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.)