Light Scattering by the Earth’s Atmosphere, Aerosols, and Clouds, Part One – Basic Concepts
Posted by Jeff Id on January 2, 2011
Guest post by Steve Fitzpatrick:
Aerosols are the 800 pound gorilla of global warming. Aerosols are claimed by many climate scientists to largely ‘off-set’ radiative forcing by GHG’s in Earth’s atmosphere, and to have greatly reduced the rate of global warming1. The magnitude of the current aerosol effect is very poorly defined, and even the IPCC says that the credible range is from quite low (~0.4 watt/M^2) to very high (~2.4 watts/M^2). For comparison, the current best estimate of total GHG forcing (all gases, not just CO2) is ~3 watts/M^2. If aerosol effects are in fact small (for example, near 0.4 watt/M^2), climate sensitivity is almost certainly quite low, and future GHG driven warming will be modest. If aerosol effects are large (near 2.4 watts/M^2) then climate sensitivity is likely much higher, and future GHG driven warming could be substantial.
Uncertainly in aerosols allow a huge amount of ‘wiggle room’ to climate models (and climate modelers!). Since almost any assumed historical aerosol profile is acceptable, assumed aerosols can be (and in fact have been) ‘tuned’ to have each model’s hind-cast reasonably match the known temperature record since the late 1800’s.
So uncertainly in aerosols inhibits progress on climate models as well, since nobody can show that a specific model is simply ‘wrong’ so long as the kludge of assumed aerosol effects is always available.
This post is not intended to stimulate debate about what the true climate sensitivity is, not intended to address the accuracy of the current estimates of aerosols, and not intended to start a debate about the accuracy of model projections of future warming. My objective is only to provide some background information about the basics of absorption and scattering of light by small particles in the atmosphere, so that you can appreciate the complexity of determining net aerosol and cloud effects, and more critically evaluate future claims of aerosol and cloud effects.
My personal background in light scattering began some 35 years ago, when I needed to understand how to correlate the attenuation of light passing through a dispersion of very small polymer particles in water to the (very small) size of those polymer particles. About 19 years ago, I co-founded a company2 which manufacturers laboratory instruments that measure the size distribution of small particles, ranging form ~30 microns to as small as <5 nm (depending on the kind of material). Accurate calculation of how small particles scatter and absorb light is one of the basic technologies used in our laboratory instruments.
1. The interaction of light with small particles
The wavelength of visible light is quite small (averaging about 535 nm wavelength in air, which corresponds to green), so we macroscopic creatures are not able to appreciate how it interacts with small objects; we can perceive only light’s macroscopic manifestations. The interaction of light with very small objects (eg small particles) is very different from what we might imagine based on our everyday perception. Visible light ranges from ~410 nm (deep violet color) to ~670 nm (deep red color). White light is a mix of all wavelengths. Shorter and longer wavelengths are not visible to humans, but the solar spectrum includes some near ultraviolet (shorter than 410 nm) and some near infrared (longer than 670 nm). The earth’s atmosphere absorbs (not scatters) ‘hard’ ultraviolet in the stratosphere, and water vapor also absorbs some of the infrared.
Figure 1. Credit: Wikepedia (http://en.wikipedia.org/wiki/File:Solar_Spectrum.png)
2. Absorption versus Scattering
It is important to understand the difference between absorption and scattering. When a photon of light is scattered, it exists after the scattering event with the same energy content (same wavelength). When a photon is absorbed, it ceases to exist, and it’s energy is converted to a different form (e.g., heat or chemical energy).
3. Rayleigh Scattering by Extremely Small Particles
Visible light passing through any transparent (AKA non-absorbing) medium is subject to ‘scattering’ by the medium. The reason is that all media (gases, liquids and solids) are not homogeneous on a very small (molecular/atomic) scale; transparent media are in fact composed of extremely small particles. Photons, which are the quanta of electromagnetic radiation, can be “elastically scattered” when they happen to strike an atom or molecule in just the right, and quite improbable, way. This kind of elastic scattering is called “Rayleigh scattering”. The scattered photon exits the encounter with the same wavelength, but going in an altered, and completely non-deterministic, direction. The most and equally probable directions post-scatter are a) along the original photon path, and b) exactly opposite the original photon path. The least probable direction is 90 degrees from the original path, but that least probable direction is still 50% as large is the most probable directions. Intermediate angles have intermediate probabilities.
The probability of Rayleigh scattering is exceedingly small when the particles are exceedingly small (like air molecules) but increases rapidly with increasing particle size relative to the wavelength of the photon. For an equal weight of particles of the same material, the scattering increases as the third power of the particle diameter.
When light of many wavelengths passes through a non-absorbing medium, shorter wavelength photons (blue, violet) are much more likely to be elastically scattered than longer wavelengths. As sunlight passes through clear air, more short wavelengths (blue, violet) are scattered than longer wavelengths (orange, red) and we see that scattered light coming from all directions in a clear sky (remember, the direction of elastic scattering is quite random). A clear sky is blue because more blue light is being scattered than red. From space, the Earth appears very blue as well… another consequence of wavelength dependent elastic scattering. The scattered diffuse light that comes from all directions in a clear sky has a strongly blue ‘color balance’, and causes the blue color hue you can see in the shadows on fresh snow or other very white surfaces.
Figure 2. Credit: Wikipedia (http://en.wikipedia.org/wiki/File:Rayleigh_sunlight_scattering.png)
About 9% (on average) of sunlight is scattered, but much more blue than red. Longer infrared wavelengths have hardly any scattering in clean air; for example, at 1250 nm (1.25 microns), the scattered fraction is <0.5%. In Figure 1, the difference between the yellow (solar spectrum above the atmosphere) and red (solar spectrum at the surface) is dominated in the visible, near UV, and near infrared regions by Rayleigh scattering. Lower sun angles increase the net path length through the atmosphere, and so increase net Rayleigh scattering. This generates the yellow-orange sunlight we see at sunset and sunrise when the sky is clear.
Purely elastic (Rayleigh) scattering is limited to particles that are very small compared to the wavelength of light, with “very small” usually considered a particle with a diameter of <10% of the wavelength. If the average wavelength of sunlight is ~525 nm, elastic scattering only takes place with particles smaller than ~53 nm. Most particles in the atmosphere (clouds and aerosols) are much larger than 53 nm, although there is a small weight fraction of sulfate aerosols that are in the Rayleigh region.
You can see the equations that describe Rayleigh scattering at Wikipedia (http://en.wikipedia.org/wiki/Rayleigh_scattering) and from many other sources.
4. Scattering by Larger Particles
Mie theory is a general solution to Maxwell’s equations for the scattering of electromagnetic radiation by spherical particles. It applies equally to particles of any size and any optical/electrical properties; it describes how microwaves interact with 1 meter metal spheres just as well as how deep ultraviolet interacts with 10 nm dielectric spheres. Rayleigh scattering is in fact an approximate solution to Mie theory; Rayleigh scattering equations are accurate only for non-absorbing particles which are much smaller than the wavelength of light.
Now the bad news: Mie theory has analytical solutions only for perfectly spherical particles (and a few other symmetrical shapes) that are of homogeneous composition. Particles with random irregular shapes (black soot, dust) and/or complex internal structures (smoke particles, pollen grains, dust) can’t be exactly handled by Mie theory.
But all is not lost. Cloud droplets are spherical and homogeneous in composition, so can be exactly treated by Mie theory. Sulfate aerosol, which is probably the man-made aerosol with the greatest effect, forms small droplets whenever the relative humidity is high (as in clouds), so these can be treated by Mie theory as well. Non-ideal particles (irregular dust particles, smoke, soot, etc.) can be handled using some approximations that are based on the optical properties and approximate size of the particles.
To get a feel for Mie scattering, it is useful to consider first how a big (say 20 microns diameter) droplet of water scatters light. At such a big size, we might be tempted to consider the droplet to interact with light much like a very small lens…. in this case, a ‘ball-lens’, which has a short focal length compared to it’s diameter. This is shown in Figure 3.
Figure 3 – A ‘ball lens’ representation of a small water droplet.
The red arrows represent typical paths light would be expected to take passing through the droplet based on refraction at surfaces (that is, based on how light interacts with a lens). If you consider both refraction and reflection from internal and external surfaces, it becomes clear that light can follow a multitude of paths through the droplet, creating a complex pattern of angular intensities of “scattered” light. But if we continue to consider the droplet to be essentially a very small, very short focal length lens, we expect the light to spread mainly in the forward direction, and at a reasonably broad angle.
Figure 4 shows the actual intensity pattern for 650 nm light passing through a 20 micron diameter water droplet, calculated exactly using Mie theory. The droplet is ~31 times larger in diameter than the wavelength. Note that 20 microns is larger than would be typically found in clouds, which generally have ~3 microns to ~15 microns droplet size (larger droplets become rain!). The light in Figure 4 enters from the left (at 180 degrees), hits the droplet that is located at the center of the diagram, and exits the droplet with an angular intensity pattern shown by the red trace.
Figure 4 – scattering of 650 nm plane-polarized light by a 20 micron diameter droplet, measured far from the droplet
Keep in mind that this is a log10-scale polar plot; each division step away from the center of the plot represents a 10-fold increase in intensity. This plot shows the scattering for light with a single polarization; the polarization reveals many details (the rapid oscillation of the intensity with angle) which become “smeared” when randomly polarized light is used. Since sunlight is randomly polarized, the overall intensity plot will have a similar appearance, but with a smoother overall appearance. By far the strongest intensity is very near the original light path (at zero degrees in the plot). This intensity peak represents light that entered the droplet very close to perpendicular to the surface, and so simply passed through with little change in direction. There is also a lot of intensity in the +/- 30 degree range of forward direction… exactly what we would expect from considering the droplet as a very small lens. The total of “forward scattered” light (everything on the right half of the diagram) dominates “back scattered light” (everything on the left) by a factor of more than 30 times. Even with a near-macroscopic particle size, forward scattering strongly dominates.
On the other hand, the substantial oscillations in intensity with angle are not at all what we would expect for a macroscopic lens. Funny things are happening to the intensity pattern that our macroscopic senses do not normally perceive. This variation in intensity begins to show how macroscopic optics fails at small sizes to accurately describe how light interacts with matter. As the droplet size falls, the deviation from macroscopic optics becomes ever more extreme. When the droplet diameter and the wavelength are comparable, the scattering pattern resembles nothing like we would expect based on macroscopic optics, and forward scattering is even more dominant.
For example, a 260 nm droplet (less than half the average wavelength of visible light) scatters more that 100 times as much light in the forward direction as in the reverse. In general, forward scattering dominates from the macroscopic size range to ~ 20% of the wavelength. Below 20% of the wavelength, there is a transition to more uniform forward versus backward scattering (Rayleigh scattering), which begins to dominate at a particles size near 10% of the wavelength. The overall scattering efficiency for non-absorbing particles always has a maximum at a certain diameter; this is the particle size where a narrow light beam is most strongly attenuated by passing through a collection of particles. Carrick found an interesting PowerPoint presentation on atmospheric aerosols: http://www.esf.edu/chemistry/dibble/presentations/IX_Aerosol.ppt,
which contains a graphic of total scattering for ammonium sulfate particles wiht 530 nm light (Figure 5).
Figure 5 – Scattering efficiency versus particle size
The maximum “scattering efficiency” is between ~400 and ~600 nm diameter, and falls rapidly for both larger and smaller particles. What this plot does not show is the tremendous dominance of forward angle scattering over reverse angle scattering for all sizes over ~100 nm diameter (50 nm radius). A narrow light beam passing through a suspension of 400 – 600 nm particles (as shown in this graphic) would be most strongly reduced in intensity, but the light scattered away from the beam would not be scattered backward; it would instead be ~99% forward scattered. The total intensity of sunlight reaching the Earth’s surface is not greatly attenuated by strong forward scattering, because even tough much of the light is “deflected” from its original path, it still makes its way to the Earth’s surface as diffuse light; the total solar intensity is not as strongly attenuated as the scattering profile might suggest.
5. Clouds Turn Light Around
At this point you may be thinking: “Now wait a minute, if most particles scatter so strongly in the forward direction, then why do clouds reflect so much light back into space?” The answer is “multiple scattering”. Sunlight entering a cloud is scattered by a droplet (or ice particle) somewhere between a fraction of a meter and several tens of meters after entry, depending on the cloud’s “optical density”. A couple of percent of the light is immediately reflected back in to space by the first encounter, and the remainder heads off at some random angle from the original direction of the sunlight… perhaps on average ~30 degrees away from the original direction, until it encounters another droplet (or ice particle) and is scattered again.
If you think about this process for a moment, and consider the size of clouds (on the order of thousands of meters), you will see that once it is inside a cloud, light pretty quickly becomes completely random in direction, and so follows a “random walk” path from particle to particle. The light can only escape by finding its way (by purely random chance) to the surface of the cloud. This escape could be at the surface through which the sunlight originally entered, or could be through the side or bottom of the cloud. How quickly the randomization of direction happens depends on the total water content (liquid and solid) of the cloud and the size of the droplets/ice particles.
With respect to reflection of light from clouds, how much is reflected depends very much on a four factors:
- The size of the scattering droplets
- The concentration of droplets
- The total depth of the cloud (that is, from the top surface to the bottom).
- How much scattered light can escape from the sides of the cloud (the ‘aspect ratio’ of the cloud).
If the total surface area of scattering droplets is large (lots of droplets of small size), then light will tend to be ‘randomized’ more quickly, so most light will (on average) remain closer to the surface of the cloud, and end up being more often reflected back into space from the surface through which it arrived… that is, higher net albedo. If the cloud consists of larger droplets and/or lower droplet concentration, then light will tend to penetrate much more deeply into a cloud before being ‘returned to space’, and albedo will tend to be somewhat lower.
A relatively shallow (in a vertical sense) uniform layer of clouds allows considerable light to escape from the bottom surface of the cloud layer (leading to lower albedo… and more light reaching the Earth’s surface), while a uniform layer of deep clouds does not allow very much light to reach the surface, and leads to much higher total albedo. An infinitely deep layer of horizontally infinite clouds leads to albedo approaching 100%, at least for non-absorbing wavelenghts. So a thick uniform layer of clouds back-scatters a large majority (approaching 90%) of visible sunlight that falls on the top of the clouds.
- Optical Absorption by Clouds
The above description of clouds assumes zero absorption of light by water. For visible wavelengths, where water (and ice) absorb very little light, this is a reasonably good approximation. But for longer wavelengths (near infrared and longer), water and ice have very strong absorption. The absorption profile for liquid water is shown in Figure 6.
Figure 6 – The absorption profile for liquid water
Keep in mind that this is a log-log plot; each division on the absorption axis represents a 10-fold change. According to Figure 6, light of 1.4 micron wavelength is reduced in intensity by 1 mm of water by a rate of ~90%!
The path of photons in a cloud is essentially random, but a typical photon can reasonably be expected to pass through many individual water droplets (or individual ice particles). Let’s assume that a typical photon passes through 1,000 droplets (particles) with an average ‘in-particle’ path length of 10 microns. This is the equivalent of 0.001 * 1000 = 1 cm of water. In this case, 1.2 micron wavelength light would be reduced by ~64% due to absorption by the water in the cloud. Longer wavelengths would be essentially 100% absorbed within the cloud.
Clouds therefore change both how energy from sunlight is absorbed and reflected. Infrared wavelengths (>1 micron) represent ~20% of total solar energy. Clouds strongly absorb this near infrared light, leading to considerable deposition of solar energy within clouds, high above the surface.
Part 2 will discuss the many kinds of aerosols and how they interact with light.
Part 3 will summarize the difficulties and uncertainties in determining net aerosol effects.