Publication: A finite element algorithm of a nonlinear diffusive climate energy balance model
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2008-07-11
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Birkhäuser
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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 R(2): 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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BERMEJO, R., CARPIO, J., DÍAZ, J. I, and TELLO, L. (2007), Mathematical and numerical analysis of a nonlinear diffusive climate energy balance model (submitted).
BADII, M. and DÍAZ, J. I. (1999), Time Periodic Solutions for a Diffusive Energy Balance Model in Climatology, J. Math. Anal. Appl. 233, 717–724.
BARRETT, J. W. and LIU, W. B. (1994), Finite element approximation of the parabolic p-Laplacian, SIAM J. Numer. Anal. 31, 413–428.
BAUMGARDNER, J. R. and FREDERICKSON, P. O. (1985), Icosahedral discretization of the two-sphere, SIAM J. Numer. Anal. 22, 1107–1115.
BUDYKO, M. I. (1969), The effects of solar radiation variations on the climate of the Earth, Tellus 21, 611–619.
CARL, S. (1992), A combined variational-monotone iterative method for elliptic boundary value problems with discontinuous nonlinearities, Applicable Analysis 43, 21–45.
DÍAZ, J. I., Mathematical analysis of some diffusive energy balance climate models. In Mathematics, Climate and Environment (eds. DÍAZ, J. I., and Lions, J. L.) (Masson, Paris 1993) pp. 28–56.
DÍAZ, J. I. (Ed.) The Mathematics of Models in Climatology and Environment, ASI NATO Global Change Series I, no. 48 (Springer-Verlag, Heidelberg, 1996).
DÍAZ, J. I., HERNÁNDEZ, J., and TELLO, L. (1997), On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in Climatology, J. Math. Anal. Appl. 216, 593–613.
DÍAZ, J. I. and HETZER, G. A quasilinear functional reaction-diffusion equation arising in Climatology, In Equations aux derivees partielles et applications: Articles dedies a Jacques Louis Lions (Gautier Villards, Paris 1998) pp. 461–480.
DÍAZ, J. I. and TELLO, L. (1999), A nonlinear parabolic problem on a Riemannian manifold without boundary arising in Climatology, Collectanea Mathematica 50, 19–51.
DZIUK, G., Finite element for the Beltrami operator on arbitrary surfaces. In Partial Differential Equations and Calculus of Variations, Lectures Notes in Mathematics, vol. 1357 (Springer, Heidelberg 1988) pp. 142–155.
GIRALDO, F. X. and WARBURTON, T. (2005), A nodal triangle-based spectral element method for the shallow water equations on the sphere, J. Comput. Phys. 207, 129–150.
GRAVES, C. E., LEE, W.-H. and NORTH, G. R. (1993), New parameterizations and sensitivities for simple climate models, J. Geophys. Res. 98, 5025–5036.
HAIRER, E., NORSETT, S. P. and WANNER, G., Solving Ordinary Differential Equations I: Nonstiff Problems (Springer-Verlag, Berlin, Heidelberg, 1993).
HEINZE, T. and HENSE, A. (2002), The shallow water equations on the sphere and their Lagrange-Galerkin solution, Meterol. Atmos. Phys. 81, 129–137.
HETZER, G. (1990), The structure of the principal component for semilinear diffusion equations from energy balance climate models, Houston Journal of Math. 16, 203–216.
HETZER, G., JARAUSCH, H. and MACKENS, W. (1989), A multiparameter sensitivity analysis of a 2D diffusive climate model, Impact and Computing in Science and Engineering 1, 327–393.
HYDE, W. T., KIM, K.-Y., CROWLEY, T. J. and NORTH, G. R. (1990), On the relation between polar continentality and climate: Studies with a nonlinear seasonal energy balance model, J. Geophys. Res. 95 (D11), 18.653–18.668.
JU, N. (2000), Numerical analysis of parabolic p-Laplacian. Approximation of trajectories, SIAM J. Numer. Anal. 37, 1861–1884.
MYHRE, G., HIGHWOOD, E. J., SHINE, K., and STORDAL, F. (1998), New estimates of radiative forcing due to well mixed Greenhouse gases, Geophys. Res. Lett. 25, 2715–2718.
NORTH, G. R., Multiple solutions in energy balance climate models. In Paleogeography, Paleoclimatology, Paleoecology 82 (Elsevier Science Publishers B.V., Amsterdam, 1990) pp. 225–235.
NORTH, G. R. and COAKLEY, J. A. (1979), Differences between seasonal and mean annual energy balance model calculations of climate and climate sensitivity, J. Atmos. Sci. 41, 1189–1204.
SADOURNY, R., ARAKAWA, A. and MINTZ, Y. (1968), Integration of the nondivergent barotropic vorticity equation with an icosahedral hexagonal grid for the sphere, Mon. Wea. Rev. 96, 351–356.
SELLERS, W. D., Physical Climatology (The University of Chicago Press, Chicago, Ill. 1965).
SELLERS, W. D. (1969), A global climatic model based on the energy balance of the earth-atmosphere system, J. Appl. Meteorol. 8, 392–400.
WILLIAMSON, D. L. (1968), Integration of the barotropic vorticity equation on a spherical geodesic grid, Tellus 20, 642–653.
XU, X. (1991), Existence and regularity theorems for a free boundary problem governing a simple climate model, Applicable Anal. 42, 33–59.