Atmospheric Aerosols

Research in atmospheric aerosols is fueled by the role they play in air pollution, climate, remote sensing, and chemistry. The latter has received much attention of late as polar stratospheric clouds (PSCs) are known to serve as centres for heterogeneous chemistry which enhance ozone-destroying catalytic cycles. Aerosols also tend to be very efficient scatterers and absorbers of solar radiation. They range in size from $<0.1~\mu$m for stratospheric sulphates and cloud condensation nuclei (CCN) to >1 mm for rain drops and hail. They also vary greatly in number density, composition and shape, factors which depend on their origin and age.

To aid in radiative transfer calculations, analysis, and retrievals, aerosol models are often employed. Aerosol models are analytic expressions relating aerosol radius to number density and usually have one or more adjustable parameters. A number of `standard' distributions have arisen over the years, each suited to describing a particular type of aerosol. Two of these will be used in this study. The first is the standard gamma distribution (Deirmendjian, 1969; Hansen and Travis, 1974),

$$n(r) = \frac{(ab)^{-(1-2b)/b}} {\Gamma [(1-2b)/b]} r^{(1-3b)/b} e^{-r/ab}$$ (3.60)

where n(r) is the number of particles per unit volume with a radius between r and r+dr, $\Gamma$ is the Gamma function, and a and b are adjustable size parameters which control the size and width of the distribution. This distribution has a maximum at r=a(1-3b). The second is the log-normal distribution (Hansen and Travis, 1974),

$$n(r)=\frac{1}{\sqrt{2\pi} \sigma_g} \frac{1}{r} \exp \left[ \frac{ -(\ln r - \ln r_g)^2}{2 \sigma_g^2} \right]$$ (3.61)

with size parameters r_g and $\sigma_g$. This distribution has a maximum just short of r=r_g. Each of these distributions are normalized such that,

$$N = \int_0^{\infty} n(r) dr = 1.$$ (3.62)

Often it is advantageous to express the size parameters of the different distributions in terms of two common parameters. This is useful for inter-comparisons between size distributions as well as in their retrieval. The area-weighted mean, or effective radius, is used as larger particles tend to be more efficient scatterers,

$$r_{\rm {eff}} = \frac{\int_{r_1}^{r_2} r^2 n(r) r dr} {\int_{r_1}^{r_2} r^2 n(r) dr}.$$ (3.63)

and similarly for the measure of the width of a distribution, the effective variance is used,

$$v_{\rm {eff}} = \frac{\int_{r_1}^{r_2} (r-r_{\rm {eff}})^2 r^2 n(r) dr} {r_{\rm {eff}}^2 \int_{r_1}^{r_2} r^2 n(r) dr}.$$ (3.64)

where $r_{\rm {eff}}^2$ in the denominator makes $v_{\rm eff}$ dimensionless (Hansen and Travis, 1974). The effective radius and variance can be expressed in terms of the standard-gamma and the log-normal size parameters as follows. For the standard-gamma,

$$r_{\rm eff}$$ = a (3.65)

$$v_{\rm eff}$$ = b (3.66)

and for the log-normal,

$$r_{\rm eff} r_g e^{5\sigma_g^2/2}$$ = (3.67)

$$v_{\rm eff} e^{\sigma_g^2}-1.$$ = (3.68)

For the remainder of this study, aerosol distributions will be described in terms of effective radius and variance.

 

Table 2.2: Aerosol size distributions and typical size parameters for four types of aerosols.

 

	Aerosol	Distribution	$r_{\rm eff}$	$v_{\rm eff}$	Number Density
		Type	($\mu$m)		(cm-3)
1	Stratospheric	Log-Normal	0.20	0.17	5.0a
	sulphate
2	Marine/	Log-Normal	1.50	0.20	100.0b
	Sea-salt
3	Cumulus	Standard	6.0	0.11	100.0c
	Cloud	Gamma
4	Cirrus	Standard	50.0	0.20	0.1c
	Cloud	Gamma

^a At 20 km.
^b For windspeeds of 8 m/s, de Leeuw (1986).
^c Rogers and Yau (1989).

Four common types of atmospheric aerosols are discussed below.

 

Stratospheric Sulphates. This type of aerosol is present throughout the stratosphere in a submicron sulphate haze, concentrated mainly between the tropopause and an altitude of $\sim$30 km. They possess large spatial and temporal variability (Turco et al., 1982, and references therein). This is especially true after a large volcanic eruption where large amounts of SO₂, which is quickly oxidized to H₂SO₄, can be injected directly into the stratosphere.

Stratospheric sulphates are spherical particles composed of water and sulphuric acid in the liquid phase. The general composition of a sulphate aerosol is represented as (1-x)H₂O+xH₂SO₄, where x is the sulphuric acid weight fraction. Generally, x is approximately 0.75 (Yue et al., 1994) but this varies with temperature and water vapour concentration. The log-normal size distribution is used to represent stratospheric sulphates. There is also some variability in the distribution size parameters: $r_{\rm eff}=0.1-0.3~\mu$m (Kent et al., 1995) and $v_{\rm eff}=0.10-0.35$ (Brogniez et al., 1997). After a volcanic eruption, $r_{\rm eff}$ may be as large as 0.5 $\mu$m (Kent et al., 1995). A typical sulphate size distribution is given in Figure 2.1.

The particle refractive index varies with temperature, humidity, composition and wavelength (Palmer and Williams, 1975; Steele and Hamill, 1981). The variation with altitude arises mainly from the change in composition. The real and imaginary refractive indices for a 0.25 H₂O+0.75 H₂SO₄ composition are shown in Figure 2.2 (Palmer and Williams, 1975).

Marine Aerosols. Marine aerosols will be present over water inside the marine boundary layer. Over the ocean, the principle constituent is sea-salt. The sea-salt aerosol is produced by the agitation of the ocean surface by wind (e.g.: Fitzgerald, 1991). Typical composition of the marine aerosol is 0.30NaCl+0.70H₂O by volume. In general, vertical profiles are strongly dependent upon height, windspeed, and atmospheric stability (de Leeuw, 1986). However, for the purposes of this study, it is sufficient to take the number density as a function of windspeed. An exponential relationship is adopted (Toba, 1961),

 

N(U) = ce^dU_w (3.69)

where U_w is windspeed, c and d are constants, and N is particle number density. Note that c corresponds to the concentration at zero windspeed. Values of c and d can be taken from de Leeuw (1986) as a function of the mean radius of the sea-salt distribution. The log-normal size distribution is used with a mode radius of 0.85 $\mu$m (see Table 2.2). The refractive index varies from 1.39+0i at 400 nm to 1.38+0i at 700 nm (de Haan, 1987).

Cumulus Clouds. Cumulus clouds are formed through convective processes. A parcel of warm air near the surface rises and cools until it becomes supersaturated. Cloud droplets are largely composed of pure water but can also have trace amounts of soot or other soluble inorganics. The vertical extent of a cloud varies greatly from a few hundred metres for fair weather cumulus up to 14 km for a towering cumulonimbus. Cloud optical depth are quite variable and can be as large as 1000. The size of the cloud droplets will depend on both the type of cloud and its maturity with droplet radii ranging from $<1~\mu$m to 100$~\mu$m. Falling raindrops have radii on the order of 1 mm. Standard gamma size distributions are quite useful for representing cloud droplet size distributions (Diermendjian, 1969). The parameters for a cumulus cloud of moderate thickness and mode radius of 6 $\mu$m are given in Table 2.2. The corresponding size distribution is shown in Figure 2.1. The real and imaginary refractive indices for water are shown in Figure 2.2 (Liou, 1992).

 

Cirrus Clouds. Cirrus clouds, formed near the tropopause, are composed of ice crystals and supercooled water droplets. Ice crystals are known to be non-spherical ranging in shape from hexagonal cross-section columns, hexagonal cross-section plates, dendrite, needle, or some combination thereof (Rogers and Yau, 1989). Factors governing their shape include temperature, saturation ratio, and atmospheric conditions (Liou, 1980). In principle, it is possible to calculate the scattering properties for any shape of particle; however, this is generally much more complicated than for spherical particles. As such, ice crystals will be assumed to follow Mie theory with an equivalent radius. The standard-gamma size distribution is adopted with a mode radius of 25 $\mu$m. The real and imaginary refractive indices for ice are shown in Figure 2.2 (Liou, 1992).