Name _________________________

Date __________________________

Meteorology 430

Fall 2010

Lab 4

**Divergence**

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 work in mathematical problems.
No credit given if only

A. General

In
this lab you will compute horizontal divergence at the 300 mb level by finite difference approximation of the
derivatives ¶u/¶x and ¶v/¶y.

B. Case Study

You
are provided with the following maps for 00 UTC 28 September 1994:

1. 300 mb analysis with isotherms and
isotachs.

2. Unanalyzed 300 mb chart with raw data.

3. 300 mb Òu wind componentÓ

4. 300 mb Òv wind componentÓ

5. NCEP
Reanalysis of 500 mb
heights, Absolute Vorticity

6. NCEP
Reanalysis of Surface Pressure, 1000-500 mb
thickness.

7. 300 mb wind vectors with data
domain and analysis grid for this exercise.

C. Nature of Analysis

As
discussed in class (and Bluestein points out), horizontal divergence is the sum of two small derivatives
that often have opposite sign.
Finite difference approximation of the derivatives often shows that the
terms themselves may be one or two orders of magnitude larger than the net
divergence when both are added algebraically. Thus, wind speed components would need to be accurate to two
or three places in order for the resulting divergence estimates to be accurate.

It
is still a useful exercise to compute divergence from the expression in
rectangular coordinates and compare with the actual divergence field as
produced by the wxp programs. The case chosen is for a situation in
which a strong jet streak was moving around a relatively strong trough over the
eastern United States.

D. General Procedure

We
are going to use a relatively coarse analysis grid. Each point at which we would like to have divergence
estimates is 2.5 degrees of latitude and 5.0 degrees of longitude from the
adjacent point. It will be
interesting to see if your analysis captures the Òsynoptic scale flavorÓ of the
wxp field.

We
also will be using a so-called Òcentered differenceÓ approach in evaluating the
derivatives. That simply means
that the analysis point is at the origin of the finite difference cross and the
end points are a certain distance +/-Æs along the x and y axes from the origin.

The
finite difference approximations of the derivative ¶u/¶x are obtained at each
of the analysis grid points and the values are then plotted in black near the
analysis point. The finite
difference approximations of the derivative ¶v/¶y are then obtained at each of
the same analysis grid points then are plotted in blue at each respective
point. ** ****The algebraic sum of the
two should be plotted in green and then contoured at intervals of 2 X 10 ^{-5}s^{-1}
and then transferred to the 300 mb wind vector chart
(with the analysis domain).
**

To accomplish the calculations the interval Æs must
be selected. To do this, lay a
blank acetate on the analysis point at 47.5N, 95W. Draw a finite difference cross with the origin at the point
47.5N, 95W. The the interval Æx should correspond to 10 degrees of
longitude AT 47.5N. The interval
Æy will always correpond to 5 degrees of latitude.

Distance in KM of 10 degrees of longitude =
_____________ = Æx

Distance in KM of 5 degrees of latitude =
_____________ = Æy

In black, draw your cross on the acetate, as shown
in class. You will then simply
move your cross from analysis point to analysis point and compute the
derivatives on the basis of the values at the ends of the axes, as discussed in
class.

Students will work cooperatively[1]
to obtain ¶u/¶x and

¶v/¶y .

E.
Thought and Other Questions

1. Compare
and contrast your divergence analysis with that of wxp (distributed
to class separately from the lab).

2. Contour the
unanalyzed 300 mb charts for
heights and isotachs using conventional intervals.
Do NOT ask. Covered in Metr
201/400.

3. (a) Estimate
the qualitative nature of the SYNOPTIC SCALE divergence
on the basis of the vorticity advection shown on the Eta
initialization for the same area as your contour chart.

(b) Estimate
the qualitative nature of the forcing for vertical motion on
the basis of temperature advection shown on the NGM initialization
for the same area.

[1] Please remember that part of the learning experience is learning to deal with the perils, pitfalls and strengths of cooperation. The idea here is to have the students themselves deal with the micro-management of the task, just as you will have to when assigned group tasks in the real world. The instructor (or overseer, or boss) should not have to deal with petty squabbles, and should only be asked to adjudicate significant issues.

Each group should select an overseer, who should also participate in the calculations and other tasks. Each group should select a spokesperson who will interact with me if problems come up. Each group should work in tandem to perform the calculations.