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Realistically rough stochastic realizations of subglacial bed topography are crucial for improving our understanding of basal processes and quantifying uncertainty in sea level rise projections with respect to topographic uncertainty. This can be achieved with sequential Gaussian simulation (SGS), which is used to generate multiple nonunique realizations of geological phenomena that sample the uncertainty space. However, SGS is very CPU intensive, with a computational complexity of O(NkNk3), where NN is the number of grid cells to simulate, and kk is the number of neighboring points used for conditioning. This complexity makes SGS prohibitively time-consuming to implement at ice sheet scales or fine resolutions. To reduce the time cost, we implement and test a multiprocess version of SGS using Python’s multiprocessing module. By parallelizing the calculation of the weight parameters used in SGS, we achieve a speedup of 9.5 running on 16 processors for an NN of 128,097. This speedup—as well as the speedup from using multiple processors—increases with NN. This speed improvement makes SGS viable for large-scale topography mapping and ensemble ice sheet modeling. Additionally, we have made our code repository and user tutorials publicly available (GitHub and Zenodo) so that others can use our multiprocess implementation of SGS on different datasets. 

Abstract. The interpolation of geospatial phenomena is a common problem in Earth science applications that can be addressed with geostatistics, where spatial correlations are used to constrain interpolations. In certain applications, it can be particularly useful to a perform geostatistical simulation, which is used to generate multiple non-unique realizations that reproduce the variability in measurements and are constrained by observations. Despite the broad utility of this approach, there are few open-access geostatistical simulation software applications. To address this accessibility issue, we present GStatSim, a Python package for performing geostatistical interpolation and simulation. GStatSim is distinct from previous geostatistical tools in that it emphasizes accessibility for non-experts, geostatistical simulation, and applicability to remote sensing data sets. It includes tools for performing non-stationary simulations and interpolations with secondary constraints. This package is accompanied by a Jupyter Book with user tutorials and background information on different interpolation methods. These resources are intended to significantly lower the technological barrier to using geostatistics and encourage the use of geostatistics in a wider range of applications. We demonstrate the different functionalities of this tool for the interpolation of subglacial topography measurements in Greenland. 

Abstract The earliest airborne geophysical campaigns over Antarctica and Greenland in the 1960s and 1970s collected ice penetrating radar data on 35 mm optical film. Early subglacial topographic and englacial stratigraphic analyses of these data were foundational to the field of radioglaciology. Recent efforts to digitize and release these data have resulted in geometric and ice-thickness analysis that constrain subsurface change over multiple decades but stop short of radiometric interpretation. The primary challenge for radiometric analysis is the poorly-characterized compression applied to Z-scope records and the sparse sampling of A-scope records. Here, we demonstrate the information richness and radiometric interpretability of Z-scope records. Z-scope pixels have uncalibrated fast-time, slow-time, and intensity scales. We develop approaches for mapping each of these scales to physical units (microseconds, seconds, and signal to noise ratio). We then demonstrate the application of this calibration and analysis approach to a flight in the interior of East Antarctica with subglacial lakes and to a reflight of an East Antarctic ice shelf that was observed by both archival and modern radar. These results demonstrate the potential use of Z-scope signals to extend the baseline of radiometric observations of the subsurface by decades. 

Abstract Subglacial topography is an important feature in numerous ice-sheet analyses and can drive the routing of water at the bed. Bed topography is primarily measured with ice-penetrating radar. Significant gaps, however, remain in data coverage that require interpolation. Topographic interpolations are typically made with kriging, as well as with mass conservation, where ice flow dynamics are used to constrain bed geometry. However, these techniques generate bed topography that is unrealistically smooth at small scales, which biases subglacial water flowpath models and makes it difficult to rigorously quantify uncertainty in subglacial drainage patterns. To address this challenge, we adapt a geostatistical simulation method with probabilistic modeling to stochastically simulate bed topography such that the interpolated topography retains the spatial statistics of the ice-penetrating radar data. We use this method to simulate subglacial topography using mass conservation topography as a secondary constraint. We apply a water routing model to each of these realizations. Our results show that many of the flowpaths significantly change with each topographic realization, demonstrating that geostatistical simulation can be useful for assessing confidence in subglacial flowpaths. 

Abstract Airborne radio-echo sounding (RES) surveys are widely used to measure ice-sheet bed topography. Measuring bed topography as accurately and widely as possible is of critical importance to modelling ice dynamics and hence to constraining better future ice response to climate change. Measurement accuracy of RES surveys is influenced both by the geometry of bed topography and the survey design. Here we develop a novel approach for simulating RES surveys over glaciated terrain, to quantify the sensitivity of derived bed elevation to topographic geometry. Furthermore, we investigate how measurement errors influence the quantification of glacial valley geometry. We find a negative bias across RES measurements, where off-nadir return measurement error is typically −1.8 ± 11.6 m. Topographic highlands are under-measured an order of magnitude more than lowlands. Consequently, valley depth and cross-sectional area are largely under-estimated. While overall estimates of ice thickness are likely too high, we find large glacier valley cross-sectional area to be under-estimated by −2.8 ± 18.1%. Therefore, estimates of ice flux through large outlet glaciers are likely too low when this effect is not taken into account. Additionally, bed mismeasurements potentially impact our appreciation of outlet-glacier stability. 

Airborne radar sounding can measure conditions within and beneath polar ice sheets. In Antarctica, most digital radar-sounding data have been collected in the last 2 decades, limiting our ability to understand processes that govern longer-term ice-sheet behavior. Here, we demonstrate how analog radar data collected over 40 y ago in Antarctica can be combined with modern records to quantify multidecadal changes. Specifically, we digitize over 400,000 line kilometers of exploratory Antarctic radar data originally recorded on 35-mm optical film between 1971 and 1979. We leverage the increased geometric and radiometric resolution of our digitization process to show how these data can be used to identify and investigate hydrologic, geologic, and topographic features beneath and within the ice sheet. To highlight their scientific potential, we compare the digitized data with contemporary radar measurements to reveal that the remnant eastern ice shelf of Thwaites Glacier in West Antarctica had thinned between 10 and 33% between 1978 and 2009. We also release the collection of scanned radargrams in their entirety in a persistent public archive along with updated geolocation data for a subset of the data that reduces the mean positioning error from 5 to 2.5 km. Together, these data represent a unique and renewed extensive, multidecadal historical baseline, critical for observing and modeling ice-sheet change on societally relevant timescales.