2. How topography controls ice sheet change

The bed topography of ice sheets is deeper in the interior than at the periphery of the ice sheet owing to lithospheric loading that depresses the crust where the overlying weight of ice is greatest (Fig. 1). As a result, Earth's remaining ice sheets both have basal topography that is largely characterized as retrograde - sloped inward to the ice sheet interior from the margins. Early research into the impact of ice sheets on retrograde bed slopes under climate warming led to the development of a theory now termed Marine Ice Sheet Instability (MISI) (e.g., Weertman, Reference Weertman1974; Mercer, Reference Mercer1978; Thomas and Bentley, Reference Thomas and Bentley1978). MISI suggests that glaciers and ice sheets resting on retrograde beds are more susceptible to rapid and irreversible mass loss as the climate warms. This is because the flux of ice through the grounding line increases with bed depth. Thus, ice sheet retreat on retrograde bed slopes results in greater flux of ice and additional retreat. This runaway process is suggested as a possible mechanism that could lead to rapid collapse of the West Antarctic Ice Sheet, with the potential for much faster rates of sea level rise than currently estimated (IPCC, 2021). Early theories regarding MISI laid the groundwork for modeling this process. This includes Schoof (Reference Schoof2007), who found that the presence of topographic overdeepenings results in hysteresis in terminus position; termini that sit on retrograde bed slopes have unstable grounding line states and can rapidly retreat given a climate perturbation, while termini that sit on prograde bed slopes are stable and can advance given a climate perturbation.

Figure 1. Topography of the Greenland Ice Sheet from BedMachine (Morlighem and others, Reference Morlighem2023) showing the location of knickpoints (black dots) and outlet glacier flow lines (black and red lines). Black lines are glaciers with knickpoints, red do not have knickpoints. All data from Felikson and others (Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020).

3. Topography observations for Greenland

While the theory and modeling of MISI demonstrated its importance, there has been little observational evidence of it in part due to the lack of adequately resolved bed topography. Bed topography became more readily resolved with the collection and publication of radar-derived bed topographic data and the use of these data via the production of BedMachine (Figure 1; Morlighem and others, Reference Morlighem2011), a data-constrained estimate of the bed elevation for the GrIS. BedMachine uses radar-derived ice thickness, surface velocity and surface mass balance data with the assumption of mass continuity to estimate bed elevation for fast-flowing portions of the ice sheet. This approach is an improvement over kriging because it provides a physically-realistic bed elevation in areas where radar data are unavailable. This technique is focused at the fast-flowing margin of the ice sheet and in the slower-flowing interior, BedMachine relies on kriging to interpolate between radar-derived ice thickness measurements to create a complete map of topography beneath the ice sheet. BedMachine has been improved over time with the addition of fjord bathymetry data (Fenty and others, Reference Fenty2020), providing seamless topography across outlet glacier termini (Morlighem and others, Reference Morlighem2023).

While BedMachine provides improvements to bed topographic estimates, the terminal regions of outlet glaciers remain poorly resolved because radar-derived ice thickness is more difficult to obtain in these wet, crevassed and deep regions. Further complicating improvements to outlet glacier topographic measurements is the fact that there are nearly 300 outlet glaciers, each with their own unique characteristics, making data collection onerous. The topography that shapes outlet glaciers partially arises because glaciers are natural erosive agents (Kessler and others, Reference Kessler, Anderson and Briner2008; Koppes and Montgomery, Reference Koppes and Montgomery2009; Love and others, Reference Love, Hallet, Pratt and O'Neel2016) capable of delivering large amounts of sediment to their termini where it often becomes visible as sediment plumes at the fjord surface (McGrath and others, Reference McGrath2010; Hudson and others, Reference Hudson2014). Glacier erosion is likely to be largest where ice is moving fastest and where there is efficient removal of sediment via an active subglacial system (Hallet and others, Reference Hallet, Hunter and Bogen1996; Cowton and others, Reference Cowton, Nienow, Bartholomew, Sole and Mair2012; Love and others, Reference Love, Hallet, Pratt and O'Neel2016; Brinkerhoff and others, Reference Brinkerhoff, Truffer and Aschwanden2017). Supraglacial water delivery to the bed downstream of the equilibrium line provides a steady water supply in summers, possibly explaining the much deeper beds observed in these locations (Fig. 2). In addition to erosion, because many outlet glaciers approach floatation toward their margins, sediment may preferentially deposit close to the terminus creating a moraine (sometimes called a sill in the literature), which also shapes the topography at termini (Figure 2; Batchelor and others, Reference Batchelor, Dowdeswell and Rignot2018). Comparisons of BedMachine to radar-derived topography in outlet glaciers reveals that there may be a systematic offset of the bed elevation between the two but that the radar-derived bed slopes are well-preserved in BedMachine (Morlighem and others, Reference Morlighem2017; Catania and others, Reference Catania2018; Narkevic and Anton, Reference Narkevic, Csatho and Anton2023). In addition, BedMachine is unrealistically smooth at small scales making it less useful for examining subglacial water routing and the influence of small-scale bed features on dynamics (MacKie and others, Reference MacKie, Schroeder, Zuo, Yin and Caers2021). Stochastic modeling of bed topography has emerged as an additional technique to simulate the most realistic bed topography using the statistics of the bed elevation uncertainty to drive the scope of simulations (e.g., Goff and Jordan, Reference Goff and Jordan1988; MacKie and others, Reference MacKie, Schroeder, Caers, Siegfried and Scheidt2020, Reference MacKie, Schroeder, Zuo, Yin and Caers2021).

Figure 2. Schematic of outlet glacier topography showing retrograde inland topography, the presence of a knickpoint at the location of the equilibrium line altitude (ELA), an overdeepening in the region of fast flow and the presence of moraines (both active and paleo) at the glacier terminus.

3.1 Topographic controls on retreat and inland thinning

Much of the dynamic mass loss for the GrIS is thought to have initiated by warm ocean temperatures and sufficient supraglacial melt to drive enhanced melt of the ice marginal region. This has been demonstrated as a consequence of 20th century ocean and atmospheric warming (Holland and others, Reference Holland, Thomas, Young, Ribergaard and Lyberth2008; Murray and others, Reference Murray2010; Straneo and Heimbach, Reference Straneo and Heimbach2013; Trusel and others, Reference Trusel2018; Wood and others, Reference Wood2021). However, while the overwhelming majority of GrIS outlet glaciers have experienced retreat (King and others, Reference King2020), acceleration (Moon and others, Reference Moon, Joughin, Smith and Howat2012) and thinning (Smith and others, Reference Smith2020), there is heterogeneity in the dynamic response of glaciers to climate (Csatho and others, Reference Csatho2014; Catania and others, Reference Catania2018; Hill and others, Reference Hill, Carr, Stokes and Gudmundsson2018; Moon and others, Reference Moon, Gardner, Csatho, Parmuzin and Fahnestock2020) with a small number of glaciers exhibiting stability over this time period. In part, this may be due to the inability for warm ocean waters to access the terminus where fjords are shallow or protected with shallow sills or paleo-moraines downstream of glacier termini (Bartholomaus and others, Reference Bartholomaus, Larsen and O'Neel2013; Carroll and others, Reference Carroll2016; Batchelor and others, Reference Batchelor, Dowdeswell, Rignot and Millan2019). However, the climate alone is not sufficient to force retreat of every glacier terminus. This was demonstrated by Christian and others (Reference Christian, Robel and Catania2022) who found that some bed bumps at glacier termini could cause persistent terminus stability even when climate change produces an increased probability of retreat. This is because ice flux reduces as ice flows up to a bed peak, flattening surface slopes and reducing the ability for climate to affect terminus position (Robel and others, Reference Robel, Pegler, Catania, Felikson and Simkins2022). The enhanced stability of glacier termini near the peaks of bed bumps may thus explain why there are a number of persistently stable glaciers despite widespread coincident warming of the ocean and atmosphere around Greenland since the late 1990s.

In addition to controlling the timing of glacier terminus retreat since the 1990s, topography also regulates how much retreat occurs. Using BedMachine data, Catania and others (Reference Catania2018) confirmed that glacier termini retreat from one bed bump to another further inland with retreat that appears insensitive to bed bumps smaller than the seasonal amplitude of the terminus. Carnahan and others (Reference Carnahan, Catania and Bartholomaus2022) examined this for neighboring glaciers Umiamiko Isbræ and Ingia Isbræ, both of which began to retreat in ~2001. While both glaciers retreated significantly, Umiamiko Isbræ restabilized on the prograde side of a large bed bump in 2010, while Ingia Isbræ has continued to retreat (Zhang and others, Reference Zhang, Catania and Trugman2023). The ongoing retreat of Ingia Isbræ was enabled, in part, because its fjord has flat bed topography, which permits low basal resistance to driving stress for several kilometers upstream of the terminus (Carnahan and others, Reference Carnahan, Catania and Bartholomaus2022). The ongoing retreat occurring for many GrIS glaciers in spite of widespread ocean cooling in ~2008 (Wood and others, Reference Wood2021) suggests that climate alone cannot sustain retreat, and that topography may permit the degree to which a climate trigger will influence future dynamics of individual glaciers.

While we have focused largely on bed topographic controls so far, we note that other variables can exert control on the pace and timing of retreat. In streaming ice, Greenwood and others (Reference Greenwood, Simkins, Winsborrow and Bjarnadóttir2021) found that along-flow bed slope was a poor predictor of retreat style with similar retreats occurring on all types of bed slopes. This suggests that bed topography alone may not be the dominant control to terminus retreat. For the relatively narrow outlet glaciers in Greenland, changes in fjord width also appear to exert control in model studies of glacier retreat (Enderlin and others, Reference Enderlin, Howat and Vieli2013; Akesson and others, Reference Akesson, Nisancioglu and Nick2018; Hill and others, Reference Hill, Carr, Stokes and Gudmundsson2018). Indeed, model simulations from Akesson and others (Reference Akesson, Nisancioglu and Nick2018) show that termini can retreat through fjord embayments even in the presence of bed topographic bumps in the bed. For the GrIS, it has been difficult to ascertain the degree to which changes in fjord width have impacted observed retreat rates because observed variations in width are small compared to variations in bed topography over the relatively short length scale of most retreats (Catania and others, Reference Catania2018).

Terminus retreat is thought to precede surface steepening, acceleration and inland thinning of outlet glaciers (Carnahan and others, Reference Carnahan, Catania and Bartholomaus2022). Inland thinning of ice is diffusive and leads to slow, long-term mass loss but represents the majority of future committed sea level rise (Price and others, Reference Price, Payne and Howat2011). The amount of inland thinning permitted is also controlled by bed topography (Felikson and others, Reference Felikson2017), with the presence of bed topographic ‘knickpoints’ - steep reaches where the bed rises from below sea level to above sea level far inland from the glacier terminus (Figures 1, 3; Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020). These knickpoints also control the degree to which interior ice accelerates in response to thinning and retreat (Williams and others, Reference Williams, Gourmelen and Nienow2021). The proximity of knickpoints to a glacier's terminus and the steepness of that knickpoint is correlated with regional topographic steepness, which likely steers outlet glacier tributaries to converge enhancing bed erosion (Kessler and others, Reference Kessler, Anderson and Briner2008; Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020). In regions of steeper terrain, there are steeper, more well-defined knickpoints, while in gentler terrain, there are no knickpoints or much gentler sloped knickpoints (Figures 1, 3; Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020). Where they are present, knickpoint locations are roughly coincident with the location of the equilibrium line, suggesting that surface meltwater is required to sufficiently lubricate the bed enabling enhanced erosion downstream of knickpoints as opposed to frozen bed conditions upstream of knickpoints (Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020). When retreat occurs on glaciers without well-defined knickpoints, inland diffusive thinning may be slower, but occurs for much longer than for glaciers with well-defined knickpoints. This suggests that glaciers without knickpoints may represent bottlenecks of mass loss; where ongoing long-term mass loss can continue well after the retreat has occurred.

Figure 3. Subglacial and surface topography along flowlines of two GrIS glaciers. Grey lines show smoothed bed topography along six individual flowlines for each glacier, black line shows the mean of all six flowlines. Blue shows ice surface topography. All topography data from (Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020). Sea level is indicated at zero elevation with a red dotted line. The approximate equilibrium line elevation is ~1500 m (Noël and others, Reference Noël, Berg, Lhermitte and Broeke2019) and is indicated for each glacier. (a) Humbolt Glacier showing an overdeepened bed near the terminus but no presence of a strong knickpoint detected. (b) Helheim Glacier showing a strongly overdeepened bed topography near the terminus and a steep knickpoint at ~35 km where inland thinning would be limited according to Felikson and others (Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020).

Given the importance of bed topography, and our knowledge that glaciers are effective at erosion, it seems logical then to suspect that topography can co-evolve with glacier dynamics. Indeed, this was proposed to explain the ‘tidewater glacier cycle’ (Meier and Post, Reference Meier and Post1987; Nick and others, Reference Nick, Veen and Oerlemans2007), which is a long-term cycle of slow terminus advance and rapid retreat initially described as typical of Alaskan tidewater glaciers. The importance of coupling sediment to ice dynamics was demonstrated by Brinkerhoff and others (Reference Brinkerhoff, Truffer and Aschwanden2017) who showed that the tidewater glacier cycle could be reproduced within a steady climate simply through interactions between ice flow, glacier erosion and sediment transport. Glacier erosion is also responsible for the creation of overdeepenings (Patton and others, Reference Patton, Swift, Clark, Livingstone and Cook2016), which then feedback onto the ice dynamics including the rate of terminus retreat (Robel and others, Reference Robel, Pegler, Catania, Felikson and Simkins2022) and the ice flux (Hooke, Reference Hooke1991; Creyts and others, Reference Creyts, Clarke and Church2013). Differences in glacier bed erosion rates are also likely responsible for the formation of knickpoints (Kessler and others, Reference Kessler, Anderson and Briner2008; Felikson and others, Reference Felikson, Catania, Bartholomaus, Morlighem and Noël2020), which suggests that long-term erosion may be responsible for the heterogeneous dynamic response in inland thinning of the ice sheet that is observed today.

4. Future research priorities

While the role of topography in controlling outlet glacier dynamics is of clear importance, our ability to actually observe subglacial topography with reasonable accuracy is quite recent. For the GrIS, considerable data acquisition occurred through CReSIS (Gogineni and others, Reference Gogineni2001, Reference Gogineni2014), NASA's Operation IceBridge (Studinger and others, Reference Studinger, Koenig, Martin and Sonntag2010; MacGregor and others, Reference MacGregor2021) and Oceans, Melting, Greenland Missions (Fenty and others, Reference Fenty2020), which provided significant improvements in the spatial resolution and coverage of bed topography in Greenland. Despite the significant funding and effort that went to securing these data, we still lack adequate topographic data for many outlet glacier terminal regions in Greenland. Thick, warm, wet and steep-walled ice conditions here pose unique challenges for airborne radar data collection. Some progress is being made to counter these challenges using unmanned aircraft, which can house lower frequency radar systems than are typically used, permitting deeper penetration (Arnold and others, Reference Arnold2018). Additional dedicated funding is needed to fully map these parts of the ice sheet, perhaps focusing on those glaciers that are most susceptible to initiating large changes in mass loss.

Similarly, additional surveying of fjord topography is needed (Jakobsson and Mayer, Reference Jakobsson and Mayer2022), particularly for fjords that are persistently chocked with melange, making the terminus region much more difficult to access via ship (e.g., Helheim Glacier). For glaciers without persistent melange, coordination across nations can crowd-source data collection to happen during periods of time when accessibility is available. Perhaps this means that we make use of even single-beam sounding from fishing and expedition ships working in Greenland. For fjords that have persistent melange, a different approach is needed that allows remote sounding of the sea floor topography. This could occur via including remotely operated vehicles (Jakobsson and Mayer, Reference Jakobsson and Mayer2022), using novel remote-sensing techniques that make use of iceberg draft heights (Scheick and others, Reference Scheick, Enderlin, Miller and Hamilton2019) and the use of airborne gravity (Boghosian and others, Reference Boghosian2015; Tinto and others, Reference Tinto, Bell, Cochran and Münchow2015). While airborne gravity provides a coarser resolution bed topography estimate compared to multibeam data, it can be done more easily by plane and with complete coverage of the terminal zone (An and others, Reference An, Rignot, Millan, Tinto and Willis2019).

Given the importance of bed topography, particularly at the ice-ocean boundary, we must next understand the pace at which topographic change is possible. Glaciologists largely assume stable bed topography over time assuming that bed erosion and deposition rates are small compared to terminus change rates (Koppes and Montgomery, Reference Koppes and Montgomery2009). Yet, sedimentation has been observed to be critical to understanding the stability state of glacier termini (Alley and others, Reference Alley, Lawson, Larson, Evenson and Baker2003, Reference Alley, Anandakrishnan, Dupont, Parizek and Pollard2007). Indeed, glacier advance has been shown to be uniquely dependent on sediments infilling into bed lows in front of the advancing terminus (Nick and others, Reference Nick, Veen and Oerlemans2007). Further, sedimentation rates at Alaskan glaciers were recently measured to be on the order of several meters per year (Eidam and others, Reference Eidam2020), which is larger than the vertical motion of the solid Earth following deglaciation, now considered an important stabilizing feedback on ice loss (Barletta and others, Reference Barletta2018). Despite its clear importance, sedimentation is either entirely missing from sea level projecting models of ice sheets (Aschwanden and others, Reference Aschwanden2019) or is modeled without clear knowledge of the types and rates of processes that contribute to moraine building (Brinkerhoff and others, Reference Brinkerhoff, Truffer and Aschwanden2017). While there has been extensive research on glacial landforms from past glaciations, most of these studies are not able to produce a precise depiction of the coincident ice dynamics at the time of deposition. Thus, we lack a set of governing equations that describe how to couple ice and sediment dynamics in a way that is consistent with observations. We thus recommend new observations of sedimentation rates that can be paired with observed glacier dynamics so that we can build equations that describe moraine-building and erosion of overdeepenings that are consistent with observations.

Finally, there is a remaining need to consider outlet glacier dynamics holistically because there are multiple processes (both internal and external to the ice sheet) that impact dynamics making it difficult to tease apart cause and effect of glacier change. Poorly constrained boundary conditions for outlet glaciers exacerbates this (Malles and others, Reference Malles2023). New observations must therefore be coupled to focused modeling of ice sheet outlet glaciers to discern the processes that are most important for accurately estimating future sea level.