Circum-Antarctic bottom water formation mediated by tides and topographic waves

Domain: earth_science
Published: 2024-03-06
Editorial outcome: minor_revision

Abstract
The downslope plumes of dense shelf water (DSW) are critical for the formation of Antarctic Bottom Water (AABW), and thus to the exchange of heat and carbon between surface and abyssal ocean. Previous studies have shown that tides and overflow-forced topographic Rossby waves (TRWs) may have strong impact on the downslope transport of DSW, but it remains unclear how the combined action of these two processes influence the descent processes of DSW, and of the resulting AABW properties. Here, with a synthesis of historical in situ observations and a set of numerical model experiments, we show that tides and TRWs play comparable roles in AABW formation: they both act to accelerate DSW descent to the abyss, leading to the formation of colder and denser AABW. Yet, tides have little impact on AABW formation unless the continental slope is steep enough to suppress TRW generation. We further characterize the dynamical regimes of dense overflows around the entire Antarctic continent based on the relative importance of TRWs versus tides. These findings highlight the pervasive role of high-frequency processes, which are not well represented in the present climate models, in the formation of AABW, and thus in the global overturning circulation.

Introduction
Antarctic Bottom Water (AABW) originates from the descent of dense shelf waters (DSW), which are formed via a combination of brine rejection during sea ice growth and ocean/ice shelf interactions around Antarctic coast1,2. Due to its relatively high density, DSW overflows across the shelf break, descends over the continental slope, entraining ambient water, to produce AABW3,4. This process ventilates abyssal ocean and impacts the heat and carbon inventory, and thus plays a key role in global ocean overturning circulation and climate5–7.

It has long been established that the Weddell and Ross Seas are the primary source regions of AABW8–10. In recent years, the Adélie coast region and Prydz Bay have also been identified as areas of AABW formation11–13. A review of nearly 50 years of direct hydrographic observations show that dense overflows are widely spread around Antarctic continental margin14 (Fig. 1a), all potentially contributing to the formation of AABW. Motivated by the increasing number of different situations in which AABW is formed, in this study we seek a general understanding of the dynamical mechanisms that govern the descent of DSW, and their influences on the entrainment that transforms DSW into AABW.

Theoretically, under the strong influence of the Earth’s rotation in polar regions, a steady downslope flow should turn westward to spread approximately along isobaths, while descending slowly via benthic layer Ekman transport15,16. Variable bathymetry may facilitate this downslope flow via topographic steering2,13,17,18. However, in situ observations show that DSW can also reach the deep ocean over a relatively short along-slope distance, even in the absence of topographic steering12,19–21. This implies that other mechanisms must serve to accelerate the descent of DSW. Two such mechanisms have been identified in previous studies: tidal effects22–25 and topographic Rossby waves (TRWs) associated with baroclinic instability of dense overflows16,26–29. However, it remains unclear to what extent tides versus TRWs influence the DSW downslope transport and entrainment, and thus the formation rate and properties of AABW, across the range of overflow regimes found around Antarctic margins.

Here, we synthesize historical in situ data in the Weddell Sea and Ross Sea, where observations are relatively abundant, and formulate an idealized high-resolution process-oriented numerical model to investigate the roles of tides and TRWs on the formation of AABW. We explore their effects across a parameter range wide enough to span the behaviors around the entire Antarctic continental margin, and generalize our findings to give a pan-Antarctic description of the dynamical regimes in different overflow sites.

Results
We first identify the modes of variability observed in Antarctic DSW overflows, using moored measurements from the two most heavily-instrumented overflow sites (see Methods). Both the Weddell Sea (Fig. 1b) and the Ross Sea (Fig. 1c) exhibit significant downslope flows with large periodic oscillations over the lower continental slope. However, there is a fundamental difference between the Ross and Weddell Seas: the oscillations in the Ross Sea are mainly diurnal, consistent with tidal fluctuations23,30, while those in the Weddell Sea have a primary periodicity of several days, consistent with TRWs29,31. However, despite the different periods and processes, both sites exhibit a close correspondence between the oscillations of the downslope flow and the water temperature. This suggests that the downslope transport of DSW is mediated by tides in the Ross Sea, and by TRWs in the Weddell Sea.

In addition to diurnal tidal oscillations, the Ross Sea also shows a spring-neap fortnightly tidal cycles with a period of approximately 14 days. The coldest waters emerge during the spring tide rather than the neap tide; the correlation between the daily tidal flow strength (black line in Fig. 1c, see “Methods”) and minimum temperature (magenta line) is −0.8. The fact that the coldest waters emerge during the spring tide therefore suggests that temperature variability is governed by the tendency of the tides to advect DSW across the continental slope22,23, rather than by the mixing induced by the tidal flow32,33. This phenomenon is robust across all the moorings on the continental slope and is further supported by other moorings farther seaward of the continental slope (Supplementary Fig. 1). In contrast, stronger tidal flow dilutes DSW on the continental shelf break (moorings M1 and CA, Supplementary Fig. 1), consistent with the influence of stronger tidal mixing32,33.

Tidal influence on Antarctic overflows
To interpret how tides and TRWs control the rate of DSW descent and entrainment, we use an eddy-resolving process-oriented numerical model with 500 m horizontal resolution in the vicinity of the DSW overflow34–36, and track the overflow with passive tracers (see “Methods” and Supplementary Fig. 2 for detailed model setup). The results show that in a Ross Sea parameter regime, tracers are advected to greater depths and retain higher concentration in the presence of tides (Fig. 2a, b), though the tracer concentrations are more diluted in the regions shallower than 500 m depth (Fig. 2c, d). Hence, tides actually reduce the rate at which DSW is mixed with overlying waters on the continental slope: zonally integrated tracer diapycnal mass flux is temporally steady and substantially stronger in the experiment without tides (Fig. 2c), but becomes weaker and exhibits periodic variations when tides are included (Fig. 2d). Figure 2e shows a large variation of the pycnocline depth in the tidal experiment—deepening of the pycnocline coincides to the downslope transport of DSW—while the pycnocline depth remains nearly steady in the absence of tides. The pycnocline deepening is induced by the flow convergence during the ebb tide (Supplementary Fig. 3), which produces a V-shaped frontal structure that drives the cold, fresher surface waters to descend to over 1000 m. In situ observations display a similar structure (Fig. 2f, g). Therefore, the tidal flow has two key effects on the DSW overflow: one is to pump the DSW quickly to the deep ocean and reduce entrainment; the other is to induce the V-shaped front that permits the DSW to entrain relatively cold, low salinity water37, instead of warm and salty circumpolar deep water (CDW) (Fig. 2f, g). This could explain the colder but fresher AABW in both observations and tidal experiment (Fig. 2f–h and Supplementary Fig. 1b).

Overflow-forced TRWs
In contrast to the Ross Sea overflow, observations in the Weddell Sea show that overflow-forced TRWs are dominant and exhibit two clusters of frequencies, with higher and lower frequencies concentrated on the upper and lower continental slope respectively, albeit with some overlap31,38 (Fig. 3a, b). Tidal flow in the Weddell Sea is strong near the shelf break region, but is relatively weak compared to the Ross Sea, and becomes much weaker on the continental slope (Fig. 3b). Taking 20 cm/s as a representative maximum cross-slope tidal flow speed at 1000 m isobath39, the estimated cross-slope excursion (see “Methods”) of the diurnal tide is about 5 km, and the corresponding vertical displacement is less than 250 m, suggesting that tides cannot produce efficient downslope transport in this region. In contrast, the stronger and lower-frequency oscillations associated with TRWs can be expected to produce larger excursions that facilitate the descent of DSW. In contrast to the Ross Sea overflow, observations in the Weddell Sea show that overflow-forced TRWs are dominant and exhibit two clusters of frequencies, with higher and lower frequencies concentrated on the upper and lower continental slope respectively, albeit with some overlap31,38 (Fig. 3a, b). Tidal flow in the Weddell Sea is strong near the shelf break region, but is relatively weak compared to the Ross Sea, and becomes much weaker on the continental slope (Fig. 3b). Taking 20 cm/s as a representative maximum cross-slope tidal flow speed at 1000 m isobath39, the estimated cross-slope excursion (see “Methods”) of the diurnal tide is about 5 km, and the corresponding vertical displacement is less than 250 m, suggesting that tides cannot produce efficient downslope transport in this region. In contrast, the stronger and lower-frequency oscillations associated with TRWs can be expected to produce larger excursions that facilitate the descent of DSW. Based on these considerations, we first neglect tides in our Weddell Sea-like experiment to investigate the role of TRWs exclusively. The model setup is similar to the Ross Sea experiment (see “Methods”), except for a spatially-varying topography to approximate the Weddell Sea continental slope. Although the setup is rather simplified and excludes tides and the inflow of the Antarctic Slope Current (ASC) from the east, the model is able to simulate TRWs that qualitatively resemble the observations (Fig. 3a–d). The downslope transport of DSW coincides with the offshore velocity associated with the TRWs (Fig. 3c), while isolated eddies form in the regions shallower than 1500 m, and confine boluses of DSW to the upper continental slope16. We explain the downslope transport from the perspective of energy conservation: the only energy source in our model is the potential energy input associated with DSW formation on the continental shelf, and this potential energy is released as the DSW slides into the deep ocean, energizing TRWs16,40. Similar to tides, TRWs can also induce a V-shaped front near the shelf break (Fig. 3e). Note that this frontogenesis occurs in the absence of winds35,41, tidal forcing42,43, and coastal freshwater inputs44. Thus TRWs may have similar effects on DSW overflows as tides, reducing entrainment and produce colder and fresher AABW. However, this cannot be demonstrated directly in our model because TRWs are internally generated and it is impossible to create a comparative experiment without TRWs for the Weddell-like model configuration.

Combined effects of tides and TRWs
According to previous studies, dense overflows are intrinsically unstable and can energize coupled TRWs that oscillate throughout the water column, but such an instability is suppressed by steep bathymetric slopes26,29. This is consistent with above analysis (Figs. 1–3) showing that a Ross Sea-like overflow (characterized by a large slope steepness, s = \Delta H / \Delta L = 0.15) exhibits no energy at TRW frequencies, while TRWs are prevalent in a Weddell Sea-like overflow where the slope is relatively gentle (0.02 ≲ s ≲ 0.07). These findings indicate that the bathymetric slope plays a key role in delineating different dynamical regimes of overflow29. However, it remains unclear to what extent tides and TRWs interact with each other and jointly influence the downslope transport of DSW.

To investigate the combined effects of tides and TRWs in different parameter regimes, we conduct a series of sensitivity experiments with varied slope inclines to simulate a range of overflow conditions around Antarctica (see Methods and Supplementary Fig. 4 and Table 1). We track the depth to which DSW has descended by finding the isobath corresponding to the DSW tracer’s center of mass, H_DSW, as a function of along-slope distance (see Methods). This diagnostic allows us to visualize the mean descent pathway of DSW (Fig. 4a). In experiments without tides, the rate at which DSW descends to the deep ocean varies non-monotonically with slope steepness. This is due to the transitions among different dynamical regimes as the slope steepness increases, with a steady, quasi-along-slope overflow when the slope is relatively steep, formation of TRWs at intermediate slope steepness, and genesis of nonlinear eddies for gentle slopes16. In Fig. 4b we highlight this non-monotonic dependence on slope steepness by averaging H_DSW between x = 585 km and x = 595 km. When tides are added, DSW is advected to the deep ocean more rapidly in experiments with relatively steep bathymetric slopes (s ≥ 0.125), whereas for gentle slopes (s ≤ 0.1) the inclusion of tides has little impact on the descent pathway (Fig. 4a, b). This is because TRWs are suppressed over steep slopes and thus tides are needed to push DSW to the deep ocean, whereas gentle continental slopes have an offshore width far exceeding the tidal excursion distance, and the development of TRWs serves as the primary driver to accelerate DSW downslope.

As has been discussed above, our simulations indicate that the downslope advection of DSW by tides reduces the cumulative entrainment of overlying waters into DSW as it descends (Fig. 2), and that TRWs might have a similar effect. To quantify the impact of tides on entrainment, we now diagnose the probability density function for the tracer as a function of the potential density:

(1)

Here p_i is the probability that tracer lies in the ith density bin, which we denote as B_i = [\rho_i, \rho_i + \Delta \rho]. The overbar indicates 10 days mean, and the density bin size is \Delta \rho = 0.002 kg/m^3. Figure 4c presents three experiments with bathymetric slopes that are steep (suppressing TRW formation), moderate (permitting TRWs) and gentle (forming nonlinear eddies), respectively (see Supplementary Fig. 5 for all experiments). Among these three experiments, DSW is lightest, and thus most strongly diluted relative to its properties on the shelf, when the slope is steep (s = 0.15). Adding tides shifts the tracer distribution to greater densities, indicating that less entrainment is occurring as DSW descends, resulting in denser AABW being formed at the bottom of the slope. In contrast, decreasing the slope steepness and allowing TRW formation lead to denser, less diluted DSW; including tides in the moderate and gentle slope cases has no significant influence on the density and tracer distribution. These results indicate that tidal advection reduces entrainment into the DSW layer only when TRWs are suppressed, and that gentle slopes (such as those in the Weddell Sea) permit DSW to descend to the deep ocean with much less modification than do steeper slopes (such as those in the Ross Sea).

Our findings regarding the importance of tides for overflows over steep slopes raise a further question: how strong must the tides be to substantially impact the descent of DSW? To investigate this, we conduct a series of sensitivity experiments with constant slope steepness (s = 0.15) but varying amplitude of the tidal forcing (see “Methods”). Figure 4d shows that the density of the newly formed AABW tends to increase with tidal forcing strength (see Supplementary Fig. 6 for H_DSW), but more DSW tracer is diluted into lighter waters when tidal flows are sufficiently strong (2K1). A plausible explanation is that tides actually have two competing effects on DSW entrainment: one is to advect DSW quickly to the deep ocean during the ebb tide and reduce the cumulative entrainment, and the other is to produce shear-driven vertical turbulent mixing, which could enhance entrainment when tides are strong. As tidal forcing continues to increase, e.g., to strengths of 3K1 and 4K1, the DSW becomes more diluted than in the experiments without tides and with weaker tides, suggesting that the effect of increased tidal mixing overwhelms that of downslope tidal advection (Supplementary Fig. 7). However, these cases correspond to tidal amplitudes much larger than those observed in the northwestern Ross Sea, where some of the strongest tidal flows were observed around Antarctica (Fig. 5b). Furthermore, both the observations (Fig. 1) and realistic models32 support that the spring tides favor the formation of AABW in the northwestern Ross Sea. We therefore infer that tidal flows favor the formation of denser AABW around Antarctica, but future work should further investigate the competing effects of tidal advection and tidal mixing on DSW overflows.

One might also expect that the density difference between DSW and surrounding waters, which control the baroclinic pressure gradient, influence the process of DSW descent. To address this issue, we conducted sensitivity experiments with different DSW densities while holding the properties of surrounding waters unchanged. To cover the typical dynamical regimes, the experiments include cases with steep (s = 0.15), moderate (s = 0.067) and small (s = 0.033) topographic slopes. The results exhibit no significant differences for the moderate and small slope cases as DSW density changes (Supplementary Fig. 8). For steep slope cases, the tidal induced AABW density increase is not significant when the DSW is lighter (Supplementary Fig. 8d), which may be explained by weaker interfacial stratification that favors the shear driven mixing under tidal forcing. Overall, varying DSW density does not substantially change the overflow dynamics, suggesting that the results are generally robust over a wider range of DSW density.

Based on above analysis, we can approximately divide the descent of DSW into four different dynamical regimes. When the slope is steep (s > 0.1) and tidal forcing is absent, dense overflows take the form of a steady, geostrophic, quasi-along-slope flow and undergo strong mixing; we refer to this as the “Mixing” regime. If there is a substantial tidal flow (here we take the maximum tidal flow speed to be larger than 20 cm/s, see Supplementary Fig. 9), the descent of DSW is accelerated and the entrainment is suppressed; we refer to this as the “Tidal” regime. Over moderate slopes (0.05 ≤ s ≤ 0.1), TRWs are generated, accelerating the descent of DSW and suppressing mixing; we refer to this as the “Wavy” regime. When the slope is gentle (s < 0.05), isolated eddies form on the upper continental slope and suppress the descent of DSW; we refer to this as the “Eddying” regime. Of these four regimes, the “Mixing” regime is least favorable for AABW formation because the combination of a steep slope and weak tides lead to relatively strong entrainment of the overflow (Fig. 4). In contrast, the other three regimes are more favorable for AABW formation. We anticipate relatively fast, localized production of AABW in “Tidal” and “Wavy” regimes, and AABW formation further downstream in the “Eddying” regime due to the slower descent rate associated with the eddy trains over the upper continental slope16.

In Fig. 5 we apply our classification to estimate overflow dynamical regimes that could arise around the entire Antarctic margins based on the observed slope steepness (Fig. 5a) and tidal flow speeds (Fig. 5b). As seen in Fig. 5c, most of the marginal regions are not in the Mixing regime and thus favorable for AABW formation, provided that DSW are produced in those regions. According to the estimated dynamical regimes in Fig. 5c, DSW overflows in the Adélie coastal region and Prydz Bay should be dominated by tides and TRWs, respectively. Analyses of available moored measurements confirm the estimate in Fig. 5c for these two regions. For the Adélie coastal region (Supplementary Fig. 10), the mooring located on the continental slope records a strong mean flow, superposed with a diurnal tidal cycle of a comparable magnitude, and a fortnightly spring-neap tidal cycle. The temperature records show similar fluctuations, with ebb tides corresponding to colder waters, suggesting that the downslope transport of DSW is mediated by tides. Spectral analysis shows two peaks corresponding to the O1 and K1 tidal constituents45, but no subtidal TRWs signal. In contrast, the overflows in Prydz Bay are dominated by a subtidal wavy signal, as reported in previous observational studies13,21. These are in general consistent with our estimation, thereby confirming the estimate in Fig. 5c.

Since the dense overflows are difficult to detect at the circum-Antarctic scale, and since coastal polynyas can be directly observed via remote sensing and are necessary to produce DSW46, we plot in Fig. 5c the observed probability of polynya occurrence based on satellite observations during 2013–2021. It is shown that in addition to the four well-known overflow sites, the polynyas are widely spread around Antarctic continental shelf, and the favorable descending regimes in most of these regions suggest that there might be additional sources of AABW, especially in East Antarctica14. Note, however, that the presence of polynyas does not guarantee the existence of local DSW varieties, because the continental shelf stratification and circulation may not support the formation of dense water12,45.

Methods
Observational data
We collected historical in situ observations in the Weddell Sea and Ross Sea, including moorings and cruise data. In the Weddell Sea, we collected data from all 19 available moorings (Fig. 3a) over the period 1968–2011 in vicinity of the overflow. The mooring records are each ~1–2 years in duration. In the Ross Sea, we collected data from the moorings from the 2003-2005 Antarctic Slope (AnSlope) program and the 2007–2011 Cape Adare Long Term Mooring (CALM) program, both of which targeted the overflow in northwestern Ross Sea. Since the moorings are deployed by different observational programs, the recorded hydrographic information and frequency of the recordings are also slightly different. To make full use of these moorings, we omitted the interannual variability and use the jointly recorded hourly temperature and current speed/directions. In addition, as tidal flow can cause significant blow-down of the moorings23,54, especially for the instruments well above the seafloor, we only used the data from the instruments closest to the seafloor, which is ~20 m ab in the Ross Sea and 25–125 m ab in the Weddell Sea. In the Ross Sea, we also used the CTD sections from the AnSlope program, to analyze the vertical/cross-slope distribution of temperature and salinity.

To validate the estimation of overflow dynamical regimes around Antarctica, we further collected the mooring observations in the Adélie coastal region. The only mooring on the continental slope is from Mertz Polynya Experiment45, which records ~500 days flow speed/direction by moored ADCP, and also records temperature by several SBE instruments. We use the velocity records at 1162 m depth (~20 mab) and the temperature records ~10 m above that depth to identify the overflow dynamics.

Model setup
The numerical model we used is Regional Ocean Modelling System (ROMS), selected for its fidelity in representing oceanic flows over steep slopes55,56. The model domain (~1200 km × 650 km) consists of an embayment (~300 km × 300 km), connected to a flat abyssal ocean of 2500 m depth via a linear slope whose steepness is varied between our experiments. There is also a trough on the western side of the embayment, with a depth of 600 m at the shelf break, increasing to 2500 m at the abyssal ocean. The transition between the shelf and the abyssal ocean were smoothed by tangent functions. For computational efficiency we used a stretched horizontal grid, with a spacing of 0.5 km near the trough mouth, increasing to ~4 km close to the open boundaries. The vertical discretization uses 60 topography-following levels with increased resolution close to the seafloor (~5 m over the upper slope). The initial stratification is adapted from in situ observations in the Ross Sea20 (Station 47), with relatively strong stratification in the upper ~200 m and a weaker stratification below (Supplementary Fig. 2). A constant Coriolis parameter of f = −1.38 × 10^−4 (72°S) is used throughout the model domain. Vertical viscosity and mixing are parameterized via the Mellor–Yamada level 2.5 turbulence closure scheme57. The benthic stress is parameterized as a quadratic drag with constant drag coefficient of Cd = 0.003.

To simulate a Ross Sea-like overflow, we set the trough width to 30 km and the slope steepness to s = \Delta H / \Delta L = 0.15 to approximate the real continental slope along the pathway of the Ross Sea overflows23. DSW is restored at the south boundary of the trough (see inset a2 of Supplementary Fig. 2), resulting in an ~0.6 Sv northward flux through the trough that is comparable to the estimated flux in the Ross Sea overflow20 (~0.8 Sv). The DSW flux is defined by the volume across the continental shelf break, computed over waters with potential densities larger than 1027.86 kg/m^3. For the simulation of the Weddell Sea overflow, the trough width is set to 50 km and the slope steepness varies from ~0.07 over the upper continental slope to ~0.02 over the lower continental slope. In contrast to the Ross Sea simulation, DSW is restored to −2.2 °C and 34.73 psu to approximate ice shelf water2,58. Here the DSW is denser than the observations in the Weddell Sea59 and the corresponding flux is ~0.7 Sv, which is somewhat smaller than observed2 (1.6 ± 0.5 Sv). For the sensitivity experiments presented in Fig. 4, we use similar model setup with the Ross Sea simulation, but changing the slope inclines and using smaller DSW flux (~0.3 Sv) to simulate a range of potential overflow sites around Antarctica.

Tides are forced at the model ocean boundaries via sea surface height fluctuations imposed by extracting the K1 component of the tides in the vicinity of the Ross Sea (Supplementary Fig. 2) from the tidal product TPXO760. Note that the model domain has been scaled relative to its counterpart of the Ross Sea, and the resulting tidal flow in our model is not sensitive to the spatial range of the extracted tidal forcing around the Ross Sea (red sector in the inset a1 of Supplementary Fig. 2).

We first run each model experiment from rest for ~60–100 days without tidal forcing, then branch off two experiments that run for an additional 30 days, with and without tidal forcing. Supplementary Fig. 4 presents the daily averaged overflow fluxes over the last 20 days of 6 different experiments, all of which indicate that the model has reached a quasi-steady state, i.e., the overflow volume fluxes are not exhibiting significant trends over this period. We then analyze the model output data of the last 10 days. Note that it is not realistic to expect complete equilibrium in this process-oriented model setup, which excludes atmospheric forcing. Note also that the differences between the overflow fluxes in our experiments with and without tides are quite variable (Supplementary Table 1); this is due to the changes of circulation and mixing on the continental shelf caused by tidal forcing.

Isobath-weighted tracer center of mass
The DSW is injected with passive tracers, which can be used to identify the pathway of dense water as it descends to the deep ocean. We track the descent pathway of DSW by computing the tracer-weighted isobath, which quantifies the depth/isobath of the DSW center of mass as a function of along-slope distance:

(2)

Here \tau and H denote the tracer concentration and the isobath depth, respectively, and the overbar indicates a 10-day average.

Tidal flow calculation
The tidal flow strength shown in Fig. 1c by the black line is calculated as

(3)

where the angle brackets indicate daily moving average.

The tidal excursion for diurnal tide can be expressed as

(4)

where T indicates the period of diurnal tide, v_m indicates the maximum cross-slope tidal flow speed. We take v_m to be 20 cm/s at 1000 m isobath in the Weddell Sea overflow, and the corresponding tidal excursion is about 5 km.

The maximum tidal flow speed shown in Supplementary Fig. 7 is calculated by first computing

(5)

where the overbars indicate a vertical average over the upper 200 m of the water column, and the angle brackets indicate daily moving average. Then we calculate the mean value of daily maximum flow speed over 10 days as the maximum tidal flow speed.

Data availability
The mooring data generated in this study have been deposited in the Figshare database61. The model data presented in this article are available on request from X.H. (hxx1119@foxmail.com).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comments for Authors\nIn this study, authors discussed the general mechanisms controlling the Dense Shelf Water (DSW) overflow off the confinental shelves across confinental slopes in the Antarcitca. By comparing idealized model simulafions and mooring observafions in southern Weddell Sea confinental slope and over the western Ross Sea confinental slope, author characterized two disfinct dynamic regimes associated with the topographic organisafions and slope steepness, namely, the Topographic Rossby Wave (TRW) regime and fidal regime. Further analysis of the model sensifivity experiments leads to a generalizafion of the dynamic regimes of the DSW overflow across the Antarcfic confinental slopes.\nI found this study very interesfing. The model results show good agreement with the observafion in Weddell Sea and Ross Sea – model well captures the preferred frequency bands of DSW overflows as observed. A counterintuifive conclusion – fidal currents, with proper topographic feature and strength, act to suppress the entrainment of ambient water into DSW hence promofing the DSW overflow currents, brings novelty into this work.\nI am convinced by the direct comparison between observafions and models in Weddell and Ross cases, but I found the generalizafion requires more robust examinafions with the addifion of observafional evidence. DSW overflow has been observed in various locafions other than Weddell and Ross. Authors need to double check the observed DSW overflow in other DSW producfion areas – e.g., Prydz Bay, Adelie Coast, southwest Weddell Sea confinental slope (studies suggested that DSW overflow here is comparable with those from Filchner Depression), where there are sufficient mooring measurements to tesfify the proposed mechanisms (see figure below). And authors have provided liftle observafional evidence here for locafions other than overflow from Filchner Sill and Tera Nova Bay.\n[FIGUREREDACTED]\nFig 1 in Amblas and Dowdeswell (2018) - The original figure from which Figure 1a in the manuscript is adapted.\nI think that the importance of this study is not just about confirming the dynamic regimes of two mooring sites, which is nicely presented, but more so about this ‘generalizafion’ of the dynamic regimes over rest of the Antarcfic confinental slopes. Therefore, I suggested authors to provide more observafional evidence from various DSW overflow sites into this work.\nSpecific comments:\n1. Line 57-60: Authors should support the model results from the explorafion of parameter space with some observafional evidence to ensure the robustness of the pan-Antarcfic dynamic regime plot.\n2. Line 83-85: Shouldn’t the stronger DSW overflow correspond to a colder pulse of temperature as expected? Authors menfioned that the fidal mixing, but cited work Muench et al. (2009) described the mixing and entrainment at the upper bound of DSW associated with fidal current, whereas the temperature at 20mab shown in manuscript marks the lower/core of the DSW overflow. I found this sentence a bit confusing.\n3. Line 87-89: Figure S1 subpanel shows the current and temperature record at M1 (further inshore), the temperature minimum corresponds to a neap fide which is somewhat different from Figure 1 WC record. How can this be consistent as claimed by authors?\n4. Line 225-229: Authors speculated two compefing mechanisms brought by fidal current on DSW descend and entrainment associated with the magnitude of fidal current. Have author considered this into the ‘generalizafion’? Wherever the fidal regime is idenfified, can the fidal current be strong enough to allow shear-driven mixing to dominate over the fidal advecfion?\n5. Figure 5c: This figure shows that the dynamic regimes are sensifive to the slope steepness. For example, in the Weddell Sea, the overflow sites from the observafion sits at the narrow band of ‘Wavy’ whereas other part of the shelf break is dominated by the ‘Eddying’ regime. This raises a concern – whether it is needed to categorize the enfire shelf break, or should one simply focus on the overflow sites where DSW mostly descends?\nAddifionally, in Weddell and Ross, if it were without the observafion, one can be illuded by this figure saying Weddell and Ross are both ‘Eddying’. Authors didn’t provide observafional evidence for other DSW overflow regions like Adelie Coast, Prydz Bay and southwestern Weddell confinental shelf break, and if one tries to idenfify the exact dynamic regimes using provided figure 5c, it may end up with finding that DSW overflow regime in Adelie Coast is a mixture of ‘Tidal’ and ‘Wavy’ with intermiftent ‘Mixing’, and Prydz Bay is ‘Wavy’ and ‘Eddying’. But are these accurate? Therefore, addifional evidence from mooring observafion is needed here. The SOOS map suggested that there are a few mooring measurements in both Prydz Bay and Adelie Coast that may be able to facilitate the required analysis (see figure below).\nSOOS map of SOOS Mooring networks (hftp://www.soosmap.aq/). [FIGUREREDACTED]\n6. Line 282-284: Both fides and TRWs accelerate DSW descent and generate V-shaped isopycnal. However, fides and TRWs exhibit disfincfively different spectral density in frequency domain. Does the different behaviour on frequency domain of two dynamic phenomena affect the DSW export differently in terms of its cumulafive volume transport, which one is more efficient?", "reviewer_2": "Albeit the mechanisms of fides and topographic Rossby Waves (TRWs) in transforming dense shelf waters (DSW) to Antarcfic Boftom Water (AABW) have been idenfified in previous studies, this work by Han et al. examines systemafically the relafive roles of fides and TRWs with respect to the steepness of boftom slope using idealized model experiments that represent the Ross Sea and the Weddell Sea, respecfively, which leads to the categorizafion of four regimes (mixing, fidal, wavy, and eddying) around the Antarcfic margin. Such a designafion could be valuable if confirmed. No doubt that the clarificafion about the role of fide in promofing rapid descent of DSW over the steep slope and the complementary effect of TRWs over the moderate slope advances our understanding of AABW formafion, but the highlight of this study, in my opinion, is Figure 5c. As such I have the following two concerns:\n1) According to Figure 5c, the large stretches outside of the Ross Sea and the Weddell Sea belong to the eddying regime, while the wavy and fidal regimes exist only near the eastern and western ends of both seas. Does this paftern, or the distribufions seen in Figure 5c in general, concur with the “observed/known” locafions of AABW formafion? In other words, Figure 5c needs to be validated.\n2) The analyses of DSW are based on tracer concentrafion rather than its T/S properfies. How the temperature and salinity consequently the differenfial density between DSW and surrounding waters affect the DSW spread (hence the conclusions) is not addressed in the manuscript."}, "author_response": "Responses to Reviewers\nGeneral response:\nWe sincerely thank the two reviewers for their constructive comments and suggestions.\nTheir common concern is the validation of Figure 5c by using additional observational\nevidences at other overflow sites. We now show that the observed overflow dynamical regimes\nin the Adelie coastal region and Prydz Bay are also consistent with our model-based estimations.\nThe following are our specific responses, with the original comments quoted in Italic font, the\nresponses in non-Italic font, and the revised sentences in the manuscript in red font.\nReviewer #1 (Remarks to the Author):\nGeneral comments for Authors\nIn this study, authors discussed the general mechanisms controlling the Dense Shelf Water\n(DSW) overflow off the continental shelves across continental slopes in the Antarcitca. By\ncomparing idealized model simulations and mooring observations in southern Weddell Sea\ncontinental slope and over the western Ross Sea continental slope, author characterized two\ndistinct dynamic regimes associated with the topographic organisations and slope steepness,\nnamely, the Topographic Rossby Wave (TRW) regime and tidal regime. Further analysis of the\nmodel sensitivity experiments leads to a generalization of the dynamic regimes of the DSW\noverflow across the Antarctic continental slopes.\nI found this study very interesting. The model results show good agreement with the observation\nin Weddell Sea and Ross Sea – model well captures the preferred frequency bands of DSW\noverflows as observed. A counterintuitive conclusion – tidal currents, with proper topographic\nfeature and strength, act to suppress the entrainment of ambient water into DSW hence\npromoting the DSW overflow currents, brings novelty into this work.\nI am convinced by the direct comparison between observations and models in Weddell and Ross\ncases, but I found the generalization requires more robust examinations with the addition of\nobservational evidence. DSW overflow has been observed in various locations other than\nWeddell and Ross. Authors need to double check the observed DSW overflow in other DSW\nproduction areas – e.g., Prydz Bay, Adelie Coast, southwest Weddell Sea continental slope\n(studies suggested that DSW overflow here is comparable with those from Filchner Depression),\nwhere there are sufficient mooring measurements to testify the proposed mechanisms (see figure\nbelow). And authors have provided little observational evidence here for locations other than\noverflow from Filchner Sill and Tera Nova Bay.\n[REDACTED]\nFig 1 in Amblas and Dowdeswell (2018) - The original figure from which Figure 1a in the manuscript is\nadapted.\nI think that the importance of this study is not just about confirming the dynamic regimes of two\nmooring sites, which is nicely presented, but more so about this ‘generalization’ of the dynamic\nregimes over rest of the Antarctic continental slopes. Therefore, I suggested authors to provide\nmore observational evidence from various DSW overflow sites into this work.\nResponse:\nThanks for your very insightful suggestions. We agree that additional observational\nevidences can make the results in this study more robust. To verify the pan-Antarctic overflow\ndynamical regimes shown in Fig. 5c, we need the mooring observations on the continental slope,\nbecause the dynamical regimes are estimated based on the slope steepness between 800-1800\nm isobaths. This further limit the available moorings in the slope regions around Antarctica.\nFortunately, there are a few moorings in the Adelie coastal region and Prydz Bay for validating\nthe overflow dynamical regimes, but no available mooring observations in the slope region of\nthe southwestern Weddell Sea. The following are the evidences observed by the moorings in\nthe Adelie coastal region and Prydz Bay, which further support our conclusions.\nFig. R1a shows the bathymetry of the Adelie coastal region and the site of the only\nmooring on the continental slope. The corresponding estimated dynamical regimes are shown\nin Fig. R1b (Zoom in of Fig. 5c), which indicates that the overflow across the mooring site\nshould be dominated by ‘Tidal’ regime. The ~500 days flow speed/direction at 1162 m depth\nrecorded by lowered ADCP, and the temperature records ~10 m above that depth can be used\nto validate the overflow dynamical regimes. As shown in Fig. R1c, the northward\n(approximately cross-slope direction) velocity shows strong mean flow, superimposed with a\nsignificant diurnal tidal cycle and a fortnight spring-neap tidal cycle. The temperature shows\nsimilar fluctuations, with ebb tides corresponding to colder waters, suggesting that the\ndownslope transport of DSW is mediated by tides. Spectral analysis shows two peaks of O1\nand K1 tidal constituents, but no subtidal topographic Rossby waves (TRWs) signal. These are\ntypical features of ‘Tidal’ regime, which is consistent with our estimation. The similar spectral\nanalysis was presented in Williams et al. (2010).\nFigure R1 (Figure S10). Adelie coast overflow observations. (a) Topography of the Adelie coastal region.\nThe red dot indicates the mooring site, and the arrow denotes the export of DSW. (b) The estimated\ndynamical regimes around the Adelie coastal region. (c) Time series of northward velocity and\ntemperature of selected 45 days. (d) Power spectral density (PSD) of northward velocity and temperature.\nFor the overflow in Prydz Bay, the mooring observations were reported in Ohshima et al.,\n(2013); however, these data are still not publicly available. Fortunately, the data and the analysis\nof these data had been shown in several published papers, which provide the necessary\ninformation that could validate the overflow dynamical regime in the Prydz Bay overflow\nregion.\nThe mooring sites are shown in Fig. R2a. The dynamical regimes along the continental\nslope of Cape Darnley are shown in Fig. R2b, which are primarily dominated by ‘Wavy’ and\n‘Eddying’, but with intermittent ‘Mixing’ and ‘Tidal’ regimes at the western side. Note the\nestimated dynamical regimes are based on local slope steepness between 800 m and 1800 m\nisobaths, while moorings M1, M3 and M4 are in deeper ocean with less steep slope. Therefore,\nthe dynamical regimes for moorings M1-M4 are prone to be ‘Wavy’ or ‘Eddying’. Fig. R2c\nshows the time series of flow speed/direction at moorings M1, M2 and M3, all exhibiting\nfluctuations of several days. Power spectral density (PSD) analysis clarify the periods of\nfluctuations (Fig. R2d), and further identify the fluctuations to be TRWs by numerical models\n(Nakayama et al., 2014). Note that we cannot distinguish the ‘Wavy’ and ‘Eddying’ regimes\nbased on the sparse overflow current observations, because they all take the form of oscillations.\nNevertheless, these observational results are in general consistent with our classifications of\noverflow dynamical regimes in this region.\n[REDACTED]\nFigure R2. Mooring observations in the Cape Darnley (Prydz Bay) overflow region. (a) The bathymetry\nis indicated by blue contours. Mooring locations are indicated by orange symbols, with the mean velocity\nat the bottom and top of the mooring shown as orange and yellow vectors, respectively. This figure is\nFigure 1 of Ohshima et al., (2013). (b) The estimated dynamical regimes along the continental slope of\nCape Darnley. (c) M1 velocity vector at 92 m above the bottom. For M2 and M3 moorings, the curves\nindicate velocity component of the mean (dominant) flow direction at 20 m (blue) and 226 m (red) above\nthe bottom. This figure is Figure S3 of Ohshima et al., (2013). (d) Fourier spectra of moorings M1 and\nM3. This figure is Figure 5a of Nakayama et al., (2014).\nWe include Figure R1 in the revised manuscript as Figure S10, and describe these further\nvalidations in the main text in Lines 278–289 in the revised manuscript: “According to the\nestimated dynamical regimes in Fig. 5c, DSW overflows in the Adelie coastal region and Prydz\nBay should be dominated by tides and TRWs, respectively. Analysis of available moored\nmeasurements confirm the estimate in Fig. 5c for these two regions. For the Adelie coastal\nregion (Fig. S10), the mooring that is located on the continental slope records a strong mean\nflow, upon which is superposed a diurnal tidal cycle of a comparable magnitude, with a\nfortnightly spring-neap tidal cycle. The temperature records show similar fluctuations, with ebb\ntides corresponding to colder waters, suggesting that the downslope transport of DSW is\nmediated by tides. Spectral analysis shows two peaks corresponding to the O1 and K1 tidal\nconstituents46, but no subtidal TRWs signal. In contrast, the overflows in Prydz Bay are\ndominated by a subtidal wavy signal, as reported in previous observational studies13,21. These\nare in general consistent with our estimation, thereby confirming the estimate in Fig. 5c.”\nSpecific comments:\n1. Line 57-60: Authors should support the model results from the exploration of parameter\nspace with some observational evidence to ensure the robustness of the pan-Antarctic dynamic\nregime plot.\nResponse:\nAs shown above, we have collected all the available mooring data that can be used to\nverify our conclusion. Although the available moorings are sparse, these additional evidences\nhave increased the robustness of the pan-Antarctic dynamic regime plot.\n2. Line 83-85: Shouldn’t the stronger DSW overflow correspond to a colder pulse of\ntemperature as expected? Authors mentioned that the tidal mixing, but cited work Muench et\nal. (2009) described the mixing and entrainment at the upper bound of DSW associated with\ntidal current, whereas the temperature at 20mab shown in manuscript marks the lower/core of\nthe DSW overflow. I found this sentence a bit confusing.\nResponse:\nThanks for this very insightful comment. Yes, mooring observations on the upper\ncontinental slope show that strong tidal flows correspond to colder DSW pulses (Whitworth\nand Orsi, 2006), and numerical experiments further suggested that the colder pulses can reach\ndeep ocean (Wang et al., 2010). In this study, we synthesize all available historical mooring\ndata in the northwestern Ross Sea to verify that tidal advection is dominant on controlling DSW\ndescent, and produce colder and denser AABW.\nThe dilution of dense overflow can be caused by interfacial (upper bound of dense\noverflow) shear-driven mixing and bottom stress induced mixing, which are both important to\nmodifying the outflow hydrographic properties. As discussed in Peters et al., (2005), the\ninterfacial shear-driven mixing cannot directly reflect the property changes of bottom layer\nwaters, because of the large thickness of overflow plumes. Besides the interfacial mixing,\nMuench et al., (2009) also emphasized that the strong benthic stress induced by a spring tide\ncan augment strong mixing to the upper interface of dense overflows, which is able to dilute\nthe outflow efficiently. We think that these results support our argument to some extent, so we\ncited this paper.\nTo avoid potential confusion, we have changed reference 32 (Muench et al., 2009) to Wang\net al., (2010) and delete this sentence and rewrite the next sentence (Lines 83-86 in the revised\nmanuscript): “The fact that the coldest waters emerge during the spring tide therefore suggests\nthat temperature variability is governed by the tendency of the tides to advect DSW across the\ncontinental slope22,23, rather than by the mixing induced by the tidal flow32,33.”\n3. Line 87-89: Figure S1 subpanel shows the current and temperature record at M1 (further\ninshore), the temperature minimum corresponds to a neap tide which is somewhat different from\nFigure 1 WC record. How can this be consistent as claimed by authors?\nResponse:\nThanks for pointing out this problem. We agree that we did not clarify this clearly in the\nmanuscript. Actually, tidal effects on dense overflows on the continental shelf are different from\nthose on the continental slope, i.e., tidal flows dilute DSW on the continental shelf (moorings\nM1 and CA), while decreasing net entrainment on the continental slope. The realistic numerical\nexperiments showed similar results (Figure 9 in Wang et al., 2010).\nHere we provide a possible explanation: Without tidal forcing, overflow speed is weak on\nthe flat continental shelf but strong on the continental slope due to gravity acceleration, and the\ncorresponding shear-driven mixing is thus weak and strong respectively; When adding tides, it\ntheoretically increases mixing throughout the water column, which is the situation on the\ncontinental shelf; In contrast, tidal advection accelerates DSW downslope descent, decreasing\nnet entrainment on the continental slope.\nWe add an additional description in the main text (Lines 88-89 in the revised manuscript):\n“In contrast, a stronger tidal flow dilutes DSW on the continental shelf break (moorings M1\nand CA, Fig. S1), consistent with the influence of stronger tidal mixing32,33.” And in Lines 94-\n96 in the revised manuscript: “The results show that in a Ross Sea parameter regime, tracers\nare advected to greater depths and retain higher concentration in the presence of tides (Figs.\n2a,b), though the tracer concentrations are more diluted in the regions shallower than 500 m\ndepth (Figs. 2c,d).”\n4. Line225-229: Authors speculated two competing mechanisms brought by tidal current on\nDSW descend and entrainment associated with the magnitude of tidal current. Have author\nconsidered this into the ‘generalization’? Wherever the tidal regime is identified, can the tidal\ncurrent be strong enough to allow shear-driven mixing to dominate over the tidal advection?\nResponse:\nYes, it is very interesting to generalize the impacts of tidal flow strength on dense overflow\nmixing. Based on our sensitivity experiments shown in the manuscript, the maximum density\nof bottom water increases as the tidal flow strength increases. However, more tracers are diluted\ninto lighter water in 2K1 experiment, and obviously the mean density decreases relative to 1K1\nexperiment (Fig. R3). This suggests that the effect of tidal mixing increases relative to tidal\nadvection for 2K1 tidal experiment, and we think that the effect of tidal mixing will\ncontinuously increase and dilute dense overflow further under stronger tidal forcing. Therefore,\nwe run another two experiments with extremely strong tidal forcing (3K1 and 4K1) to\ninvestigate this further. The results show that the DSW is more diluted than the experiments\nwithout tides and with weaker tides, which indicates that tidal mixing completely overwhelms\ntidal advection in 3K1 and 4K1 experiments.\nFigure R3 (Figure S7). Probability density of volume-integrated tracer mass versus fluid potential density\nfor experiments with different tidal forcing but constant slope steepness ( ).\n𝑠=0.15\nHowever, the 2K1 tidal forcing already produces a very strong tidal flow (> 0.5 m/s) that\nis comparable to the observed strongest tidal flow around Antarctica. Therefore, we think that\nthe conclusion in this study is suitable to circum-Antarctica conditions. To fully generalize the\nimpacts of tides on AABW properties, we need to investigate several potential factors\ncomprehensively by using a realistic model, e.g., dense overflow flux, tidal flow strength, the\ncontinental slope steepness, and so on. The impacts of these factors need to be investigated in\ndetails and are out of scope of this study. Therefore, we think that these will need to be done in\nthe future.\nWe have included Figure R3 in the revised manuscript as Figure S7, and added more\ndiscussion in the main text (Lines 231-239 in the revised manuscript): “As tidal forcing\ncontinues to increase, e.g., to strengths of 3K1 and 4K1, the DSW becomes more diluted than\nin the experiments without tides and with weaker tides, suggesting that the effect of increased\ntidal mixing overwhelms that of downslope tidal advection (Fig. S7). However, these cases\ncorrespond to tidal amplitudes much larger than those observed in the northwestern Ross Sea,\nwhere some of the strongest tidal flows were observed around Antarctica (Fig. 5b). Furthermore,\nboth the observations (Fig. 1) and realistic models32 support that the spring tides favor the\nformation of AABW in the northwestern Ross Sea. We therefore infer that tidal flows favor the\nformation of denser AABW around Antarctica, but future work should further investigate the\ncompeting effects of tidal advection and tidal mixing on DSW overflows.”\n5. Figure 5c: This figure shows that the dynamic regimes are sensitive to the slope steepness.\nFor example, in the Weddell Sea, the overflow sites from the observation sits at the narrow band\nof ‘Wavy’ whereas other part of the shelf break is dominated by the ‘Eddying’ regime. This\nraises a concern – whether it is needed to categorize the entire shelf break, or should one simply\nfocus on the overflow sites where DSW mostly descends?\nResponse:\nThanks for pointing this out. We agree that the overflow dynamical regimes are sensitive\nto the local slope steepness. To date there have been only several well identified overflow sites,\nincluding the Ross Sea, Weddell Sea, Prydz Bay and Adelie coastal region. However, more and\nmore overflow sites are being discovered as observations increase (Amblas and Dowdeswell,\n2018), that could potentially contribute to AABW formation. Therefore, we estimate the\noverflow dynamical regimes of the entire shelf break, which could be used to infer the places\nthat favor the formation of AABW and guide the overflow observations in the future.\nAdditionally, in Weddell and Ross, if it were without the observation, one can be illuded by this\nfigure saying Weddell and Ross are both ‘Eddying’. Authors didn’t provide observational\nevidence for other DSW overflow regions like Adelie Coast, Prydz Bay and southwestern\nWeddell continental shelf break, and if one tries to identify the exact dynamic regimes using\nprovided figure 5c, it may end up with finding that DSW overflow regime in Adelie Coast is a\nmixture of ‘Tidal’ and ‘Wavy’ with intermittent ‘Mixing’, and Prydz Bay is ‘Wavy’ and ‘Eddying’.\nBut are these accurate? Therefore, additional evidence from mooring observation is needed\nhere. The SOOS map suggested that there are a few mooring measurements in both Prydz Bay\nand Adelie Coast that may be able to facilitate the required analysis (see figure below).\n[REDACTED]\nSOOS map of SOOS Mooring networks (http://www.soosmap.aq/).\nResponse:\nThank you very much for the suggestions and the useful information for mooring networks.\nThe DSW overflows across the continental shelf through narrow troughs with the horizontal\nscale on the order of 10 kilometers, so the overflow dynamical regimes are sensitive to local\nslope steepness. In Figure 5c, we estimate the dynamical regimes by local slope steepness\nwithout doing any along-slope average or smoothing, and thus the overflow dynamical regimes\nalternate frequently in some places (e.g., Fig. R2c) due to variable bathymetry. Considering the\nnecessary spatial scale for the growth of waves, this may limit the development of the ‘Wavy’\nand ‘Eddying’ regimes. Although the dynamical regimes are variable, the observed overflow\ndynamical regimes are consistent with our estimation, as shown in Fig. R1 and Fig. R2.\nCurrently, Fig. 5c is a rough estimation of circum-Antarctica overflow dynamical regimes,\nwhich need to be improved as observations increase, especially for identifying the minimum\nspatial scales allowing the dynamical regimes to fully develop. We have added more discussion\nin the main text (Lines 312-317 in the revised manuscript): “One caveat is that the estimated\ndynamical regimes are sensitive to local slope steepness, and alternate frequently along the\ncontinental slope in some places (Fig. 5c). Considering the necessary spatial scale for the\ngrowth of waves, variable bathymetry along the continental slope may limit the development\nof ‘Wavy’ and ‘Eddying’ regimes. Therefore, Fig. 5c could be improved by further observations\nthat, for example, can offer information about the minimum spatial scales allowing the\ndynamical regimes to fully develop.”\n6. Line282-284: Both tides and TRWs accelerate DSW descent and generate V-shaped\nisopycnal. However, tides and TRWs exhibit distinctively different spectral density in frequency\ndomain. Does the different behaviour on frequency domain of two dynamic phenomena affect\nthe DSW export differently in terms of its cumulative volume transport, which one is more\nefficient?\nResponse:\nTides and TRWs can both modulate DSW export in the form of periodic downslope flows,\nbut their frequencies are different, which potentially influence the efficiencies of DSW\ndownslope transport.\nAs shown by the pathway of the tracer center of mass (Fig. R4), tidal modulated DSW\ntransport is only important for steep slopes where there are no TRWs, and becomes almost\nnegligible when TRWs occur for gentle slopes. These are consistent with our general\nunderstanding that tides are driven by external forces and advect DSW across the continental\nslope, and thus the tidal flow speed (excursion) and the width of continental slope are important\nfor DSW downslope transport. For less steep slopes, the continental slope is wider because of\nthe constant depth of abyssal ocean in our model setup, while tidal flow is weaker under a\nconstant tidal forcing. Therefore, tidal excursion is relatively small compared to the width of\nthe continental slope for a gentle slope. In contrast, the mechanism of TRWs on DSW transport\nis that the baroclinic instability of dense overflows release potential energy to energize TRWs\nby sliding into deep ocean. Therefore, DSW can continuously slide into deep ocean for gentle\nslopes where TRWs occur. The mathematical model for DSW descent rate has been presented\nin Han et al. (2023), which suggests that the transport efficiencies do not rely on the frequencies\nof TRWs.\nOverall, the differences of tides and TRWs on DSW downslope transport are due to their\ndifferent dynamics, rather than the differences of frequency domain. Tides and TRWs dominate\nthe DSW transport for steep and gentle slopes respectively, which are the basements of our\nclarification of ‘Tidal’ and ‘Wavy’ regimes.\nFigure R4 (revised Figure 4a,b in the manuscript). Simulations investigating the influences of tidal flows\nand continental slope steepness on DSW descent. (a) Isobath corresponding to the DSW tracer center of\nmass, as a function of along-slope distance downstream of the trough. The solid thick curves indicate the\nsimulations without tidal forcing, while the dashed curves indicate the corresponding simulations that\ninclude tidal forcing. The semi-transparent red shading denotes the zonal range that we calculate the\naveraged DSW tracer-weighed isobath shown in panel b. (b) Zonally-averaged DSW tracer-weighted\nisobath for different experiments, with and without tidal forcing.\nReferences:\nAmblas, D., & Dowdeswell, J. A. (2018). Physiographic influences on dense shelf-water cascading down\nthe Antarctic continental slope. Earth-Science Reviews, 185, 887–900.\nhttps://doi.org/10.1016/j.earscirev.2018.07.014\nHan, X., Stewart, A. L., Chen, D., Liu, X., & Lian, T. (2023). Controls of topographic Rossby wave\nproperties and downslope transport in dense overflows.Journal of Physical Oceanography.\nhttps://doi.org/10.1175/JPO-D-22-0237.1\nMuench, R., Padman, L., Gordon, A., & Orsi, A. (2009). A dense water outflow from the Ross Sea,\nAntarctica: Mixing and the contribution of tides.Journal of Marine Systems,77(4), 369-387.\nhttps://doi.org/10.1016/j.jmarsys.2008.11.003\nNakayama, Y., Ohshima, K. I., Matsumura, Y., Fukamachi, Y., & Hasumi, H. (2014). A numerical\ninvestigation of formation and variability of Antarctic Bottom Water off Cape Darnley, East\nAntarctica.Journal of Physical Oceanography,44(11), 2921-2937. https://doi.org/10.1175/JPO-D-14-\n0069.1\nOhshima, K. I., Fukamachi, Y., Williams, G. D., Nihashi, S., Roquet, F., Kitade, Y., Tamura, T., Hirano,\nD., Herraiz-Borreguero, L., Field, I., Hindell, M., Aoki, S., & Wakatsuchi, M. (2013). Antarctic Bottom\nWater production by intense sea-ice formation in the Cape Darnley polynya. Nature Geoscience, 6(3),\n235–240. https://doi.org/10.1038/ngeo1738\nPeters, H., Johns, W. E., Bower, A. S., & Fratantoni, D. M. (2005). Mixing and entrainment in the Red\nSea outflow plume. Part I: Plume structure.Journal of Physical Oceanography,35(5), 569-583.\nhttps://doi.org/10.1175/JPO2679.1\nWhitworth, I., & Orsi, A. H. (2006). Antarctic Bottom Water production and export by tides in the Ross\nSea. Geophysical Research Letters, 33(12). https://doi.org/10.1029/2006GL026357\nWang, Q., Danilov, S., Hellmer, H. H., & Schröter, J. (2010). Overflow dynamics and bottom water\nformation in the western Ross Sea: Influence of tides. Journal of Geophysical Research: Oceans, 115(10),\n1–16. https://doi.org/10.1029/2010JC006189\nWilliams, G. D., Aoki, S., Jacobs, S. S., Rintoul, S. R., Tamura, T., & Bindoff, N. L. (2010). Antarctic\nbottom water from the Adélie and George V Land coast, East Antarctica (140–149 E).Journal of\nGeophysical Research: Oceans,115(C4). https://doi.org/10.1029/2009JC005812\nReviewer #2 (Remarks to the Author):\nAlbeit the mechanisms of tides and topographic Rossby Waves (TRWs) in transforming dense\nshelf waters (DSW) to Antarctic Bottom Water (AABW) have been identified in previous studies,\nthis work by Han et al. examines systematically the relative roles of tides and TRWs with respect\nto the steepness of bottom slope using idealized model experiments that represent the Ross Sea\nand the Weddell Sea, respectively, which leads to the categorization of four regimes (mixing,\ntidal, wavy, and eddying) around the Antarctic margin. Such a designation could be valuable if\nconfirmed. No doubt that the clarification about the role of tide in promoting rapid descent of\nDSW over the steep slope and the complementary effect of TRWs over the moderate slope\nadvances our understanding of AABW formation, but the highlight of this study, in my opinion,\nis Figure 5c. As such I have the following two concerns:\n1) According to Figure 5c, the large stretches outside of the Ross Sea and the Weddell Sea\nbelong to the eddying regime, while the wavy and tidal regimes exist only near the eastern and\nwestern ends of both seas. Does this pattern, or the distributions seen in Figure 5c in general,\nconcur with the “observed/known” locations of AABW formation? In other words, Figure 5c\nneeds to be validated.\nResponse:\nWe sincerely thank the reviewer for this very helpful suggestion, which is also the concern\nof another reviewer. To verify the pan-Antarctic overflow dynamical regimes shown in Fig. 5c,\nwe need the mooring observations on the continental slope, because the dynamical regimes are\nestimated based on the slope steepness between 800-1800 m isobaths. This further reduces the\nnumber of the available moorings around Antarctica. Fortunately, there are a few moorings in\nthe Adelie coastal region and Prydz Bay, which can be used to validate Fig. 5c.\nFig. R1a shows the bathymetry of the Adelie coastal region and the site of the only\nmooring on the continental slope. The corresponding estimated dynamical regimes are shown\nin Fig. R1b (Zoom in of Fig. 5c), which indicates that the overflow across the mooring site\nshould be dominated by ‘Tidal’ regime. The ~500 days flow speed/direction at 1162 m depth\nrecorded by lowered ADCP, and the temperature records ~10 m above that depth can be used\nto validate the overflow dynamical regimes. As shown in Fig. R1c, the northward\n(approximately cross-slope direction) velocity shows strong mean flow, superimposed with a\nsignificant diurnal tidal cycle and a fortnight spring-neap tidal cycle. The temperature shows\nsimilar fluctuations, with ebb tides corresponding to colder waters, suggesting that the\ndownslope transport of DSW is mediated by tides. Spectral analysis shows two peaks of O1\nand K1 tidal constituents, but no subtidal topographic Rossby waves (TRWs) signal. These are\ntypical features of ‘Tidal’ regime, which is consistent with our estimation. The similar spectral\nanalysis was presented in Williams et al. (2010).\nFigure R1 (Figure S10). Adelie coast overflow observations. (a) Topography of the Adelie coastal region.\nThe red dot indicates the mooring site, and the arrow denotes the export of DSW. (b) The estimated\ndynamical regimes around the Adelie coastal region. (c) Time series of northward velocity and\ntemperature of selected 45 days. (d) Power spectral density (PSD) of northward velocity and temperature.\nFor the overflow in Prydz Bay, the mooring observations were reported in Ohshima et al.,\n(2013); however, these data are still not publicly available. Fortunately, the data and the analysis\nof these data had been shown in several published papers, which provide the necessary\ninformation that could validate the overflow dynamical regime in the Prydz Bay overflow\nregion.\nThe mooring sites are shown in Fig. R2a. The dynamical regimes along the continental\nslope of Cape Darnley are shown in Fig. R2b, which are primarily dominated by ‘Wavy’ and\n‘Eddying’, but with intermittent ‘Mixing’ and ‘Tidal’ regimes at the western side. Note the\nestimated dynamical regimes are based on local slope steepness between 800 m and 1800 m\nisobaths, while moorings M1, M3 and M4 are in deeper ocean with less steep slope. Therefore,\nthe dynamical regimes for moorings M1-M4 are prone to be ‘Wavy’ or ‘Eddying’. Fig. R2c\nshows the time series of flow speed/direction at moorings M1, M2 and M3, all exhibiting\nfluctuations of several days. Power spectral density (PSD) analysis clarify the periods of\nfluctuations (Fig. R2d), and further identify the fluctuations to be TRWs by numerical models\n(Nakayama et al., 2014). Note that we cannot distinguish the ‘Wavy’ and ‘Eddying’ regimes\nbased on the sparse overflow current observations, because they all take the form of oscillations.\nNevertheless, these observational results are in general consistent with our classifications of\noverflow dynamical regimes in this region.\n[REDACTED]\nFigure R2. Mooring observations in the Cape Darnley (Prydz Bay) overflow region. (a) The bathymetry\nis indicated by blue contours. Mooring locations are indicated by orange symbols, with the mean velocity\nat the bottom and top of the mooring shown as orange and yellow vectors, respectively. This figure is\nFigure 1 of Ohshima et al., (2013). (b) The estimated dynamical regimes along the continental slope of\nCape Darnley. (c) M1 velocity vector at 92 m above the bottom. For M2 and M3 moorings, the curves\nindicate velocity component of the mean (dominant) flow direction at 20 m (blue) and 226 m (red) above\nthe bottom. This figure is Figure S3 of Ohshima et al., (2013). (d) Fourier spectra of moorings M1 and\nM3. This figure is Figure 5a of Nakayama et al., (2014).\nWe include Figure R1 in the revised manuscript as Figure S10, and describe these further\nvalidations in the main text in Lines 278–289 in the revised manuscript: “According to the\nestimated dynamical regimes in Fig. 5c, DSW overflows in the Adelie coastal region and Prydz\nBay should be dominated by tides and TRWs, respectively. Analysis of available moored\nmeasurements confirm the estimate in Fig. 5c for these two regions. For the Adelie coastal\nregion (Fig. S10), the mooring that is located on the continental slope records a strong mean\nflow, upon which is superposed a diurnal tidal cycle of a comparable magnitude, with a\nfortnightly spring-neap tidal cycle. The temperature records show similar fluctuations, with ebb\ntides corresponding to colder waters, suggesting that the downslope transport of DSW is\nmediated by tides. Spectral analysis shows two peaks corresponding to the O1 and K1 tidal\nconstituents46, but no subtidal TRWs signal. In contrast, the overflows in Prydz Bay are\ndominated by a subtidal wavy signal, as reported in previous observational studies13,21. These\nare in general consistent with our estimation, thereby confirming the estimate in Fig. 5c.”\n2) The analyses of DSW are based on tracer concentration rather than its T/S properties. How\nthe temperature and salinity consequently the differential density between DSW and\nsurrounding waters affect the DSW spread (hence the conclusions) is not addressed in the\nmanuscript.\nResponse:\nThanks for your very insightful suggestions. The density differences between DSW and\nsurrounding waters potentially influence our conclusions. Here, we carried out additional\nexperiments with different DSW density, but holding the properties of surrounding waters\nunchanged. To cover the typical dynamical regimes, the experiments include steep, moderate\nand small topographic slopes. We vary the density of DSW by restoring salinity to different\nvalues, with constant potential temperature of -1.9℃. Since the maximum salinity of the DSW\npresented in the manuscript is 34.8 psu (Fig. S2), we restore the maximum salinity to 34.7 and\n35 psu to simulate lighter and denser DSW respectively.\nThe results show that the downslope transport of DSW exhibits no significant differences\nfor moderate and small slope experiments as DSW density changes (Figs. R5b,c). For the steep\nslope experiments without tides (Fig. R4a), the descent of DSW is slightly more efficient as the\nDSW density increases, owing to the farther offshore travels of the denser DSW during the\ngeostrophic adjustment process. The effects of tides on DSW descent show no substantial\ndifferences: tidal advection facilitates DSW descent for steep slopes, while no significant\ninfluences for gentle slopes when TRWs or eddies form. As expected, the AABW density\nincreases as the DSW density increases, and the tides have no substantial influences on density\ndistributions for moderate and small slope experiments (Figs. R4e,f). For steep slope\nexperiments (Fig. R4d), tidal induced density increase is not significant when the DSW is\nlighter, which may be explained by weaker interfacial stratification that favors shear instability\nunder tidal forcing.\nOverall, varying DSW density does not change the results substantially, suggesting that\nour conclusion is generally robust and appropriate for a pan-Antarctica description of AABW\nformation.\nWe have added some discussion in the main text (Lines 240-250 in the revised manuscript):\n“One might also expect that the density difference between DSW and surrounding waters,\nwhich controls the baroclinic pressure gradient, influences the process of DSW descent. To\naddress this issue, we conducted sensitivity experiments with different DSW densities while\nholding the properties of surrounding waters unchanged. To cover the typical dynamical\nregimes, the experiments include cases with steep ( ), moderate ( ) and small\n( ) topographic slopes. The results exhibit n𝑠o =si0g.n1i5ficant differen𝑠ce=s 0fo.0r6 t7he moderate\na𝑠nd= s0m.0a3ll3 slope cases as DSW density changes (Fig. S8). For steep slope cases, the tidal induced\nAABW density increase is not significant when the DSW is lighter (Fig. S8d), which may be\nexplained by weaker interfacial stratification that favors the shear driven mixing under tidal\nforcing. Overall, varying DSW density does not substantially change the overflow dynamics,\nsuggesting that the results are generally robust over a wide range of DSW density.”\nFigure R5 (Figure S8 in the revised manuscript). The impact of the density difference between DSW and\nsurrounding waters on the overflow properties. We vary the DSW density by restoring the salinities on\nthe continental shelf to different maximum values, with a constant potential temperature of -1.9℃. The\nred, green and blue curves correspond to the DSW with maximum salinities of 34.7, 34.8 and 35 psu\nrespectively. The solid thick curves indicate the simulations without tidal forcing, while the dashed\ncurves indicate the corresponding simulations that include tidal forcing. (a-c) Isobath corresponding to\nthe DSW tracer center of mass, as a function of along-slope distance downstream of the trough. The top\nto bottom panels correspond to steep (s=0.15), moderate (s=0.067) and small (s=0.033) slopes,\nrespectively. (d-f) Probability density function of tracer as a function of potential density, computed over\nthe area downstream of the semi-transparent red shading shown in Fig. 4a.\nReferences:\nNakayama, Y., Ohshima, K. I., Matsumura, Y., Fukamachi, Y., & Hasumi, H. (2014). A numerical\ninvestigation of formation and variability of Antarctic Bottom Water off Cape Darnley, East\nAntarctica.Journal of Physical Oceanography,44(11), 2921-2937. https://doi.org/10.1175/JPO-D-14-\n0069.1\nOhshima, K. I., Fukamachi, Y., Williams, G. D., Nihashi, S., Roquet, F., Kitade, Y., Tamura, T., Hirano,\nD., Herraiz-Borreguero, L., Field, I., Hindell, M., Aoki, S., & Wakatsuchi, M. (2013). Antarctic Bottom\nWater production by intense sea-ice formation in the Cape Darnley polynya. Nature Geoscience, 6(3),\n235–240. https://doi.org/10.1038/ngeo1738\nWilliams, G. D., Aoki, S., Jacobs, S. S., Rintoul, S. R., Tamura, T., & Bindoff, N. L. (2010). Antarctic\nbottom water from the Adélie and George V Land coast, East Antarctica (140–149 E).Journal of\nGeophysical Research: Oceans,115(C4). https://doi.org/10.1029/2009JC005812"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revision was completed comprehensively. The authors included addifional mooring observafion to support their model results with good consistency. They added extra explanafions over ambiguous/confusing places here and there as pointed out in the first review report. Statements are appended in the revised text where the circum-Antarcfic dynamic regime map is discussed, this is important for readers to view this 'extrapolafion' with caufion, which is good. Therefore, I am happy to suggest the acceptance of this revised manuscript. Well done!", "reviewer_2": "The authors have addressed my quesfions in the previous round of review by adding analyses and discussions to further support Fig. 5c, as well as another set of sensifivity experiments to demonstrate the effects of relafive density between the DSW and the background water. It is interesfing to see the discussion about the localness of designated regimes (lines 329-334), which brings up an issue that Fig. 4a seems to suggest there are already large differences at an along-shore distance of 620 km (i.e., in the trough). As such it would be interesfing to show the DSW evolufion/processes in the near field among these experiments and how the near field is related to the downstream development.\nSpecific points:\n1. Lines 19-20: This study did not discuss the resulfing AABW properfies. What are the implicafions of the three (6 considering fides) cases in Fig. 4c regarding the AABW properfies? Does it mean that the AABW has the highest density in the “eddying” regime, but it resides in the depth range of 1000-1200m, not reaching the lower slope?\n2. Line 292: Change “Analysis” to “Analyses”.\n3. Rewrite the sentence in lines 293-296."}, "author_response": "Reviewer #2 (Remarks to the Author):\nThe authors have addressed my questions in the previous round of review by adding analyses and\ndiscussions to further support Fig. 5c, as well as another set of sensitivity experiments to\ndemonstrate the effects of relative density between the DSW and the background water. It is\ninteresting to see the discussion about the localness of designated regimes (lines 329-334), which\nbrings up an issue that Fig. 4a seems to suggest there are already large differences at an along-\nshore distance of 620 km (i.e., in the trough). As such it would be interesting to show the DSW\nevolution/processes in the near field among these experiments and how the near field is related to\nthe downstream development.\nSpecific points:\n1. Lines 19-20: This study did not discuss the resulting AABW properties. What are the\nimplications of the three (6 considering tides) cases in Fig. 4c regarding the AABW properties?\nDoes it mean that the AABW has the highest density in the “eddying” regime, but it resides in\nthe depth range of 1000-1200m, not reaching the lower slope?\nResponse:\nThanks for your very insightful comments. Fig. 4c indeed implies that the AABW has the\nhighest density in the ‘eddying’ regime, because gentle slopes cause slower geostrophic flow (Nof,\n1983), thus weaker shear-driven mixing. Considering that we set constant DSW density over a range\nof sensitivity experiments, we did not use the words like ‘denser’ or ‘lighter’ to describe newly\nformed AABW to avoid potential confusions, especially for the Ross- and Weddell-like experiments.\nThe DSW densities in these two regions are different, which contributes to making differences in\nthe resulted AABW densities. Instead, we emphasize the effects of the net entrainment during the\nDSW descending process on the resulted AABW properties. We have some discussion in the\nmanuscript (Lines 175-178): “These results indicate that tidal advection reduces entrainment into\nthe DSW layer only when TRWs are suppressed, and that gentler slopes (such as those in the\nWeddell Sea) permit DSW to descend to the deep ocean with much less modification than do steeper\nslopes (such as those in the Ross Sea).”\nAlthough the descent rate is slower in ‘eddying’ regime, the dense water can gradually descend\nto deeper ocean as flowing further downstream (Fig. 4a). The related statement lies in the manuscript\n(Lines 220-223): ” We anticipate relatively fast, localized production of AABW in ‘Tidal’ and ‘Wavy’\nregimes, and AABW formation further downstream in the ‘Eddying’ regime due to the slower\ndescent rate associated with the eddy trains over the upper continental slope16.”\nFig. 4 | Simulations investigating the influences of tidal flows and continental slope steepness on\ndense overflows. a Isobath corresponding to the dense shelf water (DSW) tracer center of mass, as a\nfunction of along-slope distance downstream of the trough. The solid thick curves indicate the\nsimulations without tidal forcing, while the dashed curves indicate the corresponding simulations that\ninclude tidal forcing. The semi-transparent red shading denotes the zonal range that we calculate the\naveraged DSW tracer-weighed isobath shown in panel b. b Zonally-averaged DSW tracer-weighted\nisobath for different experiments, with and without tidal forcing. c Probability density function of tracer\nas a function of potential density for experiments with three different slope inclines, with and without\ntidal forcing, computed over the area downstream of the semi-transparent red shading shown in panel a.\nThe orange vertical line indicates the maximum potential density in the simulation prior to DSW\nproduction. d Similar to panel c, but for varying tidal forcing strengths with constant slope steepness\n(𝑠=0.15).\n2. Line 292: Change “Analysis” to “Analyses”.\nCorrected.\n3. Rewrite the sentence in lines 293-296.\nResponse:\nThanks for your careful reading of this manuscript. We agree that there are some problems of\nthat sentence, so we have now rewritten that sentence to “For the Adelie coastal region\n(Supplementary Fig. 10), the mooring located on the continental slope records a strong mean flow,\nsuperposed with a diurnal tidal cycle of a comparable magnitude, and a fortnightly spring-neap tidal\ncycle.”\nReference:\nNof, D. (1983). The translation of isolated cold eddies on a sloping bottom. Deep Sea Research Part\nA. Oceanographic Research Papers, 30(2), 171-182."}]

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