Kinked Contours

Date : 8 May 1999

If you look at weather analyses more than occasionally, I am sure that some time you saw a map which looks like this:

The feature I particularly refer to here is the shape of the isobars at the front. Though observations often indicate that isobars kink along a front as shown, the situation may be more subtle. Actually, the shape shown may be valid for a trof (or localized minima) of any type of contour, not only isobars. A surface trof coinciding with a front is a special case of the general situation for which the trof line may lag or much more often precede the front (i.e., a prefrontal trof):

A front is obviously not an infinitesimally small boundary between cold and warm air (strictly, dense and light air) as depicted, but a transition zone between 2 such air masses. In the AMS publication Mesoscale Meteorology and Forecasting, Howie Bluestein presents a discussion of fronts which includes among more complicated things a simple frontal model. A sloping frontal boundary separates air masses of differing densities as illustrated below:

He called the x-axis above the y-axis, but I thought that might be a bit confusing. He took the right diagram from Petterssen's Weather Analysis and Forecasting book. The equation:

dP = P/x dx + P/z dz

P : surface pressure

is pressure change, written as differential form. Thus he mentions that the simple equation:

dz/dx = ([P/x]c - [P/x]w) / (g (rc - rw))

r : density

relates variables in the diagram. Subscripts c & w refer to cold & warm sides of the frontal boundary, respectively. Please notice that dz/dx (Dz/Dx, which is (change of z) ÷ (change of x)) is simply slope of the front. Examination of the equation suggests that the greater the pressure gradient is on the cold than the warm side, the greater the slope of the front. You probably notice that pressure gradients are typically greater behind cold fronts than ahead of them, thus they are depicted as sloping more steeply. That's also a reason for the strong, cold, gutsy winds behind them. I am straying from the main purpose of the article though.

My main purpose is discussion of shapes of isobars along fronts. Please notice the kink drawn along the front. The greatest pressure gradient is shown on the cold side of the fronts, as discussed above. Though such a simplification can be helpful, pressures and densities are not really discontinuous along a front. Furthermore, a 500 mb analysis from this winter indicates that contours may kink at those altitudes also:

Fronts are generally poorly defined if existent there, though temperature gradients and sharp wind turns or shifts are evident in the data. The point I hope I am illustrating here is that not only do the geopotential height contours likely kink, but so do the isotherms and probably any contours including a curve of localized minimum values with larger values on either side. In my previous discussion of a detailed surface analysis, I speculated about a thermodynamical reason isobars may kink at fronts. That was probably incorrect, if for no other reason because such a relatively small temperature difference wouldn't likely cause such a large hydrostatic pressure difference. Confused yet If so, I apologize; but consider the following:

On the 500 mb chart above, a closed Low is embedded in a larger broad trof. A unique single contour must exist in the geopotential height field which exactly meets from either side, as illustrated. A geometrical term probably exists for this, of which I am unaware. But that's my argument - the point at approximately 5620 gpm which must exist illustrates that the kinks seen on weather charts probably are more because of a geometrical necessity than (thermo)dynamics. Thus, I think of no good reason why the kink should exactly correspond with the front as typically drawn, per se; though dynamics tend to cause such an occurrence because of gradient wind considerations (wind shift should roughly correspond with sharp pressure gradient).

Comments? Disagreements? Questions? If so, please inform me.


Text and embedded images are copyright of Joseph Bartlo, though may be used with proper crediting.

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