Conclusions:

1. Motivation: Johnson(1997) suggested that spurious numerical generation of entropy (s = cp ln ) is present in atmosphere models, and that the cold bias in the extratropical UT/LS region simulated by climate models develops as a sink for the excess entropy by radiating energy to space at a lower temperature. • Aim: To quantify the entropy produced by model diffusion in a dry, adiabatic baroclinic wave lifecycle simulated by the Reading Spectral Model. • Large local sources and sinks (~2Wm-2K-1, shown right) mostly cancel but the residual is a small, systematic positive source. The entropy generated by the diffusion is calculated locally by dividing the heat addition due to diffusion by the temperature (ie. cp Tdiff / T). The meridional section on the far left shows that the largest sources and sinks of entropy are at the surface fronts but that there are also smaller ones higher up, indicating mixing in the region of the tropopause fold. The profile shows the contribution of each region to the global entropy change over the lifecycle; roughly half of the production is in the boundary layer region (defined as the lowest 1km). The change in global mass-weighted entropy is shown here for a range of diffusivities (left) and resolutions (right; note the energetics of the four cases are significantly different after the time marked). A correction has been applied to account for a slight drift in the total energy of the model. Theory: the horizontal scale of the surface fronts is limited to just above the gridscale by the diffusion. This occurs for all diffusivities and so the total amount of entropy produced is relatively invariant. At higher resolutions less mass has to be moved across isentropic surfaces to limit the scale of the fronts and a balance between diffusion and straining is reached earlier. • Conclusions: • Over days 5 to 10 the source averages 3mWm-2K-1 and varies little with diffusivity or increased resolution (at least above T63). • This source is comparable to the small terms in the entropy budget (e.g. frictional heating 7mWm-2K-1 from Peixoto et al. (1991)) and also to Johnson’s estimate of a 2mWm-2K-1 error leading to a cold bias of 10K. • However in Johnson’s theory it is the region bounded by the 300K and 325K surfaces which cools to offset an entropy source there, and in this lifecycle the source from diffusion is seen to be small in that region. There are clearly entropy errors of this size in GCMs in general (Goody (2000)), but if Johnson’s theory is correct it must be the representations of moist and diabatic processes which give significant spurious entropy sources in this region. References: Goody, R.: Sources and sinks of climate entropy. Q. J. R. Meteorol. Soc. (2000), 126, pp. 1953-1970 Johnson, D. R.: “General Coldness of Climate Models” and the Second Law: Implications for Modelling the Earth System. J. Clim. (1997), 10, pp. 2826-2846 Peixoto, J. P., A. H. Oort, M. de Almeida and A. Tome: Entropy Budget of the Atmosphere. J. Geophys. Res. (1991), 96, D10, pp. 10981-10988