Related papers: The Mid Pleistocene Transition from a Budyko-Selle…
A dynamical system derived from a conceptual climate model is investigated. The model is often referred to as Budyko-Sellers type Energy Balance Model (EBM), or in short, the Budyko model. The focus of this study is on the mathematical…
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…
M. Budyko and W. Sellers independently introduced seminal energy balance climate models in 1969, each with a goal of investigating the role played by positive ice albedo feedback in climate dynamics. In this paper we replace the relaxation…
Due to climate change, the interest of studying our climatic system using mathematical modeling has become tremendous in recent years. One well-known model is Budyko's system, which represents the coupled evolution of two variables, the…
We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type…
In this paper, we study two Energy Balance Models with Memory arising in climatology, which consist in a 1D degenerate nonlinear parabolic equation involving a memory term, and possibly a set-valued reaction term (of Sellers type and of…
The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate…
Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time in…
We present a phase-space model that simulates Pleistocene ice volume changes based on Earth's orbital parameters. Terminations in the model are triggered by a combination of ice volume and orbital forcing and agree well with age estimates…
The glacial cycles are attributed to the climatic response of the orbital changes in the irradiance to the Earth. These changes in the forcing are to small to explain the observed climate variations as simple linear responses. Non-linear…
Using a recent conceptual model of the glacial-interglacial cycles we present more evidence of Milankovitch cycles being the trigger for retreat and forming of ice sheets in the cycles. This model is based on a finite approximation of an…
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo -- a key parameter in climate…
The Milankovitch theory states that the orbital eccentricity, precession, and obliquity of the Earth influence our climate by modulating the summer insolation at high latitudes in the northern hemisphere. Despite considerable success of…
Simulations show that sliding bilayers of colloidal particles can exhibit a new phase, the ``melt-freeze'' phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological…
This article is concerned with the dynamics of glacial cycles observed in the geological record of the Pleistocene Epoch. It focuses on a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res.,95, D2 (1990), pp. 1955-1963],…
A "toy" model, simple and elementary enough for an undergraduate class, of the temperature dependence of the greenhouse (mid-IR) absorption by atmospheric water vapor implies a bistable climate system. The stable states are glaciation and…
We present a non-isothermal mesoscopic model for investigation of the phase transition dynamics of thermoresponsive polymers. Since this model conserves energy in the simulations, it is able to correctly capture not only the transient…
The climate record preserved in polar glaciers, mountain glaciers, and widespread cave deposits shows repeated occurrence of abrupt global transitions between cold/dry stadial and warm/wet interstadial states during glacial periods. These…
We prove the existence, uniqueness, and comparison of solutions for a nonlinear stochastic parabolic partial differential equation that includes the Solar variability in terms of a multiplicative Wiener cylindrical noise in the term of the…
Glacial cycles redistribute water between oceans and continents causing pressure changes in the upper mantle, with consequences for melting of Earth's interior. Using Plio-Pleistocene sea-level variations as a forcing function, theoretical…