Synoptic Meteorology Lab 7
Mar 4, 2010
Frontogenesis
Please print out the following maps, for 00 UTC 01 February 2002. Please zoom in the domain a bit more than usual (e.g.
garea=24;-105;46;-70 and proj=lcc/25;-88;55).
You can complete this lab using gdplot2. Or you can use GARP. To use GARP for this case study, just type in casestudy on
bat and a little window should pop up, where you select the 2002 Kansas winter storm. Then you open the Model Plan
Projection within GARP. Make sure to select the same model data that you have been using in gdplot2. Note that many
functions such as frontogenesis and Q vectors are built-in.
You are expected to generate 4 maps, and answer 4 questions.
A1. Map geopotential height (thick solid contour, 30 m interval), temperature C (dashed or red contour, 3K interval) and
frontogenesis [frnt(thta,wnd)] (use contours or some color fill) at 900 mb.
A2. as above, but for geostrophic frontogenesis, i.e. frontogenesis by the geostrophic wind.
For both maps, note that the frontogenesis function is expressed in units of K/(100 km) /(3 hours).
We have shown (or will show) in class that geostrophic frontogenesis is proportional to the cross-isentrope component of
the Q vectors. T test this,
A3. Map geopotential height (thick solid contour, 60 m interval), potential temperature C (dashed or red contour, 3K
interval), Q vectors, and geostrophic frontogenesis [frnt(thta,geo)] (contours or color fill) at 800 mb.
Note that the gempak frontogenesis function corresponds with eqn (7.11) in Martin (2006), i.e. it is just the frontogenesis
due to the horizontal flow (2D frontogenesis).
FRNT Frontogenesis ( K / 100 km / 3 h )
FRNT (THTA, V ) = 1/2 * CONV * MAG ( GRAD (THTA) ) * ( DEF * COS (2 * BETA) - DIV )
where
CONV = unit conversion factor = 1.08E4 * 1.E5
BETA = ASIN ( ( - COS (DELTA) * DDX (THTA) - SIN (DELTA) * DDY (THTA) / MAG ( GRAD (THTA) ) )
DELTA = 1/2 ATAN (SHR / STR )
DIV(V) = DDX ( u ) + DDY ( v )
SHR(V) = DDX ( v ) + DDY ( u )
STR(V) = DDX ( u ) - DDY ( v )
DEF(V) = ( STR (V) ** 2 + SHR (V) ** 2 ) ** 0.5
The most important term offsetting this 2D frontogenesis is the tilting of isentropes by vertical flow. The magnitude of the
isentrope tilting term is given by
STAB(TMPC) * (DDX ( OMEG )**2 + DDY ( OMEG )**2)**0.5
A4. Map geopotential height (thick solid contour, 30 m interval), temperature C (dashed or red contour, 3K interval) and
the isentrope tilting term (use contours or some color fill) at 900 mb.
Questions
B1. Explain why 2D frontogenesis occurs where it does, in terms of the other fields plotted.
B2. Verify that that the isentrope tilting term is large in the same regions where the 2D frontogenesis term is large. (Note:
because the units are different, and the magnitude of the isentrope tilting term is plotted, neglecting its sign, you cannot
ascertain whether the two terms tend to cancel each other, rather than reinforce each other.)
B3. Explain the difference between total and geostrophic frontogenesis, especially in the vicinity of any fronts.
B4. Does it appear that geostrophic frontogenesis is proportional to the magnitude of the cross-isentrope component of the
Q vectors?