Drivers of Antarctic sea ice advance

Domain: earth_science
Published: 2023-10-05
Editorial outcome: accept

Abstract
Antarctic sea ice is mostly seasonal. While changes in sea ice seasonality have been observed in recent decades, the lack of process understanding remains a key challenge to interpret these changes. To address this knowledge gap, we investigate the processes driving the ice season onset, known as sea ice advance, using remote sensing and in situ observations. Here, we find that seawater freezing predominantly drives advance in the inner seasonal ice zone. By contrast, in an outer band a few degrees wide, advance is due to the import of drifting ice into warmer waters. We show that advance dates are strongly related to the heat stored in the summer ocean mixed layer. This heat is controlled by the timing of sea ice retreat, explaining the tight link between retreat and advance dates. Such a thermodynamic linkage strongly constrains the climatology and interannual variations, albeit with less influence on the latter.

Introduction
The Antarctic sea ice seasonal wax and wane is one of the most spectacular, climate-related signals, with large consequences for the global ocean water mass structure and circulation1–3, the Earth’s energy budget4, and marine ecosystems5,6.

The seasonal cycle of Antarctic sea ice is marked by two key transitions between open water and ice-covered conditions: advance and retreat. Advance or retreat are defined as the first day in the year when smoothed-in-time sea ice concentration exceeds or falls below 15%7–9. Over the last 40 years, changes in the timing of Antarctic sea ice advance and retreat have been documented from satellite-based passive microwave sensors7,10. The changes, highly variable regionally, were attributed to wind-driven changes in ice transport and seasonal thermodynamic ice-ocean feedbacks7,11–15. Yet interpretation is complicated: strong interannual variability dominates the trends in the last two decades16 and drivers involve multiple oceanic and atmospheric processes7,10,17,18, in a context of limited understanding of the drivers of sea ice advance and retreat.

Sea ice advance and retreat are influenced by different processes implying specific observational needs and problems. In this paper, we focus on the fundamental drivers of the sea-ice advance date and on links to the sea-ice retreat date. Sea-ice advance can be controlled either by the freezing of seawater or by sea-ice drifting from already frozen areas19–22. Freezing starts ultimately once the entire mixed layer, having warmed up from solar absorption in spring and summer then cooled down through fall, approaches the freezing temperature23,24. Close to the winter sea ice edge, freezing can, however, be inhibited by entrained25 or advected20 oceanic heat into the mixed layer.

As such, one can hypothesize that the date of sea ice advance is controlled by the upper ocean heat content, surface fluxes, sea ice thermodynamics and drift. To understand these contributions, we relate climatological dates of sea ice advance derived from passive-microwave sea ice concentration26 to recently available observational datasets. They include passive microwave-based sea ice concentration budget diagnostics that split sea ice changes into dynamic (i.e., drift-related) and thermodynamic (i.e., related to freezing) process contributions22; thermal infra-red radiance satellite sea surface temperature27 (SST); compilations of in situ hydrographic measurements28 which now provide a detailed climatological view of the upper oceanic thermohaline structure under Antarctic sea ice, thanks to animal-borne sensor records29. Combining these sources, we highlight a strong overarching contribution of upper ocean thermodynamics in setting the climatological date of sea ice advance and an important role for ice drift in an outer band, with a width of a few degrees of latitude. We then provide evidence that these mechanisms also contribute to a certain extent to observed interannual changes in the timing of sea ice advance.

Results
Sea ice advance: local freezing or import of remote ice?
The satellite-based sea ice concentration budget, based on sea ice drift and coverage retrievals from AMSR-E products over 2003–201011,18, is used to assess how thermodynamic (i.e., freezing of seawater) and dynamic (i.e., import of sea ice) processes control the spatial variability of climatological dates of advance (da) (Fig. 1a). The sea-ice concentration budget cannot be evaluated prior to da, when the processes leading to sea ice advance take place, because of missing ice drift data and large sea ice concentration errors in the low-concentration ice near the ice edge. Instead, we evaluate the thermodynamic (Th) and dynamic (Dy) contributions to the total sea ice concentration tendency over the 30 days following da, as well as their ratio (Dy/Th) (Fig. 2; see Methods), which delineates regions where transport or freezing dominates sea ice concentration changes.

Following sea ice advance, freezing (Th > 0; Fig. 2a) dominates sea ice concentration tendencies (|Dy/Th| < 1; Fig. 2c) in most of the seasonal ice zone except in a circumpolar band close to the sea ice edge where ice import (Dy > 0, Fig. 2b) takes over freezing (|Dy/Th| > 1) or where net melting occurs (Th < 0). This is consistent with previous work, based on sea ice concentration or volume budget decomposition, which showed that the wintertime ice edge is sustained by ice transport rather than freezing20,22,30. We refer to the region south of the |Dy/Th| = 1 contour, as the inner zone and north of this contour, as the outer zone. The latter represents 32% of the seasonal ice zone area. These zones are robust to the choice of the time window over which the budget is integrated following da, being weakly sensitive to the window size from 15 to 60 days (Supplementary Fig. 1). We retain a time window of 30 days as a compromise between the needs to be close enough to the time of advance and to maximize the number of useable observations (Supplementary Fig. 1).

We find the inner and outer zones hydrographically differ at the time of advance. Indeed, the sea surface temperature at the date of advance (SSTda), evaluated from an infrared satellite SST climatology (2003–2010)27, is consistent with our analysis of the sea ice concentration budget (Fig. 2d). First, similar spatial structures are seen, which is remarkable since both sources are independent. In particular, SSTda is significantly warmer than the freezing temperature (Tf) in the outer zone (median +/− IQR: 0.6 +/− 0.3 °C). Also, the 5% highest values of SSTda - Tf (i.e., > 1 °C and higher than the uncertainty of the SST product, Supplementary Fig. 2), are found in or very close to the outer zone contour (Fig. 2d). The median SSTda - Tf is lower in the inner zone (0.4 +/− 0.2 °C) than in the outer zone, however this difference is not significant, which may reflect uncertainties in the exact position of the inner-outer zone boundary, or in SSTda. Nevertheless, these findings are robust to the choice of alternative SST products (satellite31 and in situ; Supplementary Figs. 2 and 3) and to the choice of a longer considered time period (1982–2018 instead of 2003–2010; Supplementary Fig. 2). Finally, a last element of interest is that the temperature profile at the base of the mixed layer is thermally unstable in the outer zone during the first three months of the advance season, according to an in situ hydrographic climatology28 (Supplementary Fig. 4). Taken together, we argue that the outer zone corresponds to where drifting ice encounters sufficiently warm waters for net basal melting to occur on the day of advance. The contrast is arguably reinforced by an unstable water column, which could lead to entrainment of warm waters into the mixed layer, opposing sea ice growth. Previous studies have also highlighted the role of oceanic heat supply as a spatial constraint to sea ice advance in the winter ice edge region20,25.

In conclusion, the sea ice concentration budget, satellite SST and in situ hydrography observations consistently suggest the climatological date of advance in the inner and the outer zones is controlled by different processes. While the onset of freezing control the date of advance in the inner zone, a more complex balance between ice import and oceanic heat supply driving basal melting primarily control the date of advance in the outer zone. We next investigate the physical processes controlling the onset of freezing.

Control of sea ice advance from ice-ocean thermodynamic processes
In the inner zone, where freezing is the main driver of sea ice advance, we expect the climatological da to be strongly linked to the climatological heat content of the mixed layer, as well as the mixed layer cooling rate during the open water season. In this section, we explore the strength of these links. We find that the spatial pattern of da relates to the spatial pattern of the seasonal satellite-based27 SST maximum (SSTmax). Maps of climatological da and SSTmax, shown respectively in Fig. 1a and c, indicate that waters with lower seasonal SST maximum freeze earlier. Moreover, a linear model attributes a large part of the spatial variance in da to SSTmax (R2 = 0.81), suggesting that SSTmax could be a proxy of the mixed layer heat gained in spring and summer, which is then lost before sea ice advance. However, a nonlinearity in the relationship appears when representing the spatial distributions of da anomalies versus SSTmax anomalies on a 2D histogram (Fig. 3a). Using a monthly climatology of mixed layer depths28, we find that this non-linearity is most obvious for the deepest mixed layers. In Fig. 3a, the non-linearity is confined in the black polygon enclosing all grid points with an average mixed layer depth deeper than 80 m. This suggests that the SSTmax is not sufficiently representative of the mixed layer heat content (MLH), and that the heat content over the entire mixed layer depth, which itself has a spatial variability, must be considered.

Based on the climatological mixed layer depth and SSTmax, we define an observational estimate of the climatological seasonal maximum of MLH (MLHmax; see Methods):

MLHmax ≈ ρcp MLDdSST : SSTmax (1)

where MLDdSST is the mixed layer depth evaluated in the month of dSST, the climatological date of maximum SST. MLHmax accounts for the variability in both SST and mixed layer depth (Fig. 1d). Strikingly, the 2D histogram of da anomalies versus MLHmax anomalies does not show any evident non-linearity (Fig. 3b). MLHmax also explains a larger part of the spatial variance in da (R2 = 0.89) than SSTmax does (R2 = 0.81, Fig. 3a). The observed relationship between MLHmax and da can be understood in the framework of a mixed layer heat budget model9 (see Methods). Integrating this budget for each (x,y) grid point over the open ocean cooling period, a direct link between da and MLHmax anomalies arises:

da(x,y) - dSST(x,y) = MLHmax(x,y) / <Q->(x,y) (2)

where:

MLHda ≈ ρcp MLDda : SSTda (3)

where MLDda is the mixed layer depth evaluated in the month of da. The average net heat loss during the cooling period <Q-> sets the rate of mixed layer heat loss. The linear relationship between MLHmax and da then suggest spatially uniform <Q->, which seems to hold overall (Fig. 3b). The scatter associated with this relationship indicates that <Q-> varies but is equally distributed around the mean, without altering the linearity of the relationship. Thus, the spatial variability of <Q-> only has a minor influence on da in the inner zone. Applying Eq. (1) to the slope of the MLHmax - da linear regression model (Fig. 3b), we estimate the average net heat loss <Q-> to 80 W/m2. This number integrates all mixed layer heat budget contributors (entrainment, advection, diffusion and air-sea fluxes) but is likely dominated by air-sea fluxes32. Such net air-sea heat loss is consistent with reanalysis-based estimates of net surface fall heat loss in Antarctic ice-free waters (e.g., ref. 33).

The date of advance in the inner zone is therefore controlled by the heat that accumulates in the mixed layer during the ice-free season. This heat is tightly related to the net radiative energy input at the ocean surface (turbulent fluxes are much weaker than radiative fluxes in the sea-ice zone34; Supplementary Fig. 5), which is itself constrained by the presence of sea ice and hence, by the date of sea ice retreat (dr). Consistently, we find a remarkably strong linear link between climatological dr and MLHmax (R2 = 0.80; Fig. 3c). This suggests that MLHmax is mostly set by the timing of sea ice retreat and weakly influenced by the spatial variability of net heat fluxes warming the mixed layer during the ice-free season (see Methods). Therefore, by controlling amount of heat accumulating in the mixed layer over the ice-free period, the timing of ice retreat indirectly controls the timing of ice advance. Comparing the climatology of dr with that of da consistently indicates that later dr is associated with earlier da, with a significant and strong linear relationship (R2 = 0.78, Fig. 3d). Previous work has already linked interannual anomalies in da to anomalies in dr7. Here, we show that this link holds for the spatial variability of climatological retreat and advance dates, and is controlled by the upper ocean heat content.

The statistical relationships between dr, MLHmax, and da are also strong in the outer zone, but generally not as much as in the inner zone (Supplementary Fig. 6). The MLHmax - da link is weaker in the outer zone (R2 = 0.83) than in the inner zone (R2 = 0.89), but still explains a large part of the da variance. Similarly, the dr - MLHmax link is weaker (R2 = 0.72, p < 0.01) in the outer zone than in the inner zone (R2 = 0.80). This general weakening and the associated larger regression errors might reflect a larger spatial variability in net heat fluxes in the outer zone (see Methods), possibly linked to the entrainment of warm waters into the mixed layer (Supplementary Fig. 4). The departure from the linear relationship occurs in regions of the outer zone that differ between the dr - MLHmax and the MLHmax - da relationships (Supplementary Fig. 7). This spatial mismatch affects the dr - da relationship, which is therefore weaker than the two others in the outer zone (R2 = 0.61), and does not explain as much of the da variance there.

In summary, the climatological dr strongly affects the climatological da in the inner zone only. By contrast, the climatological MLHmax determines the climatological da throughout the seasonal ice zone, regardless of the processes (freezing or ice import) increasing sea ice concentration at that time.

From spatial to interannual variability
Thermodynamic processes in ice-free waters provide strong constraints to the climatological date of advance. Whether such mechanisms also apply at interannual time scales is not straightforward. Stammerjohn et al.7 disclosed significant correlations between detrended dates of retreat and subsequent advance over 1980–2010. An ice-ocean thermodynamic feedback was hypothesized to explain this link. The same mechanism was also identified in the Arctic7–9,35. However, observations and CMIP5 model analyses suggest that thermodynamic processes are less effective at explaining interannual variations than they are for the mean state8,9. Based on what precedes, we question to which extent our findings on the mean state can be applied to interannual variations.

We expect the ice-ocean thermodynamic feedback to operate in agreement with our dr - MLHmax - da framework: an earlier retreat on a given year would lead to a higher maximum MLH and a later advance. We examine these links at the interannual time scale, using the SST as a proxy for the MLH, due to the limited spatial coverage of interannual mixed layer depth data. Based on detrended time series over 1982-2018, we find significant and relatively strong negative links between anomalies of dr and subsequent SSTmax (p < 0.05 and r = -0.6 +/− 0.2; Fig. 4a), and positive links between anomalies of SSTmax and subsequent dates of advance (p < 0.05 and r = 0.5 +/− 0.2; Fig. 4b) in large parts of the seasonal ice zone. As a result of the thermodynamic linkage between dr, SSTmax, and da, we also find relatively strong correlations between detrended anomalies of sea ice retreat and subsequent advance date (p < 0.05 and r = -0.5 +/− 0.2; Fig. 4c), consistently with Stammerjohn et al.7. However, those correlations are weak or statistically insignificant close to the seasonal ice zone edge and also in the East Antarctic and Maud Rise sectors, which indicates that processes distinct from the ice-ocean feedback are also strongly involved (Fig. 4a–c).

The mean state-based decomposition between an inner and outer zone seems relevant to better constrain the role of ice transport and melt processes at the interannual timescale. To explore this idea, we examine the interannual standard deviation in the date of advance. We find that interannual variability is highest within or close to the outer zone (Fig. 4d). This suggests that high interannual variability in the timing of advance is due to variability in either sea ice drift, which relates to variability in winds11 or in ocean heat input20, or both. By contrast, the lower variability in da in the inner zone could relate to a more prevalent control of thermodynamics on the date of advance. Spatial patterns of detrended correlations between dr, SSTmax and da are also generally in line with the inner-outer zones decomposition. The largest correlations are found in the inner zone (Fig. 4a–c), consistently with thermodynamic processes driving sea ice advance there. However, one difference with our findings related to mean state is that drift and melt processes may also considerably contribute to interannual variability in the date of advance in the inner zone, as indicated by locally existing weak and low significance dr - SSTmax - da correlations there (Fig. 4a, b). For instance, close to Maud Rise, the correlations between dr and da are significant (Fig. 4c) but not between dr and SSTmax (Fig. 4a) and between SSTmax and da (Fig. 4b). The effects of oceanic heat entrainment36,37 and advection14,15 might be more suited to explain the variability in this region, despite being located in the inner zone. We therefore surmise that the inner-outer zones boundary may not be as clear for interannual variations in the date of advance than it is for the climatology.

Ultimately, the drivers of the spatial variability in the climatological date of advance also contribute to a certain extent to the interannual variability. Nonetheless, heat fluxes and transport processes exert a stronger influence on the timing of advance at the interannual time scale, compared to the mean state. Future work may help to clarify the exact role of such processes.

Methods
Observational data sources
We assess the relationships between the date of sea ice advance and the state of the underlying ocean based on a number of observational datasets. We use daily passive microwave sea ice concentration (SIC) from the EUMETSAT Ocean and Sea Ice Satellite Application Facility26 (OSISAF) over 1982–2018 (OSI-450 from January 1982 to April 2015, and OSI-430-b after April 2015). For the sea surface temperature (SST), we use a daily satellite product available from 1982, based on thermal infra-red radiance measurements, and taken from the global L4 (gap-free, gridded) European Space Agency (ESA) SST Climate Change Initiative (CCI) analysis with a resolution of 0.05°27, provided with an estimate of the analysis uncertainty on the SST.

We also use a gap-filled monthly 1979–2018 climatology of mixed layer depth and stratification, based on in situ observations28. Conductivity–temperature–depth (CTD; 1970–2018), Argo floats (Argo international programme44; 2000–2018) and marine mammal-borne sensor profiles (Marine Mammals Exploring the Oceans Pole to Pole programme45; 2004–2018) were included. Generalized least squares linear-regressions of individual in situ profiles are performed around each grid point to produce gridded maps of climatological mean fields.

Other datasets are used to support our analysis. To evaluate the radiative heat fluxes during the open water season, we derive a daily climatology of surface shortwave and longwave radiative fluxes from the FH-series data of the International Satellite Cloud Climatology Project46,47, available over 1982-2016 (ISCCP). Finally, we use NOAA Advanced very High Resolution Radiometer (AVHRR) Optimum Interpolation (OI) 0.25° daily SST v2.0 analysis data31, also referred to as Reynolds’ SST, to ensure the robustness of our analysis.

All data were interpolated on the OSI-SAF Equal-Area Scalable Earth 2 (EASE2) 25 km grid.

Diagnostics of sea ice and ocean seasonality
Climatological mean dates of sea ice retreat (dr) and sea ice advance (da) are derived from the 15% daily sea ice concentration, applied over 1982–2018. These dates are defined consistently with previous work7,9,16,48. dr is defined as the first day filtered sea ice concentration drops below 15% while da is the first day filtered sea ice concentration exceeds 15%. To ensure dr and subsequent da of the same yearly seasonal cycle are retained, we looked for da (dr) starting on a month where no sea ice advance (retreat) occurs, on average over 1982–2018. We select the January 1 of the year for dr, and the majority (>99%) of da occurs after those dates.

To obtain a meaningful 1982–2018 climatological average of da and dr, a missing value is assigned where the number of years with undefined da and dr (corresponding to year-round ice-free or ice-covered grid points) is less than one third of the total number of years in the considered period, following ref. 9.

Other climatological diagnostics were calculated to diagnose the seasonality of upper ocean thermodynamics, using the ESA CCI satellite SST over 1982–2018. For each year, the seasonal maximum of SST, SSTmax and date when this maximum is reached, dSST were identified during the open water season, between dr and da of the corresponding year. We also calculated the yearly SST on the days of advance (SSTda) and retreat (SSTdr). Then, the 1982–2018 average of each of the four ocean seasonality diagnostics was obtained following the same method as for climatological dr and da.

Decomposition of sea ice concentration budget at the time of advance
To explore the respective role of ice dynamics and thermodynamics in setting da, we evaluate the dynamic and thermodynamic contributions to the sea ice concentration budget at the time of advance. We identify regions of ice import/export, ice melt/growth and regions of dominant dynamic/thermodynamic contributions. We use the sea ice concentration budget decomposition outputs from ref. 22 available at daily frequency between 2003 and 2010. We also use a 2003–2010 climatology of da, for temporal consistency. These outputs are obtained based on the technique developed by ref. 11 from daily sea ice concentration (NASA Team algorithm49) and ice drift fields derived from AMSR-E brightness temperature by a cross-correlation algorithm50,51. The sea ice concentration, is decomposed as:

∂SIC / ∂t = ∇ : (uSIC) + residual (4)

The ice concentration flux divergence represents the effects of ice drift. The residual includes both the effects of sea ice processes (melting/freezing) and mechanical redistribution through ridging and rafting. However, mechanical redistribution usually occurs for high sea ice concentration. Thus, we consider the residual as purely thermodynamic. Evaluating the different terms of the previous equation at the time of advance requires analyzing the output of the sea ice concentration budget for sea ice concentration below 15%. However, the budget is not defined at large sea ice concentration because of missing ice drift data and large sea ice concentration errors. To overcome this limitation, we diagnose total sea ice concentration increase (ΔSIC), as well as percent dynamic (Dy) and thermodynamic (Th) contributions to sea ice concentration tendency during a period on length Δt following da.

The diagnostics are defined as such:

ΔSIC = 1/Δt ∫ da to da+Δt (∂SIC/∂t) dt (5)

Dy = 1/Δt ∫ da to da+Δt (∇ : (uSIC)) dt (6)

Th = 1/Δt ∫ da to da+Δt (residual) dt (7)

To choose the most suitable upper bound of integration, the sensitivity to Δt of the contours delimiting our regions of interest (Th=0, Dy=0 and |Dy/Th|=1) was assessed (Supplementary Fig. 1). For varying Δt from 15 to 60 days, we find that the Th=0 and |Dy/Th|=1 contours vary only little. More precisely, regions of sea ice melt (Th < 0) and dominant dynamic contribution (|Dy/Th| > 1) are consistent both in location and percentage of total seasonal ice zone area, strengthening our confidence that they are a close representation of the sea ice concentration budget prior to da. Hence, our regions of interest should be at similar location and have a similar area at the time of sea ice advance than in any of the time periods Δt within 2 months following da. We choose Δt = 30 days as a compromise between a low proportion of missing values in the considered seasonal ice zone and the proximity in time to da.

The dr - MLHmax - da relationship in a simple heat budget model framework
The mathematical description of the simple thermodynamic framework used to explain spatial variations in the timing of advance is an updated version of the framework developed by ref. 9 in the context of Arctic sea ice, based on the heat budget in the mixed layer. We define the heat stored in the mixed layer, termed mixed layer heat content (MLH) as:

MLH = ρcp hT (8)

where h is the mixed layer depth, T, the mixed layer temperature, ρ, the reference density of seawater, and cp, the specific heat of seawater. The model is based on the temperature balance equation52, which writes as:

∂MLH / ∂t (t,x,y) = Qt (t,x,y) (9)

where Qt is the net heat flux (sum of air-sea fluxes, entrainment, diffusion and advection). Integrating the MLH budget during mixed layer heating (from dr to dMLH) and cooling (from dMLH to da) periods we get:

da(x,y) - dSST(x,y) = MLHmax(x,y) / <Q->(x,y) (10)

MLHmax(x,y) - MLHdr(x,y) = <Q+>(x,y) (dMLH(x,y) - dr(x,y)) (11)

where dMLH is the date of maximum MLH. <Q+> and <Q-> are respectively the mean total net heat flux during the heating and the cooling periods:

<Q->(x,y) = 1 / (da(x,y) - dMLH(x,y)) ∫ dMLH to da (Qt(t,x,y)) dt (12)

<Q+>(x,y) = 1 / (dMLH(x,y) - dr(x,y)) ∫ dr to dMLH (Qt(t,x,y)) dt (13)

Combining Eqs. (12) and (13), we obtain a relationship between dr and da:

da(x,y) - dMLH(x,y) = (<Q+>(x,y) / <Q->(x,y)) * rMLH * (dMLH(x,y) - dr(x,y)) (14)

with:

rMLH(x,y) = (MLHmax - MLHda) / (MLHmax - MLHdr) (15)

If T is at the freezing point on dr and da, then MLHda ≈ MLHdr and rMLH ≈ 1.

Perfectly linear relationships between climatological da and MLHmax anomalies, MLHmax and dr anomalies would respectively suggest uniform spatial distributions of <Q-> and <Q+>. Resultingly, the relationship between da and dr anomalies would also become linear (if rMLH ≈ 1).

Definition of the observational MLH
Using the monthly climatology of mixed layer depth from ref. 28 and the ESA CCI SST diagnostics (e.g., SSTmax, SSTdr, SSTda), we estimated the observational MLH for any date, t, during the open water season as:

MLH(t) ≈ ρcp MLDt : SSTt (16)

where MLDt is the monthly mixed layer depth evaluated on the month of the given date, t (e.g., MLD is evaluated on the month of climatological seasonal maximum of SST, dSST). The SST is in degrees Celsius. Using this observational estimation of the MLH, we obtain:

MLHdr ≈ ρcp MLDdr : SSTdr;
MLHmax ≈ ρcp MLDdSST : SSTmax;
MLHda ≈ ρcp MLDda : SSTda;

Data availability
The present analyses are mostly based on publicly available observational data. OSI-SAF sea ice concentration data are available from https://osi-saf.eumetsat.int/products. Sea ice concentration budget decomposition outputs are available upon request. Sea surface temperature data are available from https://cds.climate.copernicus.eu/cdsapp#!/home for the ESA CCI product and from https://www.ncei.noaa.gov/products/avhrr-pathfinder-sst for the NOAA AVHRR product. ISCCP radiative surface heat fluxes are available from https://isccp.giss.nasa.gov/projects/flux.html. Climatological fields of mixed layer depth and stratification are available from https://zenodo.org/record/4073174#.YA_jsC2S3XQ. Source data are provided with this paper.

Code availability
All scripts used for generating the plots in this paper are available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General feedback\n1) The presentation in this manuscript is fairly clear and rigorous, with results that add to previous\nstudies of a similar vein. In my estimation the main new results are quantifying the SST near the time\nof ice advance and showing that the MLH is a slightly better predictor of the advance date than SST\nis alone in the inner zone and a substantially better predictor in the outer zone. The authors do a\ngood job of citing the literature specific to ice advance and retreat. They might find some additional\nimportant previous work in the predictability literature.\nGiven that the main contributions are quantitative estimates of known relationships and\nmechanisms, I think this paper could be strengthened if the authors said more about how their\nresults could be used to evaluate and improve CMIP models. What matters most? Is it the size of the\ninner and outer zones that matter, the correlations or regression coefficients among certain\nvariables, the distributions of the quantities in the 2D histograms, etc. Which are the target metric\nmodels should aim for to achieve specific purposes.\n2) The speculaton about how ice-ocean feedback will be \"reinforced\" with global warming is too\nhand wavy in my view. What does it mean to \"reinforce\". Does this mean to maintain or strengthen\nthe feedback? I don't think global warming would strengthen the feedback due to the competing\neffects discussed lines 240-243. I recommend removing this speculation about global warming\nreinforcing the feedback but keep the discussion about competing effects. In addition, it would be\nuseful if the authors could say what the metric of reinforcing a feedback is and how could we\nobserve or model it.\n3) I'd like the authors to consider the consequences of their assumptions in more detail. I appreciate\nthat they have tried in various ways to do so already.\nThe number one issue I have along these lines is knowing whether I believe that a budget 30 days\nfollowing is a good representation of the budget prior to da. Stating that it doesn't matter if that\nwindow is anywhere from 15 to 60 isn't sufficient since all of the windows are still past da. Whether\nthe budget after da is a good representation of the budget before da could be tested in a model with\nprescribed winds. Alternatively the authors could embrace the budget following the advance date\nfor what it is, and explain why we should be interested in this time period. For example, we might be\ninterested in the consequences of sea ice advance on the budget, rather than vice versa.\nI was not sure if this 30-day shift is used for the other parts of the analysis near the advance date as\nwell.\nFor example, is the SST in Fig 1d \"at the date of advance\" as stated at lines 93 and 105, or is it the\nSST for 30 days following it. I'm just as interested if it is the 30 days following it (maybe even\nmore interested). In any case, please clarify and if it is the 30-days after, then don't say \"at\".\n4) It would also be good to know what error is incurred by assuming no mechanical redistribution\nduring the 30 days following da. A sea ice model could be consulted to estimate this error too.\nMechanical redistribution can only reduce SIC, so neglecting it is a systematic bias that leads to an\nunderestimate of sea ice growth.\n5 ) One of the cooler results in my view is the estimate of the mean SST_da in the outer zone,\nfinding that it is quite a bit warmer than -1.8 C. I'm really dying to know the mean SST_da is in the\ninner zone too, and recommend this number also be included.\nSpecific feedback\nThere are many variables used in this paper. A table of them would be nice for the reader (and might\nhelp the authors keep track of them too).\nline 40-41: This is an odd thing to say: focus on one and seek to understand another.\nline 54: When I read this, I wondered why is it desirable for the observations to be from independent\nsources when they are observations of different things. I think line 105 largely explains why, but I\nwas left hanging all that time!\nline 65: I don't like seeing that T>0 close to the date of advance. I suggest considering using H or\nsomething else for thermodynamic, rather than T since T as temperature is so ingrained.\nline 100: \"sea ice transport is mostly set by seawater freezing\" sounds odd. Maybe instead say the\n\"sea ice advance is mostly set by seawater freezing\".\nline 125: The quantity in Fig 1c is labeled SST_da (the caption and line 105 calls it \"at the time of\nadvance\") but here the text says Fig 1c has SST_max which I would expect to be quite different Is\nthis a mix up or just not explained well?\nline 132: I don't know what I'm supposed to see as \"standing out clearly\" in Fig 3b. Am I supposed to\nbe looking at the polygon in Fig 3a?\nLine 144: Is this supposed to refer to Fig 3b?\nline 172: MLD_cp is never defined\nMethods\nThe text doesn't say what dataset is used for sea ice drift, other than AMSR-E. Please give a citation\nto the product. Apologies if one of those citations is it, but none seemed likely.\nline 275: filter not filtering\nline 279: 10/1982 to 19/1983 is not clear. It sounds like 13 months.\nline 282-284: I'm not following this. Why is da or dr ever undefined?\nline 313-315: the lower limit of the integral has a erroneous subscript rather than just da", "reviewer_2": "Review of “Recent decline in Antarctic sea ice cover from 2016 to 2022: Insights from satellite\nobservations, Argo floats, and model reanalysis” by Kshitija et al.\nA substantial volume of recent work has focused on identifying the drivers of Antarctic sea ice\nchange over the satellite record. Winds have been shown to be important in driving variability.\nThis interesting study fills an important gap in the knowledge by demonstrating the role of the\nsummer ocean and highlighting the need to understand changes in both the temperature and depth of the\nmixed layer.\nThe authors combine remote sensing data products and new in situ observational datasets to\ninvestigate the processes modulating the timing of sea ice advance. They demonstrate that the\nseasonal ice zone can be divided into an “inner” region, just over 2/3 of the total seasonal ice zone,\nwhere the freezing ocean sets the sea ice advance, and an “outer zone”, about a third of the total\nseasonal ice zone, where sea ice advance is a balance between the import of ice and melting.\nDespite the different processes operating in these zones, the date of sea ice advance is strongly\nlinked to the amount of heat in the mixed layer. This work supports previous studies that have\nshown the link between the timing of sea ice retreat and the timing of its subsequent advance and,\nfurthermore, demonstrates that the heat storage in the summer ocean mixed layer can explain this\ncorrelation.\nI enjoyed reading the manuscript and think it would be of interest to a wide variety of researchers as\nit provides more context on the variability of Antarctic sea ice. The manuscript is well-structured and\nwell-written – I particularly appreciated the mini summaries at the end of each section. The figures\nare generally of high quality and support the narrative. I have one reservation about the conclusion,\nwhich I note below, along with some minor typos.\nOne of the interesting results from your analysis is that the correlation between the date of\nretreat and subsequent date of advance, first noted by Stammerjohn et al, 2012, holds for much of the\n“inner” zone, where the thermodynamics set the date of advance. The “inner” zone in the Indian\nOcean sector doesn’t show a significant correlation (Fig 4a). Clearly, the ocean feedback in response\nto the timing of the retreat doesn’t hold in this region. You show only a minor influence on the\nspatial variability of Q in the “inner” zone. Does the lack of correlation in this region affect your\nconclusion that the MLH controls the link between, e.g., early retreat and later advance?\nIt would be good to be consistent with the arrangement of the letters that label the figures - e.g. in\nFig 1, ‘b’ is top right, whereas in Fig 2, ‘b’ is bottom left.\nFig 2 - do ‘a’ and ‘b’ have the same colorbar?\nLine 101: do you mean to reference Fig 2?\nLine 105: add 'the' to the end of the line\nLine 132: should this refer to fig 3a rather than fig 3b?\nLine 142: you might consider referring to Fig 2b.\nLine 172: please define MLDCP\nLine 278: typo - change \"or\" to \"of\"?\nLine 280: Is da (dr)1 day 1 of advance and retreat? It might be helpful to define this somewhere.\nLine 281: May 1st seems a very safe start date for calculating dr. Jan 1st seems to be a bit closer to\nthe advance - is there ALWAYS retreat in Dec? I suspect so, but maybe you could add the earliest\ndate of advance in the satellite product to satisfy that you always retain the subsequent date of\nadvance?", "reviewer_3": "This paper provides a quite straightforward, but illustrative examination of the role of upper ocean\nheat absorption in driving the length of the open water season, and subsequent retreat of sea ice in\nsummer. Much of the analysis is simplified, and only climatological behaviour is examined (perhaps\nbecause of the scarceness of data on mixed layer depth for earlier periods). There are two main\nconclusions. First, it is shown that thermodynamic ice growth dominates the southern regions during\nice advance, and dynamics dominate the outer pack. This is not surprising, and consistent with\nresults such as those of Haumann et al (2016), who show that ice growth dominates ice-ocean\ninteractions in the south, and melt in the north. These are not exactly the same, so it’s not simply a\nrehash of old results, but the results of Haumann et al are primarily because of the relative roles of\nthermodynamics and dynamics. The reasons for the differences (say, between their Figure 3 and\nyour figure 2) would have been interesting to discuss. That said, I do think this is a useful result.\nThe second main result shows that this difference causes a relationship between the date of advance\nand retreat and the mixed layer heating in the inner zone, and weaker in the outer zone. Again,\nperhaps not terribly surprising, as other publications have shown that correlations between advance\nand retreat dates are stronger for months where ice extent is less (i.e. in the inner zone), and\nparticularly for the date of retreat and the following date of advance. However, while the reasoning\nhas previously been attributed to the ice-ocean heating feedback, it has not been explicitly shown as\nit is here. So again, this paper shows this nicely in a simple way.\nMy main criticism (if you can call it that) is not about the correctness of any of the results, but that\ndoing so with climatology only explains a general, not so unexpected behaviour, and so cannot\naddress how much these processes might have contributed (as a feedback) to recent sea ice\nvariability or trends. This is perhaps unfair, as I realize looking at interannual variability and trends\nwas not the author’s intention. But as my impression is that the results are not unexpected, the\nimpact will be less.\nWhat would have made the paper more impactful would have been to explore in more detail the\ninterannual and spatial variability. For example, figure 4 seems underexplored. Also, the\nrelationships shown in Fig 3 are strong, but much of the ‘interesting’ signal is in the deviations from\nthese relationships that likely govern how advance, retreat, and mixed layer heating vary spatially\nand interannually. I would have appreciated some analysis of how these relationships (and in S3 and\nS4) might vary spatially, and whether they might have changed over time. There is also no analysis of\nwhat may be driving the differences between the inner and outer pack (merely statements about\ndifferences in drift and melting). For example, some papers have shown differences in ocean heat\nflux convergence control differences in the inner and outer zone due to changes in stratification (e.g.\nZ. Su, GRL, 2017). This would affect the homogeneity of Q, and thus the linearity of your fits. If the\nstratification in the outer pack is weak, then thermodynamic growth is retarded not so much by\nremnant summer warming (which may have dispersed over the much longer ice-free period), but by\nentrainment of ocean heat. Lastly, I think your spatial variability in figure 2b near the ice edge\nmaximum reflects spatial variability in advection, which as noted above will have a very significant\nimpact on your interpretation here because the open water period at the ice edge maximum\napproaches 12 months.\nNevertheless, the present work does provide a good foundation for exploring these issues in a\nsubsequent paper.\nDetailed comments:\n1. I suppose you are constrained by space, but I felt like a few more sentences in the introduction\nproviding more insight into the current understanding of causes of observed trends would be\nhelpful, beyond saying “multiple process are involved” with a cite to a 2012 paper. For example,\nmany papers (some of which you cite) provide some explanation, both atmospheric and oceanic, and\nassociated feedbacks for much of the recent variability. You are quite correct that there is a lot of\nuncertainty and it is complicated!\n2. Line 37 – I think “weak fundamental understanding of the drivers of sea ice advance and retreat”\nis a bit strong. I think we understand the proximal drivers quite well, but not their relative roles in\ndriving the observed interannual variability.\n3. Line 106 “by an infrared satellite SST product\n4. Line 105-113. I don’t quite understand how the SST product can be valid in this area for the\ndate of advance, because in figure 2 it appears like you have SST retrievals where you have sea ice cover.\nThe data would not be valid here. Is it from some days before the advance? In any case, this does\nnot seem surprising at all. I am not aware of systematic comparisons with SST, but several papers\nhave noted waters above freezing and their role in delaying advance.\n5. Figure 3 – It is not entirely clear to me what data are used here. The caption says 1983-2018\nclimatological maps, and the text says monthly climatologies, so have you used climatological (i.e.\nnot varying with year) MLDs and annually varying SSTs? Or have you used both annually varying SSTs\nand MLDs, or something else? If it is annually varying MLDs, then it is highly likely that some of the\nolder period is very data sparse (pre Argo and pre marine mammal data), and that could account for\nsome of the data spread. If either is climatological, then I would not be surprised at all by the spread\nand then I question how accurate this analysis is. This is perhaps the main reason you might look at\nonly the climatologies – because the MLD data is sparse, and looking at annual variability and trends\nmay be prone to significant errors.\n6. Lines 145-150 (see also note below on lines 345-365). If I understand correctly, you are using a\nrelationship between the date of advance, date of SST max, the MLH, and the heat loss. This could\nbe made more clear, as when reading I was confused as to whether you actually estimated the fluxes\nor not.\n7. Given that you are assuming Q is uniform everywhere, then the deviations from linearity are\nentirely unsurprising in figure 3, and I am not sure you can claim it is due to issues with using\nSST to describe MLH. Have you checked to see if these deviations are occurring in places where\nheat fluxes could be unusual?\n8. Line 180-182 – the devil is in the details here! Yes, you show that the relationships are broadly\nlinear and so Q is fairly uniform, but this does not mean that the variability in Q is not very\nimportant for driving variability in da or dr, and this is really what would be most relevant to\nrecent sea ice variability, and would require a much more in depth analysis. So I don’t think you\ncan say it is weakly influence (the variability appears to be a pretty good number of days, if da-dsst is suggestive). It would be nice to know what that variability is compared to the interannual\nvariability of da.\n9. Line 182-184. I think this is maybe one of the more significant results, and perhaps should be in\nthe main paper. But it is perhaps not surprising that the mixed layer heat increase is driven by the\nradiative fluxes. It glosses over a lot, of course, and it would be interesting if you could show\nregional variations. i.e. does it matter more in the Ross Sea vs say, the east Antarctic? I do think\nyou overinterpret the significance a bit. The scatter is not so small, and is due to advective heat and\nturbulent fluxes (and also uncertainty, of course) For instance, the turbulent fluxes can be as large as\nthe net longwave flux. In some areas, advection of heat may be very important. And of course, the\nvariance around this line is important in understanding the spatial and temporal variability.\n10. Line 189 – I am not clear on how reference 7 was not also making the link on the seasonal scale?\n11. Line 199-201. There is some prior work that suggests these links (off the top of my head, I think a\na Reid et al. paper has a diagram that shows the persistence of anomalies, which for winter and\nspring would represent the outer region based on ice extent).\n12. Also in Methods, you need to provide more information on the time periods for the various\ndata sources for MLD and the gap-filling procedure.\n13. Methods – you do not state what data you have used for sea ice drift.\n14. Line 341 – “horizontal velocity”\n15. Lines 345-365 – I am not 100% sure I understand what you did here. At first, it seemed you\ncomputed the mixed layer heat from the total fluxes, but nowhere do you explain how you\ncomputed the horizontal advective fluxes, the entrainment flux or the diffusive flux, or what\nvalues you use for the various coefficients. So it looks like you don’t actually compute fluxes, but\nestimate if they are important for this broad-scale analysis by the fits in figure 3, and are only\nderiving a relationship between the flux, the MLH and the date of advance and retreat. This is not\nvery clear, as elsewhere you describe using flux estimates (but for what, I am not sure). If I am\ncorrect, this description could be clearer if you simplified by deleting the equation on 338 and start\nfrom the equation on 343 (please number your equations!), and just explain that Qt is the total net\nflux as you do, and that you are not attempting to estimate it. If I am wrong, and you do compute the\nfluxes, then you need to explain a lot better.\n16. Ref 30 – formatting issue here."}, "author_response": "Drivers of Antarctic sea ice advance\nSubmitted to Nature Communications\nResponse to reviewers\nK. Himmich, M. Vancoppenolle et al.,\nJune 2023\n______________________________________________________________________________________________________________\n______________________________________________________________________________________________________________\nReviewer #1\n______________________________________________________________________________________________________________\nGeneral feedbacks:\n1) The presentation in this manuscript is fairly clear and rigorous, with results that add to\nprevious studies of a similar vein.\nIn my estimation the main new results are quantifying the SST near the time of ice advance and\nshowing that the MLH is a slightly better predictor of the advance date than SST is alone in the\ninner zone and a substantially better predictor in the outer zone. The authors do a good job of\nciting the literature specific to ice advance and retreat. They might find some additional\nimportant previous work in the predictability literature.\nAnswer:\nThank you for your comment and your suggestion. Indeed, previous work in the predictability\nliterature supports that anomalies in the date of advance are driven by ice ocean feedbacks.\nActions:\n● We added new references in the introduction where we refer to thermodynamic\nfeedbacks driving sea ice advance:\nLines 33-34: “The changes, highly variable regionally, were attributed to wind-driven changes in\nice transport and seasonal thermodynamic ice-ocean feedbacks ([...] Bushuk et al 2021; Holland et\nal 2013).”\n● We also used those citations to interpret our new Figure 4\nLines 255-256: “The effects of oceanic heat entrainment and advection (Bushuk et al 2021;\nHolland et al 2013) might be more suited to explain the variability of this region, despite being\nlocated in the inner zone.”\nmechanisms, I think this paper could be strengthened if the authors said more about how their\nresults could be used to evaluate and improve CMIP models.\nWhat matters most? Is it the size of the inner and outer zones that matter, the correlations or\nregression coefficients among certain variables, the distributions of the quantities in the 2D\nhistograms, etc.\nWhich are the target metric models should aim for to achieve specific purposes.\nAnswer & Action:\nYou are correct, we were not fully explicit as to how our results could be used to evaluate ocean\nand sea ice models. However, it is hard to be prescriptive in advance in terms of the tools to be\nused for model evaluation without trying them.\nNevertheless, two lines of evaluation are possible and we now refer to them in the main text:\n● Check whether the inner and outer zones exist and how they are positioned. This would\nhelp to evaluate whether a model realistically reproduces the thermodynamic and\ndynamic processes leading to sea ice advance.\n● Check the relations between SST_max / MLH_max / dr and da against observations (slope\nand correlation coefficient). This would help to verify the existence of the\nthermodynamic control of sea ice advance by the ocean ML (and not by something else).\nBoth evaluations would help to better characterize ocean-ice-atmosphere interaction processes,\nproviding more interesting evaluation than static metrics (i.e. ice extent).\nLines 271-276: “Our results can be used to evaluate the model representation of the processes\ndriving sea ice seasonality in the Southern Ocean against observations. Primarily, the inner-outer\nzone decomposition provides a specific approach to validate the ice concentration budget during\nthe ice advance season. Additionally, an examination of the different relations embedded in the dr-\nMLHmax-da framework can serve as a robust approach to verify the existence of the\nthermodynamic control of sea ice advance by the ocean. ”\n2) The speculation about how ice-ocean feedback will be \"reinforced\" with global warming is too\nhand-wavy in my view. What does it mean to \"reinforce\". Does this mean to maintain or\nstrengthen the feedback? I don't think global warming would strengthen the feedback due to the\ncompeting effects discussed lines 240-243. I recommend removing this speculation about global\nwarming reinforcing the feedback but keep the discussion about competing effects. In addition,\nit would be useful if the authors could say what the metric of reinforcing a feedback is and how\nwe could observe or model it.\nAnswer & Action:\nAs you pointed out, we only aimed to describe the competing effects of MLD changes and\ntemperature changes on sea ice advance. Phrasing it as a “feedback reinforcement” was indeed\nnot the most suitable way to describe this mechanism. We reformulated this part of our\ndiscussion on long-term changes.\nLines 283-286: “Arguably global warming will be associated with earlier retreat and warmer\nsurface waters, providing more heat to the mixed-layer in summer, delaying sea ice advance.\neffects of the temperature increase.”\n3) I'd like the authors to consider the consequences of their assumptions in more detail. I\nappreciate that they have tried in various ways to do so already.\nThe number one issue I have along these lines is knowing whether I believe that a budget 30\ndays following is a good representation of the budget prior to da. Stating that it doesn't matter if\nthat window is anywhere from 15 to 60 isn't sufficient since all of the windows are still past da.\nWhether the budget after da is a good representation of the budget before da could be tested in a\nmodel with prescribed winds.\nAnswer:\nYou are correct. That the inner-outer zones size and location is not sensitive to the time window\nof calculation after da only shows that our division of the SIZ is robust over the 15 to 60 days\nfollowing the date of advance (see Figure S1).\nHowever, we find hydrographic evidence that the SIC budget-based inner and outer zones are a\nclose (but imperfect) representation of the processes occurring prior and at the date of advance:\nthe outer zone contour corresponds mostly to the highest SST (see Figure 2) and the ML is\nda\nthermally unstable at the start of the advance season in the outer zone (see Figure S4).\nIt is true that this could be tested in a model. However, we would also not be certain if the sea ice\nconcentration budget is well represented in the model and consequently, if the inner and outer\nzones are well represented as well.\nActions:\n● We clarified the hydrographic evidences showing that the inner-outer zones are\nindeed representative of the processes occurring before sea ice advance:\nLines 88-91: “We find the inner and outer zones hydrographically differ at the time of\nadvance. Indeed, the sea surface temperature at the date of advance (SSTda), evaluated\nfrom an infrared satellite SST (climatology (2003-2010), is consistent with our analysis of\nthe sea ice concentration budget (Fig. 2d).”\nLines 99-105: “Finally, a last element of interest is that the temperature profile at the base\nof the mixed layer is thermally unstable in the outer zone (Nt^2 < 0) during the first three\nmonths of the advance season, according to an in situ hydrographic climatology28\n(Supplementary Fig. 4). Taken together, we argue that the outer zone corresponds to\nwhere drifting ice encounters sufficiently warm waters for net basal melting to occur on the\nday of advance. The contrast is arguably reinforced by an unstable water column, which\ncould lead to entrainment of warm waters into the mixed layer, opposing sea ice growth. “\n● We mentioned that the there is an uncertainty on the exact outer zone contour:\nLines 95-97: “The median SSTda- Tf is lower in the inner zone (0.4 +/- 0.2 °C) than in the\nouter zone, however this difference is not significant, which may reflect uncertainties in the\nexact position of the inner-outer zone boundary, or in SSTda.”\nand explain why we should be interested in this time period. For example, we might be\ninterested in the consequences of sea ice advance on the budget, rather than vice versa.\nAnswer:\nThis is possible and we thank you for the suggestion. However, we consider this would imply a\nwide range of processes unexplored here, and so out of the scope of this paper, as we are\ninterested in what drives sea ice advance dates and not the other way around.\nI was not sure if this 30-day shift is used for the other parts of the analysis near the advance date\nas well.\nFor example, is the SST in Fig 1d \"at the date of advance\" as stated at lines 93 and 105, or is it the\nSST for 30 days following it. I'm just as interested if it is the 30 days following it (maybe even\nmore interested). In any case, please clarify and if it is the 30-days after, then don't say \"at\".\nAnswer & Action:\nYou are right, this was not always clear in the main text. We did write ‘at’ only to refer to the SST\nevaluated on the exact day of sea ice advance at lines 89 and 120 (previously 93 and 105). But\nwe were indeed unclear when referring to the budget calculated in the 30 days following da\nwhen we wrote “close to the date of advance”. We clarified this.\nLine 66: “[...] over the 30 days following da [...]”\nLine 69: “Following sea ice advance [...]”\n4) It would also be good to know what error is incurred by assuming no mechanical\nredistribution during the 30 days following da. A sea ice model could be consulted to estimate\nthis error too. Mechanical redistribution can only reduce SIC, so neglecting it is a systematic bias\nthat leads to an underestimate of sea ice growth.\nAnswer:\nYou are correct, neglecting mechanical redistribution could induce an underestimation of\nthermodynamic sea ice growth. To ensure our main result (i.e. the inner-outer zones contour) is\nnot affected by mechanical redistribution, we identified the regions where such a process is\nlikely to occur over the 30 days following advance, following the method of Holland & Kimura\n(2016), as shown in the Figure A. The figure shows that mechanical redistribution is only likely\nto occur in the inner zone, which would not be affected by the corresponding bias. Therefore,\nmechanical redistribution does not affect the main results of our analysis.\nwith corresponding regions where mechanical redistribution possibly occurs delimited\nby the pink contour\n5) One of the cooler results in my view is the estimate of the mean SST_da in the outer zone,\nfinding that it is quite a bit warmer than -1.8 C. I'm really dying to know the mean SST_da is in\nthe inner zone too, and recommend this number also be included.\nAnswer:\nIn the inner zone, SST_da is also above the freezing point on average by 0.4 +/- 0.2 °C, compared\nto 0.6 ± 0.3 °C in the outer zone. On average, SST_da is thus not significantly lower in the inner\nzone than it is in the outer zone.\nHowever, the frequency of the highest above freezing SST_da is higher in the outer zone than in\nthe inner zone which is what matters the most to support the existence of our outer zone (Figure\nB).\nFinally, as noted in the main text and in the Supplementary Materials, the closeness of the\naverage SST_da in the two zones can be explained by:\n● Errors and spatial averaging effects on the SST product which might increase SST_da to a\ntemperature above the freezing point in the inner zone (see Figure S2).\n● The outer zone contour as diagnosed from the budget 30 days following da is not perfect.\nSome grid points located in the inner zone following da might in fact be in the outer zone\nprior to da.\nAction:\n● We added the mean SST_da in the inner zone and we mentioned the possible\nreasons for the closeness with the average SST_da in the outer zone:\nin the main text:\nLine 95-97: “The median SSTda- Tf is lower in the inner zone (0.4 +/- 0.2 °C) than in the\nouter zone, however this difference is not significant, which may reflect uncertainties in the\nexact position of the inner-outer zone boundary, or in SSTda.”\nzone (orange)\nSpecific feedback on results:\nThere are many variables used in this paper. A table of them would be nice for the reader (and\nmight help the authors keep track of them too).\nAnswer & Action:\nWe think this comment might belong to NC editorial policy and will figure that out with the\neditor at a later stage. Meanwhile, we use less acronyms and explicitly refer to several\nvariables for more clarity.\nline 40-41: This is an odd thing to say: focus on one and seek to understand another.\nAnswer & Action:\nThanks for pointing that out. We changed the phrasing.\nLines 39-40 “In this paper, we focus on the fundamental drivers of the sea-ice advance date and on\nlinks to the date of sea-ice retreat.”\nline 54: When I read this, I wondered why is it desirable for the observations to be from\nindependent sources when they are observations of different things. I think line 105 largely\nexplains why, but I was left hanging all that time!\nAnswer & Action:\nWe think it might not be useful to say this at this early stage in the paper. We now only\nmention it on line 91 (formerly 105).\nline 65: I don't like seeing that T>0 close to the date of advance. I suggest considering using H or\n6\nsomething else for thermodynamics, rather than T since T as temperature is so ingrained.\nAnswer:\nIt might be confusing, it is true. We followed your advice and changed T’s into Th’s (D’s were\nchanged into Dy’s for consistency).\nline 100: \"sea ice transport is mostly set by seawater freezing\" sounds odd. Maybe instead say\nthe \"sea ice advance is mostly set by seawater freezing\".\nAnswer:\nThis is a mistake, thank you for spotting it. However, the sentence no longer exists.\nline 125: The quantity in Fig 1c is labeled SST_da (the caption and line 105 calls it \"at the time of\nadvance\") but here the text says Fig 1c has SST_max which I would expect to be quite different Is\nthis a mix up or just not explained well?\nAnswer & Action:\nFig. 1c shows the seasonal maximum of SST (SST_max). The label and caption are consistent with\nthis. Former line 125 also refers to SST_max.\nHowever, former line 105 refers to SST_da which is shown in Fig. 2d. We forgot to mention the\ncorresponding figure and that might have been confusing. Sorry about that. We now refer to\nFig. 2d when presenting SST_da.\nLine 89-91: “[...] (SSTda), evaluated from an infrared satellite SST (climatology (2003-2010),\nis consistent with our analysis of the sea ice concentration budget (Fig. 2d). ”\nline 132: I don't know what I'm supposed to see as \"standing out clearly\" in Fig 3b. Am I\nsupposed to be looking at the polygon in Fig 3a?\nAnswer & Action:\nWe are indeed referring to the polygon but the text was not explicit enough on that matter. We\nnow explicitly mention that the nonlinearity is contained in the black polygon.\nLines 139-140: “In Fig. 3a, the non-linearity is confined in the black polygon enclosing all grid\npoint points with an averaged MLD over the open water season, greater than 80 m.”\nLine 144: Is this supposed to refer to Fig 3b?\nAnswer & Action:\nYes, but the reference was not explicit. We now explicitly refer to Fig. 3b.\nLines 148-149: “Strikingly, the 2D histogram of da anomalies versus MLHmax anomalies does not\nshow any evident non-linearity (Fig. 3b).”\n7\nline 172: MLD_cp is never defined\nAnswer & Action:\nOur mistake. MLD_cp was not the right variable name but it was used to refer to the averaged\nMLD over the open water season. We now explicitly describe the right variable in the\ncaption.\nLine 176-178: “In a, the black polygon highlights high mixed layer depths, enclosing grid points\nwith a mixed layer deeper than 80 m on average over the open water season”\nSpecific feedback on methods:\nThe text doesn't say what dataset is used for sea ice drift, other than AMSR-E. Please give a\ncitation to the product. Apologies if one of those citations is it, but none seemed likely.\nAnswer & Action:\nWe indeed forgot the citations to the product (Kimura and Wakatsuchi 2011; Kimura et al.\n2013). Apologies. We now give more details on the ice drift data and added the\ncorresponding references in the Methods section.\nLines 343-344: “[...] and ice drift fields derived from AMSR-E brightness temperature by a cross-\ncorrelation algorithm (Kimura and Wakatsuchi 2011; Kimura et al. 2013)”\nline 275: filter not filtering\nAnswer & Action:\nThanks for spotting this mistake. We corrected it, line 318.\nline 279: 10/1982 to 19/1983 is not clear. It sounds like 13 months.\nAnswer & Action:\nYou are correct, this sentence was not clear. We also judged it was not really useful to\nunderstand our methods. We removed this sentence and referred to 1982 instead of 1983\nas the start of the time period over which most of the study is based.\nline 282-284: I'm not following this. Why is da or dr ever undefined?\nAnswer & Action:\nThe dates of advance and retreat are not defined for multi-year ice or open ocean. We now\nexplain this more explicitly.\nLines 326-327 “[...] a missing value is assigned where the number of years with undefined da and\ndr (corresponding to year-round ice-free or ice-covered grid points) [...]”\n8\nline 313-315: the lower limit of the integral has a erroneous subscript rather than just da\nAnswer & Action:\nOur mistake, that was a typo that we corrected, lines 361-363.\n_\n9\n_____________________________________________________________________________________________________________\nReviewer #2\n______________________________________________________________________________________________________________\nGeneral feedback:\nReview of “Recent decline in Antarctic sea ice cover from 2016 to 2022: Insights from satellite\nobservations, Argo floats, and model reanalysis” by Kshitija et al.\nA substantial volume of recent work has focused on identifying the drivers of Antarctic sea ice\nchange over the satellite record. Winds have been shown to be important in driving variability.\nThis interesting study fills an important gap in the knowledge by demonstrating the role of the\nsummer ocean and highlighting the need to understand changes in both the temperature and\ndepth of the mixed layer.\nThe authors combine remote sensing data products and new in situ observational datasets to\ninvestigate the processes modulating the timing of sea ice advance. They demonstrate that the\nseasonal ice zone can be divided into an “inner” region, just over 2/3 of the total seasonal ice\nzone, where the freezing ocean sets the sea ice advance, and an “outer zone”, about a third of the\ntotal seasonal ice zone, where sea ice advance is a balance between the import of ice and\nmelting. Despite the different processes operating in these zones, the date of sea ice advance is\nstrongly linked to the amount of heat in the mixed layer. This work supports previous studies\nthat have shown the link between the timing of sea ice retreat and the timing of its subsequent\nadvance and, furthermore, demonstrates that the heat storage in the summer ocean mixed layer\ncan explain this correlation.\nI enjoyed reading the manuscript and think it would be of interest to a wide variety of\nresearchers as it provides more context on the variability of Antarctic sea ice. The manuscript is\nwell-structured and well-written – I particularly appreciated the mini summaries at the end of\neach section. The figures are generally of high quality and support the narrative. I have one\nreservation about the conclusion, which I note below, along with some minor typos.\nAnswer:\nThank you!\nOne of the interesting results from your analysis is that the correlation between the date of\nretreat and subsequent date of advance, first noted by Stammerjohn et al, 2012, holds for much\nof the “inner” zone, where the thermodynamics set the date of advance. The “inner” zone in the\nIndian Ocean sector doesn’t show a significant correlation (Fig 4a). Clearly, the ocean feedback\nin response to the timing of the retreat doesn’t hold in this region. You show only a minor\ninfluence on the spatial variability of Q in the “inner” zone. Does the lack of correlation in this\nregion affect your conclusion that the MLH controls the link between, e.g., early retreat and later\nadvance?\nAnswer:\nadvance. Figure 4 is based on detrended inter-annual anomalies and hence, relates to\ninterannual variability.\nDrivers of the climatological date of advance are not exactly the same as the driver of inter-\nannual variability. Variability in heat fluxes and transport processes appear to have a larger role\nto play at the interannual time scale.\nActions:\n● We have rewritten the section “From spatial to interannual variability” (formerly\n“From spatial to temporal variability”) to better highlight that the climatology and\ninterannual variations are not precisely driven by the same processes (Lines 220-\n262).\n● We also explicitly specify that in the Abstract and the Introduction.\nLines 23-24: “Such thermodynamic linkages strongly constrain the climatology and\ninterannual variations, albeit with less influence on the latter. ”\nLines 55-57: “We then provide evidence that these mechanisms also contribute to a\ncertain extent to observed interannual changes in the timing of sea ice advance.”\nSpecific feedbacks:\nIt would be good to be consistent with the arrangement of the letters that label the figures - e.g.\nin Fig 1, ‘b’ is top right, whereas in Fig 2, ‘b’ is bottom left.\nAnswer & Action:\nThanks for pointing that out. We followed your advice to be more consistent.\nFig 2 - do ‘a’ and ‘b’ have the same colorbar?\nAnswer & Action:\nYes. We changed the position of the colorbar for more clarity\nLine 101: do you mean to reference Fig 2?\nAnswer:\nYou are correct. However, the sentence no longer exists.\nLine 105: add 'the' to the end of the line\nAnswer & Action:\nThanks for spotting the mistake. We modified the sentence.\nan infrared satellite SST climatology (2003-2010)”\nLine 132: should this refer to fig 3a rather than fig 3b?\nAnswer & Action:\nYes. Our mistake again. Apologies. We now refer to the right figure, line 137.\nLine 142: you might consider referring to Fig 2b.\nAnswer & Action:\nDo you mean Fig. 3b? We now explicitly refer to Fig. 3b in line 149.\nLine 172: please define MLDCP\nAnswer & Action:\nOur mistake. MLD_cp was not the right variable name but it was used to refer to the averaged\nMLD over the open water season. We now explicitly describe the right variable in the\ncaption.\nLine 139-140 “the black polygon encloses grid points with an averaged MLD over the open water\nseason above 80 m”\nLine 278: typo - change \"or\" to \"of\"?\nAnswer:\nThanks for spotting the typo, however the sentence no longer exists.\nLine 280: Is da (dr)1 day 1 of advance and retreat? It might be helpful to define this somewhere.\nAnswer:\nWe do consider the date of advance and retreat as the respective first days of the advance and\nretreat seasons. Based on observations, the start of the advance and retreat seasons typically\ncorresponds to a threshold sea ice concentration of 15%. Accordingly, in the text we refer to da\n(dr) as the first day sea ice concentration exceeds (drops below) 15% (lines 319-321).\nLine 281: May 1st seems a very safe start date for calculating dr. Jan 1st seems to be a bit closer\nto the advance - is there ALWAYS retreat in Dec? I suspect so, but maybe you could add the\nearliest date of advance in the satellite product to satisfy that you always retain the subsequent\ndate of advance?\nAnswer & Action:\nthose dates. We clarified in the Methods that the majority (99%) of da and dr occur after\nthe chosen start dates.\nLine 323-324: “We selected January 1st of the current year as the start date for da, and May 1st of\nthe previous year for dr, since the majority (> 99%) of da and dr occurs after those dates.”\n13\n______________________________________________________________________________________________________________\nReviewer #3\n______________________________________________________________________________________________________________\nGeneral feedback:\nThis paper provides a quite straightforward, but illustrative examination of the role of upper\nocean heat absorption in driving the length of the open water season, and subsequent retreat of\nsea ice in summer.\nMuch of the analysis is simplified, and only climatological behaviour is examined (perhaps\nbecause of the scarceness of data on mixed layer depth for earlier periods).\nThere are two main conclusions. First, it is shown that thermodynamic ice growth dominates the\nsouthern regions during ice advance, and dynamics dominate the outer pack. This is not\nsurprising, and consistent with results such as those of Haumann et al (2016), who show that ice\ngrowth dominates ice-ocean interactions in the south, and melt in the north. These are not\nexactly the same, so it’s not simply a rehash of old results, but the results of Haumann et al are\nprimarily because of the relative roles of thermodynamics and dynamics. The reasons for the\ndifferences (say, between their Figure 3 and your figure 2) would have been interesting to\ndiscuss. That said, I do think this is a useful result.\nAnswer & Action:\nWe reckon you mean Figure 4c of Hauman et al. (2016) which shows the mean annual ratio of\nfreshwater flux due to dynamic processes (export / import) over the freshwater flux due to\nthermodynamic processes (freezing or melting).\nThere is indeed a link with our Figure 2c. The 2 figures are shown below, in Figure C.\nYou are correct, our decomposition is consistent with theirs, at a particular moment of the sea\nice seasonal cycle (at the time of advance).\nHowever, they are some methodical differences which would make further comparison too\nspeculative:\n- They use a volume budget whereas we use a concentration budget.\n- Our budget is strictly observation-based whereas they use a model-based sea ice\nthickness.\nWe now refer to Haumann et al.\nLines 72-74 “This is consistent with previous work, based on sea ice concentration or volume\nbudget decomposition, which showed that the wintertime ice edge is sustained by ice transport\nrather than freezing ([...] Haumann et al., 2016). ”\nThe second main result shows that this difference causes a relationship between the date of\nadvance and retreat and the mixed layer heating in the inner zone, and weaker in the outer zone.\nAgain, perhaps not terribly surprising, as other publications have shown that correlations\nbetween advance and retreat dates are stronger for months where ice extent is less (i.e. in the\ninner zone), and particularly for the date of retreat and the following date of advance. However,\nwhile the reasoning has previously been attributed to the ice-ocean heating feedback, it has not\nbeen explicitly shown as it is here. So again, this paper shows this nicely in a simple way.\nMy main criticism (if you can call it that) is not about the correctness of any of the results, but\nthat doing so with climatology only explains a general, not so unexpected behaviour, and so\ncannot address how much these processes might have contributed (as a feedback) to recent sea\nice variability or trends. This is perhaps unfair, as I realize looking at interannual variability and\ntrends was not the author’s intention. But as my impression is that the results are not\nunexpected, the impact will be less.\nAnswer:\nWe are convinced that climatology must be understood before internal variability, and highlight\na very strong (R^2 = 0.9) relationship in the climatology. We think that is an impactful result\nbecause many factors (air-sea-air fluxes, transport, entrainment) could have weakened the\nrelationships at stake. It is also an impactful result because it provides an important constraint on\nfuture long-term Antarctic sea ice changes as explained in the Discussion section.\nThe question of variability is wider because those factors have more influence on the date of\nadvance at the interannual timescale, as we now emphasize in our last Results section (“From\nspatial to interannual variability”).\nWe are currently working on a separate study focusing on the question of the recent variability\nin sea ice seasonality.\nActions:\n● We have rewritten the section “From spatial to interannual variability” (formerly\n“From spatial to temporal variability”) (Lines 220-262).\n15\n● We also explicitly specify that there are differences between drivers of the mean\nstate and interannual variations in the Abstract and the Introduction.\ne.g. Lines 23-24: “Such thermodynamic linkages strongly constrain the climatology and\ninterannual variations, albeit with less influence on the latter. ”\nLines 55-57: “We then provide evidence that these mechanisms also contribute to a\ncertain extent to observed interannual changes in the timing of sea ice advance.”\n● We now better explain the implications on long-term changes of progressing the\nunderstanding of the mean state in a separate Discussion section.\ne.g. lines 278-281: “Furthermore, our results provide important constraints on future\nlong-term Antarctic sea ice changes. Given how strong the dr-MLHmax-da relationships are\nin the recent mean state, it can be argued that these will still hold for the future Antarctic\nsea ice mean state, providing helpful constraints to project long-term future changes.\nIndeed, the increased skill of the MLHmax-da relationship, compared to SSTmax-da (Figs.\n3a and b) emphasizes the importance of considering changes not only in the mixed layer\ntemperature but also in mixed layer depth to fully understand long-term changes. ”\nWhat would have made the paper more impactful would have been to explore in more detail the\ninterannual and spatial variability. For example, figure 4 seems underexplored.\nAnswer:\nThank you for the suggestion. We did expand our analysis of interannual variability to a\nreasonable extent. We added some panels to Figure 4 to show more explicitly how the\nthermodynamic processes driving spatial variability of the mean state also contribute to driving\ninterannual variability in the date of advance. We also discussed a bit more the regional\npatterns.\nHowever, going too far is out of scope: we estimated that a more thorough analysis on variability\nand trends is out of the scope of this study, because the drivers differ.\nActions:\n● We modified our Figure 4 and rewrote the corresponding analysis (Lines 220-\n262).\n● We now explore more in details the regional patterns of Figure 4\nLines 253-257 “However, one difference with our findings related to mean state is that\ndrift and melt processes may also considerably contribute to interannual variability in the\ndate of advance in the inner zone, as indicated by locally existing weak and low significance\ndr- SSTmax-da correlations there (Figs. 4a and b). For instance, close to Maud Rise, the\ncorrelations between dr and da are significant (Fig. 4c) but the ones between dr and\nSSTmax (Fig. 4a) and SSTmax and da are not (Fig. 4b). The effects of oceanic heat\nentrainment and advection might be more suited to explain the variability in this region,\ndespite being located in the inner zone. ”\nInterannual variability in passive-microwave (OSI-SAF, 1982-2018) date of advance and\nhow it relates to variability in date of retreat and seasonal maximum SST (CCI, 1982-\n2018). a Standard deviation in the date of advance, b correlation coefficient between detrended\ntimeseries of dates of retreat and subsequent dates of advance, c of dates of retreat and\nsubsequent seasonal SST maximum and d, of seasonal SST maximum and subsequent dates of\nadvance. Beige shading b, c, and d indicates where correlations are not statistically significant at\nthe 95% level. The black contour delimits the same inner-outer zone limit derived from the SIC\nbudget and shown in Fig. 2d. White patches indicate regions out of the seasonal ice zone.\nAlso, the relationships shown in Fig 3 are strong, but much of the ‘interesting’ signal is in the\ndeviations from these relationships that likely govern how advance, retreat, and mixed layer\nheating vary spatially and inter-annually.\nAnswer:\nWe agree that interesting signals come from deviations from the linear relationship. We had\nstudied in detail those deviations, as a preliminary analysis.\ndistribution of errors to the relationship (see below Figure D). However, the spatial patterns\ncould not be interpreted without having access to the entire observational heat budget in the\nML. This will be done in a model in a following study.\nFigure D – Spatial distribution of errors on the dr-MLH -da linear regressions. Errors\nmax\nare defined as the residuals of a, the da vs MLH and b, the MLH vs dr linear\nmax max\nregressions. Residuals are calculated as the difference between the actual value of a given\ngrid point and the predicted value based on the model fit.\nI would have appreciated some analysis of how these relationships (and in S3 and S4) might\nvary spatially, and whether they might have changed over time.\nAnswer & Action:\nWe tested how these relationships varied (a) regionally (according to the regions of Parkinson et\nal., (2012); see upper Figure E) and (b) inter-annually (see lower Figure E).\n(a) Overall, our relationships still hold regionally.\n(b) We could not assess how the relationships involving the MLH vary over time because of\nsparse interannual MLD data. Instead, we used the seasonal maximum SST as a proxy of\nthe maximum MLH and assessed the strength of our relationships for each individual\nyear:\n- R2 is on average lower when calculated on individual years than when calculated\nbased on the climatology. We think there might be some compensation of spatial\nanomalies in heat fluxes when calculating the climatology which smooths their\nspatial distribution and strengthens the linearity of the relationships.\n- However, R2 is still high for the dr / SST / da relationships, on average.\nmax\n- It is substantially weaker for the dr / da relationship, but this is consistent with\nour previous analysis (see lines 208-2010; and Figure S6): “The departure from\nthe linear relationship occurs in regions of the outer zone that differ between the\ndr-MLHmax and the MLH_max-da relationships (Fig. S6). This spatial mismatch\naffects the dr-da relationship, which is therefore weaker than the two others in the\nouter zone (R2=0.61), and does not explain as much of the da variance there.”\nThese results again show that the main drivers of climatological dates of advance have a\nweaker influence at the interannual timescale, possibly due to a larger role of variability\nin heat fluxes and transport processes. We now better emphasize that in the section\n“From spatial to interannual variability” (Lines 220-262).\nregressions of Figure 3, S3,S4. Colored dots are yearly values. Colored lines and regional\nvalues. Green is for the inner zone, red for the outer zone. Black dots are the average of\nyearly or regional values. Blue stars are the climatological values given in Figure 3, S3, S4.\nThere is also no analysis of what may be driving the differences between the inner and outer\npack (merely statements about differences in drift and melting). For example, some papers have\nshown differences in ocean heat flux convergence control differences in the inner and outer zone\ndue to changes in stratification (e.g. Z. Su, GRL, 2017). This would affect the homogeneity of Q,\nand thus the linearity of your fits. If the stratification in the outer pack is weak, then\nthermodynamic growth is retarded not so much by remnant summer warming (which may have\ndispersed over the much longer ice-free period), but by entrainment of ocean heat.\nAnswer:\nThank you for the suggestion.\nFollowing your suggestion, we evaluated the stratification at the base of the ML during the\nadvance season to assess the possible role of stratification and entrainment in defining the outer\nzone.\nat the base of the ML in the outer zone, indicating that entrainment of warm water possibly\noccurs in the outer zone at that time. This could possibly prevent freezing from occurring and\ndelay sea ice advance, as you pointed out\nHowever, we are again limited by the available observation of the heat fluxes in the ML: the\nexact contribution of entrainment to the excess of heat at the time of advance cannot be clearly\nquantified without having access to a complete heat budget.\nAction:\n- We explicitly emphasize that the inner and outer zones are hydrographically\ndifferent.\nLine 88 “We find the inner and outer zones hydrographically differ at the time of advance.“\n- We refer to the possible delay of sea ice advance due to entrainment in the outer\nzone, with reference to Z. Su, GRL, 2017.\nLine 99-105 “Finally, a last element of interest is that the temperature profile at the base\nof the mixed layer is thermally unstable in the outer zone (Nt^2 < 0) during the first three\nmonths of the advance season, according to the in situ hydrographic climatology\n(Supplementary Fig. 4). Taken together, we argue that the outer zone corresponds to\nwhere drifting ice encounters sufficiently warm waters for net basal melting to occur on the\nday of advance. The contrast is arguably reinforced by an unstable water column, which\ncould lead to entrainment of warm waters into the mixed layer, opposing sea ice growth.\nPrevious studies have also highlighted the role of oceanic heat supply as a spatial\nconstraint to sea ice advance in the winter ice edge region (Su, 2017; Bitz et al., 2005).”\n- We refer to this as a possible cause for the weakening of the relationships of Fig. 2\nin the outer zone .\nLine 201-202 “This general weakening and the associated larger regression errors might\nreflect a larger spatial variability in net heat fluxes in the outer zone (see Methods),\npossibly linked to the entrainment of warm waters into the mixed layer (Supplementary\nFig. 4). “\n- We refer to previous literature linked to this in the Introduction.\nLine 43-44 “Close to the winter sea ice edge, freezing can, however, be inhibited by\nentrained (Su, 2017) or advected (Bitz et al., 2005) oceanic heat into the mixed layer.”\n- We added the figure below in the Supplementary Materials.\nMonthly temperature contribution to the stratification at the base of the ML (Nt^2).\nMaps\nare climatological, and constructed from in situ observations over 1979-2018. Red contours\ndefine the monthly climatology (over 1982-2018) of sea ice extent of the corresponding month,\nderived from passive microwave data. The black contour defines the limit between the inner and\nouter zones.\nLastly, I think your spatial variability in figure 2b near the ice edge maximum reflects spatial\nvariability in advection, which as noted above will have a very significant impact on your\ninterpretation here because the open water period at the ice edge maximum approaches 12\nmonths.\nAnswer:\nWe understand that you refer to rapid spatial changes in date of retreat near the ice edge and\nattribute them to advection. This seems indeed likely as these regions are in the outer zone\n(tailored for the date of advance). However, variations in date of retreat are out of the scope of\nthe manuscript, therefore, we did not modify the manuscript. As a side note, our filtering SIC\neffectively caps the ice-free season values smaller than 15 days.\nNevertheless, the present work does provide a good foundation for exploring these issues in a\nsubsequent paper.\nAnswer:\nThank you! We are indeed working on these issues right now.\nSpecific feedbacks:\n1. I suppose you are constrained by space, but I felt like a few more sentences in the introduction\nproviding more insight into the current understanding of causes of observed trends would be\nhelpful, beyond saying “multiple process are involved” with a cite to a 2012 paper. For example,\nmany papers (some of which you cite) provide some explanation, both atmospheric and oceanic,\nand associated feedbacks for much of the recent variability. You are quite correct that there is a lot\nof uncertainty and it is complicated!\nStammerjohn et al. (2012) is the last main reference focusing specifically on drivers of changes\nin the dates of Antarctic sea ice advance and retreat. However, you are correct that there are\nmany references discussing more generally the recent changes in Antarctic sea ice that we did\nnot include there. We added a few more recent references in a sentence finalizing the\nparagraph.\nLine 34-37‘’ Yet interpretation is complicated: strong interannual variability dominates the trends\nin the last two decades and drivers involve multiple oceanic and atmospheric processes ([...],\nMeehl et al., 2019; Eayrs et al., 2021), in a context of limited understanding of the drivers of\nsea ice advance and retreat. “\n2. Line 37 – I think “weak fundamental understanding of the drivers of sea ice advance and\nretreat” is a bit strong. I think we understand the proximal drivers quite well, but not their\nrelative roles in driving the observed interannual variability.\nAnswer & Action:\nWith this sentence we meant to indicate the lack of studies focusing specifically on the\nfundamental drivers of the dates of advance and retreat in the Southern Ocean.\nBut you are correct, our wording is too strong because we have some understanding, especially\nfrom previous studies on the seasonal cycle of sea ice extent. We now use “limited” instead of\n“weak” (line 37).\n3. Line 106 “by an infrared satellite SST product\nAnswer:\nThanks for spotting the mistake. The sentence has changed in the modified manuscript.\nLines 89-90 “[...] evaluated from an infrared satellite SST climatology (2003-2010) [...]”\n4. Line 105-113. I don’t quite understand how the SST product can be valid in this area for the\ndate of advance, because in figure 2 it appears like you have SST retrievals where you have sea\nice cover. The data would not be valid here. Is it from some days before the advance? In any case,\nthis does not seem surprising at all. I am not aware of systematic comparisons with SST, but\nseveral papers have noted waters above freezing and their role in delaying advance.\nAnswer:\nBoth interpolated SST products that we use (ESA CCI & Reynolds; see Methods) provide data at low ice\nconcentration and keep those after quality control. However, you are definitely correct\nthat these can be deemed largely uncertain at the date of advance.\nBeing aware of that is why we analyze these two fairly different products of SST (and not just\none). All products give a consistent picture of larger SST_da-Tf in the outer zone, despite\nuncertainties of SST_da. Please refer to Figure S2.\nthe date of advance). We find that the distribution of in situ SST on the day of advance is in line\nwith the satellite SST on the day of advance (see below Figure).\nActions:\n● We added the figure below in the Supplementary Materials.\n● We referred to the newly added Supplementary Figure in the main text.\nLine 97-98 “Nevertheless, these findings are robust to the choice of alternative SST\nproducts (satellite and in situ; Supplementary Figs. 2 and 3)”\n.\nNew Figure S3\nComparison of satellite and in situ SST on the day of advance. Frequency histograms of SST\nat the date of advance (SSTda) referenced to freezing temperature (Tf, assumed constant at -\n1.8°C), derived from satellite (ESA CCI) and from in situ SST.\n5. Figure 3 – It is not entirely clear to me what data are used here. The caption says 1983-2018\nclimatological maps, and the text says monthly climatologies, so have you used climatological\n(i.e. not varying with year) MLDs and annually varying SSTs? Or have you used both annually\nvarying SSTs and MLDs, or something else? If it is annually varying MLDs, then it is highly likely\nthat some of the older period is very data sparse (pre Argo and pre marine mammal data), and\nthat could account for some of the data spread. If either is climatological, then I would not be\nsurprised at all by the spread and then I question how accurate this analysis is. This is perhaps\nthe main reason you might look at only the climatologies – because the MLD data is sparse, and\nlooking at annual variability and trends may be prone to significant errors.\nAnswer:\nIn our Figure 3, we only use climatological data for each variable so our analysis is consistent.\nThis is explicitly explained in line 147-148: “Based on the climatological MLD and SSTmax,\nwe define an observational estimate of the climatological seasonal maximum of MLH”.\nYou are right, the choice of using only climatological data was driven by the sparseness of MLD\nat the interannual timescale.\n23\n6. Lines 145-150 (see also note below on lines 345-365). If I understand correctly, you are using\na relationship between the date of advance, date of SST max, the MLH, and the heat loss. This\ncould be made more clear, as when reading I was confused as to whether you actually estimated\nthe fluxes or not.\nAnswer & Action:\nThank you for this comment, we understood that the way we estimated the mean flux (<Q->)\nwas unclear. We added a sentence to clarify how we estimate mean flux.\nLine 162-163 “Applying equation (1) to the slope of the MLHmax-da linear regression model (Fig.\n3b), we estimate the average net heat loss <Q-> to 80 W/m2. ”\n7. Given that you are assuming Q is uniform everywhere, then the deviations from linearity are\nentirely unsurprising in figure 3, and I am not sure you can claim it is due to issues with using\nSST to describe MLH. Have you checked to see if these deviations are occurring in places where\nheat fluxes could be unusual?\nAnswer & Action:\nThe uniformity of Q is not an assumption, it is a possible consequence of the linearity of the\nMLH -da relationship of Figure 3b. We realize it might not have been clear enough in the\nmax\nMethods (and in the main text, as stated in the previous answer).\nAs for the deviation from linearity, they could indeed point to specific spatial patterns of Q (see\nFigure D). However, we do not have good observations of Q to check this (Q is the total heat flux\nin the ML during the cooling period). We plan on working on this question using a model in the\nfuture.\nWe clarified that uniform Q is a consequence of the linearity of the MLH -da relationship\nmax\nin the Methods section.\nLines 400-401 “Perfectly linear relationships between climatological da and MLHmax anomalies,\nMLHmax and dr anomalies would respectively suggest uniform spatial distributions of <Q-> and\n<Q+>. ”\n8. Line 180-182 – the devil is in the details here! Yes, you show that the relationships are broadly\nlinear and so Q is fairly uniform, but this does not mean that the variability in Q is not very\nimportant for driving variability in da or dr, and this is really what would be most relevant to\nrecent sea ice variability, and would require a much more in depth analysis. So I don’t think you\ncan say it is weakly influenced (the variability appears to be a pretty good number of days, if da-\ndsst is suggestive). It would be nice to know what that variability is compared to the interannual\nvariability of da.\nAnswer & Action:\nDrivers of mean state differ from drivers of interannual variability. Here in the context of the\nparagraph, we were discussing the mean state (based on climatological variables). The revised\nversion makes that clearer.\nAs we mentioned before, the scope of our paper is mostly on mean state, not on variability.\nnot exactly the same.\ne.g. Lines 260-262: “Nonetheless, heat fluxes and transport processes exert a stronger influence\non the timing of advance at the interannual time scale, compared to the mean state. Future work\nmay help to clarify the exact role of such processes.”\n9. Line 182-184. I think this is maybe one of the more significant results, and perhaps should be\nin the main paper. But it is perhaps not surprising that the mixed layer heat increase is driven by\nthe radiative fluxes. It glosses over a lot, of course, and it would be interesting if you could show\nregional variations. i.e. does it matter more in the Ross Sea vs say, the east Antarctic? I do think\nyou overinterpret the significance a bit. The scatter is not so small, and is due to advective heat\nand turbulent fluxes (and also uncertainty, of course) For instance, the turbulent fluxes can be as\nlarge as the net longwave flux. In some areas, advection of heat may be very important. And of\ncourse, the variance around this line is important in understanding the spatial and temporal\nvariability.\nAnswer:\nThis is indeed a significant result. But we think it is not useful to the main questions of this paper\nto go into further analyses of this result.\nWe did assess how this relationship varies spatially and found that it remains strong regardless\nof the region (see Figure E).\n10. Line 189 – I am not clear on how reference 7 was not also making the link on the seasonal\nscale?\nAnswer & Action:\nThanks for pointing that out. The “seasonal scale” was not the right formulation for what we\naimed to say. We reformulated the corresponding sentence.\nLine 193-195 “Here, we show that this link holds for the spatial variability of climatological\nretreat and advance dates, and is controlled by the upper ocean heat content.”\n11. Line 199-201. There is some prior work that suggests these links (off the top of my head, I\nthink a a Reid et al. paper has a diagram that shows the persistence of anomalies, which for\nwinter and spring would represent the outer region based on ice extent).\nAnswer & Action:\nApologies but we can’t seem to find the reference you are referring to. Note that we refer to\nother references on predictability of the sea ice edge in the same section.\nLines 255-257: “The effects of oceanic heat entrainment and advection (Bushuk et al 2021;\nHolland et al 2013) might be more suited to explain the variability of this region, despite being\nlocated in the inner zone.”\n25\n12. Also in Methods, you need to provide more information on the time periods for the various\ndata sources for MLD and the gap-filling procedure.\nAnswer & Action:\nThanks for the suggestion. We added more details on the product in the Method section.\nLines 303-307 “Conductivity-temperature-depth (CTD; 1970-2018), Argo floats (Argo\ninternational programme; 2000-2018) and marine mammal-borne sensor profiles (Marine\nMammals Exploring the Oceans Pole to Pole programme; 2004-2018) were included. Generalized\nleast squares linear-regressions of individual in situ profiles are performed around each grid point\nto produce gridded maps of climatological mean fields.”\n13. Methods – you do not state what data you have used for sea ice drift.\nAnswer & Action:\nWe indeed forgot the citations to the product (Kimura and Wakatsuchi 2011; Kimura et al.\n2013). Apologies. We now give more details on the ice drift data and added the\ncorresponding references in the Method section\nLines 343-344: “[...] ice drift fields derived from AMSR-E brightness temperature by a cross-\ncorrelation algorithm (Kimura and Wakatsuchi 2011; Kimura et al. 2013).”\n14. Line 341 – “horizontal velocity”\nAnswer:\nOur mistake. The corresponding sentence is no longer in the revised version.\n15. Lines 345-365 – I am not 100% sure I understand what you did here. At first, it seemed you\ncomputed the mixed layer heat from the total fluxes, but nowhere do you explain how you\ncomputed the horizontal advective fluxes, the entrainment flux or the diffusive flux, or what\nvalues you use for the various coefficients. So it looks like you don’t actually compute fluxes, but\nestimate if they are important for this broad-scale analysis by the fits in figure 3, and are only\nderiving a relationship between the flux, the MLH and the date of advance and retreat. This is\nnot very clear, as elsewhere you describe using flux estimates (but for what, I am not sure). If I\nam correct, this description could be clearer if you simplified by deleting the equation on 338\nand start from the equation on 343 (please number your equations!), and just explain that Qt is\nthe total net flux as you do, and that you are not attempting to estimate it. If I am wrong, and you\ndo compute the fluxes, then you need to explain a lot better.\nAnswer & Action:\nThank you for the suggestion and apologies for the confusion. Please refer to the answer to your\nspecific reviews no. 6 and 7.\nFollowing your suggestion, we deleted the equation of former line 338 to clarify the\nmethods.\n26\n16. Ref 30 – formatting issue here.\nAnswer & Action:\nOur mistake. We corrected the formatting issue.\nReviewer #1 (Remarks to the Author):\nThe authors were very thorough in their revisions. Figs S3 and 4 are nice new additions. I have a\nbetter understanding of the work now too, and have learned that only the SIC tendencies lag the\ndate of ice advance. The tendencies are used to characterize the sea ice processes occuring in the\ninner/outer zones. I suppose it is reasonable to assume that these processes are essentially the same\nbefore and after ice advance. I accept that the authors don't want to analyze sea ice model results,\neven though I think it would strengthen their case for analyzing sea ice concentration tendencies\nafter the date of advance.\nI think there are enough gems in this paper to warrent publication. I think the partitioning into\ninner and outer zones will be beneficial for further process-level investigation and for climate\nmodel evaluation.\nA few type-os, etc:\nLine 63 has an extra \"not\"\nLine 65-68 consider adding a few words to say that Th and Dy are proportions ot the total sea ice\nconcentration tendency.\nLine 101 please define N_t^2 (it is also not defined in Fig S4). You might find the following paper a\ngood one to review too\nhttp://dx.doi.org/10.1175/jpo-d-18-0184.1\nLine 238 The qualifying sentence about weak/insignificance in large parts of the seasonal ice zone\nconfused me. Were the correlations just quoted excluding the seasonal ice zone? I didn't see any\nmention of a specific domain.\nLine 348 I think this should read \"represents the flux divergence of sea ice\". It doesn't make very\ngood sense they way it was written.\nLine 357 I think (Delta sea ice concentration) -> (Delta SIC)\nLine 358 I think D -> Dy and T -> Th\n______________________________________________________________________________________________________________\nDrivers of Antarctic sea ice advance\nSubmitted to Nature Communications\nResponse to reviewers\nK. Himmich et al.,\nAugust 2023\n______________________________________________________________________________________________________________\nReviewer #1\n______________________________________________________________________________________________________________\nGeneral feedbacks:\nThe authors were very thorough in their revisions. Figs S3 and 4 are nice new additions. I have a\nbetter understanding of the work now too, and have learned that only the SIC tendencies lag the\ndate of ice advance. The tendencies are used to characterize the sea ice processes occuring in the\ninner/outer zones. I suppose it is reasonable to assume that these processes are essentially the\nsame before and after ice advance. I accept that the authors don't want to analyze sea ice model\nresults, even though I think it would strengthen their case for analyzing sea ice concentration\ntendencies after the date of advance.\nI think there are enough gems in this paper to warrent publication. I think the partitioning into\ninner and outer zones will be beneficial for further process-level investigation and for climate\nmodel evaluation.\nAnswer:\nThank you!\nSpecific comments:\nLine 63 has an extra \"not\"\nAnswer & Action:\nThanks for spotting this mistake. We removed the duplicate, line 62.\nLine 65-68 consider adding a few words to say that Th and Dy are proportions ot the total sea\nice concentration tendency.\nAnswer:\nActions:\n● We replaced “to the sea ice concentration budget” by “to the total sea ice\nconcentration tendency”.\n● Lines 64-66: “Instead, we evaluate the thermodynamic (Th) and dynamic (Dy)\ncontributions to the total sea ice concentration tendency over the 30 days following da […]”\nLine 101 please define N_t^2 (it is also not defined in Fig S4). You might find the following paper\na good one to review too\nhttp://dx.doi.org/10.1175/jpo-d-18-0184.1\nAnswer:\nWe should have been more explicit on the definition of Nt^2, you are right.\nAs for the Wilson et al. (2019) paper, it does give very useful insights on processes influencing\nthe mixed layer stability in winter but does not look at summer processes, about which are we\nare the most interested.\nActions:\n● We now only refer to the stability of at the base of the mixed layer in the main text.\n● Lines 91-92: “ […] the temperature profile at the base of the mixed layer is thermally\nunstable in the outer zone during the first three months of the advance season […]”\n● We explicitly define Nt^2 in the analysis of Supplementary Figure 4:\n● “N t 2 is proportional to the vertical temperature gradient at the base of the mixed layer:\n𝜕𝑇\n𝑁# = 𝑔𝛼 ) \n\" 𝜕𝑧\nwhere 𝑇 is the temperature at the base of the mixed layer, 𝛼, the thermal expansion\n) \ncoefficient at constant pressure 𝛼 = − -/. and 𝑔, the gravity acceleration. 𝑁# < 0 (𝑁# > 0)\n\" \"\n./\"\nindicates a negative (positive) temperature gradient and an unstable (stable) temperature\nprofile at the base of the mixed layer.”\nLine 238 The qualifying sentence about weak/insignificance in large parts of the seasonal ice\nzone confused me. Were the correlations just quoted excluding the seasonal ice zone? I didn't\nsee any mention of a specific domain.\nAnswer:\nYou are also correct; we were not specific enough on where correlations are significant or not\naccording to Figure 4.\nActions:\n● We added that correlations are significant in “large part of the seasonal ice zone”:\n2\n● Lines 186-187 : “Based on detrended time series over 1982-2018, we find significant and\nrelatively strong negative links […] in large parts of the seasonal ice zone.”\n● We also specified in which regions correlations are weak and insignificant:\n● Lines 190-191: “. However, those correlations are weak or statistically insignificant close\nto the seasonal ice zone edge but also in the most East Antarctic and Maud Rise sectors […]”\nLine 348 I think this should read \"represents the flux divergence of sea ice\". It doesn't make very\ngood sense they way it was written.\nAnswer & Action:\nWe rewrote the sentence for more clarity.\nLines 294-295: “The ice concentration flux divergence represents the effects of advection and\ndivergence of sea ice caused by ice drift.”\nLine 357 I think (Delta sea ice concentration) -> (Delta SIC)\nAnswer & Action:\nThanks for spotting this mistake. We corrected it, line 302.\nLine 358 I think D -> Dy and T -> Th\nAnswer & Action:\nThanks for spotting this mistake. We corrected it, line 303.\n3"}]

Decision letter