Name _________________________
Date __________________________
ERTH 465
Fall 2015
Lab 4
Analysis of 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. Unanalyzed 300 mb chart with raw data.
2. 300 mb “u wind component”
3. 300 mb “v wind component”
4. NCEP
Reanalysis of 500 mb heights, Absolute Vorticity
5. NCEP
Reanalysis of 1000 mb heights, 1000-500 mb thickness.
6. NCEP
Reanalysis of 500 mb Vertical Velocity.
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 the same distance on the meridians (but it won't be 2.5 degrees, as explained in class. 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).
Map Analysis
To get a feeling for the synoptic pattern, first contour the unanalyzed 300 mb charts for heights and isotachs using conventional interval (12 dm for height contours in solid black; 20 knot intervals in solid purple starting at 50 knots for isotachs). Use acetate first and get approval from me before transferring to the final copy.
Calculation
To accomplish the calculations the interval Æx and Æy 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 5 degrees of latitude. The interval Æy will always correpond to the magnitude of 5 degrees of latitude (as explained in class).
= 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.
Teams:
Nick, Amanda
Devin, Xiomara
E. Thought and Other Questions
1. Compare
and contrast your divergence analysis with that from the North American Reanalysis.
2. (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.