The following is a transcript courtesy of Howard “Cork” Hayden, Emeritus Professor of Physics, UConn, [email protected]
One truth at a time
This short essay is the tenth in a series of fundamental (that is, comprehensive) physics dealing with the topic of climate.
Remember that it’s not my intention to get into the details of wind, rain, snow, storms, historical climates, Milankovitch cycles, or any of the general topics discussed about climate. What I will discuss is some simple physics.
The absence of Stefan-Boltzmann
The Stefan-Boltzmann law of radiation states that radiation emitted through a small hole in a cavity, summed up over the entire spectrum, is equal to
where BILLION is the Kelvin temperature. The equation has been around since 1884, and was put on a solid theoretical foundation by Max Planck in 1900. Curiously, it also applies to solids as diverse as stars, hot stars, the earth’s surface, including the oceans and the cosmic background radiation. That is the principle of operation of a non-contact thermometer.
One would therefore expect to see references to the Stefan-Boltzmann radiation law and the Planck curve in every IPCC report. Search IPCC Evaluation report revealed that no one has the word Stefan or Boltzmann until AR6(published year Do not quote, quote or distribute sample) in 2021. The number 5.67 appears nowhere except for some table entries that have nothing to do with the Stefan-Boltzmann constant. Name Planck occurred only in relation to the Max-Planck Institute in four Evaluation report. In AR5 (2014), we were introduced to jargon Planck’s response (to be discussed) but nowhere — repeat NOWHERE—Is there any mention that Stefan-Boltzmann’s law always applies to surfaces. Nor, more importantly, does this law actually apply to the model’s predicted surface temperature.
Planck Feedback (aka Planck Feedback)
Search Planck’s response on the internet and you see this line repeating ad nauseum: “The Planck response is the most basic and common climate response, and is present in all climate models. It is simply an expression of the fact that a warm planet radiates into space more than a cold planet.” In Lesson 3, we proved that statement false with two examples. (1) Earth with same albedo but with or without greenhouse effect (IE, warmer of colder) emitting identical IR to outer space. (2) Venus, with its lead molten surface temperature, emits less infrared radiation into space than Earth does.
The Planck response, however, has some value. Imagine that someone sprinkles
the right kind of Pixie Dust all over the earth to warm the surface. It will radiate more IR and set up an imbalance so that the heat radiated to space (about 60% of the surface radiation) will exceed the heat absorbed by the sun (Ioutside > Iin ). The imbalance will continue (and diminish) until the earth cools down to the condition it was in before the Pixie dust was covered. This is actually a negative feedback mechanism that tends to keep the surface temperature constant, but most certainly it doesn’t determine what that temperature is. In particular, it is of no use in calculations Equilibrium Climate sensitive (ECStemperature increases because CO2 doubles when Iout = Iin ).
Add the greenhouse effect!
If the greenhouse effect is increased, such as an increase in CO2 or H2O in the atmosphere, then IR emissions into space will decrease. That imbalance ( Ioutside < Iin ) warms the surface until equality between incoming solar heat and outgoing heat radiation is re-established. (Climate modelers note: During this time, the warming planet radiates less infrared rays into space than it did when it cooled.) In this real case, the increase in the greenhouse effect occurs before the temperature increases, unlike the Pixie-Dust scenario. It is important to remember that the only source of heat for the earth is sunlight.
It is important that when Planetary Heat Equilibrium is restored — that is, when Ioutside =Iin (ISun / 4) (1 – α) – additional greenhouse effect (“forced radiation”) must equal additional surface radiation unless there is a change in either Isun or albedo α. Recall the Climate Constraint Equation from Lesson 4:
If the greenhouse effect WOOD increase (say) 2 W/m2 and sunlight and albedo remain constant, then surface irradianceBILLION4 must increase by the same 2 W/m2, and that fact tells us exactly what the temperature rise will be: 0.36oC for this numerical example.
Asking the wrong question
Let’s say we have a warehouse that holds all kinds of furniture, and that warehouse is perfectly insulated. Tell us how much the temperature of the warehouse will rise if we add a certain amount of heat to it. We can calculate the temperature rise if we know the mass and heat capacity of everything inside the warehouse.
Now, let’s ask what will be the increase in earth’s temperature if we add a certain heat flux in so many watts per square meter across the planet. Heat flux (Iextra) will have completely different effects on one square meter of ocean, one square meter of desert, one square meter of puddles, one square meter of rock or one square meter of grass. Perhaps with our encyclopedic knowledge of the materials per square meter of our planet’s surface, we could use a supercomputer to figure it out, but that’s basically a chore. .
Solution: Ask an answerable question
Turn that difficult question around and ask: “If the temperature is increased by an amount (∆BILLION), more heat is released (∆I) does it radiate? Stefan-Boltzmann’s law provides a clear answer, and does so with a slide rule instead of a supercomputer. (NB: If you include emitters, the numbers vary slightly, but not enough to balance the Climate Constraint Formula in Lesson 4.)
The goal of the IPCC (aside from scaring the public) is to identify ECSEquilibrium climate sensitivity, which is the increase in surface temperature (∆BILLIONsurfing) due to a doubling of CO2 concentrations. Of course, they are free to speculate, but they have an intellectual obligation to see if ECS meaningful. All they had to do was apply Stefan-Boltzmann’s law to increase their predicted temperature.
If they did, they would find that 16.4 W/m2 (for 3oC) the increase in radiant flux strongly contradicts the 3.71 W/m2 of “radiant force” their models say causes it 3oC increase in temperature. They are free to give an explanation, but they must first apply Stefan-Boltzmann’s law to ECS. Maybe in a few decades, the IPCC will make this discovery.
Howard “Cork” Hayden, Emeritus Professor of Physics, UConn, [email protected]
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