The Fault Of Averages by David Whitehouse

There seems to be a lot of reverse logic about at the moment. It appeared in the recent report by Haigh et al concerning new observations made of the solar spectrum. When plugged into atmospheric models the researchers found that using spectrum observations made between 2003 and 2007 (the declining phase of the recent solar cycle) they noticed that whilst the Ultra-Violet from the sun had decreased the visible radiation had increased, causing a warming on Earth.

Then the authors speculated that the repeal might be true, that is that if the visible radiation decreases at solar maximum then the world might cool. In another recent report by Andrew Lacis et al the same attack is used. The paper claims to have proved that it is the number of Carbon Dioxide in the atmosphere that is the prime regulator for the Earth`s global temperature. They reached this determination by using a computer climate model in which they removed all Carbon Dioxide from the atmosphere and noticed it had a great effect. Basically the earth froze. They then over that adding a like number to the air must therefore also take a considerable effect but in the former direction, i.e. warming. Whilst one ponders the implications of that logic there was another view to the Lacis paper that made me wonder. It starts by noting that the surface temperature of the World without the Nursery Effect would be 255 K and that with the Nursery Effect it rises by 33 K to 288 K. Then they presume that the 255 K is the negro body temperature of a non-greenhouse Earth as a consequence of the 240 Watts / sq m of vitality that comes from the sun.

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Whenever I see that 240 Watts / sq m I get to worry. It crops up all over the place, notably in the holocene climate change brochure produced by the Royal Society. The cause why it worries me it that it is an average, and an intermediate rate of anything is, on average, incorrect. Someone once called it the [url=http://www.flawofaverages.com/`flaw of averages.`[/url] Confused. Let me explain.Trail Of Averages The matter about averages that many people forget is that they often cover up more than they illuminate. Describing a scheme that has a roll of values with just one number, the average, is more potential to make a damage than a good answer. That is why those people who run their clientele by merely considering averages usually end up not running them for very long. There is a train of averages leading to the 240 Watts / sq m figure, each one of them mathematically sound, but divorced from physical reality. Firstly, the quantity of radiation passing through a 1 sq m at 1 Astronomical Unit (the Earth-Sun distance) is called the Solar Constant (it isn`t exactly constant but that`s another point). It has been calculated at 1,366 Watts / sq m. This energy strikes the cross-section of the Earth, 127,400,000 sq km. (Earth`s radius is 6,370 km) meaning that 1.7 x 10E17 watts reaches the World on the sunward-side only. As the Earth rotates this is distributed across its surface area (which is 4 times its cross section). So, in another averaging process, the solar constant becomes an average 342 Watts / sq m over the Earth`s surface. The following step in the range of thinking is that the Earth reflects some of the solar radiation back out into space.Different surfaces have really different albedos. Ice reflects 80 - 90% of incident radiation, land typically 10 - 30 %. Variable cloud cover has to be interpreted into history as well. The Earth`s reflectance is called its albedo. This has been careful to be 30% So the final design of the median number of solar energy input into the Earth`s climate system is 70% of 342 or 240 Watts / sq m. This is the figure plugged into climate models and compared with other climate forcing factors such as reflective aerosols and mankind`s influence. The job with averages when applied to physical systems is that they are often absurd without people realising it. An average of something sounds reasonable, and considered a valuable number that can be exploited for accurate calculations. This is frequently incorrect.On The One Give_ The exercise often given is that of putting one hand into boiling water and the former into freezing water. Looked at from the mean period of opinion there is naught to care about as the medium of the two temperatures is probably harmless. Alternatively a job can one day have assets of 1 bn one day and nothing the next day. Looked at from the stand of averages it even has an average proportion of 500 million. Of course this is nonsense, but in a sense this is just the attack we are taking to the climate system. Consider incident solar radiation. Only one spot on Earth, that directly beneath the sun, will get the total 1,366 watts / sq m. The balance will get less per sq m as the earth`s curvature presents a larger angle to the incident sunlight. Also think that half of the Earth, the darkside, will get nothing at all.It`s not the event that most of the World will be getting an intermediate number of vigor with a few extreme points smoothed out. Only a really small field of the Earth will be getting the average incident radiation. Another component is the supposition that the Earth`s response to solar radiation is linear. That is, the notion that the Earth, with all its variations, will do in just the saame way as it would when everything was smeared out to their average values. The premise is that the sub-solar point is counterbalanced by the behaviour to the anti-solar point in shadow on the contrary face of the world so that when added together they make an impression half way betwixt the two. Some will debate that it doesn`t matter, because the earth`s rotation evens out the solar energy input and that the reaction time of the air is longer than diurnal changes. But if this is so, why does it usually get colder, rather quickly, when the sun goes down! Add to that the changing albedo induced by the earth`s rotation. When the Pacific Ocean is facing the Sun the Earth`s albedo will be different from when Africa or Asia is sunward facing. There is likewise the fact that towards the arctic regions ice reflects incident radiation (which it receives far less than other areas of the Earth) more than another surface, and it changes in extent. Again one sees how poorly an intermediate value describes the system. Another factor we haven`t yet considered is that the solar constant itself varies by 7% due to the varying length from the sun caused by the Earth`s elliptical orbit. Despite all this one can see the respect of averages. An intermediate energy input into the climate system is useful because it is a static figure that can placed alongside mankind`s energy input into the climate system from greenhouse gasses. Thus we deliver a natural 240 watts / sq m and mankind`s addition of 1.6 watts / sq m. But the thought that a single figure, 240 Watts / sq m can name the rude energy input into the climate system, and that additional factors can be added to it to decide whether the Earth will get warmer or colder is a gracious part of arithmetic. Whether it really means anything is debateable.

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