Introduction

Five decades of radioglaciology (the use of radio waves to investigate ice masses of all types) since the first data were published have seen a progression of instruments and platforms, as well as data processing and analysis approaches applied to a growing data archive (e.g. Stern, Reference Stern1930; Steenson, Reference Steenson1951; Robin, Reference Robin1975; Gogineni and others, Reference Gogineni, Chuah, Allen, Jezek and Moore1998; Dowdeswell and Evans, Reference Dowdeswell and Evans2004; Allen, Reference Allen2008; Turchetti and others, Reference Turchetti, Dean, Naylor and Siegert2008). Radar-sounding (also known as ice-penetrating radar) data have been used to observe ice thickness, basal topography and englacial layers across Antarctica and Greenland, as well as many ice caps and glaciers. Major data-collection efforts started in the late 1960s and early 1970s, including a collaboration between the Technical University of Denmark, Scott Polar Research Institute, and National Science Foundation (TUD-SPRI-NSF) to map the bed of Antarctica. Other early surveys were also led by Russia, Germany, Iceland, Italy, China, and Canada (among others) across Antarctica and Greenland, as well as Iceland, Arctic Ice Caps, and mountain glaciers (e.g. Drewry, Reference Drewry1983; Bingham and Siegert, Reference Bingham and Siegert2007; Björnsson, Reference Björnsson and Pálsson2020; Popov, Reference Popov2020). Planetary radar sounders have also been used, or are planned, to observe the subsurface and near-surface conditions of Mars, Earth's moon, comets and the icy moons of Jupiter (e.g. Seu and others, Reference Seu2007; Jordan and others, Reference Jordan2009; Kofman and others, Reference Kofman, Orosei and Pettinelli2010; Bruzzone and others, Reference Bruzzone2013; Kofman and others, Reference Kofman2015; Patterson and others, Reference Patterson2017; Blankenship and others, Reference Blankenship2018). Fully exploiting the valuable information from these data, such as ice-sheet bed topography, the distribution of subglacial water, the spatial variation of basal melt, the transition between frozen and thawed bed conditions, englacial temperature, histories of accumulation, flow, and the distribution of age in ice masses remains an active area of international research. In this review paper, and the thematic issue of the Annals of Glaciology on ‘Five decades of radioglaciology’ to which it belongs, we present recent advances in the field in the context of their history and future prospects. We include papers published in this issue, topics presented at an International Glaciological Society Symposium on the same theme hosted at Stanford University during the summer of 2019, and work added to the published literature since the last thematic Symposium and Annals issue focused on radioglaciology in 2014.

Data

The data collected by radar surveys in the last five decades have transformed our appreciation of glacier and ice-sheet beds and how ice flows over them. Prior to this era, such information was gained from seismic data, taking orders of magnitude longer to acquire. Early radar surveys witnessed significant improvements in survey design, instrument capability (e.g. the Technical University of Denmark System), platforms (e.g. the US Hercules LC-130) and coastal airstrips, leading to systematic surveys of the Greenland and Antarcticice sheets (Sorge, Reference Sorge1933; Robin, Reference Robin1958; Gudmandsen, Reference Gudmandsen1975; Drewry, Reference Drewry1983). In the case of Antarctica, the TUD-SPRI-NSF collaboration collected over 400 000 line-km of data during the 1970s and, in some regions, these data provide the only measurements ever taken. By the early 1980s, those first long-range airborne radar surveys had ended, giving way to regional studies collected by, for example, Russian and German programs and the US Support Office for Aerogeophysical Research (SOAR) in Antarctica (Blankenship and others, Reference Blankenship1993; Behrendt and others, Reference Behrendt1994; Bell and others, Reference Bell1998; Hempel and others, Reference Hempel, Thyssen, Gundestrup, Clausen and Miller2000; Masolov and others, Reference Masolov, Popov, Lukin, Sheremetyev and Popkov2006; Dean and others, Reference Dean, Naylor, Turchetti and Siegert2008; Turchetti and others, Reference Turchetti, Dean, Naylor and Siegert2008). Other examples include surveys of glaciers and ice caps in Iceland, Alpine glaciers, Svalbard and the Russian and Canadian Arctic (e.g. Dowdeswell and others, Reference Dowdeswell1986, Reference Dowdeswell2002, Reference Dowdeswell, Benham, Gorman, Burgess and Sharp2004; Björnsson and others, Reference Björnsson1996; Fürst and others, Reference Fürst2018; Pritchard and others, Reference Pritchard, King, McCarthy and Mayer2020).

In the early 2000s, the Bedmap Consortium produced a new compilation of radar data from Antarctica for which the TUD-NSF-SPRI data still formed by far the most significant contribution, with dozens of other regional-scale surveys that form a patchwork coverage of parts of the ice sheet while other regions remained completely free of data (Lythe and Vaughan, Reference Lythe and Vaughan2001). Bedmap2 followed a decade later, including additional regional surveys as well as long- and medium-range airborne studies returned in 2008 by the US–UK–Australia–China–French ICECAP project and NASA's Operation IceBridge (OIB) (Holt and others, Reference Holt2006; Vaughan and others, Reference Vaughan2006; Bell and others, Reference Bell2011; Young and others, Reference Young2011; Ross and others, Reference Ross2012; Fretwell and others, Reference Fretwell2013). However, several regions remained free of data (Pritchard, Reference Pritchard2014). Other compilations are now due that will incorporate new data that have been acquired to fill many of Bedmap2's gaps, including, for example, across Marie Byrd Land, West Antarctica, the Recovery Basin/South Pole, the Dome F region and Princess Elisabeth Land, as well as newly remastered TUD-NSF-SPRI film data and updated thickness measurements for the Ross Ice Shelf (Tang and others, Reference Tang, Guo, Sun, Wang and Cui2016; Young and others, Reference Young, Schroeder, Blankenship, Kempf and Quartini2016; Popov, Reference Popov2017; Humbert and others, Reference Humbert, Steinhage, Helm, Beyer and Kleiner2018; Jordan and others, Reference Jordan2018a; Karlsson and others, Reference Karlsson2018; Morlighem and others, Reference Morlighem2019; Paxman and others, Reference Paxman2019; Schroeder and others, Reference Schroeder2019; Tinto and others, Reference Tinto2019). Compared to Antarctica, surveys of Greenland starting in the 1990s by the University of Kansas as part of NASA's Program for Arctic Regional Climate Assessment (PARCA) and later OIB have led to relatively abundant and mutually interpretable observations of the ice-sheet bed and englacial properties (Bamber and others, Reference Bamber2013; Gogineni and others, Reference Gogineni2014; MacGregor and others, Reference MacGregor2015a; Morlighem and others, Reference Morlighem2017).

In addition to the collection of radar sounding profiles, interpolation is a critical component of producing bed topography maps. Previous approaches focused on grid interpolation techniques such as spline interpolation or kriging (e.g. Fretwell and others, Reference Fretwell2013). However, in many regions, this gridded topography falls short of capturing topography at the scales most critical for resolving ice-flow processes (Durand and others, Reference Durand, Gagliardini, Favier, Zwinger and Le Meur2011; King and others, Reference King, Pritchard and Smith2016; Bingham and others, Reference Bingham2017; Kyrke-Smith and others, Reference Kyrke-Smith, Gudmundsson and Farrell2018). For this reason, other approaches, such as mass-conservation modeling or geostatistical approaches, which can provide multiple observation-consistent realizations, provide improved interpolations of bed topography (e.g. Rasmussen, Reference Rasmussen1988; Warner and Budd, Reference Warner and Budd2000; Goff and others, Reference Goff, Powell, Young and Blankenship2014; Morlighem and others, Reference Morlighem2017; MacKie and others, Reference MacKie and Schroeder2019).

Future surveys are unlikely to resemble those conducted previously since ice-sheet models require that data are collected with strategies optimized for their purpose, including flowlines for process interpretation, ground-based time-series for local process monitoring, and repeat flights (Kingslake and others, Reference Kingslake2014; Nicholls and others, Reference Nicholls2015; Chu and others, Reference Chu2016; Khazendar and others, Reference Khazendar2016; Holschuh and others, Reference Holschuh, Parizek, Alley and Anandakrishnan2017; Davies and others, Reference Davies2018; Schroeder and others, Reference Schroeder, Hilger, Paden, Young and Corr2018; Young and others, Reference Young2018; Bartlett and others, Reference Bartlett2020). These process- and site-specific surveys can also take advantage of systems with wider bandwidths and larger antenna arrays that provide enhanced performance, but with more limited range (e.g. Rodriguez-Morales and others, Reference Rodriguez-Morales2013; Kjær and others, Reference Kjær2018). Ultimately, new platforms, such as rovers, drones and satellites stand to transform the way radar-sounding observations are made (Jezek and others, Reference Jezek2006; Koh and others, Reference Koh, Lever, Arcone, Marshall and Ray2010; Arcone and others, Reference Arcone2016; Freeman and others, Reference Freeman, Pi and Heggy2017; Dall and others, Reference Dall, Corr, Walker, Rommen and Lin2018; Carrer and others, Reference Carrer, Gerekos and Bruzzone2018; Gogineni and others, Reference Gogineni2018; Culberg and Schroeder, Reference Culberg and Schroeder2019; Arnold and others, Reference Arnold, Leuschen, Paden, Hale and Keshmiri2020).

Systems

Early radar sounding systems spanned a range of frequency, bandwidth, power and array configurations including both short mono-pulse and chirped-waveform systems (Allen, Reference Allen2008; Gärtner-Roer and others, Reference Gärtner-Roer2014). However, until the 1990s (and the availability of faster and lower-cost electronics) the data recorded remained ‘incoherent’, limiting the azimuth resolution and processing gain below that achievable with phase-coherent stacking and Synthetic Aperture Radar (SAR) processing (Musil and Doake, Reference Musil and Doake1987; Hamran and Aarholt, Reference Hamran and Aarholt1993; Leuschen and others, Reference Leuschen, Gogineni and Tammana2000; Legarsky and others, Reference Legarsky, Gogineni and Akins2001; Hélière and others, Reference Hélière, Lin, Corr and Vaughan2007; Peters and others, Reference Peters2007). For stationary ground-based systems, a similar gain in the achievable post-processing signal tonoise ratio (SNR) and range-estimate precision has been achieved by coherent ‘phase-sensitive’ frequency-modulated continuous wave (FMCW) radars (Nicholls and others, Reference Nicholls2015).

Just as coherent radar sounders enabled improved along-track resolution and processing gain, the development of systems with multi-channel cross-track arrays improved cross-track resolution, processing gain, clutter discrimination and swath mapping (Gogineni and others, Reference Gogineni, Chuah, Allen, Jezek and Moore1998; Paden and others, Reference Paden, Akins, Dunson, Allen and Gogineni2010; Wu and others, Reference Wu2011; Rodriguez-Morales and others, Reference Rodriguez-Morales2013; Castelletti and others, Reference Castelletti2017; Holschuh and others, Reference Holschuh, Christianson, Paden, Alley and Anandakrishnan2020; Scanlan and others, Reference Scanlan, Rutishauser, Young and Blankenship2020). This is also true for ground-based multiple input, multipleoutputimplementations of the ‘phase-sensitive’ FMCW radars mentioned above (Young and others, Reference Young2018). While these multi-channel sounders do achieve some diversity in viewing angle and englacial propagation, true bistatic observations and tomographic inversions can be exploited to provide much richer constraints on subsurface properties including, for example, using commercial pulsed ground-penetrating radar (GPR) systems in common mid-pointor borehole configurations to achieve wider (though coherence-limited) offsets (e.g. Kofman and others, Reference Kofman2015; Holschuhand others, Reference Holschuh, Christianson, Anandakrishnan, Alley and Jacobel2016; Patterson and others, Reference Patterson2017; Church and others, Reference Church2019).

The evolution of distinct radar sounding systems has resulted in a diversity of frequencies, spanning HF (3–30 MHz), VHF (30–300 MHz), UHF (300 MHz–3 GHz) and higher frequency bands (Gudmandsen, Reference Gudmandsen1975; Paden and others, Reference Paden2005; Hélière and others, Reference Hélière, Lin, Corr and Vaughan2007; Peters and others, Reference Peters2007; Allen, Reference Allen2008; Shi and others, Reference Shi2010; Hindmarsh and others, Reference Hindmarsh2011; Rignot and others, Reference Rignot, Mouginot, Larsen, Gim and Kirchner2013; Rodriguez-Morales and others, Reference Rodriguez-Morales2013; Dall and others, Reference Dall, Corr, Walker, Rommen and Lin2018; Yan and others, Reference Yan, Gogineni and O'Neill2018). Although, this diversity can make it challenging to compare or combine distinct datasets, it also offers the opportunity to probe the radio-frequency responseof the ice sheet to constrain conditions and processes with greater fidelity (e.g. Carrer and Bruzzone, Reference Carrer and Bruzzone2017; Winter and others, Reference Winter2017).

In addition to systems capable of recording amplitude, phase and channel information, radar sounder development has also included systems that record multiple polarizations (e.g. Vaughan and others, Reference Vaughan2006; Dall and others, Reference Dall2010). These systems allow for the analysis of crystal-fabric orientation from polarization information (Doake and others, Reference Doake, Corr and Jenkins2002; Fujita and others, Reference Fujita, Matsuoka, Maeno and Furukawa2003; Matsuoka and others, Reference Matsuoka2003; Eisen and others, Reference Eisen, Hamann, Kipfstuhl, Steinhage and Wilhelms2007; Drews and others, Reference Drews2012; Li and others, Reference Li2018; Wang and others, Reference Wang2018; Jordan and others, Reference Jordan, Schroeder, Castelletti, Li and Dall2019). This information can be used to constrain the depth distribution of the crystal orientation fabric along survey lines, enabling the investigation of processes occurring in ice masses, comparison to ice-dynamic models, and interpretation of particle-astrophysical observations (e.g. Jordan and others, Reference Jordan, Schroeder, Castelletti, Li and Dall2019, Reference Jordan, Schroeder, Elsworth and Siegfried2020a,b; Shoemaker and others, Reference Shoemaker2020).

Technical advances in available hardware have also allowed the development of stationary systems designed for long-term (several months to years) autonomous operation with repeated observations over cycles ranging from minutes to days, targeting the temporal evolution of a particular site (Nicholls and others, Reference Nicholls2015; Kendrick and others, Reference Kendrick2018; Mingo and others, Reference Mingo, Flowers, Crawford, Mueller and Bigelow2020; Vankova and others, Reference Vankova2020). To further address the power demands of generating an active radar signal (particularly in the extreme resource constraints of planetary missions) passive radar sounding is also being developed as a new radioglaciological technique to exploit Jovian radio noise, or that from the Sun, as sources for radio echo detection, with the promise to enable pervasive monitoring of subsurface conditions by low-cost, low-power sensor networks (Romero-Wolf and others, Reference Romero-Wolf2015, Reference Romero-Wolf2016; Schroeder and others, Reference Schroeder2016b; Peters and others, Reference Peters, Schroeder, Castelletti, Haynes and Romero-Wolf2018).

Processing

Processing radar-sounding data turns low-SNR, low-resolution, high-clutter raw data into usable radargrams. With the exception of a subset of short-pulse systems such as commercial GPRs and some legacy sounders still in use today nearly all radar sounder processing begins with pulse-compression of a chirped waveform using some windowing function for range-sidelobe suppression, some amount of on-board pre-summing to increase SNR and moderate data-rates, and filtering (e.g. Peters and others, Reference Peters2007; Booth and others, Reference Booth, Clark and Murray2010; Lilien and others, Reference Lilien, Hills, Driscol, Jacobel and Christianson2020; Wang and others, Reference Wang2020). For coherent radar-sounding data, along-track SAR focusing is also nearly ubiquitous to improve the SNR, signal to clutter ratio and azimuth resolution (Legarsky and others, Reference Legarsky, Gogineni and Akins2001; Hélière and others, Reference Hélière, Lin, Corr and Vaughan2007; Peters and others, Reference Peters2007). Additionally, azimuth processing that evaluates along-track coherence, multiple apertures, large coherent apertures, layer-specific phase histories, or squinted processing, enhance layer resolution or provide information about the scattering function and fine-scale geometry of the bed (e.g. Oswald and Gogineni, Reference Oswald and Gogineni2008; Schroeder and others, Reference Schroeder, Blankenship, Raney and Grima2014a; Heister and Scheiber, Reference Heister and Scheiber2018; Castelletti and others, Reference Castelletti, Schroeder, Mantelli and Hilger2019; Ferro, Reference Ferro2019). For multi-channel sounders, cross-track processing can considerably increase the level of resolution, with large benefits for tomographic swath imaging of the ice bottom and internal structure, in particular of irregular disturbances of basal ice, such as folds or entrained matter (e.g. Paden and others, Reference Paden, Akins, Dunson, Allen and Gogineni2010; Wu and others, Reference Wu2011; Rodriguez-Morales and others, Reference Rodriguez-Morales2013; Castelletti and others, Reference Castelletti2017; Young and others, Reference Young2018).

In addition to the instantaneous or single-survey coherence required for focusing and array processing, modern high-stability and low-noise systems make it feasible to perform repeat-pass interferometric analysis on sounding data from ground-based platforms (Kingslake and others, Reference Kingslake2014; Nicholls and others, Reference Nicholls2015). While point-based observations of phase changes over time periods, ranging from months to years, are now widespread, for example, to deduce basal melt rates of ice shelves and vertical velocities in ice sheets, its spatial application to large airborne surveys is relatively recent and, as yet, rarely applied (e.g. Corr and others, Reference Corr, Jenkins, Nicholls and Doake2002; Castelletti and Schroeder, Reference Castelletti and Schroeder2017; Stewart and others, Reference Stewart, Christoffersen, Nicholls, Williams and Dowdeswell2019).

Another critical area of innovation in radioglaciological data processing and analysis is automatic methods for radargram image interpretation. These include algorithms for layer tracking, bed and surface mapping and basal feature categorization (Sime and others, Reference Sime, Hindmarsh and Corr2011; Crandall and others, Reference Crandall, Fox and Paden2012; Ferro and Bruzzone, Reference Ferro and Bruzzone2012; Ilisei and Bruzzone, Reference Ilisei and Bruzzone2015; Panton and Karlsson, Reference Panton and Karlsson2015; Carrer and Bruzzone, Reference Carrer and Bruzzone2016; Rahnemoonfar and others, Reference Rahnemoonfar, Fox, Yari and Paden2017; Berger and others, Reference Berger2018; Donini and others, Reference Donini, Thakur, Bovolo and Bruzzone2019). Success of these approaches is a prerequisite to be able to cope efficiently with the data volume of future surveys and effectively exploit their information content.

Ice sheet and glacier bed conditions

Five decades of radioglaciology have produced a diverse array of information pertaining to subglacial conditions. The vast majority of surveys have been motivated by the primary imperative of locating the bed reflector either to estimate the total volume and sea-level potential of the major ice sheets or to map basal topography (e.g. Bailey and others, Reference Bailey, Evans and Robin1964; Gudmandsen, Reference Gudmandsen1969; Bamber and others, Reference Bamber2013; Fretwell and others, Reference Fretwell2013). In the last two decades, the emphasis has expanded to the investigation of the geometric, thermal and material properties of the basal interface, by using the sounder-appropriate radar equation to solve for either basal reflectivity or echo character (Peters and others, Reference Peters, Blankenship and Morse2005; Oswald and Gogineni, Reference Oswald and Gogineni2008; Schroeder and others, Reference Schroeder, Blankenship and Young2013; Grima and others, Reference Grima, Schroeder, Blankenship and Young2014b; Haynes and others, Reference Haynes, Chapin and Schroeder2018b; Haynes, Reference Haynes2020).

Radar sounding data encode a range of information about the roughness of the basal interface. The most common glaciological definition of roughness is the extent to which terrain varies vertically over a given horizontal distance (Rippin and others, Reference Rippin2014). As mapped across a number of regions of Antarctica and Greenland, roughness variations at the multi-kilometer scale inform us about present and past ice-stream and ice-stream tributary locations (Siegert and others, Reference Siegert2004; Bingham and Siegert, Reference Bingham and Siegert2007, Reference Bingham and Siegert2009; Rippin and others, Reference Rippin2014; Frank and others, Reference Franke2020). Additionally, basal roughness at the wavelength-scale can affect the character of the reflected echo including its specularity (or spread in Doppler), waveform abruptness, statistical distribution of echo amplitudes, as well as the radar-derived topography itself (Goff and others, Reference Goff, Powell, Young and Blankenship2014; Grima and others, Reference Grima, Blankenship, Young and Schroeder2014a; Rippin and others, Reference Rippin2014; Schroeder and others, Reference Schroeder, Blankenship, Raney and Grima2014a; Jordan and others, Reference Jordan2017; Heister and Scheiber, Reference Heister and Scheiber2018; Eisen and others, Reference Eisen, Winter, Steinhage, Kleiner and Humbert2020; Franke and others, Reference Franke2020; King, Reference King2020). Principles from these studies have also been translated to paleoglacial landscapes and have also been compared to contemporary bed morphology and lithology (Gudlaugsson and others, Reference Gudlaugsson, Humbert, Winsborrow and Andreassen2013; Schroeder and others, Reference Schroeder, Blankenship, Young, Witus and Anderson2014c; Falcini and others, Reference Falcini, Rippin, Krabbendam and Selby2018; Cooper and others, Reference Cooper2019; Muto and others, Reference Muto, Alley, Parizek and Anandakrishnan2019; Holschuh and others, Reference Holschuh, Christianson, Paden, Alley and Anandakrishnan2020).

In radioglaciology, although reflectivity is used as an umbrella term encompassing all methods used to interrogate variations in the magnitude of the bed echo, it most commonly and appropriately refers to changes in the material properties (and therefore Fresnel reflection coefficient) of the ice–bed interface (Peters and others, Reference Peters, Blankenship and Morse2005). While there are challenges in correcting or constraining attenuation or surface roughness losses, the basal thermal state (frozen or thawed and the presence or absence of water) fundamentally affects the reflection coefficient (Peters and others, Reference Peters, Blankenship and Morse2005; Matsuoka, Reference Matsuoka2011; Schroeder and others, Reference Schroeder, Grima and Blankenship2016a). The reflection coefficient can provide a constraint on where the bed is frozen or thawed, the reach and character of ocean water at the grounding line, and basal conditions of ice streams (Peters and others, Reference Peters, Blankenship and Morse2005; Jacobel and others, Reference Jacobel, Welch, Osterhouse, Pettersson and MacGregor2009; Ashmore and others, Reference Ashmore, Bingham, Hindmarsh, Corr and Joughin2014; Christianson and others, Reference Christianson2016). The presence and volume of inferred basal water bodies have also been used to place constraints on the basal thermal state and/or geothermal flux, while layer drawdown has also been used to constrain basal melt rates and geothermal flux (Fahnestock and others, Reference Fahnestock, Abdalati, Joughin, Brozena and Gogineni2001; Catania and others, Reference Catania, Conway, Raymond and Scambos2006; Buchardt and Dahl-Jensen, Reference Buchardt and Dahl-Jensen2007; Schroeder and others, Reference Schroeder, Blankenship, Young and Quartini2014b; Rezvanbehbahani and others, Reference Rezvanbehbahani, Stearns, Kadivar, Walker and van der Veen2017, Reference Rezvanbehbahani, Stearns, van der Veen, Oswald and Greve2019; Seroussi and others, Reference Seroussi, Ivins, Wiens and Bondzio2017; Jordan and others, Reference Jordan2018a,Reference Jordanb).

Perhaps the most widely and successfully studied basal feature with radar sounding data has been subglacial water bodies, particularly subglacial lakes in Antarctica using the principle that subglacial water results in reflections brighter than surrounding bed echoes in radar data (Oswald and Robin, Reference Oswald and Robin1973; Peters and others, Reference Peters, Blankenship and Morse2005; Wright and Siegert, Reference Wright and Siegert2012). Because of the coherent specular character of subglacial water, small fractional areas can dominate the echo both in terms of reflectivity and geometric spreading (Haynes and others, Reference Haynes, Chapin and Schroeder2018b). This has been exploited to automatically detect lakes in radar sounding data (Carter and others, Reference Carter2007; Ilisei and others, Reference Ilisei, Khodadadzadeh, Ferro and Bruzzone2018). Additionally, lake-bottom echoes have been used to probe water thickness and conductivity (Gorman and Siegert, Reference Gorman and Siegert1999). Surface altimetry data have also been used to infer active lakes around Antarctica where the ice surface has been observed to rise and fall, yet, surprisingly, these lakes typically do not have higher reflectivities than their surroundings in radar data, showing that we still have much to learn about Antarctic subglacial lakes (Carter and others, Reference Carter2007; Smith and others, Reference Smith, Fricker, Joughin and Tulaczyk2009; Siegfried and others, Reference Siegfried, Fricker, Carter and Tulaczyk2016; Carter and others, Reference Carter, Fricker and Siegfried2017; Siegert, Reference Siegert2018). This is also emphasized by different observations with different systems of the same regions, leading to contrasting interpretations (e.g. Bell and others, Reference Bell, Studinger, Shuman, Fahnestock and Joughin2007; Humbert and others, Reference Humbert, Steinhage, Helm, Beyer and Kleiner2018). Recent advances in the analysis of subglacial hydrology from radar sounding data has focused on subglacial water systems beyond Antarctic subglacial lakes (e.g. Young and others, Reference Young, Schroeder, Blankenship, Kempf and Quartini2016). This includes utilizing bed-echo strength and character to investigate water body geometry and dynamic configuration, catchment-scale drainage systems and grounding zones (Schroeder and others, Reference Schroeder, Blankenship and Young2013, Reference Schroeder, Blankenship, Raney and Grima2014a; Ashmore and Bingham, Reference Ashmore and Bingham2014; Christianson and others, Reference Christianson2016). In Greenland, a range of studies has investigated the distribution of subglacial water, including lakes, topographically controlled seasonal storage and gradients in water near the onset of fast flow (Oswald and Gogineni, Reference Oswald and Gogineni2008; Palmer and others, Reference Palmer2013; Chu and others, Reference Chu2016, Reference Chu, Schroeder, Seroussi, Creyts and Bell2018b; Jordan and others, Reference Jordan2018b; Oswald and others, Reference Oswald, Rezvanbehbahani and Stearns2018; Bowling and others, Reference Bowling, Livingstone, Sole and Chu2019). Hypersaline lakes have also been identified beneath Devon Ice Cap in Arctic Canada (Rutishauser and others, Reference Rutishauser2018).

Radio-wave attenuation

Laboratory analyses of radio-wave absorption in ice, as well as radar sounding data from the field, have revealed that while relatively homogeneous ice is a very low-loss medium for radio-waves at VHF frequencies, there is a loss of returned power englacially due to dielectric absorption of radiowaves in ice. Dielectric absorption is proportional to the electrical conductivity of the ice, which is related to ice temperature and the presence of impurities (Glen and Paren, Reference Glen and Paren1975; Johari and Charette, Reference Johari and Charette1975; Moore and Fujita, Reference Moore and Fujita1993; Stillman and others, Reference Stillman, MacGregor and Grimm2013; Pettinelli and others, Reference Pettinelli2015). Without sufficiently distinct basal echo signals (e.g. relative changes that delineate sharp boundaries, such as ice stream shear margins) or sufficiently effective corrections, uncertainty in englacial attenuation can obfuscate the interpretation of basal reflectivities (Matsuoka, Reference Matsuoka2011; Siegert and others, Reference Siegert2016; Schroeder and others, Reference Schroeder, Grima and Blankenship2016a).

Empirical methods for estimating englacial attenuation using bed echoes range from simple linear fitting to adaptive or model-informed fitting (Jacobel and others, Reference Jacobel, Welch, Osterhouse, Pettersson and MacGregor2009; Wolovick and others, Reference Wolovick, Bell, Creyts and Frearson2013; Ashmore and others, Reference Ashmore, Bingham, Hindmarsh, Corr and Joughin2014; Jordan and others, Reference Jordan2016; Schroeder and others, Reference Schroeder, Seroussi, Chu and Young2016c). Englacial layers themselves have also been used to derive attenuation (Matsuoka and others, Reference Matsuoka, Morse and Raymond2010; MacGregor and others, Reference MacGregor2015b). These approaches can also be intercompared or combined (e.g. Hills and others, Reference Hills, Christianson and Holshuh2020; Jeofry and others, 2020). Additionally, investigating attenuation with variable offset can constrain englacial, attenuation, though there is a limit on the maximum offset achievable with commercial GPR systems (Holschuhand others, Reference Holschuh, Christianson, Anandakrishnan, Alley and Jacobel2016). These empirical attenuation values can either be used to correct losses to enable reflectivity interpretation or interpreted themselves as a proxy for englacial temperature.

In addition to applying empirical methods that estimate and correct for attenuation, attenuation rate can also be modeled (Matsuoka and others, Reference Matsuoka, MacGregor and Pattyn2012). This approach can be used when correcting attenuation effects or constraining the bed conditions using layer power (MacGregor and others, Reference MacGregor2015b; Chu and others, Reference Chu, Schroeder, Seroussi, Creyts and Bell2018b). Modeled attenuation can be compared to observations to constrain englacial temperature, parameterize basal conditions to match surface velocities or to quantify englacial water from persistent firn aquifers (Forster and others, Reference Forster2014; Schroeder and others, Reference Schroeder, Seroussi, Chu and Young2016c; Chu and others, Reference Chu, Schroeder and Siegfried2018a; Holschuh and others, Reference Holschuh, Lilien and Christianson2019).

Englacial structure

The study of radar-derived englacial properties dates back almost to the beginning of radioglaciology (e.g. Harrison, Reference Harrison1973; Gudmandsen, Reference Gudmandsen1975; Paren and Robin, Reference Paren and Robin1975). The englacial information that radar data contain has the potential to provide insights into ice-flow processes as well as climatic forcings. The layers have thus been widely used with models for ice-core site selection, stratigraphic control and inferring accumulation histories (see below) (e.g. Jacobel and Hodge, Reference Jacobel and Hodge1995; Cavitte and others, Reference Cavitte2016; Parrenin and others, Reference Parrenin2017). In recent years, the radioglaciological community has seen an increase in the retrieval of such information from radar data although barriers remain to the widespread usage of englacial stratigraphy. This is due to the fact that a substantial amount of manual work is generally needed to convert the stratigraphic information into, for example, dated isochrone surfaces that can readily be used by ice-flow models. Attempts to overcome this obstacle include methodologies focusing on quantifying the slope of the stratigraphy and extracting information from slopes instead (Panton and Karlsson, Reference Panton and Karlsson2015; Holschuh and others, Reference Holschuh, Parizek, Alley and Anandakrishnan2017; Castelletti and others, Reference Castelletti, Schroeder, Mantelli and Hilger2019). Studies focusing on the reorganization of ice flow often avoid tracing isochrones and take a qualitative approach. For example, imprints of shear margin migration or change in flow direction are typically identified based on the amount of stratigraphic disruption. Examples include studies showing changes in ice-flow structure or folded stratigraphy in Greenland and entrained debris in a glacier in Patriot Hills, West Antarctica (Catania and others, Reference Catania, Conway, Raymond and Scambos2006; Martín and others, Reference Martín, Gudmundsson, Pritchard and Gagliardini2009; Dahl-Jensen and others, Reference Dahl-Jensen2013; Bell and others, Reference Bell2014; Bingham and others, Reference Bingham2015; Kingslake and others, Reference Kingslake, Martín, Arthern, Corr and King2016; Winter and others, Reference Winter2019; Ross and Siegert, Reference Ross and Siegert2020). Advances in processing radargrams to extract ice-sheet structure make it possible to interpret these features in regions of complex flow (Elsworth and others, Reference Elsworth, Schroeder and Siegfried2020).

The tracing of englacial isochrones in the radar data acquired over Greenland between 1993 and 2013 by the University of Kansas Center for Remote Sensing of Ice Sheets and OIBis a vital step forward in the efforts to make englacial stratigraphic information readily available (Gogineni and others, Reference Gogineni, Chuah, Allen, Jezek and Moore1998, Reference Gogineni2001; MacGregor and others, Reference MacGregor2015a; Arnold and others, Reference Arnold2018). The resulting data archive has increased the availability of traced isochrones by orders of magnitude. Derived results include evidence of Holocene deceleration of the Greenland ice sheet, and improved constraints on its internal temperature (MacGregor and others, Reference MacGregor2015b, Reference MacGregor2016). In Antarctica, no such large-scale synthesis has been undertaken, but the SCAR AntArchitecture project has the potential to address this critical gap. Several studies have successfully linked isochrones between deep ice-core sites: the interior Antarctic ice-core sites are now linked from Dome Concordia through Vostok to Dome Argus, and Dome Fuji has been linked to the EPICA-DML (European Project for Ice Coring in Antarctica Dronning Maud Land) ice-core site (Cavitte and others, Reference Cavitte2016; Winter and others, Reference Winter, Steinhage, Creyts, Kleiner and Eisen2019). These efforts will play a key role in identifying optimal drill sites for the Oldest Ice (ice older than 1.5 million years, Fischer and others, Reference Fischer2013).

Other important derived products from traced isochrones are the past accumulation rates and patterns (e.g. Eisen, Reference Eisen2008). Recent work in this area has been carried out on time-scales ranging from annual to centennial to millennial (Eisen and others, Reference Eisen2008; Medley and others, Reference Medley2014; Nielsen and others, Reference Nielsen, Karlsson and Hvidberg2015; Grima and others, Reference Grima2016; Karlsson and others, Reference Karlsson2016; Koenig and others, Reference Koenig2016; Koutnik and others, Reference Koutnik2016; MacGregor and others, Reference MacGregor2016; Lewis and others, Reference Lewis2017; Cavitte and others, Reference Cavitte2018; Karlsson and others, Reference Karlsson2020; Montgomery and others, Reference Montgomery, Koenig, Lenaerts and Kuipers Munneke2020). Efforts to automate layer tracing continue, which include methodologies that use seed points to initiate semi-automatic tracing routines as well as fully automatic schemes. In parallel, the extra-terrestrial radar community has been working toward automatically extracting layer information from the Martian orbital radar sounders (Ferro and Bruzzone, Reference Ferro and Bruzzone2012; Onana and others, Reference Onana, Koenig, Ruth, Studinger and Harbeck2015; Xiong and others, Reference Xiong, Muller and Carretero2018; Xiong and Muller, Reference Xiong and Muller2019). Delf and others (Reference Delf, Schroeder, Bingham and Giannopoulos2020) (this issue) present some strategies for assessing automated algorithms inherited from both terrestrial and planetary work.

Interpretation

The history and dynamics of glaciers and ice sheets are written into radar-sensitive properties of these ice masses. Interpretation of radar data may be qualitative or quantitative, with the latter facilitated by process-based models in particular. In its most common form, however, interaction between radioglaciology and models is often limited and one-directional: radio-echo sounding of ice depth furnishes the basal boundary condition for ice-flow models (e.g. Fretwell and others, Reference Fretwell2013). While gaps in our knowledge of basal topography have spurred model development, radar studies have produced a trove of other data and discoveries, including, for example, evidence of retreat, past flow, basal accretion, firn-aquifers and ice-shelf conduits, that remain under-exploited by theory and models (Conway and others, Reference Conway, Hall, Denton, Gades and Waddington1999; Siegert and others, Reference Siegert2004; Bingham and Siegert, Reference Bingham and Siegert2007; Bell and others, Reference Bell2011; Morlighem and others, Reference Morlighem2011; Forster and others, Reference Forster2014; Bons and others, Reference Bons2016; Drews and others, Reference Drews2017; Jordan and others, Reference Jordan2018a; Leysinger Vieli and others, Reference Leysinger Vieli, Martín and Hindmarsh2018; Holschuh and others, Reference Holschuh, Lilien and Christianson2019; Langhammer and others, Reference Langhammer, Grab, Bauder and Maurer2019).

Theoretical work has established relationships between the architecture of internal layers and ice-sheet accumulation, topography, rheology and dynamics (e.g. Nereson and Waddington, Reference Nereson and Waddington2002; Siegert, Reference Siegert2003; Hindmarsh and others, Reference Hindmarsh, Leysinger Vieli, Raymond and Gudmundsson2006; Parrenin and others, Reference Parrenin, Hindmarsh and Rémy2006; Martín and others, Reference Martín, Gudmundsson, Pritchard and Gagliardini2009; Felix and King, Reference Felix and King2011). Internal layers have been integrated with models to determine ice rheology and to understand flow history, including migration of ice streams, divides and domes (e.g. Nereson and Raymond, Reference Nereson and Raymond2001; Ng and Conway, Reference Ng and Conway2004; Catania and others, Reference Catania, Conway, Raymond and Scambos2006; Gillet-Chaulet and others, Reference Gillet-Chaulet, Hindmarsh, Corr, King and Jenkins2011; Pettit and others, Reference Pettit2011; Drews and others, Reference Drews2015; MacGregor and others, Reference MacGregor2016). The discovery of deep internal structures that do not conform to the bed has prompted new model exploration of englacial and basal processes including interpretation of their radar scattering character, with implications for interpreting ice-sheet dynamics and the climate archive (e.g. Bell and others, Reference Bell2011, Reference Bell2014; Dahl-Jensen and others, Reference Dahl-Jensen2013; Wolovick and others, Reference Wolovick, Bell, Creyts and Frearson2013; Wrona and others, Reference Wrona, M, S and D2017; Kjær and others, Reference Kjær2018; Goldberg and others, Reference Goldberg2020).

In addition to englacial layers, radar sounding data have been used to detect channels under ice shelves that have also been the focus of a suite of model investigations (e.g. Jenkins, Reference Jenkins2011; Le Brocq and others, Reference Le Brocq2013; Sergienko, Reference Sergienko2013; Drews, Reference Drews2015; Alley and others, Reference Alley, Scambos, Siegfried and Fricker2016). Theory and observation are yielding new insight into ice–ocean interactions and real-time geomorphic processes in grounding zones, the influence of topography on channel position and formation, and the uncertain relationship between channels and ice-shelf stability (e.g. Gladish and others, Reference Gladish, Holland, Holland and Price2012; Greenbaum and others, Reference Greenbaum2015; Khazendar and others, Reference Khazendar2016; Drews and others, Reference Drews2017; Gourmelen and others, Reference Gourmelen2017; Jeofry and others, Reference Jeofry2018).

With so much radioglaciological data, the advent of resources such as ice-sheet-wide radiostratigraphic archives should help operationalize data–model integration (MacGregor and others, Reference MacGregor2015a). But how are such archives best exploited? Inverse methods present a natural approach, although the persistent problem of non-uniqueness demands care in defining the problem, choosing the tools and incorporating constraints (e.g. Waddington and others, Reference Waddington, Neumann, Koutnik, Marshall and Morse2007; Eisen, Reference Eisen2008; Gudmundsson, Reference Gudmundsson, VP, P and UK2011; Koutnik and Waddington, Reference Koutnik and Waddington2012; Nielsen and others, Reference Nielsen, Karlsson and Hvidberg2015; Koutnik and others, Reference Koutnik2016). Computational costs of large-scale models further demand attention to efficiency, for example, by the use of adjoint methods (e.g. Hascoët and Morlighem, Reference Hascoët and Morlighem2018). Consideration should also be given to the information content of different variables, including those sensitive to basal processes, as well as to the limitations of rendering 3-D effects in 2-D data (Leysinger-Vieli and others, Reference Leysinger-Vieli, Hindmarsh and Siegert2007; Holschuh and others, Reference Holschuh, Parizek, Alley and Anandakrishnan2017; Young and others, Reference Young2018). While we must devise modeling strategies to make best use of the data, this is far from a case of models simply lagging observations. Challenges remain in combining disparate datasets, conditioning data for comparison with modeling and utilizing radiometric, interferometric and polarimetric information in modeling (e.g. Hindmarsh and others, Reference Hindmarsh, Leysinger Vieli and Parrenin2009; Schroeder and others, Reference Schroeder, Seroussi, Chu and Young2016c; Castelletti and others, Reference Castelletti2017, Reference Castelletti, Schroeder, Mantelli and Hilger2019; Winter and others, Reference Winter2017, Reference Winter, Steinhage, Creyts, Kleiner and Eisen2019; Chu and others, Reference Chu, Schroeder, Seroussi, Creyts and Bell2018b; Jordan and others, Reference Jordan, Schroeder, Castelletti, Li and Dall2019). Finally, data–model interaction is a two-way street: testable hypotheses produced by theory and models may suggest new observational targets or provide new reasons to tap the rich radioglaciological archive (e.g. Raymond, Reference Raymond1983; Arthern and others, Reference Arthern, Hindmarsh and Williams2015).

Planetary radioglaciology

The bulk of extra-terrestrial ice-sounding data stems from the planet Mars, specifically from the two orbital radar sounders: MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding) onboard the European Space Agency's Mars Express, and SHARAD onboard the Mars Reconnaissance Orbiter launched by NASA (National Aeronautics and Space Administration, USA) (SHAllow RADar, Seu and others, Reference Seu2007; Jordan and others, Reference Jordan2009). The difference in frequency between the two sounders allowed for different penetration depths and thereby different insights into the planet's ice bodies (MARSIS operated at 1.3–5.5 MHz in its subsurface sounding mode while SHARAD used 15–25 MHz). Although both instruments are now inactive, analysis of the data is ongoing and continues to contribute to our understanding of water ice on Mars. The results from the radar sounders documented the high water content of the Martian water-ice reservoirs (e.g. Grima and others, Reference Grima2009). These have now been supplemented by more detailed studies of the composition of the polar ice bodies, the immediate subsurface of the north pole, and the mid-latitude water ice reservoirs (Guallini and others, Reference Guallini2018; Mirino and others, Reference Mirino, Frigeri, Orosei, Rossi and Cantini2018; Petersen and others, Reference Petersen, Holt and Levy2018; Putzig and others, Reference Putzig2018; Nerozzi and Holt, Reference Nerozzi and Holt2019). In addition, the radar sounding has confirmed areas on the planet also contains significant volumes of buried water ice (Bramson and others, Reference Bramson2015; Stuurman and others, Reference Stuurman2016). One of the most prominent findings is the discovery of a signal that shares similarities with those of a liquid water body (Orosei and others, Reference Orosei2018). In the MARSIS data, this proposed ‘subglacial lake’ has characteristically bright and specular reflections and was found 1.8 km below the South Polar Layered Deposits. The salt content and/or heat flux necessary to form and sustain such a lake is, however, still debated (Sori and Bramson, Reference Sori and Bramson2019). In addition to these findings, the radar data have successfully been utilized to gain insights into the glaciological and climatological processes on the planet, including the deformational properties of Martian water ice, and the past climate history and accumulation patterns of both the North Polar Layered Deposits and the South Polar Layered Deposits (Karlsson and others, Reference Karlsson, Schmidt and Hvidberg2015; Parsons and Holt, Reference Parsons and Holt2016; Smith and others, Reference Smith, Putzig, Holt and Phillips2016; Whitten and others, Reference Whitten, Campbell and Morgan2017; Nerozzi and Holt, Reference Nerozzi and Holt2018; Lalich and others, Reference Lalich, Holt and Smith2019; Schmidt and others, Reference Schmidt, Hvidberg, Kim and Karlsson2019). The radar data have also been used to reconcile observations from visual imagery with the radar-imaged englacial stratigraphy (Christian and others, Reference Christian, Holt, Byrne and Fishbaugh2013; Lalich and Holt, Reference Lalich and Holt2017).

Moving further afield, two radar sounders are now under preparation to probe the subsurface of the Jovian system. Two instruments have been selected for upcoming missions to Ganymede and Europa: the 9 MHz frequency Radar for Icy Moons Exploration (RIME) instrument on board the European Space Agency's Jupiter Icy Moons Explorer (JUICE) and the 9 and 60 MHz frequency Radar for Europa Assessment and Sounding: Ocean to Near-surface (REASON) instrument on board NASA's Europa Clipper (Bruzzone and others, Reference Bruzzone2013; Pappalardo and others, Reference Pappalardo2015; Lorente and others, Reference Lorente2017; Blankenship and others, Reference Blankenship2018). These sounders are designed to probe the moons' interiors and have penetration depths which are functions of surface roughness, volume scattering, ice-shell thermal structure, chemistry and the character of the ice/water interface (Moore, Reference Moore2000; McKinnon, Reference McKinnon2005; Blankenship and others, Reference Blankenship, Young, Moore and Moore2009; Bruzzone and others, Reference Bruzzone2011; Schmidt and others, Reference Schmidt, Blankenship, Patterson and Schenk2011; Berquin and others, Reference Berquin, Kofman, Herique, Alberti and Beck2013; Grima and others, Reference Grima, Schroeder, Blankenship and Young2014b; Pettinelli and others, Reference Pettinelli2015; Di Paolo and others, Reference Di Paolo2016; Grima and others, Reference Grima2016; Aglyamov and others, Reference Aglyamov, Schroeder and Vance2017; Heggy and others, Reference Heggy, Scabbia, Bruzzone and Pappalardo2017; Kalousová and others, Reference Kalousová, Schroeder and Soderlund2017; Campbell and others, Reference Campbell, Schroeder and Whitten2018; Gerekos and others, Reference Gerekos2018; Michaelides and Schroeder, Reference Michaelides and Schroeder2019; Culha and others, Reference Culha, Schroeder, Jordan and Haynes2020). The addition of a dual-channel VHF band on REASON also allows for characterization of the European ionosphere, altimetric investigation of Europa's shell and tides, and dual-frequency or interferometric clutter discrimination (Grima and others, Reference Grima, Blankenship and Schroeder2015; Carrer and Bruzzone, Reference Carrer and Bruzzone2017; Castelletti and others, Reference Castelletti2017; Haynes and others, Reference Haynes, Chapin, Moussessian and Madsen2018a; Steinbrügge and others, Reference Steinbrügge2018; Scanlan and others, Reference Scanlan2019). Finally, the ability of both instruments to record strong Jovian emissions raises the possibility of using those emissions to probe the ice shell using passive radio sounding (Romero-Wolf and others, Reference Romero-Wolf2015; Schroeder and others, Reference Schroeder2016b; Peters and others, Reference Peters, Schroeder, Castelletti, Haynes and Romero-Wolf2018).

In addition to Mars and the icy Jovian Moons, radar sounding is also being deployed to investigate ice on other planetary bodies. For example, NASA's Lunar Reconnaissance Orbiter was equipped with a radar sounder in the gigahertz frequency range in order to search for water ice on Earth's moon (Nozette and others, Reference Nozette2010). The data reveal the existence of large deposits of relatively clean ice in the polar regions (Spudis and others, Reference Spudis2013). Unfortunately, measurements temporarily discontinued after an instrument failure in 2011, but have resumed in a bi-static configuration (Patterson and others, Reference Patterson2017). Additionally ESA's Rosetta mission included the bistatic CONSERT experiment (COmet Nucleus Sounding Experiment by Radiowave Transmission), which performed the first tomographic imaging of the interior of a comet (Glassmeier and others, Reference Glassmeier, Boehnhardt, Koschny, Kührt and Richter2007; Kofman and others, Reference Kofman2015).