  We have previously shown that the nonlinear growth of a finite-amplitude
perturbation to a basic state given by a baroclinic zonal flow on the
$\beta$-plane in a thermal quasigeostrophic reduced-gravity model can be a
priori bounded. In this note we show that, unlike we stated earlier, Lyapunov
stability can be proved even when buoyancy varies linearly with the meridional
coordinate. In addition to rectifying our earlier results we expand them by
deriving an instability saturation bound by making use of the existence of such
a class of Lyapunov-stable basic states. This bound can be smaller than that
one we estimated before, reinforcing our previous conclusions. We also present
a numerical test of the accuracy of the derived bound.
