where 
x is a distance. Consequently, if in the same distance
the difference in pressure is increased, the PGF is greater, or
similarly, if the difference is the same, the smaller the distance
between two set values of pressure, the greater the PGF.
An isobar is a line of constant pressure. Every value on
an isobar is the same. Likewise, an isotherm is a line of constant
temperature and an isoheight is a line of constant height. When
determining the strength of the PGF, it is useful to look at the
distance between two isobars of a set difference, 
. The closer
the isobars, or the tighter they are packed, the stronger
the PGF.
Because of a difference in pressure, air will travel from high
to low pressure to try to balance the imbalance. If one imagines
a marble rolling down an incline from high to low, one can visualize
air traveling "down the gradient". Therefore, the stronger
the gradient, the faster the winds.
Combining the Forces
Newton saidthatany change in motion must be the result of applied
external forces. In the atmosphere, these forces are gravity and
PGF (pressure gradient force) in the vertical, which gives us
the hydrostatic balance; and PGF, coriolis, centrifugal and frictional
forces in the horizontal (or compass directions). We will now
try to understand how these forces combine to produce the winds.
Case I Linear Upper-Level Flow (Geostrophic)
p- p -------------------------------- z- z
p -------------------------------- z CF=PGF
p+ p -------------------------------- z+ z
Click here for a the Geostrophic
Wind graphic
At "steady-state", the two forces are counterbalanced,
i.e. the resultant force is zero. The wind blows parallel to the
isobars with no acceleration.
RULE 1: PGF always act from high to
low.
RULE 2: Coriolis force always act to the
right of the motion.
Buys-Ballot Law: With the wind at your back, low pressure
is to your left.
Case II Curved Upper-Level Flow (Gradient)
We now add curved flow to the above which means we will have to
consider the effects of centrifugal force.
This time, coriolis force needs to balance both PGF and centri- fugal, hence V > Vg or Coriolis force does not "Supergeostrophic". need to be as great as in PGF + Centri = CF the geostrophic case, hence V < Vg or "Subgeostrophic". PGF= Centri + CF
Supergeostrophic Scenario (Ridge)
Subgeostrophic Scenario (Trough)
RULE 3: Centrifugal force always acts outward from the
radius of curvature.
Cyclonic: the direction the earth rotates. In the NH,
counterclockwise,
in the SH, clockwise. Indicates the flow around a low. The opposite
is anticyclonic.
Case III Curved Flow with Friction (Surface Winds)
Adding friction to the winds tends to slow the wind speed and
hence deflect it across the isobars toward low pressure. As a
result, wind will converge toward the center of the low and diverge
from the center of a high.
Graphic Coming Soon
RULE 4: Friction always acts opposite the direction of
motion, causing the wind to deflect across the isobars toward
lower pressure.
Vertical Balance - The Hydrostatic Equation
Air does not fall or fly away from the earth because there exists
a balance of forces in the vertical direction as well. Gravity,
which is accelerating the air toward the earth, is balanced by
the PGF in the vertical, or PGF = g. If we manipulate this equation
by substituting terms from the ideal gas law, and apply calculus,
we obtain a relationship between T and z, which states that
the thicker the atmosphere, the warmer the temperatures.
This is known as the thickness relation. Here z refers
to the distance between two pressure levels. In meteorology, it
is often the distance between 1000 mb and 500 mb. Simply stated,
the thicker the layer, the warmer the temperatures.
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