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.