Explaining the Weddell Polynya -
a Large Ocean Eddy Shed at Maud Rise
D. M. Holland
Supplementary Material
The occurrence of the Weddell Polynya and its study is important for at least two reasons. First, it impacts the global ocean circulation by modifying the rate of formation of Antarctic bottom waters. It has been noted (1) that the bottom waters flowing out of the Weddell Sea (2) into the abyssal global ocean are heavily influenced by climate-regulated sea-ice dynamics in the Weddell Sea, and in particular by the appearance of large polynya. As the Weddell Sea is the primary bottom water formation area in the Southern Hemisphere, interannual anomalies in its bottom water outflow impact the global ocean circulation. Secondly, this polynya may affect the global carbon cycle. In seasonally frozen seas, the sea-ice cover forming in early autumn prevents atmospheric carbon dioxide, dissolved in the surface waters and assimilated in summer by marine microalgae, to return to the atmosphere in winter. A polynya that forms in seasonally sea-ice covered areas could contribute disproportionately to the sequestration of atmospheric CO2 and thus modulate the rate of air-sea carbon exchange (3).
The dynamical mechanism explaining the polynya is triggered when a modest, impulsive change in a southeastward ocean flow toward the Maud Rise generates a cyclonic eddy that is spawned off its northeast flank. The cyclonic eddy induces a divergent strain in the overlying sea-ice cover via an Ekman stress. This in turn leads to a large, crescent-shaped polynya which atmospheric thermodynamical interaction further enhances by rendering the ocean surface waters statically unstable, inducing vertical convection, and thus bringing to the surface warm, deep waters. The polynya so created is then advected southward around the east flank of the seamount by the mean background flow of the Weddell Gyre (4) and then southwestward. To understand such a non-obvious explanation for the occurrence of the Weddell Polynya, it is necessary to consider the interconnections between observational, theoretical, and modeling aspects of this phenomenon, both in a historical context and the new one offered here.
From a survey of the satellite observational record, quite a number of transient polynya can be identified. During 1980, for example, one such opening appeared on the northeast flank of the Maud Rise and took on an elongated shape (Supplementary 
Fig. 1a). Another opening appeared during 1994 and was much better resolved in detailed structure because of improvements in satellite instrument capabilities. That event also occurred on the northeast flank of Maud Rise and clearly took on a crescent shape (Supplementary 
Fig. 1b). Again a similar feature appeared over the northeast flank during winter of 1996 (Supplementary 
Fig. 1c).
These three polynya occurred during mid-winter with the sea-ice cover at or near its maximum extent over the Weddell Sea. In early fall of 1998 a polynya was observed to the west-southwest of Maud Rise, well away from the seamount. It gradually appeared as the seasonal sea-ice cover advanced northward over the area (Supplementary 
Fig. 1d). The polynya did not form after the area became covered in sea-ice but rather represented an area of ocean that, for some unknown reason, did not allow a sea-ice cover to form in the first instance. A month later, as the seasonal sea-ice continued its northward advance, another polynya appeared, this one along the east flank of the Maud Rise. Again, that polynya did not form after the area had become sea-ice covered, but only as the advancing seasonal sea-ice cover swept northward over the area and enveloped the polynya by encircling its perimeter.
From satellite data we see that a polynya may form along the northeast and east flanks of the Maud Rise and in a region to the west-southwest, away from the Maud Rise. Only a polynya at the northeast flank, crescent in shape, was ever actually observed to form in situ, that is, while an existing sea-ice cover prevailed. It appears that a polynya in other locations forms by having the seasonally advancing sea-ice cover close in around its perimeter.
A novel interpretation of these satellite observations is that the Weddell Polynya of the mid 1970s was initiated by an oceanic process that was triggered along the northeast flank of the Maud Rise. That perturbation was advected southward along the east flank and subsequently departed from the Maud Rise and followed along a west-southwest route. This scenario of advection of a disturbance in the sea-ice - ocean system, one that was initiated at the northeast flank, is consistent with the pattern of mean ocean flows in and round the Maud Rise region (4).
In the Maud Rise region, good use may be made of detailed knowledge of the observed bathymetry (5), hydrography (6), and mean ocean flow past the seamount (7) to help construct a meaningful idealization of this physical environment. The observed bathymetry (Supplemental 
Fig. 2a), salinity (Supplemental 
Fig. 2b), and temperature (Supplemental 
Fig. 2c) used as a basis for such an idealization, highlight the basic structure of the physical environment -- a seamount overlain by a salinity-stratified fluid with the temperature field having a subsurface maximum. An idealization of the bathymetry in the Maud Rise leads to the geographically restricted computational domain (Supplementary 
Fig. 3a) used in the study.
At the eastern extension of the basin-scale, cyclonic Weddell Gyre, the flow that impinges upon the Maud Rise may approach from the northwest. An analysis of climatological hydrographic data (6) indicates that a flow toward the southeast is the geostrophicaly favored flow direction for waters impinging upon the seamount (Supplementary 
Fig. 3b). The maximum velocity recorded by current meters placed on the northern flank of Maud Rise was 6.0 cm/s toward the southeast (7). This direction then serves as the basis for the idealized flow that is forced toward the idealized seamount. There are almost certainly significant fluctuation in the approach direction, anything ranging from a purely eastward flow to a southward flow, to a westward flow depending on how the larger-scale flow environment changes. As well as transients in flow direction, it is reasonable to expect that transients in flow strength occur. Observed currents over the northern flank have shown a standard deviation of the same magnitude as the velocities themselves, indicating a relatively high variability of the low-frequency flow at the Maud Rise (7).
The first explanation for the occurrence of the polynya considered the possibility that slow winds at the center of transient high and low pressure systems would delay sea-ice formation by restricting heat fluxes from the ocean to the atmosphere. A polynya would then arise naturally (8). It has also been demonstrated (9) that a polynya, once established, impacts the large-scale atmospheric winds and temperatures through the enhanced ocean to atmosphere fluxes brought on by the polynya itself. In either case, it remains unclear, however, that an atmospheric mechanism can explain the initiation of the polynya, particularly so with respect to the polynya's repeated occurrence in proximity to the seamount. That is not to say atmospheric feedbacks are irrelevant. It has been found, for example, that the thermal wind field of the lower atmosphere can interact with the heat emanating from a polynya so as to prolong the lifetime of the polynya (10).
Others argue that a polynya originates when a special area of the ocean surface is preconditioned and rendered more favorable to static instability and hence vertical convection. That special area experiences upwelling of warm, salty water that can supply enough heat to melt existing ice or prohibit its formation, even in the middle of winter. This hypothesis has been explored (11, 12) but the mechanism for the preconditioning itself has not been identified thus making this approach to polynya formation an incomplete one. Surface ocean feedbacks are important to the polynya, once established, as are the atmospheric feedbacks, but neither provides an adequate explanation of the initiation of the polynya, particularly with respect to a recurring geographic location, as implied by the satellite observations. Partly for this reason, attention has been turned to the Maud Rise seamount to determine what role it might play.
It has been proposed that the formation of a Taylor cap - that is a region of trapped fluid above the seamount - is one manner in which the local topography could play a role in polynya formation (13). The precept is that the trapped fluid might become more susceptible to convective overturning than the surrounding waters. This effect has been studied in an ocean model (14) where the presence of a Taylor cap over a seamount was found to produce enhanced convection compared to locations further away. Observational data, however, do not support the initiation of a polynya over the actual seamount itself, but further away off the flanks.
The ocean component (15) of the numerical model used in this study has an isopycnic vertical coordinate and thus describes the ocean as a stack of shallow water layers, with each layer upward in the water column representing fluid of a lighter density. The fluid in each layer is evolved by solving conservation laws for the mass, momentum, heat, and salinity content of the layer. The exception is the topmost layer that serves as an interface to the ocean interior below and to the sea-ice and atmosphere above. That special layer, referred to as the mixed layer, has its properties governed by a turbulent kinetic energy balance (16).
The sea-ice component is constructed by mimicking, almost exactly, an isopycnic layer of ocean fluid. By placing an additional shallow-water layer of fluid atop the ocean mixed layer, and by making some modifications to the physical prescription of that layer, a convenient sea-ice model is created. A first modification is that the momentum law of the ocean fluid has its Newtonian stress-strain relationship replaced by a plastic, cavitating-fluid rheology (17). A second modification is that the conservation relation for ocean salinity is replaced by a conservation relation for sea-ice concentration. The latter is defined as the percentage fraction of a given area of ocean surface that is covered by sea ice. The remaining modifications are to the turbulent and radiative fluxes as appropriate to a sea-ice covered ocean surface (18).
The sea-ice - ocean model is configured in a domain that represents an idealization of the Maud Rise and surrounding abyssal plain (Supplementary 
Fig. 4a). The water in the channel is assigned properties representing an idealization of the observed hydrographic data. Accordingly, a vertical salinity gradient of 34.35 psu near the surface to 34.65 psu at depth is adopted (Supplementary 
Fig. 4b). The model stratification is principally due to the salinity field in this setting and is taken to be surface intensified in accordance with observations. This creates a modest strength pycnocline region at a depth of 200 m below the surface. The water temperature, also horizontally uniform, is assigned to be at the freezing point for the mixed-layer waters (Supplementary 
Fig. 4c) that are in contact with a sea-ice cover. Below the mixed layer the waters everywhere are assigned a temperature of -1.0 ºC, except between the depths of 200 and 500 m, where the temperature is set as 0.0 ºC as a representation of the warm, deep waters in the region. The initially imposed uniform ocean flow is assigned a strength of 10 cm/s. Observations taken nearby in the region suggest a mean flow of about 5 cm/s with periodic excursions up to 15 cm/s (19). Thus the model choice of initial impulse velocity is a meaningful one.
The model configuration described is a rational, simplified, representation of the bathymetric, hydrographic, cryospheric, and atmospheric conditions that exist over the Maud Rise region during austral mid-winter. One can always opt to include greater details, features, and processes in a model to obtain a closer approximation to nature, but in the present instance the described model constitutes all the main ingredients needed to trigger the formation of an open-ocean polynya. Numerous other model configurations have been tested, some more realistic and including more accurate bathymetry and atmospheric forcing, and others even more idealized. Planning is currently underway for a future study using a fully-coupled atmosphere - sea-ice - ocean model on a southern-hemispheric domain. The presently described model configuration, however, represents the simplest model that contains all of the essential components that make a topographically-generated, open-ocean polynya. It does so without including extraneous factors that would only obfuscate, rather than highlight, the central dynamical mechanism leading to open-ocean polynya formation.
A thorough analysis of the mechanisms by which ocean flows interact with topography and a sea-ice cover has been undertaken in a separate study (20). That study provides, in a generalized setting, the theoretical foundation central to understanding how a transient ocean flow past a seamount can create an open-ocean polynya. The present report is an application of that theory to the specific context of the Weddell Polynya so as to clearly explain satellite observations of the polynya (Supplementary Figs. 1a,b,c,d).
The following animations (21) depict the evolution of selected model fields. Each animation includes brief introductory text followed by a sequence of 30 frames. The numerical model is run for a simulation period of 30 days and each frame depicts one day of simulated time. The model seamount is centered at 2 ºE and 65 ºS and extends just over one degree in each horizontal direction. Locally, spherical coordinates are not used and so one degree, in either longitude or latitude distance, spans about 111 km on this model grid. Also, note that the imposed mean background ocean flow is from right to left (i.e., the opposite direction to that presented in Figs. 3a and 3b of the Science Report).
Animation 1: Ocean Mixed-Layer Depth
The ocean mixed layer is initially set to a uniform depth of 40 m everywhere (corresponding to blue shading). A plan-view animation of the model domain shows the mixed-layer depth evolving along the left-flank (in the downstream sense) of the seamount to a depth of almost 1 km (corresponding to red shading) by the end of the simulation. A black, dashed oval shape indicates the position of the underlying idealized seamount.
Animation 2: Ocean Temperature Structure
The ocean temperature structure is initially set to the freezing point (corresponding to blue shading) in the mixed layer and -1 ºC water (corresponding to a green shading) in all deeper layers. The exception is the relatively warm water of 0 ºC (corresponding to red shading) placed over the depth range from 200 m to 500 m as a representation of the warm, deep waters. A vertical-transect animation, cutting south-to-north and traversing the model seamount, shows the evolution of the temperature structure. The mean background ocean flow is into the plane of the transect. Penetrative, open-ocean convection occurs over the left-flank (in the downstream sense) of the seamount and shows that warm, deep waters are brought into the surface layer.
Animation 3: Sea-Ice Concentration
The sea-ice concentration is initially set to a uniform 100 % coverage (corresponding to red shading). A plan-view animation shows that by the end of the simulation, a large, crescent polynya (corresponding to blue shading) has opened on the left-flank (in the downstream sense) of the seamount. A black, dashed oval shape indicates the position of the underlying idealized seamount.
The ocean model's early response to an initially imposed barotropic flow field is largely a barotropic response. However, over the first few days of the simulation, the large-scale flow field begins to feel the presence of the seamount and adjusts accordingly. It does this principally by conserving potential vorticity, a quantity that is in fact exactly conserved in the discretized conservation laws employed in a layered, ocean-model framework. There are, of course, sources and sinks of vorticity that arise from interaction of the ocean flow with, for example, the seamount through a quadratic drag law that exerts a bottom Ekman stress on the ocean fluid leading to a bottom torque. There is also a surface Ekman stress on the ocean fluid due to the presence of the overlying sea ice. Additionally, the sidewalls exert a frictional force and thus a torque. Even with all such frictional torques in operation, the modest frictional coefficients used imply that the ocean fluid largely conserves its initial potential vorticity over the relatively brief integration period.
Depending on the strength of the initial impulsive background flow, and the frictional parameters describing the interaction of the ocean with the seamount and the sea ice, the model's left-flank cyclonic eddy can either stay adjoined to the seamount or shed. In the context of the Maud Rise mean environmental flow, a cyclonic eddy that is shed would move downstream and travel in a clockwise fashion about the seamount starting from the northeast flank until it reached the southeast flank where it would then continue with the mean flow until it departed on a west-southwest tract, away from the seamount.
The simulation results demonstrate that the shedding of a cyclonic eddy initiates the formation process of a transient polynya. It is argued that the sequential shedding of multiple eddies leads to the creation of a super polynya. As is evidenced in the 1998 satellite data (Supplementary Fig. 1d), where two transient polynya were simultaneously observed, it is not unreasonable to expect that in a single winter season several large cyclonic eddies can be shed. It is also plausible that the shedding process might be particularly strong for some particular winter, or that it might span across several winters, and thus produce a super polynya as in the 1970s.
Polynya forming in the open ocean have long been held to have a thermodynamical origin associated with the upwelling of warm deep waters, a process brought on by static instability and vertical convection. It is perhaps surprising then to find that thermodynamic mechanisms play only a secondary role in the formation of this polynya. The primary mechanism, dynamical in origin, responsible for the opening of the sea-ice cover in the vicinity of the Maud Rise is a cyclonic eddy shed from the northeast flank of the Maud Rise that generates a divergent Ekman stress in the overlying sea-ice cover. That stress opens the sea-ice and marks the birth of a new polynya. The ultimate fate of that polynya is a function of the initial strength of the shed eddy. A weak eddy will produce a small opening that is quickly closed up by new sea-ice growth; a strong eddy will produce a sea-ice opening sufficient to bring on secondary thermodynamic process leading to open-ocean convection and polynya enhancement. Once generated the cyclonic eddy is advected downstream with the mean ocean currents -- first southward and then west-southwest. The actual location of the appearance of a polynya depends, simply enough, on there being sea-ice cover in existence when an eddy is present. An eddy that is shed, but without any ambient sea-ice cover, will advect downstream and will only 'appear' as a polynya once the seasonal sea-ice cover advances northward past the eddy feature.
Does this theory fit with observational knowledge? From the satellite record of sea-ice coverage, the answer is yes. To see this clearly we need to consider the record in two parts. The first concerns a polynya that appears (Supplementary Figs. 1a, 1b, 1c) in mid-winter when the eastern Weddell Sea is almost completely sea-ice covered. In that scenario, the satellite record indicates that a polynya shows up along the northeast flank of the Maud Rise, but nowhere else in the vicinity. A second type of polynya is one that 'appears' while the sea-ice cover is advancing northward, during fall. In the instance that a cyclonic eddy has been shed some months earlier and is traveling downstream in sea-ice free waters then it is only when the seasonal advance of the sea-ice cover meets the southward or west-southwest propagating cyclonic eddy that a polynya might appear at a location other than the northeast flank of the seamount. In fact, at least one such observation (Supplementary Fig. 1d) shows a fall in which the northward advance of the sea ice encircles two such patches.
Another salient point with respect to observational knowledge about polynya formation is that it is commonly believed that the west-southwest region, away from the seamount, is somehow the favored position for polynya formation because polynya are often observed in that location (Supplementary Fig. 1d). This is largely a reflection of the sea-ice cover being climatologically present in that region for approximately nine months per year. By contrast, the northeast flank of the seamount, the region proposed by the new theory as being the polynya birthplace, is only covered by climatological sea-ice cover during six months of the year. It is reasonable that cyclonic eddies, shed from the northeast flank and then advected with the mean flow, are then more likely to be observed as polynya, in a statistical sense, in the west-southwest region away from the Maud Rise.
The new theory also has concordance with hydrographic observations. A large cyclonic eddy has been observed in the west-southwest region away from the Maud Rise (22). It is noted that such a feature, being ultimately a consequence of the conservation of potential vorticity, need first travel southward along the east flank of the Maud Rise. There is no apparent mechanism by which a cyclonic eddy can travel southward along the west flank of the Maud Rise. For this reason, it is claimed that cyclonic eddies seen far to the west-southwest of the Maud Rise, away from the seamount, have traveled along the east flank of the seamount, and in fact have been generated at the northeast flank in response to transients in the mean ocean flow imposed upon the seamount.
It has been observed that there exists a halo of anticyclonic vorticity along with uplifted isotherms along the southwest flank of the Maud Rise as well as the large, cyclonic patch further to the west-southwest, away from the seamount, mentioned above. These two patches of opposite vorticity waters are consistent with that which follows from the dynamical arguments following from the new theory (23). It should further be noted that while observations were actually being made of the halo of anticyclonic vorticity along the southwest flank (22), a polynya appeared on the northeast flank (Supplementary Fig. 1b). A curious phenomenon readily explained by the dynamical mechanism of the new theory but very difficult to explain based on a purely thermodynamics mechanism, although the latter type of argument is often put forward.
A future challenge remains to accurately hindcast and forecast actual polynya events in the Weddell Sea now that the mechanism of formation is in hand. To do this, a better understanding of the processes that lead to variations in the wind and density driven components of the mean flow of the waters of the Weddell Sea will be needed, and possibly even a look further afield into the entire Antarctic region and to variations associated with phenomenon such as the Antarctic Circumpolar Wave (24). We can then question how fluctuations in the atmospheric circulation and variations in the import of water masses from distant oceans produce a variability that leads to fluctuating currents impinging upon Maud Rise. Predicting the onset of the next super polynya will require that knowledge.
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