Name _________________________

Date __________________________

Meteorology 403

Fall 2008

Lab 3

**Divergence**

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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

answer
is provided.

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. NGM Initialization of 500 mb heights, Absolute Vorticity

6. NGM Initialization 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 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 NAM
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.