Climate entropy budget of the HadCM3 atmosphere–ocean general circulation model and of FAMOUS, its low-resolution version

Abstract

The entropy budget is calculated of the coupled atmosphere-ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be *50 mW m -2 K -1 , a value intermediate in the range 30-70 mW m -2 K -1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (*38 mW m -2 K -1 ). Another 13 mW m -2 K -1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m -2 K -1 . The material entropy production within the ocean due to turbulent mixing is *1 mW m -2 K -1 , a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m -2 K -1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

“…(13)- (15) it is seen that in our model the material entropy production is defined as a positive-definite functional of the climate temperature field, i.e.Ṡ mat =Ṡ mat [T (x)]. Using T (x) from FAMOUS, the value of the material entropy production we estimate is about 47 mW m −2 K −1 , that is around 5 mW m −2 K −1 less than the value diagnosed from FAMOUS in Pascale et al (2011a). This is due to the the fact that here we use time means (·) for calculations and at the surface Q sw /T s − Q sw /T s ∼ 5 mW m −2 K −1 in the FAMOUS climatology.…”

“…The interior of the ocean is neglected. Although the material entropy production due to the small-scale eddy turbulence (∼1 mW m −2 K −1 ) is negligible when compared to the material entropy production of the whole climate system (∼50 mW m −2 K −1 , see Shimokawa and Ozawa, 2001;Pascale et al, 2011a), the ocean meridional heat transport is of the same order of magnitude of the atmospheric one (Paltridge, 1978;Trenberth et al, 2009). Therefore the consequence of this omission may be an enhancement of the atmospheric meridional heat transport and consequently a reduction of the surface meridional gradient.…”

“…The material entropy production at this point can be expressed in terms of the radiative heating rates (as shown in Goody, 2000;Pascale et al, 2011a;Lucarini et al, 2011, also known as the inverse formula):…”

“…The total material entropy production of the climate system has been estimated from general circulation models to be about 50 mW K −1 m −2 and most of it is associated with the hydrological cycle whereas only a small (10 %) fraction is associated with large scale meridional heat transport (Ambaum, 2010;Fraedrich and Lunkeit, 2008;Pascale et al, 2011a). On the basis of this, recently Lucarini et al (2011) have questioned the appropriateness of 2-box models as the paradigmatic one used by Lorenz et al (2001) as a tool to investigate MEP.…”

Thermodynamics of climate change: generalized sensitivities

“…Even if the general validity of MEPP is unclear (Dewar, 2005;Grinstein and Linsker, 2007), its heuristic adoption in climate science has been quite fruitful (Kleidon and Lorenz 2005;Kleidon et al, 2006;Kunz et al, 2008), and has stimulated a detailed re-examination of the importance of entropy production in the climate system (Peixoto and Oort, 1992;Goody, 2000;Ozawa et al, 2003). Moreover, this has resulted into a drive for adopting of a new generation of diagnostic tools based on the 2nd law of thermodynamics for auditing climate models (Fraedrich and Lunkeit, 2008;Pascale et al, 2009; and for outlining a set of parameterisations to be used in conceptual and intermediate complexity models, or for the reconstruction of the past climate conditions (Fraedrich, 2001). Recently a link has been found between the Carnot efficiency, the entropy production and the degree of irreversibility of the climate system (Lucarini, 2009b).…”