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“Hockey Stick - Michael Mann

There has been a lot of controversy about the “hockey stick”, at least in the mass media. Since paleoclimate is outside my knowledge base, I’m going to redirect you to read Dummies guide to the latest “Hockey Stick” controversy at RealClimate. The “problems” with the “hockey stick” are highly mathematical, and I hope it’s written at a level that you can understand.

Galactic Cosmic Rays and Clouds

I don’t know anything about galactic cosmic rays, but Recent Warming But No Trend in Galactic Cosmic Rays might. I’ve reproduced their figure showing temperatures in white, and GCR in red.

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The Earth emits radiation according to the Stefan-Boltzmann law (same as the sun). This says that the power (or energy per area) radiated is proportional to the temperature to the fourth power - σT⁴. So the total energy emitted is the energy per area times the area. But in this case, we need to use the surface area of the entire Earth - 4πR². Thus the total energy emitted is 4σT⁴πR².

When we set these two values equal, we get S₀(1-A)πR²=4σT⁴πR². Cancelling out the πR² on both sides gives us S₀(1-A)=4σT⁴. Since we know S₀ and σ and A (about 0.3 for the Earth), we can solve for T. We end up with a value of 254.8 Kelvin (-18.3 C / -1 F). The measured average temperature of the earth is around 15 degrees Celsius. What did we do wrong? We didn’t account for the effect of greenhouse gases.

Greenhouse gases are radiatively inactive in the visible spectrum, and radiatively active in the infrared. The majority of incoming solar radiation is in the visible spectrum. Most of this shortwave radiation passes through the atmosphere and is absorbed by the surface. The earth, like every other object with a temperature greater than absolute zero, radiates. The amount and at what frequency is determined by its temperature. The higher the temperature, the more an object radiates, and at higher frequencies. The earth is a lot cooler than the sun, thus the earth emits its radiation at a lower frequency - in the infrared.

As I said before, greenhouse gases are active in the infrared, which means that the radiation that the earth emits will be absorbed by these gases. Then, because the gases have a temperature above absolute zero, they emit radiation. But, this emited radation is radiated isotropically - meaning in all directions. Thus, for each photon that is absorbed by a greenhouse gas, half of the energy will be sent back towards the surface. So the surface of the earth is heated by the sun and the atmosphere and its temperature is greater than if it was heated by the sun alone.

[Added June 5, 2007]
The striked sentance above makes it sound like the atmosphere re-radiates energy it absorbs. This is incorrect. The atmosphere radiates because it has a temperature above absolute zero.

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This is an open response to Ponder the Maunder. A copy will be sent via email to the author.

Common Sense
Common sense is the collection of prejudices acquired by age eighteen.
Albert Einstein. Quoted in E T Bell Mathematics, Queen and Servant of the Sciences. 1952.

Common sense is not always right. Newton’s first law says that an object in motion will remain in motion at a constant velocity until a force is applied. Common sense tells us that an object in motion will steadily decrease its speed until it stops. Friction is what causes objects to slow down. It is not trivial to think of a frictionless world. In a frictionless world, you would not be able to walk, because it’s the friction between your shoe and the floor that allows you to propel yourself forward.

Common sense tells us that a heavier object falls faster than a lighter object. Newton’s third law of motion tells us that the acceleration of an object due to gravity is the same; a hammer and a feather will both accelerate towards the Earth at exactly the same rate.

Einstein’s theory of special relativity says that the velocity of light is a constant, and that both space (length) and time are variable. Common sense tells us that neither space nor time can vary.

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The American Meteorological Society defines an air mass as

A widespread body of air, the properties of which can be identified as 1) having been established while that air was situated over a particular region of the earth’s surface (airmass source region), and 2) undergoing specific modifications while in transit away from the source region. An air mass is often defined as a widespread body of air that is approximately homogeneous in its horizontal extent, particularly with reference to temperature and moisture distribution; in addition, the vertical temperature and moisture variations are approximately the same over its horizontal extent. The stagnation or long-continued motion of air over a source region permits the vertical temperature and moisture distribution of the air to reach relative equilibrium with the underlying surface.

Air masses are typically classified by their temperature and moisture content. They can either be hot or cold; wet or dry. Hot air masses originate over the tropics and are called tropical (T) and cold air masses originate over the poles (P). Air masses that form over the ocean are called maritime (m), while those forming over land are called continental (c). When combined, we have four different types of air masses: continental tropical (cT), maritime tropical (mT), continental polar (cP), and maritime polar (mP). There is a fifth type of air mass called arctic (A) that is just a very cold continental polar air mass. The figure below shows the air masses that affect the United States, and paths they could take.

When two different air masses converge, they produce a front. In future posts I’ll define the different kinds of fronts and what weather can be expected from them.