Remarks on quasi-equilibrium theory

A recent article by J. I. Yano has indicated that there is an inconsistency in the original formulation of the quasi-equilibrium theory of Arakawa and Schubert. He argues that this inconsistency results from a contradiction in the two asymptotic limits of the theory; that is, the fractional area covered by convection, and the ratio of the convective adjustment and large-scale timescales cannot simultaneously go to zero, sigma --> 0 and tau(ADJ)/tau(LS) --> 0. Yano cites the heat engine theory proposed by Renno' and Ingersoll as "formally establishing'' this contradiction. It is demonstrated in this paper that the quasi-equilibrium framework originally developed by Arakawa and Schubert is perfectly consistent with the heat engine theory for steady-state convection, that is, when the timescale associated with the large-scale forcing tau(LS) approximates the effective adjustment timescale of the large-scale ensemble of convective clouds tau(EFF). Indeed, the quasi-equilibrium framework states that, on the large scale, the atmosphere is in quasi steady state.