The RES data were obtained in early June or late May each year from 2014 to 2020 during the annual field trips of the Iceland Glaciological Society on Vatnajökull. The original profile grid over the ESC first measured in 2014 consists of two sets of parallel profiles, perpendicular to each other (Fig. 2b). This profile grid has since then been re-measured every year (Fig. 2–4) following a pre-planned track in the navigation instrument of the snowmobile. This typically results in < 10 m planar offsets between profiles from individual years, except when profiles are intersected by new crevasse formations. Dates and specific remarks concerning individual RES surveys are given in Table 1.

The RES data were acquired using surveying practices developed previously in Iceland (e.g. Björnsson and Pálsson, 2020; Magnússon et al., 2021). The radar transmitter and receiver unit were placed on two sledges separated by distance, a (35–45 m varying between surveys), in a single line and towed along the ice surface using a snowmobile. The low radar frequency applied (5 MHz centre frequency) generally secures clear backscatter from the glacier bed beneath 200–700 m of temperate ice found at the ESC and nearby. During a RES survey, the radar transmits a pulse, which travels as a direct wave along the glacier surface between transmitter and receiver triggering the recording of the receiver (developed by Blue System Integration Ltd.; see Mingo and Flowers, 2010), as well as penetrating into the glacier. The penetrated signal is backscattered from englacial reflectors or the bed up to the receiver at the surface, which records the strength of both the direct and backscattered signal. The signal strength is recorded as a function of detection time relative to the triggering by the direct wave and adding to it the travelling time of the direct wave between transmitter and receiver (using 3.0×108 m s-1 as the speed of the radar wave in air), which yields the two-way travel time of the backscattered signals. Each recording corresponds to 256 or 512 RES measurements stacked to increase signal-to-noise ratio. The sounding plus processing time of the stacked measurements of each recording is ∼ 1 s. The strong direct wave from the transmitter is estimated as the average waveform measured with the RES over several-kilometre-long segments. This is then subsequently subtracted from the corresponding RES recordings. The remaining backscatter is amplified as a function of travel time in order to have the backscatter strength roughly independent of the reflectors depth.

The snowmobile towing the radar was equipped with a Differential Global Navigation Satellite System (DGNSS) receiver. A centre position, M, between transmitter and receiver is assigned to each RES recording. It is derived from the GNSS timestamp obtained by the receiver unit for each RES sounding, and the corresponding position of the DGNSS on the snowmobile projected back along the DGNSS profile by a distance corresponding to half the antenna separation (a/2) plus b, the distance from the RES receiver sledge to the snowmobile (∼ 20 m). Both a and b were obtained with a tape measure for each survey and assumed fixed for each survey date. When surveying profiles without taking sharp turns, the horizontal accuracy of M is expected to be < 3 m, but errors are mainly due to variation in distance to the snowmobile, inexact timing of each RES survey (due to slightly varying sounding and processing time) and the towed sledges not always accurately following the path of the snowmobile. The vertical accuracy is < 0.5 m.

The obtained RES recordings along with M for each recording and corresponding transmitter and receiver 3D positions (a/2 behind and in front of M, respectively, along the DGNSS profile) were used as input into 2D Kirchhoff migration (e.g. Schneider, 1978), programmed in MATLAB (^®MathWorks). The migration was carried out assuming a radar signal propagation velocity through the glacier (cgl) of 1.68×108 m s-1 (corresponding to cgl for dry ice with a density of 920 kg m-3 (e.g. Robin et al., 1969); the choice of cgl and validation from borehole survey is discussed in Sect. 4.1.3) and a 500 m radar beam width illuminating the glacier bed. This results in profile images as shown in Fig. 2. The horizontal and vertical resolution of these images is 5 and 1 m, respectively. This corresponds roughly to the horizontal sampling density when measuring with a ∼ 1 s interval at ∼ 20 km h-1 and an 80 MHz vertical sampling rate (in 2014–2017; it is 120 MHz for an upgraded receiver unit used in 2018–2020).

Backscatter from the glacier bed, which at this stage can be both ice–bedrock and ice–water interfaces, is usually recognized as the strongest continuous reflections in the 2D migrated amplitude images. The next steps including reflection tracing and subsampling of traced reflections from a 5 m interval to a 20 m interval with filtering and masking of traced reflections near sharp turns in profiles are the same as in Magnússon et al. (2021).

At this stage, both the repeated migrated RES profiles as well as traced reflections were projected to a length axis common with the axis of the 2014 survey (the 2018 survey for the new profiles measured since 2018) to allow direct comparison. A slight difference in integrated length along profiles, due to a slight difference profile location between years, can otherwise obscure comparison between profiles. The projection onto a common length axis was only done for segments where the repeated profiles are < 50 m from the original profile. At locations where this deviation was 15–50 m it was considered whether differences in traced reflections were related to a mismatch between profile locations. The traced reflections were first compared in areas at or outside the rim of the ESC, undoubtedly showing a fixed bedrock surface for all surveys. The median elevation difference for the traced reflection in these areas, when compared to the master (2014), was used to bias-correct individual surveys in 2015–2020 towards the master, always resulting in < 2.5 m vertical shift (in 2018 and later, the shift is obtained from comparison with an interpolated bedrock DEM based on surveys from previous years). At this stage, the comparison of the profiles (Figs. 2–3) reveals areas for which the elevation of the traced reflections (median corrected in 2015–2020) is unchanged at the temporal minimum, between two or more survey dates, indicating reflections from bedrock for corresponding surveys. The comparison also reveals areas where the traced reflection of a given survey is clearly above the traced reflection of another, designating a reflection from an elevated ice–water interface. This helps identify the parts of a profile that are reflections from the lake roof (Fig. 3), which for the ESC is not at all revealed by a flat reflective surface. It also reveals that the edge of the lake is commonly characterized by relatively steep side walls, which further helps pinpointing the lake edge where repeated reflections from the bedrock were not obtained, as in 2016 and 2019 when the lake area was at its smallest. The lake margin was then approximated in between the RES profiles to obtain the lake outlines and area (Fig. 4). Some of the RES profiles in 2014 and 2015 did not fully span the areal extent of the lake. The lowering during the 2015 jökulhlaup (see Sect. 2.4) was therefore used to further guide the approximation of the 2015 lake margin where RES observations on the lake edge are not available. The obtained 2015 coverage and observed advance of the margin in 2014–2015 from the RES profiles were considered when approximating the 2014 lake margin. The outlines of the lake margin in 2016–2020 were, however, obtained from the RES data alone by manually drawing lines between obtained lake margin positions in profiles. For some years, a part of the lake margin is rather subjectively drawn. This is particularly the case for the south part of the lake margin in 2017, which should only be considered as a rough estimate (dotted line in Fig. 4d) since this part of the lake margin was beneath the snow-covered supraglacial lake (Fig. 5), which obstructed the RES signal obtained in this part of the cauldron. In 2018, the supraglacial lake was smaller and the margin of the subglacial lake had advanced beyond the extent of the supraglacial lake; hence the supraglacial lake did not obscure the detection of the subglacial lake margin. Similar defects in the 2020 RES data (Fig. 2i), likely caused by englacial water bodies, made it impossible to detect part of the southern lake margin. The approximated margin in 2020 (dotted line in Fig. 4g) is, however, constrained by traced reflections from bedrock a short distance south of the drawn margin; hence the lake area in 2020 cannot be much larger than the estimate presented here. Based on the above, we expect the uncertainty of the lake area to be ∼ 0.1 km2 for all years except in 2017 and 2020 when we estimate the uncertainty as ∼ 0.3 and ∼ 0.2 km2, respectively.

The records of traced reflections were split in two groups, using the lake outlines derived above: (i) reflections from bedrock and (ii) reflections from the roof of the subglacial lake. The former data group was merged into a single data set. This includes data from profiles obtained in the vicinity of the ESC outside the area of repeated RES survey (mostly in 2017 and 2019; see Fig. 4d and f). The traced bedrock reflections display good coverage across the bedrock beneath the cauldrons except where the lake was present for all surveys (Fig. 4). In addition, the bedrock elevation beneath the cauldrons has been measured directly through two boreholes (Gaidos et al., 2020), which were located within the RES data gap. From the bedrock record, including borehole measurements, a bedrock DEM (Fig. 6a) with 20 m × 20 m cell size has been constructed using the kriging interpolation method (processed using Surfer 13 © Golden Software LLC).

The filtered and revised records of traced reflections from a given year obtained within the corresponding lake margin were assumed to originate from a lake roof. The lake roof records of individual survey epochs were then differenced from the interpolated bedrock DEM to obtain lake thickness for each data point. The lake outlines were converted to input data points (with 20 m interval) with a prescribed lake thickness of zero before interpolating each lake thickness map (using the kriging function in Surfer 13) for each year (Fig. 6). At a few locations, minor adjustments of the interpolated maps were made because of disagreement between crossing profiles. This only occurred in areas of very steep topography in the lake roof where 2D migration tends to fail, particularly for profiles driven perpendicular to the slope direction of the underlying lake roof (see Sect. 4.1.2). In such cases, the manual adjustment favoured data from profiles which were more parallel to the roof's slope direction. Lake volumes (Fig. 6) were obtained by integrating the individual thickness maps. In 2020, only the area could be obtained from the RES data; the lake topography was only partly surveyed (Fig. 6h) due to strong internal reflections (see Sect. 2.1), prohibiting direct integration of the lake volume. In this case, the volume of the lake was estimated assuming a linear relation between the lake area and volume using the values obtained in 2014–2019 (Fig. 6i).

The DEMs used to measure the surface lowering of the ESC during the jökulhlaup in 2015 were deduced from interferometric synthetic aperture radar (InSAR) data acquired during the TanDEM-X satellite mission on 23 September and 10 October, a few days before and approximately a week after the jökulhlaup. The DEMs are processed by extracting the topographic information from the InSAR data in the same manner as described by Rossi et al. (2012). Differencing the two DEMs reveals the area affected by the depletion of the subglacial lake as a clear anomaly, outlined in Fig. 7a, as well as surface lowering above the flood route from the lake south of the cauldron. The DEM difference was corrected for near-homogenous surface elevation changes between the two dates, unrelated to the jökulhlaup, and for slowly varying elevation errors in the DEMs, e.g. caused by different penetration of the radar signal into the glacier surface at the two dates (Rossi et al., 2016). Around the outlined anomaly, excluding the flood route, a ∼ 500 m wide reference area was defined, where the elevation changes due to the 2015 jökulhlaup are expected to be insignificant (within few decimetres). The least-squares method was used to fit a linear plane through the obtained elevation difference within this reference area, which we then subtracted from the elevation difference between the two DEMs.

The DEM prior to the jökulhlaup in early August 2018 was constructed from a DEM obtained as part of the ArcticDEM project (Porter at al., 2018) in August 2017, corrected with the DGNSS profiles acquired on 4 June during the 2018 RES survey of the ESC (Fig. 4e). The elevation changes, during the jökulhlaup, were obtained by comparing this DEM with the airborne radar altimetry profiles with an approximate accuracy of 1–2 m (for more details, see Gudmundsson et al., 2016), acquired on 9 August, a few days after the jökulhlaup (Fig. 7d). The difference between the DEM and the radar-altimetry profiles was interpolated with kriging to obtain a map of elevation changes during the jökulhlaup. To compensate for surface elevation changes from 4 June and 9 August, unrelated to the jökulhlaup, a linear plane was again subtracted from the obtained map of elevation changes. The linear plane was obtained in the same way as for the jökulhlaup in 2015, except the westernmost part of the reference area from 2015 was excluded, due to elevation changes related to a jökulhlaup from the WSC, which occurred at the same time as the flood from the ESC in 2018.

To obtain a measurement of water volume released during the jökulhlaups, the elevation changes were integrated within the outlined area of lowering due to the depletion of the lake. The area where this lowering was more than a few decimetres is quite distinctive in the 2015 elevation change map. The less accurate elevation change map during the 2018 jökulhlaup, due to the sparse altimetry data after the jökulhlaup (profile location shown in Fig. 7d) and a larger time gap between the pre-jökulhlaup DEM and the jökulhlaup (∼ 2 months compared to only few days in 2015), made it difficult to directly outline the area of lowering in 2018. It was therefore assumed that the lowering area was the same as in 2015 (dashed line in Fig. 7c). The integrated volume change within this area was 280 ± 5 GL for the jökulhlaup in 2015 and 180 ± 18 GL in 2018. The uncertainty corresponds to a possible bias of 0.25 and 1.0 m for the elevation change maps for in 2015 and 2018, respectively, for the area of integration. It is approximated from the variations in obtained elevation difference outside the area of integration. The volume change during the jökulhlaup, corresponding to the water released from the lake, consists of both the volume integrated from the surface elevation change detectable from the DEMs and the formation of crevasses, which can penetrate deep into the glacier and are not represented in the post-jökulhlaup elevation data. The crevasse field surrounding the ESC after the jökulhlaup in 2015 formed an ∼ 8 km long arc. Assuming that the cumulative width of the crevasses across the 300–400 m wide crevasse field is 100 m at the surface and that this width decreases linearly with depth to 0 m at 100 m depth results in a volume of 40 GL (Guðmundsson et al., 2018). In 2018, the crevasse field had a similar area (shorter arc but wider) resulting in the same crevasse volume estimate. The uncertainties of these estimates are assumed to be rather high, or 50% of the derived values. Combined with the uncertainty of volumes from the DEM difference results in 20 and 30 GL uncertainty in the lake release volume in the 2015 and 2018 jökulhlaups, respectively.

We did not attempt to estimate the uncertainty of the lake volumes derived from the RES data directly. Various factors, which are difficult to quantify, can contribute to this uncertainty, and the dependency between different uncertainty factors is unclear and therefore problematic to combine into a single value (discussed further in Sect. 4.1). Instead, the lake volumes derived from the RES data were validated by comparing them with the volume of water released during jökulhlaups, obtained from measured surface lowering (Figs. 7–8). The results of the validation are described in Sect. 3.1.

The evolution of the lake area inferred from the RES surveys in 2014–2020 is shown in Fig. 4. The minimum area of 0.5–0.6 km2 was observed less than a year after the 2015 and 2018 jökulhlaups, while the maximum of 4.1 km2 was observed in June 2015, ∼ 4 months prior to a jökulhlaup. At the time of this observed maximum lake area in 2015, almost 5 years had passed from the previous jökulhlaup from the ESC in July 2010 (Guðmundsson et al., 2018). In comparison, the lake had expanded to 3.2 km2 in June 2018, 2 months prior to the 2018 jökulhlaup.

The lake development in terms of volume and shape is shown in Fig. 6. The strong positive linear relation between the area and volume of the subglacial lake is demonstrated in Fig. 6i. The variation of lake volume obtained with RES and the estimated volumes of water released during the jökulhlaups extracted from surface elevation changes (Fig. 7c–d) are displayed in Fig. 8. The RES surveys indicate lake volumes < 50 GL in 2016 and 2019, less than a year after jökulhlaups, which strongly suggests that the lake drained completely or was reduced to an insignificant volume in the preceding jökulhlaups. The lake volume prior to each jökulhlaup and the released volumes during them should therefore be comparable, further justifying the validation of the RES results (Sect. 2.5). A maximum volume of 250 GL is derived for June 2015 compared with a volume of 320 ± 20 GL released during the jökulhlaup ∼ 4 months later. The survey in June 2018 yields a volume of 185 GL, while the released volume in August the same year was 220 ± 30 GL. At the onset of the 2018 jökulhlaup, the water volume in the lake had already been estimated to be 180 GL, using the available RES record from the ESC in 2014–2018 (Guðmundsson et al., 2018). Some of the difference between the volumes obtained from RES in June 2015 and 2018 and from surface lowering during jökulhlaups 2–4 months later is likely explained by more rapid lake growth during summers compared to winter due to inflow of meltwater from the glacier surface. With this in mind, the errors in RES volumes were probably < 20 % and < 10 % in 2015 and 2018, respectively. The development of the lake volume in 2010–2020, assuming it drained completely in the jökulhlaup in July 2010, mimics a sawtooth curve (Fig. 8a) with an approximately fixed filling rate of ∼ 60 GL a-1 between jökulhlaups (Fig. 8b). The values in 2014 and 2015 are slightly offset from this trend, possibly due to a less dense profile network then than for later surveys. If the RES surveys of 2014 and 2015 are excluded, the filling rate between jökulhlaups is ∼ 65 GL a-1. Given how well the combined record of lake volumes from RES and observed surface lowering fit a linear relation with time elapsed since the previous jökulhlaup (Fig. 8b), we expect the uncertainties in the RES volumes to be 10 %–20 %, as in 2015 and 2018, except when the lake is small (< 100 GL) and therefore not posing significant hazard (uncertainties > 10 GL should be expected with this approach). By measuring a denser RES profile network as done since 2018, the uncertainty has probably decreased to ∼ 10 % for favourable surveying conditions.

It is worth noting how poorly the measured surface elevation at the ESC centre correlates with the lake volume beneath the cauldron (Fig. 8). This indicates the governing role of ice dynamics for filling up the cauldron surface depression, while the contribution of water accumulation in the lake to surface elevation changes is small in comparison; large proportions of the accumulated water simply replace ice melted beneath the cauldron.

A striking feature in the lake shape for all observations is steep side walls, clearly represented in Fig. 9a–b, typically exceeding 45∘ slopes and sometimes even 60∘. Despite the apparent linear relation between the lake volume and area (Fig. 6i), the overall shape of the lake varies substantially during the study period. In 2014 and 2015, before the jökulhlaup in autumn 2015, the water was distributed much more evenly over the lake area than in 2018. Even though the lake volume and area in 2018 were close to the values obtained for 2014, the lake water was more concentrated close to the ESC centre with the maximum lake thickness above the crater-shaped bed depression beneath the eastern side of the ESC (Figs. 6–8), ∼ 0.5 km east of the boreholes (Figs. 6a and 7a). The shape of the subglacial lake margin also differed between 2015 and 2018. The steep side walls still surrounded the main bulk of the lake in 2018. However, the lake generally extended a few hundred metres outside these walls with an area of 10–30 m thick water layer (see Fig. 6f and left side of Fig. 9b). This clear difference in the lake shape before the 2015 and 2018 jökulhlaups is also apparent in the lowering during these jökulhlaups (Fig. 7c–d). Despite greater lake thickness beneath the ESC centre in 2018 (Figs. 9a–b and 7a–b) the surface elevation was similar to that in 2015 (Figs. 9a–b and 8a). Prior to the 2018 jökulhlaup, the ice above the lake was, however, relatively thin; in 2017 the minimum ice thickness was only ∼ 150 m, but it had increased to ∼ 180 m in 2018. Prior to the 2015 jökulhlaup, when the lake water was more evenly distributed, the corresponding values were ∼ 260 and ∼ 280 m in 2014 and 2015, respectively. The outward migration of the lake margin, typically by 50–150 m, appears as outward propagation of the steep ice walls that defined the lake margin. The steep side walls also seem to characterize the lake margin in 2017, but this was quite different in 2018. Due to the formation of previously mentioned 10–30 m thick water layer surrounding the steep lake walls in 2018, the lake margin typically advanced by 100–1000 m (Fig. 6e–f).

When comparing the obtained lake thickness map prior to jökulhlaups and the subsequent lowering (Figs. 7 and 9), the surveyed shape of the lake and the lowering shows strong similarities. The lowering appears like a spatially filtered version of the lake thickness shape, with the maxima at approximately the same location and substantial lowering (> 5 m) extending typically 200–500 m outside the lake margin as obtained from the RES survey (Fig. 7). Figure 7e–f shows the derived difference between the lake thickness in spring 2015 and 2018 and the lowering during the jökulhlaups a few months later when the lake most likely drained completely or was reduced to an insignificant volume (Fig. 8). This difference, therefore, indicates where the ice became thinner or thicker during and shortly after the jökulhlaups, as well as the outlines of excessively crevassed areas formed during these floods. The main thinning areas as well as the main crevasse areas are located at or outside the main ice walls of the lake. In 2015, this coincides with the lake margin but not in 2018 as mentioned above. The main exception from this is the derived thinning in the northern part of the ESC in 2015, which extends significantly into the cauldron. The lake thickness in this area is, however, not covered with direct RES observation (red profiles in Fig. 7a); hence, the apparent thinning may be an artefact, as the relatively sparse RES profiling did not capture the amount of water stored in this area prior to the 2015 jökulhlaup. This further suggests that the true lake volumes in 2014 and 2015, based on the RES data, are underestimated. The thickening areas approximately correspond to the lake roof within the ice wall of the lake and the surrounding crevasse fields formed during the jökulhlaups. The thickening in 2015 was widespread, typically less than 40 m, and at the centre of the cauldron our estimation suggests thinning, but that may be due to scarce bedrock data at this location (Fig. 6a). In 2018, the thickening was much more localized and exceeded 40 m for substantial part of the area where the ice grew thicker. In both jökulhlaups, the area above the crater-like bed depression beneath at the eastern side of the cauldron yielded by far the greatest thickening. In 2015, the derived thickening at this location was up to 110 m, while in 2018 it was up to 170 m.

There are various uncertain factors, which may contribute to errors in the results derived from the RES data. This includes uncertain value of cgl, limitations of the 2D migration applied and interpolation errors due to sparse data coverage for obtaining both the bedrock DEM and the lake thickness maps. Each of these factors may produce systematic errors, which can lead to an either underestimated or overestimated lake volume. Below we further discuss these limitations and conclude with remarks on how these errors relate to the validation (see Sect. 2.5 and 3.1).

The repeated RES surveys in 2014–2020 yield new insight into the shape of the subglacial lake beneath the ESC and how it has evolved in recent years. The steep, almost step like, side walls (Figs. 2, 6 and 7) differ from the typical conceptual models of lakes beneath ice cauldrons (e.g. Björnsson, 1988; Einarsson et al., 2017) with the lakes drawn with smooth, approximately parabolic or elliptic, cross sections. It is also different in form from attempts to approximate the lake shape based on the difference between cauldron surface elevation shortly before and after a jökulhlaup (Einarsson et al., 2017). The observed step-like structures in the lake shape may be an indication of intensive melting at the lake roof and the upper part of the ice walls, with much lower melt rate on the lower part of the ice walls. The difference in lake shape before the 2015 and 2018 jökulhlaups (see Sect. 3.2) was at least partly caused by changes in the geothermal area below the ESC. Temperature profiles within the subglacial lakes beneath the Skaftá cauldrons have revealed temperatures of 3–5 ∘C that are mostly independent of lake depth, thus enabling effective convection to take place (Jóhannesson et al., 2007; unpublished data at the IMO). Chemical analyses of the water in the WSC lake revealed a component of geothermal fluid of deep origin at ∼ 300 ∘C (Jóhannesson et al., 2007). In 2016–2018 the main vents of the geothermal area, forming centres of strong convection plumes with peak basal melting directly above, were probably close to the two main maxima in lake thickness observed in all 3 years at approximately the same location (Fig. 6d–f). These maxima, indicating the locations where most ice had been replaced by meltwater since the 2015 jökulhlaup, were beneath the east side of the cauldron, above the west side of a sharp crater-like depression in the bedrock (Sect. 3.3) and ∼ 800 m farther west, close to the cauldron centre. The same maxima had started forming in 2019 (Fig. 6g) and at least the eastern one had continued growing in 2020 (Fig. 6h). During the period 2010–2015 these two vents in the geothermal system were probably not as powerful as in 2015–2018, explaining the large difference in minimum ice cover thickness for these two periods (260–280 m in 2014–2015 vs. 150–180 m in 2016–2018). A substantial part of the geothermal power in 2010–2015 was likely released by other parts of the geothermal area beneath the ESC, which typically are much weaker or dormant, explaining the relatively uniform lake thickness in 2014 and 2015. Such a temporal increase in geothermal activity in 2010–2015 probably occurred near the northernmost and southernmost part of the lake in 2014 and 2015. The observed lowering during the jökulhlaup from the ESC in 2010 and the evolution of the ESC since the mid 20th century (Gudmundsson et al., 2018) indicate that this behaviour in 2010–2015 was unusual for the geothermal area, and the activity in 2015–2018 resembles more the behaviour prior to 2010. Even though the distribution of the released geothermal energy was different for the two periods, the net power of the geothermal area was probably similar, as represented in a similar rate of water accumulation in the lake over time (Fig. 8b).

Despite the indication of changes in the geothermal area, it should be kept in mind that the lake accumulated water for 5 years before the jökulhlaup in 2015 compared with 3 years for the 2018 flood. Some of the difference in lake shape may be due to this. However, the thickening of the ice cover in 2017–2018 (∼ 30 m a-1 at the cauldron centre) and the outward migration of steep ice walls seem too slow to explain the different lake appearance in 2015 compared with 2018. The difference in lake shape may, however, have contributed to the earlier onset of the jökulhlaup in 2018. The shallow lake area outside the steep ice walls in 2018 may be an indication that the glacier outside the walls had started to float up as a consequence of high water pressure in the subglacial lake. This high subglacial water pressure likely extended somewhat away from the lake through connections in the subglacial drainage system outside of the lake. This may have contributed to the onset of a jökulhlaup 2 months later.

The RES surveys in 2014–2020 have revealed supraglacial lakes as temporal features sometimes forming in the ESC, and even though englacial water bodies and layers are generally found beneath the cauldron, it seems that in 2020 these features were more prominent than in other years. This highlights the temporal variability in the englacial and supraglacial hydrology at or beneath the ESC. As suggested by Gaidos et al. (2020), the englacial water bodies may play an important role in the triggering of jökulhlaups from the Skaftá cauldrons. A jökulhlaup from the WSC in 2015 was most likely triggered via the drilling of a borehole at the cauldron centre, which created a pressure connection between the subglacial lake and an englacial water body above it (Gaidos et al., 2020). Sudden drainage of supraglacial lakes down to the glacier bed (e.g. Das et al., 2008) also highlights these lakes as a potential trigger of jökulhlaups from subglacial lakes, which should be studied further.

The jökulhlaup in 2015 has been the subject of recently published studies. Ultee et al. (2020) estimated the tensile strength of the glacial ice from the location of crevasse fields formed during the jökulhlaup, and Eibl et al. (2020) studied the seismic tremor related to the jökulhlaup and the potential of using seismic array measurements of the tremor for early warning of subglacial floods. The jökulhlaup in 2018 has not yet received similar attention. The GNSS station, operated by IMO, was running at approximately the same location near the centre of the ESC (Fig. 7) during both jökulhlaups.

During the weeks prior to the jökulhlaup the station had been rising relatively fast likely due to rapid inflow meltwater from the glacier surface. The rate of uplift was ∼ 0.12 and ∼ 0.16 m d-1 the last days before the jökulhlaups in 2015 and 2018, respectively. This may be due to a similar rate of inflow; the ∼ 30 % larger floating ice cover is attributed to lower uplift rate in 2015. The start of the jökulhlaups was observed as the end of these uplift periods in the late evening of 26 September 2015 and 1 August 2018. The start of the jökulhlaup was substantially slower in 2015. The station subsided by ∼ 2 m during the first day of the jökulhlaup in 2018, while in 2015 it took almost 3 d to reach a similar subsidence (Fig. 10). The difference in lake area between 2015 and 2018 can only partly explain the slower initial subsidence during the 2015 jökulhlaup.

After 2 m subsidence, the GNSS station dropped by 60 m in 2015 and 81 m in 2018 over a period of ∼ 40 h. Then, ∼ 4.7 and ∼ 2.7 d into the jökulhlaup in 2015 and 2018, respectively (times marked with circles in Fig. 10a), the station subsidence started to decelerate, and at the same time an eastward motion started. This was followed by a period of decelerated subsidence lasting for ∼ 7 h in 2015. This period probably corresponds to the time when a “keel” at the bottom of the floating ice cover clashes with the bedrock beneath or close to the station. The net subsidence of 68 m at the end of this period (marked with grey triangle in Fig. 10a) fits well with the 67 m lake thickness obtained at the GNSS station as the difference between the bedrock DEM (the GNSS station was located less than 80 m from boreholes where the bedrock elevation was measured directly) and the traced lake roof elevation in June 2015. In 2018, the period of decelerating subsidence lasted for a day. The 94.5 m net subsidence by the end of this period (marked with black triangle in Fig. 10a) is substantially less than the 140 m lake thickness obtained 50 m north of the station in 2018. This lake thickness is, however, obtained at the side of a steep up-doming of the lake roof. The traced lake roof elevation at this location in 2018 was therefore sensitive to the limitation of the 2D migration (Sect. 4.1.2) and likely corresponds to a reflection from the lake roof 100–200 m farther north-north-east.

It is worth noting that during the main subsidence period in 2018, a sudden temporal deceleration occurred in the subsidence as well as in ice flow direction after only 15 m subsidence ∼ 1.6 d into the jökulhlaup (marked with star in Fig. 10a). Such a deceleration is not observed in 2015 and may be caused by floating ice, atop of the 10–30 m thick water layer around the main water chamber, moving against the bedrock a few hundred metres south of the GNSS station. Whilst a supraglacial lake inhibited complete mapping south of the GNSS station, traced reflections from RES data 450 m south of the station indicate grounded ice or lake roof only few metres above the bedrock.

After the period of decelerating subsidence in the late stage of the jökulhlaups, the subsidence temporally sped up again in both jökulhlaups. The speed-up was quite significant in 2015 but only minor in 2018. The station reached a total subsidence of 82.6 m in ∼ 6.9 d during the 2015 jökulhlaup (grey square in Fig. 10a) and 95.6 m in ∼ 4.5 d, 3 years later (black square in Fig. 10a). The horizontal motion of the station continued to decelerate and change direction for a bit more than a day during both jökulhlaups. This probably marks the jökulhlaup terminations ∼ 8 and ∼ 6 d after they started in 2015 and 2018, respectively. Lake water was probably still draining slowly from beneath the areas where the lake was thickest both in 2015 and 2018, east and west of the GNSS station, beyond the period of subsidence as recorded by the GNSS station, during the period of gradual slowdown in horizontal motion. At the end of the 2015 jökulhlaup, the station was located on a relatively steep northward-sloping glacier surface (Fig. 7e). The lowering during the final phase of this jökulhlaup, when the station is moving rapidly in the north direction (Fig. 10b), is therefore to some extent ice motion parallel to the glacier surface slope. The station lowered by 15.5 m and moved by a similar distance northwards during this period. The ice surface geometry near the station in the late stage of the jökulhlaup may favour local thinning due to strong tensile strain rates, which may also partly explain the net thinning of the ice obtained near the station in 2015 (Fig. 7e). In 2018, the GNSS station ended at a relatively flat area, resulting in much less subsidence and horizontal motion during the final phase of the jökulhlaup.

The motion of the GNSS station during the jökulhlaups gives insight into the scale of the events in terms of ice movements, which further helps understand the difference between obtained lake thickness prior to the jökulhlaups and the surface lowering during the jökulhlaups (Fig. 7). In addition to the subsidence > 70 m in a single day in 2018 (> 50 m in 2015), the maximum horizontal velocity of the station was above 10 m d-1 in 2018 and around 20 m d-1 in 2015. The net horizontal displacement during the jökulhlaup, which did not follow a straight line, was approximately 30 m in 2015 and 20 m in 2018 (Fig. 10b). We may expect the horizontal displacement at the location of the station at the cauldron centre to be substantially less than near the sides of the cauldron where the ice flux towards the cauldron centre is highest. There, the net horizontal displacement may exceed 100 m. With this in mind, it is easier to understand how thickening of ice at a given location may be up to 170 m as estimated in 2018 (Fig. 7f). The 100–200 m high walls of the main water chamber in 2018 with slopes sometimes exceeding 60∘ (Fig. 9b) possibly moving many tens of metres inwards may therefore produce a > 100 m increase in apparent ice thickness near the pre-jökulhlaup ice walls. The extension of the thickening area into the main crevasse field at the north side of the ESC in 2018 (Fig. 7f) is probably an expression of ice dynamics of this kind. Even though the ice in this area became thicker, it suffered high tensile strain rates causing the crevasse formation. This effect is, however, expected to be largest in the east side of the cauldron where the estimated ice thickening is by far greatest (Fig. 7e–f). In this area, we observe the steepest and highest ice walls of the lake prior to the jökulhlaups, particularly in 2018. This was also the area surrounded with the largest crevasses in 2018 (Fig. 1d). Additionally, the bedrock at this location is steeply inclined towards a deep bedrock depression beneath the thickest part of the lake (Figs. 6–7). This may enhance sliding of the ice towards the depression centre during the jökulhlaup; inward sliding of the ice walls would produce stronger apparent thickening than if these ice walls would only be tilted inwards without sliding along the bed.

When the net inward horizontal motion decreases from ∼ 100 m to zero over a distance of few hundred metres, we may expect that thickening of the ice caused by compressional straining during the jökulhlaups was several tens of metres, which is comparable with the ice thinning observed outside the lake (Fig. 7e–f) by tensile straining. The high compressional strain rates are evident in compressional ridges that are formed near the centre of the cauldron during jökulhlaups (Fig. 1f) as well as the high uplift rate of the GNSS station after the jökulhlaups. In 2018, the uplift rate of the station the first days after the jökulhlaup was ∼ 0.7 m d-1 (Fig. 10a). When the surface elevation of the cauldron was mapped on 9 August, the station had risen by almost 3 m from its lowest elevation (on 5 August), likely due to post-jökulhlaup ice thickening caused by compressional straining. The post-jökulhlaup strain rates are expected to be much lower than during the jökulhlaups; the horizontal velocity of the GNSS station during them was an order of magnitude higher than after they ended.

The data sets obtained during the jökulhlaups in 2015 and 2018 could be further used to extract information about the mechanical properties of glacial ice, such as parameters describing viscous and elastic deformation and fracture strength. Interpretation of the available data about ice surface lowering and the geometry of the ice shelf and subglacial water body in terms of mechanical properties requires the coupled modelling of the dynamics of the ice shelf and outflow from and the water pressure in the subglacial lake. For modelling the collapse of the cauldron during these jökulhlaups, the RES observations define the shape of the lake at the start of drainage, and the subsidence of the GNSS station can be used as a constraint on the water outflow from the lake during the jökulhlaup. The time-dependent pressure in the lake is required as a boundary condition to describe to what extent the weight of the overlying ice is supported by stresses in the ice and to what extent the ice floats on the subglacial water body. The result of such a modelling experiment, mimicking the observed elevation changes and crevasse formation, may advance the modelling of ice dynamics during extreme strain rates, such as for glacier calving. Such a model, which may require a particle-based model of glacier dynamics to fully include the brittle behaviour of the glacier ice (Åström et al., 2013), could also be used to estimate temporal variations in the lake water pressure during the jökulhlaup. This might answer whether sudden temporary drops of water pressure in the lake may trigger a decrease in pressure within the uppermost part of the geothermal system beneath the ESC, which is considered to be the cause of powerful low-frequency seismic tremor pulses (Eibl et al., 2020; Guðmundsson et al., 2013b) that have often been observed near the end of jökulhlaups from the Skaftá cauldrons.