Reply to: “Impact of marine processes on flow dynamics of northern Antarctic Peninsula outlet glaciers” by Rott et al.

I n Tuckett et al. 1 , we report short-term speed-up events of Antarctic Peninsula outlet glaciers. Modelled surface melting, observations of surface meltwater, and speed-up event characteristics led us to propose speed-ups were a consequence of meltwater reaching the ice-bed interface; a meltwater hypothesis. Rott et al. 2 replicate the velocity data and show that during one event, sea-ice conditions change ~90 km from three glaciers, and at the front of another, leading Rott et al. 2 to propose a sea ice hypothesis: that sea-ice movement away from glacier fronts reduces back-stress triggering acceleration. Simultaneously Rott et al. 2 , argue that the ice velocity observations are biased due to measurement artefacts. Here, we defend the meltwater hypothesis, present evidence against the sea-ice hypothesis, and examine potential bias in our glacier velocity measurements. Although sea-ice evacuation is coincident with the March 2018 speed-up event observed in Tuckett et al. 1 , changes in sea-ice characteristics are not synchronous across all studied glaciers.

structure coincident with the speed-up events (Supplementary Table 1).

Supplementary Note 2: Determination of grounding-line position
Rott et al. [2] use unpublished and unavailable data to claim that the majority of regions of interest (ROIs), within which velocity data were analysed by [1], are located on floating ice.
To evaluate this claim, we performed additional mapping of the grounding line position, using the Reference Elevation Model of Antarctica elevation model [4]. These data were broadly coincident with our velocity data. To identify grounding line position, we used a break of slope technique (similar to that undertaken by [2]), identified visually on digital elevation models and slope maps, aided by along-flow elevation profiles.
For Jorum, Crane and Cayley glaciers, the grounding line is easily distinguishable due to the abrupt change in slope and surface texture (Fig. 2 in the main text). In the case of Hektoria glacier, highlighted in [2], the position of the grounding line is uncertain due to the presence of an ice plain. This is especially the case when using the break of slope technique, where multiple breaks in slope are apparent across a wider grounding zone rather than a distinct grounding line (Friedl et al., 2019). Figure 2 in the main text shows the grounding line position determined here in relation to the ROIs of [1]. Using our grounding line positions, 18 ROIs (50%) are positioned on fully grounded ice, 11 (30.6%) are partially grounded (either on the grounding line or within a grounding zone), 6 ROIs (16.7%) are positioned on floating ice and 1 (2.8%) was mistakenly placed over melange/new sea ice (Fig. 2 in the main text). In the main article, we refer to figures that exclude Hektoria. It is clear that the grounding-line position of Hektoria Glacier is highly uncertain due to the presence of an ice-plain (Fig. 2 in the main text; [5]).

Supplementary Note 3 -Ice velocity and dB changes during surface melt events
As pointed out by [2], changes in surface moisture affect radar penetration, altering the phase centre depth. This introduces a bias in our velocity estimates, which alters according to glacier flow direction and topography in relation to satellite radar line of sight. This bias was not considered in [1]. Regardless of surface conditions, the effect of this bias should be zero for glaciers flowing parallel to the satellite heading angle. During a transition which encompasses wet to frozen to wet conditions, maximum apparent slow-down should be at +90 degrees (approximately aligned with typical flow of west coast glaciers) and maximum apparent speed-up at -90 degrees (approximately aligned with typical flow of east coast glaciers). When the surface changes from frozen to wet to frozen, the opposite is true: the maximum apparent speed-up should be at +90 degrees, with a maximum apparent slow-down at -90 degrees from the satellite heading angle. In each case, the apparent maximum slow-down and speed-up should be of a similar magnitude, assuming the surface returns to the pre-event state.
To estimate the impact of the phase centre depth bias on our velocity results, we compared the magnitude and sign of the speed change between consecutive image pairs to variations in the radar backscatter data. We established a winter backscatter baseline and identified the surface as 'melted' when the dB values were more than 4 dB below winter values [6], or 'frozen' if the dB values were greater than this threshold. This allowed us to compare the velocity response of our study glaciers during melt events to that which would be expected from the phase centre depth bias alone. Unfortunately, our analysis is limited by the fact that the glaciers of the Antarctic Peninsula do not flow uniformly in a radial pattern, meaning that we cannot sample equally across all flow directions. An additional complication is that surfaces may also have different wetting and refreezing patterns through time (e.g. not conforming to either a wet-frozen-wet or frozen-wet-frozen pattern).
Our analysis shows that although there are changes in ice velocity that are consistent with that expected from changes in the phase centre depth, as noted by [2], there remains a discernible signal of ice flow variations that we maintain are related to surface melting. During many of the melt events, there is a pattern of an apparent speed-up/slow-down of ice flow perpendicular to the satellite heading angle, which we attribute to the bias effect. However, there are also substantial variations in ice flow where the flow direction is more closely aligned with the satellite heading angle, whose pattern and magnitude support the meltwater hypothesis as their cause. This is most clearly demonstrated by a new ROI from Edgeworth Glacier There are also occasions when we record a speed-up on glaciers where the surface remains wet (based on our dB analysis) across a melt event (i.e. when the surface does not refreeze between melt events that occur within consecutive velocity pairs). For example, at Jorum glacier, we observe a speed-up event during a period when the backscatter remains persistently below the winter value (Supplementary Figure 2). In these cases, we would not expect an apparent change in ice flow from the phase centre depth bias, but might expect an acceleration based on the meltwater hypothesis, given that the surface is melting throughout.
A further line of evidence suggests that the phase-centre depth bias is not greater in magnitude than the speed-up events themselves. If the penetration depth bias was the sole contributor to our observed speed-up events, we would expect any speed-up/slow-down during wetting to be balanced by an equal and opposite effect during re-freezing (as the bias effect happens in reverse). Our time-series clearly show that the majority of speed-up events produce a net positive effect as the subsequent slow-down does not offset the speed-up (e.g. Fig. 1 in main text). The exception is Cayley Glacier where there is less melt. As a result, we cannot rule out that the phase centre bias is the principal cause of velocity variations at this site.

Supplementary Note 4 -Ice velocity errors and impact of surface melting on ice velocity
In addition to the phase centre depth bias, [2] raise the issue of other contributing errors in the retrieval of glacier velocity that are not accounted for in [1]. The error estimate in [1] is derived from average apparent velocities over bedrock areas. The use of average velocities obtained over stable bedrock regions is frequently used to estimate measurement error for intensity tracking of radar imagery [7] or as one of a combination of methods [8]. The low-magnitude, high-frequency variability that we observe in our velocity data is most prominent closer to the glaciers' termini, and almost absent beyond the ROI that is situated 8 km up glacier (Supplementary Figure 4 in [1]), suggesting a marine cause, possibly related to tidal sea surface height variations [1]. Unpublished ice velocity data from the western margin of the Greenland Ice Sheet, estimated using the same processing chain as used in [1], show over-winter flow variations of +/-20 m/yr around a consistent longer-term trend suggesting that our method is capable of recording steady ice flow. That the mean speed of Flask Glacier (not studied in [1]), from GPS data mentioned in [2], and our mean speed from Jorum Glacier are similar, cannot be used as evidence that our velocity spikes are artefacts, as the transient nature of the speedup events means they do not currently substantially affect seasonal mean velocity. It is also not clear from [2] what the units of the variability shown by the GPS-derived ice velocity data are According to [9], there are three main sources of error for feature tracking of ice velocity using Sentinel-1 data: errors caused by inaccuracy in the cross-correlation process and mis-alignment of image pairs, errors due to ionospheric disturbances, and errors induced by geocoding (errors in the digital elevation model (DEM) used to geocode the displacements from radar to ground coordinates). Note that bias introduced by changes in the depth of the scattering phase centre is not listed as a significant source of error, nor have we been able to find any previous studies using Sentinel-1 data to quantify ice velocities that have included this in their error calculations.
The input radar data are aligned in GMTSAR to sub-pixel precision based on precise orbits and topography (https://topex.ucsd.edu/gmtsar/tar/GMTSAR_2ND_TEX.pdf). The typically low displacement values that we record over stationary regions of the radar images (as reported in [1]) suggest that the image alignment is effective. There remains the possibility that the cross-correlation procedure tracks spurious surface features that do not reflect the ice motion. Our code employs several methods to limit this, both in the pre-processing of the radar images (e.g. high pass Butterworth filter -to highlight short wave-length surface features [10]), and in the filtering of the velocity product (strain-constrained image segmentation filter, signal to noise filter, flow direction filter etc.).
Based on our processing of ice velocity data over the Greenland Ice Sheet and parts of East Antarctica, significant ionospheric disturbances create a distinct linear pattern of high displacement stripes. [9] indicate a maximum error related to such features of 0.25 m/d (~91 m/yr). We do not, however, see evidence of significant ionospheric effects in our Antarctic Peninsula data, yet we nevertheless include in our code a filter to minimise such artefacts if detected (https://www.math.univ-toulouse.fr/~weiss/). Overall, the largest reliably quantifiable potential error comes from ionospheric disturbances, which according to [9] has a maximum value of 91 m/yr. We have implemented this error figure in our new analysis ( Fig. 1 in main text; Supplementary Figures 1 and 2). Our speed-up events are typically much greater in magnitude than this.