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

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## 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.

## Keywords

Entropy budget General circulation models Material entropy production## Notes

### Acknowledgments

Salvatore Pascale would like to thank Robert Plant for the help provided in the diagnostic coding. Jonathan Gregory was partly supported by the Joint DECC, Defra and MoD Integrated Climate Programme, DECC/Defra (GA01101), MoD (CBC/2B/0417_Annex C5). The authors also thank the two anonymous reviewers for their comments, which led to significant improvements on the original version of the manuscript.

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