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Mapping Glacier Basal Sliding Applying Machine Learning
During the RESOLVE project (“High-resolution imaging in subsurface geophysics: development of a multi-instrument platform for interdisciplinary research”), continuous surface displacement and seismic array observations were obtained on Glacier d’Argentière in the French Alps for 35 days in May 2018. The data set is used to perform a detailed study of targeted processes within the highly dynamic cryospheric environment. In particular, the physical processes controlling glacial basal motion are poorly understood and remain challenging to observe directly. Especially in the Alpine region for temperate based glaciers where the ice rapidly responds to changing climatic conditions and thus, processes are strongly intermittent in time and heterogeneous in space. Spatially dense seismic and Global Positioning System (GPS) measurements are analyzed applying machine learning to gain insight into the processes controlling glacial motions of Glacier d’Argentière. Using multiple bandpass-filtered copies of the continuous seismic waveforms, we compute energy-based features, develop a matched field beamforming catalog and include meteorological observations. Features describing the data are analyzed with a gradient boosting decision tree model to directly estimate the GPS displacements from the seismic noise. We posit that features of the seismic noise provide direct access to the dominant parameters that drive displacement on the highly variable and unsteady surface of the glacier. The machine learning model infers daily fluctuations and longer term trends. The results show on-ice displacement rates are strongly modulated by activity at the base of the glacier. The techniques presented provide a new approach to study glacial basal sliding and discover its full complexity.
Exploring ice sheet model sensitivity to ocean thermal forcing and basal sliding using the Community Ice Sheet Model (CISM)
Abstract. Multi-meter sea level rise (SLR) is thought to be possible within the next few centuries, with most of the uncertainty originating from the Antarctic land ice contribution. One source of uncertainty relates to the ice sheet model initialization. Since ice sheets have a long response time (compared to other Earth system components such as the atmosphere), ice sheet model initialization methods can have significant impacts on how the ice sheet responds to future forcings. To assess this, we generated 25 different ice sheet spin-ups, using the Community Ice Sheet Model (CISM) at a 4 km resolution. During each spin-up, we varied two key parameters known to impact the sensitivity of the ice sheet to future forcing: one related to the sensitivity of the ice shelf melt rate to ocean thermal forcing (TF) and the other related to the basal friction. The spin-ups all nudge toward observed thickness and enforce a no-advance calving criterion, such that all final spin-up states resemble observations but differ in their melt and friction parameter settings. Each spin-up was then forced with future ocean thermal forcings from 13 different CMIP6 models under the Shared Socioeconomic Pathway (SSP)5-8.5 emissions scenario and modern climatological surface mass balance data. Our results show that the effects of the ice sheet and ocean parameter settings used during the spin-up are capable of impacting multi-century future SLR predictions by as much as 2 m. By the end of this century, the effects of these choices are more modest, but still significant, with differences of up to 0.2 m of SLR. We have identified a combined ocean and ice parameter space that leads to widespread mass loss within 500 years (low friction and high melt rate sensitivity). To explore temperature thresholds, we also ran a synthetically forced CISM ensemble that is focused on the Amundsen region only. Given certain ocean and ice parameter choices, Amundsen mass loss can be triggered with thermal forcing anomalies between 1.5 and 2 ∘C relative to the spin-up. Our results emphasize the critical importance of considering ice sheet and ocean parameter choices during spin-up for SLR predictions and suggest the importance of including glacial isostatic adjustment in ice sheet simulations.
The Annual Glaciohydrology Cycle in the Ablation Zone of the Greenland Ice Sheet: Part 2. Observed and Modeled Ice Flow
Ice velocities observed in 2005/06 at three GPS stations along the Sermeq Avannarleq flowline, West Greenland, are used to characterize an observed annual velocity cycle. We attempt to reproduce this annual ice velocity cycle using a 1-D ice-flow model with longitudinal stresses coupled to a 1-D hydrology model that governs an empirical basal sliding rule. Seasonal basal sliding velocity is parameterized as a perturbation of prescribed winter sliding velocity that is proportional to the rate of change of glacier water storage. The coupled model reproduces the broad features of the annual basal sliding cycle observed along this flowline, namely a summer speed-up event followed by a fall slowdown event. We also evaluate the hypothesis that the observed annual velocity cycle is due to the annual calving cycle at the terminus. We demonstrate that the ice acceleration due to a catastrophic calving event takes an order of magnitude longer to reach CU/ETH ('Swiss') Camp (46km upstream of the terminus) than is observed. The seasonal acceleration observed at Swiss Camp is therefore unlikely to be the result of velocity perturbations propagated upstream via longitudinal coupling. Instead we interpret this velocity cycle to reflect the local history of glacier water balance.
A time-dependent ice sheet model - Preliminary results
A numerical model of ice sheet flow is developed, and preliminary results are described. This model includes vertical resolution of temperature, stress, and strain rate which represents a considerable improvement over previous vertically averaged ice sheet models. The model follows the flow of ice along a flow line within an ice sheet drainage basin. Longitudinal stresses and basal sliding are included. Basal sliding is dependent on the base shear stress and a specified distribution of basal water pressure. The numerical methods used to solve the coupled set of stress and velocity equations for the static and time-evolutionary cases are discussed. A steady state profile simulating an ice stream is calculated for a particular set of input parameters, and changes in the profile are examined for different choices of parameters. Preliminary studies of response behavior are completed using a simplified ice sheet geometry with a fixed terminus or grounding line. The results of these studies illustrate ice sheet thinning in response to a lowered sea level or to a reduction in the extent of ice rises (or pinning points) within ice shelves.
Evolution of the Antarctic Ice Sheet from 2000–2300 and beyond: model sensitivity and uncertainty analysis using MPAS-Albany Land Ice
We present a description of the Antarctic Ice Sheet model configuration submitted to the ISMIP6-Antarctica-2300 experiment using the MPAS-Albany Land Ice model, along with three new sets of simulations: (1) a set of extended simulations to 2500 for three forced experiments and to 2775 for the control experiment; (2) a sensitivity analysis of our model configuration to parameters controlling basal sliding and sub-shelf melt, and to model structural choices including the choice of the energy and stress balances; and (3) a 72-member ensemble run on graphics processing units (GPUs) and analysis of variance to determine the primary sources of uncertainty in our ice-sheet model projections. Our extended simulations predict rapid retreat beginning after 2300 for SSP1-2.6 forcing and after 2500 for present-day (control) forcing, primarily in the Amundsen Sea Embayment. We find that varying the sub-shelf melt parameter between the 5th to 95th percentile values for a mean-Antarctic calibration target results in an up to ∼ ± 40 % change in sea-level contribution relative to our baseline simulations that used the median value. Using a linear basal sliding law reduces sea-level contribution by 51 %–73 % relative to our baseline nonlinear sliding law with an exponent of 1/5. When using basal sliding law exponents of 1/3 and 1/10, the overall difference from our baseline simulations at 2300 is on the order of 10 %. The Amundsen Sea Embayment region displays a strongly non-linear dependence of mass loss on the sliding law exponent, with no discernible relationship between the sliding law exponent and the mass loss by 2300, while the sectors feeding the Ross and Filchner-Ronne ice shelves exhibit more mass loss with a more-plastic sliding law. Our model fidelity sensitivity experiments reveal a 9 %–31 % increase in sea-level contribution when using a depth-integrated stress balance approximation relative to our three-dimensional solver, while using a fixed-in-time temperature field increases sea-level contribution by 14 %–88 % relative to two thermomechanically coupled configurations. Our 72-member ensemble and analysis of variance show that the uncertainty in long-term projections is dominated by the choice of Earth system model forcing and the presence or absence of hydrofracture forcing, rather than uncertainty in sliding and sub-shelf melt parameters.
Increased Water Storage at Ice-stream Onsets: A Critical Mechanism?
The interdependence of rapid ice flow, surface topography and the spatial distribution of subglacial water are examined by linking existing theories. The motivation is to investigate whether the acceleration of an ice-stream tributary contains a positive feedback that encourages the retention of subglacial water that leads to faster flow. Periodically varying surface and bed topographies are related through a linear ice-flow perturbation theory for various values of mean surface slope, perturbation amplitude and basal sliding speeds. The topographic variations lead to a periodic variation in hydraulic potential that is used to infer the tendency for subglacial water to be retained in local hydraulic potential minima. If water retention leads to enhanced basal sliding, a positive feedback loop is closed that could explain the transition from slower tributary flow to faster-streaming flow and the sustained downstream acceleration along the tributary-ice-stream system. A sensitivity study illustrates that the same range of topographic wavelengths most effectively transmitted from the bed to the surface also strongly influences the behavior of subglacial water. A lubrication index is defined to qualitatively measure the heterogeneity of the subglacial hydrologic system. Application of this index to field data shows that the transition from tributary to ice stream closely agrees with the location where subglacial water may be first stored.
Ice-sheet model sensitivities to environmental forcing and their use in projecting future sea level (the SeaRISE project)
Ten ice-sheet models are used to study sensitivity of the Greenland and Antarctic ice sheets to prescribed changes of surface mass balance, sub-ice-shelf melting and basal sliding. Results exhibit a large range in projected contributions to sea-level change. In most cases, the ice volume above flotation lost is linearly dependent on the strength of the forcing. Combinations of forcings can be closely approximated by linearly summing the contributions from single forcing experiments, suggesting that nonlinear feedbacks are modest. Our models indicate that Greenland is more sensitive than Antarctica to likely atmospheric changes in temperature and precipitation, while Antarctica is more sensitive to increased ice-shelf basal melting. An experiment approximating the Intergovernmental Panel on Climate Change’s RCP8.5 scenario produces additional first-century contributions to sea level of 22.3 and 8.1 cm from Greenland and Antarctica, respectively, with a range among models of 62 and 14 cm, respectively. By 200 years, projections increase to 53.2 and 26.7 cm, respectively, with ranges of 79 and 43 cm. Linear interpolation of the sensitivity results closely approximates these projections, revealing the relative contributions of the individual forcings on the combined volume change and suggesting that total ice-sheet response to complicated forcings over 200 years can be linearized.
Supraglacial River Forcing of Subglacial Water Storage and Diurnal Ice Sheet Motion
Surface melting impacts ice sheet sliding by supplying water to the bed, but subglacial processes driving ice accelerations are complex. We examine linkages between surface runoff, transient subglacial water storage, and short-term ice motion from 168 consecutive hourly measurements of meltwater discharge (moulin input) and GPS-derived ice surface motion for Rio Behar, a ∼60 sq. km moulin-terminating supraglacial river catchment on the southwest Greenland Ice Sheet. Short-term accelerations in ice speed correlate strongly with lag-corrected measures of supraglacial river discharge (r = 0.9, τ = 0.7, p < 0.01). Though our 7 days record cannot address seasonal-scale forcing, diurnal ice accelerations align with normalized differenced supraglacial and proglacial discharge, a proxy for subglacial storage change, better than GPS-derived ice surface uplift. These observations counter theoretical steady state basal sliding laws and suggest that moulin and proglacially induced fluctuations in subglacial water storage, rather than absolute subglacial water storage, drive short-term ice accelerations.
Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem : given parameter inputs, solve the governing equations to determine output quantities of interest. In contrast, in this paper, we consider the broader question: given a (large-scale) model containing uncertain parameters, (possibly) noisy observational data, and a prediction quantity of interest, how do we construct efficient and scalable algorithms to (1) infer the model parameters from the data (the deterministic inverse problem ), (2) quantify the uncertainty in the inferred parameters (the Bayesian inference problem), and (3) propagate the resulting uncertain parameters through the model to issue predictions with quantified uncertainties (the forward uncertainty propagation problem )? We present efficient and scalable algorithms for this end-to-end, data-to-prediction process under the Gaussian approximation and in the context of modeling the flow of the Antarctic ice sheet and its effect on loss of grounded ice to the ocean. The ice is modeled as a viscous, incompressible, creeping, shear-thinning fluid. The observational data come from satellite measurements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal sliding parameter, represented by a heterogeneous coefficient in a Robin boundary condition at the base of the ice sheet. The prediction quantity of interest is the present-day ice mass flux from the Antarctic continent to the ocean. We show that the work required for executing this data-to-prediction process—measured in number of forward (and adjoint) ice sheet model solves—is independent of the state dimension, parameter dimension, data dimension, and the number of processor cores. The key to achieving this dimension independence is to exploit the fact that, despite their large size, the observational data typically provide only sparse information on model parameters. This property can be exploited to construct a low rank approximation of the linearized parameter-to-observable map via randomized SVD methods and adjoint-based actions of Hessians of the data misfit functional.
SHMIP The subglacial hydrology model intercomparison Project
Subglacial hydrology plays a key role in many glaciological processes, including ice dynamics via the modulation of basal sliding. Owing to the lack of an overarching theory, however, a variety of model approximations exist to represent the subglacial drainage system. The Subglacial Hydrology Model Intercomparison Project (SHMIP) provides a set of synthetic experiments to compare existing and future models. We present the results from 13 participating models with a focus on effective pressure and discharge. For many applications (e.g. steady states and annual variations, low input scenarios) a simple model, such as an inefficient-system-only model, a flowline or lumped model, or a porous-layer model provides results comparable to those of more complex models. However, when studying short term (e.g. diurnal) variations of the water pressure, the use of a two-dimensional model incorporating physical representations of both efficient and inefficient drainage systems yields results that are significantly different from those of simpler models and should be preferentially applied. The results also emphasise the role of water storage in the response of water pressure to transient recharge. Finally, we find that the localisation of moulins has a limited impact except in regions of sparse moulin density.
Wintertime Supraglacial Lake Drainage Cascade Triggers Large‐Scale Ice Flow Response in Greenland
Surface melt forces summertime ice-flow accelerations on glaciers and ice sheets. Here, we show that large meltwater-forced accelerations also occur during wintertime in Greenland. We document supraglacial lakes (SGLs) draining in cascades at unusually high elevation, causing an expansive flow acceleration over a ~5,200 km 2 region during winter. The three-component interferometric surface velocity field and decomposition modeling reveal the underlying flood propagation with unprecedented detail as it traveled over 160 km from the drainage site to the margin, providing novel constraints on subglacial water pathways, drainage morphology, and links with basal sliding. The triggering SGLs continuously grew over 40 years and suddenly released decades of stored meltwater, demonstrating surface melting can impact dynamics well beyond melt production. We show these events are likely common and thus their cumulative impact on dynamics should be further evaluated.
Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization
Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.
Implementation and Initial Evaluation of the Glimmer Community Ice Sheet Model in the Community Earth System Model
The Glimmer Community Ice Sheet Model (Glimmer-CISM) has been implemented in the Community Earth System Model (CESM). Glimmer-CISM is forced by a surface mass balance (SMB) computed in multiple elevation classes in the CESM land model and downscaled to the ice sheet grid. Ice sheet evolution is governed by the shallow-ice approximation with thermomechanical coupling and basal sliding. This paper describes and evaluates the initial model implementation for the Greenland Ice Sheet (GIS). The ice sheet model was spun up using the SMB from a coupled CESM simulation with preindustrial forcing. The model's sensitivity to three key ice sheet parameters was explored by running an ensemble of 100 GIS simulations to quasi equilibrium and ranking each simulation based on multiple diagnostics. With reasonable parameter choices, the steady-state GIS geometry is broadly consistent with observations. The simulated ice sheet is too thick and extensive, however, in some marginal regions where the SMB is anomalously positive. The top-ranking simulations were continued using surface forcing from CESM simulations of the twentieth century (1850–2005) and twenty-first century (2005–2100, with RCP8.5 forcing). In these simulations the GIS loses mass, with a resulting global-mean sea level rise of 16 mm during 1850–2005 and 60 mm during 2005–2100. This mass loss is caused mainly by increased ablation near the ice sheet margin, offset by reduced ice discharge to the ocean. Projected sea level rise is sensitive to the initial geometry, showing the importance of realistic geometry in the spun-up ice sheet.
Description and evaluation of the Community Ice Sheet Model (CISM) v2.1
Abstract. We describe and evaluate version 2.1 of the Community Ice Sheet Model (CISM). CISM is a parallel, 3-D thermomechanical model, written mainly in Fortran, that solves equations for the momentum balance and the thickness and temperature evolution of ice sheets. CISM's velocity solver incorporates a hierarchy of Stokes flow approximations, including shallow-shelf, depth-integrated higher order, and 3-D higher order. CISM also includes a suite of test cases, links to third-party solver libraries, and parameterizations of physical processes such as basal sliding, iceberg calving, and sub-ice-shelf melting. The model has been verified for standard test problems, including the Ice Sheet Model Intercomparison Project for Higher-Order Models (ISMIP-HOM) experiments, and has participated in the initMIP-Greenland initialization experiment. In multimillennial simulations with modern climate forcing on a 4 km grid, CISM reaches a steady state that is broadly consistent with observed flow patterns of the Greenland ice sheet. CISM has been integrated into version 2.0 of the Community Earth System Model, where it is being used for Greenland simulations under past, present, and future climates. The code is open-source with extensive documentation and remains under active development.
Basal hydraulic conditions of Ice Stream B
Fifteen boreholes have been drilled to the base of Ice Stream B in the vicinity of UpB Camp. The boreholes are spread over an area of about 500 x 1000 m. Several till cores were retrieved from the bottom of the 1000-m-deep holes. Laboratory tests using a simple shear box revealed a yield strength of basal till of 2 kPa. This agrees well with in-situ measurements using a shear vane. Since the average basal shear stress of Ice Stream B with a surface slope of 0.1 degree is about 20 kPa, the ice stream cannot be supported by till that weak. Additional support for this conclusion comes from the basal water pressure that has been measured in all boreholes as soon as the hot water drill reached bottom. In several boreholes, the water pressure has been continuously monitored; in two of them, over several years. The water pressure varies but stays within 1 bar of flotation where ice overburden pressure and water pressure are equal. The ratio of water and overburden pressure lies between 0.986 and 1.002. This is an extremely high value as compared to other fast-moving ice masses; e.g., Variegated Glacier in surge has a ratio of 0.8, and Columbia Glacier - a fast-moving tidewater glacier - has a ratio of 0.9. It implies that water flow under the glacier occurs in a thin film and not in conduits that would drain away water too rapidly. It also implies that basal sliding must be very effective. Water flow under the glacier was measured in a salt-injection experiment where a salt pulse was released at the bottom of a borehole while 60 m down-glacier, the electrical resistance was measured between two other boreholes. A flow velocity of 7 mm/s was obtained.
Links Between Acceleration, Melting, and Supraglacial Lake Drainage of the Western Greenland Ice Sheet
The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6-41% above spring velocity lasting approximately 40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for approximately 1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to 1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and 2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow.
Links Between Acceleration, Melting, and Supraglacial Lake Drainage of the Western Greenland Ice Sheet
The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6-41% above spring velocity lasting 40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for approx 1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to (1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and (2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow.