Vertical Variation

The vertical distribution of aerosol mass concentration typically shows an exponential decrease with altitude up to a height Hp and a rather constant profile above that altitude (Gras 1991). The aerosol mass concentration as a function of height can then be expressed as

where M(0) is the surface concentration and Hp the scale height. Jaenicke (1993) proposed values of Hp equal to 900 m for the marine, 730 m for the remote continental, 2000 m for the desert, and 30,000 m for the polar aerosol types. The corresponding vertical aerosol mass concentration profiles are shown in Figure 8.29.

The aerosol number concentration may increase or decrease exponentially with altitude and one suggestion of a form of the profile is (Jaenicke 1993)



Global Warming Chemistry

Mass Concentration, fig m"3

FIGURE 8.29 Representative vertical distribution of aerosol mass concentration (Jaenicke 1993).

and Nb is the number concentration of the background aerosol aloft. For marine aerosol H'p varies from — 290 to 440 m. Note that if H'p is negative n = -1, and (8.56) can be rewritten as

Because in this case N(0) <C NB, the equation has the correct limiting behavior both for z —> 0 and z —► oo.

These vertical profiles are rough representations of long-term averages. Significant variability is observed in aerosol concentrations in anthropogenic plumes, areas influenced by local sources, or during nucleation events in the free troposphere.


8.1a Given the following data on the number of aerosol particles in the size ranges listed, tabulate and plot the normalized size distributions h^{Dp) = n^(Dp)/N, and h°N(logDp) = n^(logDp)/Nt as discrete histograms.

Size Interval, Mean of Size Interval, Number of Particles



in Inter








































8.2a For the data given in Problem 8.1, plot the surface area and volume distributions ns(pp), (logDp), nv(Dp) and n°v{\ogDp) in both nonnormalized and normalized form as discrete histograms.

8.3a You are given an aerosol size distribution function such that nM{m)dm = aerosol mass per cm3 of air contained in particles having masses in the range m to m + dm. It is desired to convert that distribution function to a mass distribution based on log Dp. Show that n°M(logDp) = 6.9 mnM(m)

8.4b Show that the variance of the size distribution of a lognormally distributed aerosol is

8.5a Starting with semilogarithmic graph paper, construct a log-probability coordinate axis and show that a lognormal distribution plots as a straight line on these coordinates.

8.6a The data given below were obtained for a lognormally distributed aerosol size distribution:

Size Interval, Hm

Geometric Mean of Size Interval, (tin

Number of Particles in Interval"




























"Assume that the particles are spheres with density pp = 1.5 g cm 3.

"Assume that the particles are spheres with density pp = 1.5 g cm 3.

a. Complete this table by computing the following quantities: ANj/ADpi, ATV,/ NADpi, ASi/ADpi, ASi/SADpi, AMt/ADpl, AM-JMAD,», AN-JAlogD,,,, ANi/NA log Z)pi, ASi/AlogDph ASt/SA\ogDpl, and AM,-/A log Dpi, AM,/ M A log Dpi, where M = particle mass.

b. Plot ANi/ A log Dpi, ASj/A log Dpi, and AM,/ A log Dpi as histograms.

c. Determine the geometric mean diameter and geometric standard deviation of the lognormal distribution to which these data adhere and plot the continuous distributions on the three plots from part (b).

8.7b For a lognormally distributed aerosol different mean diameters can be defined by

where v is a parameter that defines the particular mean diameter of interest. Show that

Plot a normalized lognormal particle size distribution over a range of Dp from 0 to 7 pm with Dpg = 1.0 pm and ug = 2.0 and identify each of the above diameters on the plot. Hint: You may find this integral of use:

8.8b The modified gamma distribution (Deirmendjian 1969) has been proposed as another function that approximates ambient aerosol size distributions, n^{Dp) = ADp exp (-BD'p), where A, b, B, and c are all positive constants.

a. Plot this size distribution for the following combinations of its parameters: A = 100, b = 3, B = 2 and c = 1,2,3

A = 100, b = 2, c = 2 and B = 1.5,2,2.5 A = 100, c = 2, B = 2 and b = 3,4,5

b. Calculate the diameter Dm at which the distribution function reaches a maximum as a function of the distribution parameters.

c. Calculate the total aerosol number concentration as a function of the distribution parameters.

d. Using the results of parts (a)-(c), discuss the effect of the four parameters on the shape of the distribution function.

e. Discuss the strengths and weaknesses of this function for the fitting of atmospheric aerosol size distributions.

8.9b Assume that an aerosol has a lognormal distribution with Dpg = 5.5 pm and

Diameter v

Mode (most frequent value) Geometric mean or median Number (arithmetic) mean Surface area mean Mass mean Surface area median Volume median

'g a. Plot the number and volume distributions of this aerosol on log-probability paper.

b. It is desired to represent this aerosol by a distribution of the form

where Fv{Dp) is the fraction of the total aerosol volume in particles of diameter less than Dp. Determine the values of the constants c and b needed to match this distribution to the given aerosol.

8.10b Given the following size frequency for a dust:

Size Interval (pm) % by Number





















a. Plot the cumulative frequency distributions (in %) of the number, surface area, and mass on linear graph paper assuming all particles are spheres with pp = 1.6 g cm"3.

b. Is this a lognormally distributed dust?

8.11b The following particle size distribution data are available for an aerosol:

% by Volume


Less than













a. What are the volume median diameter and geometric standard deviation of the volume distribution of this aerosol?

b. What is the surface area median diameter?


Aitchison, J., and Brown, J. A. C. (1957) The Lognormal Distribution Function, Cambridge Univ. Press, Cambridge, UK.

Barrie, L. A. (1986) Arctic air pollution: An overview of current knowledge, Atmos. Environ. 20, 643-663.

Bashurova, V. S. et al. (1992) Measurements of atmospheric condensation nuclei size distributions in Siberia, J. Aerosol Sci. 23, 191-199.

Blanchard, D. C., and Cipriano, R. J. (1987) Biological regulation of climate, Nature 330, 526.

Blanchard, D. C., and Woodcock, A. H. (1957) Bubble formation and modification in the sea and its meteorological significance, Tellus 9, 145-152.

Covert, D. S., and Heintzenberg, J. (1993) Size distributions and chemical properties of aerosol at NY Alesund, Svalbard, Atmos. Environ. 21 A, 2989-2997.

d'Almeida, G. A., and Schutz, L. (1983) Number, mass and volume distributions of mineral aerosol and soils of the Sahara, J. Climate Appl. Meteorol. 22, 233-243.

Deepak, A., and Gali, G. (1991) The International Global Aerosol Program (IGAP) Plan, Deepak Publishing, Hampton, VA.

Deirmendjian, D. (1969) Electromagnetic Scattering on Spherical Poly dispersions, Elsevier, New York.

De Leeuw, G. (1986) Vertical profiles of giant particles close above the sea surface, Tellus 38B, 51-61.

Fitzgerald, J. W. (1991) Marine aerosols: A review, Atmos. Environ. 25A, 533-545.

Gras, J. L. (1991) Southern hemisphere tropospheric aerosol microphysics, J. Geophys. Res. 96, 5345-5356.

Haaf, W., and Jaenicke, R. (1980) Results of improved size distribution measurements in the Aitken range of atmospheric aerosols, J. Aerosol Sci. 11, 321-330.

Heintzenberg, J. (1980) Particle size distribution and optical properties of Arctic haze, Tellus 32, 251-260.

Heintzenberg, J. (1989) Arctic haze: air pollution in polar regions, Ambio 18, 50-55.

Hering, S. V., and Friedlander, S. K. (1982) Origins of aerosol sulfur size distributions in the Los Angeles basin, Atmos. Environ. 16, 2647-2656.

Hobbs, P. V., Bowdle, D. A., and Radke, L. F. (1985) Particles in the lower troposphere over the high plains of the United States. 1. Size distributions, elemental compositions, and morphologies, J. Climate Appl. Meteorol. 24, 1344-1356.

Hoppel, W. A., Fitzgerald, J. W., Frick, G. M., Larson, R. E., and Mack, E. J. (1989) Atmospheric Aerosol Size Distributions and Optical Properties in the Marine Boundary Layer over the Atlantic Ocean, NRL Report 9188, Washington, DC.

Ito, T., and Iwai, K. (1981) On the sudden increase in the concentration of aitken particles in the Antarctic atmosphere, J. Meteorol. Soc. Jpn. 59, 262-271.

Jaenicke, R. (1993) Tropospheric aerosols, in Aerosol-Cloud-Climate Interactions, P. V. Hobbs, ed., Academic Press, San Diego, CA, pp. 1-31.

Jaenicke, R., and Schutz, L. (1978) Comprehensive study of physical and chemical properties of the surface aerosol in the Cape Verde Islands region, J. Geophys. Res. 83, 3583-3599.

Jaenicke R., Dreiling V., Lehmann E., Koutsenogii, P. K., and Stingl, J. (1992) Condensation nuclei at the German Antarctic Station Vonneymayer, Tellus 44B, 311-317.

John, W., Wall, S. M., Ondo, J. L., and Winklmayr, W. (1990) Modes in the size distributions of atmospheric inorganic aerosol, Atmos. Environ. 24A, 2349-2359.

Koutsenogii, P. K., and Jaenicke, R. (1994) Number concentration and size distribution of atmospheric aerosol in Siberia, J. Aerosol Sci. 25, 377-383.

Koutsenogii, P. K., Bufetov, N. S., and Drosdova, V. I. (1993) Ion composition of atmospheric aerosol near Lake Baikal, Atmos. Environ. 27A, 1629-1633.

Leaitch, W. R., and Isaac, G. A. (1991) Tropospheric aerosol size distributions from 1982 to 1988 over Eastern North America, Atmos. Environ. 25A, 601-619.

Lewis, E. R., and Schwartz S. E. (2005) Sea Salt Aerosol Production: Mechanisms, Methods, Measurements, and Models, American Geophysical Union, Washington, DC.

Li, X., Maring, H., Savoie, D., Voss, K., and Prospero, J. M. (1996) Dominance of mineral dust in aerosol light scattering in the North Atlantic trade winds, Nature 380, 416-419.

Meng, Z., and Seinfeld, J. H. (1994) On the source of the submicrometer droplet mode of urban and regional aerosols. Aerosol Sci. Technol. 20, 253-265.

Meszaros, A., and Vissy, K. (1974) Concentration, size distribution and chemical nature of atmospheric aerosol particles in remote ocean areas, J. Aerosol Sci. 5, 101-109.

Monahan, E. C., Fairall, C. W., Davidson, K. L., and Jones-Boyle, P. (1983) Observed interrelationships amongst 10-m-elevation winds, oceanic whitecaps, and marine aerosols, Quart. J. Roy. Meteorol. Soc. 109, 379-392.

NARSTO (2003) Particulate Matter Science for Policy Makers, Electric Power Research Institute, Palo Alto, CA.

O'Dowd, C. D., and Smith, M. H. (1993) Physicochemical properties of aerosols over the Northeast Atlantic: Evidence for wind-speed related submicron sea-salt aerosol production, J. Geophys. Res. 98, 1137-1149.

Ott, S. T„ Ott, A., Martin, D. W., and Young, J. A. (1991) Analysis of trans-Atlantic saharan dust outbreak based on satellite and GATE data, Mon. Weather Rev. 119, 1832-1850.

Ottar, B. (1989) Arctic air pollution: A Norwegian perspective, Atmos. Environ. 23, 2349-2356.

Prospero, J. M. (1995) The atmospheric transport of particles to the ocean, in SCOPE Report: Particle Flux in the Ocean, V. Ittekkot, S. Honjo, and P. J. Depetris, eds., Wiley, New York.

Prospero, J. M., Nees, R. T., and Uematsu, M. (1987) Deposition rate of particulate and dissolved aluminum derived from Sahara dust in precipitation in Miami, Florida, J. Geophys. Res. 92, 14723-14731.

Pruppacher, H. R., and Klett, J. D. (1980) Microphysics of Cloud and Precipitation, Reidel, Dordrecht, The Netherlands.

Radke, L. F., Lyons, J. H., Hegg, D. A., and Hobbs, P. V. (1984) Airborne observations of Arctic aerosols. I: Characteristics of Arctic haze, Geophys. Res. Lett. 11, 369-372.

Rahn, K. (1981) Relative importance of North America and Eurasia as sources of Arctic aerosol, Atmos. Environ. 15, 1447-1456.

Savoie, D. L., and Prospero, J. M. (1989) Comparison of oceanic and continental sources of non-seasalt sulfate over the Pacific ocean, Nature 339, 685-687.

Schneider, J. K., and Gagosian, R. B. (1985) Particle size distribution of lipids in aerosols off the coast of Peru, J. Geophys. Res. 90, 7889-7898.

Schroeder, W. H., Dobson, M., Kane, D. M., and Johnson, N. D. (1987) Toxic trace elements associated with airborne particulate matter: A review, J. Air Pollut. Cont. Assoc. 37, 1267-1285.

Shaw, G. E. (1984) Microparticle size spectrum of Arctic haze, Geophys. Res. Lett. 11, 409-412.

Shaw, G. E. (1985) Aerosol measurements in Central Alaska 1982-1984, Atmos. Environ. 19, 20252031.

Shaw, G. E. (1986) On physical properties of aerosols at Ross Island, Antarctica, J. Aerosol Sci. 17, 937-945.

United States Environmental Protection Agency (U.S. EPA) (1996) Air Quality Criteria for Particulate Matter, EPA/600/P-95/001, Research Triangle Park, NC.

Wall, S. M., John, W., and Ondo, J. L. (1988) Measurement of aerosol size distributions for nitrate and major ionic species, Atmos. Environ. 22, 1649-1656.

Warneck, P. (1988) Chemistry of the Natural Atmosphere, Academic Press, San Diego.

Wittig, A. E„ Anderson, N„ Khlystov, A. Y., Pandis, S. N., Davidson, C., and Robinson, A. L. (2004a) Pittsburgh Air Quality Study overview, Atmos. Environ. 38, 3107-3125.

Wittig, A. E„ Takahama, S., Khlystov, A. Y., Pandis, S. N„ Hering, S., Kirby, B., and Davidson, C. (2004b) Semi-continuous PM2.5 inorganic composition measurements during the Pittsburgh Air Quality Study, Atmos. Environ. 38, 3201-3213.

Zhu, Y., Hinds, W. C., Kim, S„ Shen, S., and Sioutas, C. (2002) Study of ultrafine particles near a major highway with heavy-duty diesel traffic, Atmos. Environ. 36, 4323-4335.

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