Related papers: Stochastic dynamics of Arctic sea ice Part I: Addi…
We analyze the numerical solutions of a stochastic Arctic sea ice model with multiplicative noise over a wide range of external heat-fluxes, $\Delta F_0$, which correspond to greenhouse gas forcing. When the noise is multiplicative, the…
The stochastic Arctic sea ice model described as a single periodic non-autonomous stochastic ordinary differential equation (ODE) is useful in explaining the seasonal variability of Arctic sea ice. However, to be nearer to realistic…
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…
The physics of planetary climate features a variety of complex systems that are challenging to model as they feature turbulent flows. A key example is the heat flux from the upper ocean to the underside of sea ice which provides a key…
We analyze the stability of a low-order coupled sea ice and climate model and extract the essential physics governing the time scales of response as a function of greenhouse gas forcing. Under present climate conditions the stability is…
In light of the rapid recent retreat of Arctic sea ice, the extreme weather events triggering the variability in Arctic ice cover has drawn increasing attention. A non-Gaussian $\alpha$-stable L\'evy process is thought to be an appropriate…
Understanding the interactions between ice sheets and global climate forcings over geological timescales is essential for projecting their future. Previous studies have highlighted the role of ice dynamics and climate interactions in…
We propose and analyse a mechanism by which $\mathrm{CO}_2$-driven radiative forcing can increase Arctic temperature variability in a stochastic Sellers-type energy-balance model. Starting from a fast-slow formulation in which insolation is…
We study the seasonal changes in the thickness distribution of Arctic sea ice, $g(h)$, under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for $g(h)$ (Toppaladoddi \& Wettlaufer \emph{Phys. Rev.…
It is well acknowledged that the sequence of glacial-interglacial cycles is paced by the astronomical forcing. However, how much is the sequence robust against natural fluctuations associated, for example, with the chaotic motions of…
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…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
A controlling factor in the seasonal and climatological evolution of the sea ice cover is its albedo $\alpha$. Here we analyze Arctic data from the Advanced Very High Resolution Radiometer (AVHRR) Polar Pathfinder and assess the seasonality…
Seasonal forecast of Arctic sea ice concentration is key to mitigate the negative impact and assess potential opportunities posed by the rapid decline of sea ice coverage. Seasonal prediction systems based on climate models often show…
The importance of snow cover and ice extent in the Northern Hemisphere was recognized by various authors leading to a positive feedback of surface reflectivity on climate. In fact, the retreat of Arctic sea ice is accompanied by enhanced…
The extent to which the ongoing decline in Arctic sea ice affects mid-latitude climate has received great attention and polarised opinions. The basic issue is whether the inter-annual variability in Arctic sea ice is the cause of, or the…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
Existing methods for diagnosing predictability in climate indices often make a number of unjustified assumptions about the climate system that can lead to misleading conclusions. We present a flexible family of state-space models capable of…
In this paper, we study the long-time behavior of a stochastic heat equation with multiplicative noise and localized control. We begin by analyzing the uncontrolled dynamics and derive explicit decay rates for both mean-square and almost…
Abrupt and irreversible winter Arctic sea-ice loss may occur under anthropogenic warming due to the collapse of a sea-ice equilibrium at a threshold value of CO$_2$, commonly referred to as a tipping point. Previous work has been unable to…