Decomposing Cloud Feedbacks Enhances Climate Science Forecasts

As I noted in a post a year ago, the properties of clouds play a significant role in climate change models. Hence, it ought to be no surprise that when forecasting climate change, there’s one huge wild card: clouds. By reflecting, absorbing, and emitting radiation, clouds (and fine particles known as aerosols) play a major role in the planet’s energy balance and thus in setting Earth’s temperature. This is given the fact that Earth's climate is the product of complex interactions between the Sun, the ocean and the atmosphere. For reference, climate scientists explore these exchanges - especially between ocean and atmosphere - using general circulation models (GCM) which compute the respective circulations in ocean and atmosphere.

Immense difficulties arise once one goes from the general to the particular.  Hence, whether an individual cloud warms the planet or cools it depends on its size, latitude, altitude, albedo, and other physical parameters. For decades, climate models have strongly disagreed on how cloud properties—and their effects on Earth’s energy budget—will change with global warming, making clouds the biggest source of uncertainty in climate model predictions.

The resolution of the problem of narrowing uncertainty to better forecast  climate change is possible  only if climate scientists can better constrain the feedbacks from clouds. Enter now new research from Zelinka et al.  which  basically decomposes cloud feedbacks to better connect them to specific physical processes.

One primary process is radiative transfer, especially in a plane parallel atmosphere. The basic layout of the problem (especially involving clouds) is well known but difficult. Thus one would wish to investigate  Rayleigh scattering in concert with standard gray atmosphere radiative transport. An equation of transfer that applies is: -dI/dt (1/k r ) = I – J

Where k is a mass scattering coefficient, r  is the molecular density (e.g. in cloud cover) and J is the vector source function for a specific intensity I. If the correct Stokes parameters (I, Q, U, V) which describe degree of polarization are included, and the right incidence angle of radiation occurs, we can expect the propagation of radiant energy from the S. hemisphere to the north very effectively.

But.....one can't forget or omit diffusive reflection and re-transmission of radiation, say arising from particulates . Chandrasekhar in Radiative Transfer, (Dover Publications) shows that for angles of incidence in the range : 0.5 < i < 0.8 radian, diffusive reflection allows the radiation reflected normal to the incidence direction to actually have higher intensity than the original. (E.g. for optical depths 1.0 < < 2.0).

In effect, if conditions in the lower atmosphere incorporate such optical depths (and angles of incidence for scattering, diffusive reflection), on account of increased presence of particulates, aerosols, we will expect to find an "anomaly" say in the temperature.

For the Zelinka team, the approach entailed using so-called cloud radiative kernels along with detailed model cloud information provided by the International Satellite Cloud Climatology Project Simulator. They calculated the feedback due to 49 different types of clouds—which were divided into seven altitude categories and seven optical depth categories. (Over the past few years, kernels have become a common tool for comparing cloud feedbacks among climate models.)

In this case, the authors refined the technique to compute the amount, altitude, and optical depth feedbacks separately for upper-level and low-level clouds. Low-level clouds are those that reside in the boundary layer, the layer of Earth’s atmosphere directly influenced by its surface. Upper-level clouds reside above the boundary layer and are affected by different processes
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Zelinka et al discovered that all climate models agree on the direction of three main feedbacks that accompany global warming. First, upper level clouds rise to higher altitudes in all models, warming the planet by trapping more heat. Although this was previously known, the positive feedback is actually smaller and better constrained than past research has suggested. Second, low-level cloud cover decreases in all models, warming the planet by reflecting less incoming sunlight back to space. And third, optical depth of low-level clouds increases in all models, cooling the planet by reflecting more sunlight.

The takeaway of the Zelinka et al paper is that treatment of radiative processes, transfer of radiation in clouds, is simplified by decomposing cloud feedbacks into the individual mechanisms in play.  This is a crucial advance given we want to understand and constrain cloud feedbacks if we wish to more accurately forecast how our planet will react to climate change.

Looking at Stellar Emission and Absorption (3)

The study of spectral lines is facilitated by using what is called the “equivalent width”. This provides the total strength of a line, yielding the same area of the line (for a rectangular facsimile) provided the depth is complete from the continuum to zero brightness.  

    We can express the equivalent width in two ways, based on frequency of wavelength, or wavelength itself, e.g.

W =   ò ^¥₀  (I _c – I _u /  I _c )du =  ò ^¥₀  (F _c – F _l / F _c ) dl

   The left side defines W in terms of the intensity from the continuous spectrum outside the spectral line where the quantity (I _c – I _u / I _c ) is referred to as the “depth of the line”, the analogous quantity to (F _c – F _l / F _c ) on the right side where we have radiant flux units. Technically, the integral should be taken only from one side of the line to the other but the limits can be as shown provided I _c    (or  F _c)  is kept constant in the neighborhood of the line.

      The Curve of Growth:

Having obtained the equivalent width, the next logical step is to generate the “curve of growth”.  Recall from the previous section that W, the equivalent width, represents the line strength. Then the curve of growth describes how the latter increases as the optical depth, τ  increases.

To fix ideas, we use a model slab of  finite thickness ds and over which the optical depth increases by d τ.  The incident intensity is  I _c  for frequencies in the neighborhood of the line,  and the intensity emerging from the opposite side is    I _u  which we seek to find.

Starting with  the original basic transfer equation based on wavelength:

dI(l)/ds = -k(l)  I(l) + k(l)  S(l)

We can derive the frequency form:

d I_u / dτ _u  =  -  I_u – S _u

We have (from the original equation) after adjusting for frequency:

d I_u / ds   =  -k _u I_u  +   k _u S _u

Where:   k _u   =   d τ _u / ds

So: 

d I_u / ds   =  -( d τ _u / ds) I_u  +   (d τ _u / ds) S _u

d I_u =   - d τ _u  I_u  +   d τ _u  S _u  =   - d τ _u   (I_u – S _u)

whence:

d I_u / dτ _u  =  -  I_u – S _u

For which the solution is found (on integration):

I_u =  I _c  exp (-τ _u)

Where:  τ _u   = N L a _u  =  N L a _o  f _u

Where ‘N’ is the number of absorbing atoms per unit volume and we already saw that:

a _o =  a _u  /  f _u = a _u [1 - e ^{-  h u o / kT}] (p e²/ mc) f

In terms of this new information, the equivalent width of the line can then be written as:

W _u =  ò ^¥₀ [1  -   exp (- N L a _o  f _u) ] du

For small x we may use the approximation that:

exp (-x) much greater than   1 – x

So rewrite the equation for  W _u:

W _u »   ò ^¥₀ [1  -  (1 - N L a _o  f _u)  du

»   ò ^¥₀   N L a _o  f _u  du » N L a _o  ò^¥₀  f _u  du

So we find W _u  depends only on the form for the broadening function.  For very weak lines, for example:

ò ^¥₀  f _u  du  much greater than   1 so that W _u » N L a _o 

Or simply proportional to N, the number of absorbing atoms. For “strong” lines the absorption near the center is very large so we can expect: N L a _o  f _u    >> 1 and with sufficient working this can be shown to give the corresponding equivalent width: W _u  = 2  D u _D

And for the moderately strong lines: 

W _u  =  2  D u _D {ln  (N L a _o/Öp  D u _D )} ^½

While very strong lines yield:

W _u  =   1/p  (N L a _o  g)^½

Where g is the damping constant.

Assembling all the diverse W _u    and plotting log W _u vs.  log (N L a _o ) one gets the curve of growth shown below: 

Here, each contribution can be separately considered, in terms of the “linear”, “saturated” and “damping” segments. The first is for the weakest lines such that W _u  is simply proportional to the number of absorbing atoms. But as more atoms are added this approximation becomes invalid and so we are in the saturated part. In effect,  the near zero slope shows the degree to which the equivalent width increases at an almost uniform rate. Finally, we have the damping segment wherein the line under consideration develops “damping wings” because the number of absorbing atoms is so large. (Bear in mind again that  a _o  is proportional to the transition probability)

Problems:

1)Consider the ionization of helium, with three stages of ionization for which the partition functions are:    Z _I =    Z ₃    =   1,  and Z ₂ =    2

With ionization energies:

 c  ₁ =   24.58 eV    and c  ₂ =   13.6 eV  

For a temperature of T = 5040 K write out two versions of the Saha equation for:

log( P _e N ₂ /N ₁)   and log( P _e N ₃ /N ₂)  

And hence, compute:   (P _e N ₂ /N ₁)   and (P _e N ₃ /N ₂)  

2)The diagram below was sketched by a first year astrophysics student. It represents part of the emission spectrum of atomic hydrogen.

 It contains a series of lines, and the wavelengths of some (in nm) are marked. '
There are no lines in the series located at less than 91.2 nm

(a)   In which region of the E-M spectrum would these lines occur?

(b) Obtain a relation between E and l   and thence find the photon energies equivalent for all the wavelengths marked.

(c)Use this information to map a partial energy level diagram for hydrogen. Show and label clearly the electronic transitions responsible for the emission lines labeled.

3)a) A stellar atmosphere is composed of pure hydrogen, at a temperature of 9600 K and with electron pressure, P _e    =  200 dyne cm ^-2 .  Use the Saha equation to compute the fraction of atoms

that are ionized in relation to the total, i.e. find:   N _II /( N _I   + N _II )  

The partition functions are:  Z _II =   1 and  Z _I =   2

Hint: Check to see whether (E ₂  -  E ₁ ) >> kT with

k =  8.6174 x 10 ^-5 eV/K

So the Boltzman factor  exp (- E2 – E1) / kT << 1

b)Repeat the exercise again for a temperature of 5040 K and 20,000 K and thence account for why the Balmer lines attain maximum intensity at a temperature of 9520 K.

(4) Calculate how far you could see through the Earth’s atmosphere if it had the same opacity as the solar atmosphere, where:

k _l   =   0.264 cm ² /g.

Take the density of Earth’s atmosphere as:

   r   =   0.0012 g cm ^-3

The density of the solar atmosphere is taken as :

r _s   =  2.5 x 10  ^-7 g cm ^-3

And we know the intensity declines over a characteristic distance (length scale) such that:

ℓ  =   1/ k _l r

Gov't Releases UFO Files: Don't Look For Alien Artifacts!

The release by the NSA of  thousands of  declassified UFO documents has the blogosphere and twitter-sphere ablaze and speculations running rampant that somewhere in those files is the 'smoking gun' for alien craft in the skies of our planet. The website for accessing the documents can be found here:

https://www.nsa.gov/public_info/declass/ufo/

But don't hold your breath trying to turn up evidence for extraterrestrials. There won't be any. Or, let me correct that by noting there might be some semblance of signal - but it's buried in tons of noise. Do you have the patience to sift through it all? When the JFK Records Act saw millions of files released from back in 1992, only a relatively few determined and hardy researchers had the diligence to plumb through them to turn up assorted nuggets, such as Oswald's CIA files - showing he'd at least been a contract agent for the 'company'.  Further work by stalwarts such as Peter Dale Scott also identified the key telegrams from the CIA Mexico City station showing indisputably how Oswald had been framed to take the fall. Of course, it's ironic that scads of lazy critics - who like to shoot from the hip on the whole JFK  assassination conspiracy issue - couldn't bestir themselves to lift one pinky finger to find a single file themselves.

Expect the same reaction from the lazy dopes if you happen to hit pay dirt by going through the UFO files from the link above. "The truth is out there" - yes, but few in the government want you to see it, as in the Kennedy assassination conspiracy.

Does this mean we are talking about actual alien ships? No, not necessarily. A common misperception is that UFOs are “flying saucers” or space ships. However, this is actually only one possible hypothesis among several. This is evident in the late J. Allen Hynek's  exacting UFO definition

“A UFO is the reported perception of an object or light seen in the sky, the appearance, trajectory and general dynamic behavior of which do not suggest a logical, conventional explanation and which is not only mystifying to the original percipients but remains unidentified, after close scrutiny of all available evidence by persons who are technically capable of making a common sense identification, if one were possible.”

The gist of the definition - however lengthy = is that one must not automatically jump to any conclusion that conflates the UFO with an extraterrestrial craft.   The difficulty in formulating UFO hypotheses, and interpreting UFO reports, is a first-hand experience for me. Not only have I investigated other people's reports (inevitable if one is involved in astronomy)  and published the results[1] but I've observed a "UFO"  myself. The incident occurred in March of 1962 at the opening of a shopping center in Carol City, Florida. While awaiting the start of festivities I happened to look up at the night sky, being the amateur astronomer that I was. Amazingly, I witnessed a brilliant orange disc, at least the same diameter as a full Moon, moving rapidly from north to south.

It hovered for two to three seconds above the crowd and I detected the odd "Oooh" or "Aaah" from random spectators. Thus, I knew I was not having a simple hallucination (at least not by myself!) The most ironic and notable thing to me was the complete absence of sound. No whirring, like one would expect from a helicopter's propeller blades, or engine noise. The object - if "object" it was - appeared to be a light source rather than just reflecting light from elsewhere. After about three seconds it took off due south at what I estimated to be an incredible speed. As a seasoned sky observer, even at the age of 16, I was able to quickly eliminate all known man-made or natural objects from consideration. The exceptional luminous and dynamical behavior allowed this. Nevertheless, to this day I am not prepared to pinpoint a specific hypothesis in any dogmatic sense. Nor am I prepared to assert it as a "craft" from another planet.

But let's say one is looking for some kind of signal from the NSA files that a real artifact exists, what would one look for? What sort of parameters, physical aspects?


As a good preliminary test,  one can do no better than enlisting Physicist Edward U. Condon’s Air Force- commissioned Scientific Study of Unidentified Flying Objects (1969, NY Times Books) While most of the cases are exposed as either natural or meteorological phenomena – or possible hoaxes- one case stands out: Case 46, p. 396 from McMinnville Ore. (11 May, 1950) that concludes - and I quote, from p. 407

:"This is one of the few UFO reports in which all factors investigated: geometric, psychological and physical appear to be consistent with the assertion that an extraordinary flying object- silvery, metallic and disc shaped flew within sight of two witnesses. "

I found the best part of the case study was the photometric analysis (pp. 402-06). This was essential in order to discriminate luminance conditions between a hypothetical hand model nearby and an actual, extraordinary, distant flying object. The key observation made by the investigators was:

"The shadowed bottom of the UFO (see image) has a particularly pale look suggestive of scattering between observer and object. If such scattering is detectable it may be possible to make some estimate of the distance involved".
From there they list a sequence of possible interpretations, including: optical fabrication or double exposure (rejected because the UFO is darker than the sky background luminance); a retouch of a drawn image (rejected because analysis of the negatives disclosed they were unretouched); physical fabrication using a 'frisbee' hand spun model (rejected because the UFO displays an off-axis pole which is never seen displaced, i.e. in rotation); model suspended from a wire (similar positions in each photo -so possible), and extraordinary flying object (since photometry suggests a large distance).

So, in the end, the last two interpretations had to be analyzed for consistency with the least likely of the two rejected.

The investigators proceeded by computation of the luminance, or the apparent brightness of an object at a distance r, normalized relative to some intrinsic value B(o) at r(o), viz p. 402:

B = B(sky) (1 - exp(-br)) + B(o) exp(-br)

where b is the scattering coefficient. In the equation, the first term (with B(sky)) represents scattered light and the second term, extinction. As the investigators noted (ibid.):

"Since all measures must be based on the witnesses' two photographs, we will determine b for the given day from the photographs themselves. Normalizing all brightnesses (measured from the film and assuming that the images fall on the linear portion of the gamma curve (see- e.g. http://en.wikipedia.org/wiki/Gamma_correction) to that of the sky near the horizon, i.e. on a line within a few thousand feet of the ground, where the UFO is constrained to be by the reported cloud height and probable nearness to the camera, we have:

B = 1 + exp(-br)[B(o) - 1]"


From the above, if the object is sufficiently distant one would have:

exp(-br) -> 0

so therefore,

B = 1 + exp (0)[B(o) - 1] = 1 + [B(o) - 1]

and B equals the sky brightness. (in optical terms, the optical depth t >> 1)

To ascertain whether the claimed sighting photographed is a fake then, all that's needed is to solve for the distance r, given a zero distance luminance B(o) cmopared to an observed luminance B. As can be seen from the equation, to do this one needs to obtain the scattering coefficient, b.

The investigators used densitometric analysis to obtain an assorted range of values for the luminance B, for different objects appearing in the photographic image - these are presented in Table 2, from the Case Study. (Shown, with comparison of two plates, 23 and 24). Since the investigators knew the distance of 'Hill 2' at 2.2 km then photometry indicated B = 0.685 for the distance hill, while the foreground foliage yielded B = 0.403.

Processing all this data in concert, the investigators obtained the distance r = 0.32 km, or just over 1,050 feet as the distance to the object - nearly one fifth of a mile. The investigators graphically illustrated the domains of the two hypotheses via their graph (Fig. 3) which is appended here. As they note (p. 406):

"If the object is a model suspended from a wire only a few meters away the surface is some 37% brighter (B = 1.21 v. B = 0.885) than the tank and the shaded portion is probably more than 40% brighter than the shadow on the tank...nearly impossible to maintain in the face of the photometry.

The shadowed side of the UFO appears so bright that it suggests significant scattering between it and the observer"

In other words, conforming with the distance calculated from the luminances..

The investigators graphically illustrated the domains of the two hypotheses via their graph shown below:

The point of all this is there appears to be at least quantitative -photometric  evidence for the existence of extraordinary craft if one knows how (and where) to look for it.

The $64 dollar question is: Are most interested people qualified to be able to perceive the evidence even if it's staring them in the face?

I suspect that depends on one's scientific background, or at least exposure to basic physics principles. This includes those pertaining to luminance and relation to brightness,  as well as geometrical factors such as being able to derive linear scales from angular  - e.g. as observed against the sky background.

So, by all means have a look at the released UFO files, but always be aware of what it is you are seeing, and also whether the parameters, physical aspects are sufficient to make any kind of determination. And lastly, whether you are really qualified to make any determination.

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[1] Transient Optical Phenomena of the Atmosphere - A Case Study, in The Journal of the Royal Astronomical Society of Canada, Vol. 74, No. 3, June 1980.