Mapping Antarctic crevasses and their evolution with deep learning applied to satellite radar imagery

The fracturing of glaciers and ice shelves in Antarctica influences their dynamics and stability. Hence, data on the evolving distribution of crevasses are required to better understand the evolution of the ice sheet, though such data have traditionally been difficult and time-consuming to generate. Here, we present an automated method of mapping crevasses on grounded and floating ice with the application of convolutional neural networks to Sentinel-1 synthetic aperture radar backscatter data. We apply this method across Antarctica to images acquired between 2015 and 2022, producing a 7.5-year record of composite fracture maps at monthly intervals and 50 m spatial resolution and showing the distribution of crevasses around the majority of the ice sheet margin. We develop a method of quantifying changes to the density of ice shelf fractures using a time series of crevasse maps and show increases in crevassing on Thwaites and Pine Island ice shelves over the observational period, with observed changes elsewhere in the Amundsen Sea dominated by the advection of existing crevasses. Using stress fields computed using the BISICLES ice sheet model, we show that much of this structural change has occurred in buttressing regions of these ice shelves, indicating a recent and ongoing link between fracturing and the developing dynamics of the Amundsen Sea sector.</p

Projected Least-Squares Quantum Process Tomography

We propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists of first computing the least-squares estimator of the Choi matrix of an unknown channel, and subsequently projecting it onto the convex set of Choi matrices. We consider four experimental setups including direct QPT with Pauli eigenvectors as input and Pauli measurements, and ancilla-assisted QPT with mutually unbiased bases (MUB) measurements. In each case, we provide a closed form solution for the least-squares estimator of the Choi matrix. We propose a novel, two-step method for projecting these estimators onto the set of matrices representing physical quantum channels, and a fast numerical implementation in the form of the hyperplane intersection projection algorithm. We provide rigorous, non-asymptotic concentration bounds, sampling complexities and confidence regions for the Frobenius and trace-norm error of the estimators. For the Frobenius error, the bounds are linear in the rank of the Choi matrix, and for low ranks, they improve the error rates of the least squares estimator by a factor d2, where d is the system dimension. We illustrate the method with numerical experiments involving channels on systems with up to 7 qubits, and find that PLS has highly competitive accuracy and computational tractability

Remote Sensing, machine learning and numerical modelling approaches to understanding the role of fractures in Antarctic Ice Sheet dynamics

The Antarctic Ice Sheet is currently losing mass. In large part, this is due to elevated flux of ice across grounding lines in West Antarctica, without the changes in accumulation over the ice sheet required to balance this. Over the last three decades, it has become apparent that the dynamics of these ice streams are highly sensitive to changes at their ocean margins, including to the floating ice shelves that extend out in front of many of them. So much so, in fact, that the dynamic imbalance of the ice sheet as a whole can be largely explained by a decrease in the amount of ice shelf buttressing in West Antarctica over recent decades, driven by enhanced sub-shelf melting due to incursions of warmer ocean waters onto the continental shelf. We have a good mechanical understanding of this process thanks to our treatment of marine ice sheet dynamics as a theory of viscous flow. However, the processes of material failure, e.g. brittle fracturing, are not included in this theory but are important in determining boundary conditions and material properties at the ice sheet margin. For example, fracturing processes are responsible for the calving of ice, which determines the position of the margin itself, and the presence of fractures alters the ability of ice to bear and transmit membrane stresses. This thesis deals with certain questions regarding the fracturing of ice, and, more generally, the sensitivity of ice stream dynamics to changes in material properties near the margin. I develop new methods for the extraction of crevasse data from satellite radar imagery, use the derived datasets to investigate changes to the structural integrity of ice shelves in the Amundsen Sea Embayment along with ice speed datasets from remote sensing imagery. I develop the capabilities of the BISICLES ice sheet model to solve inverse problems, and perform sensitivity analysis and diagnostic modelling, to investigate the sensitivity of ice dynamics to buttressing by landfast sea ice, and investigate links between observations of fracturing and isotropic ‘damage’ - a scalar field aiming to characterise how fractures change the large-scale material properties of the ice. In chapter 2, I develop deep learning-based computer vision methods for the extraction of crevasses and calving fronts from Sentinel-1 synthetic aperture radar (SAR) imagery of the Thwaites Glacier Ice Tongue. I examine the concurrency of structural change and large fluctuations in ice speed in this area, measured using observations of ice speed derived from Sentinel-1 SAR data. By solving inverse problems for the softness of the ice shelf given observations of ice speed, I show that the quantity of rifts matches well the timeseries of ice softness in the shear margin - showing a link between the two and indicating that crevassing is dynamically important for the region. I show that the increases in crevassing and acceleration of the ice tongue reverse on timescales of years, indicating that any feedback between the two is not the dominant cause of change in the region. In Chapter 3, I develop the crevasse-mapping procedure of chapter 2 into a process that can be used to generate pan-continental mosaics of crevasses on grounded and floating ice. This involves the use of deep learning methods similar to those of chapter 2, and the new ‘parallel structure filtering’ algorithm. I go on develop a method for quantifying structural change on ice shelves by measuring (roughly speaking) the local density of fractures. I show, in line with other literature, that there have been structural changes in parts of the Pine Island, Thwaites and Crosson Ice Shelves that contribute to ice shelf buttressing. Chapter 4 is a bit of a detour from the theme of crevasses. Instead, through a case study on the Larsen-B Embayment, I look at whether landfast sea ice can provide buttressing to glaciers/ice shelves in the way that ice shelves provide buttressing to ice streams. I present satellite data showing the evacuation of landfast sea ice from the Larsen-B Embayment at the start of 2022, the subsequent disintegration of the Hektoria/Green/Evans and Crane Ice Shelves, and the acceleration by ∼ 100 m/yr of Hektoria, Green and Crane Glaciers. I use diagnostic modelling and sensitivity analysis, with a representation of the landfast sea ice as a thin meteoric ice shelf, to suggest that the observed changes to the glaciers are not due to a loss of direct mechanical buttressing by the landfast sea ice. In Chapter 5, I focus on the process of solving inverse problems for the control fields representing slipperiness at the base of grounded ice, and the material softness of the ice from observations of ice speed using BISICLES. This is an ill-posed problem suffering underdeterminedness and poor conditioning. I introduce two methods of using the crevasse data generated using the methods described in chapter 3, along with data on surface strain rates, as prior information to help with this, and apply it to a case study focused on Pine Island Glacier. I show that, by doing so, one can arrive at softness fields that resemble the crevasse patterns seen on floating ice without harming the solution misfit. However, I also show that the use of crevasse data on grounded ice does not result in more plausible-looking solutions, indicating that the crevasses here do not dominate our uncertainty in the rheology of ice

Projected Least-Squares Quantum Process Tomography

13+9 pages, 8 figuresWe propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists of first computing the least-squares estimator of the Choi matrix of an unknown channel, and subsequently projecting it onto the convex set of Choi matrices. We consider four experimental setups including direct QPT with Pauli eigenvectors as input and Pauli measurements, and ancilla-assisted QPT with mutually unbiased bases (MUB) measurements. In each case, we provide a closed form solution for the least-squares estimator of the Choi matrix. We propose a novel, two-step method for projecting these estimators onto the set of matrices representing physical quantum channels, and a fast numerical implementation in the form of the hyperplane intersection projection algorithm. We provide rigorous, non-asymptotic concentration bounds, sampling complexities and confidence regions for the Frobenius and trace-norm error of the estimators. For the Frobenius error, the bounds are linear in the rank of the Choi matrix, and for low ranks, they improve the error rates of the least squares estimator by a factor $d^2$, where $d$ is the system dimension. We illustrate the method with numerical experiments involving channels on systems with up to 7 qubits, and find that PLS has highly competitive accuracy and computational tractability

Amundsen Sea Embayment ice-sheet mass-loss predictions to 2050 calibrated using observations of velocity and elevation change

Mass loss from the Amundsen Sea Embayment of the West Antarctic Ice Sheet is a major contributor to global sea-level rise (SLR) and has been increasing over recent decades. Predictions of future SLR are increasingly modelled using ensembles of simulations within which model parameters and external forcings are varied within credible ranges. Accurately reporting the uncertainty associated with these predictions is crucial in enabling effective planning for, and construction of defences against, rising sea levels. Calibrating model simulations against current observations of ice-sheet behaviour enables the uncertainty to be reduced. Here we calibrate an ensemble of BISICLES ice-sheet model simulations of ice loss from the Amundsen Sea Embayment using remotely sensed observations of surface elevation and ice speed. Each calibration type is shown to be capable of reducing the 90% credibility bounds of predicted contributions to SLR by 34 and 43% respectively

The effect of landfast sea ice buttressing on ice dynamic speedup in the Larsen B embayment, Antarctica

We observe the evacuation of 11-year-old landfast sea ice in the Larsen B embayment on the East Antarctic Peninsula in January 2022, which was in part triggered by warm atmospheric conditions and strong offshore winds. This evacuation of sea ice was closely followed by major changes in the calving behaviour and dynamics of a subset of the ocean-terminating glaciers in the region. We show using satellite measurements that, following a decade of gradual slow-down, Hektoria, Green, and Crane glaciers sped up by approximately 20%-50% between February and the end of 2022, each increasing in speed by more than 100ma-1. Circumstantially, this is attributable to their transition into tidewater glaciers following the loss of their ice shelves after the landfast sea ice evacuation. However, a question remains as to whether the landfast sea ice could have influenced the dynamics of these glaciers, or the stability of their ice shelves, through a buttressing effect akin to that of confined ice shelves on grounded ice streams. We show, with a series of diagnostic modelling experiments, that direct landfast sea ice buttressing had a negligible impact on the dynamics of the grounded ice streams. Furthermore, we suggest that the loss of landfast sea ice buttressing could have impacted the dynamics of the rheologically weak ice shelves, in turn diminishing their stability over time; however, the accompanying shifts in the distributions of resistive stress within the ice shelves would have been minor. This indicates that this loss of buttressing by landfast sea ice is likely to have been a secondary process in the ice shelf disaggregation compared to, for example, increased ocean swell or the drivers of the initial landfast sea ice disintegration