Preparatory Exercise #6
ATMS 111 – Understanding the Atmosphere (Lab)
Air Pressure
Due: 9 Nov 2015
In order to receive full credit for each correct response, you must show the steps taken to arrive at
the result.
  z  z B 
p( z )  p( z B ) exp

H 

and


z  zB 
H  

 ln p( z )  ln p( zB )
where p(z) is the air pressure [hPa] at altitude z [meters], p(zB) is the air pressure [hPa] at some
lower altitude zB [meters], H is scale height [meters], exp{} is the exponential function equal to
(2.71…) raised to the {} power, and ln[] is the natural logarithm of [].
(1) You take air pressure measurements at two different altitudes on your hike up Mt. Pisgah; 925
hPa at 2677 feet and 850 hPa at 5010 feet. Use these data points to determine the scale
height (H) and write the expression for your pressure function p(z) below plugging in the
proper values at Mt. Pisgah in for p(zB), H, and zB. [10 points]
(2) Upon returning from Mt. Pisgah, you discover that the Kestrel used to make the air pressure
measurements consistently reports air pressure that is 3 hPa too low. Make a correction to
your Mt. Pisgah pressure observations and derive a new pressure function p(z) using the
corrected air pressure observations and the same altitude observations in Problem (1). Use
these data points to determine the corrected scale height (H) and plot (using Excel) the
pressure function p(z) along the X-axis and altitude along the Y-axis over the altitude range
extending from 850 to 1500 meters, plotting a data point every 50 meters [a total of fourteen
vertical levels] in elevation. Write the expression for your corrected pressure function p(z)
below using the correct values at Mt. Pisgah for p(zB), H, and zB. [30 points]
(3) You return to Mt. Pisgah on Day 2 {a different day from your hike in Problem (1)} and, with an
accurate Kestrel, you determine that the scale height of Day 2 is exactly 1000 meters smaller
than the scale height estimated on the original day of your Mt. Pisgah hike using the
information from Problem (2). Assuming that the air pressure at 2677 feet on Day 1 and 2
were identical, what type of change in the air temperature between 2677 and 5010 feet in
elevation would cause the scale height to decrease 1000 meters between your original visit
and the Day 2 visit to Mt. Pisgah? [Hint: think about the difference in density between
warm and cold air (City 1 and City 2 illustration). 10 points]
(4) Analyse the 1004, 1012, and 1020 mb isobars on the sea level pressure map displayed on the
back of this page. [Analysis is worth 50 points]