Aerosols and Solar Extinction



Desert Aerosols, Doha, Qatar – Click to enlarge

Aerosols directly and indirectly effect the Earth’s radiation budget and climate.  As a direct effect, aerosols absorb and scatter sunlight, affecting the spectral intensity of solar radiation reaching the earth’s surface.   As an indirect effect, atmospheric aerosols modify cloud formation processes and how clouds affect the energy budget.

Aerosol are of interests here because they have major impact on the performance of solar power systems.  Aerosol optical depth (AOD) measures solar extinction due to aerosol absorption and scattering.    AOD is a scalar with no unit of measure and is defined by an integrated extinction coefficient over a vertical column of air or air mass.  In general terms, the impact of the extinction coefficient on solar intensity will change during the day as the length of the sunlight path through the atmosphere changes with the solar zenith angle.

Types of Aerosols


Source: Dr. Kelly BeruBe, Cardiff School of Biosciences

Aerosols are small particles suspended in the air.  Aerosols are present in the  stratosphere, the troposphere, but are mostly found in the atmospheric boundary layer.  Aerosol concentrations depend on location, local weather conditions, annual or diurnal cycles, and the presence of nearby or regional sources.

Aerosols are produced naturally or by human activities.   The types of aerosols present in the air include:1

  • Water vapor, water droplets and ice particles,
  • Dust, soil and mineral particles;
  • Assorted pollen species;
  • Organic carbon caused by fires;
  • Black carbon from fossil fuel burning, energy production processes, and volcanoes;
  • Brown carbon, which is formed by smoldering or incomplete combustion;
  • Marine aerosols, such as sea salt from wave action and sulfates from phytoplankton;
  • Industrial  and social byproducts, such paint, cement and car tire particles; and
  • “Smog,” a soup of chemical species formed by photochemical reactions.

Aerosol Sizes


 Aerosols scatter and absorb light depending on their size relative to the wavelength of light.  Aerosols can range in size from 1 to 105 nm in radius.  Very small aerosols (called Aitken particles) range from 1 to 10 nm;  large particles from 102 to 103 nm are the product of stable particle clusters; and aerosols in the 103–105 nm range are giant coarse particles formed by condensational growth.2.  A representation of the number and volume of aerosols by size is shown at left.3

Aerosol Measurement

The measurement of aerosols is highly uncertain.  Measuring atmospheric aerosols is a challenge due to the large scope in particle size, shape, concentration and  composition. No single instrument can measure all the aerosol properties, and detection methods of the smallest sub-3 nm particles are still developing.

Sky_RadiometersAs a result, scientists, businesses, and government agencies rely on an array of tools to monitor aerosols.  Core tools include satellite, aircraft, and ground-based instruments, as well as atmospheric models. Of all the tools, sky radiometers directly measure AOD and the radiation by wavelength that aerosols scatter and absorb in the atmosphere.  These instruments are well suited for solar power applications (while other instruments are required to assess particle types, concentrations, and chemistry).

The first satellite instrument capable of crudely monitoring aerosol optical depth from space—the Advanced Very High Resolution Radiometer (AVHRR)—provided optical depth readings in the visible and near-infrared spectrum, beginning in the late 1970s.  Over the following decades, the instruments have grown more precise.  Newer radiometers include:4

  • NASA’s Multi-angle Imaging SpectroRadiometer (MISR) and the Moderate Resolution Imaging Spectroradiometer (MODIS), which view aerosols at multiple angles and wavelengths;
  • The Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observer (CALIPSO), which uses laser-based technology to provides detailed vertical profiles of aerosol plumes and clouds; and
  • the Aerosol Polarimetery Sensor (APS), which is the only satellite currently capable of making measurements that can distinguish the various species of aerosols.

Source: Nasa Earth Observatory System. Image and data from the MODIS and CALIPSO missions

New insight can be gained by combining satellite data sources, as shown at left.  While important progress has been made in data collection, its important to stress that the resolution of data across sources is inconsistent; the scope of variables is generally limited;  and spatial gaps are frequent.  At the same time, the status of aerosol models does not support multi-source data assimilation and reanalysis  activity.  As a result, the quality of aerosol data is much lower when compared to other climate variables.

Gas Absorption and Scattering

Gases impact radiation through selective absorption at certain wavelengths. Gas absorption of sunlight is important for three reasons:5

  • Absorption affects light intensity and visibility.;
  • Absorption heats the air and prevents some solar radiation, including harmful forms of UV from reaching the ground; and
  • Absorption breaks gases into smaller molecules, driving atmospheric photochemistry.

Molecular absorption primarily due to ozone, water droplets and CO  is negligible within the visual spectrum and on the order of 0.01 to 0.016 per air mass.  At this magnitude, solar power systems will not be impacted.  The exception is when the solar zenith angle is 80 degrees or more, as shown below.  The R code to recreate the graph is also supplied.


The scattering of light in the atmosphere due to gases is Rayleigh scattering and has a large impact on solar extinction. O2 and N2 are the most abundant gases in the air, and they scatter short wavelengths much more effectively than they do long wavelengths.  As a result, Rayleigh scattering gives the sky its blue color.6.  Rayleigh scattering will impact the performance of solar power systems on the order of 0.145 magnitude per air mass at sea level.7

Particle Absorption and Scattering

The strongest particle absorbers of solar radiation are black, brown and organic carbon.  The soil dust components hematite (Fe2O3) and aluminum oxide (Al3O3) are also capable of radiation absorption. However, most of the mineral particles found in dust are weak radiation absorbers.8.  For example, particle absorption is typically as low as 10-15% of total solar extinction 9.  NASA MODIS and GOCART data for the Middle East also reveals an average  impact on the order of 0.07 per air mass due to particle absorption, with extreme values observed as high as 0.15 per air mass.

Radiation_ScatteringParticulate scattering, on the other hand, accounts for as much as 85-90% solar extinction.10.  Particle scattering has a combination of  effects, as shown at left.  When light waves approach a spherical particle, it can reflect off the particle (A, D, E), refract inside the particle several times (B), diffract around the edge of the particle (C), or be impacted by some combination of effects (D, E).  The result is that light is scattered in all directions, but forward scattering (B and C) is most common.[Jacobson, M (2005), Ibid].  In the Arab Gulf countries, MODIS and GOCART data confirm that solar extinction due to particle scattering has an average magnitude of 0.63 per air mass, with extreme dust storms as high as 2.25 per air mass.


A Basic Equation for Solar Extinction Modeling

The amount of irradiance by wavelength on the ground, \small{F_t(\lambda)} can be related to the amount of irradiance at the top of the atmosphere, \small{F_{to a}(\lambda)} as follows:

(1)   \begin{equation*}\small{ ln[F_t(\lambda)] = F_{toa}(\lambda) + \sigma(\lambda) AM(\theta_{Z}) } \end{equation*}

where \small{\sigma(\lambda)} is the total extinction coefficient by wavelength and is negative in value; and \small{AM(\theta_Z)} is the air mass for the solar zenith angle at the time of observation.

ExtinctionCoefEquation (1) is overly simplified given basic absorption and scattering processes in the  air.  However, the simple model is convenient for estimating the value (or slope) of the total extinction coefficient.  To this end, solar irradiance must be measured at different zenith angles and plotted against the estimated air mass.  Results from one field experiment are shown at left.  The chart confirms that the extinction coefficient is greater (e.g. steeper) for blue light than for visible light:11

In practice, the total extinction coefficient observed by wavelength must be broken down further:12

(2)   \begin{equation*}\small{ \sigma(\lambda) = \sigma(\lambda)_{s,g} + \sigma(\lambda)_{a,g} + \sigma(\lambda)_{s,a} + \sigma(\lambda)_{a,a} + \sigma(\lambda)_{s,w} + \sigma(\lambda)_{a,w} }\end{equation*}

where the individual coefficients define scattering and absorption from gases, aerosol particles, and water vapor, respectively.

AOD Definition and Equations

The formal definition of aerosol optical depth looks at solar extinction and the spectral irradiance that reaches different levels of the atmosphere. Hence, the  next step is to define the vertical or incremental distance along which radiation travels. Given a solar beam, this vertical component is defined by

(3)   \begin{equation*}\small{ dz = \cos(\theta_Z)dS_b }\end{equation*}

optical_depth2where \small{dS_b} is the incremental air mass or distance along the sunlight beam, and \small{\theta_Z} is the solar zenith angle.  The solar zenith angle is the angle between the surface normal (a line directed from the center of the Earth that extends vertically at 90-degrees above the surface) and the direction of the Sun. The figure at right shows the relationship between \small{dz}, \small{dS_b}, and \small{\theta_Z}.

Incorporating the total spectral extinction coefficient over an incremental distance gives an optical depth (dimensionless). Optical depth quantifies scattering and absorbing that occurs between the top of the atmosphere and a given altitude. The optical depth increases from zero at the top of the atmosphere to a maximum at the ground. The incremental optical depth is13

(4)   \begin{equation*}\small{ d\tau(\lambda) = -\sigma(\lambda)dz = -\sigma(\lambda)\cos(\theta_Z)dS_b }\end{equation*}

which increases in the opposite direction from incremental altitude. Finally, integrating equation (4) from the top of the atmosphere (\small{z = S_b = \infty}) to any altitude \small{z}, which corresponds to a location \small{S_b} along the beam of interest, gives the optical depth as

(5)   \begin{equation*}\small{ \tau(\lambda) = \int^z_{\infty} \sigma_{\lambda}dz = \int^{S_b}_{\infty}\sigma_{\lambda}\cos(\theta_Z) dS_b }\end{equation*}

Interpreting and Visualizing AOD Data

An aerosol optical depth of less than 0.05 indicates a clear sky with relatively few aerosols and maximum visibility, whereas a value of 1 indicates hazy conditions. Optical depths of 1 to 2 are frequent in the Arab Gulf and represent weak to moderate dust storms.  AOD values above 2 indicate very high concentrations of aerosols typical of the most extreme dust events.  The following animation presents daily average AOD as a function of time and location, focussing on Saudi Arabia and the GCC countries.  R code to recreate the animation is located here.

Aerosol Animation GOCART

Estimating Terrestrial Radiation Using AOD

In physical optics, the Beer–Lambert law relates the extinction of light to the properties of the material through which it is traveling.  In the case of a sunbeam, the law states that there is an exponential relationship between the total irradiance at the top of the atmosphere, \footnotsize{F_{toa}(\lambda)\} and the irradiance received on the ground,  \footnotsize{F_t(\lambda)}, given aerosol attenuation:14

(6)   \begin{equation*}\small{ F_t(\lambda) = F_{toa}e^{-\alpha l c} }\end{equation*}

where \small{\alpha}  is the sum of the aerosol absorption and scattering coefficients, \small{l} is the path length of the sunbeam, and \small{c} is the aerosol concentration. The product of \small{\alpha} and \small{c} in the exponent can be interpreted as aerosol optical depth, \small{\tau_{\lambda}} as measured by in situ tools; and \small{l} can be defined as the air mass, \small{AM(\theta_Z)}. Hence:

(7)   \begin{equation*}\small{ F_t(\lambda)= F_{toa}(\lambda)e^{-\tau_{\lambda} AM(\theta_Z)} \end{equation*}

Taking the natural log of both sides we derive the linear form of equation (1), where the simple extinction coefficient is now defined by AOD.


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Show 14 footnotes

  1. Jacobson, Mark, “Aerosol Emission and Nucleation,” Fundamentals of Atmospheric Modeling,2nd Edition, Cambridge University Press, New York
  2. Eltbaakh, Youseff, et. al (2012), “Solar Attenuation By Aerosols: An Overview,” Renewable and Sustainable Energy Reviews, 16: 4264-4276.
  3. Seinfeld and Pandis (2006), Atmospheric Chemistry and Physics, Wiley & Sons.
  4. Kaufman, Y., et. al. (2002), “A Satellite View of Aerosols in the Climate System,” Nature, 419: 215-223
  5. Jacobson, Mark, (2005), “Radiative Energy Processes”, Fundamentals of Atmospheric Modeling, 2nd Edition, Cambridge University Press, New York
  6. Wagonner, A, (1981), “Optical Charactaristics of Atmospheric Aerosols,” Atmospheric Environment, 15:1891-1909
  7. Hayes and Latham (1975), “A Rediscussion of Atmospheric Extinction and the Absolute Spectral-Energy Distribution,” Astrophysical Journal, 197:593
  8. Jacobson, M (2005), Ibid
  9. Moore, et. al. (2004), “A Comparison of Similar Aerosol Measurements Made on the NASA P3-B, DC-8, and NSF C-130 Aircraft During TRACE-P and ACE-Asia,” Journal of Geophysical Research, 109: D15S15
  10. Moore (2004), Ibid.
  11. Palmer and Davenhall (2001), The CCD Photometric Calibration Cookbook, Starlink Cookbook 6
  12. Jacobson (2005), Op.Cit
  13. Jacobson (2005), Ibid
  14.  .H. Lambert (1760), Photometry: On the Measure and Gradations of Light, Colors, and Shade,  p. 391.