Homework Questions for Chapter 12 - Mid-Latitude Cyclones

Consult Syllabus for Due Date

Questions 1 and 2 will be turned in for a grade.

SHOW ALL WORK , CIRCLE THE CORRECT ANSWER, PLEASE BE NEAT AND STAPLE YOUR HOMEWORK!

ALSO, PLEASE USE A SPREADSHEET FOR ALL GRAPHS

Follow the Problem solving steps discussed in class

1.  Consider an area of low pressure with a fixed depth, D located at 45 degrees north.  Assume that the air within this column is rotating cyclonically with a tangential wind speed of 10 m/s.  Further assume that the radius of this rotating column of air is 1000 km.

a.  What is the planetary vorticity for this column of air?  The planetary vorticity, f, is defined as 2Wsinf where W is the planetary rotation rate and f is the latitude.

b.  What is the relative vorticity for this column of air?  Relative vorticity is defined as: z_r = Dv/Dx - Du/Dy

c.  Assume that the absolute vorticity for the column of air does not change with time.  If the column is moving northward, how will the relative vorticity change?  How will this affect the central pressure of the low?  Explain with the aid of a diagram.

2. Mid latitude cyclones are important for transporting heat poleward.  This can, in part, be accomplished by advecting cold air southward and warm air northward.  The magnitude of the temperature advection can be expressed as:

Temperature Advection 

where U is the west-east component of the wind and V is the north-south component of the wind.  T is the temperature of air. 

Let's say that you are on the east side of an upper-level trough.  The isotherms are oriented west-east and the winds are 20 knots out of the south.  The temperature increases by 5 K as you move southward by 100 km.

a.  Draw a picture of this situation.

b.  What is the magnitude of the temperature advection?  Is it warm or cold air advection? 

c.  Let's say that the air at 3 km has an initial temperature of 0 degrees Celsius.  If the southerly air flow is also ascending in a saturated manner by 1 km, what will be the final temperature at your location two hours later?  You can assume that the saturated ascent occurred over the two hour period of time and that the parcels of air ended up at 3 km.

3.  Would a wave cyclone intensify or dissipate if the upper trough were located to the east of the surface disturbance?  Explain with the aid of a diagram.

4.  Explain why at 500 mb, when cold-air advection is occurring, the air temperature does not drop as fast as it should.

5.  Over the earth as a whole, would you expect the atmosphere to be mainly barotropic or baroclinic?  Explain.

6.  Baroclinic waves seldom form in the tropics.  Why?

7.  If you only had isotherms on an upper-level chart, how would a cut-off low appear?

8.  How are short waves identifiable in weather data?  Another words, which maps would you use to identify their location?  Where are they today?

9.  Identify regions of cold-air advection and warm-air advection today over the U.S. and Canada.  By looking at representative soundings, how do the winds at low levels change direction with height in the region of cold-air advection and warm-air advection? 

8.  Suppose that the earth stops rotating.  How would this affect the earth's vorticity?  What would happen to the absolute vorticity of a moving air parcel?  If the parcel were initially moving southwestward, how would its direction change, if at all?

9.  Assume that the lapse rate is 6.5 degrees Celsius per kilometer here at LSC.  If cold-air advection is occurring aloft such that at 500 mb (6 km AGL) the rate of cooling is 0.2 degrees Celsius per hour, what will be the resultant lapse rate 6 hours later?  Has the atmosphere stabilized or destabilized?

EXTRA CREDIT:  Consider a rotating tube of air where the axis of rotation is parallel to the ground.  Physically, how can one generate vertical vorticity from this horizontally oriented rotating tube of air?