Corresponding author: L. Copland, Department of Geography, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada. (email@example.com)
 Ground penetrating radar (GPR) surveys of the 205 km2Milne Ice Shelf conducted in 2008 and 2009 are compared with radio echo sounding (RES) data from 1981 to provide the first direct measurements of thinning for any northern Ellesmere Island ice shelf. Our results show an average thinning for the ice shelf as a whole of 8.1 ± 2.8 m, with a maximum of >30 m, over this 28-year period. Direct-line comparisons along a 7.5 km transect near the front of ice shelf indicate a mean thinning of 2.63 ± 2.47 m over the same period. Reductions in areal extent (29%, 82 ± 8.4 km2: 1950–2009) and volume (13%, 1.5 ± 0.73 km3 water equivalent (w.e.): 1981–2008/2009) indicate that the Milne Ice Shelf has been in a state of negative mass balance for at least the last 59 years. A comparison of mean annual specific mass balance measurements with the nearby Ward Hunt Ice Shelf (WHIS) suggests that basal melt is a key contributor to Milne Ice Shelf thinning. Glacier inflow to the ice shelf has also reduced markedly over the past 28 years. The transition of ice shelf ice to lake ice was the most important source of mass loss. A 28.5 km2 epishelf lake now exists on the landward side of the ice shelf. Given these recent changes, disintegration of the Milne Ice Shelf will almost certainly continue in the future.
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 The once continuous Ellesmere Ice Shelf (EIS) covered an area of ∼9,000 km2 when first discovered by Aldrich and Peary at the end of nineteenth century [Vincent et al., 2001]. Radiocarbon dating of driftwood and proxy indicators in sediment cores from the rear of the ice shelves indicate that they formed during a period of relatively cooler climate ∼4000–5500 years ago and have remained since then in spite of a warm period that occurred ∼1000 years ago [Antoniades et al., 2011; England et al., 2008]. Today, >90% of the original EIS's area has been lost, with the majority of this mass loss taking place during the early to mid-twentieth century [Koenig et al., 1952; Hattersley-Smith, 1963]. By the 1950s only individual ice shelves remained, situated in isolated fiords and embayments [Jeffries, 2002]. Rapid disintegration over the past decade, which began with fracturing of the Ward Hunt Ice Shelf (WHIS) in 2000–2002 and included the complete loss of the Ayles Ice Shelf in 2005 and Markham Ice Shelf in 2008, reduced the total number of Canadian ice shelves from six to four [Copland et al., 2007; Vincent et al., 2009]. Other losses in 2008 included calving of 60% (122 km2) of the Serson Ice Shelf and part (42 km2) of the Ward Hunt Ice Shelf [Vincent et al., 2011]. All of these losses are regarded as permanent, as there is no evidence of ice shelf re-generation at the present day [Mueller et al., 2008].
 Over the past 50 years, average annual Arctic air temperatures have increased at about twice the global average of 0.13°C decade−1 [ACIA, 2005; Lemke et al., 2007]. Reductions in Arctic Ocean sea ice extent (10.7% per decade for 1979–2007) and thickness (∼50% reduction in mean thickness between 1980 and 2008) have accelerated over the last decade [Kwok and Rothrock, 2009; Stroeve et al., 2008]. Significant periods of ice shelf disintegration (1930s–1960s and 2000–present) appear to have coincided with periods of relatively warm air temperatures in the 1930s and 1950s (1.0°C to 1.5°C above 1900–2000 mean) and 1980s to the present (2.0°C above 1900–2000 mean) and with low concentrations of Arctic Ocean sea ice [Bradley, 1990; Mueller et al., 2008].
 Previous research has been conducted to determine overall changes in ice shelf extent [Mueller et al., 2006; Vincent et al., 2001], and surface mass balance [Braun et al., 2004; Hattersley-Smith and Serson, 1970], yet little is known about the impact of the observed warming on ice shelf thickness. This study addresses this issue by determining change in ice thickness and volume for the Milne Ice Shelf over the past 28 years. To this end, ground penetrating radar (GPR) profiles of the Milne Ice Shelf from 2008 and 2009 are compared with 1981 airborne radio echo sounding (RES) measurements [Prager, 1983; Narod et al., 1988] to derive the first direct measurements of thickness change for any northern Ellesmere Island ice shelf. Changes in ice shelf area since 1950 are also quantified, and the role of variability in glacier inputs and surface and basal melt are investigated.
2. Study Site
 The Milne Ice Shelf is located at the mouth of Milne Fiord (82°44′N, 81°45′W) between Cape Evans and Cape Egerton, and covered an area of ∼205 km2 in 2009 (Figures 1 and 2; see also Table 1). Accumulation occurs via glacier inflow, surface snowfall, and basal freeze-on of water. Ablation occurs via surface and basal melt, and calving [Dowdeswell and Jeffries, 2012; Jeffries, 2002; Vaughan, 1998]. The ice shelf's surface topography is characterized by a series of distinctive ridges and troughs that parallel the coast and the prevailing wind direction [Crary, 1960; Hattersley-Smith, 1957; Jeffries, 1992]. The nature of these ridges, with larger more developed ridging and a longer wavelength indicating thicker ice, formed the basis of Jeffries' [1986a] morphological classification of the ice shelf. Moving from the Arctic Ocean (front) to inland (rear), Jeffries [1986a] divided the Milne Ice Shelf into the Outer, Central and Inner Units. The large Milne Glacier (∼55 km long, 4–5 km wide; Figure 1c) and its southwest tributary (Glacier 5) flow into the southern part of Milne Fiord, but do not contribute mass to the ice shelf at the present-day. Five tributary glaciers (Glaciers 1–4 and 6) flank the sides of the fiord, and at least one (Glacier 3) still provides input to the ice shelf.
Table 1. Milne Ice Shelf Area, 1950–2009
287 ± 0.5
Air photo mosaic
15 Jul 1950
281 ± 0.5
Air photo mosaic
29 Jul 1959, 17 Aug 1959
250 ± 0.5
Air photo mosaic
24 Jul 1984, 24 Aug 1984
214 ± 0.3
ERS-1, standard beam
19 May 1993
206 ± 0.3
ASTER Level 1B
23 May 2001, 19 Sep 2001
205 ± 0.3
ASTER Level 1B
21 Jul 2009
 The northern extent of the Outer Unit forms the ice shelf front and the boundary with the Arctic Ocean (Figure 1c). This unit is characterized by a series of large, near-parallel ridges and troughs with a maximum amplitude of ∼7.5 m and receives glacier input from the low-lying ice caps of Cape Evans and Cape Egerton [Jeffries, 1986a]. Old multiyear landfast sea ice (MLSI) typically fringes the front of the Outer Unit and protects the ice shelf from wind and wave action. The Milne Re-entrant, which was located in the northwestern section of the Outer Unit near Cape Evans, was an expanse of MLSI that replaced a portion of the ice shelf that calved in ∼1965 [Jeffries, 1987; Jeffries and Krouse, 1987]. The Central Unit, located between the Outer and Inner Units, is characterized by contorted and bifurcating ridges (with troughs up to 5 m deep) [Jeffries, 1986a], which become increasingly disorganized with distance from the coast.
 The Milne Fiord epishelf lake, which Jeffries [1986a] originally referred to as the Inner Unit, is situated behind the Central Unit. Epishelf lakes are unique cryospheric features formed by the trapping of a layer of floating freshwater from summer melt of snow and glacier ice behind an ice shelf [Veillette et al., 2008]. This freshwater layer is covered by perennial lake ice and is isolated from the underlying salt water by differences in water density, resulting in a highly stratified water column [Mueller et al., 2003].
 No long-term meteorological data exist for the Milne Ice Shelf. The nearest permanent (Environment Canada) weather stations at Alert (82°32′12″N, 62°16′08″W) and Eureka (79°58′08″N, 85°55′08″W) are about equidistant (∼320 km) from the ice shelf (Figure 1). Average annual temperatures (1970–2000 Climate Normals) were −18°C at Alert and −20°C at Eureka, while total annual average precipitation was 153 mm and 75 mm, respectively (http://www.climate.weatheroffice.ec.gc.ca). Along the northwest coast of Ellesmere Island, National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis showed an increase in daily annual surface air temperatures (SATs) of ∼0.5°C decade−1 over the period 1948–2007 [Mueller et al., 2009]. Annual average surface air temperature recorded by an automated weather station at Purple Valley, Nunavut (located near the rear of the Milne Ice Shelf; Figure 1) between 1 June 2009 and 31 May 2010 was −17°C, with maximum and minimum temperatures of 14°C and −49°C, respectively (http://tinyurl.com/milnewx).
3.1. Ice Shelf Area: 1950–2009
 We used a combination of aerial photographs (1950, 1959 and 1984) and satellite imagery (1993, 2001 and 2009) to compute ice shelf area. Monochrome trimetrogon (1950) and vertical (1959, 1974 and 1984) aerial photographs obtained from the National Air Photo Library (Ottawa, Canada) were scanned at 600 dots per inch. Complete aerial photographic coverage of the Milne Ice Shelf was available for 1959. Aerial photographs for 1974 were limited to the ice shelf front, so total area was not computed for that year; however the images were used to monitor change in the ice shelf front and to identify large calving events. Coverage for 1950 and 1984 was only ∼80% complete, but, for these years, incomplete coverage in the center of the ice shelf did not affect area computation for the ice shelf as a whole. Where missing coverage included a fiord sidewall, the location of the ice margin was interpolated using images from the closest year. In 1950 about one third of the ice shelf front did not have nadir coverage, so oblique left and right-looking scenes were used to provide information about the position of this ∼6-km long section.
 The scanned aerial photographs were georeferenced to a 21 July 2009 Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) scene (15 m resolution) using a minimum of 20 evenly distributed ground control points (GCPs). The georectification process was undertaken in ArcMap® 9.3 using a first-order polynomial and mosaicked in ENVI® 4.4. Where visible, GCPs were preferentially selected over permanent land features (e.g., mountain peaks, fiord valley walls), which produced a root mean squared error (RMSE) of <15 m. However, ∼15% of the photographs only captured snow and ice, so large semi-permanent ponds on the ice shelf surface were used as GCPs for these cases, which resulted in a maximum RMSE of 28.7 m for these photographs. To determine the accuracy of the georectification process we measured the difference in position of distinctive overlapping features (e.g., ice cracks) on adjacent georectified images, which produced an upper bound of uncertainty of ∼200 m. The final overall uncertainty for each aerial photograph mosaic was then computed from the sum of: i) the mean RMSE; ii) aerial photograph resolution; iii) qualitative mosaicking uncertainty. This produced an estimated uncertainty of ±2.7% for computations of the total ice shelf area.
 Milne Ice Shelf area over the past two decades was computed from a 19 May 1993 (European Remote Sensing Satellite (ERS-1) image, 12.5 m resolution), and ASTER L1B scenes from 23 May 2001, 19 September 2001 and 21 July 2009 (15 m resolution;Table 1). As with the aerial photographs, all satellite images were coregistered to the 21 July 2009 ASTER image. Uncertainty in area computations derived from satellite imagery was taken as the sum of the image resolution and the coregistration uncertainty of 100 m. This equates to 1.5% and 1.6% of the total ice shelf area computed from ERS-1 and ASTER imagery, respectively. Polygons delineating Milne Ice Shelf in 1950, 1959, 1984, 1993, 2001 and 2009 were digitized in ArcMap® 9.3 and the total ice shelf area for each year was computed (Table 1). The uncertainty associated with change in ice shelf extent between years was assumed to be independent, so the sum of squares of individual areal uncertainty was used to estimate error in this case.
Table 2. Changes in Ice Thickness and Specific Mass Balance for the Period 1981–2009 for Segments Along the Northern 7.5 km of the Transect From A (km 0) to B (km 11.3) (Figure 1c and Figure 3a)
Distance From A (km)
1981 Mean Thickness (m)
2009 Mean Thickness (m)
Total Thickness Change (m)
Thickness Change Error (+/− m)
Annual Specific Mass Balance (m w.e. yr−1)
0.16 ± 0.07
0.16 ± 0.08
0.05 ± 0.08
−0.15 ± 0.09
−0.31 ± 0.09
−0.24 ± 0.08
−0.16 ± 0.07
−0.10 ± 0.06
3.2. Ice Thickness Measurements: 2008/2009
 In April 2008 the Milne Ice Shelf was traversed with sled-mounted Sensors and Software Pulse EKKO Pro® 50 MHz and 250 MHz GPR systems towed behind a snowmobile at ∼20 km hr−1. An integrated single frequency global positioning system (GPS) receiver (accuracy ±5 m) recorded the position every ∼5 m. The 2008 measurements indicated that the more portable 250 MHz system was able to penetrate the thickest-known parts of the Milne Ice Shelf (Figure 1, black triangle), so in 2009 the 250 MHz system was used exclusively. In 2009 profiles were recorded on 23 May, 30 May, and 3 June, with a particular effort made to re-profile transects first measured in 1981 (section 3.3).
 GPR data post-processing, performed with Sensors and Software EKKO_View Deluxe®, involved the removal of traces when the sled was stationary, signal saturation correction, frequency filtering (trace differencing high pass spatial filter), and radar gain adjustments. A two stage Digital Video Logger gain filter was applied to account for the reduction in returned power with depth, which visually enhanced the bottom reflection at the expense of internal resolution [Sensors and Software, 2006]. Owing to the large difference in dielectric properties of ice and water, the bottom of the ice shelf (ice-water interface) was clearly identifiable in most traces. Ice thickness was determined via a combination of manual and automated selection using Sensors and Software IcePicker R4®. We used a radar wave velocity (RWV) of 0.170 m ns−1, based on a common midpoint survey conducted on 28 May 2009 on Milne Fiord epishelf lake. This velocity is consistent with previous studies on cold glacier ice [Macheret et al., 1993; Woodward and Burke, 2007]. Two-way travel time (ns),t, was converted to ice thickness, T(m), by:
Where v is the propagation velocity for cold ice (0.170 m ns−1) and s is the antenna separation (0.4 m for 250 MHz, 2.0 m for 50 MHz). Accuracy of the GPR's integrated GPS system was confirmed by comparison of measurements of easily identifiable features (e.g., ice cracks and the ice shelf front) in the radargrams with satellite imagery and independent GPS waypoints. Total error for ice thickness measurements derived from the GPR data was taken as the sum of:
 i) GPR system resolution; this is typically taken as 10% of the transmitted wavelength, [Bogorodsky et al., 1985] which equates to ±0.07 m for a center frequency of 250 MHz and ±0.34 m for 50 MHz.
 ii) Reflection picking error; this represents the ability to consistently identify the bed reflection in different traces, and was quantified via an analysis of 14 crossover points in the 2009 GPR transects [Mortimer, 2011]. Difference in average ice thickness within a radius of 5 m (GPS precision) from these points was ±0.78 m.
 Combining these factors, uncertainty in GPR-derived ice thicknesses was ±0.85 m at 250 MHz and ±1.12 m at 50 MHz. Ice thicknesses were converted to water equivalent (w.e.) using an ice density of 0.90 g cm−3.
3.3. Ice Thickness Change: 1981–2008/2009
 We compared the 2008/2009 ice thickness data set to ice shelf thickness measurements from a radio echo sounding (RES) survey conducted by the University of British Columbia in June 1981 [Narod et al., 1988; Prager, 1983]. The 1981 ice shelf thickness data was collected using an 840 MHz RES system mounted on a Twin Otter aircraft [Narod et al., 1988]. Parallel survey lines with a horizontal spacing of ∼1 km were flown at an air speed of ∼215 km hr−1 and ground clearance of ∼120 m. An Omega navigation system (positional uncertainty ∼1 km [Prager, 1983]) provided positional information. Data processing performed by Prager  and Narod et al.  used a propagation velocity of 0.176 m ns−1 to compute ice thickness, with error for 100 m thick ice stated as ±3 m.
 Magnetic data tapes from the 1981 survey are no longer available. Data from 1981 was limited to paper copies of the 1981 flight line map, a thickness contour map derived from the RES data, and a ∼11.3 km long radargram covering the Outer Unit of the ice shelf from Point A to B (Figure 1c). Milne Ice Shelf thickness change between 1981 and 2009 was determined from direct comparison of ice thicknesses re-measured along a section of the 1981 radargram and comparison of ice thicknesses for the entire ice shelf from contour maps.
3.3.1. Direct Line Comparison
 Changes in ice shelf thickness (m) and mean annual specific mass balance (m w.e. yr−1) were quantified along the northern ∼7.5 km of the ∼11.3 km 1981 RES radargram based on a repeat GPR profile undertaken on 3 June 2009 (Figure 1c). Two-way travel time (TWTT) for each return in the 1981 data set [Narod et al., 1988, Figure 7] was extracted from the paper radargram using DataThief® III image analysis software. This TWTT was converted to ice thickness using a RWV of 0.170 m ns−1. The location of the 1981 transect (Figure 1c, points A and B) was obtained from a scan of the flight line map [Narod et al., 1988, Figure 6a] georeferenced to the 21 July 2009 ASTER scene and projected to WGS84 UTM 17N. Due in part to difficulties in negotiating the terrain by snowmobile, the 2009 GPR transect could not be completed in a line exactly coincident with the 1981 flight line (Figure 1c). Therefore, an across-track correction was used to project the 2009 transect to the 1981 flight line, ranging from 350 m at the southernmost point to −10 m at the northernmost point (Point B). To enable point to point comparison between the 1981 and 2009 data sets, a spline interpolation (1 m spacing) was applied to both lines.
 Comparison of the 1984 aerial photograph mosaic with the 21 July 2009 ASTER scene suggests that the position of the ice shelf front near Point B has remained relatively unchanged (within a distance of ∼100 m) over this period. In addition, the position of a large crack (located at km 4.3 in Figure 3a), identified in both the 1981 and 2009 transects by the presence of a downward-dipping hyperbola on either side of a gap in the GPR/RES traces, has remained constant (within ∼10 m) between the 1984 aerial photograph and 2009 satellite scene [Mortimer, 2011, Figure 4.5]. Since the location of these two features has remained essentially fixed between 1981/1984 and 2009 they were used to assist in computing the geolocation error and to refine the horizontal distance of the 2009 transect with respect to the 1981 flight line in two ways:
 (i) The geolocation uncertainty for the 1981 radargram was determined by comparing the horizontal distance measured from the radargram to that obtained from the Narod et al.  flight line map and the 1984 aerial photograph mosaic for two line segments (Figure 3a): from point B and the crack at km 4.3, and between the crack at km 4.3 and a second crack at km 1.7. For both segments, the position of the respective features agreed to within 230 m, which we take to be the geolocation uncertainty. This is considerably better than the 1 km positional uncertainty reported by Prager , and is closer to the 200 m precision of the instrument reported by Narod et al. .
 (ii) The length of the 1981 and 2009 transects was verified by computing the along-track distance from point B to the distinctive crack at km 4.3. This comparison indicated that the 2009 projected transect was 346 m shorter than the 1981 transect; to address this, a 5.2% linear stretch was applied to the 2009 data. This resulted in a smaller mean thickness difference, suggesting that stretching the locations is a more conservative approach than not correcting for the misalignment.
 We assessed the impact of the ∼350 m positional uncertainty between the two data sets by incrementally shifting the position of the 2009 transect in the along-track direction relative to the 1981 transect. The mean difference in thickness was calculated for each of these lagged comparisons and compared to the un-shifted data (Figure 3b). Here, a negative value (−350 m) denotes a 350 m shift toward Point A and a positive value (+350 m) indicates a 350 m shift toward Point B. The greatest mean thinning (at a shift of −26 m) was 0.6% greater than the un-shifted mean thinning value. The smallest mean thinning was 30% smaller than the un-shifted value, but this value was found at a shift of +350 m where the alignment of the crack and the outer edge of the ice shelf is unlikely.
 Cumulative error was computed for all points along the 7.5 km transect. We use the relative uncertainty estimated by Narod et al.  for the 1981 RES data (±3%) and the relative uncertainty of the 250 MHz GPR system (±0.85 m) for the 2009 data. If the change in ice thickness between 1981 and 2009 was greater than the cumulative error the change was considered to be significant. Mean uncertainty in our measurement of direct thickness change was ±2.47 m.
3.4. Overall Ice Thickness and Volume Change
 In addition to our direct line comparison of ice thickness change we produced digital thickness models (DThMs) of the entire ice shelf for 1981 and 2008/2009 to compute total thickness and volume change for the 28-year period. A digitized copy ofPrager's  contour map (contour spacing 10 m) was georeferenced to the 21 July 2009 ASTER scene. Ice thicknesses for the 1981 contour map were computed using a RWV of 0.176 m ns−1 [Prager, 1983]. To enable comparison with our 2008/2009 measurements, we recalculated all 1981 ice thicknesses to a RWV of 0.170 m ns−1. For regions where no bottom echo was detected in the 1981 survey the ice thickness was assumed to be thinner than the minimum resolvable ice thickness of 9.7 m [Prager, 1983].
 An inverse distance weighted interpolation (IDW) was performed in ArcMap® 9.3 to produce the DThMs. The digitized 1981 contour lines were used as input point features to create a raster (cell size 90 m) of ice thicknesses for the entire ice shelf. The 1981 (thickness) raster was then clipped to the 1984 area polygon (the closest year to 1981 for which aerial photography is available). A contour map of present-day ice thickness was developed from the 2008/2009 GPR point measurements. Satellite imagery from 2009 (ASTER and RADARSAT-2) was used to aid in extrapolation of the contour lines to areas not traversed by the GPR. Specifically, areas with similar surface characteristics to those traversed by the GPR were assigned similar thickness values (e.g., shallow contour lines were drawn around cracks and lakes; thicker contour lines were drawn around regions where tributary glaciers flow into the ice shelf). Interpolation was performed following the same procedure as the 1981 data. The 2008/2009 raster (cell size: 90 m) was clipped to the 2009 ASTER-derived polygon to produce the 2008/2009 DThM (Figure 4). With a 10 m contour interval, the ridges and troughs on the ice shelf surface are not visible in our 2008/2009 map, as was also the case with Prager's  map.
 The 2008/2009 DThM was subtracted from the 1981 DThM to investigate spatial patterns of thickness change (Figure 4c). Ice shelf volume for 1981 and 2008/2009 was also computed from the DThMs. Volume change (1981–2008/2009) was taken as the difference between the two individual bulk volume measurements. Because ice thickness across the Inner Unit was below the minimum resolvable thickness of 9.7 m, only the Outer and Central Units are included in our final volume and thickness calculations. Milne Ice Shelf area and thickness change for the Inner Unit is treated separately (see section 3.5).
 Error in volume estimates arose from both area and thickness computations and in the production of a continuous surface from point measurements. For this study, errors attributed to the production of a continuous surface (e.g., due to IDW interpolation) could not be computed because of the lack of independent data sets against which the extrapolations could be checked. Instead, error for total ice shelf volume was taken as the direct sum of the relative uncertainties for areal extent (1984 and 2009) and ice thickness (1981 and 2008/2009), equating to ±5.7% (±0.67 km3) and ±3.6% (±0.35 km3) for 1981/1984 and 2008/2009, respectively. Uncertainty in our estimate of volume change for the Outer and Central Units was taken as the square root of the sum of the squared error of these absolute uncertainties. Dividing this cumulative uncertainty (0.73 km3) by total measured volume change (1.5 km3) yields a relative uncertainty of 49% for our estimate of volume change between 1981/1984 and 2008/2009.
3.5. Epishelf Lake Development
 Given that Milne Fiord contains both ice shelf ice and lake ice, we also monitored changes in ice type through time. Lake ice was not included in our calculation of ice shelf area (lakes within any ice shelf polygon were subtracted from the total ice shelf area). Instead, lake ice area was determined separately for each year. Poor image quality prohibited lake area calculation for 2001 and only total epishelf lake area could be computed for 1993. In our image interpretation, the following criteria were used to distinguish between lake ice and ice shelf ice:
 1) Surface topography: the presence (for ice shelf ice) or absence (for lake ice) of a well-developed ridge and trough surface distinguishes the two ice types [Montgomery, 1952].
 2) Tone and texture: in aerial photographs lake ice is distinguishable from ice shelf ice by its reflective light gray tone and texture. In Synthetic Aperture Radar (SAR) scenes epishelf lakes appear bright white. This high backscatter is produced by the freshwater layer underneath perennial lake ice. In contrast, regions underlain by salt water provide a darker return [Veillette et al., 2008].
4.1. Area Change: 1950–2009
 The area of the Milne Ice Shelf decreased by 29% (82 ± 8.4 km2) between 1950 and 2009. The ice shelf, which covered 287 ± 7.7 km2 in 1950, reduced in size over each successive time period analyzed in this study (Figure 2 and Table 1). Aside from the calving of 26 km2 of ice sometime between 1959 and 1974 (Figure 5) [Jeffries, 1986b], the position of the ice shelf front remained essentially unchanged over the 59-year period. Instead, the majority of the area loss occurred from the Inner Unit. The position of the rear of the ice shelf moved seaward ∼8–10 km between 1950 and 2009, which resulted in a loss of 59 km2 of ice shelf ice. Area loss at the rear of the ice shelf primarily resulted from deterioration of the Inner and Central Units as ice shelf ice (thicker ice with a ridged surface) transitioned to lake ice (thinner ice with a smooth surface) (Figure 6). Terminus advance of the surge-type Milne Glacier [Jeffries, 1984] by >5 km between 1950 and 2009 also contributed to Inner Unit area loss because glacier ice displaced the Inner Unit ice shelf ice [Mortimer, 2011].
 The calving of 26 km2from the northwest corner of the Milne Ice Shelf between 1959 and 1974 was the most significant change in the ice shelf front over the entire 59-year study period. This calving occurred along pre-existing fractures that are visible on the air photos (Figure 5a). In 1959, the ice in the northwest corner had a well-developed ridge and trough surface similar in appearance to the rest of the Outer Unit. In 1974 this ice was absent and had been largely replaced by MLSI (Figure 5b). The total area loss measured for this event was 21% less than what was reported by Jeffries [1986b], which may be largely attributable to improvements in geospatial analysis and measurement techniques.
4.1.1. Lake Development
 Image analysis revealed an increase in total lake area (ice marginal lakes and Milne Fiord epishelf lake) from 4.3 km2 in 1950 to 35.8 km2 in 2009 (Figure 6). During the first two decades of this study, lake area was limited to small ice marginal lakes, whose area increased to 5.0 km2 in 1959 and 17 km2 in 1984. The increase in lake area between 1959 and 1984 was largely due to the change from ice shelf ice to lake ice in the Inner Unit. The replacement of the Inner Unit with an epishelf lake became apparent in the first available SAR imagery in 1993. The bright white backscatter characteristic of freshwater underneath lake ice [Veillette et al., 2008] was visible in the 19 May 1993 ERS-1 scene and spanned the entire width of Milne Fiord. By 2009 the epishelf lake had an area of 28.5 km2. The presence of an epishelf lake across the entire width of the fiord is significant because it indicates that the Milne Ice Shelf was no longer physically connected to Milne Glacier by 1993. The Milne Glacier tongue has advanced ∼1.9 km since then but has not broken up considerably since it is surrounded by perennial epishelf lake ice [Mortimer, 2011]. This loss of contact means that the Milne Glacier has not provided any direct mass input to the Milne Ice Shelf since at least this time.
4.2. Milne Ice Shelf Thickness and Volume: 1981 and 2008/2009
 From our GPR data, the present-day (2008/2009) mean thickness of the Milne Ice Shelf is 55 ± 1.1 m, with a standard deviation of 22 ± 0.44 m and maximum of 94 ± 1.9 m. Considerably thicker ice was reported in 1981; mean ice thickness across the entire ice shelf was ∼68 ± 2 m with a maximum thickness of >97 m [Prager, 1983]. Our GPR profiles revealed marked spatial variability in ice thickness, with the Outer Unit consisting of very thick ice (70–80 m) that thinned rapidly toward the ice shelf front (20–30 m) and averaged ∼20 m in proximity of the rehealed fractures (Figure 4). Ice in the Central Unit was consistently thinner (average ∼50 m) and much more variable; both the maximum (94 m) and minimum (<10 m) measured ice thicknesses were located in this unit.
4.2.1. Thickness Change Along Common Transect: 1981–2009
 Direct comparison of ice thicknesses between 1981 and 2009 for a 7.5 km transect revealed an average thinning of 2.63 ± 2.47 m. However, considerable spatial variability exists in both the magnitude and type (thinning or thickening) of change observed (Figure 3a and Table 2). Substantial losses occurred across the seaward ∼5 km of the ice shelf, while some thickening is apparent in the locations furthest inland from the ice shelf front (Figure 3a). The histogram of thickness differences indicates that thinning dominated overall (Figure 3a, inset). Mean specific mass balance along the entire transect was −0.085 ± 0.079 m w.e. yr−1.
 Due to differences in instrument footprint, we computed averages for individual 1 km segments of the 7.5 km long transect. From these 1 km averaged segments, maximum thickening was 5.01 ± 2.11 m (km 3.80 to km 4.79) and maximum thinning was 9.69 ± 2.80 m (km 7.80 to km 8.79) (Table 2). Mean specific annual mass balances for 1981–2009 ranged from slight gains for the innermost 3 km of the transect (0.05 ± 0.08 to 0.16 ± 0.07 m w.e. yr−1) to marked losses for the outermost 4.5 km of the transect, reaching a maximum of −0.31 ± 0.09 m w.e. yr−1 over km 7.80 to 8.79 (Table 2).
4.2.2. Overall Thickness and Volume Change: 1981–2008/2009
 DThM differencing indicates that most of the Milne Ice Shelf experienced thinning over the past 28 years (Figure 4c), with the Outer Unit experiencing the least amount. Maximum thinning occurred immediately to the south of the rehealed fracture near the border between the Outer and Central Units. Total volume of the Outer and Central Units was 11.3 ± 0.64 km3 w.e. in 1981 and 9.8 ± 0.35 km3 w.e. in 2008/2009. This equates to a 13% (1.5 ± 0.73 km3 w.e.) reduction in volume and an average thinning of 8.1 ± 2.8 m (0.26 ± 0.09 m w.e. yr−1) for the Outer and Central Units over the 28-year period. Volume loss attributed to conversion of the Inner Unit to epishelf lake not included in these estimates was 0.4 km3 w.e..
5.1. Area Change
 Our analysis has revealed substantial attrition in overall extent, thickness and volume of the Milne Ice Shelf. The measured 82 ± 8.4 km2(29%) reduction in area between 1950 and 2009 occurred due to losses from the front (calving), rear (epishelf lake formation) and sides (expansion of ice-marginal lakes). Overall, the majority of losses occurred at the rear where a 28.5 km2 epishelf lake replaced the former Inner Unit (Figure 6a). The growth and expansion of both epishelf and marginal ice-dammed lakes is important for the stability of the Milne Ice Shelf because lakes that penetrate to the ocean below indicate that the ice shelf has become detached from the fiord walls at these locations, making it more vulnerable to future calving events.
5.2. Thickness Change
 The average change in thickness for the Milne Ice Shelf's Outer and Central Units, derived from DThM differencing, was −0.26 ± 0.09 m w.e. yr−1between 1981 and 2008/2009. Over the same period, the mean specific annual mass balance along the re-profiled transect was −0.085 ± 0.079 m w.e. yr−1. Our measurements of ice shelf thinning are corroborated by changes in the depth of the Milne Fiord epishelf lake's halocline, which corresponds to the minimum ice shelf draft [Veillette et al., 2008]. In spring 1983, this layer was found ∼17.5 m below the ice surface [Jeffries, 1985]. In contrast, shallower haloclines have been observed over the past 5 years (15.6 m in 2006, 16.5 m in 2007, and 14.6 m in 2009) [Mortimer, 2011; Veillette et al., 2008; Veillette et al., 2011]. The observed ∼3.5 m reduction in halocline depth between 1983 and 2009 implies that the minimum ice shelf thickness has reduced; it is not, however, a measure of overall thinning. Nevertheless, this independent measure provides confidence that the Milne Ice Shelf has experienced thinning over the past 28 years.
 The estimated average thickness change (−8.1 ± 2.8 m) that we observed between 1981 and 2008/2009 is not uniformly distributed across the ice shelf (Figure 4c). The Outer Unit experienced relatively low and spatially variable changes in ice thickness over the 28-year period, as was observed with the re-profiled transect (Figure 3a), while a higher rate of thinning was observed in the Central Unit. Some of the variability in thickness change seen in Figure 4cis also likely due to differences in the 1981 and 2008/2009 contour maps. Specifically, the lack of detail present in the 1981 contour map resulted in a DThM that failed to capture small scale features and resulted in an under-representation of 1981 ice thickness variability compared to 2008/2009. For example, thinner ice in the vicinity of the rehealed fractures visible on the 1981 radargram is not captured in the 1981 contour map. Other important features visible in the 2008/2009 DThM that were not observed in 1981 include two areas of thin ice, one located immediately to the south of the east to west-running rehealed fracture (∼30 m thick) and another (∼20 m thick) located to the southwest of where the two rehealed fractures meet (Figure 4). Despite these inconsistencies there is overall agreement between the DThM differencing and direct line comparison which provides confidence in the overall patterns of change.
5.3. Epishelf Lake Development
 The transition of the Milne Ice Shelf Inner Unit (ice shelf ice) to the Milne Epishelf Lake (lake ice) was the largest observed change in area over the entire period. As early as the 1950s, the shorter wavelength of the Inner Unit's ridges and troughs suggested thinner ice [Jeffries, 2002]. However, the absence of field measurements prior to the 1980s limits our ability to determine if the Inner Unit was ice shelf ice, lake ice, or a transitional ice type (Figure 6). In 1983, water profiling by Jeffries  in the Inner Unit revealed a ∼17.5 m deep freshwater layer below a 3.19 m thick ice layer. Prager  noted an absence of bottom echo (meaning that the ice was <9.7 m thick) in the 1981 RES surveys over much of the Inner Unit. These field measurements suggest that the epishelf lake was present prior to 1984, yet this ice continued to be referred to as ice shelf ice [Jeffries, 1986a].
 The advance of the Milne Glacier at the rear of the ice shelf adds further ambiguity regarding the ice type present in the Inner Unit/epishelf lake area prior to 1993. Seaward advance of the Milne Glacier's terminus was observed over each successive time interval between 1950 and 2009, but the mechanism by which ice shelf ice is replaced by glacier ice is unclear.
 In 1959 it appears as though Milne Glacier's terminus had pushed the Inner Unit ice forward and compressed the ridges and troughs near the glacier's terminus [Jeffries, 1984]. This may indicate that the Inner Unit consisted of thinner ice at this time (Figure 6b, yellow ellipse). By 1984 the Inner Unit's ridges and troughs were less pronounced and their orientation less regular, suggesting that the ice was in a transitional state between true ice shelf ice and lake ice (Figure 6, red rectangles). In 2009 the entire Inner Unit's surface was smooth, consisting of lake ice, and the compressed rolls and troughs seen in the 1959 and 1984 air photos were absent. This is important because it indicates a change in ice type was occurring before 1993. The gradual transition from ice shelf ice to lake ice that occurred throughout the second half of the twentieth century highlights an important mechanism of ice shelf mass wastage. Mass loss at the rear of the ice shelf is a key process for Canadian Arctic ice shelf stability. Our results reinforce the fact that calving from the front is not the only important mechanism for ice shelf mass loss but that melt and disintegration from the rear must also be considered.
5.4. Ice Shelf Mass Inputs From Glaciers
 Observed decreases in Milne Ice Shelf areal extent, thickness, and volume are linked to changes in its mass gains and losses. Glaciers were an important mass input during the formation of the Milne Ice Shelf [Jeffries, 1986a]. Aerial photographs and satellite imagery from 1950 to 2009 show significant retreat, which reduced input from Glaciers 1–4 and 6 to the ice shelf (Figure 2) [Mortimer, 2011]. In 1959, all five tributary glaciers terminated on the ice shelf with Glaciers 1, 2, and 6 extending at least 4.5, 2.5 and 1.5 km onto the ice shelf, respectively. By 1993 most glacier termini were located near the fiord sidewall and by 2011 glacier flow onto the ice shelf was limited to a single tributary glacier, Glacier 2. Speckle tracking of 2011 RADARSAT-2 image pairs indicates flow of 40 to 55 m yr−1 where this glacier enters the ice shelf [Van Wychen, pers. comm., 2011]. If we assume an ice thickness of ∼100 m at this location across the ∼2 km wide terminus, a velocity of 55 m yr−1 would provide 0.0099 km3 w.e. yr−1 of glacier ice to the ice shelf. This accumulation source equates to 0.048 m w.e. yr−1across the 2009 ice shelf area. While glacier input is not the sole source of accumulation (surface precipitation and basal freeze-on being other important factors), this estimate suggests that current glacier input would compensate for less than 20% of the annual average thinning (0.26 m w.e. yr−1; 1981–2008/2009) and is therefore insufficient to balance mass losses.
5.5. Comparison of Milne and Ward Hunt Ice Shelf Thinning
 Our direct transect comparison and DThM differencing demonstrates that the Milne Ice Shelf has been in a state of negative mass balance for at least the past 28 years. Negative surface mass balances have also been documented for the nearby Ward Hunt Ice Shelf (WHIS) where the mean annual surface mass balance between 1989 and 2003 was −0.07 m w.e. yr−1, with negative summer balances (mean: −0.20 m w.e. yr−1) dominating positive winter balances (mean: +0.15 m w.e. yr−1) [Braun et al., 2004]. These mass balance measurements are based on ice surface lowering and do not include mass gains or losses at the ice shelf base or from internal accumulation. However, comparison between cumulative surface mass balance (−1.03 m, 1989–2003) and estimates of total ice shelf thinning (∼15 m, 1981–2002) [Braun, 2012] on the WHIS suggests that most of the net losses have occurred from the ice shelf base. It is acknowledged that the WHIS mass balance network was limited to only six stakes for the period 1989–2003, and is thus not a representative sample of this region's highly variable accumulation and ablation [Braun et al., 2004]. However, if the rate of surface mass loss for the WHIS (−0.07 m w.e. yr−1, 1989–2003) were applied to the Milne Ice Shelf, thinning due to basal melt would constitute ∼73% (0.19 m w.e. yr−1) of the overall average thickness change for the Central and Outer Units. Although our estimate of basal melt is based on a rudimentary calculation of ice shelf thinning, it does suggest that loss at the ice shelf base is a key contributor to thinning of northern Ellesmere Island ice shelves.
5.6. Milne Ice Shelf Stability and MLSI Change
 The Milne Ice Shelf has undergone significant mass loss and structural weakening over the past 59 years as evidenced by the development of new cracks (between 1981 and 2008/2009), as well as the lengthening of existing cracks (between 1950 and 2009) [Mortimer, 2011]. This weakening is important given that the twenty-first century breakups of the Ayles and Ward Hunt ice shelves occurred along pre-existing fractures [Copland et al., 2007; Mueller et al., 2008]. The replacement of Inner Unit ice with epishelf lake ice and recent thinning of this freshwater layer also signal an overall negative mass balance [Veillette et al., 2008] and this appears to have accelerated over the 59-year study period. These changes indicate that the Milne Ice Shelf is now apre-weakened ice shelf that, under the current climate, can no longer regenerate and is structurally unstable [Glasser and Scambos, 2008].
 Once an ice shelf has entered a pre-weakened state, the presence of MLSI and pack ice becomes critical for its stability by providing a buttressing effect and protecting the ice shelf against wind, wave and tidal action [Copland et al., 2007; Jeffries, 2002]. Following the ∼1965 ice shelf calving event, old, thick MLSI was able to establish itself in the Milne Re-entrant area and remain in place until February 1988 [Jeffries, 1992]. Satellite imagery from 1993 shows the development of a ridged MLSI surface in this area, which indicates regrowth after the 1988 calving [Jeffries, 2002]. These observations suggest that conditions favoring MLSI growth (cold temperatures and stable sea ice conditions over a period of several years) were present for much of the second half of the twentieth century and that calving was generally an infrequent event. This is consistent with the pattern of breakup events observed for the Nansen and Sverdrup Ice Plugs, to the west of the ice shelves, where occasional breakups in the 1970s to 1990s occurred within a context of general stability [Pope, 2010].
 MLSI extent in front of the Milne Ice Shelf reduced by 71% (10.7 ± 0.2 km2) from 1993 to 2009, with frequent calving from the same area [Mortimer, 2011]. Stable MLSI was no longer able to re-grow to a substantial thickness between breakup events and was instead replaced by thinner and weaker first- and second-year sea ice. This was the case during the 2005 and 2008 northern Ellesmere Island ice shelf breakup events, when pre-weakened ice shelf ice was less able to withstand the effects of tides, waves, and offshore winds [Copland et al., 2007; Vincent et al., 2009].
 The Milne Ice Shelf has experienced significant mass losses since the mid-twentieth century. Measured reductions in ice shelf area of 29% (82 ± 8.4 km2) between 1950 and 2009, and reductions in volume of 13% (1.5 ± 0.73 km3 w.e.) between 1981 and 2008/2009, indicate that it has been in a state of overall negative mass balance since at least 1950. Accumulation from factors such as precipitation, basal accretion and glacier mass input has not balanced losses due to calving, surface and basal melt, and glacier retreat. Mean annual specific mass balance, computed from direct line comparisons over 1 km segments, ranged from 0.16 ± 0.07 m w.e. yr−1 to −0.31 ± 0.09 m w.e. yr−1 for the period 1981 to 2009, with a mean of −0.085 ± 0.079 m w.e. yr−1.
 In contrast to all other northern Ellesmere Island ice shelves, which have experienced dramatic increases in fracturing and breakup over the last decade, the Milne Ice Shelf's area (∼205 km2) has remained unchanged since at least 2001. One possible explanation for the apparent stability of the Milne Ice Shelf is the favorable physiography of Milne Fiord [Jeffries, 1986a; Veillette et al., 2008]. The presence of Cape Egerton on the eastern side of Milne Fiord acts as a protective barrier for the Outer Unit by buffering it from the dominant sea ice drift patterns originating from the northeast [Pope, 2010]. While the complex physiography of northern Ellesmere's coastline may therefore play an important role in slowing the disintegration of the Milne Ice Shelf, it does not prevent thinning and weakening of the ice shelf. The Milne Ice Shelf, which formed under past colder conditions, is not in equilibrium with the current climate. Given the pre-weakened nature of the ice shelf, it is likely that over the next few decades the Milne Ice Shelf will follow the pattern of breakups recently observed for all other northern Ellesmere Island ice shelves.
 We would like to thank the Canada Foundation for Innovation, the Ontario Research Fund, the National Science and Engineering Research Council of Canada, the Garfield Weston Foundation, the Polar Continental Shelf Program (to which this is contribution 00911), the Northern Scientific Training Program, and the University of Ottawa for financial and logistical support. Aerial photographs were provided through an agreement with the National Air Photo Library, Ottawa. Satellite imagery was provided by the Alaska Satellite Facility and NASA's EOS gateway. We would also like to thank the First Canadian Ranger Patrol Group and Sierra Pope for contributions to fieldwork, as well as Carsten Braun and an anonymous reviewer for comments on the manuscript.