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It is obvious that before the Industrial Revolution began (around 1800), the concentration of carbon dioxide in the atmosphere was fairly constant. In fact, ice core data note 7 extends this data and this relatively constant graph line back for a VERY long time, 419,000 years (around 420 computer screens to the left), where it was NEVER above 300 ppmv. SINCE the Industrial Revolution began, and we started burning a lot of fossil fuels (coal, oil and natural gas), the curve goes wildly upward, and WILL cross through where the red blotch is far above the existing graph.
We will often abbreviate "parts per million" of the total atmosphere as ppm.
It might be useful to refer again to that Footnoted Vostok ice-core data graph note 7. If THIS (Scripps) graph is compressed horizontally by a factor of 400 to match the Vostok graph, the graph line then TURNS ABSOLUTELY STRAIGHT UP! In fact, the graph still slants slightly to the right, but it could not be displayed, because that side tilt would be less than 1/4 of a pixel width of the computer display! So look again at Footnote 7 and consider the graph to stop and turn absolutely straight upward! You may have heard spokespeople claiming that, Oh, the atmosphere goes through natural variations and there is not anything unusual happening now. They have obviously never seen a graph go along decently for 419,000 years and then abruptly make an absolute right-angle turn straight upward!
Also: Prior to around 1965, there was extremely little awareness that carbon dioxide even had ANY significant greenhouse effect. It was discovered in a peculiar way! When the US and Soviet Unions were planning to send spacecraft to land on Venus, they assumed that the very bright white color of Venus' clouds, which reflect 76% of the sunlight coming at Venus, were CLEARLY causing all that solar heat energy to be reflected off into space. So they assumed that the surface temperature of Venus would be cooler than Earth! In fact, all scientists then confidently calculated the expected surface temperature of Venus to be about -41°C or -42°F, extremely cold. note 11
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 332°K or 59°C or around 140°F. 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 232°K or -41°C or -42°F. 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 600°F (315°C), 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 860°F (460°C)! Consider that! Logically, the surface of Venus SHOULD be around -42°F (-41°C) but it ACTUALLY is +860°F (460°C). 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.
Looking at the graph above, where it had been pretty smooth and constant for 800 years, and then to see the extreme upturn of the curve in recent decades, even if viewers do not fully understand, they must certainly see that this COULD BE a problem. But when you then realize that our CURRENT lifestyles GUARANTEE that the curve will rise to at least where the red blotch is, FAR above the basic graph, in less than another hundred years, the certainty of a dire problem has to be obvious. In fact, a very grim reality is that it seems fairly unlikely that ANY humans will still be alive to see that graph get to the red blotch (in just 100 years). Before that day, when little kids today might still be alive, the Earth will have gotten so warm that no plants will be able to draw enough water up from the soil to keep their leaves from drying out and shriveling and dying. And once ALL food supplies (plants) are then gone, human and animal life will have no possible way of surviving more than a few months.
The Physics of THIS presentation is generally only about the situation that we ALREADY have caused, the 390 ppm that the Scripps graph shows for today, which is due to the previous decades of our burning fossil fuels for a thousand reasons. Calculations regarding what we might or might not do in the future is outside the realm of rigid Physics analysis, but there are clearly even more grim things ahead for us, since we all LOVE our prosperity and modern lifestyles.
Unfortunately, once the added carbon dioxide is in the atmosphere, it stays there! You may have seen scientists on TV talking about the carbon dioxide emitted by the very first Model T automobiles, or even earlier coal-fired factories, all still being in the atmosphere.
So even though THIS presentation is centered on PAST errors and the 390 ppm carbon dioxide concentration we already have, the red blotch that is so far above the basic graph lets us see what we are already planning for our children and grandchildren! Because, you and I and everyone else will NOT give up what we call modern living, to all live nearly Stone Age lives! These paragraphs about the future seem very appropriate here, since no one else seems to realize the gravity of the situation.
There are truly frightening things to come! Any Almanac can confirm that we are currently adding from 25 to 30 billion metric tons of carbon dioxide to the atmosphere every year. note 16 Many reference books can confirm that there are currently around 3,000 billion tons of carbon dioxide in the entire atmosphere. note 16 (The table in this footnote also has that yearly data for each of the past 50 years and some other years.) The point is that each year, we are increasing that CUMULATIVE total amount by nearly an extra percent.
Now look at 100 years from now, the year 2108, when many kids today are likely to still be alive. Even with the most conservative possible approach, the ACTUAL increase over those coming 100 years, would therefore be at least a 50% increase, assuming that we do not INCREASE the amount of fossil fuel burning, or 390 * (1.00 + .50) which is about 586 ppm. note 16 If leaders today are concerned at the consequences of the current 390 ppm, which has never happened before, they should probably be even more concerned for their children and grandchildren, who are nearly certain to be in a totally unknown environment due to the 586 ppm of carbon dioxide. note 16
This is NOT "a thousand years from now". It is a time where some kids living today will still be alive and will have to deal with. Given that the discussion and calculations below indicate that even the current 390 ppm is extremely likely to cause the entire extermination of all plants on Earth, and then therefore humans and animals, what would 586 ppm do?
So, even the BEST hopes that world leaders express, still lead to total disaster, our self-created extermination of mankind and all animals on Earth, and in a terrifyingly short time.
This following presentation does not even consider any future possibilities for making things even worse than they are today! Much of the following discussion and calculations are based on a scenario that will never happen, of EVERY car, truck, airplane and train being immediately scrapped world-wide, and every furnace and industrial process that uses fossil fuels would be removed and dismantled, and every coal-fired electric generation plant being permanently dismantled. THAT situation would result in the current 390 ppm not increasing any more, but it will not reduce significantly, possibly for millions of years, until organic materials get covered over by sediments and compressed into limestone and new petroleum, natural gas and coal. Which doesn't do us the slightest amount of good!
I wonder when it will finally dawn on people that we have been loading straws on a camel's back for the 200 years of the Industrial Revolution, and that when businesses and political leaders PROMISE to think about reducing the number of straws we will add in the future, they NEVER even consider stopping adding more straws completely! So they all merrily believe that they are free to keep adding straws onto that camel's back, in rather large numbers! As long as they PROMISE to think about adding fewer straws at some time in the (distant) future, they believe that all will be well. Have none of them ever heard the Fable where A SINGLE STRAW broke the camel's back? They all seem to assume that as long as THEY PERSONALLY were not the ones that added that fatal straw, they could deny culpability. But when this particular camel dies, there will be no one left living to listen to any denials!
In the early 1800s, we had a very strong camel, and we were loading a moderate number of straws on its back (rarely more than a billion tons of carbon dioxide in any specific year) note 16. But as we have "advanced" our society, we have been using larger and larger shovels to load straws on the camel. THIS year we will add around 30 billion tons of NEW carbon dioxide to the atmosphere. NEXT year we will add yet another 30 billion tons more. And every year after that! Does this make ANY sense whatever? note 16
If we had any sense, we SHOULD HAVE been finding ways to REDUCE the number of ADDITIONAL straws we kept adding, but we do not seem capable of looking toward the future. At some point, someone will add that straw, on top of the many millions before it (some of which YOU provided), which breaks the camel's back. A terrifying part of this is that there is compelling evidence that this MAY HAVE ALREADY OCCURRED, that the camel is already wobbling. But until we actually see blood coming out of the camel, we have no intention of slowing down adding more and more and more additional straws. After all, for anyone to be expected to give up a modern lifestyle? To submit to any suffering whatever? Other than a token number of people, everyone will disclaim any culpability and live merrily on! Really unbelievable! But possibly as soon as 2080 or 2090, the Earth may become an extremely quiet place, with no animals and no humans anywhere. Shouldn't someone actually CARE?
Many Native American Indian Tribes had a brilliant perspective, of only making decisions after considering the impact on their descendents SEVEN GENERATIONS after them. Our leaders would never dream of such attitudes, and they prefer to instead make choices which increase THIS QUARTER'S NET PROFITS.
Many skeptics (and all businesses!) claim that there is no actual problem! They point out that whether or not there is more carbon dioxide in the atmosphere, the Earth's average temperature has only been seen to have risen by about 1.1°C from about 13.75° C in 1900 up to about 14.9°C today. (2°F rise from 56.75°F up to 58.75°F). They ASSUME that if it had only risen by ONE degree Celsius in a hundred years of Industrial Revolution, then it CAN'T rise drastically above that now. They are wrong! In fact, in September 2009, the prestigious Hadley Centre of the British Met Office announced that they now believe that we are facing a certain 4°C or 7.2°F rise during THIS century, and possibly as soon as the year 2060. They admit that they are being very conservative, and that the rise could be far greater than that! They also find that the Arctic region might rise spectacularly faster, up by 15.2°C or 27.4°F during this century! They say that many regions of Africa are likely to rise by around 10°C or 18°F! This information was presented at a respected Conference at Oxford University.
In November, 2009, some experts are now talking about worldwide temperature rise of more than 6°C in coming decades.
A few researchers (including me) have tried to warn about such coming disasters for a number of years. To deaf ears!
The Oxford Conference still has an element of optimism that may be misplaced. They announced that IF fossil fuel burning was SOON controlled and then reduced, we might avoid these disastrous near future events. I think they were wrong in that optimism. This presentation and the related one centered on Global Warming, discuss an aspect of the problem that no one else seems to have yet recognized. We only SEE limited temperature rises, BECAUSE the Earth is extremely massive and its Crustal rocks are really bad at conducting heat inward. So even when we are causing the AIR to be heated up to an equilibrium temperature that is far hotter than we now measure, the colder ground quickly cools that air. The calculations in the related presentation seem to indicate that there should be about a 140-year lag time before the actual average Earth temperature achieves its equilibrium. And if that understanding is correct, then we have even bigger problems! There is a decent chance that by sometime early in 1997, we had already burned enough fossil fuels to cause a situation around 140 years later where no plants may be able to live on Earth. That would mean no food for any animals or humans. This is REALLY bad!
There seem to be thousands of people who enjoy going on TV to announce every imaginable OPINION. They seem to be focused on sugar plums and other fantasy dreams. Often those people have no education in the important scientific fields, and/or they have some personal (financial) interest in promoting one or the other side of the story. It is sad that modern society has devolved to the point that BOTH sides of such issues are simply able to pay large enough amounts of money to noted people to get their side of the story presented as having credibility. Leadership today seems to have become equated with spin! The actual FACTS are never important, as long as every situation can be spun to look attractive. So it is all very confusing to the public, who necessarily have to believe the "experts" in such subjects, due to the complex and advanced nature of processes involved. In many cases, even the best science still does not have complete understandings of many things, which adds to the frustration of everyone regarding not really knowing what is actually happening.
This presentation is the result of many years of research by a respected Nuclear Physicist. Physicists (hopefully) to not concede actual truth just to receive some cash payment or some high-paying job, as we are expected to always be accurate and truthful in our research and our conclusions.
This actually has been a WONDERFUL fact for billions of years, because the effects have allowed the Earth to warm up enough to be compatible with organic life forms.
SMALL and SLOW changes have always occurred in the amount of carbon dioxide in the atmosphere, but recent human activities have cause really huge changes, increases, in the amount of carbon dioxide in the atmosphere. During the 20th Century, human activities increased the total amount by about 1/3, as we humans had added around 700,000,000,000 tons of carbon dioxide to the atmosphere by releasing it from fossil fuels. (See the table in the Footnotes). In the current 21st Century, our activities will certainly add another 1,600,000,000,000 tons more, to cause the amount of carbon dioxide in the atmosphere to then be MORE THAN DOUBLE any amount that the Earth's atmosphere has ever contained before. No one can possibly know all the effects of such drastic changes, but we know of a few, and those seem to destine the end of mankind forever.
An interesting additional effect of a slight warming of the oceans is that just a 1°C rise in the temperature of the oceans causes around a FIVE PERCENT REDUCTION in the amount of carbon dioxide that is dissolved in the oceans. It turns out that COLD water can contain a lot more carbon dioxide in it than warmer water can. This means that even a slight warming of the Earth will cause a secondary effect of releasing a very large amount of additional carbon dioxide from the waters of the oceans, which will add even more carbon dioxide to the atmosphere, which has the effect of causing the heating of the Earth to occur even more.
Over some thousands of years, that increased plant growth would again re-vegetate the Earth with other species of plants, which were created from the water vapor and the carbon dioxide. This gradually results in a slight reduction of the carbon dioxide concentration in the atmosphere (because it gets used up to make all those new plants), possibly down to the 280 ppm or even further to say 260 ppm. That lower amount means that less outgoing Earth radiation would get trapped in the atmosphere, and more would be able to radiate away, thus COOLING the Earth's average temperature by possibly several degrees. This means that some thousands of years after the slight INCREASE in the Earth's temperature, an effect occurs which naturally reverses the effect and returns the Earth back toward a lower Equilibrium temperature. If that decrease was great enough to reduce plant growth world-wide, the situation then develops that is like what we first started with. The average temperature of the Earth has therefore not been precisely constant, but it varies back and forth over very long periods of time.
The result is that we now measure around 390 ppm of carbon dioxide in the atmosphere today. Since no concentration greater than 300 ppm appears to have ever existed before in the atmosphere, there are no prior examples for us to learn from. But the implications are horrendous.
Our CURRENT lifestyles indicate that we will cause that concentration to increase to at least 586 ppm, roughly double anything ever existing before. No "assumptions" are even required for this number! In the Footnotes note 7, we show the ACTUAL cumulative amount of carbon dioxide in the entire Earth's atmosphere, in tons, and we show the number of ADDITIONAL tons that we have added in each of the past 50 years. Unless the entire population of the world is suddenly willing to abandon nearly all aspects of modern life, we can expect to continue to add AT LEAST AS MUCH each year in the future as we are doing now. Probably MORE! By just noting the current total of around 3,000 billion tons, and the fact that we are currently adding around 15 billion tons (by actual measurement) each year, means that in 100 years we will have added 15 * 100 or 1500 on top of the existing 3000, for a new total of around 4,500 billion tons, which happens to be about that 586 ppm concentration.
I have never seen anyone address "the near future" in any way other than in assumptions and speculations which are baseless. Remembering that THIS whole presentation is about THINGS WE HAVE ALREADY DONE, it seems reasonable to note the following. We are currently adding around 25 to 30 billion tons of CO2 each year. If we take the most conservative possibility (15), this means that about 30 billion tons is added each two years. We know that the entire atmosphere currently contains around 3,000 billion tons. This means that we are increasing the amount by about 1 additional per-cent every two years. For the coming 100 years (50 of these 2 year intervals), and we continue to add the CURRENT amounts each year, it is easy to see that around 2108 AD, it should then be 390 * (1.0 + 0.50) or around 586 ppm. That is nearly DOUBLE the concentration of the highest amounts that had occurred before 1900 AD. But NO government leader is yet even talking about staying at current levels, but instead "reducing future increases". But even that is not realistic, because China and India are building thousands of new coal-fired electric power plants every year, and manufacturing countless millions of new vehicles. The demand for burning fossil fuels is RAPIDLY growing. A hundred years from now, in 2108 AD, it seems UNLIKELY that the CO2 concentration in the atmosphere will be less than 600 ppm, and quite possible far higher still. Since no one seems to even worry about the consequences of what we have already done, there certainly is no one planning future societies regarding 600 ppm CO2 in the atmosphere!
This particular presentation has added in the analysis of the process of the warming of the Earth itself, to determine the time-scale which will apply. The conclusion here is that the average temperature of the Earth will have risen to its Equilibrium temperature after a delay of around 140 years. IF no one ever burned any fossil fuels again after today, that means that the average temperature of the Earth will rise by around 25°F (14°C) over the next 140 years. In the Tropics, the daytime temperature is often around 140°F (60°C) now, and if that rises to 165°F (75°C), plant processes cannot bring up sufficient water from the soil to keep from drying out and dying. Even in the Temperate regions of the Earth, like the United States, there are no conventional crops that could survive with a 25°F (14°C) average temperature rise. In addition, many seeds NEED to experience freezing temperatures in winter, and when that would no longer occur, those seeds would generally become inert.
This presentation is meant to aid in dealing with all the confusion. It will 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 specific 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 occasionally 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 true that things are terribly bad? Is President Bush's opinion true that there is not even any such thing as global warming? Both sound very convincing to their own 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!
As a Research Physicist, I have spent a number of years studying the scientific processes that represent energy flows in the Earth's environment, and I present 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. I have often tried to separate away the very worst of the math into footnotes! 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 even 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 that College Professor in Oregon who has personally NEVER gone up those 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 on such preposterous claims to avoid hurting their business profits. It would obviously be really bad for him 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, and he includes enough statements that sound scientific, 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, still billions of extra tons every year) 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!
A frightening number of people today seem to understand "science" as entirely different from that! They think that someone "comes up with an idea" and then "finds ways to prove it is true!" It might be handy if that were true, but it turns out that the MAJORITY of scientific research results in findings that PROVE THAT THE ORIGINAL HYPOTHESIS WAS WRONG! And this is where the terrible difference shows up! Someone who "insists on proving that he/she is right" then SELECTIVELY picks experiments or data that appears to support the hypothesis, while absolutely avoiding ever mentioning any experiments or data that contradicts it. In true scientific investigation, BOTH MUST BE CAREFULLY EXAMINED. The first person here is nearly guaranteed of "finding the proof he/she insists on finding" but it is meaningless. The second person here might not "find some miraculous result, but WILL "advance the sum total knowledge of science."
With this preamble, this presentation gives the pure science behind each of the various subjects involved, and includes the actual calculations and the actual logic 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.
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 400,000,000,000,000 cubic feet of carbon dioxide to the atmosphere EVERY YEAR! That is about 1,000,000,000,000 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 twelve times every minute, which turns out to be around 600 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 THREE people exhale a ton of carbon dioxide per year. There are over six billion of us living (and breathing)! Astoundingly, we humans collectively exhale TWO 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 two 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 had 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.
. There is simple and absolute logic that exists
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). note 22 That value of the Solar Constant is more technically referred to as the Air Mass Zero Insolation, per that footnote.
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.
Note: There are some textbooks which present the following logic and calculations in a slightly different way, where they consider the energy flow for one-square-foot or one-square-meter of SURFACE area. The logic is exactly the same, but the numbers are obviously different; instead of presenting the TOTAL energy flow rates for the entire Earth, they are considering a tiny fraction of that area. Their approach often includes another factor, 4, in their calculations. That doesn't really apply here (except in our footnotes), but it seems necessary to refer to that factor. The Solar Constant is the INSTANTANEOUS energy flow for one square meter of area, directly facing the sun (and above the atmosphere). Think about the situation of the Earth and Sun. The area of the Earth which intercepts sunlight is Pi times the Earth's radius squared, also called the Projected area. But we live on the SURFACE of the Earth. It turns out that the total surface area of a sphere is given by FOUR times Pi times the Earth's radius squared. After all, half the time, any area of the Earth's surface is in night, pointed away from the Sun. Even during the daytime, the Sun is rarely exactly overhead. The collective geometric effects of these things is that the Solar Constant value of 1353 watts per square PROJECTED area, is sometimes described as an AVERAGE of 1353/4 watts (or 338 watts) per square meter of SURFACE area, in from the Sun for the whole surface area of the Earth. We think their way can be a little confusing (as it probably has been here!) and so we choose to consider the TOTAL EARTH ENERGY FLOW RATES instead of just for an average square meter of real Earth surface area! There is NO doubt that the Sun sends the 172.33 PW of energy at the Earth!
Our drawing shows that 172.33 PW of energy being divided up into two different arrows coming in to Earth. They are the same, but we are distinguishing here (the left arrow) representing the energy that actually gets ABSORBED by the Earth and (the next arrow) representing the energy that immediately REFLECTS OFF of the Earth (and therefore has no significant effect on 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 we have assumed that it was likely to be relatively close to what it is today, at around 34%, in these calculations. As already noted, some researchers feel that the early Earth had an Albedo which was a little lower, at 30% or 31%, which slightly changes these numbers. 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 (early) 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!)
. 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. (FAR toward the right on these charts). Those gases in the atmosphere absorb that heat. That causes the atmosphere there to become a little warmer, and the then-extra-heated warmer gases then re-radiate much of that energy, roughly half going upward and out toward space and roughly half going back downward toward the Earth.
Water vapor tends to be fairly low in the Earth's atmosphere, while carbon dioxide can be in much more of the thickness of our atmosphere. This effect tends to make carbon dioxide have a greater effect than it might otherwise be expected to have.
We have also added some arrows at the top of these graphs, which require some explanation! Any object that is heated releases RADIATION to get rid of some of that heat. The wavelength of the radiation is dependent on the temperature of the source. Scientists including Planck, Wein, Stefan, and Boltzmann developed equations that describe those effects.
Since the Sun's surface is around 5760°K, the wavelength of the MEDIAN radiation in is around 0.709 micron, a reddish color. This is represented by the LONGER downward (orange) arrow. There is also a different wavelength which is the one that is most intense, which is at 0.503 microns (a greenish color), which is represented by the attached shorter arrow to the left in the graph.
Different parts of the Earth are at different temperatures, so they radiate at different wavelengths. We show the MEDIAN (13.2 microns) and peak (9.3 microns) wavelengths for the radiation from the hotter Equator regions (as red arrows), and also for the radiation from the colder Polar regions (16.1 microns and 12.4 microns) (as blue arrows).
It might be noted that SOME of the radiation from the Equator regions has a chance of escaping, as the absorbtivity of carbon dioxide is not quite as high for some of those wavelengths. But the absorbtivity of carbon dioxide for the Polar regions is consistently near 100%. Many scientists seem mystified as to why the North Polar region is warming up several times faster than the rest of the planet. Part of the explanation seems pretty obvious when this differential absorption of carbon dioxide is considered.
They also seem oblivious to the fact that the SAME effect is necessarily happening near the South Pole. Few people seem to have cared about how FAST the Antarctic ice is melting, but everyone will soon be shocked when researchers start monitoring the rapidity of the ice disappearing down there. The CONSEQUENCES of that melting is horrific, specifically regarding the fact that there is enough ice on Antarctica to melt to cause ALL the world's oceans to rise by more than 300 vertical feet! MOST of the world's large cities were built near the oceans, and they WILL all be (permanently) flooded as the Antarctic ice melts. My (conservative) calculations seem to suggest that by 2070 or 2080, enough Antarctic and Greenland ice will have melted to eliminate all those cities from being habitable, except by fish!
About half of the radiation which the Earth sent up to get absorbed in the atmosphere, then gets re-radiated back down toward the surface of the Earth 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.
This effect changes with the amount of carbon dioxide or water vapor present. When the amount is SMALL, then the amount of heat re-radiated back down toward Earth is essentially PROPORTIONAL to the temperature variance of the Earth's surface. (The graphs of the Vostok data show this for the various maxima and minima points). This is called a LINEAR relationship between the temperature of the Earth's surface and the amount of carbon dioxide in the atmosphere. This is ONLY TRUE when the amount of carbon dioxide (or water vapor) is SMALL. The reason is this. The small FRACTION of carbon dioxide in the atmosphere only causes a SMALL amount of additional heating of the atmosphere. And since only half of that will later get radiated DOWNWARD toward the Earth's surface (with the other half being radiated UPWARD toward outer space) the GROSS AMOUNT of the re-heating of the Earth is minimal. Such a situation would be pretty close to being a direct proportionality. And THAT therefore would only increase the surface temperature by a very small amount, and a "second iteration" of this effect would be extremely small. BECAUSE the process would therefore be a SINGLE ITERATION, it would be extremely close to being a LINEAR relationship between carbon dioxide content and the Earth's surface temperature. note 71
This situation changes drastically when the amount of carbon dioxide is very high. It can become a NON-LINEAR relationship. And this is why. There are multiple iterations involved in heat energy being radiated back and forth between the warmed atmosphere and the warmed Earth. The result is that the net sum of all these iterations is an asymptote of a maximum possible temperature for the surface of the Earth.
The current situation is one where the Earth's atmosphere has an opacity regarding outgoing infrared radiation from the Earth of around 85.4%. No one has ever analyzed this matter to know whether that level of opacity implies a linear relationship or one where there is an asymptote. note 71
Consider the absolute limiting case, where the Earth's atmosphere has so much Carbon dioxide and water vapor in it where it absorbs 100% of the radiation being sent upward from Earth. (We are going to make an assumption here in that the Earth's atmosphere behaves as though it has "one-layer". Venus happens to be a situation where its atmosphere [of 95% carbon dioxide] behaves as though it is MANY layers. In that case, some of the logical simplifications here do not apply and a more complex analysis is required. It also resulted in what is referred to as a runaway Greenhouse effect on Venus, where the surface temperature is currently around 860°F or 460°C.) note 71
In our case, we know that the Earth RECEIVES the 113.74 PW of energy from the Sun. Due to Equilibrium considerations, we see that it then RADIATES that same 113.74 PW up toward outer space. But since the atmosphere would absorb ALL of it, NONE would directly get out to space! But instead, that heated atmosphere would radiate half (56.87 PW) of that energy upward and outward, to be lost to space, but it would also radiate another 56.87 PW of (infrared, heat) energy back down toward the Earth. (that is one iteration). Given sufficient time to attain equilibrium, the Earth's surface would rise to a temperature to now radiate away (113.74 + 56.87) 170.61 PW. But now the atmosphere would absorb ALL this 170.61 energy. So now it would radiate half of that, 85.31 PW outward toward space and also half downward to the Earth. Notice that we now have 113.74 + 85.31 or 199.05 PW getting to the Earth, which gets it up to an even higher temperature. (this is the second iteration, this time adding another 28.44 PW). A third iteration would add yet another 14.22 PW. And then another 7.11 PW and then 3.56 PW, and 1.78 PW, etc.
It is a simple Algebraic Summation to calculate the total of this infinite number of iterations. In this limiting case of the atmosphere absorbing 100% of outgoing radiation, the Algebraic total would turn out to be 227.48 PW of TOTAL OUTGOING RADIATION from the surface of the Earth. With a one-layer model for the atmosphere, THIS IS THE LIMITING CASE.. We can then use the Stefan-Boltzmann equation to determine the maximum possible temperature for the Earth's surface. It is actually a PROPORTION of temperature based on the original Equilibrium temperature of the Earth (which we had calculated as 250.5°K or -8.7°F or -22.6°C); over the early Earth's equilibrium temperature which would result in a MAXIMUM Earth Average temperature of about 76.6°F or 24.8°C.
THIS implies that the (average) temperature of the Earth's surface has an asymptote at 76.6°F (24.8°C), as long as our one-layer-atmosphere assumption is true. The LINEAR relationship between carbon dioxide concentration and Earth temperature was true for LOW levels of carbon dioxide, but that relationship curves away from the linear relationship into one where additional amounts of carbon dioxide would not cause any increases at all in the Earth's temperature!
Notice that this limiting case is somewhat self-perpetuating, in that some of the very same heat energy can be radiated back and forth many times between the Earth's surface and the warmed gases of the atmosphere, due to the atmosphere containing either or both of water vapor and carbon dioxide. Again, if you pile on a thicker or better blanket over your body, you are actually not creating any extra heat energy, but you have the sensation you are much warmer, because your own body heat is able to benefit you more than once! note 71
Please note that we still have Equilibrium in this situation. The Sun is sending in 113.74 PW and 113.74 PW more infrared radiation would be coming down from the heated atmosphere, exactly providing the 227.48 PW that the 76.6°F (24.8°C) surface radiates upward. The Sun is sending IN the 113.74 PW of power, and the total of what the heated atmosphere radiates off to space is also 113.74, again exactly balancing.
Water vapor is generally very low in the atmosphere, the bottom 5 kilometers or so, being involved with our weather systems. You might have noted that jet airliners nearly always fly ABOVE all clouds at their 10 km altitudes. Its concentration in the atmosphere greatly depends on evaporation from the oceans, and its AVERAGE 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 is an assortment of other gases in the atmosphere which also absorb some 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 now in the 390 ppm range, only about 2 ppm of the atmosphere is methane gas. This results in that gas being worthy of serious attention, but it is currently of relatively less importance regarding Global Warming.
But notice that the media frenzy regarding methane gas being a 'severe threat' to global warming is essentially frivolous! Not only is this only 1/200 of the quantity of carbon dioxide, but look at how narrow the two absorption peaks are in the graph. Spokespeople seem to have thought that they could distract attention from carbon dioxide to methane by making public statements which are simply not true!
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 three separate arrows. Because we know that the surface temperature of the Earth was then (1900 AD) around that 13.75°C, much warmer than was true with the original Equilibrium, there has to be some source for the extra energy that warmer Earth was 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 13.75°C must necessarily be radiating away 195.86 PW of power.
How could this be?
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 much of that energy (164.24 PW of the 195.86 PW) gets ABSORBED in the atmosphere, primarily by the carbon dioxide and water vapor in it. Then, the (now warmer) atmosphere radiates 82.12 PW of that power back down to Earth's surface.
This allowed the Earth's surface to be in energy Equilibrium at that 13.75°C 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 (our first new arrow). Actually, the Earth-atmosphere combination has to lose a total of 113.74 by radiation (which are our second and third new arrows), 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.
The centrally important result here is that the Earth RECEIVES only the consistent incoming 113.74 PW but the logic and figures above show HOW the Earth could currently be hot enough to be radiating away far MORE energy (the 195.86 PW) without violating the Conservation of Energy!
It is also 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, the situation is more complex than that! That RESULTANT fraction is very large due to the multiple times that energy can go back and forth! 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 greater than the actual fraction captured in any cycle. In an attempt at clarification of this effect, imagine for a moment that EXACTLY 2/3 of the energy radiated upward from the Earth gets absorbed into the atmosphere. Which would mean that 1/3 would then get radiated back down to Earth. But that 1/3 would eventually get re-radiated back up again from the Earth's surface (for a second iteration). So now we have 2/3 of THAT 1/3 get re-absorbed by the atmosphere (now 2/9), and half of THAT gets re-radiated back down to Earth (now 1/9). And if we continue through another iteration, we would find that another 1/27 would be radiated back down toward Earth, and then another 1/81 in the following iteration, and so on, forever. The TOTAL effect of the atmosphere would therefore NOT be the simple 1/3 (like we have simplified into for this discussion), but instead it is a TOTAL of 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 etc. The sum of this infinite series is a simple algebra problem which is exactly 1.5 in this case. The point being made here is that the "single-time" effect would then appear to be 1.0, but the cumulative effect turns out to be 1.5 times that much energy (re-radiated back to Earth in smaller and smaller amounts each time!)
This might seem to be an odd point to make, but it is actually quite important. Say that the amount of carbon dioxide in the atmosphere continues to rise where 9/10 gets absorbed by the atmosphere in each iteration. The amounts of the iterations would then become 1 + 0.45 + 0.205 + 0.09225 + 0.0415 etc for which the infinite sum is 1.82. This seems to be close to what the current data suggests, where we have an INPUT of the 113.74 PW, but that enables the Earth to radiate away: 113.74 (the 1 portion); 51.18 PW (the 0.45 portion, due to the second iteration); 23.31 PW (the 0.205 portion, due to the third iteration); and so on, where the TOTAL radiated by the Earth would then be (1.82) 207 PW.
The ULTIMATE maximum summation of such terms would then be exactly two times the input energy, which does not change. This reasoning implies that the MAXIMUM the Earth should be able to radiate away would be 3 * 113.74 or 227.48 PW. If we apply the Stefan-Boltzmann formula (backwards) we can determine that the MAXIMUM rise over the early Earth's equilibrium temperature would result in a MAXIMUM Earth Average temperature of about 76.8°F or 24.9°C.
If this reasoning is valid, of a single-layer atmosphere, it could be INCREDIBLY GOOD NEWS! It would indicate that the higher temperatures calculated here, which were based on the clearly LINEAR relationship which has applied for most of ancient history, would not and possibly COULD NOT occur! IF it turns out that the WORST THAT WE COULD EVER DO was to cause 77°F (25°C), no matter how wildly we continue to dump carbon dioxide into the atmosphere, at least that implies that MANY plants would still ALWAYS be able to live, meaning that there would forever be a food supply for people and animals!
Getting back to our drawing above, it might therefore 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. The simple application of Algebraic Mathematical Summation can be used to accurately present that collective effect, as noted here!
NOTE: There is very strong evidence that this linear proportion has always existed in the past. The Summation argument presented above implies that for small or moderate amounts of carbon dioxide, a linear relationship would be quite accurate. It would only be where the iteration terms in the Summation become large, as is becoming true now, that the relationship would veer away from being that nearly linear relationship. That is a simple Algebra Summation problem.
It is generally accepted that the average Earth temperature probably fell to around 2°C or 36°F 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 = 44°F as the equilibrium temperature rise at that ancient time. Since this is based on the initial equilibrium temperature of -9°F, this gives an equilibrium temperature at that ancient time of 35°F, a remarkably good match to the 36°F mentioned above. This then strongly establishes that the linear proportion is valid.
The Vostok graphs also roughly confirms this. We are talking about ice age temperatures which were around 23°F (13°C) lower than today, when the CO2 was 188 ppm. The Vostok graphs show that they found the temperature was around 9°C lower than today, which is 16°F lower. That is not strict linearity, but it is within the range of the accuracy of the data.
We can better think of all this by using that last drawing above. We know that there are around 3,000 billion tons of carbon dioxide already in the atmosphere. We know that we are currently adding around 25 to 30 billion new tons of carbon dioxide every year directly due to burning fossil fuels. This is only an 0.7% 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 0.7% 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!) (0.12°C or 0.21°F). 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 1.0°C 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 1°C or 2°F 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 9°C or 16°F 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.
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 83°F (28°C) 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 45°F (7°C). You were expected to go to sleep, as in a remote cabin or a tent, where there was no furnace or stove. So you find all the blankets you can, or multiple sleeping bags. You happen to find twelve thick blankets and you stack them all up on top of you! The room still might stay around 45°F (7°C), but under your pile of blankets, it soon gets up to a comfortable 68°F (20°C). What is the SOURCE of that added heat? YOU are! Fine. You LIKE the 68°F (20°C)! But you are not too smart (sorry!) and you do not throw off any blankets! A little while later, it is 80°F (27°C) 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! This is equivalent to the situation in which we now find ourselves. There does NOT seem to be any reason for concern, as the current temperature is still pretty nice!
Remember that there is NO furnace in the room, and no heat source at all, except your body! And your body keeps pumping out around 80 to 100 Kilo-Calories of heat, or around 350 to 400 Btus of heat, every hour. Maybe your giant pile of blankets only allows 100 Btus of heat to escape through them. At the start, this was great, with the excess heat your body was creating quickly warming you and the bed up. At some point, you threw some blankets off!
You may remember something like this happening to you, where you got 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 throw off some of the blankets.
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 25 to 30 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 80°F (27°C). 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 on 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 80°F (27°C), 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 305°F (152°C). 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 305°F (152°C). 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 extra 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 180°F (82°C). Even cacti have trouble at such extreme temperatures. 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 10°C (or 18°F) 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 3°C (or 5°F) 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 3°C rise by around 2050. (That is actually a greater sea level rise than I am expecting, but on the same scale.)
In September 2009, the prestigious Hadley Centre of the British Met Office announced that they now believe that we are facing a certain 4°C or 7.2°F rise during THIS century (up to 65.95°F or 18.9°C), and possibly as soon as the year 2060. They admit that they are being very conservative, and that the rise could be far greater than that! They also find that the Arctic region might rise spectacularly faster, up by 15.2°C or 27.4°F during this century! (up to possibly 86.15°F or 30.1°C) They say that many regions of Africa are likely to rise by around 10°C or 18°F (up to above 24.9°C or 76.75°F)! This information was presented at a noted Conference at Oxford University, in September 2009.
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 83°F (28°C). 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 83°F (28°C). We note that the British Prime Minister recently (Feb 2007) announced a personal vow to keep global warming from ever exceeding 3°C (which is 5°F). 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! By the early 1990s, the US had already completely mined all of the economically-accessible Uranium for nuclear power plants (ALL of the 40+ US Uranium mines closed some years back), and now the US 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 (known) 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!
Greenland's much smaller (about 1/7 the area) and thinner 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 83°F (28°C) that it should already be, all those ice fields will certainly completely have melted, raising the world's oceans by around 440 feet. This number is firmly supported by scientific data from many sources. Ice from on Greenland, 22 feet rise; ice from on Antarctica, around 230 feet rise; water level rise due to the Earth's crust under Antarctica rebounding upward roughly half a mile due to no longer having all that weight of ice upon it; which would cause sea levels to rise just over 100 feet; the density of ocean water slightly decreasing due to warming, 48 feet rise; melting of the many glaciers on Earth, such as in the Himalayas and in Siberia, Canada and Alaska, around 50 feet rise. These different factors add to a 450 foot rise in ocean levels. Again, each of the separate component parts of that are broadly confirmed scientifically.
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 in reasonable agreement with Antarctica representing 260 feet, Greenland 23 feet and the rest, so it gives decent confirmation of the very large coming sea level rises.
In October 2010, scientists in Antarctica indicated that they believe that if just 10% of the ice on Antarctica melts, that will cause the oceans sealevels to rise by about 19 feet. They mentioned that MOST of the tall buildings in Manhattan, New York would then have their entire first floors under the ocean. (They did NOT mention that under those conditions, severe ocean storms would cause as high as 60 foot waves pummeling the sides of those buildings, where they could not survive long. But their point is that no one would then live in Manhattan anyway. The same scientists said that they now believe that enough ice from Antarctica will melt by the end of THIS century to cause a rise of 23 feet in ocean sea levels. They also indicated that if the entire West Ice Sheet and East Ice Sheet on Antarctica melt, that ocean levels would rise 150 to 190 feet or more. Those scientists are NOT taking into account that the removal of the weight of all that ice will cause the Earth's crust under Antarctica to rebound upward around half a mile. THAT effect will cause yet another 100 feet rise in sealevels. They do not know when that might happen, but several of the scientists had expressed great fear over the fact that they are seeing the ice melting at faster and faster rates. They also pointed out that an ice dam called the Ross Ice Shelf is acting to hold back the West Ice Sheet from slding downhill and out into the ocean. It sounded like they thought this could happen very rapidly and fairly soon, but they did not express any predictions on that.
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 83°F (28°C), 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!)
This all figures to only take as long as it takes the Earth to heat up those 25°F (14°C). 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!
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, 25°F (14°C) 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 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.
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 60,000,000,000,000 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 those 30,000,000,000 tons of carbon dioxide. For starters, that is 1,500,000,000 full tanker truckloads! Which is around FOUR MILLION FULL TRUCKLOADS EVERY DAY! 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 800,000 might be realistic. That would mean that every single one of them would have to transport 2,000 truckloads each year, or more than five 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 30,000,000,000 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 55 miles in diameter would just about hold one year's worth! That is roughly 120,000 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!
Global Warming Solutions
This amount of radiation has a number of small regular variations. The Eccentricity of the orbit of the Earth causes us to be about 1.5% farther from the Sun early each July, which by the inverse square relationship of radiation to distance, means that the Solar Constant at the Earth's distance then is around 3% lower than that, or around 1308 W/m2, and also about 1.5% closer to the Sun each early January, which results in around 1398 W/m2 at that time. In addition, the Sun's structure has some regular variations of output, of around 2%, which is generally only in the far ultraviolet. This web-site uses a value for the Solar Constant at the AVERAGE Earth distance from the sun of 1353 W/m2, in accordance with the NASA chart we include below in note 22. Modern orbital satellites are able to detect some radiation in the extreme ultraviolet which has caused modern values of this number to be around 1% higher, at 1373 W/m2, but then they also needed to increase the albedo of the Earth by a similar fraction to account for the fact that none of that extreme ultraviolet light ever gets to the Earth's surface. (again, see footnote 22 for the NASA graph showing the extreme dropoff in far ultraviolet.) The net effect for our purposes, regarding energy that gets through the atmosphere to the Earth, is negligible, and we choose to use the long accepted NASA number.
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 the Air Mass Zero value, above our atmosphere) note 22.
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 immediately 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.
The value we have just gotten is based on the Projected Area of the Earth toward the Sun. It is NOT the "average" energy rate for any actual area on Earth. It turns out that geometrically, a sphere has a total surface area equal to exactly four times the projected area. Therefore, the energy flux (flow rate) we just obtained would need to be divided by four to get an AVERAGE energy flow rate for any location on Earth. This can be understood easily by realizing that every point on the SURFACE of the Earth is facing AWAY from the Sun exactly half the time, and is also facing somewhat away from the sun for most other hours of each day. There would actually only be one instant, at noon, for some locations, where the Sun was exactly overhead where the instantaneous Insolation was the actual energy flow coming in. (You might see Insolation values given as around 223 W/m2 or 71 Btu/f2/hr. Those numbers in other references are AVERAGE values over the entire SURFACE AREA of the Earth. Our discussion will stay with the Solar Constant times the projected area. Those other references use a value of 1/4 the Solar Constant times the four times the ACTUAL SURFACE AREA, which therefore is discussing the same TOTAL energy flow.
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. This is the ACTUAL AVAILABLE TOTAL INCOMING ENERGY.
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 considering here of 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 * σ * T4
where Q(rate) is the total rate of energy flow outward, σ 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.)
3.937 * 109 = T4
250.5°K = T
This is the same as -22.7°C or -8.8°F.
This is therefore the average Earth temperature that is the Equilibrium temperature for the Earth at our distance from the Sun, -8.8°F (-22.7°C).
Other references used a slightly lower Albedo for the young Earth of around 0.31. That then calculates to an Equilibrium temperature of 253.3°K or -19.9°C or -3.7°F. We will use the -9°F in our calculations rather than the -4°F used in some other similar calculations. The difference does not materially affect our results, except in a very minor way. (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.)
If you carefully examine the Insolation graph again note 22, you will see several additional curves in addition to the theoretical Black Body curve and the Air Mass Zero curve which applies out in space. They are lower curves due to the atmosphere absorbing some of the energy on its way in to the Earth. The graph refers to them as Air Mass One, where they account for the reflectivity of each type of molecule at each wavelength. One of those lines also accounts for the selective molecular absorbtivity of different molecules at different wavelengths.
End of footnote 1
End of footnote 2
End of footnote 3
The Handbook of Chemistry and Physics indicates that the average thermal conductivity of the Earth's Crust is 0.97 Btu/hr/ft2/°F/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 1°F for each 100 feet (1°C per 50 meters) in depth.
We will use conventional thermal heat conductivity formulas here:
Q = A * ΔF * (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 Δt 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 83°F equilibrium temperature is 25°F above the actual earth average temperature of 58°F, so Δt is 25 here. L is one. So we get a value for hm 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, hm 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 (due to the interior source of heat in the Earth), the rock is already at the target 83°F 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 1°F 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 58°F to the 2900 foot depth of 83°F. 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 25°F. The AVERAGE current temperature of the rock between 400 and 2900 feet deep is therefore halfway between these two limits, or 70.5°F. We have now simplified this calculation into the heat needed to heat 375,000 pounds of rock by 12.5°F plus 60,000 pounds of rock by 25°F. 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 1°F. 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.
The truly correct scientific way to calculate this involves Calculus, but the results are virtually identical to this simplified presentation (which I felt was more understandable to many people).
This is the BEST or LONGEST time delay! If the forced convection situation of moving air applies very regularly, this period could be shorter.
The oceans behave differently, but with similar net effects. Thermal conductivity of water is much better than for rock, but when ocean water gets warmed, its density slightly reduces and it tend to rise. This causes the warmed water to generally stay near the surface, with much less heat being carried downward by either convection or conduction. This effect is clearly seen that even near the Equator, where the water near the very bottom of the ocean is generally near freezing temperatures. In any case, the result is that even though water has some characteristics that might seem to enable faster heat transfer into the Earth, that does not generally happen.
End of footnote 4
End of footnote 5
However, Antarctica represents a far bigger disaster in the works. Antarctica is around 5,400,000 square miles (14,245,000 km2) in area. Sonar soundings indicate that the ice on Antarctica averages around 1.5 miles (2000 meters) thick. That means there is around 8,100,000 cubic miles (28,500,000 km3) of ice sitting on Antarctica. (nearly all of it currently above sea level). Actually, there may be more than that! It is known that the weight of all that ice has depressed the Crust of the Earth there by around 560 meters (1900 feet) and so as the ice melts and the weight is removed, the Crust will rise back up. That may then add additional ice AND WATER to the problem, ice which is currently below sea level but then would be above and then melted! So the total of volume of ice which might be added to the ocean volume might instead be around 36,500,000 km3.
That is 28.5 million (or 36.5 million) cubic kilometers of ice that would melt to become virtually the same quantity of water that would get added to the oceans. Any good resource can confirm that there are around 361.3 million square kilometers of ocean surface. Simple division says that if all that ice on Antarctica melted, the sea levels would all rise by 28.5/361.3 kilometer or 78.9 meters or around 260 feet! (or more, 36.5/361.3 kilometer or 101 meters or around 330 feet!) How hard is that to calculate? In any case, even a mere ten-foot rise which would destroy many huge world cities would hardly be a start of Antarctica melting!
The PBS programs also note that roughly 1/3 of the North Polar Cap is already GONE, melted! (2006)
In early 2008, a group of highly respected Arctic researchers announced that by September 2013 (in just FIVE YEARS), the ENTIRE Arctic Polar Cap will have melted and the entire Arctic Ocean will be navigable! (during September 2013)
In October 2010, researchers in Antarctica have said that they expect more than 10% of the ice on Antarctica to melt by the end of this century, and that will cause the world's oceans to all rise by at least 23 feet (just from Antarctica, and other scientists say that another 23 foot rise during this century will be due to the Greenland ice melting. The melting of glaciers around the world is being watched, although no one seems to be predicting sea level rises due to them melting.) So the nearly certain sea level rise by the end of this century is at least 50 feet. The vast majority of large cities in the world will therefore all be gone, with the first several floors of all of their buildings having disappeared under the ocean. End of footnote 6
In fact, that data shows that there was NEVER any time when the concentration even got up to or above 300 ppm (or below about 182 ppm) during the past 419,000 years, Here is the published Vostok data (in Nature, June 3, 1999) from the highly respected Vostok ice core research:
In other words, there is NO DATA in Earth's history which might help us know what might happen if and when the concentration would ever rise above 300 ppm! Now look at the most recent decades in the Scripps graph again, and the red blotch way up above!
We note one additional important fact from this pair of graphs from the highly respected Vostok research. The temperature graph follows the carbon dioxide graph moderately well as to shape, but note that where there was a change of around 100 ppm, either up or down, in the upper graph, there was around a corresponding 10°C (or 18°F) change in the Earth's average temperature. This is important in this presentation because we have recently (1850 - 2008) caused an increase of OVER 100 ppm (so far) in CO2 concentration (from around 280 to 390 ppm). The Vostok data from these graphs seems to indicate that we should therefore EXPECT that our enormous contributions of carbon dioxide into the atmosphere (mostly from buring fossil fuels) has ALREADY created the circumstances where at least a 10°C or 18°F rise in average world temperature, which is in fairly good agreement with the 25°F (14°C) rise which was calculated in this presentation's logic. There are people constantly getting themselves on TV who keep announcing that there MIGHT be a ONE DEGREE RISE in the next century or two! Wherever those people got their College Degrees, those Institutions might deserve some careful scrutiny! Such people should look at data such as these graphs, to see that we HAVE ALREADY certainly caused a worldwide temperature increase of at least 10°C or 18°F. You may have also noticed in the news that Russia, China, India, Canada the US and many other countries are working as fast as they can to find and dig up all the fossil fuels they can! They seem to only now REALLY be getting going at using up fossil fuels, just in these past few years. Their efforts will make that Scripps graph curve even farther upward, if that is even possible!
As humans discovered the Industrial Revolution, where initially coal was burned to power many factories, when THAT fossil fuel was burned (oxidized), the carbon which had been trapped in the coal then combined with oxygen from the air to create carbon dioxide. note 13 These footnotes give the actual (basic) Bio-Chemistry which shows that for each pound of coal burned, about three pounds of carbon dioxide is formed. note 13 This is similarly true of all other fossil fuels: petroleum note 14, gasoline, home heating oil note 14, natural gas note 15, etc.
End of footnote 7
Billions Metric Tons
|Total Mass of Carbon Dioxide|
in the Earth's Atmosphere
Billions Metric Tons
The second column gives the (average of the) ACTUAL MEASURED CO2 concentrations at the South Pole since regular measurements have been recorded since 1958. The third column gives the DIFFERENCE of the year value with the previous year, that is, the INCREASE in carbon dioxide concentration in the atmosphere.
The fourth column is the ACTUAL AMOUNT OF INCREASE of carbon dioxide in the Earth's, in billions of Metric Tons, during that year. The numbers in this column are based on the following:
The total mass of the Earth's atmosphere is 5.136 * 1015 Metric Tons. This number is extremely well confirmed, and YOU can even confirm it! The "atmospheric pressure" (14.7 pounds per square inch in the English system) is actually simply the total weight of all the air stacked above that square inch, all the way to the top of the atmosphere. So simply multiplying that number by the total area of the Earth's surface (in square inches!), the product is the total mass (weight) of the entire Earth's atmosphere.
The concentrations of carbon dioxide are specified in PARTS PER MILLION, so we need to take this into account. There is one further complication. The concentrations are measured in VOLUME and not WEIGHT or MASS. (ppmv and not ppmm). Therefore, we need to also take into account that carbon dioxide has a higher density than normal air, by the factor of the molecular weight ratio. Carbon dioxide has an atomic weight of 44. The mixture of nitrogen and oxygen which makes up nearly all of our atmosphere has an atomic weight of around 28.8. This makes the density of carbon dioxide 1.529 that of air. Therefore, we applied these two factors to the differential value in column three to calculate the actual number of tons of carbon dioxide which was added to the atmosphere during that previous year, in column four.
The value in column five is the cumulative total of the increases, which is therefore the ACTUAL running total number of billions of tons of carbon dioxide in the entire atmosphere of the Earth. It is also exactly proportional to the column two value of ppmv.
We will shortly discuss the situation where we will continue with similar usage as today for the next 100 years. Realistically, this is extremely conservative, because it does not consider the additional burning of fossil fuels in China or India or many other countries.
Billions Metric Tons
|Total Mass of Carbon Dioxide|
in the Earth's Atmosphere
Billions Metric Tons
End of footnote 16
So, for example, in 1998, official reports describe that the US sent 1,494.0 MMTCe of carbon dioxide into the atmosphere. We therefore need to multiply this value by 3.667 to get 5.498 billion tons of actual carbon dioxide that the US emitted that year. Since official documents indicate that was 24.3% of the world total, we can then see that the entire world emitted 22.63 billion tons of carbon dioxide that year.
You might have noted that there was only a 19.48 billion tons increase in the atmosphere that year. Where did the other three billion tons go to? It turns out that carbon dioxide is extremely soluble in water, and that year, it was absorbed into the oceans. This brings up another important matter, the fact that the solubility of carbon dioxide in water is EXTREMELY dependent on the temperature of the water, with the greatest solubility being in very cold water. When the temperature of the water changes by just a single degree (C), the solubility can change by around 5%. This means that even rather small changes in ocean temperatures can cause enormous amounts of extra carbon dioxide to be absorbed in the oceans or released from the oceans! Things like El Nino and La Nina change the temperature of large areas of ocean, which seems certain to have huge secondary effects on the carbon dioxide balance. I have never seen any researchers yet address this issue.
So there is yet another dreadful consequence of the Earth rising even one degree C in temperature, that massive ADDITIONAL carbon dioxide will then be released from the ocean waters, compounding the entire problem even more!
End of footnote 8
Published records showed that the US emitted a total of 5.498 billion tons of actual carbon dioxide in 1998. (of a world total of 18.96 billion tons.) There were then around 300 million of us in the United States, so we might fairly say that we each, man, woman and child, caused the emission of around 18.33 tons of carbon dioxide, (5498/300) so one might say that each American (including little babies!) had a Carbon Footprint of over 18 tons (of carbon dioxide) in 1998. However, the US changed policy some years back and decided to ONLY count the carbon atoms in that carbon dioxide, which makes for a somewhat smaller number! Atomic Carbon is actually about 27% of carbon dioxide by weight. By only counting the carbon atoms, they can therefore also correctly say that each American was responsible for about 5 tons of actual carbon atoms that were sent into the atmosphere (but ALL of them were as carbon dioxide atoms, and not one was ever a loose carbon atom! So the reason for the change of description appears to have been entirely political, just to make it APPEAR that the US was not sending such extraordinary amounts of carbon dioxide into the atmosphere! In any case, there are some people who use this peculiar method of description to say that we Americans are each responsible for a Carbon Footprint of around 5 tons each year. There are also people who see that 82% of that carbon dioxide production is directly due to the combined usage of motor vehicles and the creation of electricity, and those people ignore our heating our homes and only say that we each are responsible for about 15 tons of carbon dioxide or 4 tons of carbon equivalent. You can see that there is quite a range of numbers which can correctly be applied here. Also, I am not so sure that tiny babies should be blamed for this, and it might be more correct to describe a HOUSEHOLD FOOTPRINT for the 80 million families (of usually two parents and about two children) in the US. In that case, the appropriate number for a HOUSEHOLD CARBON FOOTPRINT might be described as being either around 70 tons of carbon dioxide or 20 tons of carbon equivalent.
Given that WE are the ultimate beneficiaries of all the electricity generated in the US and of all the vehicle traffic, but that we also primarily heat our homes and buildings with the rest, a case can be made that charitability of reducing the numbers might be inappropriate!
For this presentation, we use a very conservative 45 tons of carbon dioxide or 12 tons of carbon equivalent per family.
The 12 ton number essentially ignores the actual carbon dioxide and instead talk about the (somewhat hypothetical) MMTCe number. That number does not even refer to any real chemical, but instead tries to use the quantity of Elemental carbon that is present. We feel that saying that each American family is responsible for a 45 ton Footprint of carbon dioxide is most correct and descriptive.
We mention that, in 1998, official reports describe that the US sent 1,494.0 MMTCe of carbon dioxide into the atmosphere. This would be 1,494 million metric tons which we might try to allocate among the 300 million of us that then were Americans. Dividing, we then confirm that each American had a Carbon (equivalent) Footprint of 1,494/300 or about 5 tons of carbon. However, the reality is no different! A family with two children would still be blamed for 4 * 5 or 20 tons of elemental carbon, or the equivalent of 20 * (44/12) 73 actual tons of carbon dioxide, each year. We have used very conservative figures in the 45 actual tons that we discuss here.
These comments are meant to confirm that the figures for numbers of tons added to the atmosphere in the table above are accurate, as they agree with other ways used to describe our CO2 emissions.
End of footnote 9
However, the highly reflective white color caused 76% of that incoming (visible) radiation to immediately be reflected away, and the calculations then indicated that the temperature of the surface of Venus was likely to be much COOLER than Earth's, even though it is closer to the Sun, at around 232°K or -41°C or -42°F. That would have been nearly 100°F colder than our Earth is!
So there had been an expectation that the surface of Venus would be quite cold! However, in 1956, preliminary radar data suggested that the surface of Venus must be around 600°F (315°C), but virtually no one believed that! Both NASA and Soviet space scientists expected to find a rather cool surface for spacecraft that were later sent to soft-land on Cenus. But when spacecraft tried to actually land on the surface of Venus, they all melted and burned up before even landing! After many tries, a very well insulated Soviet craft landed and survived for a few minutes, and it found that the surface temperature of Venus is around 860°F or 460°C! Consider that! Logically, the surface of Venus SHOULD be around -42°F but it ACTUALLY is +860°F. 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 amazing effect, and the incredible consequences it can have.
However, for many years, few researchers seemed to realize that the carbon dioxide in the Earth's atmosphere has the exact same effect. It was only in the 1990s that the full consequences regarding Earth began to be understood. During the 1990s, there were thousands of Research Studies funded which collected data regarding the effects on plants of various levels of future increases of carbon dioxide in the atmosphere. There will be much more evidence of this presented below.
End of footnote 11
or carbon plus oxygen from the air gives carbon dioxide back to the air and energy.
(If there is sulfur mixed into the coal, then there is also Chemically: S + H2O + O2 gives H2SO3, which is sulfurous acid, which causes acid rain.)
There are many different types of coal that exist, and they each have different chemical compositions. However, the coals that are most usable as fuels tend to have at least 80% carbon in them.
Our coal is therefore about 80% Carbon.
A pound of Coal therefore contains very close to 0.8 pound of carbon in it. If it is burned extremely completely, we can assume that ALL that carbon will combine with oxygen from the air to form carbon dioxide. Using atomic weights again, we see that carbon dioxide is 12 + 16 + 16 or 44, since oxygen is 16. When the 12 weights of carbon is burned (oxidized), it therefore forms 44 weights of carbon dioxide. We had 4/5 pound of carbon to start with so we multiply 4/5 * 44/12 to get 44/15 or 2.93 pound of carbon dioxide formed for each pound of Coal burned.
We can examine the official Reports for any year, regarding the CONSUMPTION of Coal in that year. Such Reports tell us that 2.148 * 109 metric tons of oil equivalent of coal was burned in the year 2000 (worldwide). Such Reports give oil-equivalent numbers, because different kinds of coal have rather different energy contents. If we take oil to contain around 19,500 Btus per pound and an average coal to contain around 13,000 Btus per pound, we then have to multiply by 1.5 (or 19,500/13,000) to get the actual amount of tons of coal burned. Therefore we have 3.22 * 109 metric tons of coal burned in 2000.
We just determined that each pound of that coal creates 2.93 pounds of carbon dioxide when it burns. Therefore, in the year 2000, the amount of coal that was burned produced 3.22 * 2.93 * 109 metric tons or 9.44 * 109 metric tons of carbon dioxide.
THIS year (2008), the massive increases in coal burning in China to produce electricity and to power their many factories indicates that at least 4.5 * 109 metric tons of coal is being burned, which is creating about 13.2 * 109 metric tons of carbon dioxide.
Consider starting with two pounds of coal, which we just discussed contains 2 * 14,000 Btus of chemical energy in it, 28,000 Btus total. In electrical energy terms, that is about 8.2 kWh of available chemical energy.
As the two pounds of coal is burned, we learned above that 2.93 * 2 pounds or 5.86 pounds of carbon dioxide is formed.
It is not possible to burn coal with perfect efficiency, and it is also not possible to transfer all the heat created into forming steam from water. The mechanisms of the steam turbine and the electrical and magnetic fields of the alternator are also not of perfect efficiency. The net effect of all of this is that roughly 30% of the original energy in the coal is converted into actual electricity. (Nuclear-powered plants are slightly more efficient, at around 32%, and fuel-oil-powered and natural-gas-powered plants are slightly less efficient, generally around 28% or 29%.) Much of the remaining 70% is INTENTIONALLY THROWN AWAY by cooling towers or equivalent equipment!
In any event, we now have 30% of the 28,000 Btus from our two pounds of coal as actual electricity, or 8,400 Btus, which is 2,46 kWh of actual electricity produced. This electricity then has to go through transformers to raise its voltage up high enough to be reasonably efficient in high-voltage transmission lines. It then is sent through such high-tension wires. The standard design rules are to design such lines so that 90% of the electricity put in one end of a 60-mile long stretch will come out the other end. Ten percent of the electricity is therefore lost as resistance heating by the wires, in every sixty miles of such lines. Once in a city, more transformers are used to lower the voltage to around 12,000 volts, for the lines that are up and down every street on utility poles. Then there is another transformer near your house that lowers that voltage even more to the 240 volts and 120 volts that you actually use in your house.
It turns out that all those transformers and especially all those wires have quite a bit of losses in them. There is another big problem! Electric power plants must constantly produce MORE electricity than is actually called for at any moment! That is just in case millions of people all decide to make toast at the same instant! Or for the more common situation where millions of people get home from work and all turn on their central air conditioners. This results in really large losses of available electricity (which CANNOT be stored in any way as the alternating current that arrives at our houses.)
For an AVERAGE home at an AVERAGE distance from an electric powerplant, roughly 60% of the electricity put in the wires at the powerplant gets wasted as resistance heating and magnetic losses and other losses, so only around 40% of that electricity put in the wires actually gets to our houses!
The OVERALL efficiency of the entire coal-fired electricity generation and distribution system is therefore 30% * 40% or around 12%! Thirteen percent is a more commonly used value, really a disappointingly low percentage! Virtually no one has ever even CARED that they have to burn enormous amounts of coal, neglecting the obvious fact that only 13% of the chemical energy that is actually in the coal that is burned actually becomes usable electricity! Shouldn't someone have CARED that we have merrily burned coal ferociously in then wasting 87% of that coal's energy? But no one has! In VERY recent years, there is STARTING to be a slight interest in such subjects, but still not much. The businesses and politicians all know that the US has hundreds of years of coal still in the ground, so they apparently see no reason to care about conserving it!
Since we are tracking the electricity from our two pounds of coal, we now find that only around 8,400 * 40% or 3,360 Btus of electricity actually gets to our house! And since 3,412 Btus is equal to one kiloWatt-hour, we have now found that each one kWh of electricity available at our homes required that two pounds of coal was burned up in that distant coal-fired powerplant. Saying this another way, for every kiloWatt-hour of electricity that you use up, there is about 5.86 pounds of carbon dioxide that gets added to the atmosphere at that distant coal-fired electric power plant.
If your own monthly electric bill shows usage of 500 kWh, that means that you are RESPONSIBLE FOR 500 * 5.86 or 2930 pounds of carbon dioxide that month, about a ton and a half. In the year, that is around 18 tons of carbon dioxide. (It is not usually counted in the Carbon Footprint estimates!)
This burning of coal to produce electricity is the primary reason that coal is consumed in the US, so making electricity accounts for most of the annual totals discussed above regarding coal burning.
We can use the information we just learned to find how much carbon dioxide that an electric powerplant releases in order to DUPLICATE the power in one gallon of gasoline. There are actually two different ways we can do this. (1) We know that a gallon of gasoline contains around 126,000 Btus (or around 37 kWh) of chemical energy in it. We just determined that two pounds of coal burned in an electric plant can be expected to provide around 0.98 kWh of electric power at our home. That electricity that arrives at our home then needs to go through a battery charger and then into a chemical lead-acid battery, with both processes having less than ideal efficiencies. The result is that around 0.64 kWh of electric energy is actually put into the batteries (from those two pounds of coal that were burned). When an electric vehicle or hybrid then uses that electricity stored in the batteries, the efficiency of the batteries are again in effect, as well as wiring, the electric motors, gears, shafts, and other mechanisms to actually make the tires of a vehicle rotate. The result is that around 0.42 kWh of ACTUAL electric energy gets used to move the vehicle.
It turns out that modern gasoline-powered vehicles are generally around 21% efficient. Therefore, of the 37 kWh of chemical energy in a gallon of gasoline, only around 7.7 kWh actually gets used to move the vehicle. We can therefore easily see that (7.7 kWh / 0.42 kWh) or about 18.5 groups of two-pounds of coal would need to be burned (at the distant electric power plant) to duplicate the actual useful benefit in a gallon of gasoline, around 37 pounds of coal! We can also see that 18.5 groups of 5.86 pounds of carbon dioxide would be released from that coal burned, or 108 pounds of carbon dioxide! A TERRIBLE situation!
We note (and calculate in a different Footnote) that an existing gasoline-powered vehicle only releases around 18.3 pounds of carbon dioxide into the atmosphere for each gallon of gasoline burned. We find it rather bizarre that politicians and the public considers it to be GREEN to consider electric battery-powered vehicles and hybrids, where they DIRECTLY CAUSE 108 pounds of carbon dioxide to be released into the atmosphere, SIX TIMES AS MUCH as the gasoline-powered vehicle causes in the first place! Is that GREEN???
If, instead, a battery-powered or hydrogen-powered or hybrid vehicle was used, we see that 108 pounds of carbon dioxide has to be released from the distant electric powerplant in order to provide the necessary electricity! Much of this is due to the fact that there are so many separate processes involved, and EACH of those processes each are less than 100% efficient. It all adds up!
So even though all the publicity and the excitement is around battery-powered vehicles being so GREEN, and that future hydrogen-powered vehicles will be the same, the fact that they have to receive their re-charging electricity from distant coal-fired electric powerplants actually makes them horribly UN-GREEN! Around six times as much carbon dioxide must be released into the atmosphere due to any electric powered vehicle than if the vehicle had had a standard gasoline engine! This is not to praise gasoline engines, as they are terribly inefficient! But the public is quite mislead by the people who are aggressively promoting electric vehicles and future hydrogen vehicles! The central claim on which people would be willing to buy such vehicles turns out to NOT be true (because the SOURCE of the electricity is from burning coal). IF the electricity could be gotten from solar or wind or hydroelectric, fine, they would be excellent! But it turns out that the practical matters in both solar PV operation and in wind turbine operation, make them VERY unlikely to actually ever provide all the miraculous claims made for them, at least for probably the next 50 years. We must remember that 51% of all the huge amount of electricity used in the United States is produced by burning coal.
The fact that the electric powerplant is many miles away seems to be the reason that people feel they can ignore whatever happens there! But it turns out that really bad things regarding carbon dioxide occur any time we want ANY electricity, whether for powering a vehicle or for making toast!
End of footnote 13 or 38
or carbon plus oxygen from the air gives carbon dioxide back to the air and energy.
There are many different types of petroleum which is pumped out of the ground. They all are primarily Carbon in composition, with the best varieties tending to be chemically around 85% Carbon . A pound of crude petroleum or its distilled products, gasoline, diesel fuel, home heating oil, jet fuel, kerosene, etc, therefore contains very close to 0.85 pound of carbon in it. If it is burned extremely completely, we can assume that ALL that carbon will combine with oxygen from the air to form carbon dioxide. Using atomic weights again, we see that carbon dioxide is 12 + 16 + 16 or 44, since oxygen is 16. When the 12 weights of carbon is burned (oxidized), it therefore forms 44 weights of carbon dioxide. We had 0.85 pound of carbon to start with so we multiply 0.85 * 44/12 to get 3.12 pound of carbon dioxide formed for each pound of Petroleum burned.
We can examine the official Reports for any year, regarding the CONSUMPTION of Petroleum in that year. Such Reports tell us that 3.54 * 109 metric tons of petroleum in the year 2000 (worldwide). If the Reports give the consumption in barrels instead, 7.33 barrels equals one metric ton. We just determined that each pound of that petroleum creates 3.12 pounds of carbon dioxide when it burns. Therefore, in the year 2000, the amount of petroleum that was burned produced 3.54 * 3.12 * 109 metric tons or 11.04 * 109 metric tons of carbon dioxide.
THIS year, we are burning up around 30 billion barrels of petroleum, which is about 4.1 * 109 metric tons of petroleum, which is creating about 12.8 * 109 metric tons of carbon dioxide.
End of footnote 14 or 1
or carbon plus oxygen from the air gives carbon dioxide back to the air and hydrogen plus oxygen from the air gives water vapor and energy.
Natural Gas is nearly all methane gas. That is chemically CH4. From Chemistry, we know that the Carbon atom has an atomic weight of 12 and each Hydrogen has one. The Methane molecule therefore has a total atomic weight of 16 (12 + 4). It is therefore 12 / 16 or 3 / 4 or 75% Carbon.
A pound of Natural Gas therefore contains very close to 3/4 pound of carbon in it. If it is burned extremely completely, we can assume that ALL that carbon will combine with oxygen from the air to form carbon dioxide. Using atomic weights again, we see that carbon dioxide is 12 + 16 + 16 or 44, since oxygen is 16. When the 12 weights of carbon is burned (oxidized), it therefore forms 44 weights of carbon dioxide. We had 3/4 pound of carbon to start with so we multiply 3/4 * 44/12 to get 11/4 or 2.75 pound of carbon dioxide formed for each pound of Natural Gas burned.
We can examine the official Reports for any year, regarding the CONSUMPTION of Natural Gas in that year. Such Reports tell us that 2.438 * 1012 cubic meters of natural gas was burned in the year 2000 (worldwide). We use the density of Natural Gas (Methane) (0.7168 gram/liter) to calculate that this amount is 1.74 * 109 metric tons of Natural Gas. We just determined that each pound of that natural gas creates 2.75 pounds of carbon dioxide when it burns. Therefore, in the year 2000, the amount of natural gas that was burned produced 1.74 * 2.75 * 109 metric tons or 4.81 * 109 metric tons of carbon dioxide.
THIS year, we are burning up about 3 trillion cubic meters of Natural Gas, which is about 2.1 * 109 metric tons of Natural Gas, which is creating about 5.9 * 109 metric tons of carbon dioxide.
End of footnote 15
At bi-weekly intervals, air samples are collected in sets of three 5-liter evacuated glass flasks, at the South Pole (Lat. 89°59'S. Long. 24°48'W.). They are analyzed for CO2 at SIO (Scripps) using a nondispersive infrared gas analyzer with a water vapor freeze trap. Calibration gases are regularly tested as well to confirm accuracy. The three sample flasks must agree within 0.40 ppmv to be considered acceptable data. Scripps has more thorough description of their procedures and equipment.
The readings are averaged to obtain monthly and annual average values. Our running display uses the annual averaged figures from this South Pole data, interpolated for each 1/10 second.
If the specific interpolated value at the South Pole for that instant were 380.0 ppmv, this means that the atmosphere was then 0.000380 carbon dioxide (by volume). It is accurately known that the total Earth's atmosphere is 5.136 * 1015 metric tonnes. It is also necessary to apply a density factor of 1.529 (of carbon dioxide to the average atmospheric mixture of gases) to convert the ppm (volume) value to ppm (mass or weight).
Therefore, it is simply necessary to multiply these three numbers: 5.136 * 1015 * 0.000380 * 1.529 to get 2984.12 billion tonnes of carbon dioxide in the entire Earth's atmosphere at that instant. THIS is the value that is continuously displayed here. The value has NOTHING to do with actual usage or consumption figures of fossil fuels, which actually generally give larger numbers for the annual increases.
Regarding the total mass of the earth's atmosphere, YOU can calculate that number, too! You already know that atmospheric pressure (at sea level) is 14.7 pounds per square inch (or 10332 kilograms per square meter). This pressure is actually due to exactly that amount of weight of atmosphere stacked above that square inch or square meter up to the very top of the atmosphere. So all we have to do is multiply that (metric) number by the total area of the surface of the earth, which is 5.10 * 1014 square meters. So YOU can calculate that the total mass of the Earth's atmosphere is 5.269 * 1018 kg or 5.269 * 1015 metric tons. For purists, the actual total mass is slightly less because continents and mountains take up some volume where air might otherwise be!
Atmospheric CO2 concentrations (ppmv) derived from flask and in situ air samples collected at the South Pole
Source: C.D. Keeling, T.P. Whorf, and the Carbon Dioxide Research Group
Scripps Institution of Oceanography (SIO)
University of California, La Jolla, California USA 92093-0444
May 2005, August 2007
Month Jan Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Ann. Avg. 1957 -99.99 -99.99 -99.99 -99.99 -99.99 313.37 -99.99 -99.99 313.87 -99.99 -99.99 314.48 -99.99 -99.99 1958 -99.99 -99.99 314.29 -99.99 -99.99 314.52 -99.99 -99.99 315.31 -99.99 -99.99 -99.99 -99.99 314.78 1959 315.09 315.14 315.09 -99.99 -99.99 -99.99 -99.99 315.96 316.22 -99.99 316.32 -99.99 -99.99 315.64 1960 -99.99 -99.99 -99.99 -99.99 -99.99 316.38 316.69 316.75 -99.99 -99.99 -99.99 -99.99 -99.99 316.45 1961 -99.99 -99.99 -99.99 -99.99 316.79 316.86 316.94 317.35 317.68 317.74 317.87 317.67 -99.99 317.08 1962 317.45 317.26 317.06 317.11 317.18 317.25 317.27 317.64 318.07 -99.99 -99.99 318.63 (317.62) 317.62 1963 318.13 317.87 317.47 317.90 318.26 318.22 318.26 318.64 318.56 319.02 -99.99 -99.99 (318.32) 318.35 1964 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 -99.99 318.68 1965 -99.99 318.68 318.56 318.68 318.89 -99.99 319.38 319.67 -99.99 -99.99 320.17 320.27 -99.99 319.42 1966 320.34 319.99 320.05 320.31 320.44 320.46 -99.99 321.08 321.35 321.46 321.56 321.07 (320.74) 320.72 1967 -99.99 321.01 -99.99 320.86 321.00 320.96 321.06 321.83 322.08 321.80 321.82 321.77 (321.33) 321.32 1968 321.53 -99.99 -99.99 321.61 321.47 321.44 321.50 -99.99 -99.99 -99.99 -99.99 322.65 -99.99 321.91 1969 322.37 -99.99 322.27 322.30 322.58 322.79 323.24 323.60 324.13 323.95 323.97 -99.99 (323.11) 323.12 1970 323.68 323.53 323.43 323.67 323.78 324.18 324.46 324.72 325.19 325.20 325.23 -99.99 (324.34) 324.32 1971 324.80 324.61 324.33 324.47 324.67 324.91 325.15 -99.99 325.77 -99.99 325.74 -99.99 -99.99 325.12 1972 -99.99 -99.99 325.05 325.17 325.31 325.82 326.13 326.85 326.54 326.79 326.94 326.82 (326.00) 326.00 1973 326.74 326.34 326.36 326.82 327.11 327.43 327.73 328.40 328.69 328.63 328.60 328.58 327.62 327.62 1974 328.30 328.08 328.09 327.90 328.01 327.88 328.46 328.68 328.94 329.04 329.12 328.99 328.46 328.49 1975 328.89 328.90 328.85 328.94 328.93 329.07 329.35 329.83 330.22 330.56 330.46 330.27 329.52 329.50 1976 330.30 330.01 329.91 329.63 329.93 329.98 330.46 331.01 331.39 331.71 331.74 331.43 330.62 330.60 1977 331.26 331.00 330.85 331.32 331.40 331.62 332.05 332.45 332.87 333.10 333.31 333.18 332.03 332.03 1978 332.83 332.71 332.83 332.98 -99.99 333.37 333.82 334.28 334.74 334.82 334.58 334.30 (333.70) 333.69 1979 334.01 334.03 333.82 334.17 334.34 334.54 335.15 335.71 335.88 336.00 336.37 336.04 335.01 335.03 1980 336.06 335.75 -99.99 336.10 336.21 336.90 337.45 337.54 337.87 337.90 337.97 338.04 (336.98) 336.98 1981 337.76 337.48 337.43 337.52 337.67 338.15 338.41 338.76 338.81 339.15 338.86 338.91 338.24 338.26 1982 -99.99 338.65 338.38 338.70 338.99 339.18 339.33 340.11 340.30 340.33 340.03 339.96 (339.39) 339.39 1983 339.86 339.84 339.85 340.31 340.63 341.00 341.41 341.88 342.33 342.29 342.54 342.35 341.19 341.17 1984 342.05 -99.99 341.71 341.84 341.87 342.01 342.80 343.20 343.46 343.50 343.32 343.15 (342.56) 342.58 1985 343.01 342.83 342.73 342.76 343.12 343.45 343.93 344.52 344.86 344.95 344.79 344.64 343.80 343.82 1986 344.63 344.57 344.50 344.62 344.69 345.02 345.54 345.93 346.18 346.16 346.17 346.04 345.34 345.32 1987 345.89 345.79 345.75 346.11 346.20 346.61 347.19 347.63 348.07 348.10 348.19 348.31 346.99 346.99 1988 348.29 348.06 347.87 348.20 348.33 348.58 349.07 349.58 349.75 349.89 349.85 349.83 348.94 348.95 1989 349.81 349.76 349.66 349.73 349.93 350.18 350.59 351.12 351.37 351.30 351.33 350.99 350.48 350.44 1990 350.76 350.40 350.64 350.90 351.36 351.59 352.05 352.55 352.75 352.57 352.83 352.63 351.75 351.77 1991 -99.99 352.34 352.28 352.44 352.54 352.96 353.39 353.67 354.09 353.89 353.95 353.77 (353.15) 353.12 1992 353.56 353.15 353.03 353.23 353.74 354.00 354.61 354.94 355.26 355.37 355.11 354.88 354.24 354.24 1993 354.72 354.49 354.22 354.42 354.50 354.84 355.20 355.70 356.04 356.05 356.02 355.69 355.16 355.16 1994 355.49 355.49 355.51 355.63 355.69 355.99 356.47 357.11 357.61 357.53 357.71 357.52 356.48 356.48 1995 357.45 357.36 357.36 357.63 357.81 357.95 358.34 358.75 359.15 359.29 359.43 359.47 358.33 358.35 1996 359.36 359.30 359.25 359.36 359.40 359.71 360.15 360.52 360.71 360.70 360.74 360.70 359.99 359.99 1997 360.56 360.46 360.32 360.48 360.58 360.90 361.24 361.52 361.95 362.01 362.11 362.15 361.19 361.20 1998 362.10 362.30 362.41 362.69 363.00 363.54 364.04 364.56 364.99 365.02 365.10 364.98 363.73 363.70 1999 364.96 364.75 364.81 364.99 365.05 -99.99 365.66 365.92 366.37 366.51 366.74 366.80 (365.66) 365.65 2000 366.46 366.49 366.76 366.45 366.58 366.78 367.10 367.53 367.65 367.75 367.88 367.83 367.10 367.05 2001 367.81 367.10 367.04 367.36 367.60 367.92 368.29 368.83 369.44 369.57 369.46 369.25 368.31 368.34 2002 369.31 369.50 369.61 369.68 369.99 370.38 370.87 371.46 371.69 371.83 371.81 371.61 370.64 370.66 2003 371.93 371.78 371.71 371.99 372.32 372.57 372.96 373.40 373.90 373.82 373.65 373.61 372.80 372.80 2004 373.59 373.41 373.85 373.88 374.06 374.46 374.85 375.35 375.52 375.60 375.51 375.25 374.61 374.61 2005 375.18 374.98 375.16 375.50 375.88 376.39 376.87 377.29 377.59 377.72 377.79 377.82 376.51 376.51 2006 377.68 377.47 377.51 377.73 377.93 378.24 378.68 379.10 379.34 379.37 379.32 379.34 378.48 378.48
Atmospheric CO2 concentrations (ppmv) derived from flask and in situ air samples collected at the Mount Mauna Loa, Hawaii
Source: C.D. Keeling, T.P. Whorf, and the Carbon Dioxide Research Group
Scripps Institution of Oceanography (SIO)
University of California, La Jolla, California USA 92093-0444
(this Mauna Loa data is generally slightly higher than that at the South Pole. We have not been able to obtain extremely recent data from the South Pole yet.)
Month Jan Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Ann. Avg. 2006 381.10 381.35 381.15 381.96 381.86 381.67 381.64 382.04 382.05 382.40 382.27 382.65 381.85 2007 382.62 382.94 382.92 383.68 383.45 383.67 383.94 383.67 384.04 384.43 384.47 384.65 383.71 2008 385.15 384.90 384.45 384.50 385.40 385.55 385.86 385.88 386.30 386.33 386.20 386.36 385.58 2009 386.64 386.60 387.25 386.77 387.07 387.17 387.28 387.65 388.00 387.18
Monthly values are expressed in parts per million (ppm) and reported in the 2003A SIO manometric mole fraction scale. The monthly values have been adjusted to the 15th of each month. Missing values are denoted by -99.99. The "annual" average is the arithmetic mean of the twelve monthly values. In years with one or two missing monthly values, annual values were calculated by substituting a fit value (4-harmonics with gain factor and spline) for that month and then averaging the twelve monthly values.
Calibration details are discussed by Francey et al. (2003). Monthly values are calculated as the mean of the daily values from a smooth curve fit to the data using curve-fitting routines described by Thoning et al., 1989, (J. Geophys. Res. 94, 8549-8565).
End of footnote 48
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. This curve on the graph needs to be Integrated over all wavelengths to get the total value of the Solar Constant of the 1,353 watts/square meter
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 14°C or 287°K, 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 5762°K, 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 250.5°K (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 287°K instead of the Equilibrium 250.5°K. 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 crude 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 312.9°K, which is 39.7°C or 103.4°F. So even if the carbon dioxide concentration would only get up to double today's (around 770 ppm) the average equilibruim temperature of the surface of the Earth would necessarily become around 45°F (25°C) hotter than today, meaning that no crops or other plants would be able to adequately respirate (daytime high temperatures of well over 150°F or 66°C), 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 absorbtivity 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.
End of footnote 48This 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 Effects of Carbon Dioxide and Sea Levels Rising as Polar Ice Melts
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.
C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago