There are two equations that form the basis for understanding ALL pressure systems and the vertical motions associated with them for which the Rossby Number is <<1. These two equations allow one to systematically understand the forcing on the basis of categories, rather than by considering each circulation system to be a different "thing". These equations work for all places and all times, whether in the past or in the future, as long as the flow is quasigeostrophic. This is the manner in which the physical processes we are studying today in the area of synoptic and mesoscale meteorology will help you understand the development (or location) of major pressure systems in the climatic past or in the climate change future.
Full Quasigeostrophic Height (Pressure) Tendency Equation
Full Quasigeostrophic Omega (Vertical Velocity) Equation
The Height Tendency Equation is a prognostic equation and the Omega Equation is a diagnostic equation. In both equations, Term A and Term B are considered together and are often referred to as "the dynamics" or "the dynamic terms". The full equations (but without Term D) form the basis (gives meteorologists the "permission") to refer to so-called Dynamic and Thermal Lows.
The equations above are only quasigeostrophic, and do not include effects related to strongly non-geostrophic features such as fronts, jet streaks, interaction of flow patterns with topography and others. Also, remember that the vertical motion associated with BUOYANCY is not considered here and is a separate topic. However, the pressure patterns and vertical motion patterns that develop as a result of the effects quantified by these equations can create environments that encourage motion of moist air masses that contribute to, for example, high CAPE situations.
Dymamic Pressure Systems
Terms A and B are strongest in the vicinity of jet streams, since vorticity advection is strongest at the core of the jet, in general, and the baroclinic pressure systems associated with the most significant temperature advection are linked to the divergence fields at jet stream levels.
Thermal Pressure Systems
Term C is strongest in the seasonally and diurnally-forced temperature patterns over the continents and the oceans. This term is associated with height (pressure) falls in areas of strong heating.
Modification of System Intensity by Friction
Term D acts to modify the pressure changes associated with the other three terms. For example, any low pressure system weakens when traversing areas of rugged terrain due to the mass convergence (filling of the low) that occurs because the balancing effect of Coriolis weakens as wind speeds abate due to friction. The opposite is true when pressure systems move over areas with less significant frictional effects (as, over the ocean).
How Do These Things Work?
In reality, of course, nature does not know these artificial boundaries. However, humans can simplify the physical explanation for pressure systems by neglecting one or more of the effects (neglecting on an order of magnitude basis).
For example, during the summer in the lower midlatitudes, jet stream effects are weak or absent...and Terms A and B can be neglected. Term D is often small also, compared to Term C. As a result, global pressure patterns are dominated by surface lows over the hot continents and surface highs over the cold oceans, in the absence of complicating factors. These are the so-called Monsoonal or Thermal Lows and Highs found in most geography and beginning meteorology texts. According to the concept map above, these lows should be warm core and the highs are cold core. (Possible Senior Thesis Topic)
During the winter, in the middle latitudes, Terms A and B can be larger than Term C, when strong jet streams are present. Terms A and B are associated with the effects linked to migratory short wave ridges and troughs in the jet stream, which in turn connect to the pressure patterns known as wave cyclones. Nevertheless, even when making this simplification, the fact that wave cyclones tend to weaken initially when passing over the cold continents (even without consideration of topography), is consistent with the above equation. (Possible Senior Thesis Topic)
During the winter during times of drought in the West, for example, it is often observed that the so-called Thermal Pressure systems (i.e., the Great Basin High) seem to dominate the pressure pattern in the West. That is because temporarily Term C dominates. (Possible Senior Thesis Topic)
During the late summer, "dynamics" often modulate the "thermal" effects in subtle ways at the latitude of California.