Earth’s atmosphere has a mass of 5.146e18 Kg. This is not controversial.

The Anthropogenic Global Warming (AGW) theory postulates that interactions between Long Wave Infrared Radiation (LWIR) in the 15 micron wavelength and CO2 molecules in the atmosphere “traps” outgoing LWIR and that a doubling of CO2 levels (from 300 ppm to 600 ppm) “traps” approximately 3.7 watts per square meter of energy in the atmosphere over Earth’s surface (with some estimates as high as 4.7 watts per square meter but most of that occurring the upper atmosphere which, even if warmed, cannot cause a rise in temperature of an already warmer atmosphere below).

NASA says the increase in CO2 over the 15 years between 2003 and 2018 years added 0.5 watts per square meter to “radiative forcing”, a term used to describe the imbalance between energy received from the Sun and energy escaping to space. In that 15 year period, CO2 concentrations in the atmosphere rose from 374 ppm to 399 parts per million. The NASA estimates are just part of a concentrated effort to blame CO2 for “climate change”. There are better estimates that deal with “radiative forcing” across a larger range of increases in CO2 concentrations.

The American Chemical Society (ACS) has published an “atmospheric toolkit” to allow students to study radiative forcing. ACS estimates that a doubling of CO2 levels from 280 ppm (the 1750 level) and 560 ppm (about 70 years from now at the current rate of fossil fuel emissions which contribute to the increases in CO2 levels of about 2 ppm per year as measured at Mauna Loa) would be to add 3.53 watts per meter squared of the so-called “radiative forcing”. MODTRAN models show 2.95 watts per meter squared which is in the same ballpark. I will be conservative and use the 3.53 watts per meter squared figure.

The surface of the Earth has an area of 510 millon square kilometers.

Anyone who has even a basic understading of physics knows that a watt is equal to one joule per second of energy, and that the specific heat capacity of Earth’s atmosphere is 1,004 joules per kilogram. Specific heat capacity is the amount of energy needed to raise 1 kg of any particular matter by 1 deg. C.

So lets do the math.

The mass of atmosphere over one square meter of Earth’s surface is equal to 5.146e18 Kg divided by 510e12 square meters or 10,090 Kg.

3.53 watts per meter squared is equal to 3.53 x 24 hours per day x 60 minutes per hour x 60 seconds per minute = 304,992 joules per meter squared per day. The “per day” figure is used since any temperature equilibrium must recognize the daily rotation of the Earth which warms during sunlight and cools during darkness and AGW theory is premised on equilibrium, albeit at a higher temperature than prevailed at lower CO2 concentrations. At a stable CO2 concentration, no increase in global average temperature occurs according to the AGW theory, although doubtless there will be changes resulting from Earth’s relationship to the sun and the sun’s own activity, unrelated to CO2 levels.

The number of joules per meter squared per day needed to heat 10,090 kg of atmosphere by 1 deg. C and keep it at that temperature is 10,090 x 1,004 = 10,130,360 whereas the “radiative forcing” provides only 304,992 joules per square meter per day.

The radiative forcing of 3.53 watts per meter squared is enough energy to raise the temperature of the atmosphere over 1 square meter of Earth’s surface by 304,992/10,130,360 = .03 degrees C. If the 4.73 watts per meter squared estimate described earlier were correct, that increase would rise to .04 degrees C.

Not surprisingly, renowned climate scientists came to the same conclusion, like the late Bill Gray who assumed CO2 levels would rise sufficiently to block 3.7 watts per meter squared of LWIR by 2100 (an effective doubling of CO2 levels from the date of his paper). He also calculated that would result in “warming” of 0.3 degrees Celsius (see note at bottom of chart below).

I don’t know about you, but I don’t find that “alarming” enough to destroy our oil & gas industry or “transition” to costly and unreliable “renewable” sources of energy.

You can check this math yourself, and do your own experiment to find the watts of energy needed to heat one Kg of water by 1 deg. C and keep it that warm. HINT: The specific heat capacity of water is 4,182 joules per Kg and the energy must be continuously applied to maintain the added warmth. If the energy to your kettle is not applied continuously, your hot water will soon cool.

That's the atmosphere

Now add in the Oceans

Michael--always appreciate the clarity of your thinking and willingness to contribute constructively to public discourse on various subjects.

In this case, however, I'm not sure simplification of the state of our understanding to this degree (sorry) is a helpful contribution.

An analogy: Knowing the specific heat capacity of down and mass of it in your sleeping bag does not lead to even a crude way of modelling the 'temperature rating' users are interested in. The thermodynamics of insulation are dominated by microconvection of air in within the down--a simplification that sets aside convection commits a gross mischaracterization.

In your treatment, modelling the air as a monolithic heat sync ignores crucial evaporative and radiative dynamics. In fact, the thrust of the article you are relying on is to argue that those factors are being overlooked by conventional climate change analyses:

"Therefore, greenhouse gases are indeed playing an important role in altering the globe’s climate, but they are doing so primarily by increasing the speed of the hydrologic cycle as opposed to increasing global temperature."

As to Gray's article, it deserves more scrutiny than you may have given it. It is work published posthumously by friends/relatives without of professional/institutional review. He was working on it a decade after leaving the academy (where his primary interest and achievements were in tropical storms, not climate or atmospheric science per se) and published by the Global Warming Policy Foundation. I'm being generous to say that this is not an ideologically disinterested organization.

In his later career, Gray's efforts to shoehorn global warming skepticism into his storm system/cycle research agenda was rebuffed by his own colleagues; his funding requests on climate change were repeatedly denied for failing to meet standards of objectivity and rigor. (The onus is on anyone who would accuse those reviewers as being 'brainwashed stooges of the mainstream agenda' of providing at least provisional evidence of such prejudice. Denial of Gray's proposals, alone, isn't that evidence; routine rejection of theoretically flawed/methodologically faulty research is how science works, by forcing researchers to reconcile their new discoveries/theories to previous findings. E.g., Einstein had to reconcile the predictive model of Special Relativity to the prior validation of Newtonian mechanics.)

I readily admit I am no kind of expert in this subject; I haven't any professional training in even an 'adjacent' branch of science, math or engineering. Like you, though, Michael, I have sufficient educational foundation, intellectual capacity and stubborn independence (some might say arrogance) to presume that the subject is accessible to me. Certainly, in this day and age, the materials are readily at hand. The challenge that public knowledge has always posed for autodidacts is we are left to our own devices with regard to curation. Bootstrapping presents a 'don't know what we don't know' conundrum.

My contribution, for what it's worth, is to recommend an impressive 'deep primer' on the relevant science assembled by at https://scienceofdoom.com/roadmap/. In my view, the author goes out of his way to eschew agenda-driven pseudoscience coming from all quarters. He is hardnosed about the science and cheeky about the politics surrounding it (starting with his naming of the site).

For my nickel, I find the dash of cynicism he brings to 'the debate' a refreshing palate cleanser we can all use.

Articles at 'Science of Doom' I found relevant to your article are:

"CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers" and, as background to that,

"The Earth’s Energy Budget – Part One"