Actively evolving subglacial conduits and eskers initiate ice shelf channels at an Antarctic grounding line

Ice-shelf channels are long curvilinear tracts of thin ice found on Antarctic ice shelves. Many of them originate near the grounding line, but their formation mechanisms remain poorly understood. Here we use ice-penetrating radar data from Roi Baudouin Ice Shelf, East Antarctica, to infer that the morphology of several ice-shelf channels is seeded upstream of the grounding line by large basal obstacles indenting the ice from below. We interpret each obstacle as an esker ridge formed from sediments deposited by subglacial water conduits, and calculate that the eskers' size grows towards the grounding line where deposition rates are maximum. Relict features on the shelf indicate that these linked systems of subglacial conduits and ice-shelf channels have been changing over the past few centuries. Because ice-shelf channels are loci where intense melting occurs to thin an ice shelf, these findings expose a novel link between subglacial drainage, sedimentation and ice-shelf stability.

For the ERS acquisitions, no second interferogram is available so that we cannot strictly separate between vertical and horizontal displacement in the topographically corrected interferogram. However, due to the steep look angle of the ERS-satellites, the interferogram is most sensitive to the vertical displacement of the ice shelf by tides which causes a dense fringe pattern signifying the grounding-zone [6]. We pick the landward limit of this pattern as a satellite-based estimate for the grounding-line location in 1996. We use a similar processing scheme for the Sentinel 1A and the ALOS-PALSAR images. In those cases, three coherent overflights are available and we calculate differential interferograms. Because the steady component of the horizontal ice flow is cancelled, this makes the grounding zone more prominent. Supplementary Fig. 1 shows the differential interferogram from 2016 alongside the picked grounding lines from 2007 and 1996. The three estimates agree in many areas and differences are often within a few hundred meters.
Next, we consider two ground-penetrating radar profiles across the grounding zone collected in 2016 (GL-GL', A2-A2' located in Fig. 1). The grounding line can be determined by looking for abrupt changes in the amplitude of the basal reflection indicating the transition from a rough/diffuse ice--bed reflector to the bright/specular ice-ocean interface. Such abrupt changes are often found [5], although a more gradual transition in basal reflectivity can also occur (e.g. when basal ice is enriched with debris [4]). For the profile GL-GL', basal reflectivity abruptly changes near kilometer 2 which is about 1 km upstream of the landward limit of tidal flexure (Fig. 3). This abrupt change hints to a water layer at the ice-bed interface which may be of continental and/or oceanic origin. For the latter, observations are similar to findings near an embayment of the Whillans Ice Stream, West Antarctica, where ocean water can penetrate upstream of the tidal flexure zone through tidal pumping forming an estuary with two-way water exchange [11,2,4]. Alternatively, we could be seeing subglacial water which is routed towards the ocean.
The profile A2-A2' (Figs. 2 and 5) is collected in an area with extensive surface (and potentially basal) crevassing making the analysis more complicated due to out of plane reflections [12]. The profile is dominated by the strong reflector A. At larger depths, we can trace another reflector along-flow which we identify as the ice--bed interface because it links with the ice-bed interface of across-flow profiles farther upstream. However, because the radar wave does likely not penetrate through reflector A, the origin of the radar reflector remains unclear and we tentatively attribute it to an off-angle reflection from a rough bed. This is supported by the fact that a similar reflector is not evident in the neighboring radar section A3-A3' which is located more centrally on top of reflector A. The disappearance of the off-angle reflector in A2-A2' after 1.8 kilometers marks in this context the grounding line. This location is only about 300 m downstream from the landward limit of tidal flexure. We receiver no reflections from the floating ice shelf in this area farther downstream.
Because the tidal flexure zones from 1996, 2007 and 2016 are very similar, we can exclude a systematic grounding-line migration in that time interval. This accords with modelling results showing that the grounding line of the Roi Baudouin Ice Shelf is topographically controlled and is unlikely to retreat even for scenarios with high basal melt rate [13]. Therefore, it is most likely that the radar-cross sections A1-A1', EuA-EuA' and C1-C1' (and the reflectors A-C seen therein) are completely on grounded ice. Ocean water may, perhaps episodically, infiltrate upstream of the tidal flexure zone, which we discuss in more detail in Section 3.2.

Supplementary Note 2: Evolution of subglacial conduits at the grounding line
We base our model of the subglacial conduits on the basic physics developed by [14] and [15] where the conduit size is determined by a balance between ice melting at the conduit walls (the heat being provided from the turbulent water flow) and creep closure (forced by the overburden ice pressure). Close to the grounding line, the magnitude of the water flux through the conduit Q is largely determined by the catchment basin farther upstream and, neglecting additional water input from melting at the channel walls near the grounding line, we consider the flux as constant. The model only considers the evolution of the conduit's cross-sectional area (S) and the hydraulic potential gradient (). In a coordinate system where x is along-flow and z in the vertical, a relationship between these two quantities follows from parametrizing the turbulent drag on the walls of the conduit, where L in the first term of the right-hand side is the latent heat describing the melting, and ̂= 2 depicts the creep closure using Glen's flow law coefficient for exponent n = 3. The advection term on the left-hand side (with ice sliding speed ), like the effective pressure gradient, becomes important near the grounding line. We apply a simplified, fixed geometry (a flat bed at a depth of b = -700 m, and a constant surface slope = 0.016, Fig. 8A) approximating the tributary Ragnhild glaciers of the Roi Baudouin Ice Shelf [16,17]. This yields a constant potential gradient 0 ≈ 180 Pa m -1 .
Using the parameters listed in Supplementary Table 1 for solving eqs. (1) and (2) subject to the boundary condition N = 0 at the grounding line results in the steady-state conduit area in Fig. 8B. Neglecting the advection term (left-hand term in eq. (2), we find that the conduit's cross-section grows substantially in a small boundary region near the grounding line which can be conceptually understood as follows: If ice floats, the effective pressure is zero and no creep closure occurs. Melting at the channel walls, on the other hand, persists and causes the cross-sections to grow to infinity in the absence of ice advection (Fig. 8B). A similar divergence also occurs at water outlets of alpine glaciers [18]. However, including the advection of a smaller conduit cross-sections from upstream limits their growth at the grounding line.
A more detailed analysis of eqs. (1) and (2) shows that the conduit cross-section at the grounding line is given by is a constant. The cross-section is larger for a larger discharge (which provides more dissipative power), smaller ice speeds (which allow more time for the conduit to grow), and smaller surface slopes (which allow the region of low effective pressure to extend farther upstream). The results shown in Fig. 8C-D consider an upper estimate (with a large subglacial discharge, Q = 100 m 3 s -1 , and low basal sliding, = 1 m a -1 ) and a lower estimate (Q = 10 m 3 s -1 and = 300 m a -1 ). These combinations bracket the observed surface velocities [9] and the estimated total subglacial melt water flux across the grounding line (~ 60 m 3 s -1 ) using a hybrid ice-stream/ice-shelf model [19].
Although the conduit predicted by this model grows substantially near the grounding line, the absolute magnitude (for the parameter-set considered here) is smaller than our observations. This is mainly because the flattening of the hydraulic potential also reduces the outflow water speed together with the melting at conduit walls (Fig. 8C, D). Additionally, the assumption of isothermal ice close to the melting point becomes increasingly violated closer to the ice-sheet surface where the ice is colder. The conduit-widening described here is, therefore, not the only mechanism which needs to be considered.
Intrusion of ocean water into the mouth of the conduit and subsequent mixing with the subglacial discharge, may amplify the melting [20] and lead to a larger cross-section than predicted by eq. (3). Such intrusion is possible because outflow speed of the subglacial meltwater decrease near the grounding line. With a depth-averaged ice velocity of 300 m a -1 an additional melt rate stemming from the ocean of ~10 m a -1 is needed to grow a conduit with a 100 m radius over a horizontal distance of 3 km. However, even these increased melt rates do not accord with our observations of surface ridges above the conduits because wall melting principally lowers the ice surface. We, therefore, discuss in the main text the impact of sedimentation at the conduit's portal. For the latter, the reduction of water outflow speed due to the conduit widening predicted by our simplified model (Fig. 8D)  The vertical displacement by tides is reflected by the dense fringe pattern, separating the grounded ice from the floating ice shelf and we find no significant temporal variations between 1996 and 2016. The ground-based radar profiles A2-A2' (Fig. 2) and GL-GL' (Fig. 4) are used to infer the grounding line with radar (red star). In GL-Gl' some water, which maybe of oceanic or continental origin, is found upstream of the tidal flexure zone indicating potential for an estaurine grounding-zone (green line).