer (i.e., the mid-thermocline) may represent a source of heat for the observed negative air-to-sea heat flux in the SL.In the IC, where air-to-sea heat fluxes are positive, the upward diffusive heat flux across the upper boundary of the WDW layer may be horizontally redistributed by the upper ocean flow field and additionally may provide heat required to melt sea ice in this 480 area.

Regional (im-)balances
When integrating over smaller regions, the heat budget does not close (see Figs. 2e, 3 and 4), indicating that noise is largely cancelled when integrating over larger areas.The noise is likely a result of (1) discrepancies in the depth range from grid cell to grid cell, (2) the nature of differentiating across grid cells, (3) due the presence of mesoscale eddies unresolved by the data 485 and methods used, and (4) aliased observations that result in a distortion of the mean state.Here, we discuss the influence of (1) unresolved mesoscale eddies and narrow currents in the eastern Weddell Gyre, (2) Maud Rise and ( 3) the open northern boundary, and discuss what might be missing that prevents the closure of our heat budget analysis.
The presence of unresolved mesoscale eddies is particularly important east of the Prime Meridian.In Fig. 1, it is clear there is a misalignment between the streamlines and temperature distribution in the eastern part of the gyre; horizontal mean advection 490 hugely dominates this region which is partially compensated by horizontal turbulent diffusion (Fig. 2).Given the domed shape of the isopycnals characteristic of a cyclonic gyre (e.g., Strass et al., 2020;Fahrbach et al., 2011), we hypothesised that a larger bias due to the horizontal gradient of the upper boundary depth (i.e., mid-thermocline, Fig. S1b) was occurring at the gyre periphery (i.e., where the slopes of the isopycnals are largest), which may be contributing to the large ellipses in horizontal mean advection at the eastern periphery of the gyre in Fig. 2a.This appears not to be the case, given there is no clear large 495 horizontal gradient in the mid-thermocline depth in the east; indeed, the largest horizontal gradient in mid-thermocline depth occurs in the very west of the Weddell Gyre, along the Antarctic Peninsula, and to a lesser extent over Astrid Ridge (Fig. S5a).
The large ellipses do, however, appear to be related to large horizontal temperature gradients (Fig. S5b).We found the largest horizontal temperature gradients unsurprisingly along the northern boundary of the Weddell Gyre (owing to the considerably warmer ACC to the north), but also in a diagonal line spanning from directly east of Maud Rise, northwards to the northeast 500 of the eastern sub-gyre (~30°E, 55°S); in other words, synchronous with the north-easternmost ellipse of heat flux divergence and south-westernmost ellipse of heat flux convergence (Fig. 2a & 2e).The strong horizontal temperature gradients therefore likely accounts for the two strongest ellipses in Fig. 2. This, along with the fact that the computation (which relies on differencing across grid cells) is sensitive to the alignment of the temperature field to the velocity field, which is imperfect, especially on such a coarse resolution grid.In particular, temperature is a more conservative (slow changing) variable in 505 comparison to the velocity field.Thus, in capturing the mean state, our depiction of the mean velocity field may be especially distorted due to aliasing of observations, which we know are biased to summer conditions, and are particularly varying on shorter timescales in the dynamic region east of the Prime Meridian.In addition to the aliasing of the observations in representing the mean state, it is possible that there is a significant additional component (in addition to mean horizontal advection) which distributes heat in the eastern part of the gyre.The question is, how much of this is a result of unresolved 510 mesoscale activity driving large temperature and velocity gradients on much shorter length scales than can be appreciated here, resulting in thus aliased observations, and whether the additional component is a real measurable yet unobserved (in this study) component, or an artefact of the method and data sources used in this study.We know that the eastern part of the eastern subgyre is dominated by an intense mesoscale eddy field (Ryan et al., 2016, Leach et al., 2011and Gordon and Huber 1984), where the boundary to the gyre is poorly-defined due to the openness of the topography.Indeed, Schröder and Fahrbach (1999) 515 suggest that there is no continuous current marking the eastern boundary, and that baroclinic shear instabilities lead to a breakdown of the eastward-flowing current in the northern limb of the gyre, and that the current "reforms" in the westwardflowing southern limb.This also aligns with the findings of Sonnewald et al. (In review), who use machine learning in a climate model to diagnose the dominating dynamic regimes in the Southern Ocean, leading them to propose a circumpolar "supergyre" which connects the Weddell and Ross sub-gyre systems.In the far-eastern sub-gyre region, recirculated "cold-regime" 520 WDW (modified primarily through heat loss) comes into contact with incoming "warm-regime" WDW (Gordon and Huber, 1984).The "warm-regime" WDW represents relatively warm WDW advected into the gyre at the eastern inflow zone at about 30° E, driven by mesoscale eddies (Deacon 1979;Orsi et al. 1993;Orsi et al. 1995;Gouretski andDanilov 1993, 1994;Ryan et al., 2016).It is therefore possible that horizontal turbulent diffusion, supposedly representative of turbulent dynamic processes within this study, is underestimated in this region.This is also implied when comparing the two terms in Fig. 2a and 525 2c: while the magnitude is much larger in Fig. 2a (horizontal mean advection), horizontal turbulent diffusion displays the opposite signs and partially compensates in the eastern sub-gyre region in Fig. 2c.
It could also be that there is a missing process, such as entrainment, that may account for the non-closure of the heat budget terms in Fig. 2e (though entrainment would constitute a heat flux divergence which may help close the heat budget of the IC, but not of the SL).Indeed, Schlosser et al. (1987) used Helium-3 tracers within the north-western Weddell Sea to estimate a 530 vertical diffusivity that is twice the value that we use here (5 x 10 -5 m 2 s -1 ) along with a rate of entrainment of WDW into the overlying WW of 15-35 m yr -1 .Behrendt et al. (2011) argue that increasing WW salinity during 1992-1996 is caused primarily by entrainment of WDW, and lists entrainment as one of three dominating causes of salinity changes to WW (the others being sea-ice formation related salt release and horizontal advection).Brown et al. (2015) also highlight the important role of entrainment in the carbon dynamics of the Weddell Gyre, by bringing dissolved inorganic carbon and salt upwards into the 535 WW from the underlying WDW.Given this work is based entirely on observations, and that we lack sufficient observations to effectively resolve the complex dynamics of the eastern Weddell Gyre, the findings here illustrate the need for better observational coverage of the Southern Ocean in the high latitudes east of the Prime Meridian, a region thus far often omitted from observation campaigns.
Maud Rise is a prominent feature in temperature (Fig. 1), mean horizontal advection (Fig. 2a), horizontal turbulent diffusion 540 (Fig. 2c) and to a lesser extent, vertical diffusion (Fig. 2d).The effect of Maud Rise on WDW temperatures is due to the presence of a Taylor column directly over Maud Rise, which has been previously observed as a stagnant column of relatively cold water surrounded by a warm halo on the flanks of Maud Rise (e.g., Muench et al., 2001;Leach et al., 2011).Regarding the heat budget terms shown in Fig. 3, mean horizontal advection results in a heat flux convergence upstream of Maud Rise, which is partially balanced by heat flux divergence due to horizontal turbulent diffusion.In contrast, downstream of Maud

545
Rise, heat flux divergence occurs due to both mean horizontal advection and horizontal turbulent diffusion in Fig. 3 (although a convergence peak in horizontal turbulent diffusion does occur directly over Maud Rise).
The effect of mean horizontal heat advection on the flanks of Maud Rise is probably mainly an artefact of the velocity field.
Since the water overlying Maud Rise is cold, and the velocity field does not adequately resolve the flow circulating the seamount (instead the streamlines in Fig. 1 cut directly East-West across Maud Rise), the heat convergence upstream of Maud Rise and divergence downstream of Maud Rise are caused by strong lateral temperature gradients between the cold water column overlying Maud Rise and the warm halo surrounding it.However, the effects of mean horizontal advection upstream and downstream of Maud Rise partially cancel each other when integrating zonally in Fig. 3. Furthermore, horizontal turbulent diffusion, which responds in a similar manner (since it is determined exclusively from observed horizontal temperature gradients, but not the velocity field, and therefore the response to Maud Rise is much smaller), acts to balance the influence of 555 mean horizontal advection upstream of Maud Rise (Fig. 3).Indeed, the overall heat loss that occurs downstream of Maud Rise in Fig. 3 is about 40 W m -2 , which is similar to previous estimates in Muench et al. (2001) and also in McPhee et al. (1999;52 W m -2 west of Maud Rise and 23 W m -2 over Maud Rise), although these authors focus on the surface heat flux, both using surface drifting buoys.
In Fig. 3, regardless of the perturbation resulting from the influence of Maud Rise, there is a build-up of heat due to mean 560 horizontal advection across the entire southern limb, even if the region over Maud Rise is removed from the integration.There is also a continual removal of heat by horizontal turbulent diffusion regardless of Maud Rise, which would be the case even if we increased the diffusivities on the flanks of Maud Rise, where deep convection has been previously observed (e.g., Akitomo, 2006), since the turbulent diffusion would cancel itself out when integrated zonally across Maud Rise (unless the diffusivities themselves were significantly different on each flank).Thus, it is important that we integrate over large areas and view these 565 results as a representation of the processes influencing large-scale heat distribution of the Weddell Gyre (such as in Section 4.2), and avoid focusing on localised regions.Ultimately, we show that heat flux divergence due to horizontal turbulent diffusion occurs on the flanks of Maud Rise, in agreement with previous studies, which show for instance that baroclinic instabilities on the flanks of Maud Rise are the source of recurrent eddies (Akitomo et al., 2006).Furthermore, Leach et al.
(2011) and Ryan et al. (2016) suggest a mixing of WDW with modified recirculating WDW downstream of Maud Rise which 570 would explain the features observed in Fig. 3, where the zonal variation in horizontal turbulent diffusion is smaller west of the Prime Meridian.
Regarding the northern limb of the Weddell Gyre, our findings imply that horizontal turbulent diffusion is a mechanism by which heat enters the region (Fig. 2c).This is in some agreement with Jullion et al. (2014), who use an inverse model based on ship-based sections along 30º E to the coast and also along the northern periphery of the gyre at about 55-60º S in order to 575 diagnose the heat budget of the full water column.They suggest that most of the heat advected into the Weddell Gyre occurs along the northern gyre periphery, rather than from the eastern periphery, and reaches the southwestern Weddell Gyre through recirculation in the interior Weddell Gyre, leading to an entrainment of heat into the Antarctic Slope Front.This analysis is not able to resolve localised features such as the Antarctic Slope Front, but there is an indication, especially from the streamlines, that recirculation of the eastern sub-gyre plays a role in the distribution of heat in the Weddell Gyre (Fig. 1).3), then we can cautiously infer that most of the remaining horizontal turbulent heat flux occurs southwards towards the ice-covered shelf seas (Fig. 2c), of 12.6 ± 3 TW (southwards having a much larger length with larger negative 615 values in Fig. 2c in comparison to the western end of the SL region, (i.e., the stipled area in Fig. 2b).
These results indicate that horizontal turbulent diffusion may play an important role in transporting heat southwards across the open northern boundary of the Weddell Gyre (Fig. 5b & S6a), and also southwards towards the continental shelves along the Antarctic coast (Fig. 2c).Furthermore, the horizontal turbulent diffusion of heat may allow for the removal of some heat from the southern limb of the Weddell Gyre (Fig. 7b & S6b), before it is able to advect westwards towards the southwestern corner 620 of the gyre, where the fragile large Filchner-Ronne ice shelf and the ice shelves of the Antarctic Peninsula are located (Hellmer et al., 2012), and where recent advance in the understanding of ocean heat fluxes have been made (Ryan et al., 2020).Since the turbulent diffusive heat fluxes are dependent on horizontal temperature gradients (related to geostrophic shear), this implies a complex interaction between the strength of the Weddell Gyre, thus mean horizontal advection, and the rate of meridional turbulent diffusion.Potentially, up to a certain point, meridional turbulent diffusion may provide a buffer, protecting the 625 southwestern gyre from increased advective heat fluxes resulting from an intensified Weddell Gyre, by also increasing in intensity (due to stronger lateral temperature gradients and velocity shear).This mechanism requires careful understanding if we are to understand the role of the Weddell Gyre in the redistribution of heat in a changing climate., or a total of +2.5 ± 0.03 TW, and IC: 0.8±0.2Wm -2 , or a total of 6.5 ± 0.1 TW).

Gridded
b. heat is diffused upwards out of the top of the layer, due to the relatively strong vertical temperature gradient 670 at the thermocline, and due to vertical instabilities at the thermocline (SL: -2.7 ± 0.5 Wm -2 , or a total or -7.2 ± 0.4 TW, and IC: -2.3 ± 0.3 Wm -2 , or a total of -17 ± 0.6 TW).This heat may eventually be lost to the atmosphere.
7. East of the Prime Meridian, 2 ellipses of strong heat flux divergence and 2 ellipses of strong heat flux convergence are found to the north and south of the eastern sub-gyre respectively.This is directly related to horizontal mean 675 advection and is likely an artifact of a misalignment between horizontal circulation and strong horizontal temperature gradients on a coarse resolution grid.However, the "misalignment" may be linked to the occurrence of unresolved mesoscale eddies that are not represented by turbulent heat flux diffusion, that may be skewing the mean state representation of the temperature and flow fields.This is possibly due to poor data coverage in a region where instabilities are likely generated from the interaction between "cold" regime recirculating WDW and incoming 680 "warm" regime WDW (Gordon and Huber, 1984 and Fig. 1).Unresolved horizontal circulation around Maud Rise adds to the uncertainty in the region.Thus, to improve estimates in the eastern Weddell Gyre, more observations are required to resolve the complex ocean dynamics on smaller length-scales in the eastern sub-gyre region.
From using Argo floats, we have described the heat budget of a 1000 m thick layer encompassing the core of WDW within 685 the Weddell Gyre.The role of mean horizontal advection is evident in feeding heat towards the southwestern Weddell Gyre, where the Filchner-Ronne ice shelves and Antarctic Peninsular are located.What is also important, however, is understanding the respective roles of mean horizontal advection and horizontal turbulent diffusion in removing some of that heat from the southern limb of the Weddell Gyre before it is able to reach the southwestern interior.This is crucial since Hellmer et al. (2012) suggest that under future climate scenarios, a redirection of the coastal current toward the Filchner-Ronne ice shelf could lead 690 to increased advection of waters into the ice-shelf cavity, leading to increased basal ice melt from 0.2 to 4 m/year.

Figure 1 :
Figure 1: Sub-surface conservative temperature at the depth of temperature maximum (Θmax) with streamlines (grey contours) of the vertically integrated stream function for 50-2000 dbar with a spacing of 5 Sv, derived from in-situ observations from Argo floats (Reeve et al., 2019, 2016).Black dots show Argo float profile positions and red stars show mooring positions used in velocity field estimates.The thick black line shows the repeat ship-based transect from Kapp Norvegia to Joineville Island.The red circles labelled 1-3 show Gunnerus Ridge, Astrid Ridge and Maud Rise, respectively.The black contours show the 1000, 2000 and 3000 m isobaths, from the general bathymetric chart of the oceans (GEBCO, IOC et al., 2003).

110
adjustments were made to the gridded velocity field prior to fitting a stream function.Firstly, long-term average velocities derived from mooring data were included at the coast near the Prime Meridian and Kapp Norvegia, to better resolve the flow which follows the coastline as it curves southwards towards the Filchner-Ronne ice shelves (the mooring positions are marked in Fig.1.See Le Piah et al. 2020 for further information about the mooring data).Secondly, the velocity field at Gunnerus Ridge (also marked in Fig.1) required special treatment.The trajectories of Argo floats show a tight, bathymetrically steered 115 flow around Gunnerus Ridge, which is lost during the objective mapping process due to larger length scales.Also, while the potential vorticity values to either side of the ridge are the same, the direction of the flow is opposing (i.e., primarily northwards on the eastern flank of Gunnerus Ridge and southwards to the west of Gunnerus Ridge; see Fig.11in Reeve et al. 2019).This https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.opposing direction is averaged out in the objective mapping.Therefore, after the objective mapping, the closest grid cells to Gunnerus Ridge are replaced with direct velocity measurements derived from the three Argo floats that drift along the ridge 120 (the Argo floats have WMO numbers: 7900164, 7900166 and 7900168).There are caveats to this decision, in that these are data points from three floats with a limited time span (from February-May 2007, and then December 2007 until April 2008), during a period when the area is ice-free.However, by making this adjustment, we improve the performance of the cost function in providing a stream function representative of the large-scale circulation, which includes a more complete inflow (in comparison to Fig. 4 in Reeve et al. 2019).The resulting stream function for the vertically integrated flow from 50-2000 dbar 125 is shown in Fig. 1, where the streamlines curve around Gunnerus Ridge, indicating the main inflow into the southern limb of the Weddell Gyre.
https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.for the diffusivities.While κv is similar to Donnelly et al.'s estimate of 2.4 x 10 -5 m 2 s -1 , our baseline horizontal diffusivity is 155 slightly larger than the 247 m 2 s -1 provided by Donnelly et al. (2017; though within range of our values provided by the uncertainty range) and is chosen in consideration of a range of values provided by Donnelly et al. (2017),Zika et al. (2009) and vertical diffusivity terms respectively (with the exception of the regions where theSevellec et al. (2022)  dataset is used, where a standard error of the mean is used, see Supplements S4).These are large ranges to account for the possible range in 190 values available in the literature, while acknowledging the lack of consensus and reliable data for this input (we discuss this further in Section 5.1.3).The derivation for the propagated errors is provided in the Supplement (S7), along with maps of the error for each heat budget term.The errors are provided in the large-scale integrations of the IC and SL in Figs.3-7(as pale blocks of colour surrounding the lines).
https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.maps provided throughout this paper show streamlines (grey contours) indicating the horizontal circulation of the Weddell Gyre derived from Argo floats (see Section 2.2 and Reeve et al. 2019 for further details).Where the streamlines are closely spaced, flow is more intense than where they are loosely spaced.The streamlines describe a double-gyre structure whereby the western sub-gyre is weaker than the elongated, stronger eastern sub-gyre.The following section is presented in 200 two parts.
https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.The heat tendency resulting from the sum of the heat budget terms (left-hand side of eq.1.2). is provided in Fig.2e.There is 235 a patchwork of negative (cooling) and positive (warming) values throughout, and overall Fig.2eis spatially mostly similar to the heat flux due to mean horizontal advection in Fig.2a.There is, however, a discernible cooling throughout the open southern limb in Fig.2e, in comparison to Fig.2a, and a clear warming along the northern limb, driven by horizontal turbulent diffusion (Fig.2c).Any non-zero value in Fig.2eshould correspond to an area of warming (positive tendency) or cooling (negative tendency) of the water column.Given that data from a 15 years-long observation period have entered the calculation, we 240 wouldn't expect the real ocean to have experienced such a patchy warming and cooling pattern, resulting -in particular -from the horizontal advection field.In chapter 4.2 we therefore perform spatial integration of the fields displayed in Fig.2a-eover distinct areas defined by the circulation (SL and IC), in order to eliminate some of the noise, such that more robust statements on the main balances between the different heat flux terms can be made on a regional scale.The uncertainties will be discussed further in chapter 5. 245 (2a) (2b) https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.(2c) (2d) https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.(2e) Figure 2: The heat budget terms from Eq. 1.2, for a layer of water 1000 m thick from the depth of the mid-thermocline: (a) mean horizontal geostrophic heat advection, (b) mean vertical advection, (c) horizontal turbulent diffusion (d) vertical turbulent diffusion and (e) the sum of the terms in a-d.Positive values indicate warming, i.e. heat transport convergence, where more heat is entering the grid cell than is leaving it, whereas negative (blue) values indicate cooling, i.e. heat transport divergence, where more heat is leaving the grid cell than is entering it.Grey and black contours provide the horizontal streamlines and the 1000, 2000 and 3000 m isobaths respectively (as in Fig. 1).The stippled areas in Figs.b and d show the regions defined as SL and IC respectively, encased in the blue streamlines used to define the SL and IC regions.These regions are horizontally integrated across in the following Section 4.2.Note the different colour scales for the horizontal versus vertical fluxes.
https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.The largest regional fluctuations within the IC (Fig. 4, upper panel) in the sum of the terms are caused by two large peaks in mean horizontal advection, east of Maud Rise, where mean horizontal advection fluctuates from -65 Wm -2 to 50 Wm -2 and

Figure 3 :
Figure 3: upper panel: the heat budget terms for the southern limb (SL) of the gyre in Wm -2 ; lower panel: the cumulative heat budget terms in Terawatts (TW).The key for the legend is listed in Table 2.The dashed vertical line marks the approximate longitude of Maud Rise, at 3º E.

Figure 4 :
Figure 4: As in Fig. 3, but for the interior circulation cell (IC) of the Weddell Gyre.

Figure 5 :
Figure 5: (a) Heat budget terms for the IC-north, west of 25°E: upper panel: zonal means in Wm -2 ; lower panel: the cumulative heat budget terms from west to east in Terawatts (TW).The key for the legend is listed in Table 2.The dashed vertical line marks the approximate longitude of Maud Rise, at 3º E. Panel b shows the zonal variation of the diffusive horizonal heat flux across the northern boundary of the northern limb of the Weddell Gyre, in W m -2 , defined by the streamline that equals 25 Sv.Negative values indicate a southward flux of heat into the eastward-flowing northern limb of the Weddell Gyre from north of the northern Weddell Gyre boundary (the subsequent cumulative horizontal diffusive heat flux across the northern boundary is provided in the Supplements in Fig. S6a).

Figure 6 :
Figure 6: θmax (°C) along the streamline Ψ = 26 Sv (i.e., the outermost boundary of the IC).The distance in km is along the streamline in a clockwise direction from 25°W, 65°S, with key locations marked using the legend.

Figure 7 :
Figure 7: (a) Heat budget terms for the IC-south, west from ~3°E (Maud Rise): upper panel: the heat budget terms in Wm -2 ; lower panel: the cumulative heat budget terms in Terawatts (TW).The key for the legend is listed in Table 2.The dashed vertical line marks the approximate longitude of Maud Rise, at 3º E. Panels b and c show the zonal variation of the diffusive horizontal heat flux in W m -2 for (b) across the boundary between the SL and the IC, and (c) across the central gyre axis from the IC-south to the IC-north, west of Maud Rise.Positive values indicate a northward flux of heat from the SL into the IC, and from the IC-south northwards into the IC-north, respectively (the subsequent cumulative horizontal diffusive heat flux across the northern boundary is provided in the Supplements in Fig.S6b-c).
than inLeach et al. (2011), but with similarities to the length-scale assumed inCole et al. (2015) of 300 km.We make the decision to use the Sevellec et al. (2022) dataset where numerous data are available, and, for within the Weddell Gyre, we arbitrarily provide a baseline range of potential values for horizontal diffusivity, in the range of that provided by Donnelly et https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.
as a heat source (heat flux convergence) within the eastward flowing northern limb of the gyre and to a lesser extent the gyre interior.In contrast, horizontal turbulent diffusion is associated with a divergent heat flux (or loss of heat) in the open southern limb of the gyre, as well as directly north of the gyre.For the most part, mean vertical advection and vertical turbulent diffusion are spatially relatively uniform, where upwelling advects heat upwards into the WDW layer, and vertical turbulent 465 diffusion removes heat through the top of that layer, upwards through the thermocline to the overlying Winter Water (WW).

580
Furthermore, inJullion et al. (2014), eddy-induced transport contributes significantly to the heat budget of the Weddell Gyre, with a heat flux of 5 ± 1 TW, out of a net heat flux of 36 ± 13 TW from the ACC into the Weddell gyre, which is primarily due to mean circulation.The results provided in Figs.2c & 5-7show agreement with this finding; the Weddell Gyre's northern limb and the IC are dominated by a convergence of heat due to horizontal turbulent diffusion.Both the southern limb and the area directly north of the Weddell Gyre in the ACC, as well as east of ~30°E, in contrast, exhibit heat flux divergence (or 585 cooling) due to horizontal turbulent diffusion (Fig.2c).This suggests that horizontal turbulent diffusion constitutes an important role in transporting heat into the Weddell Gyre along the open northern boundary as well as from the East-(although large uncertainty in the east requires some caution), in agreement withJullion et al. (2014).The heat fluxes provided here are somewhat more than the eddy induced heat transport fromJullion et al. (2014) across both the northern and eastern boundary, which, however, accounts for the whole water column, across 2 hydrographic sections which represent the entire open 590 boundary of the Weddell Gyre.We expect their eddy heat flux estimate to exhibit major uncertainties, as it is firstly based on https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 Author(s) 2023.CC BY 4.0 License.a station spacing of the temperature and velocity profiles that are not nearly eddy resolving (especially along the northern boundary of the gyre) and secondly represents a one-time snapshot.According to Tamsitt et al. (2016) and Naveira Garabato et al. (2011), major topographic features result in a divergence of horizontal and vertical eddy heat fluxes, leading to substantial warming in association with regions of enhanced mesoscale 595 energy.Thompson & Salleé (2012) use particle advection experiments to show that the enhancement of eddy kinetic energy occurs downstream off topographic obstacles, which may explain cross-front exchange associated with jets in the lee of topographic features.This may explain the heat flux divergence due to horizontal turbulent diffusion that occurs in the lee of Maud Rise (Fig. 2 and 3).It may also help to explain the fluctuations along the northern limb of the Weddell Gyre in Figs.2a and 2e, where the topography is complex, creating an open-ocean northern boundary to the Weddell Gyre.Indeed, the 600 alternating bands of convergence and divergence along the northern limb of the gyre between 30° W and 20° E in Figs.2a and 2e appear to reflect the underlying bathymetry, though the alternating bands are also likely due to the effects of meandering of the northern boundary on a coarse resolution grid.There is also a relatively strong heat flux divergence due to horizontal turbulent diffusion along the southern boundary of the Weddell Gyre towards the coastline in Fig. 2c, especially between 40 and 10° W, and between Astrid ridge and Gunnerus 605 ridge (between 10 and 30° E), indicating that horizontal turbulent diffusion may also constitute an important role in transporting heat towards the shelves along the southern coastline.Indeed, enhanced diffusive mixing over the continental slope (region not covered by this study) has been observed in the southwestern Weddell Sea (Fer er al., 2016; Daae et al., 2009).We are unable to directly compute turbulent heat fluxes across the southern boundary of the southern inflow limb toward the shelf edge due to the requirement of differencing across grid cells, and caution should be made with any attempt at inferring fluxes 610 due to the large uncertainty of computing the heat budget at the boundary.Yet, we may estimate the shelf-ward heat flux indirectly.Fig. S6b reveals the net diffusive heat flux across the northern boundary of the southern inflow limb to amount to 6.4± 0.6 TW.If we subtract this value from the total heat flux divergence due to horizontal turbulent diffusion of the SL of 19 ± 2 TW (Table climatologies of temperature and velocity derived from Argo floats spanning 2002-2016 were used to determine the 630 heat budget of a 1000 m thick layer encompassing the core of WDW within the Weddell Gyre.This investigation was to https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.establish the mechanisms by which heat is distributed throughout the Weddell Gyre, implicitly assuming non-divergent, geostrophic flow conditions.The mechanisms are summarised in the form of a basic schematic in Fig.8, and interpreted below.

Figure 8 :2
Figure 8: Schematic of proposed mechanisms by which heat is transported throughout the Weddell Gyre, based on interpretation of results in Sections 4 & 5.3.3.The blue-scale colour shading shows Θmax and the black contours show the stream function with 5 Sv spacing, as in Fig. 1.The numbered keys assigned to each feature (arrows and circles) are described in Table 4.Where the colour of the number and feature are red, heat flux convergence (heat source) is indicated, and where they are blue indicates heat flux divergence (heat sink).The horizontal turbulent diffusive fluxes, indicated by small curved arrows (2,7,8), change from blue to red to indicate a direction of heat flux (i.e., in 2, horizontal turbulent diffusion removes heat from the SL northwards into the IC, and southwards to the Antarctic coastline (8), and in 7, removes heat from north of the gyre, into the northern limb of the IC).The change in colour from red to orange of the arrow in the SL (1) and IC-south (4) indicates cooling along the advective pathway as heat is removed from both areas, whereas the change in colour from pale blue to red of the arrow in the northern limb (6) indicates warming of the advective pathway as heat is diffused southwards from across the northern boundary, and to a lesser extent as heat is advected northwards downstream of Maud Rise to circulate the eastern sub-gyre (3).The blue circles with the central black dot (5) demonstrates the upwards loss of heat through the thermocline by vertical turbulent diffusion.The upper left inset shows an example of the vertical temperature profile, with -DV indicating a vertical diffusion of heat upwards out of the layer through the thermocline, and +AV indicating a vertical advection of heat upwards into the layer from below.

Table 1 .
A summary of the associated data source, method and citation for each variable required in the heat budget (Eq.1.2 in Section 3, and column 2 below).

temperature fields derived from Argo floats: All
Argo float data available for the Weddell Gyre region between 2002 and 2016 were used in this study to create gridded fields of velocity and conservative temperature.The latter was derived using the TEOS-10 program in MATLAB (McDougall

Table 2 : Explanations of the abbreviations used in Figs. 3-8.
https://doi.org/10.5194/egusphere-2023-21Preprint.Discussion started: 10 January 2023 c Author(s) 2023.CC BY 4.0 License.programs that contribute to it (http://www.argo.ucsd.edu,http://argo.jcommops.org).The Argo Program is part of the Global Ocean Observing System.The GEBCO Digital Atlas is published by the British Oceanographic Data Centre on behalf of IOC and IHO, 2003.The mean velocities derived from mooring data were provided by Nicolas Le Paih, to whom the authors are indebted to.The horizontal diffusivities were provided by Florian Sevellec (Sevellec et al., 2020).KR is supported through 705 the grant 424330345 of the Deutsche Forschungsgemeinschaft within the framework of SPP 1158 Antarktisforschung.The study also makes a contribution to EU SO-CHIC programme (grant number 821001) through the involvement of TK.This study is a contribution to the project T3 of the Collaborative Research Centre TRR 181 "Energy Transfers in Atmosphere and Ocean" funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation; project no.274762653).MV was funded by the BMBF project APEAR (#03V01461).