Satellite altimetry detection of ice shelf-influenced fast ice

. The outflow of supercooled Ice Shelf Water from the conjoined Ross and McMurdo ice shelf cavity augments fast ice thickness and forms a thick sub-ice platelet layer in McMurdo Sound. Here, we investigate whether the CryoSat-2 satellite radar altimeter can detect the higher freeboard caused by the thicker fast ice and the buoyant forcing of the sub-ice platelet 10 layer beneath. Freeboards obtained from CryoSat-2 were compared with four years of drill hole measured sea ice freeboard, snow depth, and sea ice and sub-ice platelet layer thicknesses in McMurdo Sound in November of 2011, 2013, 2017 and 2018. The spatial distribution of higher CryoSat-2 freeboard concurred with the distributions of thicker ice shelf-influenced fast ice and the sub-ice platelet layer. The mean CryoSat-2 freeboard was 0.07-0.09 m higher over the main path of supercooled Ice Shelf Water outflow, in the centre of the sound, relative to the west and east. In this central region, the mean CryoSat-2 derived 15 ice thickness was 35 % larger than the mean drill hole measured fast ice thickness. We attribute this overestimate in satellite altimeter obtained ice thickness to the additional buoyant forcing of the sub-ice platelet layer. We demonstrate the capability of CryoSat-2 to detect higher Ice Shelf Water influenced fast ice freeboard in McMurdo Sound and the wider application of this method as a potential tool to identify regions of ice shelf-influenced fast ice elsewhere on the Antarctic coastline. thus a comparable means to assess the effects of the SPL on freeboard to thickness conversion assuming hydrostatic equilibrium. Fast ice thicknesses derived from sea ice freeboard in McMurdo Sound were overestimated on average by 12% and up to 19% due to the buoyancy effect of the SPL freeboard and snow layer depth in McMurdo Sound by Price et al. (2015) showed that the ESA retracker tracked between the surface of the snow and the snow-ice interface. Price et al. (2019) assessed the sensitivity of CS2 Level 2 185 SIN product derived sea ice thicknesses to variable penetration depths into the snow layer in McMurdo Sound in November 2011. They found the closest agreement with in situ measurements when the penetration depth into the snow layer was assumed to be 0.05-0.10 m. In this study, we compare CS2 obtained freeboard with in situ measurements to identify the best matching freeboard interface or penetration depth for each individual CS2 track. drill hole METs along-track. The freeboard interface that produced the closest matching CS2 ice thickness and drill hole MET was then selected. If neither snow freeboard (Eq. (1)) nor sea ice freeboard (Eq. (2)) produced matching drill hole MET and CS2 ice thickness profiles, we estimated a penetration depth and applied Eq. (3). Four CS2 tracks in the east, 7 in the centre, and 3 in the west (refer to Fig. 1 for regional locations) produced expected freeboard magnitudes 255 relative to the median SSH. The sea ice surface was the dominant freeboard interface in the west and centre, except for 2011 and 2017 which had deeper snow coverage across the sound. In the east, the best matching freeboard interfaces were the sea ice surface in 2017, the snow surface in 2013, and penetration depths of 0.11 m and 0.12 m into the snow layer in 2011 and 2018, respectively. If sea ice freeboard or a penetration depth was determined for a CS2 track, a correction for the propagation of the radar wave through the snow was applied according to Kurtz et al. (2014). outflow, in snow CryoSat-2 forcing of the SPL.


Introduction
Ice shelves are the floating extension of the grounded Antarctic ice sheet and buttress the flow of the grounded ice streams (Fürst et al., 2016). Ice shelves and outlet glaciers comprise 74 % of the Antarctic coastline (Bindschadler et al., 2011) presenting an 25 enormous interface where the ocean can directly interact with the grounded ice sheet. Ocean-driven basal melting near the grounding zones of outlet glaciers and the frontal zones of large ice shelves drives half of the net mass loss of ice shelves (Rignot et al., 2013, Depoorter et al., 2013. Cold and relatively fresh meltwater from ice shelves reduces the temperature and the density of the upper surface ocean, stabilising the upper water column and enhancing the thickness of sea ice near ice shelves (Hellmer, 2004, Gough et al., 2012. 30 Fast ice is attached to the coast via land, ice shelves, glacier tongues or between shoals or grounded icebergs (Massom et al., 2010). When fast ice attaches to ice shelves or outlet glaciers it forms an important interface between the ice sheet and open ocean/pack ice (Giles et al., 2008, Massom et al., 2018. Fast ice affects ice sheet mass balance by providing mechanical stability and by buttressing glacier tongues (Massom et al., 2010) and ice shelves from the impacts of ocean swell (Massom et al., 2018). 35 Coastal polynyas play a critical role in transporting heat energy from the ocean surface to the Antarctic ice sheet margin in the grounding zones of ice shelves and outlet glaciers (Silvano et al., 2018). Sea ice formation and brine rejection within coastal polynyas form a highly saline and dense water mass called High Salinity Shelf Water (HSSW) (Ohshima et al., 2016). HSSW is maintained at the surface freezing temperature (~-1.9 °C) (Foldvik et al., 2004) and is sufficiently dense to circulate at depth 40 into the cavities of adjacent outlet glaciers and ice shelves where it can drive basal melting in the grounding zone (Jacobs et Gemma M. Brett 1 , Daniel Price 1 , Wolfgang Rack 1 , and Patricia J. Langhorne 2 https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License. al., 1992) forming Ice Shelf Water (ISW) (MacAyeal, 1984). ISW is characterised as being potentially supercooled (i.e., potential temperature below the surface freezing point) (Jacobs et al., 1985) and can rise in buoyant plumes along the base of ice shelves (Jenkins and Bombosch, 1995).

45
As ISW rises from depth, it can become in situ supercooled Kvinge, 1974, Jenkins andBombosch, 1995) and frazil ice crystals can form (Holland and Feltham, 2005). The frazil ice can grow into larger platelet ice crystals (Langhorne et al., 2015, Leonard et al., 2011, Smith et al., 2001 which can freeze into the base of nearby sea ice to form consolidated platelet ice (Smith et al., 2012, Smith et al., 2001. The consolidation of platelet ice augments sea ice formation (Eicken and Lange, 1989) and increases the sea ice thickness (Gough et al., 2012. An unconsolidated mass of platelet ice 50 crystals called a sub-ice platelet layer (SPL) can form beneath the sea ice once the conductive heat flux from the sea ice to the atmosphere becomes sufficiently low or the supply of frazil and platelet ice crystals abundant enough to overtake thermodynamic sea ice growth (Dempsey et al., 2010, Gough et al., 2012. The signature of supercooled ISW can thus be identified from thicker sea ice with incorporated platelet ice and by the presence of an unconsolidated SPL (Langhorne et al., 2015). 55 In addition to the thicker ice shelf-influenced sea ice, the buoyant forcing of the SPL increases the sea ice freeboard (i.e., the height of the sea ice surface above sea level) (Gough et al., 2012, Price et al., 2014. Sea ice thicknesses obtained through satellite altimetry assumed to represent consolidated sea ice thickness are consequently overestimated (Price et al., 2014). The magnitude of the SPL buoyancy is dependent on the thickness of the layer and the solid ice fraction, i.e., the fraction of solid 60 ice per unit volume (Price et al., 2014). The buoyant forcing of a SPL with a thickness of one metre and a solid fraction of 0.25 has the potential to induce a 1-2 cm increase in freeboard height for typical first-year fast ice in McMurdo Sound (Gough et al., 2012).
The conditions of ice shelf geometry and sub-ice shelf circulation required for ISW to reach the upper surface ocean are not 65 satisfied at all ice shelves (Langhorne et al., 2015) and the distribution of ice shelf meltwater in the Southern Ocean is not well known (Kusahara and Hasumi, 2014). Langhorne et al. (2015) collated observations of frazil and platelet ice in the upper surface ocean in Antarctic coastal regions and found positive occurrences where the water temperature at 200 m depth was less than 0.5°C above the surface freezing point (refer to Fig. 1a for a map of locations updated by Hoppmann et al. (2020)). (Hughes et al., 2014, Lewis and Perkin, 1985, Mahoney et al., 2011, 70 Robinson et al., 2014 where it significantly influences fast ice formation and forms a thick SPL.

ISW reaches the upper surface ocean in McMurdo Sound
Given the difficulty of accessing fast ice in Antarctic coastal regions and the logistical constraints of carrying out field observations with ground-based methods, it is possible that other unobserved regions are influenced by the outflow of ISW in the upper surface ocean. A means to identify these regions in large-scale satellite assessments is highly desirable. The detection 75 of ISW influence on fast ice via satellite altimetry is in theory possible through the identification of regions with 'anomalously' higher freeboard driven by thicker ice shelf-influenced sea ice and the buoyant forcing of a SPL, if present (Price et al., 2014).
The pulses emitted from satellite laser altimeters reflect from the ice-air or snow-air interface and thus measure the height of the sea ice freeboard plus the addition of a snow layer, if present (henceforth referred to as snow freeboard). Microwave radar 80 waveforms emitted from satellite radar altimeters penetrate into the snow layer. The penetration depth of radar waves into the snow layer is dependent on the backscattering properties of the snow (Kwok, 2014, Price et al., 2015, Willatt et al., 2011. The dominant backscattering surface for radar waveforms can thus be some unconstrained interface between the top of the snow and the sea ice freeboard (Price et al., 2015, Price et al., 2019. https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.
Here, we investigate whether the CryoSat-2 (CS2) satellite radar altimeter can detect the influence of ISW on fast ice in 85 McMurdo Sound by identifying the higher ice freeboard caused by thicker ice shelf-influenced fast ice and the buoyant forcing of the SPL beneath. Multiple years of field observations and a highly detailed knowledge of the spatial distributions of snow, fast ice and SPL thicknesses, and the circulation of the supercooled ISW recommends McMurdo Sound as an ideal location for this study. CS2 measurements of freeboard obtained using a supervised retrieval procedure were compared with four years of drill hole measured freeboard, fast ice and SPL thickness, and snow depth over the fast ice in McMurdo Sound. We describe 90 the study area, in situ datasets and summarise the technical specifications of the CS2 satellite radar altimeter and CS2 data product in section 2. We describe the methods applied in section 3 and the results in section 4. In section 5, we discuss the results and the outlook for satellite altimetry assessments of ice shelf-influenced fast ice.

Study area and datasets 95
In the western Ross Sea, an interactive system is at play between coastal polynyas, the conjoined McMurdo and Ross Ice Shelf, and fast ice in the field study area in McMurdo Sound (Brett et al., 2020). McMurdo Sound is geographically delineated by the Victoria Land Coastline in the west, Ross Island in the east, and the McMurdo Ice Shelf in the south (Fig. 1). The fast ice in McMurdo Sound is predominately first-year ice that typically forms between April and December and then breaks out in the following summer (Kim et al., 2018). 100 The outflow of supercooled ISW from the McMurdo Ice Shelf cavity augments fast ice formation (Robinson et al., 2014), fast ice thickness (Gough et al., 2012, Langhorne et al., 2015 and forms a thick SPL in McMurdo Sound (Dempsey et al., 2010, Gough et al., 2012, Langhorne et al., 2015. In the central-western region of the sound, a consistent pattern of thicker ice shelf-influenced fast ice with a substantial SPL beneath has been observed in proximity to the ice shelf 105 margin in multiple studies, e.g., Brett et al. (2020), Price et al. (2014). This pattern is driven by the outflow of supercooled ISW from the centre and west of the McMurdo Ice Shelf cavity and its subsequent circulation along the Victoria Land Coastline (Hughes et al., 2014, Lewis and Perkin, 1985, Robinson et al., 2014. The effect of supercooled ISW is most pronounced within ~30 km of McMurdo Ice Shelf (Brett et al., 2020, Hughes et al., 2014 but could extend 200-250 km to the north (Stevens et al., 2009, Hughes et al., 2014. ISW circulation has been modelled to increase fast ice growth by 9 ± 4 cm yr −1 110 100 km north of the ice shelf edge (Hughes et al., 2014). Indeed, thicker ice shelf-influenced fast ice (>2 m) and SPLs (0.1-0.2 m) were measured in drill holes ~85 km north of the McMurdo Ice Shelf in , and 2017(Brett et al., 2020, Price et al., 2014. Satellite altimetry assessments of fast ice freeboard have previously been carried out in McMurdo Sound with the ICESat-1 115 laser altimeter (Price et al., 2013) and CS2 (Price et al., 2015, Price et al., 2019. In the ICESat-1 study, a peak in multi-year snow freeboard, centred around longitude 165°E, was observed in the south of McMurdo Sound between 2003 and 2009, when ocean circulation in the region was altered by the passage of large tabular icebergs . The peak in multi-year fast ice freeboard coincided with the thickest SPL and the main path of ISW outflow. The SPL contribution to satellite altimeter derived fast ice thickness in McMurdo Sound was quantified using surface elevation measurements obtained 120 with a Global Navigation Satellite System (GNSS) rover (Price et al., 2014). GNSS surface elevation (calibrated to local sea level) is analogous to satellite altimeter measured snow freeboard and was thus a comparable means to assess the effects of the SPL on freeboard to thickness conversion assuming hydrostatic equilibrium. Fast ice thicknesses derived from sea ice freeboard in McMurdo Sound were overestimated on average by 12% and up to 19% due to the buoyancy effect of the SPL. 125 https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.

Ground validation with drill hole measurements
Ground validation for the CS2 measured freeboard and derived ice thickness was provided by extensive drill hole measurements The 'anomalously' higher sea ice freeboard is driven by the combined upward (positive) buoyancy of the thicker ice shelf-150 influenced fast ice and the ice mass within the SPL beneath. The addition of a snow layer, if present, provides an opposing downward (negative) forcing. A combined 'Mass Equivalent Thickness' (MET) was calculated according to Price et al. (2019) to sum the consolidated sea ice thickness and the unconsolidated SPL thickness times the solid fraction, i.e., the thickness of the solid mass of ice in the SPL. It is difficult to physically measure the solid fraction without disturbing the natural state of the SPL. Numerous methods to indirectly derive the solid fraction have been applied including the hydrostatic equilibrium 155 assumption (Price et al., 2014), electromagnetic induction techniques  and thermistor probe data , Gough et al., 2012. https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License. Table 1

CryoSat-2 satellite radar altimeter 170
The principle payload of CS2 is the combined Synthetic Aperture Radar (SAR) and interferometric radar altimeter which operates in three modes: 1) Low Resolution Mode, 2) SAR mode, and 3) Combined SAR and interferometer (SIN) mode (Bouzinac, 2012, Wingham et al., 2006. CS2 predominantly operates in SIN mode over coastal fast ice regions including McMurdo Sound. The number of measurements obtained in SIN mode decreases by a factor of four relative to SAR mode (Wingham et al., 2006). Highly specular reflectors such as leads significantly off-nadir can dominate the returning radar echo 175 or 'snag' introducing a range error and an underestimate in surface elevation. However, in SIN mode this range error can be corrected by determining the across-track angle to off-nadir returns and thus more data can be retained relative to SAR mode (Armitage and Davidson, 2014). Depending on the surface geometry and satellite orbit, the radar footprint of CS2 is ~300 m along-track and ~1.5 km across-track (Wingham et al., 2006).

180
The ESA Level 2 retracking point is found using a model-fitting approach and is defined relative to the entire echo waveform (Bouzinac, 2012, Price et al., 2015. The dominant backscattering surface assumed for this retracker is the snow-ice interface. However, an assessment of the influence of the snow layer on the radar waveform by comparison with coincident in situ measurements of freeboard and snow layer depth in McMurdo Sound by Price et al. (2015) showed that the ESA retracker tracked between the surface of the snow and the snow-ice interface. Price et al. (2019) assessed the sensitivity of CS2 Level 2 185 SIN product derived sea ice thicknesses to variable penetration depths into the snow layer in McMurdo Sound in November 2011.
They found the closest agreement with in situ measurements when the penetration depth into the snow layer was assumed to be 0.05-0.10 m. In this study, we compare CS2 obtained freeboard with in situ measurements to identify the best matching freeboard interface or penetration depth for each individual CS2 track.
Geo-located Baseline-C Level 2 SIN data generated from the 'CryoSat-2 Ice Processor' were used for this assessment. The 190 Level 2 SIN data product provides a surface height relative to the WGS84 ellipsoid for each location along-track with geophysical corrections applied to the range measured by the satellite (Wingham et al., 2006, Bouzinac, 2012. Applied geophysical corrections vary according to the surface type classification and are described in detail with their sources in Bouzinac (2012) and Webb and Hall (2016). Atmospheric propagation corrections (ionospheric and dry/wet tropospheric) are always applied to account for the time delay introduced as the altimeter pulse passes through the Earth's atmosphere. Satellite 195 altimeter derived surface elevations must additionally be corrected for the shape of the geoid, tidal height, inverse barometric effect and dynamic ocean topography before freeboard can be obtained (Price et al., 2015, Ricker et al., 2016. However, the level of accuracy required for these corrections is difficult to attain with models. In general, freeboard is determined relative to a local

Supervised CryoSat-2 retrieval of ISW influenced freeboard
By assessing individual CS2 track profiles, significant CS2 height outliers (i.e., WGS84 -54 m≤CS2 height≤-60 m) were identified and removed. Surface elevation retrievals were then obtained by applying the MSS and all ocean/tidal corrections and then de-trending for the EGM 2008 geoid (refer to Appendix A for further information). A supervised retrieval procedure 215 was applied to obtain freeboard from the Level 2 surface elevations by identifying the relative SSH manually with satellite imagery. The fast ice edge and open water along-track was identified in NASA MODerate resolution Imaging Spectroradiometer (MODIS) optical images acquired on the day of the CS2 overpass. The relative SSH was defined as the median value of the CS2 surface elevation retrievals over 25 km of adjacent open water along-track. The median value was chosen because the mean was skewed by significant noise in the CS2 surface elevation measurements. 220 Supervised retrievals of fast ice freeboard from CS2 surface elevations were applied to 20 CS2 tracks between latitudes 77.4°S and 78°S in McMurdo Sound over the four study years. CS2 freeboards derived relative to the median SSH were then compared with coincident spline interpolated drill hole measured snow and ice freeboards along-track. Fourteen out of the 20 (70%) tracks produced CS2 freeboard magnitudes relative to the median SSH that aligned with the drill hole measurements. Figure  225 2 shows an along-track profile of spline interpolated drill hole measured sea ice and snow freeboard, and sea ice and SPL thicknesses and combined MET in the centre of the sound with CS2 freeboard measurements from an overpass on the 15 November 2017. CS2 freeboard increased towards the ice shelf in the south with increasing fast ice and SPL thicknesses and combined MET.

235
Sea ice thickness (Ti) was calculated from freeboard assuming hydrostatic equilibrium which asserts that the ratio of freeboard (Fb) to total ice thickness is proportional to the ratio of the densities of sea ice (ρi) and seawater (ρw) (Zwally et al., 2008). The addition of the snow layer (Ts) to freeboard height, the snow density (ρs), and the buoyancy effect of the SPL, if present, must be taken into account (Price et al., 2014). Constant values for ρw, ρi and ρs of 1027 kg m -3 , 925 kg m -3 and 385 kg m -3 , were respectively assumed to facilitate inter-comparison and to adhere to the rationale and error propagation in Price et al. (2014). 240 CS2 ice thickness was calculated from CS2 freeboard by assuming that the dominant backscattering surface for the ESA Level 2 retracker is either 1) snow freeboard, 2) sea ice freeboard, or 3) some penetration depth ( ) into the snow layer by respectively applying equations 1, 2 and 3 from Price et al. (2019). A correction for the propagation of the radar wave through the snow layer was applied according to Kurtz et al. (2014). 245 250 To select the best-matching freeboard interface for each track, CS2 ice thicknesses obtained from Eq. (1) and (2) were compared with interpolated drill hole METs along-track. The freeboard interface that produced the closest matching CS2 ice thickness and drill hole MET was then selected. If neither snow freeboard (Eq. (1)) nor sea ice freeboard (Eq. (2)) produced matching drill hole MET and CS2 ice thickness profiles, we estimated a penetration depth and applied Eq.

Supervised CryoSat-2 retrieval of ISW influenced freeboard
The mean drill hole sea ice and snow freeboards, and snow-corrected CS2 freeboard for first-year fast ice were calculated (over equivalent distances) for each CS2 track, and then averaged regionally for the 3 tracks in the west, 7 in the centre and 4 in the east (refer to Fig. 3 and Table 1). The mean regional drill hole sea ice and snow freeboards were highest in the centre at 265 0.25 m and 0.32 m, respectively, and slightly lower in the west at 0.22 m and 0.27 m. In the east, the mean drill hole sea ice and snow freeboards were 0.14 m and 0.30 m, respectively. The mean regional CS2 freeboard followed the same trend of higher freeboard in the centre (0.31 m), decreasing to the west (0.24 m) and east (0.22 m). In the centre of McMurdo Sound, we estimate a mean CS2 derived freeboard difference of 0.07 and 0.09 m relative to the west and east, respectively. This difference is 28-36 % of the mean drill hole measured sea ice freeboard. We interpret this freeboard distribution across the 270 main path of supercooled ISW outflow as being largely due to the thickness change of the ice shelf-influenced fast ice with a SPL beneath, rather than due to gradients in snow thickness.  Table 1). The mean regional values for the tracks in the west, centre and east are shown with a solid line to illustrate the mean freeboard distribution across McMurdo Sound. The longitudes are taken from where each CS2 track crossed latitude 77.7°S.

Table 1: Mean interpolated drill hole (DHint) measured sea ice and snow freeboards (Fb) and CS2 freeboards for first-year fast ice only
(over equivalent distances) for individual CS2 tracks in the west, centre and east. Regional mean values for tracks in the west, centre 285 and east are given and these statistics are used in Fig. 3 and 4. If sea ice freeboard or a penetration depth was determined for a CS2 track, a correction for the propagation of the radar wave through the snow was applied according to Kurtz  Over the main supercooled ISW outflow region in the centre of the sound, CS2 freeboard and CS2 ice thickness increased towards the ice shelf in the south concurrently with increasing fast ice and SPL thicknesses and combined MET (Fig. 4a, c, e, and g). In comparison, CS2 freeboard and CS2 ice thickness in the east where the influence of ISW is less significant, showed a marginal increase towards the ice shelf in 2013 (Fig. 4d) and almost flat profiles in 2011, 2017 and 2018 (Fig. 4b, f, and h 300 respectively). In 2011 (Fig. 4a) and 2017 (Fig. 4e), CS2 freeboard was higher near the McMurdo Ice Shelf in the centre of the sound and this could be attributed to the thicker SPLs or the deeper and more wind-compacted snow observed in these years by Brett et al. (2020). In 2011, no drill hole measurements were made south of latitude -77.83° on the centre profile (Fig. 4a) and we were unable to determine why the first-year fast ice freeboard was significantly higher near the McMurdo Ice Shelf. CS2 freeboard measured south of -77.83° on this track was thus excluded from the calculation of the mean value (Table 1). 305 https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.
In 2013, the CS2 track in the centre (Fig. 4c) on 3 November had minimal snow coverage and best matched with sea ice freeboard. The CS2 track in the east (Fig. 4d) on 27 November 2013 had deeper snow and best matched with snow freeboard.
The drill hole measurements made every kilometre along the CS2 track in the east on 27 November 2013 by Price et al. (2015) are shown in this profile (Fig. 4d). The increasing trend towards the McMurdo Ice Shelf is evident in both the CS2 freeboard and CS2 ice thickness on the 2013 central profile when compared to the 2013 eastern profile, most markedly over multi-year 310 ice in the southwest of the sound (77.85°S to 77.87°S) in Fig. 4c.
The regional mean interpolated drill hole sea ice, SPL thicknesses and combined MET along the seven CS2 tracks in the centre of McMurdo Sound were 2.26 m, 3.90 m, and 3.08 m, respectively. The mean CS2 ice thickness for these seven tracks was 3.04 m, corresponding to a 0.78 m overestimate relative to the drill hole measured sea ice thickness in this region. The regional 315 mean snow depth in the centre was 0.07 m over the four study years.
To assess the spatial distributions of higher satellite altimeter obtained freeboard and resultant thicker ice, CS2 freeboard and CS2 ice thickness from 4 tracks distributed across McMurdo Sound in November 2013 were spline interpolated. To circumvent substantial noise in CS2 freeboard and derived ice thickness, a running mean of three measurements (corresponding to ~1 km) 320 was applied along-track prior to applying the interpolation. Figure 5 shows maps of the distributions of CS2 freeboard, CS2 ice thickness and drill hole measured MET in McMurdo Sound in November 2013. Different scales for freeboard height and thicknesses were used to highlight the similarity in the patterns of CS2 freeboard, CS2 ice thickness and drill hole MET. CS2 freeboard height (Fig 5a) and CS2 ice thickness (Fig 5b) concurred with the thickness distributions of drill hole measured ice shelf-influenced fast ice, SPL (Fig. 1) and combined MET (Fig 5c)    The geophysical corrections should not have a major impact on obtained freeboard if the retrieval of the relative SSH is robust (Ricker et al., 2016). CS2 freeboard was obtained relative to a SSH measured along-track and the distance to open water did not exceed ~25 km in all study years. Identifying the relative SSH along-track is complicated by interference and noise 380 introduced by sea surface conditions and by the presence of pack ice. We observed thin nilas or some pack ice beneath several CS2 tracks. We used in situ measurements to assess the accuracy of the relative SSH identification by comparing the magnitude of the resultant CS2 freeboards against drill hole measured freeboard. However, for automated freeboard retrievals and for regions of coastal sea ice without in situ measurements or open water nearby, poor identification of the relative SSH could introduce significant error and bias in the CS2 derived freeboard. 385

Satellite altimetry measured freeboard and sea ice thickness
The assumed freeboard interface will significantly affect the resultant sea ice thickness obtained from the hydrostatic equilibrium equations. The calculated CS2 ice thickness will be overestimated if sea ice freeboard is assumed and full penetration of the radar wave into the snow layer does not occur. Alternatively, calculated CS2 sea ice thickness will be 390 underestimated if snow freeboard is assumed and full or partial penetration of the radar wave into the snow layer occurs. Price et al. (2019) found that the sea ice thicknesses in McMurdo Sound obtained by either assuming snow or ice freeboard using Eq. (1) or (2), respectively, would produce a difference in thickness of 1.7 m. The sensitivity of the derived sea ice thickness to variable penetration depths into the snow layer was also assessed. This was an important consideration when assessing and comparing trends in CS2 ice thicknesses from the east and the centre of McMurdo Sound in this study. The freeboard to 395 thickness conversion will also be affected by applying constant values for the density of sea ice, snow and seawater. However, an error propagation analysis of the effects of the density values of sea ice, snow and seawater in the hydrostatic equilibrium equation carried out by Price et al. (2014) found that the assumed freeboard interface contributed the greatest error in the derived ice thickness.

400
To ensure that the best-matching freeboard interface or penetration depth for each track was selected, we compared calculated CS2 ice thicknesses from equations 1, 2 and 3 with interpolated drill hole MET along-track. Additional validation for the selected freeboard interface was provided by 1) comparing resultant profiles of CS2 freeboard with coincident interpolated sea ice and snow freeboard along-track, and 2) by comparing mean values of CS2 freeboard, and interpolated drill hole sea ice and snow freeboard for each individual track. 405 https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.
In the west and centre, the sea ice surface was the dominant freeboard interface, except in years with deeper snow coverage.
In the east, the best matching freeboard horizons was variable from year to year and ranged from the snow surface to the sea ice surface or a mid-depth penetration. The mid-depth penetration into the snow in 2011 and 2018 agreed with the dominant ESA Level 2 backscattering horizon identified between the surface of the snow and the sea ice in Price et al. (2015) and is 410 comparable to the upper limit penetration depth of 0.05-0.10 m estimated across the sound by Price et al. (2019) in November 2011. This general pattern reflects the distribution and composition of the snow in McMurdo Sound. The snow in the east was generally deeper, more densely-packed, and wind-compacted relative to the centre and west where the snow was sparse, loosely-packed and where full penetration of the radar wave would more likely occur. The contrasting distributions in the snow and thicker ISW influenced fast ice and SPL from east to west was advantageous. We had confidence that the trends of higher 415 freeboard and thicker CS2 obtained ice thickness observed in the centre relative to the east did not result from the addition of the snow layer to ice freeboard which would have a more significant effect in the east.

CryoSat-2 satellite altimeter detection of ISW influenced fast ice
CS2 conclusively detected the influence of ISW on fast ice in McMurdo Sound each study year. The spatial distribution of 420 higher CS2 obtained freeboard and thicker CS2 ice concurred with the distributions of thicker ice-shelf influenced fast ice and SPL and prior observations of ISW and effective negative ocean heat flux in McMurdo Sound (Barry and Dayton, 1988, Dempsey et al., 2010, Langhorne et al., 2015, Lewis and Perkin, 1985, Robinson et al., 2014. In the centre, CS2 freeboard and CS2 ice thickness increased concurrently with increasing fast ice and SPL thicknesses towards the ice shelf in the south on all the central profiles. The mean CS2 freeboard value in the centre over the main path of supercooled ISW outflow was 425 0.07 m and 0.09 m higher than the west and east, respectively, where the influence of ISW is less pronounced. The magnitude of this freeboard difference agrees with the 1-2 cm increase in freeboard for every metre of SPL obtained by Gough et al. (2012) using thermistor probe data. This higher freeboard centred at longitude ~165°E was also observed in McMurdo Sound by Price et al. (2013) with ICESat-1 over multi-year ice. The regional mean CS2 ice thickness in the centre was 0.78 m or 35 % greater than the mean drill hole measured sea ice thickness. We mainly attributed this overestimate in satellite altimeter 430 derived ice thickness to the additional buoyant forcing of the sub-ice platelet layer.

Outlook for satellite altimetry detection of ice shelf-influenced fast ice freeboard
Here, we made steps towards developing a satellite-based method to identify and constrain regions of Antarctic coastal sea ice that are being influenced by ISW outflow in the upper surface ocean. We have demonstrated the potential scope to carry out 435 satellite altimetry assessments of regions where ISW and platelet ice have already been detected at the surface, and to identify other unknown regions where ISW is reaching the upper surface ocean. Regions of anomalously higher freeboard could indicate thicker fast ice and the influence of ISW. This would require prior knowledge of the age and formation conditions of the fast ice (e.g., deformed ice will be thicker) and most critically the depth of the snow layer, if present. To improve uncertainty surrounding the radar altimeter penetration and snow depth CryoSat-2 could be used in tandem with ICESat-2 laser altimeter 440 which measures snow freeboard.
Once regions of ISW outflow are identified, long-term interannual variability in ice shelf and sea ice interactions could in theory be monitored with satellite altimetry. The presence and abundance of both consolidated platelet ice and the SPL provide some insight into the processes at play within inaccessible ice shelf cavities, and the volumes of ISW outflowing in a region 445 (Langhorne et al., 2015). With long-term monitoring, this could provide information on the effects of variability in the atmospheric and oceanographic interactions on HSSW-driven ISW formation within ice shelf cavities. https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.
However, significant challenges are presented, notably the noise in the CS2 measurement, interference from land, inaccuracies of geophysical corrections, the identification of relative SSH, the range resolution of SIN, and inadequate knowledge of the 450 snow distribution in Antarctica and penetration depth of the radar waveform. Recently, a retracking algorithm was developed with the capability to retrieve both the backscattering horizon for the air to snow and snow to sea ice interface from the CryoSat-2 Level 1b waveform (Fons and Kurtz, 2019) which showed significant promise. However, ice freeboard was overestimated in regions of large snow depths which concurred with a similar effect on CS2 obtained freeboard in deep snow deposits on Arctic sea ice (Ricker et al., 2015). 455

Conclusion
The outflow of supercooled Ice Shelf Water (ISW) from the conjoined McMurdo-Ross ice shelf cavity results in a consistent pattern of thicker fast ice with a substantial sub-ice platelet layer (SPL) in the central-western region of McMurdo Sound. The thicker fast ice and the buoyant forcing of the SPL result in higher freeboards. Here, we investigated if the CryoSat-2 satellite radar altimeter is capable of detecting this higher freeboard. CryoSat-2 ice freeboard was obtained from the surface elevation 460 measurements by applying a supervised retrieval procedure which manually identified the relative sea surface height alongtrack in satellite imagery. CryoSat-2 ice freeboard was then compared to four years of drill hole measured ice and snow freeboard, sea ice and SPL thicknesses, and snow layer depths on the fast ice in McMurdo Sound.
The spatial distribution of higher CryoSat-2 derived ice freeboard concurred with the distribution of thicker ice shelf-influenced 465 fast ice and the SPL in late spring of 2011, 2013, 2017 and 2018. In the centre of McMurdo Sound, increasing trends in CryoSat-2 obtained freeboard and ice thickness were observed with increasing fast ice and SPL thicknesses towards the McMurdo Ice Shelf every year. Over the four study years, we observe a mean CryoSat-2 obtained freeboard difference of 0.07-0.09 m across the main path of ISW outflow in McMurdo Sound. We interpret this freeboard distribution as being largely due to the thicker ice shelf-influenced fast ice and the substantial SPL across the main path of supercooled ISW outflow, rather 470 than due to gradients in snow thickness. CryoSat-2 derived ice thickness were 35 % greater than drill hole measured fast ice thickness in the centre of the sound which we mainly attribute to the additional forcing of the SPL.
Several important factors complicate the identification of fast ice freeboard measured by satellite altimeters including inadequate knowledge of the snow layer in Antarctica, lack of adjacent open water nearby, the identification of a relative sea 475 surface height and inaccuracies in the modelled geophysical corrections and geoid surface. We were able to constrain these uncertainties and have confidence in the retrieved CryoSat-2 freeboard given the availability of in situ information for validation. The geophysical corrections applied to the CryoSat-2 Level 2 SIN product and the effects of de-trending for the geoid over ice-free open water in McMurdo Sound were assessed during the study period to provide confidence in the CryoSat-2 measured freeboard and derived ice thickness. 480 The thinner and generally non-compacted snow layer in the centre, west and northwest where the influence of Ice Shelf Water is most pronounced aided the detection of ice shelf-influenced freeboard with the CryoSat-2 radar altimeter, as it reduced the complication with uncertainty of penetration depth into the snow layer and interpretation of the assumed backscattering/freeboard interface. It is possible that many unobserved regions of coastal sea ice around Antarctica are 485 influenced by the outflow of ISW in the upper surface ocean and the presence of platelet ice. We have shown that the CryoSat-2 satellite radar altimeter is capable of detecting this higher freeboard driven by this outflow and provide a proof-of-concept demonstration for the wider application of this method. https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.

Appendix A 490
The spatial distribution and magnitude of the geophysical corrections applied to the CS2 Level 2 SIN product and the effect To summarise, the flattest profiles every year in McMurdo Sound were obtained from the CS2 height with the MSS and all ocean corrections applied, and then de-trended for the EGM 2008 geoid. We were unable to clarify why the CS2 Level 2 SIN product with atmospheric, ocean corrections, and the MSS applied produced the flattest profiles when additionally de-trended for the EGM 2008 geoid. This indicates that the geoid is de-trended for twice, once with the MSS correction and then again 530 with the EGM 2008 geoid. The MSS model applied in the study region is unclear from the information provided by ESA and is either the Aviso CLS01 (Webb andHall, 2016, Bouzinac, 2012) or CLS 2011 (Skourup et al., 2017). https://doi.org/10.5194/tc-2020-286 Preprint. Discussion started: 22 October 2020 c Author(s) 2020. CC BY 4.0 License.

540
Data availability. The European Space Agency Level 2 Baseline C SIN mode (SIR_SIN_L2) product was obtained at http://science-pds.cryosat.esa.int/ last accessed on 6 March 2019. The in situ data included in this study will not be available at the time of publication but it is intended that it will be deposited in a data repository.
Author contributions. GB collected in situ data in 2017 and 2018, designed the methodology, carried out all satellite data 545 processing and analysis, and wrote the manuscript with input from all co-authors, in particular DP who significantly contributed to all stages of this study. DP wrote the scripts used to process the CryoSat-2 Level 2 SIN data. WR contributed significantly to the development of the methodology and manuscript editing, and WR and DP collected in situ data in 2011 and 2013. PL contributed to the manuscript development, coordinated the field programs and collected in situ data in 2011, 2013 and 2017. 550 Competing interests. The authors declare that they have no conflict of interest.