Global Warming and Climate Change - The Actual Physics and Calculations

Sadly, the majority of the "experts" who are seen on TV have NOT spent their careers researching the subjects they are trying to speak about. Most DO have some Degree that is in some related area, as both camps know that is important regarding gaining credibility. But it seems to rarely mean that they speakers truly have a deep knowledge of the subjects involved.

This presentation is meant to aid in dealing with all the confusion. It would require you to spend some time and even effort, but this presentation hopefully includes both the description of each aspect of the larger subject and also the mathematical and logical basis for attempting to get to understandings and conclusions for yourself. Essentially, with some time and effort, YOU should be able to make even better and more knowledgeable speeches than most of those TV speakers do!

As a personal observation, I note that rarely seems to happen! It appears that most people today who have interest in subjects such as this one buy some book or read some article by some author, and without further thought, simply ACCEPT the opinions and conclusions of that author. Such authors virtually NEVER provide the math or the logic they used to get to their conclusions or discuss whatever assumptions they had to accept in that process. That is why this presentation sort of REQUIRES you to invest some time and effort. Rather than "accepting the opinions" of some Physicist, it is hoped that you will scribble down some calculations of your own, to either confirm or deny calculations and statements made here. The subject is TOO IMPORTANT for you to simply accept ANYONE'S opinions. Is Vice President Al Gore's opinion that things are terribly bad true? Is President Bush's opinion that there is no such thing as global warming true? Both sound very convincing to their followers! Hopefully, if you struggle through this presentation, you may be able to form your own conclusions, to decide if EITHER of them is right or not!

A Research Physicist has spent a number of years studying the scientific processes that represent energy flows in the Earth's environment, and he presents here the results of several years of that research. It is arranged such that most readers should be able to do any necessary math to either confirm or deny statements made here. These subjects are too important to simply have to believe some spokesperson who may or may not actually understand the science involved. At the very end of the Footnotes, there are some brief references to the far more advanced math that is commonly used in the actual advanced science research, but this presentation attempts to only use math that is familiar to nearly everyone.

As a Physicist, I find it darkly amusing that so many people read a few paragraphs of some author, and suddenly start believing that they are now an absolute expert on all these advanced subjects. An interesting example is a College Professor in Oregon who has personally NEVER gone up the nearby mountains, but he constantly gives speeches where he explains to listeners that NO melting of glaciers has occurred! He even sometimes claims that the glaciers there are getting larger! It turns out that he is paid a lot of money by business groups which need to insist such preposterous claims to avoid hurting their business profits. It would be really bad if he would ever actually go up those mountains, as he would then SEE that HALF the glaciers are GONE, with more disappearing all the time. But he gives so many speeches that there are a lot of people who believe what he tells them. Does it frighten you that he purports to be an expert regarding LOCAL mountains but he has NEVER even taken a few hours to go up them to actually see the situation?

This discussion is essentially about THINGS THAT HAVE ALREADY HAPPENED. Many political leaders seem to think that we are currently fine and that all they have to do is SOMEDAY avoid adding even more carbon dioxide to the atmosphere. That is definitely NOT the case. Again, this discussion and the included calculations are primarily regarding EXISTING amounts of carbon dioxide in the atmosphere. NO ONE knows what the future will be, even scientists! A central point of this presentation is that even if everyone on Earth suddenly and immediately chose to not add a single extra pound of carbon dioxide to the atmosphere, we still have a truly catastrophic future to look forward to. The fact that political leaders still seem comfortable with adding massive (but reduced) additional amounts of carbon dioxide to the atmosphere FOR MANY MORE YEARS into the future, simply suggests that they do not (yet) really comprehend the terrible nature of our situation.

Politicians and business leaders have said astounding things regarding global warming and climate change over the past 35 years! People seem to feel free to express absolutely any personal opinion, if they think they cannot be proven wrong, and if they believe that opinion affects whether their businesses make billions of dollars or not! Didn't we learn anything from the tobacco companies that KNEW that they were causing hundreds of thousands of people to die each year from cancer, as early as the 1950s, but STILL absolutely insisted that they were innocent, into the 1990s? Didn't we all realize that they had outright lied to the public for around 40 years while they became some of the largest and most powerful corporations on Earth? And can't we see that there are vested interests that now want to insist that there is no such thing as global warming, or if not that, that mankind has nothing to do with it, because of economic threats to their corporations? Of course, there are groups with opposing views that see no problem in disrupting countless millions of dollars of business for a few dozen spotted owls or the equivalent.

Businesspeople discovered long ago that if you ask a hundred "experts" in any field, you will certainly find at least one that agrees with your point-of-view! Especially if the "expert" knows that he will get very large amounts of money, and probably a guaranteed future cushy job as a result! If there were some business today that felt it could make billions of dollars by insisting that the Earth is Flat, they nearly certainly could find some "expert" who would be willing to attest to that being true. It would NOT mean that it were actually true!

With this preamble, this presentation gives the pure science behind each of the various subjects involved, and includes the actual calculations that support the statements made. This is presented so that virtually anyone should be able to do the same calculations and logic to confirm these statements.

One important finding in this research is that it seems that all previous researchers have considered the interactions of sunlight, winds, oceans, ocean flows and all that, but that they seem to have never considered the effect of how massive and how poorly-heat-conducting the Earth's Crustal rocks are. An extremely important consequence of this is that the atmosphere cannot possibly adjust to any new equilibrium temperature without also heating (or cooling) the Earth itself as well. These calculations suggest that this factor causes around a 140-year lag in atmospheric and Earth temperature changes behind changes in the carbon dioxide content of the atmosphere. This appears to be an explanation for why science has not (yet) seen the far greater temperature changes that all scientists have expected from such great changes in carbon dioxide concentration; they are simply still to come, with the very worst to come more than a hundred years from now.

We note that nearly all political and business leaders have a very bad misunderstanding about a critical aspect of this subject. They all seem to think that all that has to be done is to get carbon dioxide emissions reduced a little "by the year 2050" and all will IMMEDIATELY be well. Or that they can continue to single-mindedly focus on profits until some LAST POSSIBLE DAY, and then make changes, and all will be well! That is NOT the case! What is critical is the CONTENT of carbon dioxide in the atmosphere! This is a cumulative effect. Actually, all the carbon dioxide that we have dumped into the atmosphere figures to stay there for thousands or millions of years! A scientist recently (early 2007) mentioned in a TV interview that the carbon dioxide released by the earliest Model T cars a hundred years ago, is still in the atmosphere! There are no known significant mechanical methods to remove it, and the natural methods of ocean creatures forming calcium carbonate and petroleum and natural gas and coal all take immensely long time intervals. Whatever carbon dioxide we put in the atmosphere, or more technically, into the Carbon Cycle, is likely to be there beyond the existence of mankind. In itself, that would not be a serious problem, except for the SCALE of the amounts we are adding to the atmosphere. We are currently adding about 144,000,000,000,000 cubic feet of carbon dioxide to the atmosphere EVERY YEAR! That is about 400,000,000,000 cubic feet each day. But each person or each business has always said "WE are adding very little and WE are not causing any problems."

There are absolutely ludicrous things presented by businesses in their attempts at sidestepping the fact that there IS a very huge problem. One of the funniest is where giant corporations now "buy carbon credits" from some remote tribal group. They claim that by paying such tribes some money, they have justified that they are then free to continue to send just as much carbon dioxide into the atmosphere! It is double-talk! That remote tribe probably was NOT going to massively start industrial operations! But the Executives of the giant corporations seem to be able to trick the public into believing that they are being "environmentally responsible" by "buying such carbon credits". The concept is absolute insanity, and it simply is a trick which allows those giant corporations to continue making the billions of dollars of profits that they insist on. And they seem to get away with it, as no one seems to think that "carbon credits" is remotely as bad an idea as it actually is. IT DOES NOT EVEN TRY TO FIX THE PROBLEM AT ALL! It merely tries to pawn off future blame on tribes around the world!

The argument of "we are a very small polluter so we cannot be having any significant effect" might be valid except for the fact that there are so many of us people on Earth! There is an interesting way to show how many of us there are! You may not realize it, but every breath you exhale contains about 4.4% carbon dioxide in it! Big deal, you say? It is true that YOU only exhale around 330 pounds of carbon dioxide in a year. (It comes from the carbon in the foods you eat and the oxygen in the air you breathe in.) But that means that every SIX people exhale a ton per year. There are over six billion of us living (and breathing)! Astoundingly, we humans collectively exhale a BILLION TONS of carbon dioxide every year! (Fortunately, when the plants grew that initially provided all (100%) of the food we eat, those plants REMOVED a billion tons of carbon dioxide from the air, so there is no bad long term effects like there is when we burn fossil fuels, where we ADD additional carbon dioxide into the mix.) (And, in case you are curious, there are NO other animals that are in such great numbers as humans where the total amount of exhaled carbon dioxide is remotely as great as what we humans exhale. It is very fortunate that Nature has established the Carbon Cycle to continually remove and replace carbon dioxide and oxygen, in a system that has been stable and reliable for many millions of years. At least until we started burning fossil fuels in massive amounts to foul up the Carbon Cycle.)

This discussion shows that recent decades of human society releasing so much new carbon dioxide into the atmosphere ALREADY has caused that our equilibrium temperature is FAR higher than the actual temperatures we are yet experiencing, and that even if we NOW suddenly totally changed our ways (which is not going to happen) and somehow stop increasing the atmosphere's carbon dioxide content, the atmosphere figures to continue to heat up for the next 140 years. This is all a FAR more serious problem than our leaders seem to comprehend. There is a valid possibility that we may have ALREADY done so much damage to the atmosphere that 140 years from now, the entire Earth may be too hot for virtually any plants to be able to survive and not wilt and die from excessive evaporation/transpiration. And if there were no plants, there would be no food for any animals or people. It turns out that this concept is not even new! (Archer and Barber, 2003, Photosynthesis and Photoconversion, Chap 1, p.4, calculated those things several years ago, and expressed their concern that the end of human and animal life may soon happen.) They also noted and calculated that if all plants were gone and people were still breathing oxygen, we would consume all the remaining oxygen in the atmosphere surprisingly quickly! (But we would run out of food far quicker.) Keep in mind that is due to things we have already done!

Only very recently (April 2007) have some scientists been (finally) trying to explain that it is therefore not nearly enough to slowly reduce carbon dioxide emissions. Some have (finally) started to say that AT MOST we may have TEN YEARS to drastically reduce carbon dioxide emissions, and they (even including ex-Vice President Gore) are even (finally) starting to say that it may already be too late to do anything to stop true catastrophe from happening. This presentation explains the Physics behind such statements.

A very interesting thing was discovered during this research! In highly respected published documents of the middle 1990s, no one then seemed yet even AWARE that carbon dioxide had such an extreme effect as it has regarding "being a blanket" in keeping the Earth's radiated heat from being able to normally escape to outer space! At that time, references to the "Greenhouse Effect" blamed water vapor, ozone, oxygen, nitrogen and artificial pollutants! (This specific text is from the extremely highly respected and trusted Mark's Standard Handbook for Mechanical Engineers, 1995.) So it is no wonder that many people now still seem ignorant of the strong effects of infrared heat absorption by carbon dioxide today!

FINALLY starting to get to the actual subject at hand!

There is simple and absolute logic that exists

1. There is a situation called Radiative Equilibrium where the energy radiated IN to the Earth (from the Sun) must, on average, equal the radiation energy the Earth radiates back out to space. Both are easily and reliably calculated. ^{note 1} (this situation is true for any object in any environment). Note: We will sometimes make an incorrect use of the term energy in this discussion, and the word power (which is energy per unit time) would be technically correct. However, we realize that in common conversation, the term energy is often used when discussing power, and we are hoping to make this presentation reasonably understandable! Energy is measured in watt-seconds or kilowatt-hours, where power is measured in watts or kilowatts. We hope no undue confusion will be caused by this.

2. With ZERO ppm (parts per million) of CO₂ in the early Earth with no atmosphere, this radiative balance was simple, based ONLY on the distance of the Earth from the Sun, the radiation rate of the Sun, and the average surface temperature of the Earth, (and therefore the outgoing infrared radiation of the Earth to outer space). There were therefore only four arrows in the schematic of energy flows, one in from the Sun, and one out from the radiation of the warm Earth, and two that represent energy reflected from the Earth, which shows that the (actual) Equilibrium temperature was then around -9ºF or -23ºC. ^{note 1} (Newton's Conservation of Energy and the Stefan-Boltzmann equation).

   We know that the Sun has created fairly constant radiation output for billions of years due to its internal nuclear fusion processes. We know that the Earth has been relatively near the same distance from the Sun as we are today. This indicates that the actual total amount of INCOMING solar energy (at the top of the atmosphere) has been fairly constant, at around the current 1353 watts per square meter of area (referred to as the Solar Constant). We know the size of the Earth has not changed, and so we know the projected area that the Earth presents to the Sun, and so we can easily calculate the total solar energy aimed at the Earth (projected area times Solar Constant). This is calculated below ^{note 1} at 1.7233*10¹⁷ watts. We are going to describe these huge amounts of power in terms of 10¹⁵ watts, called peta-watts or PW, so we are going to call this 172.33 PW.

   We show two different arrows coming in to Earth. They are the same, but the left arrow here is to indicate the energy that gets ABSORBED by the Earth and the next arrow is to indicate the energy that immediately REFLECTS OFF of the Earth. No one actually knows what the reflectivity, or what is called Albedo, of the Earth was before it had any atmosphere or white clouds or oceans, but it was likely to be relatively close to what it is today, at around 34% (possibly slightly lower but still close, certainly over 30%). Therefore we know that the early Earth immediately reflected away that 34% of 172.33 PW or 58.59 PW, telling us the power in both the second and third arrows in our drawing. This also tells us that the first arrow must necessarily represent the remaining 66% or 113.74 PW.

   Once the Earth had warmed to the extent necessary where its surface temperature reached a specific temperature that was stable, called Equilibrium, then the fourth arrow we show, of the RADIATION that the Earth gives off to outer space, must have also been 113.74 PW. This situation would enable the surface of the Earth to remain at reasonably constant (average) temperatures, a situation that could continue without change for a very long time!

   The Earth eventually established an atmosphere, and then rain and oceans. This did not materially change much, except that we now have a new pair of arrows that show solar energy bouncing off the atmosphere. This probably slightly increased the Albedo of the Earth, especially due to the white clouds that now could be in that atmosphere, but otherwise no tremendous changes occurred regarding the energy balance of the Earth. (Our drawing seems to have had the arrow on the right vanish, but please realize it should still be there!)

3. The incoming sunlight is a combination of infrared, visible and ultraviolet light, because the Sun's surface temperature is around 11,000ºF or 6,000ºC. (Planck's Law, Wien's Law). Since the Earth's surface temperature is now around 14ºC, those same Laws show that all outgoing radiation is far in the infrared. Without any atmosphere, that difference in wavelength (color) would not have mattered as all the radiation could pass freely in both directions, and that radiative equilibrium would exist. When an atmosphere developed, most of it (nitrogen and oxygen) is essentially equally transparent to incoming and outgoing radiation. But a few types of components of the atmosphere behave differently for the two.

   Blanketing Effect or the Greenhouse Effect

   There are two specific compounds that are in significant quantity in the atmosphere, carbon dioxide and water vapor, which are each much less transparent to infrared radiation than to the other colors of light. As a result, these two compounds pretty much allow the INCOMING (shorter wavelength, mostly visible and ultraviolet) solar radiation to come through freely. (toward the left on these charts) But those two gases absorb significant fractions of the outgoing much longer wavelength far-infrared radiation. (toward the right on these charts). Those gases absorb that heat and the then-heated warmer gases then re-radiate much of that energy, roughly half going up and out toward space and roughly half going back downward toward the Earth. This effect therefore provides an additional heat source for the Earth's surface, keeping it warmer than would otherwise be true, an effect generally called the Greenhouse Effect. The effect is extremely similar to why a blanket keeps you warmer, even though it does not produce any of its own heat; it simply enables your own body heat to remain near you.

   The water vapor is generally very low in the atmosphere, being involved with our weather systems. Its concentration in the atmosphere greatly depends on evaporation from the oceans, and its effects are therefore relatively constant over extended periods of time, although locally there are regularly great variations.

   The far greater contribution to the Greenhouse Effect is from the carbon dioxide in the atmosphere, primarily because it is present through the entire depth of the atmosphere, but also for more technical reasons.

   There are an assortment of other gases in the atmosphere which also absorb a lot of infrared, such as methane, but the total amount of methane in the atmosphere is very small when compared to carbon dioxide. Where the concentration of carbon dioxide is in the 280 ppm to 390 ppm range, only about 2 ppm of the atmosphere is methane gas. This results in that gas being worthy of watching, but of relatively less importance regarding Global Warming.

4. With around 280 ppm of CO₂ consistently present in the atmosphere during many centuries prior to 1800, ^{note 2} the "blanket effect" of that amount of CO₂ had raised that equilibrium temperature (by around 1900) by about 66ºF, up to about 13.75ºC or 56.75ºF. ^{note 3}

   This has complicated our picture! Everything shown on the left is still completely true, as we still have the same amount of energy coming in from the Sun, roughly the same amount reflecting back off to space. That means that the Earth is still receiving the net 113.74 PW of energy from the Sun. However, we have now divided up the previous single outward radiation arrow on the right into several arrows. Because we know that the surface temperature of the Earth was then around that 13.75ºC, much warmer than was true with the original Equilibrium, there has to be some source for the extra energy that warmer Earth is now radiating outward. Using the Stefan-Boltzmann relationship as shown in the footnotes, we can easily determine that an Earth's surface at an average temperature of 13.75ºC must necessarily be radiating away 195.86 PW of power.

   Ah, but we know that we only receive 113.74 PW (net) from the Sun. How is this possible? It is due to the effect indicated by the first crooked arrow on the right in our drawing. Consider this arrow to represent 82.12 PW of power. It goes upward as part of the 195.86 PW of power radiated from the relatively warm Earth. But it gets ABSORBED in the atmosphere, primarily by the carbon dioxide and water vapor in it. Then, the (warm) atmosphere radiates that 82.12 PW of power back down to Earth's surface.

   This allowed the Earth's surface to be in energy Equilibrium at that 13.75ºC temperature. We received 113.74 PW from the Sun, and another 82.12 PW in this far infrared (invisible to us) radiation from the warmed atmosphere, and therefore the surface received a total of 195.86 PW of power to be able to then radiate 195.86 PW from the surface.

   Note that the full 195.86 PW radiated from Earth does NOT actually get through the atmosphere to be lost to space. We just saw that 82.12 PW were removed from that outward flow. Actually, the Earth-atmosphere combination has to lose a total of 113.74 by radiation, for the overall Equilibrium of the combination. This happens in an interesting way, being represented by the final two arrows on the right in our drawing. We will discuss the rightmost arrow first. Remembering that we heated up the atmosphere, and that warmed atmosphere RADIATED DOWNWARD the 82.12 PW needed for Equilibrium of the surface situation. But the atmosphere is not smart enough to know to only radiate downward! The reality is that it also radiates the very same amount UPWARD, out to space! So that last slightly-kinked arrow represents another 82.12 PW of radiation that left the Earth's surface and got absorbed by the atmosphere, BUT which then got radiated UPWARD rather than downward.

   We now know the power in the remaining arrow, the radiation from the Earth's surface that actually goes straight on through the atmosphere to outer space, it is 195.86 - 82.12 - 82.12 or 31.62 PW.

   If you examine this situation, you can see that every point is in thermal Equilibrium, the Earth's surface, the atmosphere, and the whole combination. THIS is the explanation why the temperature of the Earth has been fairly constant for the thousands of years of civilization, until around 1900. It also explains why it was moderately constant, but with variations such as ice ages, over millions of years. As the surface of the Earth would warm a little, more plants could grow, each REMOVING more carbon dioxide from the atmosphere by photosynthesis, thereby slightly reducing the remaining amount of carbon dioxide remaining in the atmosphere, and therefore allowing more of the Earth's radiation to escape through the atmosphere, cooling the Earth back down. It was naturally self-correcting. That is why it was always close to an Equilibrium situation; that when changes occurred, there were generally secondary effects that cancelled the changes in the long run.

   You probably already noted that the actual total amount of power that escapes from the Earth-atmosphere system is 31.62 + 82.12 or 113.74 PW. This is exactly in accordance with the total (net) energy coming in to be absorbed by the Earth-atmosphere from the Sun, so we have the needed Equilibrium there.

   It is important to notice in the calculations above that the carbon dioxide and water vapor (and lesser components such as methane and ozone) in the atmosphere of the year 1900 necessarily captured a total of 164.24 PW of the 195.86 PW the Earth surface tried to radiate away. A HUGE fraction! You might see how and why if MORE carbon dioxide or water vapor was put into the atmosphere (as we have been massively doing by burning fossil fuels), that 164.24 PW absorbed certainly increases to an even larger fraction. THAT is the problem we face!

   Actually, that fraction is so large that it actually multiplies its effect! Infrared heat can keep going back and forth between the atmosphere and the surface of the Earth many times, making the total effect of this situation even greater. In our drawing above, it might be more accurate to show the first kinked line on the right to be extended to be a long zig-zag line, where each downward portion represents additional energy which acts to heat up the Earth's surface. This effect is somewhat reduced by the fact that the Earth is so massive and such a poor conductor of heat that it heats and cools very slowly.

5. We have ALREADY added so much carbon dioxide to the atmosphere (especially during the past 50 years) that we are now (2007) at close to 390 ppm ^{note 2} concentration (measured in many research locations, including the South Pole).

6. Given that the proportion that 280 ppm of CO₂ caused a 66ºF rise, then 390 ppm of CO₂ MUST cause a 92ºF rise, which means that the CURRENT Equilibrium temperature MUST ALREADY BE 83ºF.

   NOTE: There is very strong evidence that this linear proportion exists. It is generally accepted that the average Earth temperature probably fell to around 2ºC or 36ºF during some Ice Ages in the past few million years. The Vostok ice-core data (Barnola, Raynaud, Lorius; 2003) gives atmospheric carbon dioxide values for the past 419,000 years which occasionally dropped to a low of around 188 ppm. To try to check if the relationship is a linear proportion, we can do a proportion calculation: (188/280) * 66 = 44ºF as the equilibrium temperature rise at that ancient time. Since this is based on the initial equilibrium temperature of -9ºF, this gives an equilibrium temperature at that ancient time of 35ºF, a remarkably good match to the 36ºF mentioned above. This then strongly establishes that the linear proportion is valid.

   Also: Prior to around 1965, there was extremely little awareness that carbon dioxide even had any significant greenhouse effect. However, when spacecraft were first sent to the planet Venus, and all quickly melted and failed, the concept started getting attention. Astronomers had long seen the very reflective white color of Venus, with a very high visual albedo of 0.76. They had used the Stefan-Boltzmann relationship to calculate what the surface temperature should be. That showed that if ALL the sunlight was captured (no albedo), the surface of Venus COULD be as hot as 332ºK or 59ºC or around 140ºF. However, the highly reflective white color caused 76% of that incoming (visible) radiation to immediately be reflected away, and the calculations then suggested that the temperature of Venus was likely to be COOLER than Earth's, even though it is closer to the Sun, at around 232ºK or -41ºC or -42ºF. So there had been an expectation that the surface of Venus would be quite cold! However, in 1956, radar data suggested that the surface must be around 600ºF, but virtually no one believed that! When spacecraft were sent to land on the surface of Venus, they all melted and burned up before even landing! After many tries, a very well insulated craft landed and survived for a few minutes, and it found that the surface temperature of Venus is around 860ºF! Consider that! Logically, the surface of Venus SHOULD be around -42ºF but it ACTUALLY is +860ºF. It was soon realized that this was because of an extreme greenhouse effect of the carbon dioxide, which makes up most of the atmosphere of Venus. This was the very first strong evidence that carbon dioxide can have that effect, and the incredible effectiveness it can have.

   We can better think of all this by using that last drawing above. We know that there are around 2,000 billion tons of carbon dioxide already in the atmosphere. We know that we are currently adding around 8 billion new tons of carbon dioxide every year directly due to burning fossil fuels. This is only an 0.4% increase per year, right? Irrelevant??? No. It DOES turn out that some of that carbon dioxide will get absorbed into the oceans, but for the moment, let's just stay with the thought of a 0.4% increase in a year. We learned above that the atmosphere is currently blocking and absorbing 164.24 PW of the radiative power the Earth's surface is giving off. You saw the absorption graphs for carbon dioxide and water vapor above, where they are nearly 100% absorbent of many far infrared wavelengths. Say that total absorption increased by just 0.4% in that year, from 164.24 PW to 164.90 PW. Looking again at our drawing, we still have the Sun providing the 113.74 net intake. But now we have the more absorbent atmosphere now making it so that half-of-164.90 PW or 82.45 PW is now being radiated back down toward the surface from the atmosphere (instead of the earlier 82.12 PW) That means the surface is then receiving a total of 113.74 + 82.45 or 196.19 PW (but it is still only radiating away the earlier 195.86 PW). By now, you are probably familiar enough with the Stefan-Boltzmann relationship to know that this means the TEMPERATURE OF THE EARTH'S SURFACE MUST NECESSARILY RISE A LITTLE BIT (and you can even now calculate how much!) (0.12ºC or 0.21ºF). You are now capable of calculating the EQUILIBRIUM temperature increase each year, for however much carbon dioxide we add to the atmosphere! (The actual rise of the equilibrium temperature is slightly less than this, because carbon dioxide is very soluble in seawater, and so some of the CO₂ that we dump into the atmosphere gets absorbed into the oceans. Our reasoning is flawless above, but the actual numbers are slightly less because of this effect.)

   By the way, you now know virtually the complete method of analysis that good researchers use regarding the math of Global Warming. You are encouraged to confirm or deny any of these figures or this reasoning, to determine your own conclusions. (For the non-math-geeks, sorry about providing so much calculation here, but these subjects are incredibly important, and I feel it important that any reader have the equations and the numbers to duplicate the numbers and the logic for him/herself. Most of the worst of the math is over, except in footnotes!)

   For the record, the figures used and calculated above were for the Earth's average surface temperature from the year 1900. As the included graph of temperature readings shows, we are now measuring an average Earth temperature which is about 1.0ºC higher than that. So those same figures for today are: Insolation, still 113.74 PW; total outgoing radiation from the Earth, 198.60 PW, of which 169.72 gets absorbed by the atmosphere, with half of that being radiated back down toward the Earth, 84.86 PW; and 28.88 PW passing through the atmosphere to be lost to deep space. The total loss of the entire system by radiation to deep space is therefore 28.88 PW plus the 84.86 PW radiated upward from the atmosphere, or a total of 113.74 PW, again showing that the total system is in equilibrium regarding the energy received from the Sun and radiated to deep space. All the logic and the equilibriums still apply.

   The main point made here is that the Earth's surface is therefore RECEIVING a greater amount of incoming energy than it can RADIATE AWAY, which therefore requires the surface to warm up that fraction of a degree to be able to radiate away sufficient energy. However, this is a Catch-22 situation, where the greater amount of new radiation from the now warmer Earth surface will cause an additional amount of (secondary) radiation going up and then coming back down from the atmosphere. The fact that the effect is therefore somewhat self-perpetuating is a great deal of why this is so very, very bad.

   This is horrific, but this all might seem impossible because we have not yet started to see any such really terrible effects. Only about 1ºC or 2ºF of total average global temperature rise has been measured during the past hundred years. As a result of the lack of extreme temperature rises, political leaders and business executives have gotten away with denying that there is even any problem. It IS coming, and it will be truly horrible!

   There will be an interesting situation which should occur when the average temperature of the Earth has risen about 9ºC or 16ºF above today. At that point, there figures to then be essentially no longer any radiation from the Earth's surface that actually gets straight through the atmosphere! The atmosphere will be absorbing ALL the outgoing radiation from the Earth! The Sun will then be providing exactly half of the energy we receive at the Earth's surface, with the other half coming from the re-radiation from the atmosphere. The atmosphere will then be radiating around 113.74 PW back down toward the Earth, and also supplying ALL the 113.74 PW in outward radiation to space! Further heating beyond that temperature figures to continue, but in more complex ways.

7. The atmosphere can heat up fairly quickly but the Earth cannot. The atmosphere cannot actually get up to that equilibrium temperature until the Earth itself warms up. The warmed atmosphere simply gives up some of that excess heat to the below-equilibrium-temperature Earth (and oceans).

   If you have ever stood near a single-pane window in extreme winter, then you know the sensation of feeling that the heat of your body is being sucked out of you to the cold window. Similarly, near Chicago, the summer weather forecasts always include the phrase "cooler near the Lake (Michigan)". Those situations are somewhat similar to the rapidly heated atmosphere being right above a much colder Earth. Once the Earth has fully heated up to that air temperature, (or if Lake Michigan would ever fully heat up to the air temperature) then that effect ends, but the Earth's Crust is primarily rock, which conducts heat rather slowly. The issue therefore becomes one of determining how quickly the Earth's Crust can warm up to a new Equilibrium temperature. The calculations are presented here. ^{note 4}

   For reference sake, this calculation of the actual physical heating of the deep rocks of the Earth calculate to require an average of around 1.17 PW of constant power transfer from the atmosphere to the Earth for those 143 years of the calculations. This fairly small amount of power (around 1/2 of 1% of the total heat flow of around 196 PW) could be represented in those drawings above as a small arrow pointed into the Earth. It slightly, but not materially, affects the exact numbers presented above. But over those 143 years, that small amount of constant power calculates to increase the Earth's interior and surface temperature as shown and calculated.

   We should probably think of the atmosphere and the first 0.6-mile thick of Earth's rock as a combined system that is getting heated up. Relatively speaking, the atmosphere has minimal total mass. Even though it can heat up or cool down in a matter of hours, it involves a rather small amount of total heat needed to do that. The countless millions of tons of rock in the first 3,000 feet thick of the Earth's crust has tremendously greater mass (and a comparable thermal capacity per pound) and so virtually all of the needed heat needs to go there to raise or lower the temperature of the combined atmosphere-rock system.

   Why pick 3000 feet? Because the Earth's internal heat (from radioactive decay in the Core) causes the temperature to rise with depth, and it turns out that around 3000 feet deep, the current temperature is around the 83ºF that we determined that the atmosphere equilibrium temperature should now be. That means that no heating of any rocks deeper than 3000 feet should be necessary.

   As a further clarification of this: The small amount (the 1/2%) of heat IN the atmosphere, which gets transferred to the rocks of the Earth at any instant is very minimal, as compared to the amounts of heat energy actually needed to warm up all that rock. So it is NOT like the atmosphere is currently really hot and needs to transfer it to the ground and rock! It should be described differently than that. This might be clearer. We know that the incoming solar energy is continuing at the same rate it has for millions of years. So it is NOT like we are being overheated in that way. This situation is very much better described as that "blanket" concept, where less heat is able to escape by outward radiation. Therefore, there is a small NET increase in heat content, continuously, every second. In any one second, it would not seem to be to be any important amount of excess heat. But it constantly and continuously adds up! The energy calculations footnoted above just show that, over a 143-year interval, the TOTAL excess heat accumulated in those seemingly irrelevant one-second contributions really add up, enough to eventually raise that mass of rock plus the mass of the atmosphere up to the (current) Equilibrium temperature. It just is occurring at a rate that seems very slow and which might seem to be able to be ignored.

   You must have gone into an extremely cold bedroom on some night of your life, say at 45ºF. You were expected to go to sleep, as in a remote cabin or a tent. So you find all the blankets you can, or multiple sleeping bags. The room still might stay around 45ºF, but under your pile of blankets, it soon gets up to a comfortable 68ºF. What is the SOURCE of that added heat? YOU are! Fine. But you are not too smart (sorry!) and you do not throw off any blankets! A little while later, it is 80ºF under your pile of blankets. NOW, you consider it extremely cozy, and might even pop your head out from under the covers. But you STILL don't throw off any blankets! Remember that there is NO furnace in the room, and no heat source at all, except your body! And it keeps pumping out around 80 to 100 Kilo-Calories of heat, or around 350 to 400 Btus of heat, every hour. Your giant pile of covers only allows 100 Btus of heat to escape through them. You may remember something like this happening to you, where you get hotter and hotter and hotter. Until you would either get up to an Equilibrium Temperature, (where the amount of heat lost through the stack of blankets exactly matches the heat production of your body, or you finally get smarter and throw off a blanket or two.

   But say that you could not throw off any blankets. THAT is our situation on Earth. The "pile of blankets" is the accumulation of carbon dioxide and water vapor in the atmosphere. We have no way to "throw them off". In fact, by constantly releasing an extra 8 billion tons of new carbon dioxide into the atmosphere each year from the burning of fossil-fuels, we are essentially still adding more and more and more blankets to our situation.

   The sad part is that we happen to currently still be in those first few minutes where we thought extra blankets were a good thing! They WERE, as long as we later had a way to throw them off! We are essentially getting near that point like when all those blankets got us up to the 80ºF. We still don't yet EXPERIENCE what the long term effects of all those blankets will be! And it is as though we are still asking people to toss more blankets in top of us! There does not YET seem to be any dark side to this situation, because all we see is that we are currently "cozy".

   But it is as though your friends were not actually your friends, and they strapped down all those blankets on top of you. You are still at the 80ºF, but you are JUST STARTING to see some really bad possibilities, of extreme overheating. And amazingly, what is the SOURCE of the heat that will soon cause you to drastically overheat (and quite possibly then even die of pyrexia [fever, over-heating]), and rather quickly? Your own body is supplying the heat! Given the information above, we could use Stefan-Boltzmann again to calculate that the Equilibrium temperature under your big stack of blankets would be around 305ºF. Of course, YOU don't know that yet. But this story with the strapped down blankets would end very badly, as your body could not survive 305ºF. What can you do about it, if you cannot throw off any of the covers? Not a thing. THAT is where we have gotten ourselves regarding releasing so much carbon dioxide into the atmosphere. NOT "in the future". ALREADY. In the PAST decades. And we have no way to now throw off any of the blankets. Astoundingly, we seem totally willing to still keep adding more and more and more blankets! Political leaders, who clearly do not understand the significance of this, simply HOPE TO REDUCE CARBON DIOXIDE EMISSIONS BY 50% BY THE YEAR 2050. You should hear that and realize what they are really saying is that we are enthusiastically adding more and more blankets, because they do not yet have a CLUE regarding how drastic this all is. They are still intending to be adding more blankets in 2050 and beyond! Just THINNER blankets on top of our existing pile! Unbelievable!

   A central point of this presentation is to try to make this logic and these calculations fully understandable by everyone. It will be absolutely necessary that our leaders fully understand all this IF they are to make the critical decisions which MIGHT allow humanity to survive beyond 140 years from now. Sadly, that time interval seems to allow current leaders and businesses to simply say "We will continue as normal for now, making a few token improvements so the public will buy our products or re-elect our Party, and we will leave it to others who follow us to make such decisions, IF they then think it is important." That mind-set is a very convenient cop-out so that business and political leaders can avoid having to make decisions that are either financially undesirable or politically unpopular. We NEED to somehow look beyond "next Quarter's Financial Statement" and "the next Election" and realize that just 160 years from now, financial profits and elections may be meaning meaningless concepts on a quiet and desolate Earth.

   The reasoning and the calculations of this presentation show that we ALREADY have "added so many blankets" that few existing plants are likely to be able to have leaves 140 years from now, because their water pumping (transpiration) systems will simply be incapable of supplying enough water to keep from all the leaves and fruit from drying up. Which means that essentially all crops and nearly all other plants will realistically die by the year 2150 or so. There really are very few existing plants that could possibly survive in Africa or Brazil where the summer noon air temperatures might get up to 180ºF. Leaf surface temperatures would be even higher. Actual crop plants are far more sensitive regarding temperature, and they would all die, too. And what would people (and animals) then eat, if there are no plants growing? THAT figures to describe the final chapter of this adventure. The most terrifying part is that this is discussing a time where grandchildren of people today may still be around in 2140 to experience how it all turns out. Shouldn't that possibility actually scare our leaders into action?

   For the record, these results of the fairly simple and obvious logic and math we have presented are not unique. In April 2006, the PBS NOVA program on Dimming the Sun discussed much of these same things, with relatively similar numbers. One expert, Doctor Peter Cox of the University of Exeter, thinks that the average global temperature might rise by as much as 10ºC (or 18ºF) by the year 2100. That is actually quite close to what these calculations seem to suggest. The NOVA program also noted that nearly all trees on Earth would die at such high temperatures, and most existing crop land would become useless, with massive famine following. Another respected expert, James Hansen of NASA was discussing an expected 3ºC (or 5ºF) rise above today's temperature, noting that three million years ago, that was the situation, and that all ocean levels were then around 25 meters (80 feet) higher than today. And Hansen was discussing that 3ºC rise by around 2050. (That is actually a greater sea level rise than I am expecting, but on the same scale.)

   This presentation is just providing you with the logic and the math that is the basis for such statements by respected experts such as Peter Cox and James Hansen. They and many other scientists have done these same examinations, but no one seems willing to let the public know what the logic and the facts are. Well, now you have them.

   It really seems incredible that virtually everyone today is so incredibly competitive regarding successful businesses that only short-term profits matter. If there is some person who claims that there might be "negative consequences 140 years from now" why should anyone really reduce the level of profits today? THAT it the terrifying thinking that will resist this recognition of what is to come. It is easy to imagine that the last few surviving people will still be trying to figure out how to maximize their financial profits, around the year 2160! Human nature is really something to behold!

   The 143-year calculated lag time is the result of how long it will take for the Earth to heat (or cool) all that rock up a new current Equilibrium temperature. This explains why we are not yet seeing any major increase in the average Earth temperature yet. The Earth's average temperature IS rising, somewhat slowly, but that is because it is still responding to effects of 140 years ago, of around 1865. We can see from the Carbon Dioxide graph ^{note 2} that the beginnings of the Industrial Revolution around 1800 already started adding carbon dioxide to the atmosphere and by 1865, we had already added significant amounts. But keep in mind that cars and electricity and electric generating plants were not even yet dreamed about or invented!

   This 140-year lag in the effects on the average world temperature is fairly clearly seen if the two graphs included in this web-page are compared, the carbon dioxide ^{note 2} and the average Earth temperature, ^{note 5} but now shifting the temperature graph about 140 years to the left (and squeezing that graph to change the scale so the graphs have the same horizontal scale.)

   Note that around 1750, there was a significant dip in the CO₂ concentration, and around 1890 there was a very similar dip in the global average temperature. Note that then there was a plateau from about 1810 to 1840 in CO₂, and a similar plateau is in the global temperature graph from about 1940 to 1970. From about 1840 to 1850 there was then a rapid increase in CO₂, and again, there is a matching rapid increase in global average temperature from about 1975 to 1985. Not only are the general shapes of the graphs fairly similar, but those brief variations also match up surprisingly well, all of which seems to support these calculations that the CO₂ we put in the atmosphere is definitely directly causing increases in the average global temperature, and about at the mathematically predicted lag time of about 140 years.

   A calculation involving Calculus and the Kelvin Integral can even more accurately calculate the amount of time that the Earth will take to rise to that current Equilibrium temperature of 83ºF. There is NO doubt that it necessarily has to get to that temperature. ^{note 3}

   Note that the most troubling part of all this is that what we are SEEING now appears to be primarily a result of CO₂ put into the atmosphere by the time of the Civil War! This helps explain the fairly small average global temperatures measured so far. When one looks at how the curve of the CO₂ proceeds after 1860, it is truly terrifying!

   The ONLY good news that seems present here is that we probably therefore have around 140 years before the global average temperature will have fully risen to the current equilibrium temperature of 83ºF. We note that the British Prime Minister recently (Feb 2007) announced a personal vow to keep global warming from ever exceeding 3ºC (which is 5ºF). Even if he and all other leaders and businessmen and drivers and electricity users would immediately and totally END all contributions to CO₂ to the atmosphere, we are destined to pass that level about 2110 anyway! And probably far more than 20 years before that! My personal guess is by 2050 (essentially the same as James Hansen of NASA predicts).

   And since few people would actually do those drastic and costly and inconvenient things, the problem and the consequences will certainly yet get even worse. Just imagine extending the graphs toward the right and curving them both even more upward!

   It really does not matter what politicians argue about or say, because no one will actually solve this because it would be too economically destructive to giant companies and cause too much hardship on all the people affected by mandatory cutbacks. No politician would ever get re-elected if he voted for such terrible rules! However, Nature seems to have planned far ahead of us! The US is already completely out of economically-mined Uranium for nuclear power plants (ALL US Uranium mines closed some years back), and only has around 4 years' supply of petroleum and about 8 years' supply of natural gas (if no imports) at current consumption rates. And the entire world really only has around 20 to 30 years supplies left of all three, particularly as China has begun consuming enormous amounts. (You can examine the official government and industry published data regarding these remarkable and frightening statements in a link at the bottom of this page.) (Note as of mid-June 2007: several American Uranium mines are planning to re-open, because the price of Uranium has recently increased by a factor of four! They expect that it will take a couple years before they can actually start supplying any Uranium. Wanna guess at what the price of electricity will do around two years from now, with that four-times-as-expensive Uranium?)

   So, even though politicians and businessmen will never be able to even slow down our immense consumption of those fuels, they will all be saved from having to make those decisions in twenty or thirty years, where there are essentially no such fuels left to argue about. Given human nature, there will be a LOT of angry people then, and tremendous wars can probably be expected, over resources that won't even then still exist! Go figure!

• It is reasonably well established that 60 million years ago, the world had risen to 72ºF and both of the polar ice caps completely melted. You read above that we are unavoidably headed for at least 83ºF, for things that have already been done by our society!

• If and when the Antarctica ice cap completely melts, that volume of ice is enough to raise all the world's oceans by around 310 feet. ^{note 6}

  Greenland's much smaller ice sheet will raise the world's oceans an additional 23 feet (as mentioned in the 2/2/07 global warming conference announcement) when it entirely melts. There are also ice fields in Siberia, Alaska and Canada, elsewhere. When equilibrium settles in with the 83ºF that it should already be, all those ice fields will certainly completely have melted, raising the world's oceans by around 400 feet. The entire State of Florida will no longer exist! Own property there? Massive amounts of human history and artifacts may be left to drown, similar to when Turkey did that with a new dam and reservoir which were built a few years ago, where archaeological cities were forever lost, except this time, world-wide.

  There are other published government figures that give a different but similar rise. That data defines the current locations of the various amounts of water on Earth: 97.1% in the oceans; 2.24% in the polar ice caps and glaciers; 0.61% in groundwater; 0.016% in lakes; 0.001% in the atmosphere; and 0.0001% in rivers. Using these figures, if the glaciers and ice caps all completely melted, then the amount of water in the oceans would increase by a factor of (97.1 + 2.24) / (97.1) or 1.02307. The current average depth of the oceans is around 12,500 feet, so with those glaciers and ice caps melted, it would necessarily rise to 12,788 feet, meaning that all sea levels would rise by 288 feet. This is better than a 400+ foot rise, but not a lot different from the figures given above.

  There is also another effect, the fact that the density of the ocean's water will slightly decrease with increasing temperature, meaning that the water of the ocean will need to take up more volume. This is also easily calculated, and it represents a separate 48-foot rise in the ocean's level, at the current equilibrium temperature of 83ºF, even if no ice had even melted! Meaning that the realistic total increase is likely to be around 450 feet vertically. We note that the city of Nashville, Tennessee is currently at altitude 440 feet! Look at where Nashville is on a map! (Washington, DC is at altitude 25 feet. Only the very top of the Washington Monument may be above the Atlantic ocean, hundreds of miles from shore, in 140 years!)

• We are still actually measuring about 59ºF as an average world temperature, mostly because the Earth is so huge and massive that it takes some time (calculated here as around 140 years) to entirely heat up deeper earth to the necessary Equilibrium temperature. NOTE that THIS HAS ALREADY HAPPENED and that it is only a matter of how long it will take the Earth to get to the Equilibrium temperature. Politicians seem to think that they still have time to make brilliant decisions to avert disaster! But they are certainly DEAD wrong about that, in that this presentation has nearly entirely discussed THINGS THAT WE HAVE ALREADY DONE! Whatever further damage we do in the future, and we will, may be nearly irrelevant, as we have already done the central crime!

• The fact that the Equilibrium temperature of the atmosphere now is already 83ºF, even far hotter than when the polar ice caps had completely melted 60 million years ago (at 72ºF), that means that we have ALREADY done so much damage that the polar ice caps will certainly again both ENTIRELY melt. The only question is how long the Earth will take to get to equilibrium. So that 300+ foot or 450-foot rise in the oceans is now, already, an absolute certainty. All that certainly will occur, well within the next 140 years.

• The most important aspect of this is that THIS DAMAGE HAS ALREADY BEEN DONE, and therefore much of the resulting equilibrium-attainment damage might easily occur DURING YOUR LIFE. NOT in a thousand years, maybe not even in a hundred, before really massive damage starts to occur. If you are young enough to still be likely to be alive in 2040, you may see Senators and Congressmen panicking over the fact that they have several feet of ocean water in their offices! And they would certainly immediately spend many billions of dollars (of taxpayer money) to make protective dikes around themselves! (in a desperate but hopeless effort.)

  This all figures to only take as long as it takes the Earth to heat up those 25ºF. True, we calculated 140 years here, which means that we will all be gone by then. But the seas will not SUDDENLY rise by that 350 feet or 450 feet on some day 140 years from now! They will gradually rise as the ice caps melt and as the ocean water density decreases and the ocean volume increases as a result. Many younger people living today seem destined to see a world where the oceans are 50 feet above where they are today. That means that New York City [currently 55 feet altitude] will soon be completely gone, and many other historic world cities will no longer exist. (In the US, Baltimore [100 feet], Boston [20 feet], Philadelphia [40 feet]. Even Nashville, Tennessee [currently 440 feet altitude] may be either oceanfront property or even under the Gulf of Mexico within 140 years!) It used to be that we only were concerned about Venice, Italy and New Orleans. Now, much of whole countries such as Bangladesh [eighth largest population in the world] and Indonesia [fourth largest population] will probably no longer even exist!

• This is not even counting the effects of everyone driving their cars on Feb 12, 2007 (tomorrow) and all days afterward, because the equilibrium keeps getting far worse. The population of the world presently adds approximately 8 billion tons of carbon dioxide to the atmosphere each year, specifically and directly from vehicles and electric power generation. That is roughly 1/220 of the total carbon dioxide already in the atmosphere. That amount of carbon dioxide that we add every year is 144,000,000,000,000 cubic feet of gas. An astounding amount.

• I estimated China's rapidly growing contribution and projected for the equilibrium temperature that should exist in 2027. It is 93ºF. Ten degrees hotter still, in just 20 years. And 35ºF above today.

• The vast majority of that carbon dioxide is put into the atmosphere from two sources, vehicle exhaust emissions and the chimney emissions of electric powerplants powered by coal, oil and natural gas. A smaller but important contribution is from heating homes and other buildings. All of these fuel sources are referred to as fossil-fuels.

• Few trees will survive an increase of 35ºF (worldwide) because the summer noon temperatures they will have to endure (and grow in) will be so hot that far too much evaporation will occur from the leaves at 140ºF and 150ºF daytime air temperatures (in US). The leaves will shrivel up and fall off! The tree will then have no way to grow, no way to do photosynthesis, no way to produce oxygen as a by-product. With far less oxygen being created by plants, humans and animals will have less oxygen to breathe. This may already be a terminal situation, where a few thousand years from now, no oxygen breathing humans or animals may be able to exist anywhere on Earth. (Archer and Barber, 2003, Photosynthesis and Photoconversion, Chap 1, p.4, calculated that to take around 4,600 years). That issue might heavily depend on whether certain types of ocean plankton can survive and prosper as the oceans greatly rise in temperature.

• Few food crops will be able to survive that great temperature increase either. That suggests that, very quickly, in months, that the entire food supply for humans and animals might end (Archer and Barber, ibid).

• African jungles already get up to 130ºF. When they regularly get up to 160ºF and 170ºF, all of THOSE trees will die, and any people there will have nowhere to hide from the sun! And nothing to eat. They will either move away or die, too. Where will they go?

Can you imagine the consequences of this? If we do nothing, catastrophe beyond imagination. But "doing something" would have to be so huge that the results would seem nearly as bad in the short run. The ONLY logical, intelligent thing to do would be to IMMEDIATELY BAN ALL VEHICLES WORLDWIDE, cars, buses, trains, airplanes, trucks, and put GM and Ford and Toyota instantly and completely out of business. Also, the majority of all electric power plants would have to be completely and permanently shut down. NOT "next week or next year or in 50 years, but TODAY". Also, absolutely stop ALL fossil-fuel heating of all buildings.

Note that doing all these horrendous things, essentially the end of modern human life, would not actually FIX the damage that we have already done, but merely keep from doing even more damage.

The world would seem to have to "stop completely" to have even a small chance of the survival of mankind and many animals.

Obviously, there are few people who would be willing to endure such hardships, because they would simply say it was all lies. I admit that I personally have no motivation to scrap my Corvettes! And I like my house heated in winter and I like to have electricity. WHO would agree to giving even one of those things up?

What this is saying is that the last year's (2006) publicity about global warming is "barely scratching the surface of the actual severity of the catastrophe."

This is bad, far worse than even I had realized. And FAR more urgent than I had realized, too. I used to assume that it would be at least centuries before significant global warming would occur. But this reasoning, all based on solid data, is irrefutable.

The NOVA program of April 2006 mentioned above actually had one good note in it! When they pointed out that the earth was far hotter around 50 million years ago, 25ºF hotter than today, the narrator noted that life struggled to survive. The useful fact here is that SOME life DID survive!

It seems important here to briefly discuss those natural processes and the sorts of causes that are now believed to be the causes of them. First, it is assumed that you know that we have seasons because the Earth's spin axis is tilted to its orbit around the Sun. As it happens, we in the Northern Hemisphere are tilted most toward the Sun around June 21 of each year, which causes the warmth of summer. It also turns out that the Earth does not go in a perfect circle around the Sun, but in a slightly (3%) elliptical orbit. Interestingly, we are now closest to the Sun on January 3 of each year!

The result of these two effect is that our (Northern Hemisphere) summers are slightly less hot, because we are then slightly farther away from the Sun (then only getting around 6% less incoming radiation and heat from the Sun.) The difference between summer and winter is therefore actually greater in the Southern Hemisphere than in the Northern!

There are some very SLOW effects that occur. All amateur astronomers are annoyed by an effect called Precession, because star maps are never exactly correct! It occurs because the Earth's spin axis is very slowly "wobbling" with a period of (currently) around 25,800 years. A direct result of that is that around 13,000 years ago, the Earth's axis was tilted the opposite way, which caused the Summer in the Northern Hemisphere to occur when we were CLOSEST to the Sun and Winter to occur when we were FARTHEST. That meant that around 13,000 years ago, (Northern) summers were hotter and winters were colder. If you happen to know that the most recent Ice Age ended around 10,700 years ago, this can start to seem to have some importance!

A second slow effect has even greater effects. We know (due to an analytical process called Fourier Analysis) that the Earth's orbital ellipticity (called eccentricity) also changes very, very slowly. We are actually headed for a time (around 24,000 years from now) when the orbit will be nearly circular (less than 1% eccentricity). But there are times when it can be as great as roughly 7% eccentricity.

Since the intensity of the Sun's radiation goes as the inverse square of the distance, that results in around a 15% difference in received energy between perihelion (nearest the Sun) and aphelion (farthest from the Sun). That is a rather large difference. When it is combined with the seasonal effect of the tilt of the axis, there CAN BE times when the two effects compound each other, where winters are extremely cold (in one or the the other Hemisphere). The fact that snow is white compounds this even more, as a Polar region covered with white snow / ice cap reflects far more sunlight away and can cause it to get even colder yet. We are currently seeing the opposite effect. In August 2007, a group of noted researchers announced that the ENTIRE North Polar Cap will have melted by the summer of 2013. At that point, the darker colors of the land and ocean surface will start absorbing much more solar energy rather than reflecting it back out into space, and the polar area will heat up even more and even faster. It has already been noticed that the North Polar region is heating up several times faster than any other part of the Earth. The white color of snow is an interesting partial cause of that!

So, yes, there ARE natural effects that cause the Earth to warm or cool. There are also situations where the carbon dioxide content of the atmosphere naturally increases and decreases, generally in response to the amount of plant life then living. But no such effects have ever had the extremely fast effects that we are seeing during the past 50 years.

After discovering these various things in careful scientific research, I did NOT want to accept them! I spent months in trying to find ANY flaws in any of the logic, the reasoning or the calculations. Sadly, I found none that were significant, and these concepts seem all frighteningly true.

Say that we do NOT find some solution to this situation, and mankind actually winds up living on a planet with such high temperatures. Man IS creative, and it seems certain that Antarctica would become a very popular place! There may even be crops that may grow there, so a limited number of humans might be able to endure. I must admit though that I am note sure I see WHY they would! They would be looking at a situation where for thousands of generations, nearly the entire world would be uninhabitable. Exactly what would they aspire to? I guess survival itself is a wonderful goal.

But it seems certain that all future people would have immense anger and hatred for the people who lived in the period between about 1950 and 2020 as having been so selfish and short-sighted to have so completely decimated the planet, its animals and its plants. They will certainly have access to historical records that will show us using a 5,000 pound SUV to do the simplest of errands and to use 750,000 pound airliners to carry 500 people who were in a hurry to get somewhere. I suspect they (if any survive) will not have much good to say about us.

Thoughts toward any Possible Solution

If the problem only involved 100,000,000 pounds of CO₂ to be removed from the atmosphere, and then stashed somewhere, such as the "sequestration" concept that is being given massive media attention and massive financing, yes, it might be possible. That would be 50,000 tons of carbon dioxide, around 5,000 full tanker truckloads or so. And that volume of CO₂ would be small enough to actually try to put into some cave or something.

However, each year, we are ADDING 16,000,000,000,000 pounds of carbon dioxide to the atmosphere! JUST to try to remove the carbon dioxide that we ADD in a given year would involve removing 8,000,000,000 tons of carbon dioxide. For starters, that is 800,000,000 full tanker truckloads! Are you starting to see why the ideas regarding trying to remove and then sequestering all that gas in the ground is so small-scale as to be ludicrous? I am not sure how many tanker trucks exist in the United States. Maybe 200,000 might be realistic. That would mean that every single one of them would have to transport 4,000 truckloads each year, or more than ten full truckloads every single day. Constant work! Where would the diesel fuel come from for all those trucks? Those people who are aggressively promoting sequestering the carbon dioxide in the ground, have certainly never bothered to calculate how much space even one year's supply of 8,000,000,000 tons would require! It is a pretty simple calculation, but I guess if they had done it, no one would then give them billions of dollars to work on it! But roughly a sphere around 40 miles in diameter would just about hold one year's worth! That is roughly 30,000 cubic miles! If you add up all the known caves in the world, there are only a FEW cubic miles of volume in them! And nearly all of them would "leak" because of faults in the rock layers or cracks etc. What a silly idea!

Possible Ways to Reduce Carbon Dioxide in the Atmosphere

Footnotes

Equilibrium temperature calculations

The average radius of the Earth is 6.367 * 10⁶ meters. This means that the total area presented to the Sun is π * r² of that or 1.2737 * 10¹⁴ meters². If we multiply the Solar Constant (1353) by this area, we get a total amount of Insolation, or total energy coming in from the Sun, of 1.7233 * 10¹⁷ watts. (This is above our atmosphere).

Some of this incoming energy is reflected away by clouds, the atmosphere and the earth itself. That fraction is called the Albedo (reflectance), and it is measured to be about 0.34, meaning that 34% of the Sun's energy aimed at the Earth gets reflected back out into space without ever doing anything to the Earth or the atmosphere . The remainder, which does not get reflected away, gets absorbed by the earth and atmosphere. This amount is therefore (1 - 0.34) * 1353 or 893.0 w/m² or 283.6 Btu/f²/hr. This is the AVERAGE figure for the entire Earth, meaning it includes those parts of the earth which are fully cloud-covered and those parts where the Sun is very low in the sky where most of the incoming energy is reflected. When the Sun is overhead on a cloudless day, around 340 Btu/f²/hr are measured locally.

Multiplying the total area of sunlight intercepted by the fraction of the Solar Constant which actually gets to the be absorbed by the Earth and atmosphere gives 1.1374 * 10¹⁷ watts of total energy coming IN to the Earth from the Sun.

Before the Earth had an atmosphere at all, this number was slightly higher, because there was no atmosphere to reflect some of that incoming energy back to space, so Earth's Albedo was probably slightly less then. We are interested here in the Earth having an initial atmosphere, but with NO carbon dioxide in it. So the Albedo would have been very close to the Albedo of today, of the combined Earth and atmosphere. Therefore, we can use the 1.1374 * 10¹⁷ watts figure as the actual total energy coming in.

For equilibrium, where the average temperature of the Earth neither rose nor fell, this incoming energy had to equal the amount of energy the Earth radiated to space. (The Earth cannot lose energy by either conduction or convection.) The Stefan-Boltzmann Equation gives the amount of this radiation (called Black Body radiation) that an object will radiate away, and it only depends on the surface area and the temperature of that surface. The equation is:

Q(rate) = A * s * T⁴

where Q(rate) is the total rate of energy flow outward, s is the Stefan-Boltzmann constant of 5.67 * 10^-8 w/m²/K⁴ and T is the surface temperature in (absolute) degrees Kelvin. Since we know what Q(rate) has to be, and we know the total surface area of the Earth, we can calculate T from this equation. So we have:

1.1374 * 10¹⁷ = 5.0948 * 10¹⁴ * 5.67 * 10^-8 * T⁴

(for clarification, the TOTAL SURFACE AREA of a sphere happens to be exactly four times the area presented to the Sun, which results in this area based on the area calculated above.)

This gives:

3.937 * 10⁹ = T⁴

250.5ºK = T

This is the same as -22.7ºC or -8.8ºF.

This is therefore the average Earth temperature that is the Equilibrium temperature for the Earth at our distance from the Sun, -8.8ºF.

Other people have used a slightly lower Albedo for the new Earth of 0.31. That then calculates to an Equilibrium temperature of 253.3ºK or -19.9ºC or -3.7ºF. We will use the -9ºF in our calculations rather than the -4ºF used in some other similar calculations. (The exact value of the albedo depends on how many white reflective clouds happen to exist at that moment, so a really stormy day can cause more reflectivity and a slightly higher albedo for a few hours.)

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Graph of Carbon Dioxide Concentration 1000ad - present

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Graph of Earth Average Temperature 1880ad - present

. The Earth has an interior heat source, due to radioactive decay of Uranium and other nuclear atoms in the Core. This results in an OUTWARD conduction of heat through the Earth's Crust. This conduction has been measured and is accurately known to be 0.02 Btu/hr/sq.ft, around 0.0046% of the Solar Constant energy coming in from the Sun. The result of this is that the Earth gets warmer as you go deeper into it.

The Handbook of Chemistry and Physics indicates that the average thermal conductivity of the Earth's Crust is 0.97 Btu/hr/ft²/ºF/foot thickness. Nearly all types of rock have a thermal conductivity that is very similar to that value. We know that the Earth gets warmer as we get deeper, due to that internal radioactive heat source in the Core, at a rate that varies with location but is commonly about 1ºF for each 100 feet in depth.

We will use conventional thermal heat conductivity formulas here:

Q = A * DF * (conductivity/thickness)

and assume that we are considering a one-foot-square column of Crust.

(I apologize to purists for using the American system here instead of staying with metric, but these numbers are more familiar for most likely readers.)

We now need to have the amount of heat transferred to the ground from the air. Standard thermodynamic equations apply. There are two possible situations, natural convection and forced convection.

For natural convection, the equation for a flat surface being cooled from below and pointing up is:

where the Grashof number, the specific heat of the air, the viscosity of the air, and the thermal conductivity of the air are used in the usual ways.

For air, at moderate temperatures, standard atmospheric pressure, with standard gravity, at sea level, this simplifies a lot to:

where the Dt is simply the temperature difference between the air and the ground, in other words, starting at the differential that the Equilibrium temperature must cause.

Our current 83ºF equilibrium temperature is 25ºF above the actual earth average temperature of 58ºF, so Dt is 25 here. L is one. So we get a value for h_m of 0.27. The heat transfer from the air to the ground is therefore 0.27 * 25 or 6.7 Btu/hr/ft².

The surface of the ground then quickly heats up, because the poor conduction through the rock below limits the total heat flow. Other, more complex, standard thermodynamic equations establish the total result of these separate effects. The net result is an initial heat transfer of around 1.98 Btu/hr/ft². This is the rate at the START of the heating process, and it gradually will reduce over the years to essentially zero when the soil has heated up to very close to the equilibrium temperature that the air is trying to be at.

For a forced convection situation, where wind is blowing the air across the land, h_m is much higher, around 7.5 for wind that is moving at 5 mph. This situation of moving air causes the transfer of the heat to the ground to be far faster, as much as 187 Btu/hr/ft². However the ground and rock are again not able to conduct very much heat away very quickly, because of the poor thermal conductivity of rock, so this very high value never actually applies in real life. So, even with wind so that there is forced convection, we are basically limited to that 1.98 Btu/hr/ft² energy flow rate

We know that because of the increase in temperature with depth, the rock is already at the target 83ºF at a depth of about 2900 feet. This is because there is little heating in about the first 400 feet and then we have that rise of 1ºF for each 100 feet additional depth, so we have 400 + 100 * 25 or 2900 feet.

Therefore no heat is needed for any rock below that level in getting up to the equilibrium temperature. This means that our one-square-foot column of rock contains a total of 2900 cubic feet of rock that must be heated up. Since the density of most types of rock is close to 150 pounds per cubic foot, this means we have a total of 435,000 pounds of rock to warm up. That rock currently is at a range of temperatures from the surface 58ºF to the 2900 foot depth of 83ºF. Commonly, there is not much rise in temperature for the first four hundred feet depth or so, so this process will have to heat that rock up the entire 25ºF. The AVERAGE current temperature of the rock between 400 and 2900 feet deep is therefore halfway between these two limits, or 70.5ºF. We have now simplified this calculation into the heat needed to heat 375,000 pounds of rock by 12.5ºF plus 60,000 pounds of rock by 25ºF. Therefore, we need to supply a total of about 6,200,000 pound-degrees of heating. That rock has a thermal capacity of around 0.2, meaning it takes 0.2 Btu of heat to raise one pound of the material by 1ºF. Therefore, we finally know how much heat is needed to heat the necessary rock, 1,240,000 Btus.

There are amounts of water and other materials, especially in the topmost hundred feet, but they have minimal effect in slightly increasing this value

We determined above that we would have about 1.98 Btu/hour entering the surface of our one-foot-square column of Crust and rock. Again, this rate will gradually and uniformly reduce throughout the period of the heating, to zero, and so we can use half that 1.98 value or 0.99 Btu/hr for further calculation. We now know how much heat has to be added to the rock and the average rate it will be added. We can simply divide to determine the expected time required for this to occur. 1,240,000/0.99 gives 1,250,000 hours, which sounds like a really long time. But that is 52,200 days or 142.9 years.

This is the BEST or LONGEST time delay! If the forced convection situation of moving air applies very regularly, this period could be shorter.

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Graph of Carbon Dioxide Concentration 1000ad - present with the Temperature Data from the other Graph superimposed IN RED but shifted 140 years to the left.

. Several recent 2005 and 2006 PBS programs have described how the ice cap on Greenland is ALREADY melting back (and falling into the ocean) at 150 FEET EVERY DAY! Each year, TEN MILES of ice near the edges of Greenland is melting and gone! This is a LOT of ice! In a hundred years, that is a THOUSAND MILES of Greenland that will be without ice, most of the entire ice cap that is on Greenland. (And this is at CURRENT melting rates, which must certainly accelerate!) However, Antarctica represents a far bigger disaster in the works. Antarctica is around 5,400,000 square miles in area. Sonar soundings indicate that the ice on Antarctica averages around 1.5 miles thick. That means there is around 8,100,000 cubic miles of ice sitting on Antarctica. (nearly all of it currently above sea level). That is 8.1 million cubic miles that would melt to become virtually the same quantity of water that would get added to the oceans. Any map or globe can confirm that there are around 140,000,000 square miles of ocean surface. (Also, 71% of the entire Earth's surface of 197 million square miles is ocean, which gives the same value.) Simple division says that if all that ice on Antarctica melted, the sea levels would all rise by 8.1/140 mile or around 310 feet! How hard is that to calculate? In any case, a ten-foot rise which would destroy many huge world cities would hardly be a start at Antarctica melting!

The PBS programs also note that roughly 1/3 of the North Polar Cap is already GONE, melted! (2006)

This is a graph (from Thekaekara, NASA, 1965-73) that presents several different important things related to the Sun. First, it presents a smooth curve that is marked as Black Body Curve 5762ºK (normalized). THIS curve shows the theoretical spectral distribution of radiation from an object that is radiating at the temperature of the surface of the Sun, 5762ºK. It is calculated by using Planck's Law and Planck's equation. The highest point on that curve is calculated by Wien's Displacement Law, which shows that for that temperature, the greatest amount of radiation is sent out at a wavelength of 0.503 micron (or 503 nm or 5030 Angstroms). The curve is clearly asymmetric, with most of its area toward the right, or longer wavelengths. As a result, there is a vertical dotted line which shows the wavelength where exactly half the radiation is sent out at longer and half at shorter wavelengths, that location on the chart being at 0.713 micron. This is interesting in that this wavelength (7130 Angstroms) is well in the red portion of the visible spectrum. In fact, the Black Body curve can be mathematically Integrated (area calculated under the curve) over a range of wavelengths to determine the fraction of solar energy which is is different portions of the spectrum. This results in 7.0% being in the ultraviolet (shorter than 0.38 micron wavelength, 47.3% being in the visible light portion of the spectrum (0.38 to 0.78 micron) and 45.7% being in the (invisible to our eyes) infrared (longer than 0.78 micron). This curve therefore gives the THEORETICAL values of the irradiance at all wavelengths, above the Earth's atmosphere.

Next, there is a curve that pretty closely follows the Black Body curve, which is marked as Air Mass Zero Solar Spectrum. This is the actual measured values for the radiation at all the various wavelengths, again still above the atmosphere. Above the atmosphere means that Air Mass Zero, or not yet having to pass through any atmosphere. The similarity to the Black Body curve essentially confirms that the Planck and Wien and other Laws are valid.

There are two remaining lines on the graph. One is the Air Mass One Solar Spectrum WITHOUT MOLECULAR ABSORPTION. This represents the remaining total of radiation that is able to penetrate the entire depth of the Earth's atmosphere (from straight above, or Normal, meaning that the light must pass through 1.0 of the depth of the total atmosphere (or mass 1.0). This value is noticeably lower, greatly because of light being reflected (or scattered) back upward toward space off of the various types of molecules and dust particles in the atmosphere. There are established reflectances for each of these components. For example, the theory of Rayleigh provides an equation for the reflectance off the nitrogen molecules and oxygen molecules. Other theories account for the dust, water vapor, etc. Collectively, this all accounts for the Earth's atmosphere's total reflectance or Albedo. Locally, it is somewhat variable due primarily to weather patterns and water vapor and cloud droplet variations, but world-wide, the total value is rather constant.

The second of these last two lines adds in the effects of the molecular absorptance of various components of the atmosphere. Toward the left edge of this graph, it is easy to see that there is a large difference (in the ultraviolet light) due to absorption by O₃ (ozone). That effect makes it safe for us to live down here on the surface, while also providing heat for the highest parts of the atmosphere. Note that there are a number of other clear wavelengths where one or another type of molecule absorbs a lot of energy. In general, these are O₂ (oxygen), H₂O (water vapor), and O₃ (ozone). It is important to notice that carbon dioxide ONLY has strong absorption lines in the far infrared region. Around 1.8 microns, carbon dioxide absorbs nearly all the solar energy at that wavelength, and from around 2.5 microns and longer, carbon dioxide also absorbs large amounts of the solar energy. (Remember the (pink) carbon dioxide absorption graph that was shown near the beginning of this presentation.)

Fortunately for us, the vast majority of the Sun's energy is below 1.8 microns or 1800 nm or 18,000 Angstroms wavelength (over 93%), so the Sun's INCOMING energy to us is not materially affected by any existing amounts of carbon dioxide in the atmosphere.

This graph therefore is a broad analysis of the Sun's incoming energy to Earth, including the specific wavelengths that happen to get absorbed by different components of the atmosphere. If any of these curves is mathematically Integrated (the area found underneath that curve), the total incoming radiation can be determined. When the Black Body curve is thus Integrated, the Solar Constant of 1353 Watts/sq.m. is confirmed, the rate at which energy arrives at the top of our atmosphere. Integrating the (lower) more complex curves gives the radiation remaining after the Albedo reflection, and then after the molecular absorption. A pretty complete picture.

Essentially the same graph can be generated regarding the radiation the Earth sends back out to space. Since we currently radiate at around 14ºC or 287ºK, the Wien's Displacement Law tells us that the maximum radiation occurs at a wavelength of 2898/287 or 10.1 microns (or 10,100 nm or 101,000 Angstroms). This is FAR off to the right of our graph above, which only extended up to 2.6 microns. This is VERY significant! Remember that carbon dioxide is an extremely good absorber above around 2.5 microns wavelength. This indicates that it is a strong absorber of essentially all the wavelengths that the Earth sends out.

This results in the conclusion that the absorption of carbon dioxide regarding outward radiation from the Earth is very closely proportional to the concentration of the carbon dioxide in the atmosphere. That statement was made above, as a conclusion that is virtually uniformly accepted by all researchers. That heat is therefore trapped in the atmosphere rather than being able to be radiated away to space.

This technical discussion is intended to help clarify the basis behind comments that refer to the many unique behaviors of our atmosphere regarding different wavelengths of light, both coming in from the Sun and being radiated out by the Earth.

If there is further interest in technical issues: We can use the Stefan-Boltzmann Law presented above for a source that is at 5762ºK, to calculate the actual radiation from a square meter of the Sun's surface (around 62.5 million watts/square meter). We can then consider the geometry of the distance of that point from the center of the Sun to the distance of the Earth (squared) for a reduction by a geometrical factor of around 43,000. This results in a calculation for the Solar Constant of around 1349 Watts/sq.m., confirming the accepted value for the Solar Constant. This is actually the reasoning used in first determining the temperature of the surface of the Sun.

We can confirm some other things as well. Given the Equilibrium temperature of the Earth as 250.5ºK (calculated far above), we could again use Stefan-Boltzmann to calculate the outgoing radiation, as being around 223.25 Watts/sq.m of the Earth's surface. The Earth's total (curved) surface is exactly four times the planar area that the Earth presents to the Sun. This confirms that the Earth necessarily ACTUALLY radiates around this level of radiation out to space (which then accounts for the four times as great INCOMING energy we discussed above of 893 Watts/sq.m. after the Albedo reflectance). Everything still balances.

However, we know that each square meter of the Earth's surface is currently actually at around 287ºK instead of the Equilibrium 250.5ºK. We can calculate the actual amount of radiation given off by the Earth's surface as being (again Stefan-Boltzmann) 384.7 Watts/sq.m. Since we just calculated that only 223.25 Watts/sq.m. actually gets through the atmosphere to be radiated out to space, we can see how significant that "blanket effect" of the atmosphere actually is, of catching around 160 Watts/sq.m. that leaves the surface of the Earth and keeps it from continuing on to be radiated off into outer space. These calculations have quantified the actual measurable effects of heat flow in the atmosphere that are greatly caused specifically by the presence of carbon dioxide in the atmosphere.

This has been presented here because it enables anyone to be able to make decent predictions regarding the future effects of increasing carbon dioxide content. That does not generally seem to get done yet! A very highly respected expert in this field has said that he fully expects the carbon dioxide concentration to rise to 900 ppm (close to triple the current level) but then he also says that he does not expect to see anything more than a minimal temperature rise! Amazing! If he would use the straightforward reasoning and calculations presented here, he should be able to easily calculate the expected temperature rise, and it is clearly FAR higher than he seems to be publicly saying! If he were correct in that 900 ppm, it seems a certainty that there would be no humans still living to witness it. Essentially all life on Earth would have ended long before that point.

As a simple example, say that the carbon dioxide content doubled that of today. The linear proportion reasoning would indicate that roughly double the atmospheric heat capture would occur, meaning around 320 Watts/sq.m rather than the current 160. We know that the Earth necessarily still will radiate the 223.25 Watts/sq.m. actually out to space (because that is required in order to maintain radiative equilibrium), which would indicate that the ground must therefore be radiating 320 + 223.25 or 543.25 Watts/sq.m. Using Stefan-Boltzmann backwards, we can easily calculate that the average temperature of the surface of the Earth would have to be around 312.9ºK, which is 39.7ºC or 103.4ºF. So even if the carbon dioxide concentration would only get up to double today's (around 770 ppm) the average temperature of the surface of the Earth would necessarily become around 45ºF hotter than today, meaning that no crops or other plants would be able to adequately respirate (daytime high temperatures of well over 150ºF), and once they would all die, no animals or humans could survive more than a few months (as noted in a respected paper published around 5 years ago, noted above).

So, for an expert to seem certain that the CO₂ concentration will nearly triple, but to then say that he expects virtually no temperature rise, seems to defy science and logic! The basics of this is NOT THAT COMPLICATED! However, it IS true that there are an immense number of smaller effects, especially interactions between concentrations of different types of materials. And some will note that there are hundreds of industrial chemicals (which we humans are also responsible for!) such as CFCs which also have thermal absorptance properties, although the actual quantities of them in the atmosphere are very tiny when compared to the massive amounts of carbon dioxide.

It IS certainly true that water vapor also absorbs a lot of the outgoing radiation from the Earth, and therefore contributes to the Greenhouse Effect or global warming in a very similar way. In fact, in some ways, water vapor can have even greater effect than carbon dioxide does. However, water vapor is virtually all in the very low atmosphere, near the Earth, where weather and clouds exist, so the relative thickness of the layer of water vapor that light must pass through is relatively small, a few miles. In contrast, carbon dioxide circulates throughout the full depth of our atmosphere, meaning that the light must pass through a far thicker layer of it. For the same thickness of layer of water vapor and carbon dioxide, and the normal current concentration levels, the "Greenhouse Effect" of the water vapor is actually greater than that of carbon dioxide. The primary difference is that we humans are not constantly causing huge additional amounts of water vapor to be added to the atmosphere. There is a natural equilibrium between the amount of water vapor in the atmosphere and the evaporation or condensation from and to the oceans. That equilibrium is primarily only dependent on the temperature of the oceans and the atmosphere. Yes, as the oceans gradually rise in temperature, more water will evaporate and become water vapor in the atmosphere. This effect will compound the global warming issue. But it is primarily a secondary problem, only occurring because the Earth and atmosphere was already heating up (due to global warming consequences primarily due to carbon dioxide.)

Many researchers have investigated these things very thoroughly and the subjects involved are actually rather complex. For example, Kiehl and Briegleb (1991) established this model for the absorptivity for narrow bands of spectral ranges of radiation by carbon dioxide. . Such relationships are based on the Stefan-Boltzmann and Planck relationships. There is a dependence on the amount of the absorber (CO₂ in this case) although it is not quite a linear relationship. (Ramanathan, 1976) proposed a functional form for the A factor: . u is a dimensionless scaled path length, which is related to the concentration of the absorber. This was included here to allow readers to realize that many very intelligent people have been studying such things for several decades, and there are not just simple guesses made regarding these subjects, as seems to be suggested by some news media reports. You might figure that other researchers (Ramanathan and Dickinson, 1979) have developed similar relationships for ozone: , and the other components of our atmosphere.

This presentation and the linked ones have been composed with the intention that anyone should be able to follow the logic and the math, and even duplicate it all for themselves (except for these more technical equations just above). These subjects are so very important, we think it is better that you check this all for yourself, rather than trusting in experts who do not always seem to have the facts straight.

Sorry that some of this has gotten pretty technical. Those parts are actually intended more for those experts to refine their views.

Much of the information in this presentation was presented in an earlier web-page (in June 2004), but without the comprehensive research basis, in my page at:
Global warming Issues Regarding Carbon Dioxide, and Sealevels Rising

I was a very minor speaker regarding the first Earth Day in April 1970 where I expressed primitive concerns on environmental issues (and was essentially totally ignored!) Even as a Nuclear Physicist, over the following decades, no people in decision-making positions ever took my concerns seriously. But back then, even I did not realize how dire the whole situation was. It was only after I had done this careful and thorough "earth-heating" calculation, a dozen times, that I finally realized, around January 2007, that we truly are a species that may be in the process of an extermination. I did the math a dozen times because I kept insisting that I must have made some error, because I did NOT want to see that depressing answer.

However, we collectively have six billion minds. If many of them come to realize that we may be facing total doom, maybe some who are far smarter than me, might have time to discover some way to save the planet and mankind. I hope so.

The Earth's Rotation as a Source for Energy
Waste Nuclear Power For Making Electricity And Heat?
The Physics of Efficiency In Electric Power Plants
Individual Ways of Reducing Your Energy Usage
Methods of Storing Energy for Later
How Much Energy Comes From the Sun? And Why is there Global Warming?
How does the Sun create so much energy?
Inventions Which Might Help Deal With Coming Energy Catastrophes
An Invention to Efficiently Make Electricity from Solar
Enormous Heating of the Atmosphere by the Alaska Pipeline
Air Conditioning without Huge Electric Bills and without Freon
A Method of Storing Summer Heat to (Nearly) Entirely Heat a House all Winter
An Extremely Highly-Efficient (and Fast, 200.0 mph) Transportation System for People and Products
The Sophisticated Woodstove I Invented in 1973

The Physics of Wood as a Heating Fuel
Why is the North Pole Heating Faster than the rest of the Earth?
A Possible way to greatly reduce Aerodynamic Drag of Airplanes

( http://mb-soft.com/public/index.html )

C Johnson, Physicist, Physics Degree from Univ of Chicago