Meteo 465 – The Middle
Atmosphere
Mid-term Open-book Exam
Assigned:
10:00 AM, 07 March 2003
Due:
10:00 AM, 24 March 2003
You should be able to answer all the questions using
the material in the chapter “Stratospheric Chemistry - Perspectives in Environmental Chemistry”, your notes, and a
reference text for things like atomic masses, air densities, etc.. You may consult texts, websites, or other
documents. However, please do not
consult each other.
1.
(15
points) I posed the following question
in class; now I will pose it again on this exam. We know that heterogeneous chemistry at low temperatures causes
rapid ozone loss at wintertime high latitudes, yet air gets as cold in the
stratosphere just above the tropical tropopause as it does in the wintertime
polar lower stratosphere. In a few
hundred words, or less, present your case for why you do or don’t think that
ozone loss in the tropical lower stratosphere is important.
2.
(20
points) It is now clear from the figure
on atmospheric heating vs. altitude that ozone absorption is mainly responsible
for the solar heating near 50 km, much to even my surprise in class.
a. Using the equation on solar heating by ozone and molecular oxygen
in the web-based notes on Stratospheric Heating and Cooling, demonstrate that
this heating is indeed due to ozone and that it makes sense that that its
maximum heating occurs near 50 km.
b. Show that O3 is more important at 50 km than O2
by estimating the relative heating rates of O3 and O2.
(hint: I suggest that you
tabulate all the terms in the equation for O3 and O2 at
10 km intervals from 30 to 70 km. Those
values that you cannot find (because they are off the graph, fill in with
reasonable values. You may not be able
to derive the correct absolute heating rates to better than a factor of 10, but
you should be able to compare the relative heating rates at the different
altitudes and the relative heating rates due to O3 and O2
at 50 km.)
3.
(25
points) The fast photochemistry of OH
and HO2. Equations &
figures are in Stratospheric Chemistry – Perspectives in Environmental
Chemistry.
(a.)
Write
down the rate equations for OH and HO2 using equations 1-22, 1-26
through 1-31, 1-34 (and assuming that the production of HOx (OH+HO2)
is due to: O3 + hn ® O(1D) + O2, followed
by O(1D) + H2O ® 2OH. Ignore reactions 1-23 and 1-25. Assume that HOCl rapidly photolyzes. Remember that reaction 1-31 is much faster
than the others.
(b.)
Assume
that HOx production equals HOx loss by reaction
1-34. Show that the reactions that
exchange HOx between OH and HO2 are fast compared to HOx
production and loss using Figure 11.
(c.)
Derive
the steady-state expression, equation 1-32.
(d.)
Simplify
the expression to contain only the dominant terms at 45 km and at 15 km.
(e.)
There
are three ozone-destroying catalytic cycles involving HOx that are
given on pages 23 and 24. Write down
the ozone loss rate expression (d[O3]/dt = ….) for these HOx catalytic
cycles.
4.
(20
points) Ozone loss in the polar
stratosphere.
(a.)
On
page 27, it states “In the lower stratosphere, where [M] = 2x1018 cm-3,
cClO = 1 ppbv, cBrO = 7 pptv, the loss rate of
ozone can approach 1 to 3 percent per day in the sunlit parts of the
vortex”. Verify this statement with
calculations.
(b.)
As
ClO gets tied up in ClONO2 (due to photolysis of HNO3,
followed by ClO+NO2+M®ClONO2+M), the
ozone destruction by ClO+BrO becomes more important. Assuming the cBrO = 7 pptv and that f
(photolysis) = 0.8, at what value of cClO are the two ozone
destruction terms in equation 1-62 equal?
(c.)
Polar
ozone loss requires sunlight to break apart Cl2O2 and
species containing bromine. At the same
time, if any HNO3 remains in the gas-phase, it too is photolyzed,
although at a much lower rate than
Cl2O2. Explain
why the photolysis of HNO3 is still effective at slowing polar ozone
loss, even though the photolysis frequency is so small compared to the
photolysis of Cl2O2.
Use numbers to support your thoughts.
(d.)
Why
is Figure 21 not sufficient to prove that the Antarctic Ozone Hole is caused by
chlorine? Think about what constitutes
proof that a process is occurring?
5. (20 points) The End-of-Mission statement
from the 1994 Airborne Southern Hemisphere Ozone Experiment / Measurements for
Assessing the Stratospheric Effects of Aircraft (ASHOE/MAESA) campaign using the NASA ER-2 high altitude aircraft
contains the following statement:
“Polar air
nearly devoid of ozone was sampled in-situ for the first time inside the vortex
near the 400 K potential temperature surface (about 16 km altitude) on 10 and
13 October. Mid-October is late in the
period of severe ozone depletion over Antarctica. This air contained little O3 (<0.4 ppmv), little or
no ClO (<100 pptv), high NO (1 ppbv), low NOy (2 ppbv), and HCl
equivalent to estimates of total inorganic chlorine (not in the form of CFCs or
CH3Cl) (2.6 ppbv).”
Given that O3 is low, show with words and chemical equations
why each other chemical species are observed to have the values that they
do.
Recall
that most inorganic chlorine is in the forms of Cl, ClO, and ClOOCl as ozone is
being destroyed. What is the time
constant for Cl, ClO, and ClOOCl to be converted into HCl when O3
drops to 0.4 ppmv? (hint: Write down the formation rate for HCl and assume that
all inorganic chlorine is initially in the forms of Cl and ClO and that Cl and
ClO are in steady-state.)