Text S6: Proglacial river discharge data and processing
Hourly proglacial discharges for Qinnguata Kuussua/Watson River (van As et al., 2017; 2019 ) were downloaded fromhttps://doi.org/10.22008/promice/data/watson_river_discharge. Proglacial discharges have been recorded at this location since 2006, using in situ pressure transducer measurements of stage (water level) and an empirical stage-discharge rating curve calibrated with intermittent in situ discharge measurements acquired from different techniques including current meters, the float method, and Acoustic Doppler Current Profiler (ADCP) transects. The discharge estimates have an estimated 15% uncertainty due to rating curve fit and errors in cross-sectional area and velocity measurements (van As et al. 2017 ).
Hourly proglacial river discharges in Akuliarusiarsuup Kuua, a major headwater tributary of Qinnguata Kuussua ~33 km upstream of the Kangerlussuaq bridge and ~2 km downstream of the ice edge, were downloaded from https://doi.org/10.1594/PANGAEA.876357. Proglacial discharges at Akuliarusiarsuup Kuua have been recorded since 2008 at a road bridge crossing (AK4 station, Rennermalm et al., 2013b; 2017 ). Stage and water temperature data are collected sub-hourly using a Solinst® Levelogger pressure transducer and atmospheric barometric pressure logger (accuracies 0.003 m and 0.05°C for the Levelogger, and 0.001 m for the barologger, respectively). Discharges are estimated from the continuously recorded stage data using an empirical stage-discharge rating curve calibrated by periodic in-situ discharge measurements collected from the bridge, using either USGS-style Price AA current meters or a SonTek River Surveyor® ADCP.
The discharge monitoring station at Kangerlussuaq was chosen as the preferred proglacial discharge dataset due its capture of proglacial outflow from a much larger area of the ice sheet, thus maximizing the likelihood of subglacial linkage to Rio Behar moulin, despite uncertain basal routing in the region (e.g. Lindbäck et al ., 2015). To convert the Kangerlussuaq time series into a measure of estimated peak daily discharge at the ice edge, a cross correlation analysis between hourly AK4 and GEUS station measurements was used to determine to estimate the mean timing difference between peak daily flows observed at Kangerlussuaq and peak daily flows at the ice edge.
During the study period, the mean time difference between daily flow peaks at Kangerlussuaq and at AK4 station (33 km distance) averaged 7.6 hours (0.83 s/m). A small additional timing correction between AK4 and the ice edge (2 km distance) is estimated as 0.46 h, by multiplying the mean Kangerlussuaq-AK4 timing correction (0.83 s/m) by 2 km. The total timing correction of 8.1 + 0.9 h was rounded to 8-h and temporally subtracted from daily peak timings observed at Kangerlussuaq bridge. Note that this 8-h proglacial correction is not the same thing as a proglacial flow routing delay because it does not distinguish between wave celerity and Lagrangian flow, but is sufficient for our purpose here, which is simply to estimate the daily timing of peak proglacial outflow at the ice edge using measurements from Kangerlussuaq. Furthermore, note that this 8-h proglacial timing correction does not represent the time difference between peak daily discharge entering Rio Behar moulin and peak daily discharge at the ice edge. Cross-correlation analysis between daily peaks in supraglacial and estimated ice-edge proglacial indicate that the moulin-edge timing difference (again, timing difference only, not subglacial routing) is ~20-h (Figure 3).
Though we generally use this corrected proglacial discharge during analysis (e.g. Figures 2, 3 & 5), we do remove the immediate linear trend from proglacial discharge when examining the lagged correlation between proglacial discharge and ice speed in order to eliminate the potential for autocorrelation.