The calculations cannot account for the smallest fraction of the effects in the atmosphere or climate. So the omissions are filled in with fake modeling. Modeling cannot account for the missing information either.
Supposedly, the calculations show that 3.7 watts per square meter of radiation less than the sun's energy would show up at the top of the atmosphere upon doubling the CO2. Failing to escape the atmosphere, this radiation supposedly creates global warming.
Radiative transfer equations are a scheme for calculating global warming. It is totally impossible to produce such a number, because infinite interactions cannot be represented by one number, and the difference between energy inflow and outflow must always average zero due to equilibrium. Disequilibrium is an impossibility.
Obviously, the air cools at night. Why would some of the heat be trapped while the rest cools? An impossibility.
It's impossible to say what the number (3.7 w/m²) is supposed to represent, since nothing about the subject can be reduced to such a number; and therefore, climatologists cannot produce a consistent description of what the number is supposed to mean. A difference between energy inflow and outflow seems to be the most common interpretation.
And then, the number is a rate of energy addition, which cannot be converted into a temperature; yet 1°C is claimed. Supposedly, a reversal of the Stefan-Boltzmann constant converts the rate into a temperature, while reversing the constant is not valid, as it applies to a surface, and there is no surface involved.
If the logic were that a temperature increase of 1°C would cause 3.7 w/m² to fall on the surface of the earth, the math didn't work that way. It produces the 3.7 w/m² first. And then, an additional 3.7 w/m² falling on the surface would also require an addition 3.7 w/m² going upward and into space. In other words, warming of the atmosphere cannot have anything to do with watts per square meter. But fake math was needed, and watts per square meter is what climatologists are familiar with. So they used a fake process to get something they were familiar with, even though the process had no relationship to anything real. There is no real number or concept to represent heat increase in the atmosphere due to the infinite variations and complexities.
Energy flows through the atmosphere in numerous unknown ways and leaves by radiating from every molecule. Science has not the slightest ability to determine how the energy is flowing. It all equalizes, so the amount entering from the sun is the same as the amount leaving from the earth. The difference is always zero. But radiative transfer equations say the difference is 3.7 watts per square meter due to human activity upon doubling the amount of carbon dioxide in the air.
To whatever extent carbon dioxide is heating the atmosphere, it should cause more radiation to escape into space from the atmosphere while less escapes from the surface of the earth. But climatologists needed a fake math and number, so they showed less radiation escaping into space and used fake radiative transfer equations to get there.
To show less radiation going into space, they had to pretend that it all starts from the surface of the earth, while the atmosphere obstructs the emission of radiation into space. The opposite is truealmost all radiation into space leaves from the atmosphere and very little from the surface of the earth.
Almost all radiation leaving planet earth leaves from the atmosphere, because radiation leaves much easier from a transparent gas than from an opaque surface. The subtraction process ignores this radiation, as if the only radiation leaving the planet started from the surface.
The atmosphere is like a heat sink in electronics. Power transistors produce a lot of heat, and it is carried away by attaching aluminum to the transistor. The aluminum absorbs the heat rapidly to cool the transistor. So the aluminum is called a heat sink. The earth's atmosphere is a heat sink. It absorbs energy from the surface as wind blows across it and carries it away to be radiated into space.
Explanation: Explaining the radiative transfer equations has never been possible, because nothing in science really does that. Climatologists show some fake math for producing the radiative transfer equations, but the math doesn't get to the claimed end result. The degree of complexity in the atmosphere is the main problem. Radiative transfer equations supposedly take care of everything that influences heat in the atmosphere and show a net result. There is way too much randomness and complexity to evaluate what heat does in the atmosphere. So where does the number (3.7 w/m²) come from? Fakes pick the desired end point and pretend that some undefinable procedures, using the world's largest computers, produced it.
After the complex computer analysis of the atmosphere for producing the radiative transfer equations, an over-simplified fudge factor is used to summarize the result. The fudge factor is simply the radiative transfer equations but replacing the world's most complex computers with a three component equation. The circumstantial absurdities of no such concepts existing indicate that climatologists started and ended with the three component fudge factor and contrived the computer work to show the same result.
Nature heats and cools the atmosphere without any such number. The reason is because heat and radiation flow infinitely in all directions. This infinite complexity cannot be represented by a number. Yet climatologists (physicists) must represent everything they do with math which yields numbers. In other words, science cannot be applied to the question, but the fakes need to pretend that they are applying science to the question by producing a number where there is no such number.
The equilibrium process with atmospheric energy has been going on as long as the planet has existed, and supposedly humans upset the balance creating a disequilibrium. There are gradual changes in the equilibrium temperature, while the net difference between inflow and outflow of energy always stays zero. But to create a fake analysis, humans supposedly caused a non-zero number to replace equilibrium.
It's because of equilibrium that heat acquired during the day is lost during the night. Any imbalance would cause an increase or decrease. The combination of increases and decreases with weather shows that equilibrium is occurring. A lock at some higher number is absurd. One climatologist tried to explain this by saying, yes, equilibrium is occurring, but greenhouse gases shift the equilibrium temperature. No way. The number 3.7 w/m² does not exist with equilibrium. The number says dis-equilibrium is occurring, and only humans did this in some unique way.
A foggy concept that sometimes seems to exist is that greenhouse gases slow the exit of radiation, while any delay results in a temperature increase. Slowing the rate of exit is not producing disequilibrium beyond short-term transitions. The number 3.7 w/m² does not represent a delay or reduced rate of exit, it represents a permanent block. A delay would have to be represented by time, not watts per square meter.
A consistent logic would say that 3.7 w/m² is a continual increase in energy, not a one-step increase. But the Stefan-Boltzmann constant is used in reverse to convert 3.7 w/m² into 1°C. It is not valid to reverse the Stefan-Boltzmann constant, because it destroys the logic of cause-and-effect relationships. Physicists went this route so they could produce a mathematical analysis with a number. They cannot produce a real mathematical analysis, because they cannot explain a mechanism for greenhouse gases heating the atmosphere.
Why didn't volcanoes produce a number for disequilibrium, as they sent CO2 into the atmosphere? Why wasn't the number negative, as oceans absorbed the CO2? Why does the graph for CO2 go up and down, while the number stays zero, and only when humans come along does the number become 3.7 w/m² difference? Nothing but fraud creates such a number for human influences. If not, what are the other numbers, and how do they compare? They have never existed and have never been evaluated.
Implicitly, there would be temporary differences between energy inflow and outflow, while temperatures change. But temporary imbalance is not what physicists claim with the results of radiative transfer equations. (The result is called "radiative forcing." Wikipedia defines radiative forcing as this disequilibrium.) They say that the number they produce is a forever, fixed quantity which goes with a particular amount of CO2 in the atmosphere. A temporary number would require a whole new analysis. The number is calculated with an over-simplified fudge factor which puts CO2 on one axis and heat produced on the other axis. The graph for the fudge factor means forever, not temporary.
Yet physicist say that radiative transfer equations are such a bit of brilliance that they can calculate the temperature of Venus with them. It's a form of worship in contempt for what science is supposed to be.
Climatologists calculated the radiation which goes from the surface of the earth to the top of the atmosphere. Numerous small slices are looked at to take into account changes in pressure as the radiation goes upward. The end result is determined by the manner in which radiation moves from one slice to the next. Saturation was removed in the calculations.
Supposedly, the calculations had the significance of showing that 3.7 watts per square meter of radiation less than the sun's energy would show up at the top of the troposphere upon doubling the CO2. Yet, scientists have variously claimed that the heating occurs at 5 km up and 9 km up, neither of which are at the top of the troposphere, which varies from about 12 to 15 km up.
Actually, it's not possible to calculate this quantity (the amount of radiation getting to the top of the atmosphere) due to the infinite complexities of radiation being emitted and absorbed by every molecule in the atmosphere and surface of the earth including oceans. Fifteen to thirty percent of the radiation in the atmosphere goes around greenhouse gases. The rest travels about 10 meters and is re-absorbed. Then it is re-emitted in less than a pico second, and the same thing happens again.
Even if everything claimed were true, there would be a huge error in not knowing whether it is 15% or 30% of the radiation that goes around greenhouse gases, yet the claim is that the radiative transfer equations only have about 1% error.
In a laboratory, radiation going through a tube of carbon dioxide is easy to measure. This was done more than a century ago. The result showed all radiation being absorbed in a short distancean effect called saturation. Scientists dropped interest in the subject of global warming for this reason.
Surely, modern scientists would have been measuring and evaluating this subject relentlessly. They surely would have. But there is not the slightest evidence of them doing so beyond critics such as Heinz Hug who are not allowed to publish their results. Measurements by Heinz Hug, which he put on the internet, showed all radiation being absorbed in 10 meters near the surface of the earth. No contradicting science has been visible beyond infantile debunking which has no meaning.
Instead of measuring, modern alarmist scientists calculate the same result, and abracadabra, most of the saturation disappears. Should scientists not be resolving the contradictions between the measured and calculated results? There is no evidence of a contradiction.
The calculated results are reduced to a simplistic fudge factor and claimed to represent an unquestionable law of physics which erases all criticism of the subject. Supposedly, there is no reason to look at criticism anymore, because the calculation rendered all criticism irrelevant at the level of the basic science of global warming. All arguments recognized by scientists are limited to secondary effects which are modeled.
There is not a correct logic for doing the radiative transfer equations. Since the only result is to show 3.7 w/m² less radiation getting to the top of the atmosphere, there must be a logical method of deriving this claim. There is none. The claim reduces saturation to a very small amount. To do this, there must be a concept of how much absorption is occurring during each step of the process, because most radiation disappears at the end of the process.
Supposedly, the absorption spectrum was pre-measured for each slice at various pressures and fed into a data base called HITRAN. But mixing the measurements and calculations doesn't get the claimed result of knowing how much radiation is left at the end of the process. To get there, a new measurement must be made after each calculation for each slice. A computer run won't do that. You say they did do that. Then why did they use HITRAN, when they had to measure each slice between each calculation? Neither HITRAN data nor additional measurements can reproduce the infinite complexities of radiation being absorbed and emitted from every molecule in the atmosphere and exposed to the atmosphere.
The fact that they used HITRAN data shows that they used ultra simplistic procedures which account for none of the complexities, and they could have used a hand calculator to add up the slices instead of the world's largest computers. Add the computers, and HITRAN is unusable. This for the unquestionable primary effect by CO2 upon which all of the rest of global warming claims are based.
There are additional complexities which overwhelm the process. One of the main problems is that there is a time factor involved, and it is totally beyond comprehension. Moving energy through radiation which is continually absorbed and re-emitted is a little bit like conduction in that the energy goes from molecule to molecule to get someplace. The energy flows from more concentrated areas to less concentrated areas. Flowing is a time based effect. The element of time is beyond analysis. It can only be measured; it cannot be calculated.
If one end of a metal rod is heated, the heat will flow toward the other end. The rate will depend upon the differences in temperature from end to end, the thickness of the metal and the amount escaping into the environment along the way. Rate is time based.
The time element enters into radiation transfer due to the fact that anytime radiation is absorbed by a molecule it will cause the molecule to vibrate, which is heat. It takes so many vibrations to release the energy as radiation. How many vibrations occur in the process of releasing radiant energy is impossible to evaluate. The time factor determines how much energy takes the form of heat and how much escapes as radiation. None of these time-based concerns can be evaluated for the RTEs.
If heat is prevented from escaping the end of the metal rod (such as insulating it), there will be more heat build-up all along the rod. The RTE analysis is a pretense that the same thing occurs in the atmosphere with radiation resulting in 3.7 w/m² less radiation at the top than there would be with half as much CO2 in the atmosphere.
This concept cannot be applied to radiation as if it were conduction. Conduction is slowed down as the differences in temperature are reduced from end to end with the metal rod. Nothing slows down the rate of radiation as temperature change occurs someplace else. In other words, there is no transfer of effect from place to place with radiation. The temperature of the emitting molecule will be the only factor regardless of what happened someplace else. Obstruction of radiation one place does not change the rate of radiation emission someplace else.
A simpler analogy would be a water pipe. Plug one end of a water pipe, and back pressure forms at the starting point. Radiation doesn't do that. Blocking radiation some place does nothing to change the rate of radiation someplace else.
Rationalizers claim that increases in CO2 in the atmosphere will obstruct the flow of radiation causing it to escape from the top of the atmosphere at a greater height. This obstruction is supposed to magically cause a temperature increase near grown level, as if the end of a water pipe were plugged causing a back-flow to the starting point.
This logic was necessary, because a previous explanation based upon energy moving from the top of the atmosphere to the bottom through direct radiation did not stand up to criticism. A very large temperature increase would be needed up high to get a small amount of energy near the surface through back-radiation.
Also ridiculous in the explanation for RTEs is the omission of radiation escaping from all parts of the atmosphere, which cannot be evaluated, as it establishes equilibrium with energy entering from the sun.
Radiative transfer equations start with a measurement of radiation flowing through a tube in a laboratory to see how much gets through a gas at what distance. Then these measurements are combined in the world's largest computers to see how much would get to the top of the atmosphere while density of the gas changes. This result would produce some sort of a graph like the fudge factor used to represent the result. The real shape would be different due to saturation, which was erased in the analysis.
But that result would not have been a complete process, because infinite complexities related to weather would influence the result. So the weather effects were modeled into the result. No way, Sam. Weathermen cannot predict the complexities for one day beyond the simplest elements, and physicists are going to predict a permanent effect which averages over time without variation calling it climate? There is no such invariable effect, as shown by the "Little Ice Age" and "Medieval Warm Period."
After averaging weather into the result, there would not be a smooth line curve to be represented by the fudge factor. The fudge factor was nothing but a contrivance with no relationship to anything that actually happens.
The latest version of computation of radiative transfer equations was produced by Myhre et al (1998)(linked on home page). They show the number for the fudge factor (5.35) in that publication.