Jun 20 2007
Does Ship Exhaust Add to the Liquid Water Content of Clouds?
Albrecht (1989) hypothesized that the observed increase in liquid water content in clouds modified by aerosols was due to the more numerous cloud condensation nuclei (CCN) providing more condensation points for the available water vapor to condense. The overall affect of this was to decrease the size of the average cloud droplet, and thus reduce collision and coalescence, which reduced the amount of drizzle.
This post is a quick back-of-the-envelope calculation that shows that any increase in liquid water content in clouds perturbed by ship effluent can not be caused by the water vapor emitted from its combustion process.
The generalized formula for the combustion of a hydrocarbon is
CxHy(Sz) + (O2 + N2) → CO2 + H2O + (O2 + N2) + {NOx + HC + OOC + C + CO + SOx}
This allows for impurities, Sulfer, and for the incomplete combustion. Using diesel fuel as our hydrocarbon, in the absense of impurities, and assuming complete combustions, the reaction is
C12H26 + O2 → CO2 + H2O
Balancing the above, we see that
2 C12H26 + 25 O2 → 12 CO2 + 26 H2O
Or to put into writing, for every two molecules of diesel fuel burned requires 25 oxygen molecules. The reaction results in the production of 12 carbon dioxide molecules and 26 water molecules.
For every liter of diesel fuel burned, 2.73 kilograms of carbon dioxide are emitted. (Jaques, 1992) The molar mass of water is 18 g/mol. The molar mass of CO2 is 44. If the combustion reaction produces 12 moles of carbon dioxide, then 26 moles of water must be produced. After a little algebra, this implies that there are 14.46 kg of water produced per liter of diesel burned. The QEII has a fuel efficiency of 29 ft per gallon. This translates into 2.855 kilograms of water vapor produced per meter travelled.
Assuming that this water is transported so that it mixes evenly in a cylindrical shape with a diameter of 5 km and a height of 500 meter - that’s a volume of 1.57 * 1011 m3 - and all condenses, the amount of additional liquid water content in the cloud is just equal to the amount of water produced divided by the volume. This turns out to be 1.85*10-4 kg/m3. For some reference, a typical value of liquid water content in stratocumulus clouds is 0.1-0.4 kg/m3. This corresponds to an increase of about 0.05%, a very small amount.
References:
Albrecht, B. A., (1989). Aerosols, Cloud Microphysics, and Fractional Cloudiness, Science 245 (4923), 1227. [DOI: 10.1126/science.245.4923.1227]
Jaques, A. P., (1992). Canada’s Greenhouse Gas Emmisions: Estimates for 1990. Environmental Protection Series, Report EPS 5/AP/4, December 1992. Environmental Protection, Conservation and Protection, Environment Canada.
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