A Finite Element Algorithm of a Nonlinear Diffusive Climate Energy Balance Model |
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| Authors: | R Bermejo J Carpio J I Díaz P Galán del Sastre |
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| Institution: | (1) Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C/ José Gutiérrez Abascal 2, 28006 Madrid, Spain;(2) Dept. Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain;(3) Dept. Matemática Aplicada, Universidad Politécnica de Madrid, E. T. S. Arquitectura. Av. Juan de Herrera, 28040 Madrid, Spain |
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| Abstract: | We present a finite element algorithm of a climate diagnostic model that takes as a climate indicator the atmospheric sea-level
temperature. This model belongs to the category of energy balance models introduced independently by the climatologists M.I.
Budyko and W.D. Sellers in 1969 to study the influence of certain geophysical mechanisms on the Earth climate. The energy
balance model we are dealing with consists of a two-dimensional nonlinear parabolic problem on the 2-sphere with the albedo
terms formulated according to Budyko as a bounded maximal monotone graph in  The numerical model combines the first-order Euler implicit time discretization scheme with linear finite elements for space
discretization, the latter is carried out for the special case of a spherical Earth and uses quasi-uniform spherical triangles
as finite elements. The numerical formulation yields a nonlinear problem that is solved by an iterative procedure. We performed
different numerical simulations starting with an initial datum consisting of a monthly average temperature field, calculated
from the temperature field obtained from 50 years of simulations, corresponding to the period 1950–2000, carried out by the
Atmosphere General Circulation Model HIRLAM. |
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| Keywords: | Climate nonlinear energy balance finite elements |
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