Study site<\/p>\n
Eqalorutsit Kangilliit Sermiat (EKaS; also known as Qajuuttap Sermia) is, to our knowledge, the only major Greenlandic tidewater outlet glacier that has continuously gained mass over the past three decades52<\/a>. At the calving front, the Eqalorutsit Kangilliit fjord is 280\u2013300\u2009m deep and filled with sediments, resulting in a flat bathymetry across the fjord. At the eastern part of the calving front, a pinning point bedrock island with about 100\u2009m in diameter emerges from a subsea ridge that separates the deep fjord from a shallower bay (Fig. 1b<\/a>). Calving at EKaS mainly consists of smaller collapses with infrequent rotational events as large as about 106\u2009m3. Between November and June, the fjord is usually covered with dense ice m\u00e9lange near the calving front. Subglacial discharge is in summer of the order of 200\u2009m3\u2009s\u22121 and is at times visible through the upwelling of turbid meltwater plumes at the calving front. Episodic outburst floods from subglacial and marginal lakes originate at the confluences of EKaS with its northwestern tributary glaciers.<\/p>\n Fibre-optic cable deployment<\/p>\n The deployed fibre-optic cable is a 10-km-long Universal Cable from the supplier NBG. It has a diameter of 4\u2009mm and is armoured by 12 steel wire stands. Two single-mode (SM) and two multi-mode (MM) fibres are guided in a gel-filled steel tube. The cable has a mass of 40\u2009g\u2009m\u22121 (3,200\u2009kg\u2009m\u22123 density) and was spooled onto a wooden cable drum with a total weight of 500\u2009kg. We deployed the cable by hand from the stern of the ice-strengthened vessel Adolf Jensen (Extended Data Fig. 1a,b<\/a>) and synchronized the cable output with the travelled GNSS track distance. Cable sections in shallow water near the eastern shore were deployed from a small, motorized landing boat. The 250-m-long cable section on land leading to the interrogators was trenched in about 20\u2009cm depth. By contrast, the entire 7-km-long submarine cable section was deployed without trenching, by letting the cable sink to the seafloor.<\/p>\n A strong optical loss in both SM fibres at approximately 960\u2009m OD along the cable occurred already during the cable deployment (Extended Data Fig. 2b<\/a>), forcing us to operate our DAS measurements atypically on one of the two MM fibres. These only experienced a co-located loss of 3\u2009dB. During our 3-week-long fibre-optic measurements, the cable suffered multiple damages. From 10 August 05:41 UTC and 17 August 04:40 UTC onwards, we were not able to measure any backscattered light from farther than 5,435\u2009m and 4,135\u2009m OD, respectively, which effectively shortened our cable to terminate at the centre of the calving front eventually. From 10 August 12:10 UTC onwards, a substantial 3.5\u2009dB loss in the MM fibre was present at 681\u2009m OD. We attribute these losses, on one hand, to kinks in the fibre-optic cable formed by seafloor currents dragging the cable and tightening loops that formed from too much slack. On the other hand, we attribute the losses to bends in the fibre because of icebergs becoming stranded on the cable in the shallow bay waters during low tide.<\/p>\n DAS interrogator setup<\/p>\n We deployed a Sintela ONYX v.1.0 interrogator for DAS at the northern shore of the bay east of the calving front (Fig. 1b<\/a>). The interrogator was situated in a waterproof aluminium box together with 12\u00d7 Yuasa 65\u2009Ah 12\u2009V gel batteries powered by 4\u2009\u00d7\u2009300\u2009Wp Goal Zero Ranger solar panels (Extended Data Fig. 1c<\/a>). We continuously recorded strain along one of the two available MM fibres in our cable at 2\u2009kHz sampling rate, 4.79\u2009m gauge length and identical channel spacing between 9 and 29 August (1,587 initial seismo-acoustic sensing sections). A data gap occurred between 20 August 13:55 UTC and 21 August 13:00 UTC (23\u2009h) because of an unexpected laser shutdown of the interrogator that was detected only a day later during maintenance. While recording, we additionally saved directly downsampled data at 100\u2009Hz, 10\u2009Hz and 1\u2009Hz sampling rates, creating a dataset of 13\u2009TB in total. Each time the effective cable length diminished, we adjusted the interrogator settings to record only the functional cable length.<\/p>\n DTS interrogator setup<\/p>\n Co-located with the DAS interrogator, we deployed a Silixa XT-DTS M interrogator for DTS. Similar to the DAS setup, the interrogator was situated in a waterproof aluminium box with 6\u00d7 Yuasa 65\u2009Ah 12\u2009V gel batteries powered by 1\u2009\u00d7\u2009300\u2009W Goal Zero Ranger and multiple smaller solar panels (33\u201368\u2009W) mounted around the box for stand-alone operation (Extended Data Fig. 1c<\/a>). We operated the DTS in single-ended configuration on one of the two MM fibres with a channel spacing of 25\u2009cm and an integration time of 5\u2009min (34,448 initial sensing sections). As a first temperature reference, we spooled up 25\u2009m of cable inside a styrofoam box that was placed inside the larger aluminium box on top of the batteries. As a second temperature reference, we spooled up 25\u2009m of cable inside another insulated box and buried it at 50\u2009cm depth in the soil. Both temperature reference sections were equipped with a PT100 thermometer directly connected to the DTS interrogator. Moreover, we used an RBRduet3 temperature and pressure sensor at the eastern cable landing location to measure near-surface water temperature. On the west shore, we spooled up the remaining cable and put it into an insulated aluminium box together with a Geoprecision M-Log 5\u2009W temperature logger. As for the DAS setup, we adjusted the DTS interrogator settings each time the effective cable length diminished.<\/p>\n Additional instrumentation<\/p>\n In July 2022, we installed three Nanometrics Trillium Compact broadband seismometers with a flat response between 120\u2009s and 100\u2009Hz on the hilltops east, south and west (QJT01, QJT02 and QJT03) of the calving front of EKaS and sampled them at 200\u2009Hz. Owing to fox bite damage, the sensors were only running continuously from 2 August 2023 12:25 UTC (QJT03), 11 August 2023 17:20 UTC (QJT01) and 14 August 2023 17:20 UTC (QJT02). On 5 August, we measured 22 vertical CTD (conductivity, temperature and depth) profiles with an RBRconcerto3 profiler from the R\/V Adolf Jensen along the fibre-optic cable deployment route parallel to the calving front. A weather station (Decagon) co-located with the interrogators collected air temperature, solar irradiation, precipitation and relative humidity in 10-min intervals starting from summer 2022. For the first days of our fibre-optic measurements until 15 August, a terrestrial radar interferometer (Gamma Portable Radar Interferometer, TRI) situated on the hill south of the calving front was scanning the calving front of EKaS in 1-min intervals and monitoring ice-flow speed and calving activity (timing, volume and locations)53<\/a>. A time-lapse camera co-located with the radar took images of the calving front in 2-min intervals until 15 August, and in 20-min intervals subsequently. Where the fibre-optic cable enters the bay, a combined temperature and pressure sensor (RBRduet3) recorded tides, wave heights and surface water temperature at a 3-s interval.<\/p>\n DTS calibration<\/p>\n We use the Python package dtscalibration (ref.\u200954<\/a>) for calibration of the raw Raman Stokes and anti-Stokes backscattering recordings from the Silixa XT-DTS M. We corrected for the optical losses in the fibre that occurred during the deployment, by applying a correction factor to fibre sections after the loss such that the corrected Stokes and anti-Stokes intensity in a 30-m region around the optical loss is linear. The 3.5-dB loss that occurred on 10 August 12:10 UTC altered the recorded backscattered light for multiple tens of metres nonlinearly. We corrected for this particular optical loss by multiplying all measurements and fibre sections before and after the loss by the ratio of the last measurement before and the first measurement after the loss occurred, assuming only small fluctuations in temperature over the 5-min measurement interval. This procedure results in Stokes and anti-Stokes data, as would be expected without optical losses along the fibre.<\/p>\n After this preprocessing, we followed a single-ended calibration procedure in ref.\u200954<\/a> to derive the differential loss \u0394\u03b1 along the fibre, the sensitivity of the Stokes and anti-Stokes scattering to temperature \u03b3, which depends on the fibre material, and a lumped factor C accounting for sensitivity of the detector, the number of molecules involved in scattering and the wavelength dependency backscattered light. The temperature for each fibre section is then obtained with the measured Stokes PS and anti-Stokes PAS intensity by<\/p>\n $$T(x,t)\\,\\approx \\,\\frac{\\gamma }{{\\rm{ln}}\\left(\\frac{{P}_{{\\rm{S}}}}{{P}_{{\\rm{AS}}}}\\right)\\,+\\,C(t)\\,+\\,\\Delta \\alpha x}$$<\/p>\n \n (1)\n <\/p>\n We solve for \u03b3 and \u0394\u03b1 by fitting the DTS temperatures at reference sections (1) inside an insulated box within the aluminium box that houses the interrogator; (2) inside an insulated box 50\u2009cm deep in the soil; and (3) a cable coil in shallow water at the shore with co-located temperature probes. Furthermore, we require the cable sections close to the shore east and west of the fjord to match while the full fibre-optic cable length is operational. We then calibrate the temperature for the entire 3-week-long measurement with fixed \u03b3 and \u0394\u03b1 values. Residuals of the calibration are shown in Extended Data Fig. 11<\/a>.<\/p>\n DAS phase to strain conversion<\/p>\n We convert raw phase \u0394\u03a6 (units of radians) recordings of the Sintela ONYX interrogator to units of strain using<\/p>\n $$\\Delta {\\epsilon }=\\,\\frac{\\lambda }{4{\\rm{\\pi }}{n}_{{\\rm{eff}}}\\,{x}_{g}\\psi \\,}\\Delta \\varPhi $$<\/p>\n \n (2)\n <\/p>\n with the vacuum wavelength of the laser \u03bb\u2009=\u20091,550.12\u2009nm, the effective refractive index of the fibre neff\u2009=\u20091.4682, the gauge length xg\u2009=\u20094.79\u2009m, and the strain-optic coefficient \u03c8\u2009=\u20090.78. The internal data flow of the interrogator applies a leaky frequency filter at 0.1\u2009Hz. For frequencies \u227210\u2009mHz, this filter acts as a differentiator, which results in phase measurements proportional to strain rate, instead of strain. Therefore, we show the DAS data in units of strain, raw phase record or normalized per channel, depending on the frequency of interest.<\/p>\n DAS temperature response<\/p>\n In the DAS recordings, a temperature increase at a given segment of the fibre-optic cable will become evident as a positive strain-rate signal (red in Figs. 5c,d<\/a> and 6b,d<\/a>). This signal has two origins: (1) the thermal expansion of the fibre-optic cable with increasing temperature; and (2) the increase of the refractive index with temperature will be sensed by a positive phase change:<\/p>\n $$\\Delta \\phi =\\,({\\alpha }_{T}+\\xi )\\Delta T\\,\\times \\frac{4{\\rm{\\pi }}{n}_{{\\rm{eff}}}\\,{x}_{g}}{\\lambda }$$<\/p>\n \n (3)\n <\/p>\n with the thermal expansion coefficient \u03b1T\u2009=\u20095\u2009\u00d7\u200910\u22127\u2009K\u22121, the thermo-optic coefficient \u03be\u2009=\u20096.8\u2009\u00d7\u200910\u22126\u2009K\u22121 (ref.\u200955<\/a>). As for frequencies \u227210\u2009mHz, our DAS recordings are proportional to strain rate (see previous section), our interrogator\u2019s response is then about \\(\\Delta \\phi =\\,\\frac{1}{13\\times 1{0}^{-3}({\\rm{K}}\\,{s}^{-1})}\\times \\frac{{\\rm{d}}T}{{\\rm{d}}t}({\\rm{K}}\\,{s}^{-1})\\), meaning that a temperature change by 13\u2009mK\u2009s\u22121 will result in a 1\u2009rad signal. \u0394\u03d5\u2009\u2273\u2009100 over less than a minute caused by the seafloor temperature drops associated with internal wave wakes resulted in faulty phase unwrapping and, therefore, subsequently wrong phase measurements56<\/a> (Fig. 6b,d<\/a>). For the maximum seafloor temperature drop of 0.8\u2009K over less than 100\u2009s (interrogator response is proportional to strain), the expected phase change would be \u0394\u03d5\u2009\u2248\u2009330.<\/p>\n Cable location<\/p>\n We expect the cable to sink to the seafloor in about 15\u2009min. The cable sinking speed is approximately determined from the force balance between the drag force per unit length<\/p>\n $$\\frac{{F}_{{\\rm{D}}}}{l}=\\frac{1}{2}{\\rho }_{{\\rm{water}}}{v}^{2}\\,{c}_{{\\rm{d}}}\\,d$$<\/p>\n \n (4)\n <\/p>\n acting on the cable during sinking with the density of water \u03c1water, the sinking velocity v, the drag coefficient cd\u2009=\u20091.0, the cable diameter d\u2009=\u20094\u2009mm and the gravitational force on the cable<\/p>\n $$\\frac{{F}_{{\\rm{D}}}}{l}\\,=\\,-g\\left({m}_{{\\rm{cable}}}-{\\rho }_{{\\rm{water}}}{\\rm{\\pi }}\\frac{{d}^{2}}{4}\\right)$$<\/p>\n \n (5)\n <\/p>\n with the gravitational acceleration g, and the mass density per unit cable length mcable\u2009=\u20090.04\u2009kg\u2009m\u22121, resulting in a sinking speed of v\u2009\u2248\u20090.4\u2009m\u2009s\u22121. Currents in the fjord are expected to be strongest at the water surface and up to 1\u2009m\u2009s\u22121 (ref.\u200957<\/a>). We, therefore, expect the cable to not be farther off the vessel deployment track than a few hundred metres in the deep fjord sections and virtually underneath the vessel track to within a couple of ten metres in the bay in which strong surface currents are absent.<\/p>\n To further constrain the location of individual cable sections in the deep fjord (Extended Data Fig. 2a<\/a>), we pick the Scholte wave arrivals from a calving event at 10 August 01:30:45 UTC (Fig. 3d<\/a>) with a short-term-average\/long-term-average (STA\/LTA) trigger of 1\u2009s\/10\u2009s in the data band-passed filtered between 1\u2009Hz and 10\u2009Hz (Extended Data Fig. 10a<\/a>). The TRI located the origin of the tsunami caused by this event at 61.310, \u221245.783 (latitude, longitude;\u00a0Extended Data Fig. 10c<\/a>). From the picked arrival times and the event location, we then run a Bayesian inversion using a Markov-chain Monte-Carlo algorithm for locating individual cable sections in the deep fjord section of our fibre-optic cable installation58<\/a>. Therefore, we follow the steps below:<\/p>\n We pick the calving front location at 40 points from Sentinel 2 imagery and interpolate linearly between the picks to get a continuous one-dimensional function of the calving front location (longitude as a function of latitude).<\/p>\n<\/li>\n Interpolate the cable deployment track west of the pinning point island, resulting in a coordinate for every DAS channel and consecutively resample this curve to only 11 anchor points\u2014one at the west shore, one where the cable enters the deep fjord and nine equally spaced (OD) in between. These nine anchor points (x,\u2009y) will be what we will invert for later (2\u2009\u00d7\u20099\u2009=\u200918 parameters). We leave the boundary anchor points to be fixed, as we know the location at the west shore, and we assume that the cable sits directly below the deployment track in the bay.<\/p>\n<\/li>\n Our observations are the relative arrival times of the Scholte wave at the cable, which we automatically picked from the DAS data (Extended Data Fig. 10a<\/a>).<\/p>\n<\/li>\n Our model (M) calculates the two-dimensional travel time between the calving event location and the DAS channel coordinates for a given velocity.<\/p>\n<\/li>\n We define a prior for our Bayesian inversion, assigning an a priori probability to the parameters that we will invert for and which are the 9 anchor points with x and y coordinates each (xn,\u2009yn), a Scholte wave velocity v, the East\u2013West coordinate of the calving event location dx (North\u2013South coordinate is derived from the shape of the calving front in (1)), and an absolute time offset dt for when calving event happened p(xn,\u2009yn,\u2009v,\u2009dx,\u2009dt). We assign a zero probability to the set of inverted parameters if the Euclidean distance between the anchor points is larger than the OD along the cable. We further assign a Gaussian probability distribution to the anchor point locations with a width of 1,000\u2009m and centred around the initial position from the cable deployment track. Last, we allow for small shifts of the calving event location and assign it a Gaussian weighting with a width of 100\u2009m around the radar-derived calving location.<\/p>\n<\/li>\n For calculating the likelihood of the chosen parameters (anchor points, Scholte wave velocity, calving event location and event time), we do a cubic interpolation of the anchor points, resulting in a location for each channel. We then run the arrival time model for the chosen parameters and define the likelihood as the absolute difference between the modelled and the picked arrival times p(tk|x,\u2009y,\u2009xn,\u2009yn,\u2009v,\u2009dx,\u2009dt), with arrival times tk and the interpolated locations for each DAS channel x,\u2009y.<\/p>\n<\/li>\n We calculate the logarithmic posterior probability as the sum of the logarithmic prior and the logarithmic likelihood<\/p>\n $$p({x}_{n},{y}_{n},v,{\\rm{d}}x,{\\rm{d}}t| {t}_{k})\\propto p({x}_{n},{y}_{n},v,{\\rm{d}}x,{\\rm{d}}t)\\,p({t}_{k}| x,y,{x}_{n},{y}_{n},v,{\\rm{d}}x,{\\rm{d}}t).$$<\/p>\n \n (6)\n <\/p>\n<\/li>\n We now initialize a Markov-chain Monte-Carlo sampler with 64 walkers for each inversion parameter, randomly distributed around the initial cable location using the affine invariant Markov-chain Monte-Carlo (MCMC) ensemble sampler emcee57<\/a> for maximizing the logarithmic probability function from (6). We run the MCMC for 50,000 steps while checking for convergence. We select only the last 10,000 steps, resulting in a posterior probability distribution estimate of the parameters we inverted for\u2014in particular, for our nine free anchor points.<\/p>\n<\/li>\n We again do a cubic spline interpolation between the nine free and two constrained anchor points to retrieve a cable geometry for each accepted inversion. From this cable geometry set, we calculate the median and the standard deviation, corresponding to the most likely cable layout given the calving event picks as well as the Scholte wave speed (Extended Data Fig. 10a,b<\/a>).<\/p>\n<\/li>\n<\/ol>\n An accurate assignment of absolute depths to cable sections leading from the submarine ridge between the fjord and the bay down into the deep fjord was unsuccessful. An attempt to match DTS recordings on cable sections between 2,820\u2009m and 3,150\u2009m OD from 9 to 10 August to the CTD temperature profiles close to the ridge from 6 August resulted in an unphysical cable layout with depth differences between adjacent DTS channels larger than the channel spacing of 25\u2009cm. The reason for this discrepancy is probably the daily temperature variability of up to 0.5\u2009K for a given depth as well as the long-term variability of several 100\u2009mK\u2009day\u22121 that impedes a direct comparison of the DTS and the non-simultaneously recorded CTD profiles (Extended Data Fig. 5<\/a>).<\/p>\n Locating fracturing and detachment events<\/p>\n Our cable layout along the calving front spans an approximately linear array of sensors. For such a linear array, hyperbolic-shaped first wave arrivals are expected from point sources (see section 7.4.2 of ref.\u200959<\/a>). In the case of a perfectly linear array, the point source origin is ambiguous and can be located on a plane that is perpendicular to the linear array. Our imperfectly linear cable layout resolves this ambiguity, allowing for event location in three dimensions. For locating both iceberg detachment and fracturing events, we fit synthetic travel time curves to the wave arrivals of the recorded DAS signal (Fig. 3a,b,d<\/a>). In the case of acoustic arrivals from glacier and iceberg fracturing events, we assume a constant three-dimensional wave speed of 1,500\u2009m\u2009s\u22121 in water, and locate the event origin for the shown events at the ice front, the bay and the fjord (Figs. 1b<\/a> and 3a,b<\/a> and Extended Data Fig. 2a<\/a>). In the case of Scholte wave arrivals from iceberg detachments, we assume a two-dimensional propagation along the water\u2013sediment interface with an unknown constant wave speed. We then invert simultaneously for the event location and the wave speed, identifying the wavefield origin at the calving front (Fig. 3d<\/a> and Extended Data Fig. 2a<\/a>).<\/p>\n Detachment event sensitivity estimate<\/p>\n The interferometrically derived subaerial calving volume integrated over 10\u2009min from the TRI does not fully resolve the single calving events observed with DAS, thus hampering an unambiguous assignment of calving volumes to DAS observations. As a result, a TRI-derived calving-volume catalogue comprises 133 events in 10\u2009days, compared to about 30,000 events observed with DAS over a similar 10-day time span (observational times do not fully overlap). Calving is expected to represent a self-organized criticality, in which the calving event rate R follows a power-law relationship with calving event volume R\u2009\u221d\u2009V\u2212b (refs. 18<\/a>,60<\/a>) and, therefore, allows us to estimate a detection threshold for our subsea DAS. An exponent b\u2009=\u20090.79\u2009\u00b1\u20090.06 fits our TRI-derived calving volume number statistics, indicating that large calving events dominate mass loss (exponent 3, much below the TRI threshold of about 5,000\u2009m3 (Extended Data Fig. 4<\/a>). The expected total calving volume observed with DAS then calculates to be around 40% larger than the total volume observed with TRI, because of the TRI missing small events. Comparing the ice flow based on a satellite-derived mean ice-flow velocity across the calving front of 4.5\u2009m\u2009day\u22121, a front width of approximately 3,500\u2009m and an average height of about 80\u2009m, and accounting for changes in the front position, the TRI detects only around 35% of the actual calved-off ice volume. However, owing to smoothing, 50% of the measured volume may get lost in the TRI detection process, increasing the TRI sensitivity up to about 70% of the actual calved-off volume. Now, considering the estimated cumulative calving volume detected with DAS is 40% larger than with the TRI, this means that DAS may detect up to about 98% of all solid frontal ablation. Note that, unlike the TRI, DAS is also able to detect submarine calving events.<\/p>\n Calving location from tsunami dispersion<\/p>\n Calving-induced tsunamis propagate as linear SGWs. We apply a frequency\u2013wavenumber (f\u2013k) transform to the DAS data (Fig. 4b<\/a>) and find good agreement between the observed f\u2013k energy distribution and the SGW dispersion relation<\/p>\n $$\\omega (k)\\,=\\,\\sqrt{gk\\,\\mathrm{tanh}(kh)}$$<\/p>\n \n (7)\n <\/p>\n with angular frequency \u03c9, wavenumber k, gravitational acceleration g and water depth h (ref.\u200961<\/a>). We dominantly observe eastward tsunami propagation (that is, energy with positive wavenumber). The tsunamis mainly occur in the SGW deep-water limit (h\u2009>\u20090.5\u03bb), where the group velocity<\/p>\n $${c}_{{\\rm{g}}}\\,\\approx \\,\\frac{1}{2}\\,\\sqrt{\\frac{g}{k}}$$<\/p>\n \n (8)\n <\/p>\n is independent of water depth. In the 300-m-deep fjord, this relation holds for wave numbers k\u2009>\u20090.01\u2009m\u22121.<\/p>\n Calving event spectrograms (Fig. 4c<\/a>) show the arrival of low-frequency energy (about 30\u2009s period) approximately 2\u2009min earlier than higher-frequency energy (around 10\u2009s period). By relating the rate of frequency shift to the distance D of the wavefield origin62<\/a>,<\/p>\n $$D=\\,\\frac{g}{4{\\rm{\\pi }}}\\frac{{\\rm{d}}f}{{\\rm{d}}t}$$<\/p>\n \n (9)\n <\/p>\n and fitting it to the spectrogram, we locate the calving event that caused the recorded tsunami 750\u2009m west of the pinning point island, which agrees with TRI backscatter imagery (latitude, longitude: 61.3088, \u221245.7740; Fig. 4d,e<\/a>). From this location, we simulate the tsunami arrivals in Fig. 4a<\/a> using the Python package pykonal63<\/a> based on the bathymetry and the general formula for the group velocity at 30\u2009mHz:<\/p>\n $${c}_{{\\rm{g}}}=\\frac{1}{2}\\sqrt{\\frac{g}{h}\\tanh (kh)}\\,\\left(1+\\frac{2kh}{\\sinh (2kh)}\\right)$$<\/p>\n \n (10)\n <\/p>\n Fjord stratification stability analysis<\/p>\n Cold and fresh water overlying warm and salty water, as we observe, are preconditions for convective salt and heat transporting processes. The Turner angle<\/p>\n $${T}_{u}=\\text{arctan}\\,\\left(\\frac{{R}_{\\rho }+1}{{R}_{\\rho }-1}\\right)$$<\/p>\n \n (11)\n <\/p>\n is a measure of the strength of the convection process42<\/a>,64<\/a>.<\/p>\n $${R}_{\\rho }=\\alpha \\left(\\frac{\\partial T}{\\partial z}\\right)\/\\beta \\left(\\frac{\\partial S}{\\partial z}\\right)$$<\/p>\n \n (12)\n <\/p>\n is the density ratio with the thermal expansion coefficient \u03b1, the haline contraction coefficient \u03b2 and the vertical temperature and salinity gradients \\(\\frac{\\partial T}{\\partial z}\\) and \\(\\frac{\\partial S}{\\partial z}\\). Turner angles of Tu\u2009=\u200950\u2009\u00b1\u20096\u00b0 (Extended Data Fig. 6a<\/a>), calculated from our CTD casts, show that weak diffusive convection is present, particularly below the subglacial discharge intrusion at about 100\u2009m depth, explaining the staircase pattern that we observe in the CTD casts (Extended Data Fig. 5<\/a>).<\/p>\n IGW analysis<\/p>\n We observe a typical triangular pattern with reversing polarity in the DAS records as propagating IGWs impinge on the steeply sloping seafloor cable (Fig. 5d<\/a>). IGW frequencies of about 0.5\u20131.0\u2009mHz (15\u201330\u2009min period) are close to and slightly below the buoyancy frequency N, calculated from CTD casts (Extended Data Fig. 6b<\/a>), representing the free oscillation mode of a stratified fluid (see equation 2.243 of ref.\u200965<\/a>),<\/p>\n $$N=\\sqrt{-(g\/{\\rho }_{0})\\,\\frac{\\partial \\rho (z)}{\\partial z}}$$<\/p>\n \n (13)\n <\/p>\n with reference fluid density \u03c10 and density gradient \\(\\partial \\rho (z)\/\\partial z\\) with depth z. The mean buoyancy frequency below 150\u2009m depth calculated from the CTD profiles is N\u2009=\u20091.4\u2009\u00b1\u20090.4\u2009mHz with a peak of N\u2009=\u20092.3\u2009mHz at 193\u2009m depth, at which a thermohaline step is located. With DAS and DTS, we predominantly measure the vertical displacement of the thermohaline steps. Along with the simplified IGW dispersion relation<\/p>\n $$\\omega =N\\text{cos}(\\theta )$$<\/p>\n \n (14)\n <\/p>\n observed IGW frequencies \u03c9\u2009N at the thermohaline steps imply \u03b8\u2009>\u200960\u00b0 with the vertical, and thus we can determine predominantly horizontal wave propagation. During the passage of an internal wave, the temperature change \u0394T(z) at a given depth z is assumed to be adiabatic, with variations only due to heaving of isotherms (vertical advection),<\/p>\n $$\\Delta T(z)\\,=\\,w(z)\\,\\frac{\\partial T(z)}{\\partial z}$$<\/p>\n \n (15)\n <\/p>\n with vertical displacement w(z). For our thermohaline staircase, we observe salinity to scale linearly with temperature, and to dominate the water density (Extended Data Fig. 7b<\/a>), implying that the IGW signal measured with DTS and DAS will be strongest at temperature steps.<\/p>\n DAS sensitivity to internal waves<\/p>\n The 5-min sampling of our DTS just barely samples the IGWs with a 15\u201330\u2009min periodicity. Vastly improved resolution is offered by our DAS data with its 2\u2009kHz sampling rate. For frequencies lower than 10\u2009mHz, as is the case for the internal waves, our DAS phase recordings are proportional to strain rate (see previous sections). IGWs become evident by the vertical displacement of the temperature steps (Fig. 5b<\/a>), as well as the horizontal propagation of IGWs along the cable (Fig. 5d<\/a>). An upward heaving of the thermohaline staircase (increasing temperature at fixed depth) will be recorded as a positive strain rate, a downward motion as a negative strain rate55<\/a>. The DAS record of IGWs, therefore, allows an independent measurement of the thermocline evolution that does not suffer from an absolute temperature calibration as the DTS record requires. As DAS accurately resolves the IGW frequency, which we observe to be close to the buoyancy frequency, temporal variations in the density gradient can be resolved.<\/p>\n Calving-induced submarine melt<\/p>\n We calculate the submarine melt rate at the calving front due to turbulent heat transfer from calving-induced IGWs following the commonly used three-equation model44<\/a>. The first equation relates the freezing temperature in the boundary layer Tb along the ice\u2013ocean interface to salinity Sb and pressure pb<\/p>\n $${T}_{{\\rm{b}}}=a{S}_{{\\rm{b}}}+b+c{p}_{{\\rm{b}}}$$<\/p>\n \n (16)\n <\/p>\n with empirical coefficients a\u2009=\u2009\u22125.73\u2009\u00d7\u200910\u22122\u2009\u00b0C\u2009psu\u22121, b\u2009=\u20099.39\u2009\u00d7\u200910\u22122\u2009\u00b0C and c\u2009=\u2009\u22127.53\u2009\u00d7\u200910\u22128\u2009\u00b0C\u2009Pa\u22121 (ref.\u200944<\/a>). The second equation is the heat balance at the interface<\/p>\n $$\\dot{m}{\\rho }_{{\\rm{i}}}[{c}_{{\\rm{i}}}({T}_{{\\rm{b}}}-{T}_{{\\rm{i}}})+L]={\\rho }_{{\\rm{w}}}{c}_{{\\rm{w}}}\\sqrt{{C}_{{\\rm{D}}}}{\\varGamma }_{{\\rm{T}}}\\,| u| \\,(T-{T}_{{\\rm{b}}})$$<\/p>\n \n (17)\n <\/p>\n with the melt rate \\(\\dot{m}\\), the density of ice \u03c1i and water \u03c1w, the specific heat capacities of ice ci and water cw, the drag coefficient CD\u2009=\u20090.01, the turbulent transfer coefficient for heat \u0393T\u2009=\u20090.01, the absolute ice-parallel speed outside of the boundary layer |u|, the ice temperature Ti, and the water temperature outside of the boundary layer T (measured by DTS). The third equation is the salt balance at the interface<\/p>\n $$\\dot{m}{\\rho }_{{\\rm{i}}}{S}_{{\\rm{b}}}={\\rho }_{{\\rm{w}}}\\sqrt{{C}_{{\\rm{D}}}}{\\varGamma }_{{\\rm{S}}}\\,| u| \\,(S-{S}_{b})$$<\/p>\n \n (18)\n <\/p>\n with the turbulent transfer coefficient for salt \u0393S\u2009=\u20093\u2009\u00d7\u200910\u22124, and the salinity outside the boundary layer S (ref.\u200966<\/a>).<\/p>\n We solve the three equations for the melt rate by using the linear relationship between the temperature and salinity from the CTD casts S\u2009=\u20090.5\u2009psu\u2009\u00b0C\u22121\u2009\u00d7\u2009T\u2009+\u200932.6\u2009psu (Extended Data Fig. 7b<\/a>) and assuming that the ice temperature equals the boundary layer temperature Ti\u2009=\u2009Tb, and meaning that all available heat is used for melting, which introduces only a minor uncertainty. From the DTS data, we calculate vertical water velocities at the fibre-optic cable and assume these to be identical adjacent to the ice. With these, we calculate melt rates of up to 1.3\u2009cm during a 3-h-long IGW wave train (0.07\u2009mm\u2009min\u22121) and peak values of up to 0.2\u2009mm\u2009min\u22121 (Extended Data Fig. 9<\/a>). For IGW with amplitudes comparable to the water depth, we expect the horizontal flow component to contribute equally to the melt rate. Appreciating the effects of surface roughness, turbulence induced by released air bubbles from melted glacier ice, as well as the uncertainty in the turbulent heat transfer, and underestimations in the velocity field derived from the DTS data due to the finite temperature resolution, we expect melt rates of more than 1\u2009mm\u2009min\u22121 (refs.\u200967<\/a>,68<\/a>,69<\/a>).<\/p>\n Calculating seafloor currents from vortex-induced vibrations<\/p>\n During the passage of IGW wakes70<\/a>, we observe harmonic oscillations of the cable typically coherent over 20\u201350\u2009m and strain signals about 10 times higher than for the rest of the cable. Two different types of vibrational modes with a distinct spectral signature are present. The first type constitutes tension-dominated cable modes with closely spaced frequencies (grey lines in Fig. 6f<\/a>) following a linear sequence, with the nth harmonic frequency following<\/p>\n $${f}_{n}=\\frac{n}{2L}\\,\\sqrt{\\frac{T}{m}}\\,,\\,n=1,2,3,\\ldots $$<\/p>\n \n (19)\n <\/p>\n with the suspended cable length L, the horizontal tension in the cable T and the cable mass per unit length m\u2009=\u20090.04\u2009kg\u2009m\u22121 (refs.\u200946<\/a>,71<\/a>). These first-kind cable modes are associated with lock-in vortex-induced vibrations (VIVs), establishing the natural frequencies of the suspended cable section.<\/p>\n The second mode type is characterized by widely spaced frequencies, also following a linear sequence fk \u221d k. They result from multiple lock-in harmonics fn, excited sequentially as the lock-out VIV frequencies<\/p>\n $${f}_{k}=\\frac{k\\,{v}_{\\perp }{\\rm{St}}}{d}\\,,\\,k=1,2,3,\\ldots $$<\/p>\n \n (20)\n <\/p>\n pass each of the lock-in frequencies fn. Here \\({v}_{\\perp }\\) is the ocean current speed normal to the cable axis, St\u2009\u2248\u20090.2, the Strouhal number describing the flow regime, and the cable diameter d\u2009=\u20094\u2009mm. From the lock-out frequencies fk, we determine the ocean current speed perpendicular to the cable (along the fjord) (Fig. 6e,f<\/a>). During IGW wake passage, the fundamental mode lock-out VIVs (k\u2009=\u20091) at the flanks of the wake range between about 2\u2009Hz and 12\u2009Hz (region between dashed white lines in Fig. 6f<\/a>), which translates to seafloor current speed between 0.05\u2009m\u2009s\u22121 and 0.2\u2009m\u2009s\u22121. Lock-in frequencies, in turn, vary only slightly over time (fundamental mode: about 2.5\u2009Hz in Fig. 6f<\/a>), as with increasing current, the cable tension T increases, on which the lock-in frequency fn is only weakly dependent \\({f}_{n}\\propto \\sqrt{T}\\) (ref.\u200972<\/a>).<\/p>\n","protected":false},"excerpt":{"rendered":"Study site Eqalorutsit Kangilliit Sermiat (EKaS; also known as Qajuuttap Sermia) is, to our knowledge, the only major…\n","protected":false},"author":2,"featured_media":6155,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[269],"tags":[6233,18,440,3297,1099,19,17,1100,6234,133,6235],"class_list":{"0":"post-6154","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-environment","8":"tag-cryospheric-science","9":"tag-eire","10":"tag-environment","11":"tag-environmental-sciences","12":"tag-humanities-and-social-sciences","13":"tag-ie","14":"tag-ireland","15":"tag-multidisciplinary","16":"tag-physical-oceanography","17":"tag-science","18":"tag-seismology"},"share_on_mastodon":{"url":"","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/6154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/comments?post=6154"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/posts\/6154\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media\/6155"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/media?parent=6154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/categories?post=6154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ie\/wp-json\/wp\/v2\/tags?post=6154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n