[1] As in Ch. 1 of this volume, we use the term "deep moist convection" rather than "thunderstorm" since not all severe forms of deep, moist convection produce lightning and, hence, thunder.

[2] We assume that the presence of the LFC implies that the convection will, indeed, be "deep" although rare exceptions to this might be found.

[3] Phillips attributes the first use of the term "quasi-geostrophic" to Sutcliffe (1939). However, Sutcliffe (1938) includes the following passage: "It is suggested that the term 'quasi-geostrophic' would be a better description in that the motion is geostrophic only to a first approximation."

[4] This also can be inferred from a static stability tendency equation; e.g., Panfosky (1964; p. 105 ff.).

[5] Obviously, there are geographical circumstances where this may not be the case. Notable exceptions include Europe and Australia, where large, arid subtropical and tropical land masses are present equatorward of mid-latitudes. Meridional flows in such places typically transport dry air poleward; moisture is brought into midlatitude regions by predominantly easterly or westerly low-level flows that have a long fetch over warm, open waters. Such flows are also strongly modulated by ETCs, of course.

[6] The term "synoptically evident" was used in Doswell et al. (1993) to imply a synoptic pattern associated with tornado outbreaks. These involve strong synoptic-scale forcing and the presence of substantial CAPE in the presence of strong flow and vertical wind shear. It is by no means "evident" in advance which days are going to produce tornado outbreaks, but it is often possible to say retrospectively that there was a strong synoptic-scale signal suggesting the possibility of such an outbreak.

[7] For some minor technical reasons, however, the QG form of PV is not a "proper" vorticity, as mentioned in Hoskins et al. (1985), Davies-Jones (1991) and Hakim et al. (1996).

[8] Note that there are two maxima in the difference field: one is north and northeast of the surface low in a region of strong, saturated ascent over the warm front, while the other is southeast of the surface low, associated with parameterized convection.

[9] The ratio of the sensible heat flux to the latent heat flux is known as the Bowen ratio (see Stull 1988, pp. 274 ff.). The surface heat balance requires that the net incoming solar radiation minus any upward heat flux from the soil must equal the sum of the sensible and latent heat fluxes.

[10] It is not obvious that viscosity in the PBL is always dominated by the presence or absence of dry convection; the presence of vertical wind shear in the PBL also contributes to eddy mixing. The diurnal growth of a neutrally-stratified boundary layer promotes mixing and so in a sheared environment produces vertical momentum transports. The momentum from higher levels mixed downward tends to reflect the flow aloft and so the isobaric crossing angles observed need not fit those expected from simple Ekman pumping. Thermal advection also complicates the simple picture of a convectively-dominated PBL.

[11] Graziano and Carlson (1987) defined this index as , where is the saturation wet-bulb potential temperature at the warmest point in the inversion, and is the vertically-averaged value of wet-bulb potential temperature between 30 and 80 mb above the ground.

[12] The reduction of eddy viscosity to negligible levels does not occur instantaneously, of course; this simplification is simply for illustrative purposes.

[13] At 30 deg latitude, the period is exactly 24 h and so the inertial oscillation is in phase with the heating cycle at that latitude.

[14] This ignores the effect of synoptic-scale ascent on the sounding itself, of course. That ascent would tend to reduce any CIN and make initiation of convection more likely.

[15] However, not every "synoptically evident" situation produces significant outbreaks of severe weather. Although major outbreaks of severe convection are often associated with vigorous ETCs, not every vigorous ETC results in severe convection.

[16] The veering of the wind through a deep layer also suggests deep warm thermal advection, which is associated with ascent, quasigeostrophically.

[17] Note that, as discussed earlier, inferring vertical motion from the rhs of the Omega Equation (Eqn. 2) can be perilous. In this case, the pattern had considerable vertical coherence and is correspondingly likely to represent the vertical motion pattern reasonably well.