RealClimate » Learning from a simple model

RealClimate » Learning from a simple model:

"A lot of what gets discussed here in relation to the greenhouse effect is relatively simple, and yet can be confusing to the lay reader. A useful way of demonstrating that simplicity is to use a stripped down mathematical model that is complex enough to include some interesting physics, but simple enough so that you can just write down the answer. This is the staple of most textbooks on the subject, but there are questions that arise in discussions here that don't ever get addressed in most textbooks. Yet simple models can be useful there too.

I'll try and cover a few 'greenhouse' issues that come up in multiple contexts in the climate debate. Why does 'radiative forcing' work as method for comparing different physical impacts on the climate, and why you can't calculate climate sensitivity just by looking at the surface energy budget. There will be mathematics, but hopefully it won't be too painful.

So how simple can you make a model that contains the basic greenhouse physics? Pretty simple actually. You need to account for the solar radiation coming in (including the impact of albedo), the longwave radiation coming from the surface (which depends on the temperature) and some absorption/radiation (the 'emissivity') of longwave radiation in the atmosphere (the basic greenhouse effect). Optionally, you can increase the realism by adding feedbacks (allowing the absorption or albedo to depend on temperature), and other processes - like convection - that link the surface and atmosphere more closely than radiation does. You can skip directly to the bottom-line points if you don't want to see the gory details."

Mathematician suggests extra dimensions are time-like

Mathematician suggests extra dimensions are time-like:

"In a recent study, mathematician George Sparling of the University of Pittsburgh examines a fundamental question pondered since the time of Pythagoras, and still vexing scientists today: what is the nature of space and time? After analyzing different perspectives, Sparling offers an alternative idea: space-time may have six dimensions, with the extra two being time-like."

“In my case, I am led to the conclusion that the ordinary four dimensional space-time extends naturally into six dimensions: the four dimensional space is hyperbolic as usual, but in the surrounding space there are equal numbers (3 each) of space and time dimensions, so the formula for s² reads something like s² = x² + y² + z² - t² - u² - v², where u and v represent the new time variables. I call this structure a (3, 3)-structure (mathematicians call it ultra-hyperbolic).”

Explosion video, shockwave

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100 tonnes of explosives go up at once.



It's the shockwave and the interesting fluid dynamics that interest me, not the enormeous xplosions

Dark Roasted Blend: Mammatus, Lenticular & Other Extreme Clouds

Dark Roasted Blend: Mammatus, Lenticular & Other Extreme Clouds:

"Mammatus Clouds, or 'breast-clouds', are fascinating formations in the sky, made mostly from the cumulus cloud base. Although they are not a sign that a tornado is about to form, they often accompany tornado-producing storms, or even may be direct byproduct of tornado activity - an aftermath of severe thunderstorms."

The exact processes that lead to the formation of mamatus clouds is unknown.

"[Lenticular] clouds are often formed by so-called "mountain waves" of air created by strong winds forced over high mountains. Then they hang over the mountains like alien "motherships"... Mount Rainier in Washington produces some of the most spectacular lenticulars."

Although the clouds are virtually stationary, the air within is usually moving very rapidly, with water condensing as it enters the cloud zone and evaporating as the air leaves.

Video - Running on "Water"

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Some time ago, I wrote about the cool properties of corn flour goop - the way it can changes it's behavior between solid and liquid form depending on how fast you hit it. I recently came across this video demonstrating this effect on a grand scale.

On a microscopic level, the corn flour goop consists of small starch particles packed close together. Separating the particles is a thin layer of water that acts like grease – allowing the particles to slide across each other and move around, as long as they move slowly. So, when you slowly push your fingers into the goop, the starch slides out of the way, allowing you to slide in easily. In this situation, the fluid applies viscous drag to the grains gently slowing their motion. However, if you try to smash your fist in quickly, the starch tries to move faster than the water can accommodate and grains come into contact. Now, the much stronger force of static friction acts between the grains – as long as they are being pushed together, there is force preventing them from sliding across each other - and the harder they are pushed together, the stronger the friction force is!

Almost instantly, long columns of starch grains are pushed together – a chain reaction of jammed particles that are held together by the stress you are applying (the force downwards from your hand) and the frictional forces that stop them slipping sideways out from under your hand like they did when you moved slowly. This "jamming" leads to "force chains" through the goop. While the stress is applied these force chains can last essentially forever, because of the static friction. Releasing the stress allows the structures to break down, returning to its fluid-like state.

Hydrogen Atom Scale Model

"And you thought there was a lot of empty space in the solar system. Well, there's even more nothing inside an atom. A hydrogen atom is only about a ten millionth of a millimeter in diameter, but the proton in the middle is a hundred thousand times smaller, and the electron whizzing around the outside is a thousand times smaller than THAT. The rest of the atom is empty. I tried to picture it, and I couldn't. So I put together this page - and I still can't picture it.

The page is scaled so that the smallest thing on it, the electron, is one pixel. That makes the proton, this big ball right next to us, a thousand pixels across, and the distance between them is... yep, fifty million pixels (not a hundred million, because we're only showing the radius of the atom. ie: from the middle to the edge). If your monitor displays 72 pixels to the inch, then that works out to eleven miles - making this possibly the biggest page you've ever seen."

Read more at www.phrenopolis.com/per...

Physics NewsUpdate - May 26, 2006. The Misshapen Solar System and Counting Terahertz Photons

PHYSICS NEWS UPDATE
The American Institute of Physics Bulletin of Physics News
Number 778  May 26, 2006  by Phillip F. Schewe, Ben Stein,
and Davide Castelvecchi        www.aip.org/pnu
 
THE MISSHAPEN SOLAR SYSTEM. Having traveled far beyond the planets
in their 28.5-year journey, the two Voyager spacecraft are providing
new information on the heliosphere, the teardrop-shaped bubble that
separates the solar system from interstellar space.   At this week's
Joint Assembly Meeting in Baltimore of the American Geophysical
Union (AGU) and several other geophysics-related societies, Ed Stone
of Caltech reported that the heliosphere is deformed, according to
Voyager observations, with the teardrop's rounded edge bulging at
the top (the northern hemisphere of the solar system) and squashed
at the bottom (the southern hemisphere). (See pictures and movies at
http://www.nasa.gov/vision/universe/solarsystem/voyager_2006agu.html
)  As Rob Decker of Johns Hopkins University Applied Physics
Laboratory explained, the asymmetry is due to a magnetic field from
interstellar space pushing on the southern hemisphere.  The field is
about 1/100,000 the strength of Earth's field but its effects can be
felt for billions of miles, since it is acting over a large area on
the very dilute gas at the solar system's edge.
The interstellar field even squashes an important spherical zone
inside the heliosphere, called the termination shock.  Analogous to
the circle that forms when water splatters on a sink, the
termination shock represents the boundary at which the rapidly
traveling solar wind (the stream of charged gas from the sun) slows
down abruptly and piles up.  Voyager 2's measurements indicate that
the southern part of the termination sphere might be a billion miles
closer to the sun than the northern part.  Moreover, forces from the
solar wind cause the termination shock to breathe in and out roughly
every dozen years.  Voyager 1 has already ventured beyond the
termination shock, to the heliosheath, the region where solar wind
and interstellar gas mix. So in a way, the end of the solar system
is not clearly defined.  Stone guesses it could be another 10 years
(3-4 billion miles) before the two spacecraft pass through the
heliopause (the very outermost boundary of the heliosphere) and
enter purely interstellar space.  The spacecraft have about another
15 years of power left in them. (Session SH02 at meeting; see
http://www.agu.org/meetings/ja06/?content=search)

COUNTING TERAHERTZ PHOTONS.  Scientists at the University of Tokyo
and the Japan Science and Technology Corporation have been able to
detect single photons in the terahertz region of the electromagnetic
spectrum for the first time.  Previously, such photons, with
energies around 4 milli-electron-volts, could not be seen singly.
THz radiation, essentially in the far-infrared, is a potentially
important telecommunications carrier.  Not only detection but
microscopy at ultra-low THz light levels can be performed.  By
scanning a quantum-dot probe (highly sensitive to THz light) across
the face of a sample, the sample can be imaged with a
spatial resolution of 50 microns (the radiation itself has a
wavelength of 132 microns).  This is even more remarkable when you
consider that the power emitted from the surface being imaged is at
the level of 10^-19 watts (0.1 attowatt).  Currently photon-counting
microscopy glimpses a few electrons at a time oscillating at THz
frequencies in semiconductor devices at high magnetic fields.
According to Kenji Ikushima  (ikushima@thz.c.u-tokyo.ac.jp), the
extraordinarily high-sensitivity of the photon counting approach
will soon facilitate the study of a molecule shaking, rattling and
rolling at THz rates, photon-counting microscopy in this  spectral
range will facility the study of a few molecules at a time
oscillating at THz frequencies in semiconductor devices at high
magnetic fields.  (Ikushima et al., Applied Physics Letters, 10
April 2006; www.dbs.c.u-tokyo.acjp/~komiyama )