1. 2 Trough
3 Ridge
1 Geostrophic Wind
Geostrophic flow (VG) in thermal
wind balance between cold polar air
(blue) and warm tropical air (red).
Pressure gradient (𝛻ϕ), induced by
the surface temperature gradient
(𝛻T), which results in a pressure
gradient force that drives the wind.
Thickness of the warm tropical
troposphere is larger than that of the
cold polar troposphere.
Curvature of the geostrophic wind
(VG) around a trough of cold air.
The direction of the pressure and
temperature gradients have been
altered, creating a second derivative
(local minimum, 𝛻2ϕ) in pressure
and temperature around which the
wind curves counter-clockwise.
The trough is an upper level low
pressure region.
Curvature of the geostrophic wind
(VG) around a ridge of warm air.
The direction of the pressure and
temperature gradients have been
altered, creating a second derivative
(local maximum, −𝛻2ϕ) in pressure
and temperature around which the
wind curves clockwise.
The ridge is an upper level high
pressure region.
Trough (Low)
Ridge (High)
𝛻ϕ
𝛻ϕ
𝛻ϕ
𝛻T
𝛻T
𝛻TVG
COLD WARM
0°C 10°C 20°C
isotherm
𝛻ϕ
𝛻T
VG
0°C
10°C
20°C
isotherm
𝛻ϕ
𝛻ϕ
𝛻T
𝛻T
𝛻ϕ
𝛻T
VG
0°C
10°C
20°Cisotherm
𝛻ϕ
𝛻ϕ
𝛻T
𝛻T
𝛻2ϕ
−𝛻2ϕ
REFERENCES:
Holton, J. R. (1992), An introduction to dynamic meteorology, 3rd ed., Academic Press, San Diego.
Martin, J. E. (2006), Mid-latitude atmospheric dynamics: A first course. John Wiley & Sons.

2. 2 Advection
1 Thermal Wind Shear
Geostrophic flow at an upper level
(VG 700), whose flow direction is
shifted from that of the geostrophic
flow at a lower level (VG 1000).
The thickness between the two
constant pressure surfaces (light
shaded region, or height of ϕ 700
minus ϕ 1000), is lower in the cold air
and higher in the warm air.
The change in direction between the
upper level and lower level flow
(i.e., the wind shear), can be
evaluated as their vector difference
(VG 700 - VG 1000), which we denote
as the thermal wind shear (VT).
From this wind shear condition, we
consider the average geostrophic
flow (VG avg) for this entire vertical
section of the troposphere, and note
that VG avg advects the average
column thickness, or temperature
gradient (𝛻T).
As such, a geostrophic flow that
backs (turns counter-clockwise)
with height implies cold air
advection.
𝛻T
VG 700
COLD
WARM
ϕ 700
ϕ 1000
COLD
WARM
VG 700
VG 1000
VG avg
VT
VT
VG 700
VG 1000
VG 1000
REFERENCES:
Holton, J. R. (1992), An introduction to
dynamic meteorology, 3rd ed., Academic
Press, San Diego.
Martin, J. E. (2006), Mid-latitude
atmospheric dynamics: A first course. John
Wiley & Sons.