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Ponded meltwater on the Larsen B Ice Shelf before its collapse has become emblematic of the destructive role of stored meltwater. The glaciers feeding Larsen B experienced a notable speed-up after the ice shelf’s 2002 collapse2. Meltwater stored in ponds loads, flexes and weakens an ice shelf3. Meltwater also deepens crevasses3. As global temperatures rise, more meltwater will form atop the ice shelves that ring Antarctica5. Ice-sheet models that project future sea-level rise include an ice-shelf hydro-fracturing mechanism that is linked to surface melting4. These models funnel the surface melt into crevasses at the grounding line (the point at which a forward-moving glacier loses contact with the ground, becoming a floating ice shelf) and calving front, where this stored water deepens the crevasses through hydro-fracturing6, eventually triggering the collapse of the ice shelves and the rapid retreat of the Antarctic ice sheets.

To understand the role of increased surface melt, we examine the Nansen Ice Shelf, where surface melt is already widespread and surface ablation is around 0.5 m yr−1. Located along the edge of the Ross Sea, the (1,800 km2) Nansen forms where the Priestley and Reeves Glaciers go afloat and merge7 (Fig. 1). There is no evidence for recent collapse of the Nansen, or of the adjacent Hells Gate Ice Shelf. Both have persisted throughout the warming period of the late Holocene era, advancing after around 5,800 years bp to their present extent8. Strong katabatic winds scour much of the ice surface of the Nansen blue ice. An elongate, low-lying shear margin separates ice from the Reeves and Priestley Glaciers (at 20 km; Fig. 1b; ref. 9). South of the shear margin, the Reeves Glacier ice contains oblique 1.5–4.5 m deep, 7–10 km long depressions that are similar to the surface expression of basal melting in Pine Island Glacier10 (Fig. 1b, R1 and R2). North of the shear margin, the Priestley Glacier ice contains 1–4 m deep linear troughs. The deepest of these troughs (P2, P3 and P4 in Fig. 1b) are associated with thinner ice11 and overlie basal crevasses12 (Fig. 1c).

Figure 1: Surface hydrology and topography of Nansen Ice Shelf.
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a, Landsat image of the Nansen Ice Shelf, showing three drainage catchments (outlined in black); the line of flight of the NASA IceBridge mission (mango); the waterfall location (star); the grounding line (blue solid and dashed lines); and the ice-shelf rift (red dotted line). White boxes indicate the locations studied for Figs 2, 3. The green dot indicates the location of the Mario Zucchelli Station weather observatory on Hells Gate Ice Shelf. b, IceBridge ice surface elevation profile across the shear-margin river and adjacent basins9. R1 and R2 are 1.5–4.5 m deep, 7–10 km long depressions; P2, P3 and P4 are 1–4 m deep troughs. c, IceBridge radar profile11. d, Water export off the shelf at a 130 m wide shear-margin river waterfall on 12 January 2014; photo credit: Robert Fletcher.

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Water was first observed on the Nansen Ice Shelf in 1909, by Ernest Shackleton’s Nimrod team traversing towards the magnetic South Pole. T. W. E. David noted that a “thaw-water stream could be heard roaring”13 along the southern edge of the ice shelf. Three years later, the Northern Party team of Scott’s British Antarctic Expedition spent January 1912 mapping the Nansen Ice Shelf. Approaching the Priestley Glacier grounding line, the team reported that the “noise of running water from a lot of streams sounded odd after the usual Antarctic silence”14. The Northern Party described surface melt forming adjacent to outcropping rocks and lateral moraines. They crossed thaw channels, streams, marginal ponds and a 15 m deep, 50 m wide ravine (Fig. 2, Extended Data Fig. 1 and Extended Data Table 1) containing flowing water15. The Northern Party repeatedly fell into thaw ponds and ice-covered streams14,15 and water filled the base of their tents16.

Figure 2: Photographs of the Nansen Ice Shelf taken by the 1912 Northern Party.
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a, This Landsat image, taken on 26 December 2013, shows the locations depicted in the photographs at the right. b, Deep, water-filled ravine. c, Surface stream on ice-shelf margin. d, Two men with a sledge on the ice shelf, showing ponded water. e, Raymond Priestley wading barefoot in water on the ice-shelf margin. f, Surface stream. g, Frozen pond. Green-bordered photos are from Corner Glacier (green dot) on the eastern side of the ice shelf. Yellow-bordered photos were taken close to the moraine camp (yellow dot). Photo credits: Frank Debenham. Locations of Northern Party camps are presented in Extended Data Table 1.

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Here, we used airborne imagery (from 1956 to 1975) and satellite remote sensing (from 1974 to 2014) to document the persistence and extent of surface melt. We also estimated the volume of water exported off the ice shelf into the ocean. Using catchment analysis and satellite imagery, we identified three types of ice-shelf drainage. Close to the Priestley Glacier grounding line, a catchment basin terminates in firn (recrystallized compacted snow from previous seasons), while a catchment close to the Reeves Glacier grounding line drains onto ice mélange that fills rifts in the ice shelf. On the outer shelf, a shear-margin catchment feeds a river that develops along the low-lying shear margin (Fig. 1a). All of these systems are active during the melt season.

The Priestley Glacier firn-terminating catchment begins at the grounding line, where meltwater forms in December along moraines and exposed bedrock (Fig. 2 and Extended Data Fig. 2). These ponds drain into the 15 m deep, water-filled ravine that was mapped in 1912 by the Northern Party (Fig. 2b). During the melt season, water fills marginal crevasses and flows around 20 km down the ice shelf across blue ice into the section of the ice shelf with thicker surface snow, where it probably saturates the firn and feeds firn aquifers. Similar firn-terminating streams have been observed on the Amery17 and Nivilsen18 ice shelves, as well as in Dronning Maud Land19,20 in East Antarctica.

The mélange-terminating Reeve Glacier grounding-line catchment, first observed in 1909, was resolved by airborne imagery in 1961 and 1975 and by commercial high-resolution satellite images from 2014 (Extended Data Fig. 2). The surface meltwater entering these rifts drains into the sub-ice cavity and may explain the relative freshness of the ice recovered from drilling into these rifts21. This connectivity of surface melt drainage to the underlying ocean is similar to the dolines (sinkholes) observed on the Larsen C22 and Amery23 ice shelves.

The majority of water exported from the ice shelf drains along the shear-margin depression, across the shear-margin catchment. Little surface debris remains on the ice shelf within this catchment. The widespread meltwater within this catchment was first resolved by a 1974 Landsat image and by airborne imagery in 1975 (Extended Data Fig. 3). In years during which the temperature is high and large volumes of melt are produced, a river forms along the low-lying shear margin and terminates at an ice-edge waterfall. Between December 1989 and January 2016, the waterfall was recorded in Landsat imagery tumbling into a developing rift in the ice shelf. The rift gradually widened until a calving event occurred in early April 2016. Similar-sized calving events have occurred twice in the twentieth century24 (Methods). However, the presence of persistent surface water on the Nansen Ice Shelf has not triggered catastrophic ice-shelf collapse. Before the 2006–2007 melt season, the satellite record is too sporadic to determine how and when the waterfall forms. The Nansen shear-margin river exported water off the ice shelf in six of the eight melt seasons between 2006 and 2015, for which satellite coverage is sufficient to determine the extent of the drainage system (Extended Data Table 2).

The development of a drainage system that exported water was well documented during the 2013–2014 and 2008–2009 (see Supplementary Videos) melt seasons. For 2013–2014, we used Landsat-8 multispectral data to map water extent25 and depth across the shear-margin catchment25 (see Methods). We determined water extent by using the normalized difference water index adapted for ice (NDWIice)25 and water depth by using the attenuation of the water-leaving reflectance in the Landsat-8 blue channel (Fig. 3 and Extended Data Figs 4, 5). On 26 December 2013, shallow surface melt (slush) was widespread on the ice shelf and water was beginning to concentrate in the shear margin river, drawing from two inland ponds. One week later (2 January 2014), the widespread shallow water had coalesced into the surface ponds; two additional ponds on the Priestly Glacier side (P2 and P3 in Fig. 1b) had drained into the river; and the waterfall was exporting water. By 5 January, two additional ponds (R2 and R3) on the Reeves Glacier side were draining into the river. By 9 January, the furthest downstream ponds on both sides of the shear margin (R1 and P1) had connected with the river. The connectivity between the ponds and the river propagated downstream towards the calving front. Thus, over the course of two weeks, an interconnected system of streams and ponds evolved to export water at the waterfall.

Figure 3: Evolution of the extent and depth of meltwater during the melt season.
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a–d, Landsat imagery of the shear-margin river from 26 December 2013 to 9 January 2014. The river’s location is shown in Fig. 1. e–h, Distribution of shallow/slushy water (less than 0.2 m deep), medium-deep water (0.2–1 m deep) and deep water (more than 1 m deep). The extent of shallow/slush water is 0.12 < NDWIice < 0.14, of medium-deep water is 0.14 < NDWIice < 0.25, and of deep water or ponds is NDWIice > 0.25. i–l, The fraction of surface area that is characterized by slush, medium and deep water. Ice-shelf water evolves from being predominantly shallow in December to predominantly deep in January. Sensitivity analysis and location are shown in Extended Data Fig. 4. Water extent and depths shown in Extended Data Fig. 5.

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For eight melt seasons, sufficient satellite coverage is available to track the development of ice-shelf hydrology, quantify the duration of meltwater export and estimate the volume of meltwater exported. When the waterfall forms, it exports water for 5–25 days, persisting for longer when the temperatures are higher. The temperature record from Mario Zucchelli Station (Fig. 1) shows that the two years during which no waterfall was observed (2006–2007 and 2009–2010) were the coolest. The waterfall’s duration increases as the number of days during which the minimum temperature is above the melting point (0 °C) at Mario Zucchelli Station increases (Extended Data Figs 6, 7). More water is exported during warmer years. As environmental forcing changes and meltwater production increases, the ice-shelf drainage system adapts, exporting more surface meltwater.

We estimated the volume of surface melt exported off the ice shelf by using Manning’s equation, which is based on airborne laser topographic measurements9 and on Landsat satellite imagery (Methods). The river drained towards the waterfall with flow speeds of 1.39–2.17 m s−1 and fluxes of around 259–806 m3. Velocities determined through feature tracking from a helicopter-based video provided slightly lower estimates (see Methods). We quantified the volume of water exported each melt season by using the waterfall export duration and the minimum flux from the Manning approach (260 m3 s−1). The calculated water export ranges from 0.04 km3 to 0.56 km3 in each season. In just seven days, the waterfall can export the entire annual surface melt volume produced by a melt rate of 0.5 m yr−1 over the shear-margin catchment. Present ice-sheet models produce rapid disintegration when surface melt rates reach 1.5 m yr−1. However, our results show that this amount of surface melt could be removed by the waterfall in 21 days (Extended Data Fig. 6). This efficient export of surface meltwater highlights the capacity of rivers to efficiently buffer ice shelves against the damaging storage of melt.

The surface melt rate of 0.5 m yr−1 on the Nansen Ice Shelf may be representative of ice-shelf hydrology in the future. With the exception of the ice shelves on the Antarctic Peninsula, the surface melt rates on Antarctic ice shelves are presently relatively low. With surface melt rates projected to increase, a key question is whether Nansen-style drainage systems will develop elsewhere and export water off the ice shelves. Using surface digital elevation models (DEMs)26, we analysed possible surface drainage networks of four large ice shelves—Amery, Filchner-Ronne, Larsen C and Ross—using a simple routing algorithm (Fig. 4; Methods). Some ice-sheet models project that these ice shelves will disintegrate quickly after the surface melt exceeds 1.5 m yr−1 within the next century4. Our analysis, however, suggests that drainage networks aligned along troughs could form where ice-flow units of variable thickness and velocity meet at shear margins, similar to the shear-margin river on Nansen Ice Shelf. As surface melt increases, shear-margin rivers may develop on these other ice shelves, extending up to hundreds of kilometres inland (for example, 80 km inland on Amery, 65 km on Larsen B, 350 km on Ross and 440 km on Filchner).

Figure 4: Surface meltwater routing on Antarctic ice shelves.
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a, Larsen C (average slope 0.14°). b, Filchner–Ronne (average slope 0.03°). c, Ross (average slope: 0.04°). d, Amery (average slope 0.07°). The routing, in black, is overlain on surface slopes. The convergence of flow from different glaciers forms topographic troughs and steeper surface slopes on ice shelves. Water will coalesce and be preferentially exported off the ice shelves along linear troughs. The mean slope of the Nansen Ice Shelf shear-margin catchment is 0.11°.

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The large-scale morphology of future drainage networks will depend on surface and basal mass balance as well as ice-shelf strain rates. Our results show (for the first time, to our knowledge) that surface meltwater on an ice shelf can be exported off the ice shelf through a hydrologic system that evolves as melt increases. We suggest that river networks that facilitate meltwater export will develop on other ice shelves as melt rates increase. Ice-shelf rivers are presently active in northern Greenland (on Petermann Glacier; Extended Data Fig. 8). These rivers, which reduce the stored surface water, will form when the ice-surface slope is sufficiently steep and the storage capacity in firn aquifers, ponds and crevasses is limited. The slope of an ice shelf’s surface is strongly controlled by the thickness of incoming ice and by the basal melt rate, which is driven by ocean temperatures. The ice-surface mass balance is controlled by surface accumulation, the persistence of katabatic winds and run-off. Comparing the atmosphere and oceanographic conditions for ice shelves with surface rivers (Nansen, Petermann, and possibly 79N in Greenland) with ice shelves on which water is retained at present (Larsen C and Amery) will advance our understanding of the role of surface river export in a warming world.

At present, surface meltwater is being produced and transported onto ice shelves around Antarctica27 and is expected to increase in the future. The dynamic nature of the Nansen surface hydrology highlights the need to accurately model surface water extent and flow across ice shelves. Export of meltwater by surface rivers may buffer the impact of warming temperatures. Thus a realistic representation of ice-shelf plumbing and surface hydrology will be essential in accurately projecting the future of Antarctica’s marine ice sheets and their potential contribution to sea levels.

Methods

Historical photographs and journals

We used original archival material from the Northern Party Expedition, part of the British Antarctic Expedition 1910–1913, together with published accounts and diaries to develop a full account of the historic observations of water on the Nansen Ice Shelf.

The Northern Party was the team from Scott’s British Antarctic Expedition 1910–1913 who studied the Terra Nova Bay region. The Northern Party conducted six weeks of mapping from the Hells Gate Ice Shelf to the Priestley grounding line in early 1912. They documented the water systems and the fossil-rich moraines.

The Northern Party images used here (Fig. 2), taken by Frank Debenham, are archived at the Scott Polar Research Institute (SPRI) Library, University of Cambridge. Some of these images (Fig. 2b, c) were also published by C.S. Wright and Raymond Priestley in 1922 (ref. 28). The images are in the SPRI collection with the following identifiers: Fig. 2b, P54/16/311, Sandstone Glacier barranca or ravine with stream at base; Fig. 2c, P54/16/280, Corner Glacier stream; Fig. 2d, P54/16/307, Sandstone Glacier, two people with sledge and water; Fig. 2e, P54/16/372, Priestley wading for mirabilite; Fig. 2f, P54/16/279, Corner Glacier with sledge; Fig. 2g, Priestley Glacier with frozen pool. Locations of the major campsites were identified from the 1912 maps, and are presented in Extended Data Table 1 and shown in Extended Data Fig. 1.

The Nimrod Expedition was led by Ernest Shackleton in 1907–1909. In 1908, T.W. Edgeworth David, Douglas Mawson and Alistair Mackay crossed the Nansen Ice Shelf on their way to the East Antarctic Plateau in search of the magnetic South Pole. David was a keen observer of surface water throughout the expedition, mapping water on the Ferrar Glacier in addition to observing water on the Nansen Ice Shelf.

The original archival material reviewed for the Northern Party included the diaries of Victor Campbell, Priestley, Debenham and George Levick, which are preserved at the University of Cambridge Polar Research Institute in Cambridge, UK. Using the maps, journals and modern imagery, we located the photos of the surface water systems described by both the Northern Party and the Nimrod expedition.

Trimetrogon aerial photography

The US Navy collected trimetrogon aerial photography (TMA) over Antarctica beginning in 1946 with Operation Highjump. The TMA images were generally collected with three cameras, positioned to take simultaneous vertical, left oblique, and right oblique images. Along a single flight line, the oblique cameras were pointed 30° off nadir. Each of the three cameras had an angular field of view of 60°, providing a 180° horizon-to-horizon coverage when the images are placed side-by-side. The majority of images over the Nansen Ice Shelf are black-and-white photographs. Later flights include only single nadir colour images. The US Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center scanned the US Antarctic film collection and worked with the Antarctic Geospatial Information Center (AGIC) to establish latitude and longitude coordinates for the single-frame records. The nominal resolution of the images varies with flight elevation. For the vertical images used over the Nansen, the high-resolution scans at 1,000 d.p.i. provide a resolution of 1–2 m. We used the AGIC data browser to review the Nansen TMA imagery. The TMA mission number, roll number and frame number are essential, as some of the imagery required geolocation owing to positioning errors that became apparent upon image analysis. We reviewed the TMA imagery over the Nansen Ice Shelf from 2 December 1956, 8 and 9 January 1957, 14 January 1961, 8 January 1975, 11 November 1984, and 5 and 11 November 1985.

Extended Data Fig. 3 includes the TMA image of the 1975 waterfall that was taken on 8 January 1975 (TMA photograph identifier CA238432V0063, available from https://earthexplorer.usgs.gov). We have also included the Landsat image from 16 January 1974 (Landsat image scene identifier LM10641141974016AAA02, available from https://earthexplorer.usgs.gov), which also shows a well defined surface drainage network as well as a waterfall on the calving front.

IceBridge airborne data

We used NASA IceBridge data for the Nansen Ice Shelf to constrain the ice thickness and surface morphology of the shear-margin river and the surface ponds on the Reeves and Priestley Glacier sides. We used the airborne topographic mapper (ATM) laser altimetry9 and multichannel coherent radar depth sounder (MCoRDS) ice-penetrating radar data11 from the 19 November 2013 flight for this analysis (Fig. 1).

Landsat images

The Landsat images shown in the Supplementary Videos and in Figs 1 and 2 are pansharpened colour infrared composites obtained using Landsat-8 channels 5 (near-infrared, 850–880 nm), 4 (red, 640–670 nm) and 3 (green, 530–590 nm).

Calculation of ice-shelf catchments and water routing

To determine the ice-shelf catchment area, we calculate water flow paths by applying a routing algorithm29 to the Bedmap2 surface elevation DEM26. No Worldview imagery over the ice shelf was available that could produce a high-resolution DEM. We evaluated other available DEMs and all produced similar catchments. The single IceBridge line was insufficient to produce a detailed DEM but closely matched the Bedmap2 surface.

We used a multiple-slope, D-infinity approach30 to calculate the flow direction after filling closed basins. These closed basins were interpreted as artefacts within the DEM, and were removed by raising their elevation iteratively to the point at which water overflows its confining pour point. We then summed the upstream contribution areas on the basis of the calculated flow directions, and delineated the surface water flow paths across the Nansen Ice Shelf. Next, we use these flow paths to determine the ice-shelf catchment area. To delineate the catchment boundaries, we defined outlet points along the ice calving front. From the calculated flow network, we identified three outlet points. We then followed a flow-direction grid backwards from these outlet points, and determined all of the cells that drain through a given outlet. The edges of these grid cells represent the boundary of the ice-shelf catchments shown in Fig. 1a.

We also applied this approach to estimate the routing for the other four large Antarctic ice shelves (Fig. 4) using Bedmap2 surface topography.

Mapping water areas and depth categories

We used data collected by the Landsat-8 sensor to estimate water area and depth over our study region. Landsat-8 was launched in 2013 and hosts the operational land imager (OLI) spectrometer, suitable for lake area and depth estimation (http://landsat.usgs.gov/landsat8.php). The OLI has enhanced (12-bit) radiometric resolution with respect to its (8-bit) predecessors, a higher signal-to-noise ratio, and an expanded dynamic range compared with Landsat-7’s enhanced thematic mapper plus (ETM+). Optical data can be used to extract both the area and the depth of supraglacial ponds using a combination of bands31,32,33. The increased scene-collection rate of Landsat-8 has also lead to increased area coverage by the sensor. Landsat-8 surface reflectance values used in this study were obtained from EarthExplorer (http://earthexplorer.usgs.gov/). Only images with less than 10% cloud cover were used (Extended Data Figs 4, 5). For each of the Landsat-8 scenes, we computed the normalized difference water index adapted for ice (NDWIice)25, defined as:

where B1 and B2 represent the blue and red bands respectively. Owing to the spectral dependency of water reflectance, those areas with deeper water will result in pixels with higher NDWIice values, and vice versa. Following ref. 25, we use the following thresholds to distinguish shallow, medium and deep waters: pixels that satisfy the condition 0.12 < NDWIice < 0.14 are classified as shallow water/slush; those satisfying the condition 0.14 < NDWIice < 0.25 are classified as medium-deep water; and those satisfying NDWIice > 0.25 are classified as deep water (for example, ponds) (see Extended Data Fig. 5).

We tested these NDWI thresholds, which had been identified over Greenland25, in our study area, to evaluate whether we could use the same ranges of NDWI to detect water in Antarctica. We identified a lake (red star in Extended Data Fig. 4a) and a region over the ocean (dark rectangle in Extended Data Fig. 4a) in Landsat images from six days in the summer months of November 2013 through January 2014. The NDWI thresholds over the lake ranged from 0.11 to 0.5 as the season progressed from early to late summer. The ocean NDWI ranged from 0.4 to 0.55. Although ground measurements are necessary to validate whether the shallow, medium and deep thresholds identified over Greenland are valid over Antarctica, this exercise demonstrates that the NDWI was sensitive to the amount of surface melt as summer progressed. On 26 December 2013 (2013 360), where the water-filled lake is visible on the satellite image, we calculated an NDWI of 0.35. The ocean in the same image had an NDWI of 0.47 (Extended Data Fig. 4b).

Mapping water depth

Water depth (z) for the locations identified as covered with water (according to the NDWI analysis) was estimated using the following procedure. The expression for reflectance immediately below the water surface for optically shallow, homogeneous water, R(0−), is given by34:

where Ad is the irradiance reflectance (albedo) of the bottom and R∞ is the irradiance reflectance of an optically deep water column. Solving this equation for z gives:

The value of R∞ is obtained from deep water (ocean) pixels within the scene, while the Ad value is obtained from pixels surrounding body waters and following the approach of ref. 35. The coefficient g accounts for losses in both upward and downward directions34 and is given by34 g≈Kd + aDu, where Kd is the diffuse attenuation coefficient for downwelling light, a is the beam absorption coefficient, and Du is an upwelling light distribution function or the reciprocal of the upwelling average cosine36. The two attenuation coefficients, g and Kd, are spectrally similar as long as the diffuse attenuation is not dominated by scattering. However, Kd and g cannot be used interchangeably and a possible range of 1.5Kd < g < 3Kd can be assumed in the case of strongly absorbing waters. In ref. 34, g is approximated to 2Kd for purposes of computation (see Table 1 of ref. 34). Here, we use the Kd values of optically pure water37. See Extended Data Fig. 5.

Record of calving on the Nansen Ice Shelf

There is evidence for three major calving events from the Nansen Ice Shelf since it was first studied in 1908. The sporadic pre-satellite record makes precise timing of the events impossible. The first complete mapping of the ice shelf was presented in the sketch map by the Northern Party 1912 and indicated that the ice shelf extended past Inaccessible Island. Subsequent imaging of the ice shelf in 1956 in the USGS TMA photographs revealed that the ice front had retreated. Thus the first calving occurred sometime between 1912 and 1955. Over the following years (1956–1963), the TMA imagery mapped the forward advance of the ice front, as well as the growth of the ‘Grand Chasm’ across the ice shelf. The next calving event occurred between the 1963 TMA image and the first satellite data in 1972. The iceberg produced in this event had a surface area of 170 km2. The most recent calving event occurred on 7 April 2016 and was observed from satellite imagery.

Water velocity from geometry and video

We used two methods to determine order-of-magnitude estimates of the water velocity and flux in the shear-margin river in January 2014: the Manning’s equation and analysis of video using feature tracking.

Our approach is based on earlier work on surface streams38,39. The first approach incorporates the Manning’s equation for open-channel flow and has been used previously on glaciers39. The volume flow rate, Q, through the surface channel is given by:

where V is the velocity; A is the cross-sectional area of the flow; Rh = A/P and is the hydraulic radius; P is the wetted perimeter; S is the slope of the channel; and n is the Manning coefficient (n = 0.015). The cross-sectional area of the flow and wetted perimeter of the channel were determined from Landsat-8 imagery analysis from a satellite image taken on 9 January 2014 together with the IceBridge laser altimetry. The slope of the channel is determined from the Bedmap2 surface DEM, which was compared with ATM lidar measurements taken in November 2013 from the NASA P3 IceBridge missions. The flow-speed estimate obtained from this analysis is between 1.39 m s−1 and 2.17 m s−1, and the volume flow rate is between 259 m3 s−1 and 806 m3 s−1. The variability in these estimates depends on the choice of channel cross-section (for example, rectangular or triangular) that controls the hydraulic radius.

The video-based feature-tracking estimate is derived from a video shot from a research helicopter on 12 January 2014 (see Supplementary Videos). The video was stabilized for motion in post processing. Imagery was spatially calibrated using ground-control points in the video that matched up with the same features in satellite imagery (Landsat-8; 4 January 2014). At every cross-channel location, we generate a space–time plot that shows features moving at a given speed as determined by the slope of the feature in the space–time plot40. We use the Radon transform to automate the determination of the along- and cross-channel velocity components. Our velocity estimates average 0.43 m s−1 and 0.53 m s−1 for the two videos that gave the best perspective to implement this technique. Using the same channel area estimates as applied in the previous technique, we estimate a volume flow rate of between 80 m3 s−1 and 197 m3 s−1.

Waterfall fluxes and exports

We have identified eight melt seasons between 2006 and 2015 for which there is sufficient satellite coverage to examine the development of the waterfall and to quantify the duration of meltwater export off the ice shelf. We use the temperature record from Mario Zucchelli Station, Terra Nova Bay, to constrain the regional temperature. An alternative would be to use the output from a regional climate model applied to Antarctica. Such model results are spatially distributed and often provide daily outputs, but freely available products such as RACMO have a spatial resolution that is too low to resolve the surface catchments of Nansen Ice Shelf effectively; one RACMO grid cell encompasses almost the entire Nansen Ice Shelf41.

The melt seasons analysed are years with a minimum of three January images available with which to quantify the waterfall duration. These years range from very warm years with extensive surface melt (2013–2014) to relatively cold years during which there was little surface melt (2006–2007). An examination of these years allows us to elucidate the relationship between surface temperatures and the amount of surface melt exported from the Nansen Ice Shelf. We use the images from these eight melt seasons to determine the volume of water exported from the ice shelf using our flux estimates from 2014. The eight melt seasons with well resolved melt sequences are: 2006–2007, 2008–2009, 2009–2010, 2010–2011, 2011–2012, 2012–2013, 2013–2014 and 2014–2015 (Extended Data Table 2).

The Nansen waterfall generally develops in late December or early January. 3 January is the average start date for the waterfall, with the earliest observed date being 26 December (in 2010), and the latest start of export being 13 January (in 2013). (The temperatures at Mario Zucchelli Station on Terra Nova Bay on the date of the first observed waterfall were as follows: 26 December 2010, 2.2 °C; 29 December 2008, 1.38 °C; 2 January 2014, 2.64 °C; 2 January 2015, 0.44 °C; 7 January 2012, 2.28 °C; 16 January 2013 (latest waterfall onset), 1.87 °C.) No waterfalls were imaged in two years: 2006–2007, when the average maximum December temperature at Mario Zucchelli Station was −0.41 °C; and 2009–2010, when the average December temperature was 0.77 °C.

The time period during which Landsat imagery resolves a shear-margin river draining in a waterfall is assumed to be the minimum export duration. There is a positive relationship between the number of days in a melt season during which the minimum temperature measured at Mario Zucchelli Station exceeded 0 °C, and the duration of meltwater export (Extended Data Fig. 6). In some years no waterfall is observed (2006–2007 and 2009–2010). For the years in which the waterfall is observed, the duration of export extends from 5 to 25 days. Owing to the low temporal resolution of the Landsat imagery, these estimates represent the minimum export duration. On the basis of the spacing of the images, we estimate the uncertainty in duration of the waterfall ranges to be from 1 to 20 days. The average uncertainty of our duration estimation is 9.4 days. Despite these uncertainties, the positive relationship between the number of days in which the minimum temperature in Terra Nova Bay exceeds 0 °C and the duration of the waterfall export indicates that the surface meltwater system removes more water in warmer years, when more melt is produced.

Next, we use the conservative meltwater export duration to determine how much melt is removed from the ice shelf by the waterfall in different years. We define the conservative export duration as the minimum number of days during which the waterfall is active. The Manning method, based on the satellite-derived DEMs from 9 January 2014, produces a minimum flux estimate of 260 m3 s–1. We determine how much water is exported for each year, assuming that this flux is maintained throughout the period during which the waterfall is observed. The daily volume exported is 0.02246 km3 at the minimum Manning flux. The annual export volume varies with the changing waterfall duration.

We compare these export volumes with the average annual estimated surface melt (0.5 m yr−1) and the amount of damage that present models assume the ice sheet will sustain annually (1.5 m yr−1) (Extended Data Fig. 7). We calculate the melt volumes in these two conditions for the catchment area drained by the Nansen shear-margin river (331 km2). The average annual surface melt is from stake measurements of surface mass loss by an Italian field program in the 1990s. A water volume of 0.16 km3 is produced in the shear-margin catchment in an average melt season. The damage threshold is based on the amount of surface melt that begins to damage an ice shelf (1.5 m yr−1) used in the Antarctic ice-sheet model of ref. 4. At the low-end Manning flux, the shear-margin river removes the average annual melt in 7 days and the damage threshold melt in 21 days.

Presence of surface water export in Greenland

We present Landsat satellite imagery and preliminary mapping of water extent from the ice shelf in front of Petermann Glacier in northwest Greenland. Although active surface rivers are present in many of the Petermann ice shelf images, no mapping of their extent, depth or persistence has been reported. Greenpeace captured iconic photos of the Petermann ‘Blue’ River during a 2009 expedition when the team kayaked in the river. We present Landsat images of the Petermann River from 15 July 2014 in Extended Data Fig. 8 (Landsat scene identifier LC80450012014196LGN00), and have calculated the water extent, finding that this 50–190 m wide river is exporting meltwater off the ice shelf into the fjord.

Data availability

The data used in this analysis are available at public repositories including the National Snow and Ice Data Center (https://nsidc.org; IceBridge data and Bedmap2 DEM), the Scott Polar Research Institute, University of Cambridge (http://www.spri.cam.ac.uk; photos presented in Fig. 2), and the USGS/Landsat/TMA photo collections (https://earthexplorer.usgs.gov/).