Homework 5: The Coriolis Parameter and the Geostrophic Wind

Due May 10.

(a) Discuss why Coriolis Effect is maximum at the Poles and minimum at the Equator. Your answer should include reasoning based upon the equation in the handout, but should also have a section giving descriptive reasoning.

(b) Calculate the value of the Coriolis acceleration at our latitude for a wind speed of 10 m s^-1. The angular velocity of the earth is 7.292 X 10^-5 s^-1 and our latitude is approximately 40⁰ N. 40⁰ is approximately 0.6891 radians.

(c) You are provided the 500 mb analysis (without data plots) for 12 UTC 9 February 2005.  Note the station in southeastern Oklahoma (indicated by the square).  The line segment shown is a portion of the "n" axis (normal to the flow) at that location, with the segment length shown there (delta n) = 300 km.

 

1.  The geostrophic wind speed can be calculated from the expression

 

 

 

 

where g is gravity, 9.8 m s^-2 , f is the Coriolis parameter, numerically equal to approximately 10 X 10^-5 s^-1 at around the latitude of the station shown, delta z is the difference in 500 mb heights normal to the flow measured along the increment delta n (remember, to estimate a gradient, take the value at location 2, furthest along the positive directon of the given axis, and subtract from it the value at location 1.)

 

Estimate the value of the geostrophic wind in meters per second, kilometers per hour and knots at the location shown and plot the value with conventional weather map symbols for wind directon and wind speed (knots) on the map.

Caution, Caution:  the challenge here will be to keep units consistent initially.  Please remember that when you solve for the geostrophic wind speed using the above expression, your result will initially be in meters per second.  You will need to convert that to kilometers per hour and knots. Remember that a nautical mile is 6040 feet.

 

2.  With a long arrow/streamline drawn right on the chart, locate the position of the fastest current (the polar jet stream).

 

Fig. 1: 500 mb chart for 1200 UTC 9 February 2005