## 1. Introduction

[2] In their elegant survey of baroclinic instability theory *Pierrehumbert and Swanson* [1995] commented that ‘baroclinic instability is unambiguously successful in explaining why differentially heated rotating planets spontaneously generate transient eddies… and has yielded insights as to the interplay of baroclinic eddies and static stability…’ (p. 461). One focus of the present work is to explore an aspect of that interplay and the consequences of the temporal variations of meridional temperature gradients (or vertical shear) and static stability. There are many facets to the interaction of these two quantities which give rise to, at first sight, surprising results, and it is clear that the understanding of the influence of Southern Hemisphere (SH) static stability on a range of timescales is essential for obtaining a more comprehensive picture of cyclonic development in a broad range of contexts. For example, *Walland and Simmonds* [1999] discussed how the southern Semiannual Oscillation (and its associated cyclonic features) exhibits two high latitude surface pressure minima during the year, with the one occurring in October being more intense than that in March. The associated meridional temperature gradient at these latitudes is, however, stronger in March. They found this apparent paradox to be explained when allowance was made for the seasonal evolution of static stability, and then the larger peak of baroclinicity occurred in October. In general, the complexity of the high southern latitude environment dictates that nonlinearities and covariances (on synoptic timescales, for example) between fundamental variables are strong [e.g., *Simmonds and Dix*, 1989; *Gulev*, 1997; *Simmonds et al.*, 2005], meaning that the estimation of nonlinear quantities (e.g., surface fluxes) from mean fields (in either a temporal sense (e.g., monthly or seasonal) or spatial sense (e.g., zonal average)) is liable to significant error.

[3] Most studies of the instabilities of the SH circulation have been undertaken with the time mean basic flows. Among these are those conducted with normal mode analysis [e.g., *Berbery and Vera*, 1996; *Walsh et al.*, 2000], and those with sophisticated global instability models [e.g., *Frederiksen and Frederiksen*, 2007]. An issue of relevance to these is that, given the intimate connection between the mean flow and cyclonic activity, it is not entirely clear how the “basic state” should be defined in such studies. *Trenberth*'s [1981] analysis of SH eddies led him to comment that ‘the “basic state” for instability studies is not necessarily the same as the observed mean flow' (p. 2604). *Holloway* [1986] also remarked that ‘… there is the disturbingly nontrivial problem of distinguishing mean and fluctuating fields… This problem is compounded when we ask the dynamical question, how are mean and fluctuating fields interrelated?' (pp. 91–92). Similar sentiments were recently voiced by *Descamps et al.* [2007].

[4] Here we address an aspect of this issue by considering the sensitivity of mean baroclinic growth rates calculated from the *Eady* [1949] formulation. Under this very commonly-used framework the maximum growth rate of eddies is proportional to the ratio of the meridional temperature gradient and the Brunt-Väisälä frequency. Because this expression for the growth rates is nonlinear, it is clear that a true appreciation of the mean Eady growth rate cannot strictly be determined from the mean atmospheric state, but rather the mean rate should be determined from the mean of the instantaneous growth rates calculated over some extended period. (Only a handful of (Northern Hemisphere (NH)) studies have adopted this approach, but they presented no quantification of the sensitivity of the growth rate calculated in these two ways.) Our goal in this paper is to quantify and explain the bias in calculating Eady growth rates using a time-mean state.