Latitudinal Comparison of the Geostrophic Wind Approximation
Jonathan D. Finch

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        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.