Mathematics and Climate

Kaper, Hans; Engler, Hans

doi:10.1137/1.9781611972610

Cited by 74 publications

(81 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The transport term presented here, which Engler and Kaper referred to as the heat transfer [12], is an alternative to the diffusion transport. In [19], North studied the Budyko model with diffusion transport term and specified a boundary condition that no heat flux would pass through the equator and the pole.…”

Section: Transportmentioning

confidence: 99%

Dynamics of the Budyko Energy Balance Model

Widiasih¹

2013

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

A dynamical system derived from a conceptual climate model is investigated. The model is often referred to as the Budyko-Sellers-type energy balance model (EBM), or in short, the Budyko model. The focus of this study is on a mathematical formulation that further develops the model by capturing the ice line dynamics and thereby places the Budyko model within the dynamical systems framework. The classical Budyko EBM is represented here as an integro-difference equation, then coupled with an ice line equation. The resulting infinite dimensional system is shown to possess an attracting one dimensional invariant manifold. The novel formulation captures solutions that others have previously obtained while also making the formulation and the analysis of the model more precise. Introduction.We investigate a dynamical system derived from a conceptual climate model. The model is a version of what is known in climate science as the Budyko-Sellers-type energy balance model (EBM). The result of this study is purely mathematical, with the main focus on the mathematical formulation that further develops the model and places it in the framework of dynamical systems. In particular, we represent the classical Budyko model as an integro-difference equation, then couple it with an auxiliary equation that prescribes the ice line dynamics. We analyze the stability of the coupled system and prove that, under certain conditions, the infinite dimensional system has a one dimensional attracting invariant manifold.Budyko-Sellers-type EBMs model the annual average temperature distribution and rest on the idea that the energy received by the planet is balanced by the energy it emits. Any imbalance in the system will result in a temperature change. The state variable of a BudykoSellers-type EBM is a latitudinally averaged temperature distribution, often referred to as a temperature profile. One feedback admitted by a Budyko-Sellers-type EBM is the ice albedo feedback, which is a positive feedback caused by the difference between the reflectivity of ice cover and that of the ocean. Much effort has been devoted to the steady state analysis of differential equations based on the two conceptual models pioneered independently by Budyko [3] and Sellers [22] in late 1960s; see, e.g., [5,17,23,9]. Here, we are concerned with

show abstract

Section: Transportmentioning

confidence: 99%

Dynamics of the Budyko Energy Balance Model

Widiasih¹

2013

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

show abstract

“…The mathematical model of CDP [22] is a combination of the diffusion and convection equations and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Here we will consider the three-dimensional CDP, which arises in mathematical modeling of atmosphere circulation in meteorology [7].…”

Section: The Mathematical Model Of the Convection-diffusion Problemmentioning

confidence: 99%

Automated Program Design – an Example Solving a Weather Forecasting Problem

et al. 2016

View full text Add to dashboard Cite

High-level algebra-algorithmic software tools for automated design of parallel code in the OpenMP environment are developed for the purpose of both producing efficient parallel code and increasing the performance of program developers. Application of the tools is illustrated with an example of a problem in atmosphere circulation modeling, represented as a service belonging to an Internet portal providing meteorological forecasting services. Results of execution of the parallel weather forecasting program on multiprocessor platforms are given.

show abstract

“…They also appear in control [8], modeling of climate [9], modern computational methods [10,11], and the dynamics of coupled oscillators [12,13]. In each of these problems, delay is a direct consequence of wave propagation without dispersion.…”

mentioning

confidence: 99%

“…To investigate theoretically the appearance of modulational instability in the system (8), (9), and (7) let us consider a cw solution in the form AðtÞ ¼ A 0 e iνt and GðtÞ ¼ G 0 , which together with (7) imply PðtÞ ¼ ðe −σL=½ΓþiðΩþνÞ − 1ÞA 0 e iνt . Following the approach described in [18] we perform linear stability analysis of cw solutions A 0 , G 0 in the limit T → ∞.…”

mentioning

confidence: 99%