GPS-derived estimates of surface mass balance and ocean-induced basal melt for Pine Island Glacier ice shelf , Antarctica

In the last two decades, Pine Island Glacier (PIG) experienced marked speedup, thinning, and grounding-line retreat, 15 likely due to marine ice-sheet instability and ice-shelf basal melt. To better understand these processes, we combined 2008–2010 and 2012–2014 GPS records with dynamic firn model output to constrain local surface and basal mass balance for PIG. We used GPS interferometric reflectometry to precisely measure absolute surface elevation (zsurf) and Lagrangian surface elevation change (Dzsurf/Dt). Observed surface elevation relative to a firn layer tracer for the initial surface (zsurf zsurf0’) is consistent with model estimates of surface mass balance (SMB, primarily snow accumulation) 20 and downward GPS velocity due to firn compaction (vfc). A relatively abrupt ~0.2–0.3 m surface elevation decrease, likely due to surface melt and increased compaction rates, is observed during a period of warm atmospheric temperatures from December 2012 to January 2013. Observed Dzsurf/Dt trends (-1 to -4 m/yr) for the PIG shelf sites are all highly linear. Corresponding basal melt rate estimates range from ~10 to 40 m/yr, in good agreement with those derived from ice-bottom acoustic ranging, phase-sensitive ice-penetrating radar, and high-resolution stereo DEM 25 records. The GPS and DEM records document higher melt rates within and near features associated with longitudinal extension (i.e., transverse surface depressions, rifts). Basal melt rates for the 2012–2014 period show limited temporal variability, despite large changes in ocean temperature recorded by moorings in Pine Island Bay. Our results demonstrate the value of long-term GPS records and interferometric reflectometry for ice-shelf mass balance studies, with implications for the sensitivity of ice-ocean interaction at PIG. 30


Introduction
The widespread availability of precise Global Positioning System (GPS) measurements has revolutionized the study of ice dynamics and glacier mass balance (e.g., Gao and Liu, 2001). Continuously operating dual-frequency GPS receivers provide high-frequency (1 Hz or less), highly accurate (< 1-3 cm) measurements of position, which can be used to derive surface velocity and elevation change. For applications involving ice dynamics, these measurements offer important constraints for the mass continuity equation, which equates surface elevation change with ice flux divergence, surface mass balance (SMB), and basal mass balance (BMB). Here, we explore a methodology to constrain each of these components directly from GPS observables.
SMB processes include precipitation, sublimation, wind redistribution of surface snow, and meltwater runoff. Regional climate models forced by reanalysis output now pro-Published by Copernicus Publications on behalf of the European Geosciences Union. 2656 D. E. Shean et al.: GPS-derived SMB and basal melt for PIG vide daily estimates of Antarctic SMB on a relatively coarse grid (∼ 5.5 to 27 km). In situ SMB measurements are, however, still essential for model calibration and validation. Traditionally, SMB is measured using stake networks, automated weather stations (AWSs), near-surface radar surveys, and firn/ice cores, all of which require substantial field operations in remote locations. These measurements also tend to bias model calibration towards accessible locations, and recent studies indicate that these biases can significantly affect mass balance results, often resulting in overestimates of cumulative balance due to poor sampling in dynamic areas (Andreassen et al., 2016).
Antarctic firn/ice core records indicate that SMB variability over most of Antarctica during the last 800 years was statistically insignificant, but accumulation increased more than 10 % for high-accumulation coastal regions (e.g., the Amundsen Sea Embayment) since the 1960s (Frezzotti et al., 2013). Historically, these areas have been poorly sampled with traditional methods, providing limited data available for validation of modeled SMB.
Accurate knowledge of firn compaction and its spatiotemporal variability is essential for interpreting observed surface elevation change in remote sensing data (e.g., satellite altimetry) and for partitioning this change into components related to ice dynamics and SMB (e.g., Shepherd et al., 2012;Wouters et al., 2015). Depth-dependent compaction rates can be estimated from a number of different methods, including vertical strain measurements (Arthern et al., 2010;Hamilton and Whillans, 1998), borehole optical stratigraphy (Hawley and Waddington, 2011), repeat phase-sensitive radio-echo sounding (pRES) measurements (e.g., Jenkins et al., 2006) and ice-penetrating radar observations of internal layers over time (e.g., Medley et al., 2014Medley et al., , 2015. In the absence of these measurements, dynamic firn models forced by modeled SMB can provide estimates of compaction rates throughout the firn column, which can be integrated to obtain estimates for the contribution of firn compaction to surface elevation change over time (e.g., Ligtenberg et al., 2011). BMB for ice shelves (i.e., bottom melting, accretion) is driven by complex ice-ocean interaction. State-of-theart ice-shelf cavity ocean circulation models offer some insight into sub-shelf ice-ocean interaction, but these models lack validation, as in situ hydrographic observations are limited, especially within the sub-shelf cavity and the iceocean boundary layer. Some direct measurements are available from autonomous submersibles (e.g., Dutrieux et al., 2014) and instrumentation deployed through ice-shelf boreholes (e.g., Stanton et al., 2013), but available data are limited to short time periods and small spatial extents. Precise measurements of surface elevation change from remote sensing observations (e.g., laser altimetry, digital elevation models (DEMs)) can also be used to infer BMB (e.g., Moholdt et al., 2014;Pritchard et al., 2012;Shean, 2016), but temporal resolution is limited, as time intervals between repeat observations are typically several months to years.
Here, we use continuous GPS records from the Pine Island Glacier (PIG) ice shelf to constrain local SMB, flux divergence, and BMB. We use changes in observed GPS antenna elevation and reflectometry-derived surface elevation to validate SMB and firn model output. Flux divergence is estimated from observed strain rates between GPS stations. These estimates are then used to isolate elevation change due to local BMB. This approach yields temporally dense records of basal melt rates at spatially sparse GPS locations, which are combined with high-resolution DEMs from the same time period to provide spatial context. These complementary results for the PIG ice shelf provide new information about the time-variable magnitude and spatial distribution of basal melting, offering indirect observations of ice-ocean interaction and BMB sensitivity to ocean heat content variability, with implications for other rapidly evolving "warm-cavity" Antarctic ice shelves.

PIG background
Pine Island Glacier is one of the largest and most dynamic ice streams in West Antarctica. Since the 1970s, PIG has experienced ∼ 30 km of grounding-line retreat along its centerline  (∼ 8 km average retreat across full width of fast-flowing trunk; Joughin et al., 2016), a ∼ 75 % increase in surface velocity , and > 100 m of thinning (Bindschadler, 2002;Pritchard et al., 2009), with accelerated retreat beginning in the 1990s. These changes have been attributed to some combination of geometric instability (i.e., marine ice-sheet instability) and external forcing (i.e., increased ocean heat content and/or changes in sub-shelf circulation) (Jacobs et al., 2011;Joughin et al., 2010).
The main shelf has complex surface topography, including kilometer-scale surface ridges and troughs that correspond to basal keels and channels, respectively (Bindschadler et al., 2011;Vaughan et al., 2012). A series of longitudinal (along-  (Christianson et al., 2016;Joughin et al., 2010) over a shaded relief map from October-December 2012 DEM mosaic. Black lines show ∼ 2-year paths between initial (green) and final (red) GPS station locations. The yellow dot shows the Evans Knoll automated weather station (AWS) and the blue squares show RACMO grid-cell centers used during analysis. The purple triangles beyond shelf front show locations of ocean mooring temperature data from Christianson et al. (2016). The white line shows approximate 2011 grounding line (Shean, 2016). Black rectangle shows location of Fig. 2a. flow) ridges and troughs are present along the shelf centerline, with transverse (across-flow) ridges and troughs along the lateral margins ( Fig. 1). Local basal melt rates vary considerably across these features Shean, 2016).
Hydrographic observations seaward of the PIG calving front in Pine Island Bay suggest that basal melting declined by ∼ 50 % between 2010 and 2012 (Dutrieux et al., 2014). Long-term 2009-2015 mooring records seaward of the southern calving front (Fig. 1) show a significant decrease in ocean temperature (∼ 1-1.5 • C) over ∼ 450-770 m depths from late 2011 to early 2012 and then again from mid-2012 to early 2013 (Christianson et al., 2016;Webber et al., 2017). These observations show that the ocean heat content at the PIG ice-shelf front varies considerably over monthly to interannual timescales.

PIG GPS sites
Several long-term GPS stations were installed on the PIG shelf as part of a larger investigation of ice-sheet, ice-shelf, and ocean dynamics (Bindschadler et al., 2011;. During the early part of this effort, two GPS stations continuously collected data from January 2008 to Jan-uary 2010: one on the southern PIG ice shelf (PIG2) and another on the fast-flowing, grounded ice upstream of the grounding line (PIG1) (Fig. 1). In addition, a ∼ 2 × 2 km array of five stations (SOW1-4, BOAR, Fig. 2) was installed ∼ 50 km downstream of the grounding line, near the center of the main shelf from January 2012 to late December 2013.
The stations used dual-frequency Trimble NetRS GPS receivers (2008-2010 sites) and NetR9 receivers (2012-2014 sites), with Trimble Zephyr Geodetic 2 antennas mounted on 12 foot (3.66 m) poles with insulating pole-base stoppers. The poles were driven into the snow by hand, with initial pole bases set ∼ 0.5-1.0 m beneath the surface (M. Truffer, personal communication, 2016).
High-resolution optical imagery and DEM data (see Sect. 2.5) over the 2012-2014 sites show that SOW1, BOAR, and SOW3 were installed with along-flow orientation in a longitudinal surface trough (Fig. 2) that overlies a longitudinal basal channel. An ice-penetrating radar profile with transverse orientation was collected upstream of the GPS array, providing ice thickness estimates of ∼ 450-460 m near the apex of a longitudinal channel and ∼ 540 m over adjacent keels . Figure 2 shows estimated ice thickness for longitudinal and transverse profiles across the GPS array.
A borehole was drilled through the ice shelf approximately 1.34 km upstream of SOW1 (K. Riverman, personal communication, 2016), and an instrument package with an upwardfacing ice-bottom altimeter (acoustic ranger) was deployed beneath the shelf from January to February 2012. Measurements from this bottom altimeter and complementary pRES experiments provided basal melt rate estimates of ∼ 14-25 m yr −1 within the longitudinal channel (Christianson et al., 2016;Stanton et al., 2013).
The 2012-2014 GPS array was located near several transverse surface depressions (Fig. 2), which are likely associated with transverse basal channels and/or rifts. Local surface slopes were ∼ 0.6-0.9 • within the largest of these depressions, immediately downstream of SOW3 and SOW4. A notable linear surface depression located approximately 1 km upstream of SOW1 (black arrow in Fig. 2) opened as a rift in ∼ 2014 (R1 in Jeong et al., 2016) and was subsequently the site of a large iceberg calving event that occurred around July 2015. The placement of the 2012-2014 GPS array near these features complicates interpretation of GPS records but also provides new constraints on the spatiotemporal evolution of strain rates and rift formation for the PIG shelf.
2 Data and methods

GPS antenna position
As described in Christianson et al. (2016), GPS data were processed using differential-carrier-phase positioning relative to bedrock GPS sites -Backer Island (BACK; www.the-cryosphere.net/11/2655/2017/ The Cryosphere, 11, 2655-2674, 2017 Dailyaveraged positions of these base stations were calculated using GAMIT and stabilized relative to a fixed circum-Antarctic reference frame using a Kalman filter (GLOBK; Herring et al., 2015). Antenna positions relative to the WGS84 ellipsoid were calculated every 30 s. We analyzed a subset of these positions sampled at 10 min intervals and removed any positions with uncertainty > 8 cm. The BOAR record was curtailed on 29 April 2013 (1.31-year duration), when an abrupt ∼ 2.0 m elevation decrease and corresponding horizontal offset occurred, suggesting that the pole fell over. We estimate initial antenna position accuracy of ∼ 1 cm. Positions were converted to a local Cartesian horizontal coordinate system with final antenna elevation values (z ant ) as orthometric height above the EGM2008 geoid (Pavlis et al., 2012). Absolute geoid errors are poorly constrained for coastal Antarctica, but relative geoid error for the cumulative horizontal displacement of the GPS array (∼ 8 km over the 2year period) should be < 1-2 cm. A constant offset of 3.71 m (3.66 m pole length + 0.053 m phase center to bottom of antenna) was removed from antenna elevation (z ant ) to estimate corresponding pole-base elevation.
We estimated vertical tidal displacement for all GPS positions on the PIG ice shelf using CATS2008A, an updated version of the model described by Padman et al. (2002). We used mean sea level pressure values from the 0.75 • grid-cell ERA-Interim reanalysis products (Dee et al., 2011) to correct for vertical displacement due to the inverse barometer effect (IBE; e.g., Padman et al., 2003). To do this, we removed the 2002-2016 median (985.21 hPa) from 6 h sea level pressure and scaled the residuals by ∼ 1 cm hPa −1 . Figure 3 shows that tidal amplitudes for the GPS sites range from approximately −0.9 to +1.3 m and IBE amplitudes range from −0.3 to +0.3 m. These signals were removed from the GPS antenna elevation (z ant ), and residual high-frequency noise was removed with a low-pass filter (1.5-day cutoff), yielding smoothed time series for further analysis (Fig. 3). We conservatively estimate final z ant absolute accuracy of ∼ 0.1 m.

Antenna-surface distance
The GPS interferometric reflectometry (GPS-IR) method provides a precise measurement of antenna phase-center height above a reflecting surface (Larson, 2016). The reflecting surface for PIG is the interface between the atmosphere and the snow/firn surface, and we define the antenna height above this interface as the "antenna-surface distance" (h ant−surf ). Figure 4 shows a schematic of this GPS site geometry.
Assuming that the GPS pole base remains fixed within its original firn layer (see Sect. 5.3 for further discussion), observed decreases in the antenna-surface distance (h ant−surf ) can be attributed to surface accumulation (e.g., snowfall, deposition of snow by wind). Conversely, an increase in antenna-surface distance can be attributed to surface ablation (e.g., melt, sublimation, removal of snow by wind) and compaction of snow and/or firn above the pole base.
We computed mean daily antenna-surface distance for all sites using L1 C/A code multipath surface reflections and the GPS interferometric reflectometry methodology outlined in  Larson et al. (2015). This method takes advantage of the fact that the interference between the direct and reflected GPS signals produces characteristic frequencies in signal-to-noise ratio data recorded by the GPS receiver; these frequencies are directly related to the distance between the GPS antenna phase center and the reflecting surface. Geodetic antennas are designed to suppress multipath, so these interference patterns are best resolved at low GPS satellite elevation angles. Reflector height solutions were calculated for elevation angles of 5-25 • , which sample the surface within a radial extent of ∼ 5-50 m. Local surface slopes at each site are negligible, eliminating the need for an azimuthal correction (e.g., Larson and Nievinski, 2013). Daily antenna-surface distance (h ant−surf ) accuracy is estimated to be ∼ 1 cm (Larson et al., 2015).

GPS-derived surface elevation
The antenna-surface distance (h ant−surf ) was subtracted from antenna elevation (z ant ) to obtain daily records of surface elevation z surf (i.e., elevation of the air-snow interface above the EGM2008 geoid), with resulting relative accuracy of ∼ 1-2 cm (absolute accuracy subject to the same ∼ 0.1 m z ant uncertainty due to tidal, IBE, and geoid corrections). The z surf surface elevation values are directly comparable with satellite or airborne laser altimetry data and stereo DEM products. We use variable name z surf rather than the more traditional glaciological variable name h to limit potential confusion between different "height" and "elevation" variables.
Continuous z surf time series were generated for all seven PIG GPS sites. The SOW3 record was curtailed on 22 August 2013, when antenna-surface distance decreased below the minimum threshold of ∼ 0.5 m (Nievinski, 2013).

GPS velocity and strain rate
Horizontal velocities for each GPS station were computed from daily mean antenna positions. We calculated principal strain rates for eight different triangular sections within the array (each defined by unique combination of three sites), using the methods outlined by Savage et al. (2001). We tested multiple time intervals for these strain rate calculations, from 2 to 120 days, and use 42 days as a compromise between temporal resolution and uncertainty (assuming uncorrelated daily position error of ∼ 1 cm). We used observed horizontal strain rates to estimate elevation change related to local flux divergence.
Some component of observed GPS surface elevation change may also be related to deformation due to local gradients in the driving stress and surface-parallel flow due to advection over basal topography. The vertical component of surface-parallel flow (V 0 in Larson et al., 2015) can be estimated using observed horizontal GPS paths and surface gradients from an independent DEM. Advection over bed topography is irrelevant for a freely floating ice shelf, and we attempt to estimate an upper bound for V 0 due to local deformation by considering local surface gradients and observed relative horizontal displacements within the 2012-2014 GPS array.

High-resolution DEMs
In addition to the GPS elevation data, we generated World-View/GeoEye stereo DEMs  with 32 m posting over the PIG shelf (Shean, 2016) to provide spatial context for the GPS time series. A total of seven World-View DEMs intersected the 2012-2014 GPS positions. We sampled DEM surface elevation at corresponding GPS po-sitions and compared with GPS-derived surface elevation where possible.
High-resolution Lagrangian Dz surf / Dt maps (see methodology in Shean, 2016; note we use D/Dt to indicate a Lagrangian differential operator) were computed for the 2012-2014 GPS sites by forward-propagating 32 m DEM pixels from two initial DEM products (2 February 2012 and 23 October 2012) using interpolated, time-variable surface velocity maps from Joughin et al. (2010) and Christianson et al. (2016). Lagrangian Dz surf /Dt maps were generated for all valid combinations of these initial DEMs and ∼ 15 subsequent DEMs (∼ 0.5-2.5 years later). Composite products were generated, with median Dz surf / Dt values assigned to initial DEM pixel locations.

Surface mass balance
We analyzed estimates of 1979-2015 monthly and 2010-2013 daily SMB for three 27 km grid cells over the PIG shelf from the Regional Atmospheric Climate Model (RACMO) v2.3 (Ettema et al., 2009;Lenaerts et al., 2012;Van Meijgaard et al., 2008;Van Wessem et al., 2014). 14 • E), providing some information on large-scale spatial variability. These values are consistent with SMB estimates of ∼ 0.5-1.0 m w.e. yr −1 derived from CReSIS snow radar data collected upstream of the PIG grounding line (Medley et al., , 2015 and SMB estimates of 0.99 and 1.06 m w.e. yr −1 for stake measurements near 2006-2008 GPS sites over the upstream PIG trunk (Scott et al., 2009). We conservatively estimate SMB uncertainty of 0.2 m w.e. yr −1 .

AWS temperature data
To provide context for surface elevation change due to surface melt events, we analyzed continuous 2011-2015 temperature data (3 h interval) from the Evans Knoll AWS (−74.85 • N, −100.40 • E; Lazzara et al., 2012), located at an elevation of ∼ 178 m (height above EGM2008 geoid) on a bedrock outcrop approximately 40 km north of the 2012-2014 GPS array (Fig. 1). We also analyzed New York University (NYU) AWS temperature data available near PIG2 from 9 January 2008 to 7 November 2009 and near BOAR from 19 January 2013 to 26 May 2015. Unfortunately, no AWS data were collected on the PIG shelf during 2012. An analysis of overlapping time periods for the Evans Knoll and 2013-2015 NYU AWS temperature records shows a median offset of +1.24 • C (Evans Knoll warmer than NYU, with normalized median absolute deviation (NMAD) of 2.76 • C), which is consistent with a dry adiabatic lapse rate and lo-cal site conditions. This offset was removed from the Evans Knoll temperature data to provide a continuous temperature estimate for the GPS sites over the full 2012-2014 period.
To provide historical context, we extracted 2 m air temperature over the PIG shelf from 0.75 • -resolution ERA-Interim reanalysis products (Dee et al., 2011) for the 1979-2015 period with 6 h interval. The median offset between the ERA-Interim temperature data and the 2013-2015 NYU AWS temperature data was +0.10 • C (ERA-Interim warmer than NYU) with NMAD 2.78 • C. This median offset was removed from the ERA-Interim temperatures. We did not attempt to correct any seasonal bias in ERA-Interim products (e.g., Jones et al., 2016).

Firn model
We used a dynamic firn model to simulate elevation change related to SMB and firn processes. Model SMB output from RACMO2.3 (Sect. 2.6) was used to force the semi-empirical 1-D IMAU-FDM dynamic firn model (Ligtenberg et al., 2011) with 3 h timestep, and IMAU-FDM output was generated at 2-day intervals. Velocity (v ice ) across the firn-ice transition (defined as the layer with 917 kg m −3 density) was assumed to be in equilibrium with average 1979-2015 SMB (ā = 0.91 m w.e. yr −1 ), so that v ice =ā ρ i . Vertical velocity components for surface accumulation, surface sublimation, surface snow drift erosion/deposition, surface melt, dry firn compaction, and a vertical buoyancy correction (over floating ice-shelf grid cells) were computed for the 2008-2010 and 2012-2014 periods (see Ligtenberg et al., 2011, for model details). These components were combined to provide time series of simulated surface elevation ( z surf ) at each GPS station. In addition, simulated elevations were computed over time for tracers corresponding to the initial surface and pole base. We conservatively estimate IMAU-FDM surface elevation uncertainty of ∼ 10 %, which corresponds to ∼ 0.05 m for z surf .

Derivation of basal mass balance
We combine the above observations and model output to estimate basal mass balance for the PIG GPS sites. Mass conservation for a column with ice-equivalent thickness H ice (after removing a thickness correction d that accounts for total air content in the firn column) relates Eulerian thickness change (dH ice /dt) with dynamic thinning or thickening due to flux divergence (∇ · H ice u, positive for extension), surface mass balanceȧ (meters ice equivalent), and basal mass balanceḃ (meters ice equivalent, defined as positive for melt): The material derivative definition relates Eulerian (fixed reference frame) and Lagrangian (reference frame moving with the ice column) thickness change: Rearranging Eq.
(1), we obtain the mass conservation equation for Lagrangian thickness change: For a floating ice shelf in hydrostatic equilibrium, we can estimate ice-equivalent thickness from air-column-corrected surface elevation (z surf − d), where z surf is measured surface elevation and d is total firn-air content: assuming a constant bulk density for ocean water (ρ w = 1026 ± 1 kg m −3 ) and ice (ρ i = 917 ± 5 kg m −3 ). We substitute Eq. (4) into (3) and rearrange to estimate basal melt rate from observed surface elevation change: Here, we assume that the total firn-air content remains constant for the period dt and drop the constant d from the material derivative term (d ≈ 12 m for the PIG shelf, with uncertainty of ∼ 2 m; see Appendix in Shean, 2016). This simplification is supported by the limited temporal variability (±0.3 m, or ∼ 1-3 %) in modeled IMAU-FDM total firn air content for the three PIG shelf grid cells during the relevant ∼ 2-year study periods.
The effects of processes that drive short-term surfaceelevation change (e.g., accumulation, melting) are largely absent below the upper few meters of the firn column. Thus, elevation change at the GPS pole base (equivalent to Dz ant /Dt for constant pole length) displays less variability than elevation change at the surface, as it is most sensitive to (1) compaction rates within the underlying firn, (2) the long-term average SMB (see Sect. 2.8), (3) BMB, and (4) flux divergence. For the pole-base depths and time periods involved in this study, the first two terms display limited to no variability, the flux divergence term is negligible, and observed Dz ant /Dt can capture basal melt rate variability that might be obscured by surface accumulation and ablation signals in observed Dz surf /Dt. as the GPS moved downstream. Velocities for grounded ice at PIG1 increased at a relatively steady rate from ∼ 420 to ∼ 460 m yr −1 as the station moved toward the fast-flowing PIG trunk (Fig. 1). Figure 5b shows the 2012-2014 velocities for the GPS array, which varied from ∼ 3830 to 4040 m yr −1 (Christianson et al., 2016). Velocities at SOW1, BOAR, and SOW3 were similar, while SOW4 (closer to shelf centerline) consistently moved ∼ 20 m yr −1 faster than these three sites, and SOW2 consistently moved ∼ 15 m yr −1 slower. Thus, there appears to be ∼ 30-40 m yr −1 dextral (right-handed) shear across the ∼ 2.4 km distance between the SOW4 and SOW2 sites. This transverse velocity gradient is also apparent in velocity mosaics (e.g., Christianson et al., 2016).
The velocity of all five stations varied by ∼ 2-4 % from 2012 to 2014, as described in detail by Christianson et al. (2016). In general, the stations displayed similar relative velocity evolution, with several abrupt > 0.1-0.2 m day −1 velocity changes during the ∼ 2-year period (Fig. 5). Figure 6 shows strain rate magnitude and direction for 8 different strain triangles within the 2012-2014 GPS array. Mean principal strain rates were +0.0018 yr −1 (extension approximately in the along-flow direction) and −0.0001 yr −1 (compression approximately in the across-flow/transverse direction). The array displayed a clockwise rotation rate of ∼ 1 • yr −1 .

Strain rate
Spatial variations of strain rates within the array are small (Fig. 6). Strain triangles including SOW1 experienced higher strain rates, while triangles including SOW3 experienced lower strain rates, despite its location within the large transverse depression (Fig. 2). Strain rate temporal variability is also limited, but there do appear to be significant changes correlated with shelf-wide velocity changes. In general, increased (decreased) extensional strain rates were observed following an increase (decrease) in absolute GPS array velocity.
Local surface slopes near SOW1, SOW2, and BOAR are negligible (< 0.2 • ), so we assume no surface-parallel vertical motion for these stations (i.e., V 0 = 0). If all of the observed ∼ 3.4 m yr −1 relative displacement between SOW1 and SOW3 was attributed to flow down ∼ 0.6 • local surface slopes at SOW3, then the associated V 0 magnitude would only be ∼ 0.03 m yr −1 , which is negligible compared to the observed ∼ 5.2 m yr −1 Dz surf /Dt.
For estimated ice-equivalent thickness of ∼ 430-500 m, the observed strain rates correspond to shelf thinning rates (DH ice /Dt) of ∼ 0.5-0.9 m yr −1 , with expected surface elevation change (Dz surf /Dt) of only ∼ 0.07-0.13 m yr −1 . Based on these estimates, we assume a value of −0.1 ± 0.03 m yr −1 for the divergence term in Eq. (5).

Antenna-surface distance
Initial antenna-surface distances (h ant−surf ) were ∼ 2.5 to 3.1 m, indicating that initial pole-base depths were ∼ 0.6 to 1.2 m below the initial surface (Figs. 7a, 8). Antenna-surface distance decreased over time at all sites, with Dh ant−surf /Dt rates of approximately −0.8 to −1.1 m yr −1 (Fig. 7a).
At both PIG1 and PIG2, there were periods of relatively rapid antenna-surface distance decrease (e.g., from May to August 2008), followed by a steady increase (e.g., August 2008 to February 2009). These changes are consistent with periods of snow accumulation followed by several months of ongoing firn compaction with limited snowfall. The 2012-2014 records show similar periods of abrupt antenna-surface distance decrease and steady increase, with more limited duration.
All GPS array records show an abrupt antenna-surface distance increase (∼ 0.2-0.3 m) between December 2012 and January 2013, which is consistent with surface melting and/or enhanced firn-compaction rates above the pole base (i.e., upper few meters of the firn column).

GPS antenna and surface elevation change
Trends in observed antenna elevation change (Dz ant /Dt) are negative and highly linear (R 2 0.98-1.00) for all PIG shelf sites, with rates of −1.6 to −2.1 m yr −1 at SOW1, SOW2, and BOAR and higher rates of −5.2 and −3.8 m yr −1 at SOW3 and SOW4, respectively (Fig. 7b, Table 1). Observed Dz ant /Dt over grounded ice at PIG1 is −7.6 m yr −1 , with apparent concave-downward curvature. This is consistent with V 0 expected for surface-parallel flow (see Sect. 2.4) and dynamic thinning over the PIG trunk associated with velocity increases in 2006-2008 GPS observations (Scott et al., 2009) and satellite records (Joughin et al., 2010;Mouginot et al., 2014).
The 2008-2010 surface elevation change (Dz surf /Dt) at PIG2 is limited (−0.13 m yr −1 ). By contrast, surface elevations decreased significantly at all 2012-2014 GPS array sites, with rates of −0.9 to −1.3 m yr −1 for SOW1, SOW2, and BOAR and rates of −4.1 and −3.0 m yr −1 at SOW3 and SOW4, respectively. Residuals about these linear fits ( Fig. 9a and b) are small for PIG shelf sites (root mean square error (RMSE) of 0.095 m for Dz ant /Dt, and RMSE of 0.143 m for Dz surf /Dt), with some seasonal to annual variability. We also note relatively abrupt (∼ days-weeks) elevation changes that occurred across all stations in the 2012-2014 array (e.g., −0.3 to +0.3 m anomaly during June 2012).

Surface mass balance
We consider surface elevation (z surf ) relative to a firn layer tracer for the initial surface elevation (z surf0 ) to estimate cumulative elevation change due to SMB after GPS installation. Observed z surf -z surf0 rates were ∼ 0.9-1.1 m yr −1 for 2008-2010 sites and ∼ 0.8-0.9 m yr −1 for 2012-2014 sites (with SOW3 at ∼ 1.1 m yr −1 ) (Fig. 9c).
The average RACMO SMB over the central PIG shelf from 1979 to 2015 is ∼ 0.9 m w.e. yr −1 . Monthly SMB climatology shows low accumulation rates of ∼ 0.01-0.04 m w.e. month −1 over the PIG shelf during the austral www.the-cryosphere.net/11/2655/2017/ The Cryosphere, 11, 2655-2674, 2017   summer (November to February) and high accumulation rates of ∼ 0.08-0.10 m w.e. month −1 during austral winter (March to October) (Fig. 9d). Daily SMB products show periods of days to weeks with increased accumulation (e.g., March 2013) that can be correlated with abrupt decreases in antenna-surface distance.
The ∼ 3-4-week period between 24 December 2012 and 17 January 2013 was relatively warm, with calibrated AWS temperatures of ∼ 1-5 • C for most days (Fig. 9e). We note that these are 2 m air temperatures and that once surface melting commenced, actual surface temperatures would be lower but still above freezing. The daily RACMO SMB data also show two accumulation events during the last week of December 2012 (Fig. 9d), which involved rain on snow (M. Truffer, personal communication, 2016). Surface elevations decreased by ∼ 0.2-0.3 m across the entire GPS array during this warm and rainy period (Fig. 9b), which is consistent with surface melting and/or enhanced firn-compaction rates. No corresponding short-term changes were recorded by the antenna elevations during the ∼ 3-4-week period (Fig. 9a), suggesting that the processes responsible for the observed surface changes did not affect the firn layers near the pole base (∼ 1.5 m depth). We note that there are many warm periods between 1979 and 2015 with greater magnitude and duration than the December 2012 to January 2013 period in the ERA-Interim 2 m air temperatures over the PIG shelf. The magnitude and timing of the simulated surface elevation variability is consistent with the detrended observed surface elevation change (Fig. 9b). The observed Dz surf /Dt trends (−1 to −4 m yr −1 ), however, cannot be explained by simulated elevation change due to SMB and firn processes (Fig. 7c).

Basal melt rates
We computed basal melt rates from surface Dz surf /Dt elevation change using Eq. (5). The resulting melt rate estimates range from ∼ 2 m yr −1 at PIG2 to ∼ 39 m yr −1 at SOW3 (Table 1).
The 2012-2014 melt rate estimates show significant spatial variability. The three upstream stations (SOW1, SOW2, and BOAR) experienced lower melt rates of ∼ 9-13 m yr −1 , while the downstream stations near the transverse depression (SOW3 and SOW4) experienced higher rates of ∼ 29-39 m yr −1 for the same time period. Figure 8 shows sampled DEM elevation compared with GPS surface elevation at each site, with statistics provided in Table 2. In general, we observe good agreement between the two datasets, with RMSE of 0.72 m and NMAD of 0.57 m for the full sample (n = 25). The DEMs display a slight bias (+0.43 m) relative to the GPS surface elevation.

High-resolution DEMs
We observe good agreement between GPS-derived (Table 1) and DEM-derived (Table 2) Dz surf /Dt trends. The shorter DEM Dz surf /Dt intervals (e.g., ∼ 1 year for SOW1 and BOAR) display larger errors than longer DEM intervals (∼ 2 years for SOW2 and SOW3). Figure 10 shows the composite DEM-derived Dz surf /Dt maps, which provide spatial context for the GPS-derived Dz surf /Dt records. Little or no elevation change was observed over longitudinal ridges, while areas within and near transverse depressions experienced enhanced thinning. This thinning was concentrated on the upstream side of the transverse depressions. The Dz surf /Dt products relative to the 23 October 2012 DEM (Fig. 10d) also show the spatial pattern of thinning associated with the rift that opened upstream of SOW1 in ∼ 2014 (Jeong et al., 2016).

Assumptions
The methods presented in Sect. 2 relied on several simplifying assumptions. We now offer further discussion of these assumptions and their potential influence on our results.

Hydrostatic equilibrium
In the absence of direct ice thickness measurements (e.g., radar profiles near PIG GPS sites), we assume hydrostatic equilibrium and use surface elevation to estimate freeboard ice thickness -a standard practice for ice-shelf studies. While this assumption can lead to increased uncertainty within a few ice thicknesses of the grounding line (Brunt et al., 2010;Griggs and Bamber, 2011), it is reasonable for the mid-shelf location of the GPS array, which in ∼ 2012, had been approaching hydrostatic equilibrium for over 10-12 years since crossing the grounding line. Previous studies using airborne ice-penetrating radar data have noted that most of the PIG shelf is generally near hydrostatic equilibrium (Bindschadler et al., 2011;Dutrieux et al., 2013;Vaughan et al., 2012). Dense radar grids, however, reveal narrow shelf-bottom channels, crevasses, and other features with horizontal length scales of ∼ 10s-100s of meters that are not apparent in ice-shelf surface topography (Langley et al., 2014;Vaughan et al., 2012). The thinner ice above these narrow features is partially supported by lateral bridging stresses, so that the corresponding surface elevation will appear higher than the expected freeboard surface elevation, providing erroneously large ice thickness estimates using Eq. (4) (Drews, 2015;Shabtaie and Bentley, 1982;Vaughan et al., 2012).
Experiments with a high-resolution ice-flow model show that wider basal channels tend to be near equilibrium, while increased bridging stresses support ice over narrow basal channels (Drews, 2015). The PIG GPS array is ∼ 2 km across, which is > 4-5× the local ice thickness (∼ 350-500 m). The ∼ 1-2 km length scale of nearby longitudinal channels/keels is > 2-3× the local ice thickness, with typical surface elevation difference between trough floors and adjacent ridge crests of < 10 m. For the observed ice thickness, magnitude, and length scale of surface variations, as well as the relatively long timescales involved, we argue that the hydrostatic assumption is reasonable, and any vertical elevation change due to evolving bridging stresses should be negligible compared to the magnitude of observed Dz surf /Dt and our conservative error estimates.

SMB spatial variability
We used modeled SMB from a single RACMO2.3 grid cell to drive the IMAU-FDM dynamic firn model, and applied the result to all GPS stations. We expect SMB to vary spatially (e.g., Medley et al., 2015) due to local environmental conditions (e.g., PIG2 elevation is > 400 m higher than SOW1-4 stations on the shelf) and local surface topography (e.g., kilometer-scale ridges/troughs), which will affect nearsurface winds and snow redistribution.
The larger z surf − z surf0 values (a proxy for surface accumulation) at SOW3 (Fig. 9c) indicate that greater local accumulation occurred at this site within the transverse depression (Fig. 2), potentially due to preferential deposition of wind-blown snow. However, we also note that the accumulation histories of SOW4, which sits near a surface ridge crest, and the three sites located on the floor of a broad, flat surface trough (SOW1, SOW2, BOAR) appear similar (Fig. 9c).
The IMAU-FDM values do not account for horizontal advection of the firn column through spatially variable RACMO fields (accumulation, surface temperature, etc.) over time. The GPS sites over the PIG shelf are moving ∼ 4 km yr −1 (Figs. 1 and 5), which is nearly double the observed PIG shelf velocities from the mid-1970s . Thus, the local firn columns beneath the GPS sites likely experienced variable SMB input over their ∼ 50-100 km horizontal path during the corresponding 1979-2015 time period. This suggests that the true firn column thickness and compaction rates may differ from the IMAU-FDM estimates. For this reason, we use a constant firn air content estimate (d ≈ 12 ± 2 m) derived from available airborne icepenetrating radar two-way travel time and altimetry surface elevation measurements (see Appendix A of Shean, 2016).

Pole settling/tilting
We now consider whether some of the observed Dz surf /Dt could be related to settling, heating, or tilting of the GPS www.the-cryosphere.net/11/2655/2017/ The Cryosphere, 11, 2655-2674, 2017 The Dz surf /Dt maps are used to calculate basal melt rates (scaling factor of ∼ 9, e.g., Dz surf /Dt of ∼ 1 m yr −1 corresponds to a basal melt rate estimate of ∼ 9-10 m yr −1 ). poles over time. We assume that the poles froze in place shortly after installation, and the contact area (∼ 1200 cm 2 for a ∼ 1 m long cylinder with ∼ 3.8 cm diameter) with surrounding firn should be sufficient to counter the downward gravitational force. Thus, we expect that antenna elevation change (Dz ant /Dt) represents rates at the base of the pole rather than rates within an overlying firn layer. A related consideration involves heating of the exposed pole during summer, which might lead to decoupling from the surrounding snow/firn and allow for additional penetration of the pole base within the firn. The pole-base stoppers should have prevented this penetration. In addition, we do not see any indication of such settling from December 2012 to January 2013, when surface elevations decreased by ∼ 0.2-0.3 m, but pole-base elevations showed little change ( Fig. 9a  and b). The lack of pole-base elevation change also suggests that surface meltwater did not percolate more than ∼ 1-2 m below the surface.
Finally, we assume that the poles were installed with vertical orientation and did not tilt over time. For an initially vertical pole with length of 3.71 m (including antenna phasecenter offset), a 10 • tilt would introduce a −0.06 m vertical antenna elevation error (−0.03 m yr −1 for a 2-year period), while a 20 • tilt would introduce a −0.22 m vertical error (−0.11 m yr −1 ). Thus, we expect vertical error associated with any tilting to be negligible compared to the large observed Dz ant /Dt (−1.12 to −7.60 m yr −1 ). These 10 and 20 • tilts could, however, introduce horizontal errors of up to 0.64 and 1.27 m, respectively, which would affect intranetwork displacement and strain rate estimates. While it is possible that some minor tilting could have occurred (especially during initial months), this was not noted during servicing/removal, and the reflectometry results do not indicate any systematic change in directional antenna-surface offset.

Strain rate length scales
We estimated ∼ 0.1 m yr −1 surface elevation change due to local flux divergence, assuming that the observed relative horizontal displacements are evenly distributed across the strain triangles, which have ∼ 1-2 km edges between GPS stations. This assumption is supported by the ∼ 1 km spatial extent of thinning signals within/near transverse depressions in the Dz surf /Dt maps (Fig. 10). Even if this strain is concentrated over a shorter distance (e.g., ∼ 200 m), this contribution only increases to ∼ 0.5 m yr −1 , which is still small compared to observed Dz surf /Dt signals of ∼ 3-4 m yr −1 . The relatively large spatial variability in Dz surf /Dt values (∼ 1 to ∼ 4 m yr −1 ) and lack of spatial variability in strain rates supports the assumption that the observed Dz surf /Dt is primarily caused by basal melt.

SMB and firn compaction
The evolution of GPS-derived surface elevation relative to a tracer for the initial surface (z surf − z surf0 ) is consistent with SMB estimates (ȧ), providing qualitative validation for the RACMO SMB and IMAU-FDM results. Based on these results, we suggest that it may be possible to extract detailed SMB records for other sites using only observed GPS antenna-surface distance and simple assumptions about firn densification (e.g., Herron and Langway Jr., 1980). The problem is further simplified for grounded ice with negligible BMB rates.
The limited variability in surface elevation at PIG2 (Fig. 7c) suggests that the observed 2008-2010 SMB over the south PIG shelf was approximately equal to basal melt during this period, assuming negligible velocity divergence for this location. We observe large surface elevation trends for the 2012-2014 GPS sites with no significant simulated D z surf /Dt trend, suggesting that SMB and firn compaction during this period were consistent with average 1979-2015 SMB (ā) values, and that the large observed Dz surf /Dt must be attributed to other processes, specifically basal melting.

Residual elevation variability
The detrended surface (Fig. 9a) and antenna (Fig. 9b) elevation residuals appear unrelated. This suggests that seasonal surface processes (e.g., accumulation influencing nearsurface compaction rates) are not responsible for driving antenna elevation variability. We considered several possible sources for the observed subannual elevation variability, including ocean (e.g., currents, sea surface height), atmospheric (e.g., pressure, temperature), and dynamic processes (e.g., resistive stress from sea ice and/or mélange in shear margins). Unfortunately, we were unable to definitively determine the cause(s) for these variations in the ∼ 2-year GPS records.
Some of the short-term (days-weeks) variability (e.g., June 2012) observed across all five 2012-2014 stations (Fig. 9b) could be related to insufficient or incorrect IBE correction. The magnitude and timing of these systematic anomalies, however, suggests that they are likely related to grounding/ungrounding events (e.g., Joughin et al., 2016).

Strain rate history, rifting, and grounding evolution
The lateral shear across the GPS array is consistent with increased longitudinal extension closer to the PIG centerline, potentially due to locally enhanced ductile deformation (i.e., "necking"; Bassis and Ma, 2015) across transverse depressions and/or expansion of basal/surface crevasses and rifts. The SOW3 station, which lies within a large transverse depression (Fig. 2), displays a slight acceleration in antenna elevation change (Fig. 9a), potentially due to increased local extension within the depression.
An upstream regrounding event would slow ice upstream of the GPS array, initially resulting in increased extensional strain rates across the transverse rifts/depressions, followed by a velocity decrease at the GPS array. Conversely, an upstream ungrounding event would initially lead to decreased extensional strain rates across the transverse rifts/depressions, followed by an increase in observed GPS velocities. We suggest that an upstream regrounding event  in ∼ June 2012 could be responsible for increased strain rates across the GPS array (Fig. 6). Similarly, an ungrounding event in ∼ April 2013 followed by a grounding event in ∼ November 2013 could explain the decrease and subsequent increase in strain rates.
There is an abrupt ∼ 0.1-0.2 m antenna elevation (z ant ) decrease at both SOW3 and SOW4 in late 2013, near the end of the records (Fig. 9a). No surface elevation (z surf ) information is available at SOW3 due to missing antenna-surface distance data for this period (see Sect. 2.3), but a corresponding surface elevation decrease is observed at SOW4 (Fig. 9b). These elevation decreases do not appear to be related to site servicing. Rather, these observations are consistent with relatively abrupt local extension within the transverse depression affecting SOW3 and SOW4 but not the upstream GPS sites. The timing of this event corresponds with observed lengthening of the large rift (R1) upstream of SOW1 (Jeong et al., 2016), supporting the hypothesis that relatively rapid, localized extension occurred across the transverse depressions and rifts during this period.

Comparison with in situ basal melt rate observations
The GPS-derived basal melt rate estimates (∼ 9-13 m yr −1 for SOW1, SOW2, and BOAR sites) appear consistent with those from bottom altimeter (∼ 14.7 m yr −1 from January to February 2012) and pRES (∼ 15-25 m yr −1 ) measurements of Stanton et al. (2013). These measurements provide some validation for the GPS results, as they are not influenced by surface mass balance and firn processes. A direct comparison may be imprudent, however, as the Stanton et al. (2013) borehole was ∼ 1.34 km upstream of SOW1 (near the R1 rift), which likely affected local melt rates, and we observe considerable ∼ kilometer-scale spatial variability in melt rates across GPS array. Furthermore, the bottom altimeter sampled a ∼ 5 cm diameter spot with unknown upstream/downstream orientation, approximately 30-40 cm from the edge of the 20 cm borehole. Aside from local melt variability expected due to turbulent flow near the altimeter pole or borehole edge, the altimeter provided a relatively small spatial sample compared to the GPS results, which are sensitive to changes in a column of ice with much larger footprint (100s to 1000s of m 2 ).

Basal melt rate spatial variability
The GPS records at SOW1, SOW2, and BOAR show similar Dz surf /Dt rates and residuals, which is consistent with their apparent orientation on the same "block" between transverse rifts/depressions (Fig. 2) and supports the hypothesis that they were exposed to similar sub-shelf circulation. The DEM Dz surf /Dt maps show enhanced surface elevation change rates, and thus higher basal melt rates, on the upstream side of transverse depressions (Fig. 10), which is consistent with increased Dz surf /Dt observed at the SOW3 and SOW4 sites. This relationship is potentially related to enhanced buoyant flow and/or turbulence over increased basal slopes (e.g., Jenkins, 2011) beneath transverse surface depressions. We also suggest that these transverse basal channels may offer conduits for meltwater flow between adjacent longitudinal channels, potentially leading to increased circulation velocity and higher melt rates within the transverse depressions.
6.6 Basal melt rate sensitivity to ocean temperature variability Christianson et al. (2016) suggest that the subtle (∼ 2-4 %) changes in 2012-2014 GPS velocity display a lagged correlation with observed variations in ocean temperature records from moorings in Pine Island Bay (see Fig. 1 for location), potentially implying causality. Our analysis supports the alternative hypothesis of Christianson et al. (2016) that these velocity variations are primarily related to upstream grounding evolution  and extension across a series of transverse depressions. Rates of antenna and surface elevation change (Dz ant /Dt and Dz surf /Dt) were essentially constant in time, with no significant variation in inferred basal melt rates during this 2-year time period. If sub-shelf melt rates beneath the GPS array covaried with observed ocean heat content beyond the shelf front in Pine Island Bay (Christianson et al., 2016;Webber et al., 2017), a significant change in both Dz ant /Dt and Dz surf /Dt would be expected during this period. The lack of any significant deviation suggests that melt rates at these sites were not noticeably affected by observed ocean temperature variability. This finding suggests that (1) these sites are not representative of melt rates for the inner shelf (e.g., those near the grounding line), (2) the oceanographic measurements near the PIG ice front are not representative of water circulating beneath these ice-shelf sites, and/or (3) local melt rates are less sensitive to the observed oceanographic changes than previously assumed.

Future work
High-resolution velocity maps derived from submeter imagery could potentially constrain local velocity divergence and length scales for observed strain between GPS receivers.
In addition, seismic data from stations deployed near the GPS array and regional sites could help constrain the timing and location of rift propagation and grounding/ungrounding events.
High-resolution (< 1 km grid) SMB output and improved dynamic firn model output would likely offer an improved understanding of local variability across the GPS array. It may also be possible to further constrain firn-compaction rates, and thus long-term SMB, using relative layer thicknesses observed in CReSIS snow radar measurements (e.g., Medley et al., 2015) or in situ pRES observations (e.g., Jenkins et al., 2006). However, airborne radar data over the PIG shelf suffer from clutter due to kilometer-scale surface/basal topography and crevasses, while the available intermittent pRES records  likely lack the sensitivity to detect small changes in firn layer thickness during the ∼ 3-week observation period.
These limitations highlight the current value of long-term GPS records to constrain surface evolution where observations are sparse and model results are poorly constrained. Expanding the scope of our study to include the full archive of geodetic GPS data for the Antarctic and Greenland ice sheets would offer a valuable new dataset for calibration/validation of models and remote sensing data.
We offer the following recommendations to improve GPS-IR results for future GPS deployments: (1) set the GPS elevation mask to 0 • (default values are typically ∼ 5-10 • ), (2) track all possible signals (L2C, L5, Galileo, and GLONASS), (3) ensure that antenna-surface distance will remain > 0.5 m between servicing visits, and (4) document and photograph GPS sites, noting antenna-surface distance and any pole tilt during install and servicing.

Summary and conclusions
We analyzed GPS records for the PIG shelf for the 2008-2010 and 2012-2014 periods. We produced daily time series of antenna-surface distance (h ant−surf ) and antenna elevation (z ant , relative to EGM2008 geoid), which were combined to accurately measure surface elevation (z surf ) at each site. The surface elevation data can be directly compared with remotesensing measurements, providing independent validation for high-resolution WorldView stereo DEM records (RMSE of ∼ 0.72 m, NMAD of ∼ 0.57 m).
The GPS-derived surface elevation data provide new information about local SMB that can be compared with coarse-resolution model output and AWS data. Surface elevation relative to a firn layer tracer for the initial surface (z surf − z surf0 ) increased at rates of ∼ 0.8-1.1 m yr −1 for all GPS sites, which is consistent with modeled SMB of ∼ 0.7-0.9 m w.e. yr −1 . An abrupt ∼ 0.2-0.3 m surface elevation decrease, likely due to surface melt and/or enhanced firn compaction, is observed across all GPS sites during a period of warmer atmospheric temperatures from December 2012 to January 2013.
Trends in observed antenna (Dz ant /Dt) and surface elevation change (Dz surf /Dt) were highly linear for all GPS sites on the PIG shelf. Observed extensional strain rates were ∼ 0.001-0.002 yr −1 for the 2012-2014 GPS array, which corresponds to only ∼ 0.1 m yr −1 surface elevation change due to local flux divergence.
An alternative form of the mass conservation equation was used to estimate BMB from observed Lagrangian surface elevation change, strain rates, and SMB. Basal melt rates were ∼ 10 to ∼ 40 m yr −1 near the center of the fast-flowing PIG shelf, and ∼ 2 m yr −1 for the southern shelf. These melt rates are similar to those derived from complementary in situ instrument records  and high-resolution stereo DEMs (Shean, 2016).
Both GPS and DEM records show higher basal melt rates within and near transverse surface depressions and rifts associated with longitudinal extension. Basal melt rates for the 2012-2014 period show limited temporal variability, despite substantial changes in ocean heat content at the ice front and likely in the ice-shelf cavity. Residual elevation change variability is likely related to upstream grounding/ungrounding events and the local evolution of transverse depressions/rifts. Our results demonstrate the value of long-term GPS records and interferometric reflectometry for constraining ice-shelf mass balance estimates.
Data availability. All GPS data are available from the UN-AVCO archive (https://www.unavco.org/data/data.html). ERA-Interim products are available from https://www.ecmwf.int/en/ forecasts/datasets/reanalysis-datasets/era-interim. AWS data are available from AMRC/AMS (https://amrc.ssec.wisc.edu/). The DigitalGlobe images used to generate DEMs were provided by the Polar Geospatial Center at the University of Minnesota, under the NGA NextView License. Derived DEM products are available upon request.
Competing interests. The authors declare that they have no conflict of interest.
Michiel van den Broeke provided RACMO SMB products. The AWS data are available from the University of Wisconsin-Madison Automatic Weather Station Program (NSF ANT-1245663). We acknowledge the substantial effort required to obtain the GPS data used in this study, involving multiple PIG field campaigns led by Robert Bindschadler and Martin Truffer, with significant contributions from many others. We acknowledge GPS data collection and archiving provided by the UNAVCO Facility with support from NSF and NASA under NSF Cooperative Agreement no. EAR-0735156. Resources supporting the DEM generation were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. We thank Laurence Padman and an anonymous reviewer for their comments and suggestions, which significantly improved this paper.
Edited by: G. Hilmar Gudmundsson Reviewed by: Laurence Padman and one anonymous referee