**Latitudinal Comparison of the Geostrophic Wind Approximation**

**Jonathan
D. Finch**

**Links**

**Main
Page**

**Elevated
Mixed Layer**

__Convective
Outlooks for Bengal__

__Special
Cases for the United States__

__Bengal
Tornadoes--background information__

__Meteorological
Charts for Historical Tornado Cases for Bengal__

**Assessing
Instability on the Front Range Without Upper Air Data**

**Potential
Temperature and Mixing Ratio--Contributions to CAPE on Elevated Terrain**

Back in the mid 1990s, when
I first started analyzing upper air charts for the Indian subcontinent,
I noticed that relatively strong

500mb flow occurred with
small geopotential height gradients. I used the geostrophic wind approximation
to help explain this.

In mid-latitudes, the coriolis
and pressure gradient forces are approximately an order of magnitude larger
than acceleration and

frictional forces. The balance
between pressure gradient and coriolis forces is termed “geostrophic balance”.
This approximation

is generally valid to within
10-20%, even at fairly low latitudes(Carlson, 1998). In the following
zonal geostrophic wind equation,

Ug is the zonal geostrophic
wind, g is acceleration due to gravity, f is the coriolis parameter and
dz/dy is the latitudinal, geopotential

height gradient.

Ug = -g/f (dz/dy)

The Coriolis parameter is
a function of sin(latitude) and is defined as twice the vertical component
of the Earth's angular velocity about

the local vertical, and
is given by:

Ug= - 67123/(sin of latitude) * (dz/dy) where z and y are in meters

For a 500mb geopotential height gradient of 60m(decreasing height poleward) over 300km or 300,000m:

Ug = -67123/(sin of latitude) * (.0002)

Ug = -13.4/(sin of latitude)

For Winnipeg, Manitoba (50N):
Ug = -13.4/(-.766)= 17.5m/s = 34kts

For Minneapolis, MN(45N):
Ug= -13.4/(-.707)= 19m/s = 36.8kts

For Amarillo, TX (35N):
Ug = -13.4/(-.573)=23.4m/s = 45.4kts

For Dhaka, Bangladesh(23.8N):
Ug = -13.4/(-.403)=33.25m/s = 64.6kts

So, if we assume that the
geostrophic approximation is valid down to 23.8N, then identical 500mb
geopotential height gradients

yield markedly different
geostrophic wind speeds at varying latitudes. For any identical, 500mb
zonal height gradient, the windspeed

at Dhaka would be (sin45/sin23.8)
1.75 times greater than at Minneapolis. This is why I use a smaller contour
interval when analyzing

upper air charts for Bengal.
Using the typical 60m interval that many use at high latitudes will simply
not work for the Bengal region. I

typically use a 30m contour
interval when analyzing 500mb charts for Bengal.

Of course, the above finding
is true for straight flow. During strong cyclogenesis or in amplified flow
regimes, the geostrophic

approximation breaks down.