Lab #9: Diagnosis of Terms in QG w-equation

Objectives: Use GEMPAK to diagnose terms in the quasi-geostrophic omega equation.

Omega Equation

One way to diagnose vertical motion in the atmosphere is to look at the terms in the quasi-geostrophic omega equation. For this lab, we will focus on two of the terms from the right hand side of the omega equation: 1) differential geostrophic vorticity advection and 2) the Laplacian of geostrophic temperature advection.

Scale Analysis

Perform a scale analysis to find a typical scale for each of the terms. For each component of each term, use values that one might encounter for typical mid-latitude weather systems. Also perform a scale analysis of the horizontal temperature advection.

GEMPAK

Now that we know a scale for each of the two terms, we can look at them for a real case. Using the same case as in Lab #8, plot the two terms from the omega equation the forecast time of your choice from the MM5 simulation (the file is written out in 3 hour intervals, out to 36 hours). Please do not choose the analysis time (f00). The file you need to use can be found at:

/class1/aos452/dtkleist/aos452/00012400.mm5v2.pres.gem

Create a four panel plot containing the following variables :

· horizontal temperature advection (not term 2) at 700 hPa – upper left

· negative Laplacian of temperature advection (term 2) at 700 hPa – upper right

· differential geostrophic vorticity advection from 850 hPa to 500 hPa – lower left

· negative omega (use color filling, see supplement for instruction) at 700 hPa, and 700 hPa heights (contour)

For each figure, omit the zero line, contour the positive values using a solid line, and contour negative values using a dashed line. Please identify the forecast time on the figure.

Hints:

First, try to do each panel separately using an x-window. Once you think you have figured out how you want that portion of the figure, add it to a script that will plot all four panels at once. Take a look at Lab #5 to see how to create 4-panel figures using scripts. Since we are focusing in on the Southeast United States, be sure to choose the garea accordingly. For each of the terms, be sure to do a phelp on the gfunc parameter to look for shortcuts to writing out long expressions (there are shortcuts for plotting advection, absolute vorticity, Laplacian, etc.). For the last panel, set the following parameters:

GFUNC = mul(-1,omeg)

SCALE = 1

Since you are doing color filling (in gray scale), I’ll let you choose appropriate values for the fint and fline parameters. I’d expect values for negative omega to range anywhere from –5 to 25, or even larger.

To be turned in (due Tuesday 15 October 2002)

Please turn in your scale analysis for the three terms as well as the four panel figure. Prepare a brief write-up of your findings for your forecast time. What are some differences between the temperature advection and the Laplacian of the temperature advection? Was the forecasted vertical motion (negative omega) successfully diagnosed by using the two terms from the QG omega equation? If there are differences, what may be causing the differences? Were their regions in which cancellation occurred between the two terms (regions of opposite sign, and therefore opposite diagniosis)? How might we check to see if there are other “reasons” for the vertical motion? Did either term from the omega equation appear larger in the scale analysis? How about from the figures? Was anything left out here from the omega equation (such as the stability parameter etc.)? How might this affect the diagnosis?

GEMPAK – Color Filling Variables

It is often beneficial to use color filling, instead of line contouring to plot certain variables. This is especially true when doing overlays of several variables. The parameter that controls contouring algorithm (whether to use lines or color filling) is ctype. You need to set this parameter to ‘c’ (for contouring) or ‘f’ (for color filling). You can also use a combination of both by setting ctype = c/f. This will do the color filling, but will also overlay the contour lines.

If you choose to use color filling instead of line contouring, you will need to specify the intervals in which you want to color fill, and the color to use for each interval. The parameters you need to change will be fint (used to define the interval) and fline (used to define the color range for each interval). Please do a phelp on each of these parameters to see how they need to be set.

For both parameters, you can set a range of values. You would set an interval (much like the cint parameter), and a range of colors to use. This is fine for grayscale figures (postscript), but the default colors used for x-window or gif images is often less than desirable. To account for this, it is possible to set specific colors for each range of values. For the fint parameter, this means setting the start/end value for each interval, separated by semi-colons. If we had some variable that we wanted to color fill using an interval of one, the parameter would be set as follows:

fint = 1;2;3;4;5;6;7;8;9;10

Once you set the fint parameter this way, you will need to set the fline parameter to account for each interval. In the above example, this means setting a color for each of the following intervals:

<1, 1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9, 9-10, >10

Notice how there are 11 intervals we need to define colors for, since we set 10 values. Just using a random set of colors, we may want to set the interval parameter as follows:

fline = 30;29;28;27;26;25;24;23;22;21;20

You always need to have one more color in the fline parameter than values in the fint parameter.

GEMPAK has a default set of colors to use, and each color has a number associate with it. If the device is set to xv (x-window), gf (gif), or psc (postscript color), the range of values for the colors goes from 1 to 31. A decent spectrum of colors exists as you work backwards from 30 (purples) down to 15 or so (reds).

If you are creating a grayscale image (postcript), the range of colors goes from 1 (black) to 20 (light gray). This is important if you are looking at graphics using an x-window, and later want to create a postcript, as the color scheme is different for grayscale.

You can type phelp colors to read up more on the color scheme within GEMPAK.

See the GEMPAK online tutorial, or use the GEMPAK help function for any other information you may need.