On the calibration of the 3/2 model

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Exploring mechanisms responsible for tidal modulation in flow of the Filchner–Ronne Ice Shelf

An extensive network of GPS sites on the Filchner–Ronne Ice Shelf and adjoining ice streams shows strong tidal modulation of horizontal ice flow at a range of frequencies. A particularly strong (horizontal) response is found at the fortnightly (Msf) frequency. Since this tidal constituent is absent in the (vertical) tidal forcing, this observation implies the action of some non-linear mechanism. Another striking aspect is the strong amplitude of the flow perturbation, causing a periodic reversal in the direction of ice shelf flow in some areas and a 10 %–20 % change in speed at grounding lines. No model has yet been able to reproduce the quantitative aspects of the observed tidal modulation across the entire Filchner–Ronne Ice Shelf. The cause of the tidal ice flow response has, therefore, remained an enigma, indicating a serious limitation in our current understanding of the mechanics of large-scale ice flow. A further limitation of previous studies is that they have all focused on isolated regions and interactions between different areas have, therefore, not been fully accounted for. Here, we conduct the first large-scale ice flow modelling study to explore these processes using a viscoelastic rheology and realistic geometry of the entire Filchner–Ronne Ice Shelf, where the best observations of tidal response are available. We evaluate all relevant mechanisms that have hitherto been put forward to explain how tides might affect ice shelf flow and compare our results with observational data. We conclude that, while some are able to generate the correct general qualitative aspects of the tidally induced perturbations in ice flow, most of these mechanisms must be ruled out as being the primary cause of the observed long-period response. We find that only tidally induced lateral migration of grounding lines can generate a sufficiently strong long-period Msf response on the ice shelf to match observations. Furthermore, we show that the observed horizontal short-period semidiurnal tidal motion, causing twice-daily flow reversals at the ice front, can be generated through a purely elastic response to basin-wide tidal perturbations in the ice shelf slope. This model also allows us to quantify the effect of tides on mean ice flow and we find that the Filchner–Ronne Ice Shelf flows, on average, ∼ 21 % faster than it would in the absence of large ocean tides

Tidal bending of ice shelves as a mechanism for large-scale temporal variations in ice flow

GPS measurements reveal strong modulation of horizontal ice shelf and ice stream flow at a variety of tidal frequencies, most notably a fortnightly (Msf) frequency not present in the vertical tides themselves. Current theories largely fail to explain the strength and prevalence of this signal over floating ice shelves. We show how well-known non-linear aspects of ice rheology can give rise to widespread, long-periodic tidal modulation in ice shelf flow, generated within ice shelves themselves through tidal flexure acting at diurnal and semidiurnal frequencies. Using full-Stokes viscoelastic modelling, we show that inclusion of tidal bending within the model accounts for much of the observed tidal modulation of ice shelf flow. Furthermore, our model shows that, in the absence of vertical tidal forcing, the mean flow of the ice shelf is reduced by almost 30 % for the geometry that we consider

A generalized weighted Monte Carlo calibration method for derivative pricing

The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To improve the accuracy, we propose a generalized version of the weighted Monte Carlo calibration method with two distinguishing features. First, we use a probability distortion scheme to produce a non-uniform prior distribution for the simulated paths. Second, we assign multiple weights per path to fit with the different maturities present in the set of benchmark options. Our tests on S&P500 options data show that the new calibration method proposed here produces a significantly better out-of-sample fit than the original method for two commonly used asset pricing models

Changes in ice-shelf buttressing following the collapse of Larsen A Ice Shelf, Antarctica, and the resulting impact on tributaries

The dominant mass-loss process on the Antarctic Peninsula has been ice-shelf collapse, including the Larsen A Ice Shelf in early 1995. Following this collapse, there was rapid speed up and thinning of its tributary glaciers. We model the impact of this ice-shelf collapse on upstream tributaries, and compare with observations using new datasets of surface velocity and ice thickness. Using a two-horizontal-dimension shallow shelf approximation model, we are able to replicate the observed large increase in surface velocity that occurred within Drygalski Glacier, Antarctic Peninsula. The model results show an instantaneous twofold increase in flux across the grounding line, caused solely from the reduction in backstress through ice shelf removal. This demonstrates the importance of ice-shelf buttressing for flow upstream of the grounding line and highlights the need to explicitly include lateral stresses when modelling real-world settings. We hypothesise that further increases in velocity and flux observed since the ice-shelf collapse result from transient mass redistribution effects. Reproducing these effects poses the next, more stringent test of glacier and ice-sheet modelling studies

Differential Geometry of Ice Flow

Flowlines on ice sheets and glaciers form complex patterns. To explore their role in ice routing and extend the language for studying such patterns, we develop a theory of flow convergence and curvature in plan view. These geometric quantities respectively equal the negative divergence of the vector field of ice-flow direction and the curl of this field. From the first of these two fundamental results, we show that flow in individual catchments of an ice sheet can converge (despite its overall spreading) because ice divides are loci of strong divergence, and that a sign bifurcation in convergence occurs during ice-sheet “symmetry breaking” (the transition from near-radial spreading to spreading with substantial azimuthal velocities) and during the formation of ice-stream tributary networks. We also uncover the topological control behind balance-flux distributions across ice masses. Notably, convergence participates in mass conservation along flowlines to amplify ice flux via a positive feedback; thus the convergence field governs the form of ice-stream networks simulated by balance-velocity models. The theory provides a roadmap for understanding the tower-shaped plot of flow speed versus convergence for the Antarctic Ice Sheet

Coupled ice shelf-ocean modeling and complex grounding line retreat from a seabed ridge

Recent observations and modeling work have shown a complex mechanical coupling between Antarctica's floating ice shelves and the adjacent grounded ice sheet. A prime example is Pine Island Glacier, West Antarctica, which has a strong negative mass balance caused by a recent increase in ocean-induced melting of its ice shelf. The mass loss coincides with the retreat of the grounding line from a seabed ridge, on which it was at least partly grounded until the 1970s. At present, it is unclear what has caused the onset of this retreat and how feedback mechanisms between the ocean and ice shelf geometry have influenced the ice dynamics. To address these questions, we present the first results from an offline coupling between a state-of-the-art shallow-ice flow model with grounding line resolving capabilities and a three-dimensional ocean general circulation model with a static implementation of the ice shelf. A series of idealized experiments simulate the retreat from a seabed ridge in response to changes in the ocean forcing, and we show that the retreat becomes irreversible after 20 years of warm ocean conditions. A comparison to experiments with a simple depth-dependent melt rate parameterization demonstrates that such parameterizations are unable to capture the details of the retreat process, and they overestimate mass loss by more than 40% over a 50 year timescal