Climate change, in the framework of the constructal law
M. Clausse1, F. Meunier1, A. H. Reis2, and A. Bejan31Laboratory of Chemical Engineering applied to Environment, Energy and Health (LGP2ES-EA21), Conservatoire National des Art et Metiers (CNAM), case 331, 292, rue St Martin, 75141 Paris Cedex 03, France 2Department of Physics and Evora Geophysics Centre, University of Évora, Ramalho, 59, 7000-67 1 Evora, Portugal 3Department of Mechanical Engineering, Duke University, Durham, NC 27708-0300, USA
Received: 21 Dec 2010 – Accepted for review: 07 Feb 2011 – Discussion started: 07 Mar 2011
Abstract. Here we present a simple and transparent alternative to the complex models of Earth thermal behavior under time-changing conditions. We show the one-to-one relationship between changes in atmospheric properties and time-dependent changes in temperature and its distribution on Earth. The model accounts for convection and radiation, thermal inertia and changes in albedo (ρ) and greenhouse factor (γ). The constructal law is used as the principle that governs the evolution of flow configuration in time, and provides closure for the equations that describe the model. In the first part of the paper, the predictions are tested against the current thermal state of Earth. Next, the model showed that for two time-dependent scenarios, (δρ = 0.002; δγ = 0.011) and (δρ = 0.002; δγ = 0.005) the predicted equatorial and polar temperature increases and the time scales are (ΔTH = 1.16 K; ΔTL = 1.11 K; 104 years) and (0.41 K; 0.41 K; 57 years), respectively. In the second part, a continuous model of temperature variation was used to predict the thermal response of the Earth's surface for changes bounded by δρ = δγ and δρ = −δγ. The results show that the global warming amplitudes and time scales are consistent with those obtained for δρ = 0.002 and δγ = 0.005. The poleward heat current reaches its maximum in the vicinity of 35° latitude, accounting for the position of the Ferrel cell between the Hadley and Polar Cells.
Clausse, M., Meunier, F., Reis, A. H., and Bejan, A.: Climate change, in the framework of the constructal law, Earth Syst. Dynam. Discuss., 2, 241-270, doi:10.5194/esdd-2-241-2011, 2011.