Text S8: Supplemental discussion of ΔS proxy and ice motion
Of the variables examined here, we conclude that supraglacial river discharge is the dominant driver of short-term variations in ice speed at our field site, due to its influence on subglacial water storage change ΔS . In the vicinity of the moulin, ΔS is strongly paced by the integrative nature of upstream surface routing through the Rio Behar catchment, which makes the timing of peak daily moulin input less variable than that of melt energy, air temperature, or ablation (Figure 3 ). Our observed ~5 h delay between peak melt energy and peak moulin input confirms previous assertions (e.g. Smith et al., 2017; Yang et al. 2018; 2020 ) that surface routing delays through supraglacial stream/river drainage catchments are both non-trivial and predictable and should be explicitly accounted for in studies of short-term ice motion. Unlike melt energy, moulin discharge does not shut down at night (Figure 4d ), perhaps helping to maintain pressurized water-filled subglacial conduits and resist conduit closure (e.g. as per Meierbachtol et al., 2013; Bartholomaus et al., 2008 ).
Our discharge-difference proxies for S and ΔS rely on a core assumption that proglacial discharges sourced from a large area can reasonably characterize basal water pressure under our much smaller study area; and that supraglacial moulin inputs transfer rapidly to the bed rather than entering englacial storage. Furthermore, we must apply a timing correction to the proglacial discharge record to compensate for the net effects of proglacial flow routing and wave celerity between the ice terminus to Kangerlussuaq bridge (35 km; SI Text S6).
While our supraglacial hydrograph and resultant qualitative ΔSproxy appear to align reasonably well with the ascent of daily peaks in ice speed, we note a varying time lag between ΔS and ice motion, as well as some non-linear behavior on the descending limb of the diurnal peaks (Figure 5c ). There are a number of possible reasons for these phenomena. One likely reason is that ice motion integrates both local and non-local forcings over long length scales (3-8 ice thicknesses), so ice dynamics from surrounding areas likely influence our field site. Similarly, supraglacial forcing of the subglacial system is not uniform over these length scales, with moulin inputs peaking at different times due to varying upstream catchment areas (Smith et al., 2017; Yang et al, 2016 ). While the Rio Behar moulin has no neighboring large moulins within 5 km, we cannot rule out the possibility of temporally asymmetric subglacial water delivery from nearby moulins. However, we observe a small secondary daily peak in our discharge-difference ΔS proxy that often coincides with a smaller secondary peak or shoulder in daily ice motion (Figure 5c ) suggesting reasonably good coupling between our regionally-influenced ΔS proxy and local accelerations in ice speed and that this small secondary ice speed peak is driven by subglacial hydrologic dynamics.