Name _________________________

 

Date __________________________

 

 

 

 

 

 

 

 

 

 

 

Meteorology 430

Fall 2010

 

 

 

Lab 2

 

Review of Basic Techniques

 

(Due Beginning of Class, Friday 10 September)

 

 

 

 

1.  All labs are to be kept in a three hole binder.  Turn in the binder when

     you have finished the Lab.

 

2.  Show all PROCEDURE.  No credit given if only

     answer is provided.

 

3.  Unless otherwise noted, you may work together.  But remember, YOU

     are the one who will be responsible for understanding the material for

     exams and when you are out in the profession.  So STRIVE to

     understand what you are doing.  Don't let someone else do your

     thinking for you.


1.  Determine the value of a degree in km at 40oN latitude (trigonometry).

 

a = radius of earth = 6370 km

 

                           r = radial distance to the axis of rotation which,

                           by simple geometry, = a cos phi where phi is  the  latitude

 

                          Circumference = 2π R

 

                           Distance (km) of 1o  =  (Circumference)/360 o

 

                           For latitude R = a and a degree is (2π 6370 km )/360 o = 111.3 km

 

                           For longitude R = r and a degree  is (2π 6370 km cos 40)  = 85.3 km

 


2.  (a)          Give the PHYSICAL INTERPRETATION of each term of

 equation (cartesian coordinate) below, where V is the three   dimensional wind vector:

 

Temperature Tendency

 

 

 A              B                       C

 

     (b)         Name each term in equation.

     (c)          Solve the equation for the local tendency.

     (d)         Expand term "C".

     (e)          Assume that dT/dt = 0 for the chart given and that there is no vertical motion. Determine the local temperature tendency at the station reporting the wind of 225o, 25 knots, shown in the diagram below.  External grid points indicated by crosses are 100 km distant from station, nominally placed at center of implied x-y coordinate cross.  Isotherms are north-south.

 

 

 

 

(a)    A is the temperature change experienced by the moving parcel, as if a thermometer moved with the air parcel..  B is the temperature change measured at a location fixed with respect to the surface of the earth.  C is the contribution to the local temperature change made by cold or warm advection.

 

(b)

 

Term A

 

Term B

 

 

Term C

 

(c)

 

 

(d) 

 

(e)

 

 

u and v are the horizontal wind components, but there is no north/south

temperature gradient in this case.  Hence,

 

 

where u = 25 knots (sin 45) = 17.68 knots = 32.5 km h-1

 

The temperature change will be entirely due to advection,

 

-1.6o C h-1


3.  (a)  Physically interpret the terms to the right of the equals sign in

           equation (2) (basic calculus)

 

                                               

    

 

 

(b)          Equations (3a,b) are the geostrophic wind components. Put (3a,b) into (2) to determine the divegence of the geostrophic wind.  Assume    g and f are constants.  I realize we have not discussed divergence, or horizontal divergence.  But this question involves you working with the mathematical operations, not the meteorological interpretation.

 

 

 

4.  (a)  Physically interpret the terms to the right of the equals sign in

           equation (2) (basic calculus)

 

                                              (2)

 

 

                                                         (3a, b)

 

     (b)         Equations (3a,b) are the geostrophic wind components. Put (3a,b)                        into (2) to determine the divegence of the geostrophic wind.  Assume                            g and f are constants.

 

(a)    ∂u/∂x is the horizontal shear of the west wind along the x axis or

         the variation of the west wind along the x axis or the variation of the west   wind speed along the  x axis.

 

         ∂v/∂y is the horizontal shear of the south wind along the y axis or

         the variation of the south wind along the y axis or the variation of the         south wind speed along the  y axis.

 

(b)

 

                                                                    (1)

 

 

                                                                            (2a, b)

 

 

 

         Put Eq 2(a,b) into (1)

 

                                              (3a)

 

 

                                                          (3b)

 

            Equation (3b) states that the horizontal divergence of the geostrophic wind is related to the variation of north-south slope of an isobaric surface along the x-axis and to the variation of the west-east slope of an isobaric surface along the y-axis.  However, the second derivatives are identical but opposite sign, so the horizontal divergence of the geostrophic wind

 

 

                                                DIVh = 0                                             (4)


4.       Obtain a plot of the NAM initialization of 500 mb heights and     absolute vorticity AND surface pressure with 1000-500 mb          thickness at initialization time for 12 UTC 31 August 2010.

         (a)      Write out the script you executed on the command line to obtain this.

         (b)     Append -p on the command line after the command to print a black and white copy to turn in with this lab.

 

5.       (a)      Use the script mod_grib -p to print out a copy of the 500 mb     heights for 12 UTC 31 August 2010.

         (b)     Annotate troughs and ridges as we did in Metr 201 (and Metr    400).

 

6.       For the sounding distributed (KOAX 12 UTC 31 August 2010), determine the

         (a)      LCL, LFC and CAPE and CIN areas for 12 UTC (first copy);

         (b)     CT, and CCL (second copy)

        

Make sure you draw everything neatly and use the correct color conventions.