Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Over the last 2 decades, the glacier has lost in excess of a trillion tons of ice, or the equivalent of 3

Since the 1990s, satellite measurements have comprehensively documented the sustained acceleration in ice discharge across the grounding line of Pine Island Glacier (PIG, Fig.

The relative impact of changes in ice geometry, basal shear stress, and/or ice rheology on the dynamics of PIG has previously been emphasized in numerical studies by, for example,

In order to comprehensively diagnose the importance of all processes that have contributed to the acceleration of PIG over the period 1996 to 2016, this study brings together the latest observations and modelling techniques. We consider how calving, ice shelf thinning, the induced dynamic thinning upstream of the grounding line, and potential changes in ice-internal and basal properties have caused a different dynamic response across the ice shelf, the glacier's main trunk, the margins, and the tributaries. Initial observations indicated that the speed-up of PIG was primarily confined to its fast-flowing central trunk

In this study we used a regional configuration of the shallow ice stream (SSA) flow model Úa

Although the aforementioned method provides insights into the individual contribution of geometrical perturbations and changes in ice viscosity and basal slipperiness to overall changes in ice flow, results will likely depend on a number of structural assumptions within the ice flow model. Previous studies have shown that different forms of the sliding law, for example, can produce a distinctly different simulated response of PIG to changes in ice thickness

The remainder of this paper is organized as follows. In Sect.

The first aim of this study is to simulate the dynamic response of PIG to a series of well-defined geometric perturbations over the period 1996 to 2016 and compare model output to observed changes in surface speed over the same time period. As detailed in Sect. 1, geometric perturbations are considered to be observed changes in the calving front position and observed changes in ice thickness of the ice shelf and grounded ice. We are primarily interested in the relative contribution of each perturbation to the observed speed-up of PIG between 1996 and 2016. Each contribution can be characterized by a relative change in velocity,

Pine Island Glacier (PIG) and its location in West Antarctica.

Our study area and model domain encompasses the 135 000 km

The surface velocity measurements used in this study were taken from the MEaSUREs database

To obtain an accurate estimate of the ice thickness distribution of PIG in 1996, we compiled a time series of surface height changes from a comprehensive set of overlapping satellite altimeter data between 1996 and 2016. The integrated altimeter trend over the 20-year time interval, shown in Fig.

The grounding line location for

Alongside the above-listed observed changes in flow dynamics and ice thickness, the calving front of PIG retreated by up to 30

To obtain an optimal model configuration for the state of PIG in 1996, we explicitly solved the stress balance by assimilating the estimated ice thickness (

The optimal model configuration in 1996 was subsequently used as the reference state for a series of numerical perturbation experiments, aimed at simulating the impact of observed changes in geometry on the flow of PIG. For each perturbation, the modified force balance (Eq.

Overview of changes along the Pine Island Glacier centreline from

Later on we show that geometric perturbations alone are not able to fully reproduce the observed patterns of speed-up across the PIG catchment. It is conceivable that, along with the evolving geometry, variations in ice and basal properties have contributed to the changes in flow between 1996 and 2016. Indeed, feedback mechanisms are likely to cause an important interdependence between geometry-induced changes in ice flow, shear softening, and/or changes in basal shear stress. Reliable observations of changes in rheology and basal properties are not available, but numerical optimization simulations can provide valuable insights into their evolution. We used the inverse method as described in Sect.

We present results for the first set of perturbation experiments, which simulate the impact of observed changes in geometry on the flow of PIG. As detailed in Sect.

Results for the relative change in surface speed,

Modelled changes in surface speed compared to 1996 for prescribed perturbations of the Pine Island Glacier geometry.

Calving as simulated in

Thinning of the ice shelf as simulated in experiment

In experiment

In the final perturbation experiment,

Although it is not unexpected to find differences between diagnostic model output and observations, the consistently suppressed response of the model to realistic perturbations in ice geometry is indicative of a structural shortcoming within our experimental design. Indeed, results show that, for a non-linear viscous bed rheology described by a Weertman sliding law with constant sliding coefficient

In transient model simulations of large ice masses such as Antarctica's glaciers and ice streams, it is common to assume that the advection of

Changes in

Alternatively, temporal changes in

We note that, in the

The relationship between changes in geometry and the dynamic response of a glacier crucially depends on the mechanical properties of the underlying bed and subglacial hydrology. So far, we have assumed that basal sliding can be represented by a non-linear viscous power law with spatially uniform stress exponent

Dependency of simulated-versus-observed changes in surface speed on the sliding-law exponent:

In order to quantify how different values of the sliding exponent affect the sensitivity of PIG to changes in geometry across the catchment, we repeated perturbation experiments

The positive correlation between the flow response and

Two interesting properties of the regression model in Eq. (

It is important to reiterate that the regression method used crucially relies on non-trivial measurements of changes in surface velocity (

In order to demonstrate the improved model response to thinning and calving for a spatially variable sliding exponent

Based on the most comprehensive observations of ice shelf and grounded ice thickness changes to date, and a suite of diagnostic model experiments with the contemporary flow model Úa, we have analysed the relative importance of ice shelf thinning, calving, and grounding line retreat for the speed-up of Pine Island Glacier over the period 1996 to 2016. The detailed comparison between simulated and observed changes in flow speed has provided insights into the ability of a modern-day ice flow model to reproduce dynamic changes in response to prescribed geometric perturbations. Significant discrepancies between observed and modelled changes in flow were found and addressed either by allowing changes in ice viscosity and basal slipperiness or by varying the mechanical properties of the ice–bed interface. For non-linear viscous sliding at the bed, geometric perturbations could only account for 64 % of the observed flux increases close to the grounding line, whereas the remaining 36 % could be attributed to large and widespread changes in ice viscosity (including damage) and/or changes in basal slipperiness. Under the alternative assumption that ice viscosity and basal slipperiness did not change considerably over the last 2 decades, we found that the recent increase in flow speed of Pine Island Glacier is only compatible with observed patterns of thinning if a heterogeneous, predominantly plastic bed underlies large parts of the central glacier and its upstream tributaries, consistent with the earlier literature.

We derived a new ice shelf height time series from measurements acquired by four overlapping ESA satellite radar altimetry (RA) missions: ERS-1 (1991–1996), ERS-2 (1995–2003), Envisat (2002–2012), and CryoSat-2 (2010–present). For this study, we constructed a record of ice shelf height spanning 20 years (1996–2016), with a temporal sampling of 3 months. We integrated all measurements along the satellite ground tracks and gridded the solution on a 3

Our adopted processing steps for RA data are a modification/improvement from

We then gridded the height data in space and time on a

The thickness changes for the ice shelf were combined with existing data for thickness changes over the same time period on the grounded ice

Ice thickness changes (

The open source ice flow model Úa

The optimization capabilities of Úa follow commonly applied techniques in ice flow modelling to optimize uncertain model parameters,

The gradient and amplitude contributions in the regularization term (Eq.

The pre-multipliers

All results presented here are based on optimization experiments with spatially constant a priori values for the rate factor and slipperiness:

Figures

The transfer amplitude

Following

The analytical expression in Eq. (

The inverse problem of inferring information about the rate factor

In the case of the

Optimal distribution of

Experiments

Perturbation experiments

Sensitivity of the relative flux changes in the

The open-source ice flow model Úa is available at

JDR and RR designed and initiated the project and prepared the manuscript. FSP processed the ice shelf thickness data. JDR performed the model simulations, carried out the analysis, and produced the figures. FSP and GHG reviewed and edited the paper.

Jan De Rydt serves as topical editor for The Cryosphere.

We would like to express our sincere appreciation for the thorough reviews by Stephen Cornford; two anonymous reviewers; and the editor, Andreas Vieli. Their insightful comments have greatly contributed to a better presentation of our work. Jan De Rydt, G. Hilmar Gudmundsson, and Ronja Reese are supported by the TiPACCs project, which receives funding from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 820575. Ronja Reese is further supported by the Deutsche Forschungsgemeinschaft (DFG) by grant WI4556/3-1, and G. Hilmar Gudmundsson by the NSFPLR-NERC grant

This research has been supported by the European Union's Horizon 2020 research and innovation programme (grant no. 820575), the Deutsche Forschungsgemeinschaft (DFG) (grant no. WI4556/3-1), and the NSFPLR-NERC (grant no. NE/S006745/1).

This paper was edited by Andreas Vieli and reviewed by Stephen Cornford and two anonymous referees.