Eas 370 Atmospheric Physics Worksheet
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2EAS 370: Atmospheric Physics
Assignment 4: Due in class Friday, December 3 at 10am.
1. At z
= 12 km altitude the pressure is p
= 200 mb. The air is dry and stationary and the
0
0
temperature has a constant value T =
100
C between 11.5 km and 12.5 km.
◦
(a) Find the pressure scale height, H
, and so write a formula for the pressure as a function
p
of height in the form p(z) = p
exp[(z
z)/H
] for z ≃ z
. (In your answer p should
0
0
0
p
be in units of mb and z in units of meters.)
3
(b) Write a formula for density (in kg/m
) as a function of height for z ≃ z
.
0
(c) Use these formulae to find the pressure and density at 12.5 km.
2. (a) Using a “skew T - ln p” chart, estimate (∂w
/∂T )
at p = 700 mb about T = 0
C.
◦
s
p
6
(b) Taking L
= 2.5 × 10
J/(kg) and c
= 1005 J/(kg K), find the saturated adiabatic
v
p
lapse rate (in K/km).
3. (a) The temperature of air in a room has a constant value of 20
C. Find the buoyancy
◦
frequency (in radians per second) and so find the period (in seconds) of vertical oscil-
lations of the air.
(b) The air conditioning system breaks down so that the room warms near the ceiling due
to the heat of people in the room. Assuming the temperature increases linearly from
20
C at the floor to 28
C at the ceiling 3.0 m above, what is the buoyancy period (in
◦
◦
seconds) in the middle of the room? (For this problem, you may assume the pressure
in the room is approximately constant from floor to ceiling.)
4. A weather balloon records the following temperatures and dew points as a function of
pressure:
Pressure (mb) 1000 940 900 780
700
600
500
400
Temperature (
C)
13
9.5
7.0
0.0 -5.0 -11.0 -20.0 -32.0
◦
Plot these points on a “skew T - ln p” chart and connect them with straight-line segments.
Looking at the resulting plot, explain what segments are stable for dry air and what
segments are stable for saturated air.
5. (a) How much energy (in Joules) in the form of incoming solar radiation lands upon a
square meter at the North Pole in the course of 24 hours during the summer solstice?
2
(In this problem, take the flux density incident upon the Earth to be F
= 1368 W/m
.
0
The tilt of the Earth’s axis to the orbital plane is 23.5
.)
◦
(b) How much energy (in Joules) in the form of incoming solar radiation lands upon a
square meter at the top of the atmosphere above the equator in the course of 24 hours
2
during the equinox? (In this problem again take F
= 1368 W/m
, but ignore the tilt
0
of the Earth’s axis.)
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