ATSC 5007 lab 31
Synoptic Meteorology Lab 4
Feb 11, 2010
Quasi-geostrophic approximation, and vertical velocity
GEMPAK has a number of diagnostic functions that we will be exploring today as we continue our examination of the 28-30 January 2002 storm. As in last week’s exercise, we will be examining model output from the Eta model. Today we will use GEMPAK to analyze key processes associated with the open wave stage of the cyclone from the Eta model grids. We will use the *.nts files that we created last week as examples of upper air maps but will focus on diagnostics of actual processes. In doing so, we will learn about some of the ways that GEMPAK is able to produce detailed maps of processes discussed in lecture that are related to the development of a frontal cyclone. We will also use diagnostic capabilities built into GEMPAK to compute new parameters that will give us insight as to the vertical structure of the cyclone. For this and some later labs, you may want to refer to a gempak document “gempak grid diagnostic functions” available on
The first task is to log onto bat and then ‘cd’ into the directory you created last week for the model output. You should have soft links to all 10 time periods of interest. Remember that you can find out what grids are in a particular GEMPAK gridfile by using the program gdinfo. We will again use the program gdplot2 to create our isobaric maps. As discussed last week, a critical parameter to set in gdplot2 is GDPFUN. This parameter sets all the variables that you want to contour.
Part A: Determining the Rossby number from Eta model grid files
To start, we will examine the quasi-geostrophic nature of our storm from 0000 UTC 28 January to 0000 UTC 01 February 2002. From the lectures we know that the Rossby number is a good measure of whether the atmosphere can be considered to be in quasi-geostrophic balance. The Rossby number is simply a ratio between the total acceleration to the Coriolis force. Assuming gradient wind conditions this is also a ratio of the ageostrophic wind to the actual wind. The ageostrophic wind, in turn, is simply the vector difference between the actual wind and the geostrophic wind. GEMPAK has many diagnostic capabilities included. To get a glimpse of the sorts of built-in functions, start gdplot2 and type ‘help gparm’. This will give a long listing of all sorts of parameters and functions. Of interest are some of the vector grids. If you peruse the listing you will find information about standard vector grids:
Standard vector grids are:
WND Total wind
GEO Geostrophic wind
AGE Ageostrophic wind
ISAL Isallobaric wind
THRM Thermal wind
The Rossby number is just a ratio of the magnitudes of the ageostrophic wind vector to the actual wind vector. This can be done in GEMPAK by using the ‘mag’ or magnitude function that is under ‘SCALAR OUTPUT GRID’ in your ‘gparm’ listing. ‘mag’ provides the magnitude of any vector. To compute the Rossby number we need to divide ‘mag(age)’ by ‘mag(wnd)’. GEMPAK allows us to do that using the function ‘quo’ (for quotient) that is one of the basic arithmetic functions in the ‘SCALAR OUTPUT GRID’ portion of the GPARM listing. We can thus specify
GDPF=quo(mag(age),mag(wnd))
as a means to compute the Rossby number. For simplicity, let’s assume that a Rossby number of 0.5 is where we might begin to argue that the atmosphere departs significantly from geostrophy.
TASK
Create maps showing contours of the 300-mb height field and Rossby numbers. Examine the 300-mb map from the 12-hour forecast period for the 0000 UTC Eta runs for 30and 31Januaryand 01 February. You can view output in xwindows for this part; don’t worry about setting parameters that look good as a Postscript file. To help in answering questions below you can keep windows open from a previous time by providing names for your xwindow. For example, setting ‘DEVICE =xw|0030’ (for 0000 UTC 30 January run although you can name it what you wish) will open a window called ‘0030’. Each time you create a new contour plot, change the name of the xwindow. You can have several windows open at once so you can compare results quickly.
A1. What are the largest values of the Rossby number at 300-mb? Where do they tend to be located in relation with the 300-mb wave pattern?
A2. As the 300-mb wave progresses eastward (and the surface cyclone deepens), what changes in the pattern of the Rossby numbers are seen?
A3. Could you classify the 300-mb trof(trough) associated with the surface cyclone as “quasi-geostrophic”? Explain. (Hint: the QG framework assumes that Ro <1)
PartB: The geostrophic vorticity approximation from Eta model grid files
One of the key assumptions we have made in deriving the QG equations is that the advective wind can be approximated by the geostrophic wind and that the actual vorticity is about equal to the geostrophic vorticity. From our analysis above, we should feel somewhat confident that the winds are reasonably close to geostrophic. Does this imply that the geostrophic vorticity is a close approximation to the actual vorticity? We will choose the 0000 UTC 01 February time period to address this question using our Eta model output.Geostrophic vorticity you may remember is related to the Laplacian of the height field and can be expressed as:
You will note that the Laplacian of a scalar field can be computed by GEMPAK (again, see ‘help gparm’ and look for ‘LAP(S)’in the ‘SCALAR OUTPUT GRID’ listing, or in the gempak document “gempak grid diagnostic functions”). The function ‘LAP’ operates on a scalar variable ‘S’. In our case here, the scalar variable is ‘HGHT’. GEMPAK is also able to compute the Coriolis parameter and the variable name is ‘CORL’. One way to specify the geostrophic vorticity is to set
GDPF = mul(quo(lap(hght),corl),9.81)
Here we are using both the ‘quo’ (divides scalar quantities) and ‘mul’(multiplies scalar quantities) functions to calculate the geostrophic vorticity. At the heart of this operation is the’lap(hght)’ term, which calculates the Laplacian of the height field. Then we need to divide by the Coriolis parameter f (“corl”), and multiply by g (9.81 m s-2). To make sure that you did it right, compare it with
GDPF = VOR(GEO)
i.e. the vorticity of the geostrophic wind. The parameter of the function ‘VOR’ is a vector V.
TASK
Create two plots (you will need to create a Postscript file and print it out) of the 300-mb height contours (60-m increment), one with actual vorticity (VOR(WND)) and the other with geostrophic vorticity at 0000 UTC on 01 Feb 2002. Please contour vorticity every 5 x 10-5 s-1 . HINT: use the ‘SCALE’ parameter to specify appropriate scaling factor or power whichin this case is 5). Save your gdplot2 script as an *.nts file and print it out. Use your analysis to answer the following questions:
B1. How do the geostrophic vorticity values compare with actual vorticity values from the Eta model? Is the geostrophic vorticity a good approximation to the actual vorticity?
B2. On the 300 mb map,show the symbol at the location of the largest (actual) vorticity values from the Eta model.
B3. Show the symbol at the location of the largest gradient of vorticity.
B4. Show the symbol at the location of the largest values of vorticity advection by the geostrophic wind.
B5. Look at the surface map you created in Lab 1. With respect to the center of low pressure at the surface, where do you find the largest values of 300 mb vorticity and vorticity advection? QG theory expects the 300 mb vorticity advection to be a maximum over the position of the surface low? Is this the case?
PartC: Examining patterns of omega from Eta model grid files
The key variable of interest in the QG system is the vertical velocity omega. Patterns of precipitation are tied to the vertical motion field. Omega is also one of the key variables contained in the Eta gridded output. We will examine the spatial distribution of omega in terms of the surface cyclone and upper level wave features for the open wave stage of the cyclone at0000 UTC 01 February 2002. It will be instructive to compare fields of omega with those implied from our idealized cyclone discussed in the lectures. From Part A we can be reasonably certain that the general guidelines for QG flows are valid for the time selected.
One word of caution: model output does not contain QG omega. The only way to obtain QG omega is by computing the “forcing terms” (related to vorticity & temperature advection), and then do a 2D or (better) a 3D inverse Laplacian operation subject to some boundary conditions. The first step is possible in gdplot2. The second is not. Note that an inverse Laplacian operator operation acts a smoother, because it is a double integral: smaller features are damped more than larger features. The omega field in the ETA model is obtained prognostically (QG omega is a diagnostic), it includes vertical advection and of course terrain. You will see wave motion and non-QG circulations along fronts, for instance. In non-hydrostatic models buoyancy can forces ascent as well. Now, omega from high resolution model like ETA contains a lot of fine detail, and in fact in realtity vertical velocity is a complex field. A highly smoothed ETA_omega would be a good first-guess surrogate for the QG omega. Fortunately, GEMPAK has some smoothing options that we will use to make the fields a bit smoother. We will use the nine-point smoother (‘sm9s’) in this exercise.
For the time listed above, you will construct maps that consist of the 1000-mb height field, the 300-mb height field and omega at various levels. The idea here is to examine how the vertical velocity field varies with height. You will be creating 4 maps, showing the vertical velocity omega at 850-, 700-, 500- and 300-mb.To answer questions, start by simply creating maps in the xwindow format. To compare multiple maps, again simply change the ‘DEVICE = XW | plotlevel’ where ‘plotlevel’ may refer to the level specified in GLEVEL (the level of omega) or any other name of your liking.Since all maps will show the 1000- and 300-mb heights, you can ‘hard wire’ them in the ‘GDPF’ parameter so that you can simply change ‘GLEVEL’ to reflect the level for omega. GEMPAK allows us to override the ‘GLEVEL’ command (using the ‘@’ sign) to show variables at a different levels. An example would be:
GDPF = hght@300 ! hght@1000 ! sm9s(sm9s(omeg))
This commands GEMPAK to show the 300-mb height field, 1000-mb height field with omega at the level specified by ‘GLEVEL’. Note the use of the ‘sm9s’ command. By nesting two smoothing commands, you can get nice fields of omega (often just one ‘sm9s’ command is sufficient).
TASK
Hand in [that is, create a Postscript file and print out] a map showing
- the 300-mb heights at 60-m contour intervals (start at8400 m),
- 1000-mb heights (solid lines – color set to 1 and thickness set to 4, 30-m contour intervals, start at 0 m)and
- 500-mb omega values (dashed lines – color set to 4, dash pattern set to 12, thickness set to 3, scale of 3 (SCALE=3) with contours every 2 units from -20 to 0 to show only rising motion).
It is expected that you have the *.nts files from last week’s exercise to help with the GDPF settings for the isobaric maps. Note: I suggest that you contour ONLY the negative omega values becausenegative omega values correspond to rising motion.Remember to save your command listing as a *.nts file. We will refer to fields of omega again next week.
Use this map and your 4 XW maps (at 850-, 700-, 500- and 300-mb) to answer the following questions:
C1. The units of omega are in Pa s-1. If we assume that to a reasonable approximation,,
then what does 1 Pa s-1 refer to in terms of a vertical velocity in units of cm s-1 and units of km day-1?
C2. At what level do you find the largest values of (negative) omega?What are the largest values of vertical velocity in units of cm s-1?
C3. Do the centers of extreme omega values (strongest updrafts) change with height? If so, how so? Is there a westward tilt with height as for the position of trofs (vorticity maxima)?
C4. Physically explain how the updraftpatterns are related tothe surface cyclone and fronts.
C5. In Lab 3 you produced maps of 300 mb divergence and ageostrophic flow at this time (0000 UTC 01 February 2002). What is the spatial relationship between the 1000 mb low, the 500 mb updraft region (omeg minimum), and the 300 mb divergence?