Estimated time series of Lagrangian basal melt rates from an autonomous phase-sensitive radar (ApRES) measurement at 79°N Glacier (Nioghalvfjerdsfjorden Glacier) in northeast Greenland since 2016. Measurement intervals ranged from one to six hours. Basal melt rates are based on the quantification of the ablation, ice deformation due to strain, and the change in ice thickness. All quantities can be estimated from vertical displacements of internal and basal returns of the transmitted signal. We divided the first echogram into 6 m long segments with 5 m overlap starting at a depth of 20 m. For each segment, we derived displacements from complex cross-correlation of the phase of all pairwise time-consecutive measurements. Afterward, we calculated the daily mean values of the displacements. We used the time-mean vertical displacement of internal reflectors to calculate the vertical strain profile. Here only those segments between 20 m below the surface and 20 m above the basal return at the last measurement were considered. In addition, we only considered measurements between October and May to avoid the influence of ablation on the calculation of the strain. The vertical strain is the depth derivative of the vertical displacement which we derived from a linear fit that best matches the vertical displacements. We use the displacement time series of the segment centered at a range of 50 m to correct for ablation. Since the ice above is affected by ice deformation, we subtract this contribution from the displacement. To derive the basal melt rate in the vertical direction, we subtract the strain contribution and ablation from the displacement of a basal reflector. We analyzed the vertical displacement for all segments within a range of 50 m below the first basal return to obtain the nadir and off-nadir basal melt rates. To represent the variability within a time series, we calculated the median melt rate next to the 25 %, 75 %, and 95 % quantile for each time step. Afterward, a 7-day moving average filter was used to smooth the time series.
