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PS 2 ATMS 358


ATMS 358: Problem Set 2 Due on Monday April 28, 2014
Please submit your homework to canvas. Bring a copy to class on Monday as we will go over the
solutions together.
1. The diagram at the left is a
“box-model” of the terrestrial
carbon cycle. Each “box” is a
region of the Earth system, and
in each box the mass of carbon
stored in that reservoir is shown
in units of Petagrams of Carbon
(1015 grams). The rate at which
carbon is transferred between
boxes is indicated by the arrow
and the value in Pg C per year.
a. Calculate the lifetime of
Carbon in each reservoir
(box) of this system.
Show your work explicitly.
b. What does your lifetime for atmospheric carbon (mostly CO2) imply about the
average time a CO2 molecule spends before being taken out of the atmosphere? Does
this lifetime bother you at all in terms of the current state of concern about reducing
atmospheric CO2?
c. What fraction of carbon in terrestrial vegetation enters the “litter”, the soil, and the
d. If soil respiration and decay, which convert organic carbon in the soil to CO2,
increases with higher temperature, using a mass balance argument, how might global
warming affect atmospheric CO2 if all else stayed the same?
2. Consider an urban area that is 20 km in extent. A steady wind blowing at 2 m/s brings clean
air into the city, and blows the polluted air out the other side. A pollutant X is formed by a
chemical reaction during nighttime, with a production rate of 1x106 molec cm-3 s-1 that is
a. What is the steady state concentration of this pollutant?
b. Is the steady state concentration ever reached in the city during a typical 12-hour long
night? If so, about how long after sunset is this reached (and how do you know)?
c. When the sun rises, P = 0, and pollutant X is destroyed by sunlight (the wind is still
blowing). X has a lifetime with respect to degradation by sunlight of 1.5 hours, and
this removal process is first-order. How long does it take for X to decrease to 5% of
its initial concentration just before sunrise?
d. Sketch the time evolution of X across 1-day.

PS 2 ATMS 358


3. Fossil fuel combustion as a source of water vapor
Current global CO2 emission from fossil fuel combustion is 7 Pg C/year. The mean
stoichiometric composition of the fuel burned is CH1.6 (one mole carbon per 1.6 moles
hydrogen). We examine here if fossil fuel combustion is a significant source of atmospheric
water vapor.
a. Write the stoichiometric reaction for the oxidation of CH1.6 by oxygen during combustion.
In other words find the coefficients a, b and c in the following combustion reactions:
b. CH1.6 + aO2 ? bCO2 + cH2O
b. Knowing that the global precipitation rate is 3 mm/day, calculate the global source
(Pg/year) of water vapor to the atmosphere. Compare to the source of water vapor from fossil
fuel combustion.
c. The fossil fuel source of water vapor could be relatively more significant in the
stratosphere as a result of aviation. Assume that the air in the stratosphere accounts for 15% of
total atmospheric mass, has a mean water vapor mixing ratio of 4 ppmv, and has a residence time
of 1 year against transfer to the troposphere. Calculate the corresponding source (Pg/year) of
water vapor in the stratosphere. Considering that aircraft account for 2% of global fossil fuel
combustion and that 2/3 of aircraft emissions are released in the stratosphere, calculate the
fraction of the global stratospheric water vapor source contributed by aircraft. Assume in your
calculation that aviation fuel has a stoichiometry of CH1.6, equal to the mean stoichiometry of
4. Production of ozone in the troposphere
The production of ozone in the troposphere begins with photolysis of NO2, by the following
NO2 + h? ? NO + O

J = 8x10-3 s-1

O + O 2 + M ? O3 + M

k = 6.1x10-34 cm6 molec-2 s-1

a. Write the mass balance equation for the concentration of atomic oxygen (O).
b. Assuming steady state for the concentration of atomic oxygen, calculate the rate of
ozone production. Assume that NO2 concentration [NO2] = 2.46x1010 molec cm-3, and the air
density is [M]=2.46x1019 molec cm-3.