the Air Vent

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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.
Credit: http://www.inlightcn.com

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
Credit: http://www.philiplaven.com/mieplot.htm

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:

  1. The size of the scattering droplets
  1. The concentration of droplets
  1. The total depth of the cloud (that is, from the top surface to the bottom).
  1. 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.

  1. 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
Credit: http://www.lsbu.ac.uk/water/vibrat.html

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.

References:

1.   http://www.ecd.bnl.gov/steve/pubs/SchwartzJClimate10WhyHasnt.pdf

2.   www.cpsinstruments.com


48 Responses to “Light Scattering by the Earth’s Atmosphere, Aerosols, and Clouds, Part One – Basic Concepts”

  1. Brian H said

    Delushious. Soup-herb!

    EDIT NOTE: “scatters more that 100 times as” “more than”.

    Just to prove I ate the whooole thing. ;)

  2. Jeff, thank you for initiating this important thread. I look forward to Parts 2 and 3. May I also say that the Schwartz et al. May 2010 paper is an excellent one which clearly highlights the key issue of aerosols. However, I believe there is one flaw in their core argument. This is the explicitly stated assumption that the problem is uncertainty about the magnitude, character and trend(s) in global anthropogenic aerosols only.

    This assumption is significantly flawed because a known effect of increase in the atmospheric partial pressure of CO2 and global surface temperatures is also increase in the growth rates of both land-based and oceanic photosynthetic biota. This in turn magnifies the rate of production of biogenic aerosols which affects both atmospheric absorption of heat and the density of Cloud Condensation Nuclei (CCN). Biogenic aerosols are also known to increase the reflectivity of clouds.

    The existing literature base suggests these biogenic aerosol effects are at least as important as the effects of power generation-, industry- and transportation-sourced anthropogenic aerosols.

    Biogenic aerosol effects are particularly important over the oceans where, locally and regionally, the magnitude of the aerosol-emitting cyanobacterial near surface biomass alters on faster timescales in response to variation in SST and hence tend to affect weather more quickly.

    Exclusive focus on the effect of only anthropogenic aerosols would therefore be significantly misguided IMHO.

  3. Leonard Weinstein said

    Steve Short,
    Since clean up of anthropogenic aerosols is limited (especially in transportation and power generation in new developing countries), and since biogenic aerosols would increase from increased temperature and CO2, it logically follows that the inhibiting effect of this combination would act as a strong negative feedback to AGW. This does not even include possible cloud negative feedback. I think this make the argument for CAGW even weaker. Thank you for the extra information.

  4. Brian H said

    Steve;
    IIRC, there are also biota resident in the upper atmosphere itself. No idea how significant they may be for aerosol / cloud formation.

  5. Steve McIntyre said

    Thank you for the excellent and interesting post. I too look forward to the sequel.

  6. PhysicalChemist said

    Steve Fitzpatrick writes with brilliant grace and clarity. Thank you for this exceptionally informative post!

  7. Dan Hughes said

    An excellent summary of important information. Thanks Steve.

  8. suricat said

    Steve Fitzpatrick.

    It’s good to see these uncertainties posted at one blog-spot, this makes it easier to point to. I can’t wait for the follow up. :)

    Best regards, Ray Dart.

  9. Carrick said

    Thanks for the nice summary.

    Carrick

  10. Kenneth Fritsch said

    Thanks, Steve Fitzpatrick for the tutorial on light scattering of small particles – it is what makes the blogosphere an exciting venue and educational tool. Particle effects brought back memories of Coulter Counter measurements on small particles using their effects on an electrical field. I was always impressed that that simple measurement would provide an estimate of the size distribution and total counts.

  11. Kenneth Fritsch said

    Jeff ID, what am rating with the rating system you have recently added? I would like to give a thumbs up for this thread introduction by Steve Fitzpatrick and not be rating my own post. I do not like ratings for individual posts as the emotional ones get favored over the thoughful ones. Rating the thread intro is a good idea – except it appears you have to post to give a rating.

  12. Happy new year!

    earth has warmed about as much as expected:

    Global average surface temperatures have increased by about 0.75 degrees Celsius since the beginning of the industrial revolution, of which ~0.6 °C is attributable to human activities. The total radiative forcing by greenhouse gases is around 3 W/m2, with which we have ‘committed’ the planet to warm up by 2.4 °C (1.6-3.6 °C), according to a climate sensitivity of 3 °C (2-4.5 °C) for a doubling of CO2. The observed amount of warming thus far has been less than this, because part of the excess energy is stored in the oceans (amounting to ~0.5 °C), and the remainder (~1.3 °C) has been masked by the cooling effect of anthropogenic aerosols.

    (based on Ram and Feng, 2009)

    Because of the large uncertainties in both aerosol forcing and climate sensitivity, one can’t reliably use the one to constrain the other. Other periods from the earth’s past often provide better constraints on climate sensitivity (e.g. http://julesandjames.blogspot.com/2006/03/climate-sensitivity-is-3c.html )

    And just a plug to my introductory posts on aerosols:
    http://ourchangingclimate.wordpress.com/2009/04/13/the-atmospheric-aerosol/
    http://ourchangingclimate.wordpress.com/2009/04/16/aerosols-clouds-and-climate/

  13. Bryan said

    This is a timely and well presentted article.

    I look forward to reading the subsequent parts.

    The splitting of the atmosphere in to scattering and non scattering models seems an artificial construct.

    Modern IPCC theory rests on a non scattering model Ramanathan and Coakley.

    http://www.agu.org/journals/ABS/1978/RG016i004p00465.shtml

    Yet sceptics and IPCC adherents both quote Chandrasekhar with approval!

    Where did it all go wrong/

  14. kim said

    Say it loud and proud.
    Say it how, say it now, all
    About Delta Tau.
    ===========

  15. Terry said

    Good Post Steve.

    In Part 2, I wonder if you might emphasize the limitations of the theory when dealing with “non ideal” particles.

    Cheers

  16. Steve Fitzpatrick said

    Bart #12,
    “Global average surface temperatures have increased by about 0.75 degrees Celsius since the beginning of the industrial revolution, of which ~0.6 °C is attributable to human activities.”

    ‘This post is not intended to stimulate debate about what the true climate sensitivity is.’ I guess you missed that part.

  17. Nic L said

    Excellent post – very informative. Thank you. I also look forward to the remaining parts.

  18. Curt said

    Steve — You say, “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.”

    Is this why “threatening” storm clouds appear darker?

  19. AMac said

    Re: Bart Verheggen #12 (Jan 3 16:08),

    Thanks for the links to your posts on aerosols, as well.

    As a well-regarded technically-literate blogger, I would be very interested in your view of Steve Fitzpatrick’s essay. Is it accurate? Are there errors or omissions you would point to? Does it present a balanced picture of the claimed subject matter?

    It’s tremendously helpful when people from “across the divide” can agree on certain basics. And, equally, to discover when seemingly authoritative, factual statements by a technically-informed person are, actually, contested by technically-informed people of a different point of view.

  20. Steve Fitzpatrick said

    Curt #18,

    “Threatening” clouds appear darker because they contain a relatively high concentration of small droplets and are quite deep… the chance that light escapes from the bottom of this kind of cloud is low, so the base of the cloud appears dark, even if the sun is shining brightly on the top of the cloud. The high content of water comes from these clouds being formed by deep convection of warm and very moist surface air; they have high potential for producing rain because their moisture content is high.

  21. kim said

    Soares correlates.
    Last quarter last century.
    Cee Oh Two and Temp.
    ==========

  22. kim said

    Teeter the Totter
    Aerosol versus Nature
    Old Sol smirks and beams.
    ===========

  23. Jeff Id said

    I got to read the original. Nobody mentioned fig 5 was missing.

  24. Steve Fitzpatrick said

    Jeff,

    A bit of formatting was messed up also, but that made little difference. If there is a specific document type you would like for the next two parts, just let me know what it is.

  25. Jeff Id said

    I agree with the others. Nice article.

  26. Lynn Clark said

    In the 2nd and 3rd paragraphs, I think that “uncertainly in aerosols” should be “uncertainty in aerosols”.

  27. Bart said

    Steve,

    I missed that part indeed. My reply was in regards to your first paragraph and the referral to the recent Schwartz article which seems central to your reasoning.

  28. Steve Fitzpatrick said

    #25,

    For sure. Please believe that the word on the paper was not the same as the word in my head…

  29. Bart said

    Jeff,

    In the dept of “consequences of global warming you hadn’t heard of before”, check this one out:

    http://www.fight-entropy.com/2011/01/temperature-and-aggression.html

    “Results indicated a direct linear increase in horn honking [as a proxy for agressive behavior in traffic] with increasing temperature.”

  30. Steve Fitzpatrick said

    Bart,

    The majority of warming has taken place where it is cold, not where it is hot. I wonder if the honking would have been increased if the other drivers had been freezing instead of sweltering? I suspect it would. Surprise, discomfort makes tempers short.

    So will global warming soon be implicated in increasing divorce rates, crime rates, high school drop-out rates, and every other social malady mankind suffers? I fear it will.

    Rubbish.

  31. Bart said

    Well, it gave me a good laugh. By the sound of it it didn’t have that effect on you.

  32. Mark T said

    “The majority of warming has taken place where it is cold, not where it is hot.”

    Interesting, too, that these are the places with the least coverage and thus, the most adjusting and, more importantly, infilling.

    Mark

  33. Alistair Davidson said

    I think your understanding of Mie theory needs a bit of work! The electromagnetic energy couples directly with the water molecules. The cross sectional area of the cylinder of radiation stretching back to the light source from which energy is abstracted is proportional to the sixth power of the droplet diameter.

    Most of the energy [85%] is forward scattered with for 20 microns diameter, a maximum peak intensity of 2.2x 10^7 relative to the original intensity of the plane wave. Furthermore, the phase of the re-emitted radiation is set by the last water molecule.

    For a 20 micron diameter droplet, the peak fo

  34. Steve Fitzpatrick said

    #33,
    “The electromagnetic energy couples directly with the water molecules.” You need to explain a bit more I think. There is certainly no coupling to molecular vibrational modes, nor coupling to electron orbitals to a higher state (as these would lead to absorption). Exactly what direct coupling to water molecules are you referring to? In reading over Chapter 4 (describing scattering and absorption by a sphere) in Bohren and Huffman, I have been unable to find even a single use of the word “molecules” in their treatment of Mie theory. WRT phase, I did not discuss this subject, so can you explain what relevance this has?

  35. Steve Fitzpatrick said

    #33,

    With regard to the 6th power function: That is true when considering a single particle. But I am more concerned about scattering per unit mass of particles as the particle size changes. Since the number of particles is inversely proportional to the cube of the particle diameter, the total scattering per unit mass of particles in the Rayleigh region is proportional to D^3. (I stated “For an equal weight of particles of the same material, the scattering increases as the fourth power of the particle diameter”, which was not correct. It should have been the “third power”; I will ask Jeff to change it.

  36. Steve Fitzpatrick said

    Bart #31,
    “By the sound of it it didn’t have that effect on you.”

    Nope. Too many people will take such things seriously.

  37. stevenmosher said

    ban horns.

  38. Brian H said

    Bart & SF;
    The takeaway is obvious! Heat makes drivers horny.

  39. Alistair Davidson said

    Steve Fitzpatrick: 2.17 pm.

    You must remember that Mie analysis is the solution of Maxwell’s equations for the specific boundary condition of a plane wave [all photons in the same direction at constant energy per unit area]. The existence of EM coupling is proved by the phenomenon of slowing of the wave in matter. What happens is that in the intermolecular space the wave moves at the speed of light and the delay per interaction is the time for quantised absorption then re-emission, giving lower average velocity. Transparency is no evidence there is no absorption/re-emission!

    Mie scattering is the same phenomenon but in a different geometry. A rider to this is that I do not agree you can assume the Mie asymmetry factor, g, is constant as claimed in all the two-stream approximations. This is because after the first scattering a light enters a cloud, the wave is no longer plane!

    It’s very easy to prove experimentally that the claim of ‘cloud albedo effect’ cooling in AR4, 175% of the raw median AGW signal, is fundamentally wrong just by looking at rain clouds. They’re darker underneath. The Sagan and subsequent analyses predict that clouds with larger droplet size/lower optical depth should transmit more light. Take away that cooling correction and the IPCC’s claim of high future CO2-AGW is baseless

    The real physics has substantial direct backscattering at upper cloud surfaces, much more efficient for larger droplet sizes, and symmetrical diffuse scattering of light allowed to enter. That implies g = 0.5. For water clouds, pollution switches off the upper backscattering so we get ‘cloud albedo effect’ heating, another form of AGW. CO2 loses its AGW monopoly so the IPCC’s claims are baseless.

    NASA appears to have realised this by 2003 when there was no experimental proof of ‘cloud albedo effect’ cooling. From 2004 it started claiming a ‘surface reflection’ process increasing the albedo of polluted clouds. That was and remains fantasy physics apparently aimed at saving face and keeping the claims of high-feedback CO2-AGW in AR4 even though there is absolutely no evidence for it!

  40. Steve Fitzpatrick said

    #39,

    Whoa friend.

    “Transparency is no evidence there is no absorption/re-emission.”

    Considering that the net (integrated) intensity of scattered light at all angles is identical to the total intensity prior to scattering, it is accurate to say that there is no net absorption due to scattering, no matter what reversible interactions between water and the EM wave are taking place within the scattering droplet. Differences in refractive index for different transparent materials are, of course, proof of the existence of reversible interactions, as is the change in refractive index with wavelength. But the point is that the interaction does not reduce total energy. Please note that your earlier claim of “a maximum peak intensity of 2.2x 10^7 relative to the original intensity of the plane wave” must be consistent with no loss or gain in energy as a result of scattering. If you consider Figure 4 in the original post, and assume the peak at 0 degrees is “2.2x 10^7 times in plane wave intensity”, then the scattering intensity shown in the rest of the graph looks most everywhere between 100 and 100,000 times the plane wave intensity. This can’t possibly be correct. Are you suggesting that the calculated scattering versus angle profile is dramatically different from what Figure 4 shows?

    “It’s very easy to prove experimentally that the claim of ‘cloud albedo effect’ cooling in AR4, 175% of the raw median AGW signal, is fundamentally wrong just by looking at rain clouds.”

    What on earth are you talking about? Deep convective clouds have 1) great depth 2) high total liquid water/ice content, and 3) rapid droplet formation rates due to rapid pressure drop (driven by rapid convection from the heat of condensation). All of which lead to smaller initial droplet size and higher optical density… and dark cloud bases. The rain that comes from this kind of cloud must (of course) reduce the optical density of the cloud, and this is easy to see in the course of thunderstorms.. clouds lighten/brighten after the rain has started falling. The darkest convective clouds are those that have not yet had much rain fall out of them.

    I think that if you read the literature on clouds and aerosols you will see quite a lot of experimental evidence that the optical density of clouds is indeed influenced by aerosols. The most obvious is the observation of higher marine cloud density along the track of large ships… ships emitting substantial quantities of aerosols in their exhaust. I have myself observed rapid cloud formation a few thousand meters above a modest-size brush fire… and I did not imagine it.

    I do not claim to know the net effect of aerosols on Earth’s albedo (nobody knows for sure, because there is huge uncertainty), but there is no reason to believe that NASA or anybody else is using ‘fantasy physics’. I don’t think a discussion based on assumed conspiracies is terribly constructive, and this is what you seem to think is happening.

  41. kim said

    Paranoia ain’t even in it. This Climate thing is an extraordinary concatenation of primal and titanic natural, ontological, and psychological forces, which we apparently poorly understand. We can only stand in awe and so struck wonder why.
    ============

  42. kim said

    OK, OK, you wonder how.
    =====

  43. Kenneth Fritsch said

    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.

    Steve Fitzpatrick, would it be possible to get a view of what particle sizes exist in the atmosphere. Specifically what sulfate entity is it that is doing the scattering.

    There was a recent article (discussed at TAV) that talked about the potential amount and size of soil particles reaching the atmosphere based on some studies that indicated previous estimates were incorrect as were the climate models that used these estimates. At the time I suggested that perhaps soil particles would be a more effective way, should the need ever arise, of seeding the atmosphere to cool the planet than would a chemical like sulfates that I assume could produced a corrosive substance like sulfuric acid.

  44. Espen said

    Thank you for this well-written and very interesting article – a pleasure to read!

  45. Alistair Davidson said

    Steve Fitzpatrick: 10.11 am: My discipline isn’t meteorology but I have ingested a lot of physics and am a dab hand at challenging status quos! The optical physics of sols, starting with Van de Hulst, appears to have developed incorrect group-think leading to diametrically wrong predictions. I could be wrong but it’s always useful to test.

    You refer to the ships’ tracks. Fine, but they’re thin clouds. Reduce cloud droplet size and optical depth increases, varying as 1/r for constant volume fraction. The increased backscattering is because to a first approximation assuming no absorption, more diffuse scattering increases that part which exits the top of the cloud.

    Twomey correctly warned you could not extrapolate his [Mie scattering] ideas to thicker clouds. This is because diffuse scattering implies a hemispherical albedo asymptoting at 0.5. Be careful because Twomey refers, as proper physicists do, to spherical albedo, so it’s unity in his papers.

    Van de Hulst’s ideas developed because he observed for liquid sols backscattered energy >50%, more than you’d expect for symmetrical diffuse scattering. He tried to explain this by ‘lumping parameters'; (1-g).tau.omega. Sagan continued along these lines and his ex-students Hansen and Lacis apparently introduced his equation into climate modelling: http://pubs.giss.nasa.gov/docs/1974/1974_Lacis_Hansen_1.pdf

    It’s equation 19. Whilst it fits albedo – apparent tau data so you can interpolate, underneath the hood it assumes constant g, not the case once light enters a cloud [has to be 0.5 for diffuse scattering], and one optical process, biased diffuse scattering. It’s a curve fit which always says ‘INCREASE’ when droplet size falls. I fundamentally disagree with this for thicker clouds; it works for thin clouds though.

    The reason is a second optical process at the cloud tops. The extreme case is cumulo-nimbus where you have a snow cap. At 0.9 albedo, c. 80% of the energy is directly backscattered and the darkness is the result of very little light entering, not biased diffuse scattering. Wrong guess, Van de Hulst. Sagan swallowed it but Twomey didn’t!

    Take a thick water cloud. Twomey would have albedo asymptoting at 0.5. However, you often get 0.7. That means 40% direct backscattering and 30% diffuse up, the same down. So how do we get this direct backscattering which shows up as angular dependent albedo superimposed on a Lambertian diffuse background?

    It’s easy to deduce. After the first scattering, 3% of the energy has been hemispherically backscattered and the rest has been mostly forward-scattered in a narrow beam which peaks at 10^5 [relative] at 5 micron diameter [polluted], 10^7 at 15 microns. Although the light is coherent, it still disperses. At the next scattering, the backscattered proportion is still c. 3% but it’s dramatically higher in absolute terms because of the initial concentration.

    No need for biased diffuse scattering: it’s two processes and because the forward-scattered peak is lower for polluted clouds and disperses much more, there’s a very strong size dependence which is why pollution switches it off. Also, there’s optical leverage; reduce direct backscattering from 40% to 20%, transmitted energy increases by a third. Work it out! This is a powerful AGW and CO2 has lost its monopoly.

    PS, there’s no particle number effect because its just a few droplets in line, but the depth of the effect is set by stereological factors and the light comes out as a cone, as observed.

  46. Alistair Davidson said

    Sorry, for diffuse scattering, random photon direction, operationally g=zero [goes from -1 to +1].

  47. Steve Fitzpatrick said

    #45 and #46,

    Perhaps it would be better to address your issues after all three parts are completed. I do not presently have time needed to address your comments in detail.

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