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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Nonlinear Parametrizations of Outgoing Longwave Radiation in Zero-Dimensional Energy Balance Models

Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 239--249 | DOI:10.5890/DNC.2016.09.004

Dmitry V. Kovalevsky

Nansen International Environmental and Remote Sensing Centre, 14th Line 7, office 49, Vasilievsky Island, 199034 St. Petersburg, Russia

Saint Petersburg State University, Universitetskaya Emb. 7-9, 199034 St. Petersburg, Russia

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A one-layer and two-layer zero-dimensional (0D) energy balance models (EBMs) of the global climate system with different approximations for parametrization of outgoing longwave radiation (OLR) are considered. Three alternative approximations for parametrizing the OLR are explored in detail: (i) the (conventional) linear approximation, (ii) the quadratic approximation, and (iii) the ‘exact’ (power 4) model. In case of one-layer 0D EBM, exact analytical solutions are derived in closed form for all three alternative approximations for parametrizing the OLR. In the numerical examples provided, the deviations of the linear approximation from the ‘exact’ model are visible, while the quadratic approximation is virtually indistinguishable from the ‘exact’ model.


The author is indebted to Prof. Genrikh V. Alekseev for helpful comments. The reported study was supported by the Russian Foundation for Basic Research, research project No. 15-05-03512-a.


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