Climate Change - Physics 101

Global Warming will Increase the Earth’s Temperature over 60⁰F Degrees.

“It does not do to leave a live dragon out of your calculations, if you live near him.”
― J.R.R. Tolkien, The Hobbit

Unless global CO₂ emissions are drastically cut over the next few decades greenhouse gases are  projected  to increase the Earth’s average surface temperature by a total of over 60⁰F Fahrenheit.

Even if you fully accept the scientific communities’ warnings concerning  Climate Change, you are probably thinking “Where did 60⁰F come from? I thought it was 2 or 3⁰F”. But the correct answer is over 60⁰F, it just depends on your starting point. 

Let’s start with the moon.  The earth and the moon are the same distance from the sun, but the moon is roughly 0⁰F while the earth is about  60⁰F. “Why is the earth’s temperature different from the moon’s? 

To solve this puzzle let’s go back to 1820, to  the beginning of climate science, when Joseph Fourier, one of the greatest mathematicians in history, had a problem. His numbers just didn’t add up, which, I suppose was rather unusual for Joseph Fourier. He had calculated that the Earths’ average temperature should be about 0⁰F, but he knew the Earth was warmer, in fact is was over 50⁰F warmer. 

Fourier didn’t solve the problem mathematically , but he did suggest a solution, Fourier postulated that Earth’s atmosphere acts like an insulator, trapping heat and warming the Earth’s surface, what we now call the “Greenhouse Effect.”

 “Climate Change” started millions of years ago and raised our earth’s temperature to about 57⁰F pre-Industrial Age. Without Climate Change  we would not be here, the Earth would be, like the moon, on average, frozen which may make for a great movie title but a rather poor living environment.  It is impossible to scientifically deny the Greenhouse Effect.  To deny Climate Change  one must postulate some other method to explain our present temperature and, following the physics applicable to our universe, there is no other method. The same science dictates that as we add additional greenhouse gases to the atmosphere the temperature will continue its’ relentless upwards track. Today we have added another 1-2 degrees to the 57⁰F rise and will undoubtedly add a couple of more degrees raising the total to over 60⁰F.

It wasn’t until after the derivation of the Stefan-Boltzmann equation (more later) that the mathematics of the warming were worked out. In 1896, Nobel Laurette Svante Arrhenius  showed how greenhouse gases in the atmosphere trap heat as it is being radiated upwards, radiating some of it back down. Arrhenius showed how additional heat and the dictates of the Stefan-Boltzmann equation, raised the Earth’s average surface temperature from about 0⁰F to about 57⁰F allowing life on Earth and fundamentally altering the climate and environment that we experience. 

The warming effect of adding additional heat trapping gasses was specifically recognized in by Arrhenius, in his treatise “Worlds in the making (in 1908!!) ” where he stated that "…If the quantity of carbonic acid [ CO₂ + H₂O → H₂CO₃ (carbonic acid)  in the air should sink to one-half its present percentage, the temperature would fall by about 4°; a diminution to one-quarter would reduce the temperature by 8°. On the other hand, any doubling of the percentage of carbon dioxide in the air would raise the temperature of the earth's surface by 4°; and if the carbon dioxide were increased fourfold, the temperature would rise by 8°."

1908!;  that only puts climate deniers about 110 years behind current scientific thought.

The science of climate change was settled by 1900. Subsequently we have been conducting a giant Earth-wide experiment to verify Arrhenius’ calculations of the effect of adding more CO₂ to our atmosphere and have unfortunately shown that he was correct. 

Since the findings of Arrhenius, the scientific community has confirmed Arrhenius’ calculations and has refined his conclusions  utilizing remarkable progress in computing capabilities, satellite observations, numerical modeling, data collection, weather forecasting, etc. 

But now, even having verified  Fourier’s theory and Arrhenius’ calculations using our Earth as a testbed, even after realizing the immense consequences of additional warming,  we are continuing the experiment by injecting about 2.7 million pounds of CO₂ into our atmosphere every second, not only continuing to prove Arrhenius correct but simultaneously proving to our grandchildren the capacity of the human mind to rationalize any facts for our short-term political or financial gain while ignoring their future. 

What is the math that allowed Arrhenius to show that Fourier was correct in his assertion? For the Earth’s temperature to remain constant, the energy absorbed by the Earth  (primarily from the Sun) must be equal to the energy emitted by the Earth. Like anything else, if the Earth absorbs more energy than it emits it will heat up, less and it will cool down.

To understand Global Warming,  we must understand that the incoming  energy from the Sun is very different than the energy radiated by the Earth back out to space. The energy from the Sun is mainly visible light, but what energy does the Earth emit? 

Here is where the Stefan-Boltzmann Equation and another law, Wien’s Displacement Law, come into play.

The simple Stefan-Boltzmann equation formulated in 1879 says that the energy radiated as electromagnetic radiation for a given area of any object is proportional to the temperature to the fourth power. 

Heat radiated per unit area =σT⁴, where σ is the Stefan-Boltzmann constant and T is in Degrees Kelvin 

Thus any object, including objects we perceive as cold, radiate energy and, as they heat up, radiate a lot more energy. But what type of energy? That is where Wien’s Displacement Law comes into play.

Wien’s Displacement law specifies the frequency range of the energy the object radiates. The energy radiated from an object is distributed around a peak frequency which is directly proportional to the object’s temperature. Thus, as an object gets hotter, it radiates at a higher frequency. This simple Law shows why a campfire emits yellow and red light while a hotter gas stove radiates blue light. The Sun, being very hot radiates visible light. The Earth being much cooler radiates infrared light. You can feel this radiation even at night when you place your hand over a hot object such as a blacktop road warmed by the Sun during the day. This different in how our atmosphere treats visible and infrared radiation  is fundamental to understanding the Earth’s climate.  

The visible light entering our atmosphere largely gets a free pass to the surface, with only about 20% being absorbed in the atmosphere. In total the oceans, surface and clouds reflect about 30% of the total incident radiation back into space (the Earth’s “Albedo” is about 0.3.). The remaining 50% of incoming solar radiation is absorbed at the surface which it heats up and is reradiated as infrared energy. 

A different fate awaits infrared on its journey through our atmosphere.  As infrared  travels upwards through the atmospheregreenhouse gases” such as CO₂, methane and water vapor that were largely transparent to visible light absorb the infrared light heating the atmosphere. The atmosphere then reemits additional infrared upward and downwards. This absorption and the subsequent emission lays the foundation for the warming. the downward radiation  adds to the incoming solar radiation to warm the surface of the Earth. Although this warming effect is significant the overall effect of atmospheric absorption is greater than just the direct heating, it is the implications mandated by the Stefan-Boltzmann equation .  

There are only three forms of heat transfer, conduction, convection and radiation. The Earth  cannot return energy into space to maintain its energy in – energy out balance by conduction or convection as it is surrounded by a vacuum. Thus it can only lose heat by radiation

As the atmosphere absorbs energy on its way upwards our Earth’s energy balance is upset; energy coming in, being visible light and largely unabsorbed, is now greater than energy going out some of which has been absorbed by greenhouse gasses. Thus we must now radiate additional energy away from the Earth to overcome this deficit. 

As we look at the formula for radiation,  the Stefan-Boltzmann Equation (Heat radiated per unit area =σT⁴), Global Warming becomes not only apparent but inevitable. The equation contains only three terms on the right side, two of them (σ  and 4) are constants, leaving Temperature as the only variable. Thus to emit more heat to make up for the absorption of outgoing infrared radiation and to regain our “energy in Energy-out balance” the Earths’ temperature  must warm up, it’s not might, could or may; it is MUST. And it is this warming that was postulated by Fourier and calculated by Arrhenius.

The extra atmospheric absorption by the increased CO₂ is easily verified. This verification doesn’t rely on conjecture or unproven scientific theories; it relies on measurement and observation. In 1971 NASA launched the IRIS satellite and in 1996 the Japanese launched the IMG satellite, both measured the radiation given off by Earth. They showed that between 1976 and 1991 there was a marked decrease in the infrared radiation that the Earth was emitting into space and the decreased emissions were mainly at the wavelengths absorbed by CO₂ and methane. 

The First Law of Thermodynamics (i.e., energy can neither be created nor destroyed) would seem to be on sufficiently firm footing to indicate that if the energy isn’t going into space it must be going someplace else, and the only possible places are melting ice or heating the atmosphere, oceans and land, all of which observations indicate are happening.  As NASA used to say on its website “Earth is receiving more energy than it is sending back to space. This means that the planet must heat up—and in fact, already is heating up—to regain balance.” 

Global Warming is incontrovertible, without any greenhouse gases, the Earth’s average surface temperature would be about zero degrees. As we add additional greenhouse gases tour atmosphere, the Earth must get warmer to regain its’ energy balance. But what difference does this warming make? Who cares if we warm 4 degrees and it is 74⁰F rather than 70⁰F? If you live in the Northern Latitudes, warming may seem quite appealing, at least during the winter. If that were all that would happen, then climate change would not be as bad as advertised. 

But that is not all that will happen. Jim Hansen, former head of the NASA Goddard Institute for Space Studies at NASA has stated, “Climate change — human-made global warming — is happening.  It is already having noticeable impacts…. If we stay on with business as usual, the southern U.S. will become almost uninhabitable.” 

Politicians who spend a great deal of time worrying about the deficit and intergenerational equity, should at least think about the climate deficit we are bequeathing to future generations. If I were a newborn and had the choice, I would take the Government Deficit over the Climate Change any day of the week. 

On a positive note the politicians who worry about the inheritance tax breaking up family farms in the Midwest will not have to worry; climate change will do it for them. Politics, especially in Texas, Kansas, Oklahoma, etc., will become a great spectator sport when the farmers realize they have been had by their neighbors in the  energy business and politicians running  a misleading campaign identical to that run by the cigarette companies for years.

Worldwide, vast areas of agricultural land will become arid and unlivable and people will be forced to migrate or starve. Other areas will see vastly increased rainfall. Agriculture worldwide will face crippling disruption at the very time when we need more food due to population growth and increased per capita consumption as the standard of living of the developing countries increases. If you don’t like the current migrant situation, “You ain’t seen nothing yet.” 

Sea level rise will bring about massive coastal flooding that will result in extreme political friction as millions of poor migrants flood into other countries. This rise is caused not only by melting polar ice but by thermal expansion as the oceans heat up. At the same time the “Evil Twin” of Climate Change, Ocean Acidification, will cause immense changes in the ocean’s marine biosphere an effect  which is an equal, if not greater, challenge than Climate Change. 

We simply cannot predict what our ultimate climate will be. In mathematical terms, weather is a “Chaotic” system, meaning that very small changes in input can cause large changes in the atmospheric circulation.  This phenomenon  prevents scientists from predicting weather more than about two weeks in the future. This inability to predict the weather a month ahead, however, does not mean we are not going to have weather next month. Neither does the fact that we can’t predict the exact outcome of climate change mean we won’t have Climate Change.

Indeed, the fact that we don’t know everything about climate change doesn’t mean that we don’t know anything; we know a great deal, most importantly we know (and satellite measurements conform) that due to our “energy-in” “energy-out” imbalance the Earth is currently absorbing the extra heat content of about five World War II Nuclear Weapons every second vis-à-vis the preindustrial age. 

We also know that with our current emissions trajectory the ultimate outcome is 100 percent catastrophic and impacts from future emissions of CO₂ must be reduced. But we continue to add  2.7 million pounds of CO₂ per second to our atmosphere and choose not to recognize the simple scientific inevitability of the consequences for the climate, environment and society. We also unequivocally know that the warming effect described by Fourier and Arrhenius has currently raised the Earth’s  temperature by close to 60⁰F compared to the moon and there is no scientific reason that it will stop as we add more heat trapping gases to our atmosphere. 

Hopefully we can act before it is too late. However, Climate Change is not an easy problem for politicians to address. Politicians with time horizons of the next election are unlikely to champion the long-term fixes needed to stop climate change as doing so would open them up to their opponent saying they are raising energy costs and killing jobs even though the short-term costs of fixing climate change pale in comparison to the long-term costs of inaction.  

Businesses can rationalize that their small part won’t make a difference and even if they radically decrease their emissions, it will only drive up their costs in a competitive market. For a description of why it is almost impossible for politicians, business’s and others to handle Climate Change. 

It is much easier to rationalize your actions or espouse scientific laws  form some yet to be discovered universe or claim that we still have time, grasping onto statements with the same scientific credibility as ‘smoking does not cause cancer’. Future social and political scientists (and our grandchildren) will question how people in the most advanced scientific nation on Earth could have denied Physics 101, science from the late 1800s and lived in a fantasyland where Joseph Fourier, Svante Arrhenius and the laws of physics seemingly never existed. For a fuller explanation of the uphill battle we have to achieve rational action on Climate Change see my paper on externalities at https://www.fortnightly.com/fortnightly/2018/06/electricity-externalities-and-regulation?authkey=d94f4bea1fdf9dc191da6e6c11c6c11949011ea31d1f4de8ebe101cbb72e7b84

Some of my statements about Climate Deniers may have seemed harsh but they pale in comparison to the harshness of the actual future we are bequeathing to our grandchildren. Our Earth’s story will continue, its future chapters are being written now but will only be deciphered later as they are indelibly written on the lives of our children and on the lives of billions of other people who will face wars, disease, mass starvation and migrations levels caused by catastrophic Climate Change and Ocean Acidification. The story will be played out on the lives of our children and our entire ecosystem, as the bumper sticker says, ”reality happens”.

“The Moving Finger writes; and, having writ,
 Moves on: nor all thy Piety nor Wit,
Shall lure it back to cancel half a Line,
 Nor all thy Tears wash out a Word of it.

 Omar Khayyann

In Memory of Jim Rogers