The increase in iceberg discharge into the polar oceans highlights the importance of understanding how quickly icebergs are deteriorating and where the resulting freshwater injection is occurring. Recent advances in quantifying iceberg deterioration through combinations of modeling, remote sensing and direct in situ measurements have successfully calculated overall ablation rates, and surface and sidewall ablation; however, in situ measurements of basal melt rates have been difficult to obtain. Radar has successfully measured iceberg thickness, but repeat measurements, which would capture a change in iceberg thickness with time, have not yet been collected. Here we test the applicability of using an on-iceberg autonomous phase-sensitive radar (ApRES) to quantify basal ablation rates of a large (~800 m long) non-tabular Arctic iceberg during an intensive 2019 summer field campaign in Sermilik Fjord, southeast Greenland. We find that ApRES can be used to measure basal ablation even over a short deployment period (10 d), and also provide a lower bound on sidewall melt. This study fills a critical gap in iceberg research and pushes the limits of field instrumentation.

Greenland's marine- and land-terminating glaciers are retreating inland due to climate warming, reconfiguring the way the ice sheet interacts with its proglacial environment. Here we use three decades of satellite imagery to determine whether the ice-sheet margin is becoming more or less exposed to marine and lacustrine processes. During our 1990–2019 study period, we find that the length of ice-sheet perimeter in contact with the ocean shrank by 12.3 ± 3.8% (196.2 ± 10.4 km), due to the retreat of marine-terminating glaciers into narrower fjords. On the other hand, we find that the length of the ice-sheet perimeter in contact with freshwater lakes exhibited more divergent trends that is better explored at regional scales. The length of ice–lake boundaries increased in southwest, north and northwest Greenland but declined in southeast and central east Greenland. The magnitude of change we document during our study period leads us to conclude that the ice sheet is poised for further, substantial reconfiguration in the coming decades with consequences for the flux of fresh water, nutrients and primary productivity in Greenland's terrestrial and oceanic environment.

Frontal ablation, the combination of submarine melting and iceberg calving, changes the geometry of a glacier's terminus, influencing glacier dynamics, the fate of upwelling plumes and the distribution of submarine meltwater input into the ocean. Directly observing frontal ablation and terminus morphology below the waterline is difficult, however, limiting our understanding of these coupled ice–ocean processes. To investigate the evolution of a tidewater glacier's submarine terminus, we combine 3-D multibeam point clouds of the subsurface ice face at LeConte Glacier, Alaska, with concurrent observations of environmental conditions during three field campaigns between 2016 and 2018. We observe terminus morphology that was predominately overcut (52% in August 2016, 63% in May 2017 and 74% in September 2018), accompanied by high multibeam sonar-derived melt rates (4.84 m d−1 in 2016, 1.13 m d−1 in 2017 and 1.85 m d−1 in 2018). We find that periods of high subglacial discharge lead to localized undercut discharge outlets, but adjacent to these outlets the terminus maintains significantly overcut geometry, with an ice ramp that protrudes 75 m into the fjord in 2017 and 125 m in 2018. Our data challenge the assumption that tidewater glacier termini are largely undercut during periods of high submarine melting.

We discuss the $\ell $ -adic case of Mazur’s ‘Program B’ over $\mathbb {Q}$ : the problem of classifying the possible images of $\ell $ -adic Galois representations attached to elliptic curves E over $\mathbb {Q}$ , equivalently, classifying the rational points on the corresponding modular curves. The primes $\ell =2$ and $\ell \ge 13$ are addressed by prior work, so we focus on the remaining primes $\ell = 3, 5, 7, 11$ . For each of these $\ell $ , we compute the directed graph of arithmetically maximal $\ell $ -power level modular curves $X_H$ , compute explicit equations for all but three of them and classify the rational points on all of them except $X_{\mathrm {ns}}^{+}(N)$ , for $N = 27, 25, 49, 121$ and two-level $49$ curves of genus $9$ whose Jacobians have analytic rank $9$ .

Aside from the $\ell $ -adic images that are known to arise for infinitely many ${\overline {\mathbb {Q}}}$ -isomorphism classes of elliptic curves $E/\mathbb {Q}$ , we find only 22 exceptional images that arise for any prime $\ell $ and any $E/\mathbb {Q}$ without complex multiplication; these exceptional images are realised by 20 non-CM rational j-invariants. We conjecture that this list of 22 exceptional images is complete and show that any counterexamples must arise from unexpected rational points on $X_{\mathrm {ns}}^+(\ell )$ with $\ell \ge 19$ , or one of the six modular curves noted above. This yields a very efficient algorithm to compute the $\ell $ -adic images of Galois for any elliptic curve over $\mathbb {Q}$ .

In an appendix with John Voight, we generalise Ribet’s observation that simple abelian varieties attached to newforms on $\Gamma _1(N)$ are of $\operatorname {GL}_2$ -type; this extends Kolyvagin’s theorem that analytic rank zero implies algebraic rank zero to isogeny factors of the Jacobian of $X_H$ .

In March 2020, at the onset of the coronavirus disease 2019 (COVID-19) pandemic in the United States, the Southern California Extracorporeal Membrane Oxygenation (ECMO) Consortium was formed. The consortium included physicians and coordinators from the 4 ECMO centers in San Diego County. Guidelines were created to ensure that ECMO was delivered equitably and in a resource effective manner across the county during the pandemic. A biomedical ethicist reviewed the guidelines to ensure ECMO use would provide maximal community benefit of this limited resource. The San Diego County Health and Human Services Agency further incorporated the guidelines into its plans for the allocation of scarce resources. The consortium held weekly video conferences to review countywide ECMO capacity (including census and staffing), share data, and discuss clinical practices and difficult cases. Equipment exchanges between ECMO centers maximized regional capacity. From March 1 to November 30, 2020, consortium participants placed 97 patients on ECMO. No eligible patients were denied ECMO due to lack of resources or capacity. The Southern California ECMO Consortium may serve as a model for other communities seeking to optimize ECMO resources during the current COVID-19 or future pandemics.

Iceberg calving strongly controls glacier mass loss, but the fracture processes leading to iceberg formation are poorly understood due to the stochastic nature of calving. The size distributions of icebergs produced during the calving process can yield information on the processes driving calving and also affect the timing, magnitude, and spatial distribution of ocean fresh water fluxes near glaciers and ice sheets. In this study, we apply fragmentation theory to describe key calving behaviours, based on observational and modelling data from Greenland and Antarctica. In both regions, iceberg calving is dominated by elastic-brittle fracture processes, where distributions contain both exponential and power law components describing large-scale uncorrelated fracture and correlated branching fracture, respectively. Other size distributions can also be observed. For Antarctic icebergs, distributions change from elastic-brittle type during ‘stable’ calving to one dominated by grinding or crushing during ice shelf disintegration events. In Greenland, we find that iceberg fragment size distributions evolve from an initial elastic-brittle type distribution near the calving front, into a steeper grinding/crushing-type power law along-fjord. These results provide an entirely new framework for understanding controls on iceberg calving and how calving may react to climate forcing.

Ice mélange has been postulated to impact glacier and fjord dynamics through a variety of mechanical and thermodynamic couplings. However, observations of these interactions are very limited. Here, we report on glaciological and oceanographic data that were collected from 2016 to 2017 at LeConte Glacier and Bay, Alaska, and serendipitously captured the formation, flow and break-up of ephemeral ice mélange. Sea ice formed overnight in mid-February. Over the subsequent week, the sea ice and icebergs were compacted by the advancing glacier terminus, after which the ice mélange flowed quasi-statically. The presence of ice mélange coincided with the lowest glacier velocities and frontal ablation rates in our record. In early April, increasing glacier runoff and the formation of a sub-ice-mélange plume began to melt and pull apart the ice mélange. The plume, outgoing tides and large calving events contributed to its break-up, which took place over a week and occurred in pulses. Unlike observations from elsewhere, the loss of ice mélange integrity did not coincide with the onset of seasonal glacier retreat. Our observations provide a challenge to ice mélange models aimed at quantifying the mechanical and thermodynamic couplings between ice mélange, glaciers and fjords.

We present a workflow to track icebergs in proglacial fjords using oblique time-lapse photos and the Lucas-Kanade optical flow algorithm. We employ the workflow at LeConte Bay, Alaska, where we ran five time-lapse cameras between April 2016 and September 2017, capturing more than 400 000 photos at frame rates of 0.5–4.0 min−1. Hourly to daily average velocity fields in map coordinates illustrate dynamic currents in the bay, with dominant downfjord velocities (exceeding 0.5 m s−1 intermittently) and several eddies. Comparisons with simultaneous Acoustic Doppler Current Profiler (ADCP) measurements yield best agreement for the uppermost ADCP levels (~ 12 m and above), in line with prevalent small icebergs that trace near-surface currents. Tracking results from multiple cameras compare favorably, although cameras with lower frame rates (0.5 min−1) tend to underestimate high flow speeds. Tests to determine requisite temporal and spatial image resolution confirm the importance of high image frame rates, while spatial resolution is of secondary importance. Application of our procedure to other fjords will be successful if iceberg concentrations are high enough and if the camera frame rates are sufficiently rapid (at least 1 min−1 for conditions similar to LeConte Bay).

Submarine melting at the ice–ocean interface is a significant term in the mass balance of marine-terminating outlet glaciers. However, obtaining direct measurements of the submarine melt rate, or the ocean heat transport towards the glacier that drives this melting, has been difficult due to the scarcity of observations, as well as the complexity of oceanic flows. Here we present a method that uses synoptic velocity and temperature profiles, but accounts for the dominant mode of velocity variability, to obtain representative heat transport estimates. We apply this method to the Sermilik Fjord–Helheim Glacier system in southeastern Greenland. Using lowered acoustic Doppler current profiler (LADCP) and hydrographic data collected in summer 2009, we find a mean heat transport towards the glacier of 29 × 109W, implying a submarine melt rate at the glacier face of 650 ma–1. The resulting adjusted velocity profile is indicative of a multilayer residual circulation, where the meltwater mixture flows out of the fjord at the surface and at the stratification maximum.

Interaction of Greenland’s marine-terminating glaciers with the ocean has emerged as a key term in the ice-sheet mass balance and a plausible trigger for their recent acceleration. Our knowledge of the dynamics, however, is limited by scarcity of ocean measurements at the glacier/ocean boundary. Here data collected near six marine-terminating glaciers (79 North, Kangerdlugssuaq, Helheim and Petermann glaciers, Jakobshavn Isbræ, and the combined Sermeq Kujatdleq and Akangnardleq) are compared to investigate the water masses and the circulation at the ice/ocean boundary. Polar Water, of Arctic origin, and Atlantic Water, from the subtropical North Atlantic, are found near all the glaciers. Property analysis indicates melting by Atlantic Water (AW; found at the grounding line depth near all the glaciers) and the influence of subglacial discharge at depth in summer. AW temperatures near the glaciers range from 4.5˚C in the southeast, to 0.16˚C in northwest Greenland, consistent with the distance from the subtropical North Atlantic and cooling across the continental shelf. A review of its offshore variability suggests that AW temperature changes in the fjords will be largest in southern and smallest in northwest Greenland, consistent with the regional distribution of the recent glacier acceleration.

Icebergs calved from tidewater glaciers represent about one third to one half of the freshwater flux from the Greenland ice sheet to the surrounding ocean. Using multiple satellite datasets, we quantify the first fjord-wide distributions of iceberg sizes and characteristics for three fjords with distinct hydrography and geometry: Sermilik Fjord, Rink Isbræ Fjord and Kangerlussuup Sermia Fjord. We estimate average total iceberg volumes in summer in the three fjords to be 6.4 ± 1.5, 1.7 ± 0.40 and 0.16 ± 0.09 km3, respectively. Iceberg properties are influenced by glacier calving style and grounding line depth, with variations in size distribution represented by exponents of power law distributions that are −1.95 ± 0.06, −1.87 ± 0.05 and −1.62 ± 0.04, respectively. The underwater surface area of icebergs exceeds the subsurface area of glacial termini by at least one order of magnitude in all three fjords, underscoring the need to include iceberg melt in fjord freshwater budgets. Indeed, in Sermilik Fjord, we calculate summertime freshwater flux from iceberg melt of 620 m3 s−1 (±140 m3 s−1), similar in magnitude to subglacial discharge. The method developed here can be extended across Greenland to assess relationships between glacier calving, iceberg discharge and freshwater production.