To measure basal melt rates, we operated an autonomous phase-sensitive radio-echo sounder ApRES; on the Ekström Ice Shelf 25km upstream of the ice shelf front (Fig. b; location at 70.82° S, 8.73° W on 2 April 2020 termed MIMO-EIS8). An ApRES is a ground-penetrating frequency-modulated continuous-wave (FMCW) radar that transmits chirps throughout 1s while it increases the frequency of the electromagnetic wave from 200 to 400MHz .

The ApRES and two skeleton slot antennas were placed below the surface for protection from wind and snowdrifts. It performed hourly measurements consisting of 20 chirps between April 2020 and November 2023. Short gaps of 2 to 3 d exist in the recorded time series (9–10 January 2021, 25–26 November 2021, 31 December 2022–2 January 2023), at which the device was dismounted and used for other measurements, and a longer gap from 1 April to 16 May 2021 also exists.

The signal processing we applied to the raw data follows the previous work by , and . First, we rejected the first chirp of each measurement and stacked the remaining chirps to get a better signal-to-noise ratio. Next, to obtain an amplitude and phase profile as a function of two-way travel time from the stacked signal, we applied a Fourier transformation. Finally, we obtained a range profile by converting the two-way travel time into a range using a propagation velocity of 168 914 kms-1 according to the ordinary relative permittivity of 3.15 . The sample spacing due to zero-padding with a pad factor of 8 is 0.053m, while the resolution of the phase is about 1°, corresponding to 1mm in range.

The determination of the basal melt rate from an ApRES time series is based on the analysis of the ice thickness change and the decomposition of the processes contributing to it . The change in ice thickness ΔH within the time interval Δt is the sum of the thickness changes caused by firn compaction ΔHf, vertical strain ΔHε and basal melting ΔHb: 1ΔHΔt=ΔHfΔt+ΔHεΔt+ΔHbΔt. Solving Eq. () for the melt rate ab gives 2ab=-ΔHbΔt=-ΔHΔt-ΔHfΔt-ΔHεΔt, where positive ab represents basal melting.

For the melt rate analysis, we follow the method described by and , which is based on the previous work by and . The ApRES time series allows for the determination of ΔH, ΔHf and ΔHε with millimetre precision. To this end, we divided the range profile into 6m long segments with 3m overlap below a depth of 10m. Around the basal reflection, identified by a strong increase in amplitude, we used a larger segment of 10m size (-9 to +1 m with respect to the basal reflection). For the basal segment, we derived displacements from complex-valued cross-correlation of the phase of all pairwise time-consecutive measurements. For each internal segment, we obtained the displacement time series from a cross-correlation of the complex signal of the first measurement (t1) with each repeated measurement (ti). We used the lag of the correlation coefficient with the highest amplitude to find the correct phase-shift minimum, the sum of which gives the vertical displacement of this segment since the time of the first measurement. During the three interruptions in the ApRES time series in January 2021, November 2021 and December 2022/January 2023, the ApRES and the antennas were locally repositioned a few metres laterally away from the previous location and placed again close to the surface to avoid burial over time. Therefore, we redefined t1 as the first measurement after these interruptions.

The change in ice thickness and the processes contributing to it can now be determined based on the vertical displacements. The cumulative change in ice thickness results from the time series of the displacement of the basal segment. The contributions of firn compaction and vertical strain must be calculated based on the vertical displacement uz of various englacial segments. The vertical strain εzz is defined as the vertical derivative of the vertical displacement uz: 3εzz=∂uz∂z. We calculated the derivative of the vertical displacements based on a linear regression analysis assuming constant strain over depth as expected for the shallow-shelf flow regime of ice shelves. Here, only those segments below the range of 100 and 30 m above the basal return were considered to avoid the influence of firn compaction and the basal return on the strain rate analysis. The linear regression analysis gives the cumulative displacement: 4uz(z)=εzzz+ΔHf, where the mean firn compaction ΔHf is the intercept at the surface. The strain contribution to the change in ice thickness ΔHε is then the integral over the ice thickness H: 5ΔHε=∫0Hεzzdz. Appendix  shows the analysis of the basal melt rate for one example from 2020 and the cumulative time series. We obtained the time series of cumulative melt by subtracting the contributions of firn compaction and strain thinning from the cumulative ice thickness change. To determine the melt rate, we calculated the gradient in a 7d moving window, which gives the 7d average melt rate. By applying the 7d moving window, variations with periods shorter than ∼16d are attenuated.

To represent the variability of the melt rate on sub-weekly timescales, we additionally calculated the melt rate using the gradient in a 1d moving window and then calculated the 7d standard deviation. The uncertainty of the vertical displacements is based on the standard error of the radar phase, which is of the order of sub-millimetres. The largest uncertainty originates from the strain analysis and its extrapolation to the ice base. The ApRES measurements at Ekström Ice Shelf allow for the determination of the depth profile of displacements from near the surface to about 90 % of the ice thickness. The only assumption we made here is that the strain in the lowest 10 % of the ice thickness is the same as above. Since the measurement location was on a freely floating part of an ice shelf, the vertical displacements are sufficiently represented by a constant strain. Thus, it is accurate to assume that the strain remains constant in the remaining 10 % of the ice thickness. On average, the uncertainty of the basal melt rate amounts to ∼ 0.02 ma-1.

To investigate the relation between sea-ice formation and an increase in melt rate, we determined sea-ice growth and concentration over the continental shelf in front of the Ekström and Atka ice shelves (Fig. b). Sea-ice growth was estimated using the simple model of , which relates the sea-ice growth to the heat loss at the ice-free ocean surface in a polynya. We used surface wind speed and air temperature from the JRA-55 reanalysis to calculate heat loss over the ice-free ocean. The sea-ice concentration and open water area were derived from AMSR-2 passive microwave data twice daily on a 3.125km grid . Time series of sea-ice growth and concentration were derived within a fixed polygon area (Fig. b) for the same period as the ApRES measurements.

This study employs a heat budget method similar to previous approaches e.g. but with differences in methodology and satellite data. While this method likely overestimates sea-ice production due to simplifications such as neglecting ocean heat flux and solar radiation, it effectively captures temporal variability and seasonality. Comparisons with other resolutions and reanalysis forcing reveal consistent patterns in variability but differences in magnitude by up to a factor of 2.

No observations of the oceanographic properties near the ApRES location have been made, except for a snapshot from the Sub-EIS-Obs ice shelf cavity CTD profiles taken in January 2019 . To assess the seasonal evolution of water masses within the cavity, we analysed hydrographic data from a CTD mooring that was installed in December 2005 as part of the “PerenniAL Acoustic Observatory in the Antarctic Ocean” project PALAOA; near the front of the Ekström Ice Shelf (Fig. b). The CTD was deployed by means of hot-water drilling through the approximately 100m thick ice shelf. At the time of the deployment, the ice shelf cavity had a thickness of approximately 160m (seafloor to ice shelf base), and the CTD was initially located 70m beneath the ice shelf base. Due to melting and advancement of the ice shelf, these initial measurements underwent slight variations over time. PALAOA yielded an almost 8-year-long record of pressure, temperature and salinity from January 2006 to May 2014. The data record is interrupted for most of 2006, due to technical problems of the CTD's cable. It was repaired in January 2007, after which records were uninterrupted until the end of the time series in May 2014. The frozen-in CTD cable prevented the retrieval of the CTD and thus its post-deployment calibration. The CTD was operated in stand-alone mode, with the sensor automatically activated every 30 min . After 9 January 2012, the sampling rate was increased to once every 10 min.

In situ measurements from the Sub-EIS-Obs and PALAOA CTDs were converted to conservative temperature and absolute salinity (referred to as temperature and salinity in the following for simplicity) using the TEOS-10 Gibbs thermodynamic potential for seawater , which was also used to derive potential density from the observations. To compare the temperature, salinity and density time series with the later-observed melt rates, sea-ice growth and concentration, we calculated seasonal composites of all products based on the multiyear data sets. For that purpose, we sorted the data according to the day of the year and computed the median, and 25th and 75th percentiles within weekly bins throughout the year.

The PALAOA CTD is located approximately 40km northeast of the ApRES location. Tidally modulated water flow velocities of 0.4–0.5 ms-1 were inferred at this site , with evidence of intense mixing below the northeastern part of the ice shelf . Tidal model simulations that align with observations at the Ekström Ice Shelf predict spring tide velocities of 0.2–0.3 ms-1 in the vicinity of the ApRES location. Given that the tidal energy is concentrated at the diurnal and semi-diurnal frequencies, this indicates tidal excursions of the order of 10kmd-1, suggesting that water masses from the PALAOA site may influence the ApRES location at timescales of days.

On horizontal scales that exceed a few tidal excursions, the diffusive nature of such tidal transports is expected to become less important, and the coherent background flow becomes more relevant. Inside ice shelf cavities, buoyancy forces resulting from water mass transformation due to basal melting may induce a cavity-wide overturning circulation . With typical flow velocities ranging from 0.1 to 0.2 ms-1, the advection timescale between the ice front and the approximately 140 km distant grounding line of the Ekström Ice Shelf is of the order of 8–16 d.

To investigate the impact of varying ocean properties on basal melt rates beneath the Ekström Ice Shelf, we employed the idealised ice-shelf plume model of , which has previously been used to describe larger-scale circulation beneath ice shelves. Assuming that circulation and mixing beneath the ice shelf are primarily driven by thermohaline processes, the model describes a buoyant meltwater-laden plume that rises along the sloping ice base. The plume expands through the entrainment of ambient ocean waters and the heat brought into the plume; as a result, it drives melting at the ice–ocean interface. Conceptually, the plume gains buoyancy because the meltwater input reduces its density compared to the salinity-stratified ambient ocean, while melt rates are parameterised as a function of the plume velocity and the difference between the plume temperature and local melting point based on a shear-driven turbulent heat flux formulation. Omitting the Coriolis effect, the system is parameterised along a one-dimensional flowline, described by four ordinary differential equations with prognostic variables for the plume thickness D, speed U, temperature T and salinity S with details of the formulation being given in . The model is steady in time, uniform in the across-flow direction and depth-integrated, leaving the along-track distance X as the only independent variable .

The Ekström Ice Shelf comprises a confined ice geometry along a quasi-one-dimensional flowline. The plume model approximates the averaged cavity circulation across the ice flow to provide an initial assessment of the dynamics of buoyant ISW that rises along the upward-sloping ice base. However, the three-dimensional circulation beneath the ice shelf is likely influenced by rotational effects. Consequently, the model results are only applicable to regions where the flow is constrained by topography . Further limitations of this approach will be addressed in the discussion. The plume dynamics are largely governed by the slope of the ice base and the density difference between the plume and the ambient ocean properties. The former is prescribed based on BedMachine and on a seismic profile running from the grounding line to the ice front of the Ekström Ice Shelf .

To investigate the impact of varying water mass properties on the cavity circulation and melt rates, we performed simulations employing different vertical profiles of ambient temperature and salinity. During late winter and spring, convection after sea-ice formation generates a well-mixed body of Winter Water (WW) that occupies the continental shelf . In late summer and autumn, stratified AASW enters the cavity, increasing the temperature and reducing the salinity (and consequently the density) in the upper portion of the water column below the ice shelf . Two profiles representing the seasonal extremes were constructed using a constant water mass end-member with a bottom temperature of -1.85°C and salinity of 34.4gkg-1, which resembles the deep part of the Sub-EIS-Obs CTD profiles that is assumed to be approximately representative for the year-round conditions in the lower part of the cavity. This end-member was linearly interpolated to the observed water masses at 150m, derived from the PALAOA CTD time series (and with temperature and salinity kept constant above to the surface), representing a simplified late winter/spring (September/October) WW extreme and a late summer/autumn (February/March) AASW extreme. These values align with the observed seasonality in the open ocean in front of the DML ice shelves and below the neighbouring Fimbul Ice Shelf .

The ApRES time series from 2020–2023 reveals a low melt rate, averaging 0.44±0.30ma-1 (mean ± standard deviation), with a seasonal melt pattern (Table , Figs.  and a). Basal melt rates are reduced to a minimum of 0.25±0.16ma-1 in summer (December, January, February; DJF; 2020–2023 average); they increase slightly to ∼0.4ma-1 in autumn (March, April, May; MAM) and during winter (June, July, August; JJA), and they reach their maximum in spring (September, October, November; SON) with an average of 0.69±0.30ma-1 (Table , Fig. ).

A variability on a monthly timescale is most pronounced when the highest melt rates occur in winter and spring. During this time of the year, the difference between the minimum and maximum melt rate within a 28 d period exceeds 1ma-1. In summer and autumn, the difference within the same time window is less than 0.3ma-1. The largest melt events that are observed from July/August to October/November occurred with intervals ranging from 2 to 4 weeks, with an average duration of 21 d. At the onset of these events, the 7 d averaged melt rate increased to 1ma-1 or more within several days. The strongest melt event occurred in September 2020, when the 7 d averaged melt rate increased from 0.21 to 1.83ma-1. After 2 weeks, the melt rate decreased again to 0.54ma-1, before the next melt event occurred. The seasonality was strongest in 2020 with, on average, 5 times higher melt rates in spring than in summer 2020/21 (Table ). In 2021 and 2022, we see a weaker seasonality with only 2 times higher melt rates in spring compared to summer. The trend of weaker seasonality from 2020 and 2022 is caused by lower melt rates in spring that decreased from 1.08±0.31ma-1 in 2020 to 0.54±0.34ma-1 in 2022.

The sea-ice growth in front of the Ekström Ice Shelf exhibits a distinct seasonal pattern, with the lowest growth rates occurring during the summer months and high rates in autumn and spring (Fig. b). In late summer and the beginning of autumn, when sea-ice concentration is at its lowest, the growth rate quickly increases, exceeding 2ma-1 and leading to a rapid increase in sea-ice concentration. When the sea-ice concentration reached a coverage of 90 % in April and May, the growth rate initially declines but increases again toward the end of winter. In October and November, sea-ice growth abruptly declines, reaching values close to zero by December and January. This decline in growth rate is followed by a decrease in sea-ice concentration with a delay of about 2 months.

The full time-series record of sea-ice growth and concentration is shown in Appendix Figs.  and . Similar to the melt rate time series, the high-resolution time series of the sea-ice growth shows an oscillatory variability on weekly timescales that is comparable to the observed basal-melt events. Although some of the melt events can be connected to a previous increase in sea-ice growth, other events in sea-ice growth occurred in autumn without an increase in the melt rate being measured. A cross-correlation analysis between sea-ice formation and melt rate, calculated for each season, revealed predominantly moderate (0.5–0.75) or low (0.25–0.5) correlation values for various lags of up to 26d. Particularly, there is no apparent agreement in 2022 and 2023 between the sea-ice growth and the melt rate (Fig. ).

The seasonalities of ocean temperature and salinity as observed from PALAOA CTD measurements 70m beneath the ice base near the ice shelf front are shown in Fig. c. The temperature exhibits a peak in February at -1.78°C, followed by a rapid decline in March and April (Fig. c). During winter and spring, the ocean temperatures reached a minimum of -1.90°C and rose again in summer. The salinity reached its lowest value of 33.8gkg-1 in February and March (Fig. c). Subsequently, the salinity continuously increased until September and reached its maximum value of 34.5gkg-1 between September and November. This maximum was followed by a slight decrease and a subsequent sharp decline in February. The potential density derived from the combination of temperature and salinity exhibits a similar pattern (Fig. d). The highest densities, which exceed the cavity mean, coincide with the enhanced melt rates observed between August and November. Outside of this period, the densities occasionally experience significant reductions, as shown by the lower quartile envelope. The full time-series record of PALAOA temperature, salinity and density is shown in Appendix Fig. .

The results of the plume model simulations show how the seasonality of varying water masses inside the ice shelf cavity may affect the melt rates below at the Ekström Ice Shelf (Fig. ). For the seasonal extremes representing autumn and spring, when densest WW is observed at the PALAOA CTD (Fig. b and c), a coherent plume ascends from the grounding line to the ice shelf front. This is evident from the smooth evolution of the plume temperature and velocities (Fig. d and e), with values exceeding 0.10ms-1 along the entire flow path. In this case, the simulated melt rates at the ApRES location are 1.0ma-1 (Fig. f). In contrast, when AASW is present inside the cavity in late summer and autumn, discontinuities in the plume temperature (e.g. approximately 19 and 102 km along the flow path) indicate that the ascending ISW detached and that a new plume is initiated locally. The reduced density difference between the ascending ISW and the ambient water results in a reduced plume velocity, averaging 0.06ms-1 (or 57 %), lower than that of the simulation representing the WW case. The decreased flow velocity of the ISW plume reduces the turbulent heat exchange at the ice–ocean interface, leading to a reduced melt rate along the entire flow path and to reduced melt rates of 0.3ma-1 at the ApRES location despite the local temperature increase.

The temperature–salinity diagram (Fig. g) compares the seasonal hydrography from the PALAOA site with the Sub-EIS-Obs CTD profiles, illustrating the relative density differences of different water masses inside the cavity. Water that interacts with the ice shelf inside the cavity will undergo a transformation along the meltwater mixing line with a constant ratio of cooling and freshening as it melts the glacier ice. The end-member temperature of this transformation is determined by the pressure-dependent local melting point, which is approximately -2.05°C at the depth of the ice base at the ApRES site.

For water masses with temperatures close to the surface freezing point, as observed in the deeper part of the Sub-EIS-Obs CTD profile, the associated density decrease that may give rise to the meltwater plume is relatively small (0.06kgm-3) compared to the seasonal density variations that are observed at the PALAOA site (>0.2kgm-3 based on the 7 d binned data). Therefore, a vigorous buoyant plume circulation can only develop when wintertime convection has eroded the stratification inside the cavity. Even the slight freshening observed at the PALAOA site in December and January (green dots) reduces the density in the upper part of the water column below that of the ascending ISW observed at the Sub-EIS-Obs CTD measurements. In this case, the ISW will not rise but detach from the ice base and mix with ambient water masses of equal density. Additional plume model simulations with an intermediate profile that resembles the Sub-EIS-Obs CTD at depth and transitions to the December/January properties observed at the PALAOA site confirm this behaviour, showing reduced melt rates of 0.6ma-1.

To further evaluate the impact of changes in plume buoyancy, we analyse the influence of ambient temperature and ocean velocity on the modulation of the melt rate, based on the three-equation formulation that is used for parameterising heat fluxes at the ice–ocean interface in the plume model. For instance, to achieve a melt rate of 0.24ma-1 that is observed during summer, a plume velocity of 0.015ms-1 is required when assuming a water temperature of -2°C (Fig. ), as observed at the ice base during the early summer of 2018/19 . Higher melt rates, as are observed during late winter and spring, can be attributed to an increase in plume temperature and/or flow velocity. To obtain the average melt rate in spring of 0.71ma-1, a 0.2°C higher plume temperature would be necessary to maintain a constant plume velocity. Conversely, an increase in plume velocity to 0.04ms-1 with a constant plume temperature of -2°C can also achieve the same melt rate. Both the plume temperature of -1.8°C and the velocities of 0.04ma-1 appear to be within a plausible range. However, for a maximum observed melt rate of 1.83ma-1, a higher temperature of up to -1.3°C would be required to maintain a constant plume velocity of 0.015ms-1. Such a high plume temperature is not anticipated at the Ekström Ice Shelf, which has the highest weekly median temperatures in the PALAOA CTD around -1.7°C, during a period of the year when the observed melt rates are lowest. If we assume that an increase in temperature alone was not the sole cause of the high melt rate, then the flow velocity of the plume must have also increased. At a constant temperature of -2°C, an increase in the flow velocity to 0.11ms-1 could have also resulted in a melt rate of 1.83ma-1, which still falls within a plausible range. This analysis suggests that the increase in melt rates in winter and spring cannot be attributed solely by warmer water, but rather to higher plume velocities.