Related papers: Analysis and numerical simulations of a landfast i…
This paper establishes the local-in-time well-posedness of solutions to an approximating system constructed by mildly regularizing the dynamical sea-ice model of {\it W.D. Hibler, Journal of Physical Oceanography, 1979}. Our choice of…
Consider the set of equations modeling the motion of a rigid body enclosed in sea ice. Using Hibler's viscous-plastic model for describing sea ice, it is shown by a certain decoupling approach that this system admits a unique, local strong…
In this paper, we initiate the rigorous mathematical analysis of the elastic-viscous-plastic (EVP) sea-ice model, which was introduced in [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849-1867]. The EVP model is one of…
This paper proves the local-in-time strong well-posedness of a parabolic-hyperbolic regularized version of Hibler's sea ice model. Hibler's model is the most frequently used sea ice model in climate science. Lagrangian coordinates are…
A significant fraction (4%-13%) of Antarctic sea ice remains stationary as landfast sea-ice ("fast ice"), typically anchored by grounded icebergs. Current global climate models do not represent fast-ice formation due to iceberg grounding,…
This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea ice model. In…
In this paper, we prove global existence and uniqueness of weak solutions to the momentum equations of Hibler's visco-plastic model for the dynamics of the arctic sea-ice covers. Although Hibler's model is standardly used in global climate…
This article develops for the first time a rigorous analysis of Hibler's model of sea ice dynamics. Identifying Hibler's ice stress as a quasilinear second order operator and regarding Hibler's model as a quasilinear evolution equation, it…
We introduce a comprehensive modeling framework for the dynamics of sea ice floes using particle, kinetic, and hydrodynamic approaches. Building upon the foundational work of Ha and Tadmor on the Cucker-Smale model for flocking, we derive a…
We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom…
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.…
Observations indicate that the Arctic sea ice cover is rapidly retreating while the Antarctic sea ice cover is steadily expanding. State-of-the-art climate models, by contrast, typically simulate a moderate decrease in both the Arctic and…
We analyze the numerical solutions of a stochastic Arctic sea ice model with constant additive noise over a wide range of external heat-fluxes, $\Delta F_0$, which correspond to greenhouse gas forcing. The variability that the stochasticity…
Within the framework of lower order thermodynamic theories for the climatic evolution of Arctic sea ice we isolate the conditions required for the existence of stable seasonally-varying solutions, in which ice forms each winter and melts…
Arctic sea ice performs a vital role in global climate and has paramount impacts on both polar ecosystems and coastal communities. In the last few years, multiple deep learning based pan-Arctic sea ice concentration (SIC) forecasting…
In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In this paper, we extend this model to the stochastic setting…
Arctic sea ice extent has drawn increasing interest and alarm from geoscientists, owing to its rapid decline. In this article, we propose a Bayesian spatio-temporal hierarchical statistical model for binary Arctic sea ice data over two…
It has been widely debated whether Arctic sea-ice loss can reach a tipping point beyond which a large sea-ice area disappears abruptly. The theory of dynamical systems predicts a slowing down when a system destabilises towards a tipping…
Sea ice plays an important role in stabilising the Earth system. Yet, representing its dynamics remains a major challenge for models, as the underlying processes are scale-invariant and highly anisotropic. This poses a dilemma:…
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations, we proposed in [D. W. Boutros, X. Liu,…