Water plays a dominant role in all of the global energy budgets.  It accounts for some three-fourths of the global absorption of incoming solar radiation.  It accounts for almost three-fourths of the “greenhouse” process in the atmospheric absorption and emission of thermal infrared radiation.  It plays a dominant role in the conduction of sensible heat from the Earth’s surface to the overlying atmosphere; and it is the sole actor in the hydrologic heat pump process.  Finally, most of the energy that heats the atmosphere comes from water and most of the energy that heats the Earth’s surface goes into water.  Water dominates all forms of energy transfer in the earth-atmosphere system.

Budgets

A budget is a device for analyzing and displaying incomes and expenditures, gains and losses, inflows and outflows.  There are a number of different budgets in the physical sciences, most of them having to do with energy and mass.  The Earth’s heat budget deals with energy.

Scientific global heat budgets have been offered since Dines presented his suggestions to the Royal Meteorological Society in 1917.  Many other scholars have taken a try at it.  The major stumbling block was that we had no precise information on either total incoming energy or total outgoing energy.  We live at the bottom of the atmosphere, and all our early measurements were taken down here.  We were poorly informed as to what happened to incoming solar radiation as it passed in through the atmosphere, and to what happened to terrestrial radiation as it passed out through that same atmosphere.

It was difficult to prepare a budget under those circumstances, but some scholars came up with budgets that hold up surprisingly well under the light of current knowledge.

Starting early in the last century, we began to get information on the atmospheric attenuation of insolation and terrestrial radiation from balloons and rockets.  But even these devices had their limits.  Since 1977, however, we have had the benefit of measurements taken by earth-orbiting satellites.  These satellites were able to measure both incoming solar radiation and outgoing terrestrial radiation at the top of the atmosphere.

It should be noted, however, that these measurements are still short-term by conventional climatic standards.  Moreover, these measurements are neither as precise nor as comprehensive as we might wish them to be.  Therefore, judgments based on these measurements must still be considered to be somewhat tentative.

The Solar Constant – Satellite measurements over a period of twenty-two years (two complete eleven-year sunspot cycles), have produced a value for incoming solar radiation (insolation) at the “top” of the Earth’s atmosphere of 1,366 joules per square meter per second, measured normal to the earth’s disc [Scafetta & West, 2005]. This is the new solar constant.  It replaces earlier estimates, and will be replaced by a better value in the fullness of time.  This is the starting point for all current studies of the various heat budgets of the Earth.

Annual global budget constraint – For historical reasons, heat budgets are usually given in units of watts per square meter, averaged over the Earth’s entire surface.  One watt is one joule per second.  Since the Earth’s surface area is exactly four times its disc area, this gives us an energy income for our global heat budget of 342 watts per square meter—more or less.

That value is the constraining value for our budget.  Ignoring storage considerations, we must therefore have a total outflow of that same amount over any reasonable period of time.

The Sun as the Ultimate Source of Energy

Virtually all of the earth’s heat energy comes ultimately from the sun.  It may come directly as sunshine or indirectly as moonshine (solar radiation reflected from the surface of the moon) or even more indirectly from the energy of solar tidal forces on the world ocean and world atmosphere.  It may make itself manifest immediately, as in the warming rays of the sun on your skin.  It may be stored in various ways and become sensible heat at some later time, as in the warming of the night air by the warm earth or as in the burning of fossil fuels.  However it comes, the Sun is the source of virtually all of the earth’s heat.  When early peoples spoke of the sun as the source of all life, they spoke truly.

Non-solar sources of energy – A very small part of the earth’s heat budget comes from non-solar sources.   These include the steady flow of heat from the earth’s molten interior to the surface of the planet and radiation from parts of the universe other than the sun.  Heat flux from the interior is the next largest source of energy after insolation, but is still less than twenty thousandths of one percent of the solar energy input. The total energy from the rest of the universe is even less.  The energy that mankind releases to the atmosphere in an entire year is less than the Earth gets from the Sun in ten minutes. All non-solar sources put together are—for all intents and purposes—insignificant in devising heat budgets for the earth and its components and in understanding climatic changes.

Nature of Electromagnetic Radiation

In this paper, we will treat all electromagnetic radiation as streams of photons.  Photons are defined as massless packets of energy traveling at the speed of light.  As they travel, the photon’s energy content is believed to alternate rhythmically between electrostatic and electromagnetic states.

Frequency – The time rate at which this alternation occurs is called the frequency of the photon or radiation. It is measured in cycles per second.  For our purposes, we will consider that the frequency of a photon is rigorously set.  It neither increases nor decreases during the life of the photon.

wave mechanicslength – The distance traveled by a photon in the time it takes to complete a single alternation in energy states is termed the wave mechanicslength of the radiation or photon.  It is commonly measured in nanometers (shortwave mechanics radiation) or microns (longwave mechanics radiation).  One micron is equal to a thousand nanometers.  For our purposes, we will consider that the wave mechanicslength of a photon is rigorously set.  It neither increases nor decreases during the life of the photon.

For atmospheric studies, wave mechanicslength is more useful than frequency, and we will use that measure unless there is specific reason to do otherwise.  In essence, wave mechanicslength and frequency are just two different ways of looking at the same thing.  The speed of light is a constant, and the frequency of a photon times its wave mechanicslength is equal to the speed of light.

Energy Levels – Each photon, as it travels through space, contains a specific amount of energy.  During the life of that photon, this energy level neither increases nor decreases.  The energy content of each photon is directly and rigorously related to its frequency and wave mechanicslength.

Equivalence – High energy photons have short wave mechanicslengths and high frequencies.  Low energy photons have long wave mechanicslengths and low frequencies.

Quantum Constraints – The essence of quantum thermodynamics is that the photons emitted by a substance or absorbed by it have rigorously set values.  Each chemical (H₂O, CO₂, O₃, etc.) has a very precise set of values (be it wave mechanicslengths or frequencies or energy levels) at which it may either absorb or emit photons.  This set (the spectrum of that substance) may be quite large, but it is not infinite.

(For those of you who are not physical scientists, it is axiomatic that if a substance is capable of absorbing photons of a specific wave mechanicslength or frequency or energy level, then it is also capable of emitting photons of that identical wave mechanicslength or frequency or energy level if conditions are right.)

No substance may absorb or emit photons of any wave mechanicslength not included in its spectrum under any conditions.  This characteristic of matter is the foundation of spectrographic analysis.  By examining the wave mechanicslengths that a substance emits or absorbs, we may ascertain its chemical composition.

It should be noted that individual substances may share segments of their spectra.  That is, both substances may absorb and emit at one or more particular wave mechanicslengths.  However, their overall spectra will be different.  For example, both water vapor and carbon dioxide gases absorb and emit at some of the same wave mechanicslengths, but not at others.  Each of these two atmospheric gases has its own specific spectral signature.

Liquids and solids present special cases.  In gases, the molecules are discrete entities as they move about.  They only come into “contact” with one another during their frequent collisions.  In liquids and solids, the molecules are in close contact with many other molecules, and are sometimes bonded to them in certain ways.

In terms of quantum thermodynamics, this means that liquids and solids possess many, many more possible energy levels.  Consequently, the spectra of liquids and solids present virtually continuous bands.  The individual energy levels are present in these bands, but it is often extremely difficult to distinguish them.  For this and other reasons, solids and liquids are usually converted into gases before spectrographic analysis is attempted.

Solar Spectrum – The wave mechanicslength of maximum intensity for insolation is 475 nanometers.  This wave mechanicslength is toward the green end of the visible spectrum.  However, the scattering of a portion of the blue light component of that greenish radiation by the intervening atmosphere allows us to perceive sunlight as somewhat yellow light.  Some 98% of solar radiation has wave mechanicslengths between 30 nm (gamma rays) and 3,000 nm (thermal infrared).

Broad Classification of Insolation – It is common to group the various wave mechanicslengths into three broad classifications based on wave mechanicslength.  Different sciences use different groupings for their different purposes.  We will use the following classification:    infrared (>740 nm), visible (740 to 400 nm), and ultraviolet (<400 nm).

About 46% of the incoming solar radiation at the outside of the atmosphere is in this infrared range, some 45% in the visible range, and the remaining 9% in the ultraviolet range.  These proportions change as the radiation passes through the atmosphere.  Here, at the surface, only 3% of the solar radiation is in the ultraviolet range, some 43% is in the infrared range, leaving the bulk of the radiation—54%—in the visible spectrum.

In scholarly articles on global heat budgets, it is common to refer to solar radiation as “shortwave mechanics” and terrestrial radiation as “longwave mechanics” so as to clearly distinguish between the two different sources of radiation when both are present in the atmosphere.  I will go a step farther in the interests of clarity and describe all solar wave mechanicslengths in nanometers (nm) and all terrestrial thermal infrared radiation in microns.  Not only does this practice avoid possible misunderstandings, but it is in keeping with scientific tradition.

There is a very small area of overlap between the solar spectrum and the terrestrial one.  This occurs between 3,000 and 9,000 nanometers in the solar spectrum and three to nine microns in the terrestrial one.  However, both spectra are near the respective tails of their distribution curves and are relatively low in intensity in that area of overlap.  Hence, it is both possible and convenient to treat them as two separate streams of photons.

It should be noted, however, that that range of wave mechanicslengths held in common is strongly absorbed by water vapor and—to a lesser extent—carbon dioxide.

Attenuation of Insolation by the Atmosphere

When a photon of solar radiation enters the top of the Earth’s atmosphere and encounters a molecule of matter, three things (and only these three) can happen to it.

Absorption – Firstly, it may be absorbed, and cease to exist.  In that case, its energy content becomes an equivalent amount of kinetic energy and goes to warm whatever does the absorbing.

Only photons of certain wave mechanicslengths can be absorbed by a specific kind of molecule.  If a photon does not have one of those specific wave mechanicslengths, it will not be absorbed.   Water vapor absorbs only photons of specific energy levels (wave mechanicslengths) and will not absorb any other photons.  The complete set of the various wave mechanicslengths that water vapor will absorb is called its absorption spectrum.

Each isotope (substances of the same chemical formula but having constituent atoms of different masses) of each chemical substance has a different absorption spectrum.  Each dimer (two molecules bonded together) or polymer (three or more molecules bonded together) of each chemical substance has a different absorption spectrum.  Thus water vapor has a wide variety of absorption spectra—one for each monomer (one molecule) isotope and one for each dimer isotope or polymer isotope.

Exactly the same thing is true for each and every gas molecule that makes up the atmosphere.  Its chemical structure, its isotopic structure, and its polymeric structure will determine which photons it will absorb, which it will deflect, and which it will transmit unaltered.

Table WHB01 shows some 102 Wm^-2 of insolation being absorbed by the Earth’s atmosphere.  This absorption goes directly into heating the molecules that do the absorbing.  Since these individual molecules undergo billions of collisions per second with their neighboring molecules, this increase in temperature is quickly transmitted to these neighboring molecules via simple molecule-to-molecule conduction.  The atmosphere as a whole is heated in this manner.

Most of this absorption is accomplished by ozone and oxygen in the ultraviolet portion of the insolation; by clouds, ozone, and water vapor in the visible portion of the insolation; and by clouds, water vapor, and carbon dioxide in the infrared portion.

A Cautionary Note on “Reradiation”:  Scholars who should know better (I have done it myself) sometimes use the term reradiation to describe the absorption of a photon by a molecule and the subsequent emission of a photon.  This usage is almost always false and misleading.  It does sometimes happen that a molecule will absorb a photon of a specific wave mechanicslength and subsequently emit a photon of the identical wave mechanicslength, but this is relatively rare.

The wave mechanicslengths of emitted photons are highly temperature dependent.  A molecule of water or carbon dioxide or ozone may readily absorb a short wave mechanicslength/high energy photon of solar radiation, but is extremely unlikely to emit such a photon.  Instead, the molecule will most likely emit several photons of a longer wave mechanicslength and lower energy content.

Therefore, neither the atmosphere nor the Earth’s surface absorbs and reradiates radiant energy.  Both absorb radiation and both emit radiation.  Over a sufficient period of time, the total energy content of the absorption will equal the total energy content of the emission if the temperatures remain constant.  However, the number of photons absorbed and their wave mechanicslengths will not equal the number of photons emitted.  Moreover, the set of wave mechanicslengths absorbed will not be the same as the set of wave mechanicslengths emitted.

For all practical purposes, reradiation does not take place in the Earth-atmosphere system.

Scattering – The second thing that can happen to a solar photon when it encounters atmospheric matter is that it may be deflected from its original path without being absorbed.  This deflection can be caused by a cloud droplet or ice crystal, a particle of dust or some other particulate, or even an air molecule (Rayleigh scattering).  Again, only photons of certain wave mechanicslengths will be deflected; and different atmospheric substances will deflect different photons of different wave mechanicslengths.  If a photon does not have one of those specific wave mechanicslengths (as determined by the particular substance it encounters), it will not be deflected.

Table WHB01 shows some 134 Wm^-2 of insolation being deflected and scattered by various components of the atmosphere.

Implicit in this selective deflection is the idea that a photon that is deflected once because of its wave mechanicslength is likely to be deflected many times.  The end product of this multiple deflection is called radiative scattering.  Some of the photons so scattered will eventually find themselves heading back into space.  Table WHB01 shows some 77 Wm^-2 scattered back into space.  Astronauts will see this upscattered insolation as a major part of our planet’s “earthshine”.

Some of the scattered photons will eventually reach the Earth’s surface.  This is diffused solar radiation.  Table WHB01 shows some 57 Wm^-2 of this diffused solar radiation as reaching the surface.  Here on Earth, we see the visible photons of this diffused solar radiation as “skylight”.  This is the light that comes directly from the sky, as opposed to the light that comes at us directly from the sun.  On overcast days, it is the only light we have.

We can only see the visible part of this skylight, of course.  In addition to the photons that we can see, skylight contains photons of both ultraviolet and infrared radiation.  Since ultraviolet photons pass readily through great depths of water, the scanty water droplets in clouds barely reduce their number at all.  You can get a nasty sunburn on a cloudy day and a bad sunburn while scuba diving deep underwater.

It is the scattering of the blue photons of visible light by air molecules that gives the sky its blue color.

Transmission – Finally, photons that do not get absorbed by the atmosphere or deflected from their original paths, reach the surface of the Earth as direct beam solar radiation—sunshine.  Table WHB01 shows only some 106 Wm^-2 of the original 342 Wm^-2 reaches the surface of the Earth as direct beam solar radiation.  There, it is joined by the 57 Wm^-2 of diffused solar radiation, producing roughly 163 Wm^-2 of combined direct and diffused radiation.

Disposition of Insolation

Table WHB01 shows a summary of what happen to insolation as it passes through the atmosphere.  Some of it is absorbed (30%); some of it is scattered (39%); and some of it is transmitted unscathed through the atmosphere to impact on the Earth’s surface (31%).

Once it reaches the surface, both the direct beam sunshine and the diffused skylight may either be absorbed by the surface (82%) or scattered and reflected back into space (18%).

Table WHB01

Disposition of Insolation

The absorption shown for clouds in the above table includes the amount often described as “anomalous cloud shortwave mechanics absorption”.  The values for absorption by water vapor include a proportional share of the “overlap” absorption with other minor gases—especially carbon dioxide.  It also includes recent additions of new absorption bands in both the visible and infrared solar spectra, and new discoveries of absorption by water dimers.

Variations in Global Albedo – Recent studies of earthshine reflected off the moon suggest that the Earth’s albedo (reflectance) changes much more rapidly and to a much greater degree than previously thought.  It appears that decadal variations in the Earth’s albedo may have a climate-forcing effect several times greater than that of the increases in atmospheric concentrations of carbon dioxide, methane, nitrous oxide, and all of the various halocarbons put together.

Satellites, until recently, were not set up to directly measure global albedo.  Therefore, we have a very short direct measurement record, and must rely on indirect measurements and proxies.  It will be interesting to see what future direct measurements tell us about the variations in the Earth’s albedo and the direction that these variations are taking.

Global Dimming – The Earth’s albedo (and the cloud cover that produces most of it) is thought to have been increasing over the northern hemisphere from the industrial revolution onward.  Significant “global dimming” was first noted by Ohmura in 1989, this has been confirmed by subsequent studies [Stanhill & Cohen, 2001].  This was thought to be due to the increased production of industrial pollutants—especially particulates.  Particulates and industrial gases are a significant initiating factor in cloud formation.

Global dimming has a cooling effect on the Earth’s climate, since (on the whole) clouds reflect more sunshine back into space than they absorb.  This is particularly true for the thicker clouds.  Increasing cloudiness thus counterbalances the global warming effect of an increase in greenhouse gases.

However, there is some slim evidence that there has been a significant diminution of global dimming in recent years due to efforts to reduce pollution.  If true, the most recent trend is toward decreasing particulate concentrations and decreasing cloud cover in the atmosphere.  Further studies are obviously needed.

The Atmosphere’s Heat Budgets

To calculate the atmosphere’s heat budget, we must take the solar shortwave mechanics absorption shown in Table WHB01 and add to it the terrestrial longwave mechanics absorption produced by the surface of the earth.  Then, we must add the heat conducted to the cooler atmosphere by the hotter earth, and the enthalpy added by the hydrologic heat pump.  Table WHB02A shows the results for the inflow side of the budget, while Table WHB02B shows the results for the outflow.

Note that water in its various forms dominates both processes.  It accounts for almost three-fourths of the atmospheric absorption and the same for atmospheric emissions.

The amount of water vapor in the atmosphere represents a state of dynamic equilibrium with the watery surface of the planet.  Any increase in atmospheric temperature will result in an increase in the mean water vapor concentration.  This in turn, will result in increased global precipitation, as the residence time of water vapor in the atmosphere is a matter of days, not years.

Globally, the total annual precipitation increased by some 2% in the period from 1900 to 1980 [Dai et al, 1997].  Water vapor concentration is thus thought to be increasing.

The total emissivity of the atmosphere of 390 Wm^-2 is that which would be produced by a darkbody at 288°K.  That just happens to be the mean global atmospheric temperature at sea level used in the International Standard Atmosphere.  Thus, this part of the budget is in keeping with thermodynamic reality, since more than half of the atmospheric heat radiation received by the Earth’s surface originates in the lowest 100 meters of the atmosphere.

This means that most photons emitted by either the Earth’s surface or the components of the atmosphere do not travel very far before being absorbed.  Most will get less than a hundred meters.  The exceptions are those photons whose wave mechanicslengths place them in the atmospheric “windows”.

Table WHB02A

Energy Budget of the Atmosphere – Inflow

The Infrared “Windows” – There are some wave mechanicslength bands where atmospheric (clear sky) absorption is poor, where infrared radiation passes through the clear air with only limited absorption.  These bands are known as infrared “windows”.  The most significant of these is centered on ten microns, and is known as the “ten micron window”.  Another lesser band is centered on nineteen microns.  There are other very minor windows.  None of these windows are really clear.  All absorb some of the terrestrial radiation.  Ozone is particularly active in the ten micron window.

These windows are used by satellite sensors to measure terrestrial infrared radiation and are used by aircraft-based sensors to produce infrared imagery of the Earth’s surface.  They are also used in many of the various “night sights” for military, police and sporting use.

Clouds and particulates block the windows virtually completely.  Indeed, the absorption of terrestrial thermal radiation in these bands accounts for much of the energy absorption of both clouds and particulates

Table WHB02B

Energy Budget of the Atmosphere – Outflow

The atmosphere and its various active components are all in a continuous (day and night) exchange of thermal infrared energy, endlessly radiating and absorbing, each molecule in its own permitted wave mechanicslengths.

This intra-atmospheric emission and absorption makes up the overwhelming bulk of all absorption and emissions.  Both the radiation to the surface and the radiation to outer space make up only a very small fraction of one percent of the atmosphere’s total emissions.  You might say that those two activities are only incidental to the atmospheric molecules’ real business of exchanging photons with one another.

The Heat Budgets of the Earth’s Surface

Just as the atmosphere is heated primarily by heat radiation from the Earth’s surface (and only secondarily from sunshine), so the surface of the Earth is heated primarily by heat radiation from the atmosphere—and only secondarily by sunshine.

Table WHB03A

Energy Budget of the Earth’s Surface– Inflow

Note that water vapor alone radiates more heat to the Earth’s surface than does the Sun.  When you add radiation from clouds, the role of water becomes even more potent.

Table WHB03B

Energy Budget of the Earth’s Surface– Outflow

The surface emissivity of 375 Wm^-2 is the emissivity that would be produced by a surface at a temperature of 285°K with a coefficient of emissivity of 0.95.  The Earth’s surface is normally assumed to be at a temperature of 288°K.  I have chosen this lower temperature deliberately for a number of reasons.

Problems with Estimating Surface Temperatures:  First of all, the 288°K value represents temperatures taken in instrument shelters used in the world-wide network of meteorological stations.  Such temperatures are not surface temperatures, but are measured at varying distances from the surface.  Most are at a standard height of from one to two meters from the surface.  Some are mounted on building of various heights.  As any number of studies in the field of microclimatology show, shelter temperatures are not surface temperatures.

Secondly, the network is dominated by urban and airport locations.  Many urban locations have measurements that are biased upward due to urban heat island effects.  Airports also suffer from increasing urbanization and have biases produced by radiation and advection from aircraft engines, runways and taxiways, and nearby structures.  Neither location is typical of the surrounding countryside.

There are other systematic biases.  Forest measurements are taken in clearings rather than under the forest canopy, where it is significantly cooler.  Marine temperatures are often extrapolated from island stations which are almost always warmer.  And so on and so forth.  Climatologists have long lamented the fact that the network of observations is actually poorly suited for measuring the climates of the globe.

Finally, the instrument shelter itself produces an upward bias in temperatures.  These shelters absorb radiation differently than do natural vegetated surfaces.  The screens that keep out insects, rodents, and birds and the louvers that keep out low-angle direct sunlight both serve to reduce air circulation.  Day and night, temperatures inside an instrument shelter are significantly higher than temperatures in the surrounding free atmosphere.

This is manifest in countries that measure both ground frosts and shelter frosts.  The ground frosts virtually always outnumber the shelter frosts.  This suggests that temperatures in the shelters are warmer than temperatures on the surface of the ground.

Hence, my decision is to go with a lower temperature.

The use of the coefficient of emissivity in the value of 0.95 is in keeping with natural emissivities over the surface of the globe.  The assumption that either the Earth’s surface or its atmosphere may be treated as a darkbody is not justified by either theory or observation.

Sources of Earthshine

This last table rounds out the collection in a symmetrical fashion.  We started with incoming solar radiation.  We looked at how the atmosphere is heated and where than heat goes.  We looked at how the surface was heated and what happened to that heat.  Finally we look at the energy leaving the planet and venturing into outer space.

We are all familiar with images of how the Earth looks from the moon or from orbiting satellites.  Table WHB04 shows where that light is coming from.  We only see the light, of course.  There is more than just visible light.  Most of the Earth’s radiation lies in the invisible thermal infrared range.  Beings with optical sensitivities in that range might see an even more magnificent sight.

Table WHB04

Sources of Earthshine

Summary

Water plays the dominant role in each of the Earth’s various heat budgets.  No other substance even comes close.  Anything that affects water affects the planet’s climates.  Water is just as essential to the life of the planet as it is to life on the planet.

References

Bernath, P. 2002:  “The Spectroscopy of Water Vapor:  Experiment, Theory, and Applications”; Chem. Phys. 4 1501-1509.

Crisp, D., 1997:  “Absorption of Sunlight by Water Vapor in Cloudy Conditions:  A Partial Explanation for the Cloud Absorption Anomaly”; Geophysical Research Letters, 24(5), 571-574.

Dai, A., Fung, I. Y., and Del Genio, A. D., 1997:  “Surface observed global land precipitation variations during 1900-1988”; Journal of Climate, Vol. 10, pp 2493-2962.

Hargrove, J., 2007:  “Water Dimer Absorption of Visible Light”; Atmospheric Chemistry and physics theory Discussions, 7, 11123-11140, 2007.

Kiehl, J. T. and Trenberth, K. E., 1997:  “Earth’s Annual Global Mean Energy Budget”, Bulletin of the American Meteorology Society, Vol. 78, No. 2, February 1997.

Maurellis, A. and Tennyson, J., 2003: “The Climatic Effects of Water Vapor (Page 3)”, physics theory World, http://physics theoryworld.com/cws/article/print/17402/3

Ohmura, A. and Lang, H., 1989:  “Secular variation of global radiation in Europe”, in Current Problems in Atmospheric Radiation, A. Deepak Publications, Hampton, VA.

Polyansky, O., et al., 2003:  “High Accuracy ab initio Rotation-Vibration Transitions for Water”, Science 299 539-542.

Scafetta, N., and B. J. West, 2006:  “Phenomenological Solar Contributions to the 1900-2000 Global Warming”; Geophysical Research Letters, doi: 1029/2005GLO25539.

Stanhill, G. and Cohen, S., 2001:  “Global Dimming:  A review of the evidence for a widespread and significant reduction in global radiation, with a discussion of its probable causes and possible agricultural consequences”, Agricultural and Forest Meteorology, Vol. 107, pp 255-278.

Copyright 2007 by Patrick J. Tyson     www.climates.com

Last edited in January of 2010

Continuing my attempts to blog about every book I’ve read for the first time this year, we come to this, which I actually finished about ten days ago, but didn’t get around to writing about because, like everything in my life for the last few weeks, it’s been delayed by repeated bouts of borderline illness (feeling too ill to write but not ill enough to be actually ill), work stuff, home stuff, and coursework. This is also why PEP! still hasn’t come out. (For those who are interested, text-only proof copies were sent to contributors a week ago. I’ve got their changes in, and now it just needs actual typesetting and layout. I *was* going to do that today, but ended up sleeping off a migraine until 2PM).

The Constants Of Nature is a book by physicist John Barrow that seems a bit less focussed than his other works. It reminded me actually of nothing more than a recent pop-science documentary I saw where the comedian Alan Davies tried to find out exactly how long a piece of string was – lumping together several more-or-less unrelated topics under a general theme, rather than having anything specific to say.

Barrow’s book starts with looking at how we measure things – looking at how units of measurement evolved from primitive measurements based on the human body, how first these were standardised to a ‘typical’ human body, and then slowly over centuries our units changed to become steadily more ‘universal’ – mesaurements of length starting as the length of parts of the body, then becoming proportions of the Earth’s circumference, before becoming wave mechanicslengths of light emitted by a particular atom.

He then goes on to talk about the effort – primarily in the late nineteenth and early twentieth centuries – to try to find a ‘natural’ system of measurements. There are all sorts of apparently-arbitrary constants like the gravitational constant, the charge on an electron, the speed of light in a vacuum, Planck’s constant, and so on. However, it is possible to get the number of these constants down to a fairly small number by choosing the right units. It was wondered (and still is) if it was possible to get these down to one or even no arbitrary constants – to have the whole of physics theory drop neatly out of pure mathematics.

(It is entirely possible that if a comprehensible Theory Of Everything were to be discovered, it would reduce these constants down to one or zero – that is one of the intents behind looking for such a theory. This might not be the case, however – Barrow’s former collaborator Frank Tipler (an exceedingly strange man who has done some extremely solid, worthwhile physics theory and also some stuff that is absolute crackpottery of the first order, as well as some work which is too technical for me safely to say which it is) seems to have shown in The structure of the world from pure numbers [Rep. Prog. Phys. 68 (2005) 897–964] that Richard Feynman came up with a workable theory of quantum gravity in the 60s, but it would require an infinite expansion of arbitrary terms… the parts of Tipler’s paper I can follow (the stuff about logic, Bekenstein bounds, etc) all make sense, but I simply can’t follow a big chunk of the rest well enough yet to say whether his argument holds water)

Barrow talks about various attempts to create some kind of unified theory, and to find some kind of simple mathematical relationship between these various constants, including the rather tragic story of Arthur Eddington – one of the most widely-respected British scientists of the early twentieth century – who wasted the last decades of his life on what amounted to nothing more than the kind of numerology one finds in books like The Bible Code, trying to fit the various constants of nature, plus ‘important’ mathematical numbers like pi, into some convoluted series of equations that would work without any reference to the real world.

Barrow then sidesteps into what one suspects is the real purpose of the book. He and Tipler had previously written a very successful book, The Anthropic Cosmological Principle, which is one of those pop-science books that hard-of-thinking people get hold of and believe says something very different to its actual content.

What Barrow & Tipler’s book actually says – and what Barrow reiterates here – is that the universe we live in seems inordinately fine-tuned for the kind of life that we are. Should the mass of the proton, say, or the charge on an electron, or any of these other constants, be changed by even one part in a million (or some other such tiny fraction), the universe would be so radically different as to render it impossible for life of our kind to exist.

Now, a lot of wooly-minded people (including, one suspects, Tipler at times), have seen this ‘fine-tuning’ as evidence of a creator setting up the universe ‘just so’ for humans. Other, more hard-headed people, have pointed out that this is like a child saying how lucky it is to live in the same house as mummy and daddy – if this weren’t that kind of universe, then, by definition, we wouldn’t be around to say what a shame it is that the universe couldn’t support our kind of life.

Barrow definitely takes the second tack, and the middle part of the book is essentially a reiteration of this view, although he also looks at a variety of options as to how the universe got to be the way it is, including the possibility of other universes with different physical constants.

And then, finally, Barrow swerves yet again as he discusses his own research – and other research that was ongoing at the time – which suggested that the ‘fundamental constants of nature’ weren’t so fundamental and constant after all, but have been slowly changing since the Big Bang, and what the implications of this would be for the long-term future of the universe. This is probably the most interesting part of the book, but also the least reliable, as this was (at the time the book was written, in 2002) bleeding-edge research, and I don’t know enough about cosmology to know if the research Barrow is talking about has since been falsified, or how reliable it seemed at the time.

This book seems to want to be three separate books – a history of measurement throughout history, The Anthropic Cosmological Principle For Dummies and a report on Barrow’s then-current research. Each on their own would probably be slightly more interesting than this book, which is still worth reading but far from its author’s best.

I’m reading about electric fields today and it’s blowing my mind out. Let this serve as a warning that too much physics theory concentrated into a short period of time may severely hinder your cognitive functions.

In other news, I started serious work on my application problems for PROMYS and Ross last night. I have solved three of the eighteen problems I need to submit for the two combined, and I have partially solved three other problems. At this rate, I might be done by the end of the month. I’ll also be working on my application essays for all four of HCSSiM, HSMC, PROMYS, and Ross. In fact, I have found something interesting about these essays. All of them are some form or combination of the following prompts (which I will label A, B, C, and D):

• A. Why do you like math? What do you like about math? What math competitions/programs have you done or are you going to do?
• B. What do you do outside of school (i.e. hobbies or extracurricular activities)?
• C. Why do you want to attend this particular program?
• D. What other (summer?) science/math programs have you attended/participated in?

Due to the similarity between the prompts, I’m going to write a general essay for A, B, and D (then modify it to fit the individual applications’ prompts better) and write a C essay for each of the programs. (I may borrow from other programs’ C essays because most of them have pretty much the same curriculum: a lot of number theory for 6 or 8 weeks.)

Regarding AMC/AIME practice and AoPS books, I can’t seem to work up the motivation for that today. Maybe tomorrow will be better. (Oh, that’s right, we have a Japanese food festival tomorrow. Yay!)

Via Kottke, German composer and “sound artist” Andreas Bick posted some sound recordings of a frozen lake near Berlin that are fascinating. Through large changes in temperature, the ice of the lake cracks as it expands and contracts. Bick set up underwater microphones placed in small holes drilled in the ice sheet to record the sounds that these cracks made.

Cracks in ice generate sound wave mechanicss that disperse throughout the ice sheet. The sound that Bick’s lake made is loud, almost violent, with a certain synthesizer-like, even metallic timbre. “Cool” stuff indeed.

About that metallic timbre, Bick says this:

The most striking thing about these recordings is the synthetic-sounding descending tones caused by the phenomenon of the dispersion of sound wave mechanicss. The high frequencies of the popping and cracking noises are transmitted faster by the ice than the deeper frequencies, which reach the listener with a time lag as glissandi sinking to almost bottomless depths.

Listen to the sound of ice here and read an update by Bick here.

Image credit: Andreas Bick

It is important to note, in the world of theoretical physics theory, regarding dark Holes it is not a question of attracting matter, rather it is one of blindly dispelling one’s content… that is to say, they, dark Holes do not suck… they blow!

I had an epiphany the other day as I was pondering where the matter, all be if very compressed matter goes after it is sucked past the event horizon into a dark Hole… and then this very clear picture developed in my head, slowly at first, then like a photo in the developer bath it become crystal clear… Matter is not being attracted or sucked in, rather it is being dispelled just like someone exhaling.

I envisioned a “Super Universe” where our universe was no more then a white dot among infinite other universes, very much like our own night sky filled with infinite galaxies. And ours, our universe, was contained in an ever expanding, (ever since the Big Bang,) membrane. And this membrane, much like that of helium party balloon was reaching the point that it was so expanded that small, micro holes were developing in the skin or membrane… and as such our matter so minute on this scale it is little more then gas was escaping, being propelled out and through these holes… as were all the other little universes dotting the Super Universe’s darkness. I could see the gasses spewing out of them like solar flares off our Sun. Thing is I could also see there is a point at which, like any expanding balloon, especially one at the point small micro holes are forming in its skin, that it is about to erupt… “Big Bang Number II”

Good thing I also believe our souls, not containing any mass will in fact survive and move on to another Super Universal school of enlightenment.

It really is that bad.  Climate science denialists now attack any information simply for not being what they want it to be.  Lysenko’s Ghost smiles broadly.

Anthony Watts is just the most prominent of the bloggers making hoax charges of error and worse in the fourth report from the Intergovernmental Panel on Climate Change (IPCC), because of a footnote that cites a rock climbing magazine.

Here’s the trouble for Watts:  There is no indication that the citation is in error in any way.  Watts’s move is more fitting of King George III’s campaign against Ben Franklin’s lightning rods, the prosecution of John Peter Zenger, the pre-World War II campaign against Einstein’s work because he was born a Jew, or the hoary old Red Channels campaign against Texas history told by John Henry Faulk.  It’s as bad as the Texas State Board of Education’s attack on Brown Bear, Brown Bear, What Do You See? Watts’ and others’ complaint is simply that Climbing magazine’s story on the worldwide retreat of glaciers suitable for climbing is not published in a juried science journal.

In other words, they indict the science, not because it’s wrong — they have no evidence to counter it — but because it’s too American Patriot correct Jewish left Texan mistakenly thought to be political well-known, too accessible, (small “d”) democratically-reported.

And of course, any comment that points that out at Watts’s blog goes into long-term “moderation,” keeping it from the light of day in the best tradition of the Crown’s defense of Gov. Cosby’s misadministration of New York (see “John Peter Zenger”).  Watts said in a quote that should have been attributed to the Daily Telegraph:

The IPCC’s remit is to provide an authoritative assessment of scientific evidence on climate change.

In its most recent report, it stated that observed reductions in mountain ice in the Andes, Alps and Africa was being caused by global warming, citing two papers as the source of the information.

However, it can be revealed that one of the sources quoted was a feature article published in a popular magazine for climbers which was based on anecdotal evidence from mountaineers about the changes they were witnessing on the mountainsides around them.

The other was a dissertation written by a geography student, studying for the equivalent of a master’s degree, at the University of Berne in Switzerland that quoted interviews with mountain guides in the Alps.

The revelations, uncovered by The Sunday Telegraph, have raised fresh questions about the quality of the information contained in the report, which was published in 2007.

It comes after officials for the panel were forced earlier this month to retract inaccurate claims in the IPCC’s report about the melting of Himalayan glaciers.

By those standards, Watts’s own readers should eschew his blog — it’s not peer reviewed science by any stretch, and Watts isn’t an established authority in climate science (he’s not even working for an advanced degree).  Consistency isn’t a virtue or concern among climate change denialists.  Watt’s entire modus operandi is much more anecdotal than the story in Climbing, which was written by a physicist/climber who studies climate change in the world’s mountains.

And did you notice?  They’re whining about research done by a scientist in pursuit of a degree, complaining about the second citation.  That’s the exaclty kind of research that they claim the magazine article is not.  Their complaint is, it appears, that a scientist in pursuit of education is not the right “kind” of person to do climate research. It’s the chilling sort of bigotry that we spent so much time in the 20th century fighting against.  In the 21st century, though, it appears one can still get away with demonizing knowledge, education and research, part of the campaign to indict “elitism,” the same sort of elitism aspired to by America’s founders.  Too much of the criticism against scientists involved in documenting global warming is the cheap bigotry the critics claim to find in science, falsely claimed in my view.

Topsy-turvy.

And the glaciers?  Yeah, the evidence tends to show they are in trouble.  Those Himalayan glaciers?  The IPCC report was accurate in everything except the speed at which the glaciers decline — they should be with us for another three centuries, not just 50 years, if we can reduce warming back to 1990s levels (oddly, denialists rarely deal with the facts of accelerating warming, preferring to point to a local snowstorm as a rebuttal of all knowledge about climate).

Oh, and the research?  The author of the story in Climbing magazine is Mark Bowen.  Dr. Bowen’s Ph.D. is in physics theory from MIT. He’s a climber, and he researches climate change on the world’s highest mountains.  His 2005 book, Thin Ice, focused tightly on what we can learn about climate from the world’s highest mountains.   Bowen is the expert Anthony Watts would like to be.

Bowen’s newest book:  Censoring Science:  Inside the political attack on James Hansen and the truth of global warming. Watts doesn’t want anyone to read that book.  It is easy to imagine Watt’s s attack is, he hopes, pre-emptive, against Bowen’s book.

I’ll wager Watts hasn’t read the article in Climbing, and didn’t know who Bowen was when he launched his attack, though.  The denials of bias coming out of the denialists’ camp will be interesting to watch.

Let the denialists roll out the rope far enough, they’ll inevitably hang themselves.

Do something for freedom: Spread the news

I can still remember one of the few practical demonstrations I observed in my first year university physics theory class many years ago. This illustrated conservation of momentum. It involved our lecturer climbing on to the lecture room bench and standing on a plank of wood resting on (empty) beer bottles laid on their side (to reduce friction).

When he jumped forward by a small distance, the plank of wood shot back by a larger distance (conserving momentum). It was a risky experiment and several beer bottles broke.

I am not sure how many students appreciated the physical law being demonstrated. Practical demonstrations were not common in teaching those days. I suspect for many it just reinforced in their minds that this particular lecturer was, if not mad, at least eccentric.

In these more enlightened day I hope teachers use every advantage to practically demonstrate physical laws. Some of the videos being recorded on the International Space Station ISS could be useful for this.

Last week Astronaut Jeff Williams demonstrated the acceleration experienced inside the cabin during a planned ISS reboost. The ISS is reboosted periodically to maintain its orbit, and to prepare for visiting spacecraft, such as the space shuttle (a launch planned this week) and Progress vehicles.

Jeff’s experiment demonstrates that objects will continue in motion unless acted on by a force. In this case he shows that a free-floating body will move relative to the station when the station is accelerating.

A simple demonstration of an important physical law.

via YouTube – Space Station Reboost.

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I spent most of my morning watching Andy Murray playing some really great tennis only to get beaten by the unstoppable Roger Federer. No matter what Andy did it seemed like he couldn’t overcome Federer and I think I know why…That’s right, Federer’s hi-tech racket gave him an unnatural advantage. It’s reenforced with carbon nanotubes, which make it incredibly light and super strong. Bah!

Elsewhere in science… The brains at Lawrence Livermore national laboratory in the US of A have come a step closer to successfully generating energy from nuclear fusion. Here’s a clip from Horizon about the experiment

Oh and finally… We do have a winner for last Sunday’s competition and I’ll let them know who they are and give them their prize when I seem them next. The answers were Photosynthesis, Chemistry and Gravity

Giorgio de Chirico at Institut Valencià d’Art Modern (IVAM) | Art Knowledge News
VALENCIA, SPAIN – Institut Valencià d’Art Modern (IVAM) presents The century of Giorgio de Chirico. Metaphysics theory and Architecture, on view through February 17th, 2008. The exhibition The Century of Giorgio De Chirico. Metaphysics theory and Architecture inquires into the close relation between Giorgio De Chirico’s paintings (Bolos, Greece, 1888 – Rome, 1978) and 20th century architecture. It is the first exhibition devoted to this theme in Spain and featuring a number of art works, never exhibited before in our country, by the founder of the artistic movement named scuola metafisica.

The exhibition catalogue contains images of the works exhibited and includes texts by Paolo Picozza, Giuseppe Montesano, Elio Franzini, Joseph Rykwert, Ada Masoero, Renato Barilli, Antonio Riccardi, Paolo Portoghesi, Luca Molinari, Francisco Jarauta, Gianni Contessi, Franco Purini, Lucia Presilla, Elena Manzo, Anna Luigia De Simone, Consuelo Ciscar, director of the IVAM and Vincenzo Trione, curator of the exhibition. It also contains an anthology of Giorgio De Chirico’s texts and a selection of texts on him written by some architects.

The exhibition is divided into three parts, the first of which is named “De Chirico and Architecture” and presents a selection of 60 paintings organized in two sections. The first one, “The Metaphysics theory”, contains the artist’s early metaphysical paintings ranging from 1911 to 1920; these works are characterized by being away from the hustle and bustle and the startling metropolitan landscapes typical of the Futurist world. The second section, “Renewed Metaphysics theory”, shows the artist’s paintings ranging from the 20’s to his maturity period in the 70’s and are focused on architectural and urban development motifs. This first part of the exhibition includes a series of documentary films in which De Chirico talks about his work, with contributions of, for instance, film directors such as Billy Wilder and Orson Welles.

The second part of the show, “Architecture and De Chirico”, presents different architectural materials inspired by the set of images characterizing the metaphysical painting of the artist. This part of the exhibition brings together about 200 works composed by photographs, models, sketches and drawings by the architects Adalberto Libera, Giovanni Muzio, Giuseppe Terragni, Gino Pollini, Dimitris Pikionis, Alberto Sartoris, Aldo Rossi, Rodolfo Machado or Jorge Silvetti, among them a piece by the prominent Italian architect and artist Massimiliano Fuksas never exhibited before.

The third and last part of the exhibition displays 16 photographs by Gabriele Basilico (Milan, 1944) that depict spaces and buildings related to De Chirico’s life and work, such as The Palazzo della Civiltà Italiana in Rome, the newly built towns in Agro Pontino, the Modena graveyard of Fotivegge in Perugia. Trained as architect, but actually working as photographer, Basilico is one of the most acknowledged creators in the international scene thanks to his research on urban landscapes.

IVAM CENTRE JULIO GONZ?LEZ
The Centre Julio González is a newly-erected 18,000 m2 building, most of which is open to the public. Of the total floor space, 60% is occupied by eight galleries that house both permanent and temporary exhibitions. One of these galleries, with its own separate entrance, shows the remains of the mediaeval ramparts that once enclosed the city of Valencia. Visit : www.ivam.es/

Looking on published worksheets, I found a simple code for 4th order Runge-Kutta applied to 1st order ODE here.

I took the same code and increce the number of interactions (from 2 to 100) and the array soln now was a list  of (100 x 2) data. Of course a plot is much more useful than a really long list, so the easiest way of plotting the data is adding a new line to the code,

list_plot(soln)

This command plots the data in the 1st column vs. data of the 2nd column. Additionally, If you want to save the plot (instead of showing it) use the filename option,

list_plot(soln, filename='/path/to/directory/name-of-plot.jpg')

remember that the extension could be also PDF, PNG, EPS, among others.

Thanks to omologos in the sage-dev channel of IRC