2.1. Satellite method

To map the spatial distribution of ice-shelf melt using satellite data, studies use repeat observations of surface elevation, which are converted into a change in thickness by assuming that the ice shelf is freely floating (in hydrostatic equilibrium). This method can be applied using repeat Digital Elevation Models (DEMs) derived from stereo satellite imagery or SAR interferometry (e.g. Shean and others, Reference Shean, Joughin, Dutrieux, Smith and Berthier2019; Bevan and others, Reference Bevan, Luckman, Benn, Adusumilli and Crawford2021). This method can measure change in surface elevation at high spatial resolution (tens of metres) but is expensive to apply over large areas. Basal melt has more commonly been measured using surface elevation observations derived from satellite altimetry missions such as ERS-1, ERS-2, Envisat and Cryosat (e.g. Rignot and others, Reference Rignot, Jacobs, Mouginot and Scheuchl2013; Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020). Repeat-track satellite altimetry can produce circum-Antarctic maps of surface elevation change, although the spatial resolution is limited by the distance between tracks.

The conversion from surface elevation change to basal melt rate is not straightforward, and requires multiple supporting data sources. The observed surface elevation change is first corrected for change in ocean surface height from tides and varying atmospheric pressure, and then the basal melt rate can be calculated using a continuity equation of the form:

(1)$${dh\over dt} = {( \rho_{w}-\rho_{i}) \over \rho_{w}} \left({M_{s}\over \rho_{i}}-\nabla \cdot ( H_{i} {\bf v}) - w_{b} \right) + {dh_{air}\over dt} ,\; $$

where h is the ice-shelf surface height relative to the height of the ocean surface, ρ _w and ρ _i are the densities of seawater and ice, M _s is the surface mass balance (typically derived from climate reanalysis), and w _b is the basal melt rate. $\nabla \cdot ( H_{i} {\bf v})$ combines terms for ice-shelf divergence ($H_{i} \nabla \cdot {\bf v}$) and advection of ice (${\bf v} \cdot \nabla H_{i}$), and is calculated from the velocity at the ice surface (v) and the effective ice thickness (H _i), which is adjusted for the firn air content (h _air, derived from firn densification modelling). If surface elevation measurements are densely-spaced, a Lagrangian reference frame can be used, allowing the advection term to be dropped (Moholdt and others, Reference Moholdt, Padman and Fricker2014). Where the Lagrangian method cannot be applied, the along-flow advection of features such as rifts tends to create artefacts in the data (Rignot and others, Reference Rignot, Jacobs, Mouginot and Scheuchl2013; Moholdt and others, Reference Moholdt, Padman and Fricker2014). Other processes such as salinity changes in ice-shelf cavities and spatial rearrangement of ocean currents can also affect ice-shelf surface elevation, but are likely a lower order influence and are not sufficiently well-known to be corrected for.

The biggest advantage of the satellite method is its wide spatial coverage, with datasets covering all Antarctic ice shelves (e.g. Rignot and others, Reference Rignot, Jacobs, Mouginot and Scheuchl2013; Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020). It can be used to identify key spatial patterns of ice-shelf melt, such as the elevated melt rates near grounding zones and calving fronts of large, cold cavity ice shelves (e.g. Fig. 1a). Where high-resolution DEMs are used, melt can be mapped on even smaller spatial scales. For example, Shean and others (Reference Shean, Joughin, Dutrieux, Smith and Berthier2019) used this method to identify differences in melt between the troughs and keels of basal channels on Pine Island Glacier. However, uncertainties in the derived melt rate can be significant because many of the data sources needed to convert surface elevation change to basal melt are poorly constrained. The method also relies on the assumption that the shelf is in hydrostatic equilibrium. This condition is typically broken around basal channels, crevasses and near the grounding line (Fricker and Padman, Reference Fricker and Padman2006), which is also a region of particular interest as it often experiences the highest melt rates.

Fig. 1. Melt rates on Filchner-Ronne Ice Shelf, from (a) satellite data (Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020) with point measurements from ApRES (Vaňková and Nicholls, Reference Vaňková and Nicholls2022) and (b) the Whole Antarctic Ocean Model (WAOM v1.0, Richter and others, Reference Richter, Gwyther, Galton-Fenzi and Naughten2022). The model captures elevated melt rates at the grounding line and calving front, but may underestimate the extent of refreezing in the centre of the ice shelf as it does not contain frazil dynamics known to be important during freezing (Galton-Fenzi and others, Reference Galton-Fenzi, Hunter, Coleman, Marsland and Warner2012). However, in situ measurements suggest that the satellite method overestimates refreezing on the western side of the shelf.

Using multiple repeat passes of a satellite can also allow a timeseries of melt rates to be developed. Recent studies have used four European Space Agency radar altimeter satellite missions (ERS-1, ERS-2, Envisat and Cryosat) to build a quarterly timeseries of elevation change on Antarctic ice shelves from 1994–2018 (Paolo and others, Reference Paolo, Fricker and Padman2015; Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020). The results have demonstrated a relationship between ice-shelf height anomalies in the Amundsen Sea sector and the El Niño-Southern Oscillation which causes variability in both ocean and atmosphere in the region (Paolo and others, Reference Paolo2018). However, converting timeseries of surface elevation change into timeseries of basal melt is challenging. The method requires multiple measurements of ice velocity, which often do not cover the necessary time period (Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020), and corrections for snowfall and firn compaction derived from climate reanalysis data have high uncertainties. This creates an ongoing need for validation of satellite-derived melt timeseries.

2.2. Field methods

Ice-shelf melt rates can be measured more directly using field-based techniques, including range finding from under-ice moorings (e.g. Stewart and others, Reference Stewart, Christoffersen, Nicholls, Williams and Dowdeswell2019; Rosevear and others, Reference Rosevear, Galton-Fenzi and Stevens2022a) and surface radar instruments (e.g. Jenkins and others, Reference Jenkins, Corr, Nicholls, Stewart and Doake2006; Vaňková and Nicholls, Reference Vaňková and Nicholls2022; Zeising and others, Reference Zeising2022). In this paper we focus on a single instrument/method: the Autonomous phase-sensitive Radio Echo Sounder (ApRES, Nicholls and others, Reference Nicholls2015), which is becoming the most common way of measuring melt in situ due to its low cost and ease of deployment. The ApRES is designed to run autonomously in the field for a period of one or more years. It recurrently emits a burst of chirps, typically every few hours, each of which is used to produce a record of amplitude and phase versus depth. Combining these records together into a timeseries, we can track internal layers and use their change in phase over time to determine their motion relative to the radar unit. By tracking the motion of internal layers in the ice as well as the base of the ice shelf, the method allows us to measure snow/firn compaction and internal thickness change. These can then be removed from the total thickness change of the ice shelf to produce a measurement of ocean-driven melt without relying on additional supporting datasets. The timeseries produced has up to millimetre-scale precision, depending on the strength of the signal and the nature of the ice base.

Possibly the greatest strength of the ApRES method is its ability to measure changes in melt rate over a variety of timescales from hourly to interannual. Given ideal conditions, the method can measure variability in melt on timescales as short as the M2 (12.4 hour) tidal component (Vaňková and others, Reference Vaňková, Nicholls, Corr, Makinson and Brennan2020a). A further advantage is that by measuring both total and internal thickness change components independently, the method can be applied in areas such as the grounding zone where the hydrostatic assumption used in satellite methods breaks down. However, the instrument performs best when located in an area with a low rate of vertical shear in ice velocity and a smooth, flat ice base. Uncertainties can become large if the instrument is placed in an area of complex basal topography, where off-nadir signals complicate interpretation of the basal reflector (e.g. Vaňková and others, Reference Vaňková, Cook, Winberry, Nicholls and Galton-Fenzi2021a). Uncertainties can also increase if the vertical strain profile is non-linear, particularly if this non-linearity is time-dependent such as under tidal flexure (e.g. Jenkins and others, Reference Jenkins, Corr, Nicholls, Stewart and Doake2006; Vaňková and others, Reference Vaňková, Nicholls, Corr, Makinson and Brennan2020a). Unlike range-finding methods, the ApRES is only able to accurately measure rates of melt and not refreezing. In areas with a thick layer of basal marine ice, increased absorption of radar wave energy may make the basal reflector difficult to detect. Where refreezing is intermittent, changes in impedance contrast at the ice base during periods of freezing cause a phase shift which interferes with the measurement of thickness change. Despite this, intermittent freezing periods can be identified and mean freezing rate inferred using amplitude and phase change measurements and their variation as a function of ApRES frequency (Vaňková and others, Reference Vaňková, Nicholls and Corr2021b).

As a field-based instrument, the cost of field logistics limits the spatial sampling that can be achieved with ApRES. Similarly, the need for maintenance visits to keep an instrument running for more than one to two years has limited the length of the timeseries collected, with the longest installation to date being only a few years compared to the 25-year satellite record of melt rates achieved by Adusumilli and others (Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020). However, where data are available they are a powerful tool for validating satellite-derived measurements of melt, and for testing numerical simulations of melt over a range of timescales.

3.1. Utilising spatial patterns of melt

The extensive spatial coverage of melt rates measured using satellite data makes them a useful tool for evaluating models of ice-shelf melt. Observed spatial patterns of melt can be informative in assessing an ocean model's ability to simulate realistic water mass properties and circulation beneath ice shelves (e.g. Fig. 1,2). Examples of this include a spatial comparison between simulated and observed melt rates by Pelletier and others (Reference Pelletier2022), which used low simulated melt rates in the Bellingshausen and Amundsen Seas to infer issues with the applied ice-shelf geometry, while Comeau and others (Reference Comeau2022) used spatial patterns of melt to assess model success in accurately predicting intrusions of CDW onto the continental shelf. The spatial patterns of melt observed on a shelf can also indicate important processes that should be included in ice-shelf cavity models. For example, Nakayama and others (Reference Nakayama, Cai and Seroussi2021a) showed that including subglacial discharge in an ice-shelf cavity model of Pine Island Glacier is important for capturing high melt rates observed near the grounding line. Ice shelf melt rates are only one tool for testing model performance, and other observations such as ship-based and seal-tagged CTD measurements, moorings and satellite sea-ice concentration estimates are critical tools for testing ocean model performance more broadly. These oceanographic observations have been the basis for recent efforts in data assimilation to optimise ocean model performance (e.g. Nakayama and others, Reference Nakayama2021c), which in future could potentially also include ice shelf melt as a parameter.

Fig. 2. Melt rates on Totten Glacier Ice Shelf, from (a) satellite data (Adusumilli and others, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020) and ApRES (Vaňková and others, Reference Vaňková, Cook, Winberry, Nicholls and Galton-Fenzi2021a) and (b) the Whole Antarctic Ocean Model (WAOM v1.0, Richter and others, Reference Richter, Gwyther, Galton-Fenzi and Naughten2022). The model does not capture elevated melt rates on Totten Glacier Ice Shelf, most likely because of underestimation of CDW crossing the continental shelf, noting that WAOM was not specifically ‘tuned’ for any one region, unlike focussed regional modelling studies which show better agreement (e.g. Gwyther and others, Reference Gwyther, Galton-Fenzi, Hunter and Roberts2014, Reference Gwyther, O'Kane, Galton-Fenzi, Monselesan and Greenbaum2018).

Satellite-derived maps of ice-shelf melt can also be a powerful tool for effectively targeting field campaigns toward particular melt processes, or for avoiding locations where the equipment might fail, such as areas with basal marine ice, which quickly attenuates ApRES signal at depth. Conversely, field deployments can be used to validate and potentially improve spatial maps of melt. In situ measurements would be particularly valuable for validation where different satellite estimates diverge, or where uncertainties in the satellite method are high. Particular targets include regions where the hydrostatic assumption of the satellite method breaks down (principally around the grounding line and above basal channels), or where the input datasets required for the satellite method have high uncertainties or biases, for example due to known issues in modelling surface mass balance on ice shelves surrounded by complex and steep topography (Lenaerts and others, Reference Lenaerts, Vizcaino, Fyke, Van Kampenhout and van den Broeke2016).

The use of field measurements for validating satellite melt products has been very limited to date, leaving satellite datasets largely untested. A recent study on Filchner-Ronne Ice Shelf found that the satellite method overestimated refreezing rates on the west of the shelf, indicating that uncertainties in the satellite data were under-reported (Fig. 1a, Vaňková and Nicholls (Reference Vaňková and Nicholls2022)). Another study on the same shelf using a non-autonomous (repeat visit) application of ApRES found that agreement between in situ and satellite-derived melt rates could be improved by careful selection of the velocity dataset used to derive vertical strain rates in the satellite method (Zeising and others, Reference Zeising2022). This illustrates how field data could be used in the future to improve satellite melt rate data, by guiding the selection of input datasets.

3.2. Utilising temporal variability in melt

Measuring the change in ice-shelf melt over time as well as its spatial variability can allow us to assess the importance of time-dependent processes such as seasonal changes in ocean properties, climate forcing variability and intermittent transport of CDW into ice-shelf cavities. ApRES measurements of ice-shelf melt are particularly useful for this type of analysis, due to their high temporal resolution. Deployments of ApRES on Pine Island Glacier (Davis and others, Reference Davis2018), Nivlisen Ice Shelf (Lindbäck and others, Reference Lindbäck2019) and Roi Baudouin Ice Shelf (Sun and others, Reference Sun2019) have been instrumental in identifying timescales and causes of melt variability, including diurnal, weekly and seasonal melt rate drivers. As with satellite data, field-based measurements of melt can be a useful tool for evaluating ice-shelf ocean cavity models (e.g. Bull and others, Reference Bull2021). For example, the ApRES deployment on Pine Island Glacier has been used to test a high-resolution ocean cavity model, confirming that the model reproduced the observed 7–10 day fluctuations in melt rate successfully (Nakayama and others, Reference Nakayama2019). However, there still remains further potential for using field observations to evaluate model behaviour over subannual timescales.

Satellite-derived timeseries of ice-shelf melt also have potential for studying interannual variations in melt rate (e.g. Adusumilli and others, Reference Adusumilli2018, Reference Adusumilli, Fricker, Medley, Padman and Siegfried2020). Nakayama and others (Reference Nakayama2021b) compared modelled and satellite-derived melt rates for Totten Glacier, finding a strong agreement in interannual variability caused by intrusions of warm modified CDW into the ice shelf cavity. However, the high uncertainties in satellite-derived melt rates mean that the observed variability can be unreliable, particularly in regions of low melt or refreezing. A recent study comparing satellite-derived timeseries of melt with data from field observations on Filchner-Ronne Ice Shelf found poor agreement in both the phase and magnitude of temporal variability, with the satellite method significantly overestimating variability on both seasonal and interannual timescales (Fig. 3, Vaňková and Nicholls (Reference Vaňková and Nicholls2022)). While further testing and development of the satellite-derived timeseries is clearly required, the longer melt record provided by satellite instrumentation (up to 25 years at present) has the potential to provide important context for evaluating the importance of short-term variability relative to long-term trends.

Fig. 3. Melt rate timeseries from three of the named sites on Filchner-Ronne Ice Shelf (see Fig 1 for locations). In situ data (red) are from a sub-ice shelf mooring pre-2015 and ApRES post-2015; satellite data shown quarterly (grey) and 1-year low-pass filtered (blue, shading shows reported uncertainty of 0.4 ma⁻¹). The satellite method generally overpredicts variability in melt in these locations.