We derive recent surface mass balance (SMB) estimates from airborne radar observations along the iSTAR traverse (2013, 2014) at Pine Island Glacier (PIG), West Antarctica. Ground-based neutron probe measurements provide information of snow and firn density with depth at 22 locations and were used to date internal annual reflection layers. The 2005 layer was traced for a total distance of 2367

The stability of the West Antarctic Ice Sheet (WAIS) is a major concern for scientists seeking to predict global sea level rise. Transport of heat from upwelling circumpolar deep water has proved to be a critical driver of Antarctic ice shelf thinning and grounding line retreat, thus initiating the acceleration of marine-terminating outlet glaciers (e.g.

As part of the iSTAR Ice Sheet Stability Programme, a traverse across the Pine Island Glacier (PIG) was carried out in 2013/2014 (T1) and repeated the year after (T2). In total 22 sites were occupied during both traverses. Boreholes of at least 13

The Alfred Wegener Institute (AWI) contributed to the iSTAR traverse T2 with radar soundings from the Airborne SAR/Interferometric Radar Altimeter System (ASIRAS) aboard the Polar 5 research plane. Previous ASIRAS missions have demonstrated its capability to track annual snow accumulation layers of the upper firn column at regional scales over Greenland

In this study we first address local departures between SMB estimates from ASIRAS and NP measurements to evaluate the uncertainty of our regional-scale ASIRAS SMB estimates. We then compare our results with those reported by ME14 and discuss differences between both data sets. Finally, we apply our new regional-scale SMB estimates to different PIG mass balance inventories to evaluate their impact in light of the current stability of the study area. We include a list of abbreviations and notations in Appendix

ASIRAS–iSTAR survey projected on polar stereographic coordinates: black lines denote the ASIRAS flight track, numbered blue circles the iSTAR sites with shallow (

The iSTAR traverse followed the PIG main trunk as well as its tributaries as shown in Fig.

Additional SMB measurements were made with a ground-penetrating radar (GPR) during traverse T1 and published in

Approximate sample bin resolution and maximum depth of SAR level_1b processed ASIRAS data with indicated standard deviation of the vertical range bin based on the two-way-travel time (TWT)-to-depth conversion of this study, CReSIS accumulation radar according to M14, and pulseEKKO PRO GPR discussed in

Compiled density–depth profiles from traverse T2 at all 22 iSTAR sites (grey lines). The black line denotes the smoothed mean profile, the red dashed line an exponential fit (units according to axis annotations), and the blue dashed lines the standard deviation intervals of the fit.

NP measurements of snow and firn density were performed at all stations during both traverses as described in

The deep firn cores (

We use a single regional density–depth profile we derive from the NP profiles of traverse T2 for the two-way-travel time (TWT)-to-depth conversion of the ASIRAS soundings. First, we merge the

ASIRAS radargram at iSTAR site 21 with surface snow reflection centred at the origin of the TWT scale. The traced internal reflection layer is highlighted in magenta; annual markers from the NP profile at the point of closest approach are highlighted in cyan. The distance and trace numbers refer to the origin of the ASIRAS track segment 20156124 (see Table

ASIRAS is a Ku-band radar altimeter which operates at a carrier frequency of 13.5

Before the layer tracing, we apply an automatic-gain-control filter to all waveforms and limit their dynamic range to twice the standard deviation centred around the mean amplitude of each waveform. This improved the signal contrast of the radargram. Initially we tested a phase-following algorithm of the Paradigm EPOS geophysical processing software to trace the selected reflection layer semi-automatically. However, this method became unstable for lower contrast and cases with close layer spacing. Furthermore, remaining SAR-processing artefacts were interfering with the phase-following algorithm. Because of the complex nature of the observed stratigraphy, as has been also reported by

Dated reflection layer year at nearby iSTAR sites. “Track number” refers to the ASIRAS flight track naming convention (year of measurement season (four digits), measurement type (one digit), profile segment number (three digits)); iSTAR site elevation in metres above ellipsoid (m a.e.) with respect to the ITRF08(2015) reference framework;

Spatial, temporal, digitization, and combined SMB measurement errors, which relate to the variability in density, dating uncertainty, and ASIRAS sampling accuracy, respectively: relative errors

We attempt to trace the 2005 reflection layer, which is covered by all NP density–depth profiles. So far, we assumed that internal reflection layers form on an annual basis during summer/autumn, but the potential formation of intra-annual reflection layers may challenge this assumption. For instance,

Following

Traced annual mean SMB between November 2004 and December 2014 from ASIRAS soundings with overlaid contour lines in metres from a digital elevation model

Experimental semivariogram of log-transformed smoothed SMB observations (dots), Gaussian fit model (black solid line), and sill and practical range parameter (dashed lines).

PP plots between SMB observations and estimates based on OK and OLK interpolation methods for varying thresholds of their maximum distance

We focus on the regional-scale variability of the SMB distribution at PIG. Figure

Aside from the choice of the translational constant

In addition to each OLK estimate, we calculate the associated interpolation error. While ME14 choose the kriging standard deviation as a measure of interpolation error, our error estimation is based on the interpolation standard deviation

Following ME14, we estimate the total error of each SMB estimate by the RSS of the measurement error and back-transformed

We have to keep in mind that the basin-wide SMB OLK estimation is limited in terms of the practical range according to Fig.

Based on the adopted OLK interpolation scheme, we produced the mean annual SMB map for the PIG basin from the ASIRAS observations in Fig.

Figure

Figure

Spatially integrated SMB (

Spatial integration of annual mean SMB from our generated hybrid maps yields the total mass input for the PIG basin, which we denote by

The Pine Island

Table

We discuss first the pronounced differences between annual layer dating from ASIRAS reflection and neutron probe density profiles at some sites and then secondly the systematic differences in SMB distribution between the results of this study and those of ME14, RACMO, and MAR.

Key to the evaluation of our selected internal reflection layer is its isochronic nature, which we assume based on matched depth–age relations from the iSTAR ground-truthing measurements. One may argue that these measurements can be subject to local noise in the density profile, which would challenge any comparison with nearby radar observations. For instance,

Nearby ASIRAS observations at site 18 and 19 in particular suggest higher SMB values compared to the dated NP profiles. Site 19 is directly located at the centre of a pronounced accumulation trough of

Additional local departures between our results and those from ME14 were identified for the northern slopes and southward interior of PIG. Because of difficulties in the layer tracing at the northern slopes, the authors of M14 had to augment their SMB estimates with results from a different layer, which they dated back to 2002 and corrected for a temporal bias to the 1985 layer based on overlapping segments. Thus, one possible explanation for the observed differences is that the true local temporal bias correction may be different from the regional-scale bias correction, which they estimate from regression models. Other possible explanations are differences in the observational coverage and local accuracy from the different interpolation methods. With regard to the southward interior, the spatial coverage is superior in the ME14 results. Despite the maximum range limit between 100 and 190

The observational SMB estimates by M14 indicate an elevation-dependent drift of simulated SMB from RACMO. The authors find that RACMO underestimates the SMB at the high-elevation interior, which would also impact our ASIRAS–RACMO-based estimates of total mass input. Indeed, this finding is also reflected in our data (see Supplement S1) and suggests that the ASIRAS–RACMO-based total mass input estimates are biased by the underestimated SMB contribution from RACMO. According to

Updated mass balance estimates

Despite the local differences in the SMB distribution, the difference between the

With regard to existing mass balance estimates for PIG, we have to take into account that basin outlines can differ significantly between studies as illustrated in Fig.

The small difference between the

Mean (

While the agreement in

Initial tests on our OLK setting revealed that the choice of the negative kriging weight correction method has a noticeable impact on the uncertainty estimates, a finding which according to our knowledge has not been reported before. However, our applied method by

Additional tests, where we used the kriging standard deviation based on non-transformed OK estimates, did not improve our interpolation uncertainty. Therefore the different choice of the interpolation uncertainty measure is not the source of the larger uncertainty range of this study. We hypothesize that despite the homoscedastic (i.e. data-value-independent) nature of the krige standard deviation, the reduction of data variance after subtracting the regression surface according to ME14 is most likely the cause of their significantly lower uncertainty estimates.

In addition to the larger uncertainty range of this study, we note that the choice between cell-by-cell summation and RSS of grid errors has a quite substantial impact on the

In addition to the uncertainty assessment in Sect.

Inspection of the artificial cluster highlighted in Fig.

Defining

If we choose the OK procedure instead,

Our analysis provides updated mean annual SMB estimates for the PIG basin and 2005–2014 averaging period based on a comprehensive airborne radar and ground-truthing survey and complementary model simulations. Based on these estimates, we calculated a total mass input of

Despite the minor changes in total mass input between both studies, the more than 2-fold uncertainty range of our results remains striking. Neither the applied model for the wave propagation speed of radar soundings nor the uncertainty related to the regional density profile can explain the larger uncertainty of this study. The same also applies for the reduced temporal averaging time. A comprehensive evaluation of our uncertainty estimation revealed that assumptions on the geostatistical interpolation error as well as grid-error dependences can have a substantial impact on the uncertainty estimation. In terms of the error partitioning, our interpolation error is the dominating source of combined grid errors. Moreover, varying basin definitions have an impact on our total mass input estimate by up to 19 %. This highlights the importance of a thorough documentation of uncertainty estimates and basin definitions to improve future intercomparisons between different SMB and mass balance inventories.

Underlying data are openly available at Pangaea

The supplement related to this article is available online at:

SK conceived of the presented idea, designed the computational framework, adapted and tested the geostatistical krige methods, accomplished the reflection layer tracing in large parts, reprocessed the neutron probe density profiles for the data calibration, and wrote the manuscript with input from all authors; VH performed the SAR level_1b ASIRAS data processing, provided the digital elevation model, and established access to the RACMO2.3p2 data; EM delivered the neutron probe density profiles; and OE contributed to layer analysis and interpretation. All authors discussed the results and contributed to revising the manuscript.

Olaf Eisen is co-editor in chief of The Cryosphere.

The authors gratefully acknowledge the excellent logistical support provided by British Antarctic Survey's (BAS) Rothera Research Station and members of the iSTAR traverse and Alfred Wegener Institute and Polar 5 flight crew during the field campaign, which has been funded by the UK Natural Environment Research Council (NERC, grant no. NE/J005681/1). The authors express their gratitude towards Andrew Shepherd, PI of the iSTAR-D project, for his general support and data contribution to this study. The authors thank Robert Mulvaney (BAS, UK) and Hannes Konrad (CPOM, University of Leeds, UK; and DWD, Germany) for provision of data sets and discussions in an early stage. The authors gratefully acknowledge the provision of RACMO2.3p2 model output by Stefan Roderick Martijn Ligtenberg and Melchior van Wessem (IMAU, Utrecht University, NL). The authors would like to thank Emerson E&P Software, Emerson Automation Solutions, for providing licenses in the scope of the Emerson Academic Program. The authors sincerely appreciate the valuable comments and suggestions by the referees and editor. The authors acknowledge support by the Open Access Publication Funds of Alfred-Wegener-Institut Helmholtz-Zentrum für Polar- und Meeresforschung.

This research has been supported by the German Ministry of Economics and Technology (grant no. 50EE1331 to Veit Helm).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Michiel van den Broeke and reviewed by Brooke Medley and two anonymous referees.