increase since 2000s (De Meij et al.,2012;Asmi et al.,2013). Models suggest that anthropogenic emissions will show a moderate decrease in the future (IPCC,2013).
1.8 Radiative Transfer
Aerosols in the atmosphere interact with the radiation. This interaction is important for the climate and for the aerosol detection and remote sensing.
Besides photochemical reactions, aerosols interact with the radiation in two ways: they can scatter or absorb radiation (Fig. 1.14). Scattering is the deviation of radiation from its original direction. It happens because of different characteristics of medium that the radiation encounters during its propagation.
Refraction, reflection, diffraction can be considered as different forms of the scattering. Absorption is the uptake of the energy of photon by absorber, and its transformation into thermal energy. The combined effect of scattering and absorption is called extinction.
Here, we consider only the elastic scattering, in which the wavelength before and after the scattering stays the same.
Figure 1.14: Interaction mechanisms between incident radiation and an aerosol particle. The figure is adapted fromSeinfeld and Pandis(1998).
Lambert-Beer law Aerosols reflect one part of the incoming solar radiation back to the space, one part is scattered in the atmosphere, and the last part is absorbed and converted into heat. The interaction radiation-aerosols is described by Maxwell equations for electromagnetic radiation. Using the Maxwell theory, the Lambert-Beer law can be derived. It describes how the light beam is reduced due to extinction by particles:
dI(λ)
dz =−bextI0(λ) (1.21)
whereI0 andIare intensities of the incoming and exiting radiation, andbext
is the aerosol extinction coefficient [m−1] that describes the rate of extinction, and which is the sum of the scattering and absorption components (bext = bscat+babs). Equation (1.21) shows that the extinction along the path of radiation through the aerosol medium is linear with the intensity of the incoming radiation.
1.8.1 Scattering
Scattering regimes The behavior of the scattering of a photon by a scatterer (molecule, particle, etc.) depends on the ratio of the size of scatterer and the wavelength of photon. If the size of the scatterer is much smaller than the wavelength of the light (Dλ), we have the Rayleigh scattering regime. In this regime the scattering is usually by gases, and there is a strong dependency on the wavelength, the scattering strongly favours shorter wavelengths I∼λ−4.
If the size of scatterer is comparable to the wavelength of the light (D∼λ), we have the Mie scattering regime. The scattering by aerosols usually falls into this scattering regime. In the Mie scattering regime, the scatterer is represented as an isotropic, homogeneous, dielectric sphere. The Mie scattering does not depend as strongly on the wavelength of the light as the Rayleigh scattering. The scattering from particles is much stronger than that from molecules, and the size of a particle also has a role. Bigger particles scatter more light.
Particles significantly bigger than the wavelength of the light (Dλ) fall into the so-called geometric scattering regime where scattering is determined by the laws of geometric optics, and which does not depend on the wavelength of the light. This regime applies only to the biggest aerosols which have very short lifetimes.
1.8. Radiative Transfer 49
Scattering phase function The scattering of the light is angle dependant, and it is the scattering phase function which describes this dependency at a given wavelength. For the Rayleigh scattering, the angle dependency is not very strong. The scattering phase function is symmetric in the forward and backward directions, and at right angles it has a half of the forward intensity.
For the Mie scattering, the angle dependency is strong and it is the strongest in the forward direction. Also, the bigger the particle is – the more dominant the forward scattering is. The forward scattering by particles can be explained in the theory by considering it with the scattering by a dipole array (Bohren, 2001). The more dipoles in the array, the more they will collectively scatter in the forward direction.
The scattering in the backward direction is called the backscattering, and it is in the basis of the atmospheric sounding by lidar systems.
1.8.2 Aerosol optical properties
Refractive index As already seen in Section1.4aerosols have different optical properties. These properties are described by the complex refractive index ñ:
˜
n=nre+inim (1.22)
The real part of the index nre describes the scattering by particles, while the imaginary part nim describes the absorption. The refractive index in atmospheric calculations has to be considered as relative to the surrounding air. The refractive index of the vacuum is ˜n0= 1 + 0i. For the air it is very close to this value, and practically they are considered identical. The refractive index depends on the physical properties of the material and the radiation wavelength.
1.8.2.1 Extinction properties of a single particle
The extinction by an aerosol particle depends of its composition, size, shape and the wavelength of the light. The size is usually expressed as the dimensionless size parameter,x:
x= πDp
λ (1.23)
For spherical particles, extinction properties can be calculated by Mie theory.
This theory enables us to determine the particle extinction cross-section,Cext
[m2], which represents a hypothetical area that describes the likelihood that a photon will interact with the particle. The extinction cross-section is a function of the size parameter and the refractive index. From it, the extinction efficiency of a single particle (or a group of monodisperse aerosols), Qext, is calculated as
Qext(Dp,n, λ˜ ) = Cext(Dp,n, λ˜ )
S (1.24)
whereSis the geometric surface of the particle [m2], and the extinction efficiency is dimensionless.
The extinction efficiency has two components, the scattering and absorp-tion efficiency, Qscat andQabs. It can also be calculated for a population of aerosols. The ratio between the scattering and extinction efficiency represents the single scattering albedo:
ω= Qscat
Qext (1.25)
The single scattering albedo for a non-absorbing particle would be equal to 1, but usually it takes values from 0.95 to 1.0. In more polluted areas with a lot of carbonaceous aerosols its values are much lower (De Leeuw et al.,2011).
1.8.2.2 Extinction properties of an ensemble of particles
If we take into account the scattering by an ensemble of particles, we can assume that the total scattered light intensity is just the sum of intensities scattered by individual particles. In this case it is considered that the exiting light rays are scattered at most only once. This is called a single-scattering approximation and it is true if the average distance between particles is much larger that the size of particles. In the atmosphere this is true even for large aerosol concentrations (Seinfeld and Pandis,1998). Here we only consider the case of single scattering approximation.
Optical depth If we consider the layer of aerosols, their summed extinction effect can be expressed by the extinction coefficient αaer [m−1] which is for monodisperse aerosols equal to the product of the particle number concentration and the extinction cross-section:
αaer=Cextn (1.26)
1.8. Radiative Transfer 51
if we consider polydisperse aerosols the extinction coefficient depends on the size distribution
αaer(λ) =Z ∞ 0
fN(Dp)Cext(Dp,˜n, λ)dDp (1.27) To calculate how much light will pass through the layer of aerosols at the height z we have to integrate Eq. (1.21):
I(λ) =I0(λ) exp
The AOD is the parameter which is frequently used to represent the extinction of the light by aerosols, or even the hint of aerosol quantities and it is the primary quantity observed and retrieved by satellites (De Leeuw et al.,2011).
From Eq. (1.28) AOD can be expressed as a negative logarithm of the fraction of the light that passes through the extinction layer. The fraction of the light attenuated in an aerosol layer is
Iext
I0 = 1−e−τ
For example, the aerosol layer of AOD of 1.0 will extinct 1−e−1= 63% of light and only 37% will pass through. The AOD in the atmosphere usually takes values from 0.05 in remote, clear environments to 2.0 or more in locations with high aerosol concentrations, like during desert dust outbreaks or in forest fire plumes.
Angstrom exponent The aerosol optical depth is the function of the wave-length of the light. This dependency is described by the Angstrom exponentα, where
τ ≈λ−α. (1.30)
The Angstrom exponent can be calculated from two optical depths at two different wavelengths
α=−logττλλ1
2
logλλ12 , (1.31)
and it can be used to calculate the aerosol optical depth at another wavelength (under assumption that it stays constant for the whole considered spectral
domain)
The Angstrom exponent can also hint about the typical size of the size distri-bution of aerosols. Smaller particles give bigger values of α. The angstrom exponent has values in the range of about 0 to 4. The valueα≈4 corresponds to the case where particles are so small that they are between the Mie and Rayleigh scattering regime. And values of the exponent around α ≈0 cor-respond to the case where particles are so big that they are at the limit of geometric optics scattering regimes. This also tells us that AOD depends on the light wavelength more strongly for small particles than for big particles (Van de Hulst, 1981).