an Francisco State University                                    Name ________________________

Department of Earth & Climate Sciences

Inclass Exercise 11: Practical Applications of the Hypsometric Equation

Due Friday 27 April 2018

(100 points)

This exercise has you working with two graphics: (a) a schematic cross-section of the troposphere on the day of the Winter Solstice with the tropopause (300 mb level) and the 500 mb levels shown; and (b) the 500 mb chart for the United States for 12 UTC March 27 2012 ; and (c) the side-by-side comparison of the soundings (on a Skew-T Log P diagram) at Dodge City, KS, Denver, CO, and Glasgow, MT.


Please note that Questions 3 and 4 require an essay type discussion response. Please answer in complete sentences organized into a few coherent paragraphs.   Answer Questions 3 and 4 on the back or on separate sheets.


1.       On map (a), 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. (25 points)


2.       On map (b), complete the following table along the cross section A-B. (20 points)


3.       The hypsometric equation given below says, qualitatively. that the thickness, given by ∆z, of an atmospheric layer bounded by two pressure surfaces (say 1000 mb at the bottom and any other level like the 500 mb level at the top) is directly proportional to the mean (virtual) temperature of the layer. To put it in different words, the warmer an air column between the 1000 mb level and, say, 500 mb, the taller it is and vice versa. Discuss how your results in (1) and (2) above are consistent with this. (35 points)






There is a general correspondence. Along the cross section there is a general decrease in temperature along with a general decrease in 500 mb heights northward. If surface pressure is roughly 1000 mb, then the hypsometric relation states that the 1000-500 mb thickness and, therefore, heights should decrease northward with temperature. Although the 500 mb temperature is not the average temperature of the air column stretching between 1000 and 500 mb it should be consistent.


4.       Examine the side by side comparison of the soundings given in (c) above, paying special attention to the environmental lapse rates beneath from the surface through 500 mb. Discuss how this side-by-side comparsion is consistent with the 500 mb height data you found in (2). (35 points)


Clearly the average temperatures (simply estimated by adding the surface temperature to the 500 mb temperature and dividing by 2) depicted by the environmental lapse rates for Dodge City, Denver, and Glasgow decrease northward, as well as the 500 mb temperatures. Thus, this is consistent with the results given in Table 2, which indicate that the 500 mb heights and temperatures generally decrease northward.


5.       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. (5 points)





500 mb Height (in meters)

500 mb Temperature

(in Centigrade)

Location 1



Location 2



Location 3



Location 4



Location 5