San Francisco State University 
Spring 2010
Metr. 201


Homework 5 Key

This exercise has you working with a schematic cross-section of the troposphere on the day of the Winter Solstice. The tropopause (300 mb level) and the 500 mb levels are shown. You'll also have to remember the geostrophic wind relation, discussed in previous weeks, to answer question 2.


1.         Draw in on the cross section the height contours for the other (900, 800, 700, 600, 400 mb ) levels in the troposphere. We'll assume that the 1000 mb level is at the ground.


See figure 1 below. I tried to draw in the intervening height contours at even intervals, further apart in the warm air and closer together in the cold air. Note that doing this creates a region of steep slopes to the contours in a zone in the middle latitudes. This is the polar frontal zone.


2.         Examine the pattern in the location indicated by the bracketed Polar Jet Stream. Describe why one characteristic of this pattern is that it implies (a) that there is a distinct polar jet stream: and (b) that the polar jet stream intensifies with height and is at maximum strength at the tropopause. [Hint: remember the equation for the magnitude of the geostrophic wind in natural coordinates.]


See figure 1 below. (a) Note that while the slope of the contours is relatively gentle in both the warm and cold air masses, in the polar frontal region the slope, (delta z/delta n) is quite steep at all elevations of the troposphere in that zone. Hence, the wind speeds are the greatest in that region and quite strong, relative to other areas in the Northern Hemisphere. This is the polar jet stream. (b) The steepness summarized in (a) increases with height in this zone to a maximum near the tropopause. Hence, the polar jet stream is the strongest in the upper troposphere.


3.         The "polar front" is the deep (through the whole troposphere) boundary between the polar air masses and the subtropical air masses (in the figure, the blue and the red colors, respectively).  On surface weather maps, the convention is to draw a line  (with symbols, as explained in class) on the warm air side of the boundary.  Place a blue "X" where you would expect the polar front to be at the surface for this schematic pattern.


See figure 1. This involves thinking in three dimensions. You are used to looking at fronts by looking on standard surface charts (looking down on the fronts). This forces you to visualize where the surface front would be located in three dimensions, really (even though this is a two dimensional chart). The warm (or equatorward) side of the polar frontal zone is on the south side of the zone.

Take a look at this more complicated analysis from May 5, 2009, showing the location of the surface (polar) front on a map of 1000-500 mb thicknesses (mean temperature of the layer from 1000-500 mb) and isobars. Note that the actual front is on the equatorward side of the greatest packing of the thickness contours. Since 1000-500 mb thicknesses are very nearly the same as the 500 mb heights, you can also make a first guess about where surface fronts will be by looking at a 500 mb chart and drawing the surface front on the equatorward side of the packing of the 500 mb height contours.

Thus, if you looked down on the troposphere from the stratosphere, you'd notice the polar jet stream extending from west to east (in the greatest packing of the height contours), with the polar front at the surface found on the warm air side of the polar jet stream.


4.         Describe how the three cell model of the General Circulation discussed in class at the latitude of the polar front generally corroborates your results in (2) and (3) above.


To corroborate the results in (2) and (3) above, the (over) simplified model of the General Circulation should show tht the polar front at the ground is located south of the mean latitude of the polar jet stream and that the polar jet stream is most intense in the upper troposphere. That's exactly what the cross-section shows.


Polar Jet Solution