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The ice shelves buttressing the Antarctic ice sheet determine the rate of ice-discharge into the surrounding oceans. The geometry of ice shelves, and hence their buttressing strength, is determined by ice flow as well as by the local…
The shallow shelf approximation is a better ``sliding law'' for ice sheet modeling than those sliding laws in which basal velocity is a function of driving stress. The shallow shelf approximation as formulated by \emph{Schoof} [2006a] is…
Liquid-water oceans likely underlie the ice shells of Europa and Enceladus, but ocean properties are challenging to measure due to the overlying ice. Here, we consider gravity-driven flow of the ice shells of icy satellites and relate this…
Numerical ice sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or…
We study a one-parameter family ($\ell=1,2,3,\ldots$) of configurations that are square-ice analogues of plane partitions. Using an algorithm due to Bratley and McKay, we carry out exact enumerations in order to study their asymptotic…
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of…
The presence of salt in ocean water strongly affects the melt rate and the shape evolution of ice, both of utmost relevance in geophysical and ocean flow and thus for the climate. To get a better quantitative understanding of the physical…
Wave erosion of ice cliffs is one of the main mechanisms for waterline ice melt for icebergs, glacier fronts, and ice-shelf fronts. Despite its importance, this process is fundamentally not well understood or extensively tested in…
Antarctic meltwater is expected to increase throughout the coming centuries and impact sea level, ocean circulation, and the coupled climate evolution. This motivates interest in understanding the ocean response to Antarctic freshwater…
We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past…
Modeling time series is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly non-uniform sampling of measurements from different sensors with different levels of accuracy, as…
The velocity field and the height at the surface of a dynamic ice sheet are observed. The ice sheets are modeled by the full Stokes equations and shallow shelf/shelfy stream approximations. Time dependence is introduced by a kinematic free…
Since the prediction of climate is mainly considered as a prediction of second kind, it is indispensable to assess the accuracy with which these boundary conditions can be determined so that we can find a reasonable answer, whether climate…
A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean…
Clouds are important components of the atmosphere. Since it is usually not possible to treat them as ensembles of huge numbers of particles, parameterizations on the basis of averaged quantities (mass and/or number concentration) must be…
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets.…
Working with a two-stage ice sheet model, we explore how statistical data assimilation methods can be used to improve predictions of glacier melt and relatedly, sea level rise. We find that the EnKF improves model runs initialized using…
Gravitational coupling between young planets and their parent disks is often explored using numerical simulations, which typically treat the disk thermodynamics in a highly simplified manner. In particular, many studies adopt the locally…
The meltwater mixing line (MML) model provides a theoretical prediction of near-ice water mass properties that is useful to compare with observations. If oceanographic measurements reported in a temperature-salinity diagram overlap with the…
Large plume-like features within the Greenland Ice Sheet disrupt radiostratigraphy and complicate the use of isochrones in reconstructions of past ice dynamics. Here we use numerical modeling to test the hypothesis that convection is a…