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I. CO₂ concentrations

The average atmospheric CO₂ mixing ratio is about 370 ppmv. Compute the following,

1. What is the column density (in DU) of CO2 in the atmosphere?

2. What are the number density and partial pressure of CO₂ at the sea level?

3. Estimate the number density and partial pressure of CO₂ at the top of Mount Everest (about 9 km above the sea level).

II. Global source of methane

Emission of methane to the atmosphere is largely biogenic and the individual sources are difficult to quantify. However, one can use a simple mass balance approach to calculate the global source.

1. Methane is removed from the troposphere by oxidation, and the corresponding lifetime of methane is known to be 9 years. Based on this lifetime, would you expect methane to be well mixed in the troposphere? Briefly explain.

2. The present-day methane concentration in the troposphere is 1700 ppbv and is rising at the rate of 10 ppbv yr^-1. Using a mass balance equation for methane in the troposphere, show that the present-day emission of methane is E = 3.0x10¹³ moles per year. For this calculation, take 150 hPa as the top of the troposphere and neglect transport of methane to the stratosphere.

III. C₂H₂/CO ratio in the US plume

Both C₂H₂ and CO are emitted from urban regions. They removed by OH oxidation. The C₂H₂/CO emission ratio in the United States has a remarkably constant value of 0.01 mole/mole. It has been proposed that the C₂H₂/CO ratio measured at the Atlantic island of Bermuda can be used as an indicator of long-range transport of pollution plumes from the United States to the island. Assess the merit of this approach with the following exercises assuming the reaction rates with OH are 2.4x10^-7 s^-1 and 8.3x10^-7 s^-1 for CO and C₂H₂, respectively.

1. The typical travel time from the United States to Bermuda is 4 days. Assuming the US pollution plume does not mix with background air, calculate the C₂H₂/CO ratio of the US plume at Bermuda.

2. Now consider the effect of dilution of the plume with background air. Consider an initial plume with 150 ppb CO and 1.5 ppb C₂H₂. As the plume travels to Bermuda, it is diluted with background air containing 80 ppb CO and 0.1 ppb C₂H₂. When the plume arrives at Bermuda, its volume has increased by a factor of 2 (50/50 mixture of the polluted and background air). Calculate the C₂H₂/CO ratio at Bermuda.

3. Is the C₂H₂/CO ratio of the US plume at Bermuda primarily a function of OH oxidation or dilution? Why?

IV. Interhemispheric exchange

In this problem we use observations of the radioactive gas ⁸⁵Kr to determine the characteristic time for exchange of air between the northern and southern hemispheres. We consider a 2-box model where each hemisphere is represented by a well-mixed box, with a rate constant k (yr^-1) for mass exchange between the two hemispheres. Our goal is to derive the residence time t = 1/k of air in each hemisphere.

Krypton-85 is emitted to the atmosphere during the reprocessing of nuclear fuel. It is removed from the atmosphere solely by radioactive decay with a rate constant k_c = 6.45x10^-2 yr^-1. The sources of ⁸⁵Kr are solely in the northern hemisphere and their magnitudes are well known due to regulation of the nuclear industry. Atmospheric concentrations of ⁸⁵Kr are fairly well known from ship observations. In 1983 the global ⁸⁵Kr emission rate was E = 15 kg yr^-1, the total atmospheric mass of ⁸⁵Kr in the northern hemisphere was m_N = 93 kg, and the total atmospheric mass of ⁸⁵Kr in the southern hemisphere was m_S = 86 kg.

1. Assume that the interhemispheric difference in the atmospheric mass of ⁸⁵Kr is at steady state, that is, d(m_N - m_S )/dt = 0 (we will justify this assumption in the next question). Express t as a function of E, k_c, m_N , m_S and solve numerically using the 1983 values.

2. The global emission rate of ⁸⁵Kr was increasing during the 1980s at the rate of 3% yr^-1. Justify the assumption d(m_N - m_S )/dt = 0. [Hint: use the mass balance equation for (m_N-m_S) to determine the time scale needed for (m_N-m_S) to adjust to steady state following a perturbation.]

[To know more: Jacob, D. J., et al., Atmospheric distribution of ⁸⁵Kr simulated with a general circulation model, J. Geophys. Res., 92, 6614-6626, 1987.]