The recent work titled “A Critical Review of Impacts of Greenhouse Gas Emissions on the U.S. Climate” by the Department of Energy-sponsored Climate Working Group including John Christy, Ph.D., Judith Curry, Ph.D., Steven Koonin, Ph.D., Ross McKitrick, Ph.D., Roy Spencer, Ph.D., has obviously stirred up the nest at National Science Foundation (NSF), a non-government organization founded around the time of Abraham Lincoln.  The nest’s response is conveniently advertised by the New York Times (NYT). This is expected and can be ignored. There is no substantive criticism by the NSF. This NYT advertisement and NSF puff follows other pieces such as the American Meteorological Association piece. Their funding is being rightly challenged.

As the late Charlie Kirk famously repeated to his crowds, “Go ahead and try to prove me wrong.”

Almost everything written here in my blog, as well as at https://climatecite.com/ and https://henryslaw.org/ about CO2 also applies to CH4, N2O and other trace gases.  CO2 and CH4 are just two of many trace gases in air and Henry’s Law applies to all of them.  “Trace” gas is defined as less than 1%.  CH4 is methane or natural gas. Henry’s Law applies to trace gases, and only the portion of the trace gas which is not reacted.  Henry’s Law, Fick’s Law, Ideal Gas Law, le Chatelier’s principle, Law of Mass Action all apply. 

CH4 concentration in air is much less than CO2.  Thus the amount of warming that can be attributed to CH4 is much less than CO2.  Only on a molecule-by-molecule comparison of CH4 and CO2 does methane contribute more “greenhouse” warming; that is a useless comparison since CH4 is so much less concentrated (far fewer molecules) than CO2 and that fact will remain the case in perpetuity as I will now explain, unless there is some huge astronomic or geotectonic event. In other words, the temporarily, relatively small perturbations in net atmospheric concentrations of trace gases like CO2, CH4, N2O which are caused by human emissions of those gases are statistically negligible within the overall net fluxes of those gases into and out of the atmosphere and are not subject to either positive or negative human interventions.  Also, the effects of these trace gases are negligible in comparison to the much larger effects of water vapor, water droplets and clouds. NSF, UN IPCC etc ignore water vapor, water and clouds and the sun and combinations of these two by contrived arguments as will be explained here by examining in detail the arguments of orthodox climatology today.

We could probably find examples of very large natural CH4 emission and absorption events which have occurred historically and then analyze them identically to our analyses of CO2 in the “Pinatubo study” Bromley & Tamarkin 2022.

The key point is that the net amounts of these trace gases contributed by humans are statistically irrelevant and negligible with regard to the net flux of those gases into and out of the atmosphere and with regard to variations (i.e., derivatives with respect to time) in those net fluxes.  Net flux is defined by Fick’s law.  (Flux is not the same as flow or flow rate.) It follows and can be shown that the radiative emissions and warming due to human-contributed trace gases is statistically irrelevant and negligible.  When trends over time have been examined by many scientists competent in statistics, then the statistical signal of the trend (also perturbations in the trend) due to the human-contributed gases cannot be distinguished from random noise signals among the variations in the much larger natural fluxes of the trace gases.

NSF, IPCC, etc disingenuously argue the case for human-caused global warming/climate change by artificially defining warming/climate change due to atmospheric water vapor,  water and clouds as feedback rather than as a direct cause. At the same time, the trace gases CO2, CH4, N2O etc are considered direct causes of global warming/climate change and then by this creative hypothesis the warming created by these trace gases increases the warming effect of water vapor, etc.  It is disingenuous because their unscientific method of ignoring the ‘elephant in the room’ and their political objective have always been to find examples (polar bears, ice melting, social justice, etc.) and attribute these as evidence of warming and climate change to humans without ever demonstrating a causal connection. And they know that. Rather than to objectively study all causes of warming and climate changes, theirs is a sin of omission.  They do the same with the sun, absurdly demoting the sun to less than human-produced CO2 as a cause of warming and climate change.   It is politics rather than science.  They want grant dollars to flow.

We can expect NSF, IPCC, etc to ignore us and people like us as they always have because their arguments and publications are a source and often the major source of their funding and egos. If skeptics are mentioned at all (including people like Fred Singer, Willie Soon, Judith Curry, Roy Spencer, Dick Lindzen, Will Happer, Clintel, and many others far more well know than us, it is via ad hominem attack and appeal to authority and consensus and other logical fallacies.  Global warming proponents believe and have said that they own the science, believe being the key concept.  It is a cult.

Now, with that lengthy introduction, I will describe first how trivial CH4 is and why from an orthodox prospective.  Just keep in mind that the same study we did with CO2 and Mauna Loa data around the period of the Pinatubo eruption, as well as the two CO2 experiments that I have suggested which we can prepare and present to judges, juries and scientists can also be done for CH4, N2O and the other trace gases.  The scientific principles are the same for all of the trace gases.  As Clint Eastwood popularized talking to criminals, “Go ahead, make my day“.

CH₄ (hereinafter CH4 for simplicity in typing) emitted from Earth’s surface—primarily from wetlands (soil and plants), livestock (animals), rice paddies, and natural gas/oil operations, with smaller contributions from humans and oceans—oxidizes in the atmosphere to carbon dioxide (CO₂) and water vapor (H₂O).  I would guess that less than 1 in 100,000 people realize that simple chemistry fact.  This conversion from CH4 to CO2 occurs mainly via gas-phase reactions in the troposphere, driven by hydroxyl radicals (OH), which are abundant due to sunlight-driven photolysis of ozone and water vapor (detailed below). The process is gradual, with CH4’s atmospheric lifetime around 9–12 years, per IPCC AR6 (2021) and NASA data.  Also another though smaller amount of the CH4 emission total is continuously converted to CO2 via a chlorine-catalyzed reaction immediately over seawater surface.  

Dominant Reactions and Stoichiometry:

The primary but continuous reaction pathway from CH4 to CO2 is initiated by abstraction (pulling away) of a hydrogen atom by OH, followed by a chain of reactions producing CO₂. Here’s the simplified sequence (full mechanism involves intermediates like methylperoxy radicals, CH₃O₂, and formaldehyde, CH₂O, but the net stoichiometry is shown):

• Initiation (rate-limiting step):
  CH₄ + OH → CH₃ + H₂O
  (This occurs ~80–90% of the time; the rest is minor attack by reaction with Cl atoms in marine boundary layers, 70% of Earth’s surface.)
• Propagation and oxidation chain:
  CH₃ + O₂ → CH₃O₂ (methylperoxy radical)
  CH₃O₂ + NO → CH₃O + NO₂
  CH₃O + O₂ → HO₂ + HCHO (formaldehyde)
  HCHO + OH → HCO + H₂O
  HCO + O₂ → HO₂ + CO
  CO + OH → CO₂ + H (which quickly forms H₂O via other steps)

Net stoichiometry:
CH₄ + 2O₂ → CO₂ + 2H₂O
(This balances: 1C, 4H, 4O on left; 1C, 4H, 4O on right. NOx radicals like NO catalyze the cycle without net consumption.) Other minor sinks include soil microbial uptake (10–30 Tg/yr) and stratospheric oxidation (5%), but tropospheric OH dominates, removing ~500–600 Tg CH₄/yr globally (per EDGAR v8.0 and NOAA data, 2023).

All of the above is standard atmospheric chemistry.

Processes Maintaining Low Atmospheric CH₄ Concentrations:

Despite massive CH4 emissions (~570 Tg/yr from sources like wetlands ~40%, agriculture ~40%, fossil fuels ~20%, per Global Carbon Project 2023), atmospheric CH₄ remains low at ~1.9 ppm (1,920 ppb as of 2024, per NOAA ESRL). This is due to efficient atmospheric oxidation by OH radicals as detailed above, which act as the “detergent” of the troposphere. OH concentration is ~10⁶–10⁷ molecules/cm³, sustained by UV photolysis: O₃ + hν → O(¹D) + O₂, then O(¹D) + H₂O → 2OH. [See footnote (1) below if needed for spectroscopy nomenclature e.g. O(¹D)]  The extremely low and persistent concentration of CH4 is also due to Henry’s Law, but orthodox climatology sources are not likely to ever admit this point because it enables their arguments to be defeated.

According to orthodox climatology, CH4 emissions have risen ~150% since pre-industrial levels due to human activity, but the atmospheric OH sink (as explained above) scales with CH4 (negative feedback) and keeps steady-state CH4 levels low, or so goes their argument. Without this, CH4 would equilibrate at a much higher amount, per modeling in Atmospheric Chemistry and Physics (2022).  Again, this orthodox explanation ignores Henry’s Law and the established facts that:

(a) the Earth’s surface has warmed since the end of the Ice Age (~10,000 years ago) and the end of the Little Ice Age (~1850), and

b) those warming trends cause increased net atmospheric concentrations (i.e. net emissions minus net absorptions) of all trace gases by reducing solubility of those trace gases in all liquids.

Estimate of Infrared Light Absorbed by Atmospheric CH₄ :

Earth’s upwelling infrared (IR) flux at the surface is ~390 W/m² (blackbody at 288 K, per Trenberth et al., 2014 diagram, updated in 2023). Atmospheric CH4 absorbs primarily in the 7.7 µm ν₄ band (strong) and weaker 3.3 µm and 6.5 µm bands, overlapping with H₂O and CO₂ but distinct enough for ~20–30% of its total “forcing” by their models.

• Total absorption by CH4: 0.5–0.6 W/m² instantaneous (direct radiative forcing, per Myhre et al., 2013, and IPCC AR6). This is ~0.13–0.15% of surface upwelling IR.
  
• Derivation: CH4’s absorption cross-section integrates to ~10–15% of the 7–8 µm window flux (30–40 W/m² escaping to space without absorbers), scaled by mixing ratio (~1.9 ppm) and vertical profile (concentrated in troposphere). Line-by-line models (HITRAN database) confirm this for clear-sky conditions.

Residence Time of Absorbed Energy in a CH₄ Molecule:

A CH4 molecule absorbs an IR photon in ~10⁻¹⁰ to 10⁻⁹ s (inverse of Einstein A coefficient for vibrational bands, ~10⁸–10⁹ s⁻¹). It then undergoes intramolecular vibrational relaxation (IVR), redistributing energy to other modes in ~10⁻¹² to 10⁻¹¹ s, followed by collisional deactivation with air molecules (dominantly N₂ and O₂) in ~1–10 ns (10⁻⁹ to 10⁻⁸ s) at 1 atm pressure. Re-emission as a photon is negligible (<1%) due to rapid collisions; instead, energy thermalizes, randomly heating the local air parcel. Net “hold time” before effective re-radiation (by the warmed atmosphere) is thus ~10⁻⁹ s per molecule, per quantum chemistry simulations in Journal of Chemical Physics (2020) and HITRAN documentation.

Comparison of Energies:

CH4’s IR absorption is tiny compared to Earth surface’s total IR emission or to solar IR input (at higher frequency), but its potency as a greenhouse gas stems from spectral overlap in IR windows with water vapor and CO2, as mentioned, “trapping” heat efficiently on a per molecule basis (GWP 28–34 over 100 years). Proponents claim total greenhouse “trapping” is ~150–160 W/m², with CH4 contributing ~0.5 W/m² directly, i.e., CH4 contributing only 0.33% of the proponent’s orthodox claim of total greenhouse trapping. Despite their own data, climate alarmists insist people of the Earth should fear CH4/methane/natural gas as part of an existential climate crisis.

How do orthodox proponents claim “trapping” works?

At sea-level pressure (~1 atm, 10¹⁹ molecules/cm³), the mean free path for collisions is only ~0.06 µm (60 nm), but each molecule is isolated in a ~10 nm “space” (cubic root of 1/density), surrounded by ~99.999% empty volume. This doesn’t prevent rapid energy sharing; it’s the collisions that matter.

I will break down the concept of “thermalization” physically, step by step, in the context of a CH4 molecule absorbing IR and then interacting with N₂ or O₂. 

What Happens Physically During Absorption and Deactivation:

1. Absorption: A CH₄ molecule absorbs an IR photon (e.g., in the 7.7 µm ν₄ bending mode), exciting a vibrational state. This adds 0.16 eV (2,500 K equivalent temperature) of energy to that bond, but the molecule as a whole remains translationally cool—it’s now “hot” internally with internal vibrations.
2. Intramolecular Redistribution (IVR): Within ~10⁻¹² s (picoseconds), the excess vibrational energy spreads across all 3N-6=9 vibrational modes of CH₄ via quantum mechanical coupling (anharmonicities in the potential energy surface). No collisions needed yet; this is like internal sloshing of waves or vibrations inside a molecule. The molecule’s average vibrational temperature rises, but it’s still isolated momentarily by empty space from other molecules.
3. Collisional Deactivation (Thermalization): Here’s where the major air gases N₂ and O₂ come in. The excited CH₄ molecule collides with a nearby N₂ or O₂ molecule (collision rate 10⁹ s⁻¹ at 1 atm, or every ~1 ns). During the brief contact (10⁻¹³ s, governed by Lennard-Jones potential), energy transfers via:
   • Vibrational-to-Translational (V-T) Coupling: Part of the vibrational energy converts to kinetic energy (translation) of the CH₄ and/or N₂. This is inelastic scattering—molecules bounce with slightly different speeds.
   • Resonant Energy Transfer (V-V): If energies match (e.g., CH₄’s ν₃ mode ~3,000 cm⁻¹ overlaps with N₂’s, but less so here), vibrations swap between molecules.
   • I will not cover “imperfect” (off axis) collisions which are the most common.  I am presenting the best orthodox case here.

Outcome: The “hot” vibrational energy in CH4 is diluted into translational kinetic energy across the colliding pair of CH4 and an air molecule like N2 or O2. Per the equipartition theorem, this kinetic energy represents random, isotropic motion (heat, as opposed to radiation) statistically distributed over all translational and rotational degrees of freedom in the local gas parcel.

What “Thermalizes” Means Precisely:

In physical terms, “thermalization” is the irreversible conversion of a photon’s directed, coherent energy (vibrational excitation in one molecule) into random thermal motion of the gas molecules—specifically, increased translational kinetic energy that equilibrates to the local temperature via the ideal gas law (½mv² = 3/2 kT). [See footnote 2 re version of Ideal Gas Law] It’s not re-emission or radiative emission of a photon, instead:

• The air parcel (thousands of molecules in a 1 µm³ otherwise empty volume) warms by a tiny fraction (10⁻⁶ K per absorption event) by collisions.
• This heat diffuses via subsequent collisions, maintaining the Maxwell-Boltzmann velocity distribution.

Quantum mechanically, it’s described by Fermi’s Golden Rule for transition rates, with cross-sections 10⁻¹⁶ cm² for V-T processes (from molecular dynamics simulations, e.g., in J. Chem. Phys. 2018). In the sparse atmosphere (99.99% empty space around air molecules), collisions are frequent enough to quench radiative emission from the gas molecule before radiative decay (ms timescale). This thermalization process (i.e., collisions rather than radiative emissions) is why greenhouse gases like CH4 warm the atmosphere ever so slightly rather than just reflecting IR. That is, according to their AGW proponents’ arguments, energy gets trapped as thermalized heat delaying escape of that heat to space. If collisions were rarer (e.g., upper atmosphere), more re-emission would occur, cooling the parcel.

The high school science student might ask here why air temperature in the desert typically drops rapidly after sunset compared to the air temperature on a tropical island? After all the CO2 and other trace gases are about the same concentration day and night in desert or on oceanic island. But water vapor, water droplets and cloud prevalence are usually very different above deserts and oceanic islands, thus cooling at night by radiation from Earth’s surface are very different in deserts compared to oceanic islands. Is the NSF smarter than a high school student?

It is important to understand the definition of “forcing” in orthodox climatology.  Radiative forcing (usually just called “forcing”) refers to the change in the balance of incoming versus outgoing radiation in Earth’s atmosphere-radiation system caused by a specific factor, such as a “greenhouse” gas like CH4. It’s measured in watts per square meter (W/m²) and quantifies how much that factor perturbs the planet’s energy budget—typically by “trapping” additional outgoing infrared (IR) radiation that would otherwise escape to space.  This is a computer modelled algorithm supporting another computer modelled algorithm to support the orthodox argument (originally expressed by former NASA GISS administrator James Hanson if I recall) that water vapor, water drops and clouds in atmosphere do not directly cause warming but are instead feedback which has been forced by increases in “greenhouse” gases like CO2.  This contrivance enables AGW proponents to eliminate water vapor, water droplets, clouds from the list of greenhouse gases, though they are the largest contributor by more than ten times. The trace “greenhouse gases” such as CO2, CH4, N2O by this contrivance are rendered statistically significant, the dominant variables. The water components are ignored. Thus human contributions to net greenhouse gases become statistically significant in their hypothesis, when in fact they are scientifically, statistically insignificant and indistinguishable from noise.  

Key Aspects:

• Instantaneous Forcing: The direct absorption of upwelling IR by the gas (e.g., CH4’s bands at 7.7 µm, etc.), without accounting for rapid atmospheric adjustments like temperature changes.
• Effective Radiative Forcing (ERF): A more comprehensive metric that includes quick feedbacks, like stratospheric cooling, but still isolates the gas’s net impact.
• Positive vs. Negative: Positive forcing (like from CH₄) warms the planet by reducing outgoing longwave radiation; it’s the driver behind concepts like global warming potential (GWP).

In the orthodox statement above: “20–30% of its forcing” means that the distinct portions of CH₄’s absorption spectrum (i.e., not overlapped by H₂O or CO₂) account for about a fifth to a third of CH₄’s total radiative forcing contribution (0.5 W/m² globally). The rest comes from overlapped regions, where CH₄ adds incrementally to the absorption already dominated by other gases. This is derived from line-by-line radiative transfer models (e.g., HITRAN database) used in IPCC assessments, ensuring we don’t double-count spectral saturation.

In orthodox climate science, “net warming” is quantified via a contrived concept called effective radiative forcing (ERF), the perturbation to Earth’s top-of-atmosphere energy balance (in W/m²) that drives surface and atmospheric temperature changes. Positive ERF inevitably leads to net warming of the system (surface ~70–80%, atmosphere ~20–30%, per energy budget models like Trenberth et al., 2014).  Climate is not measured or experienced at the top of the atmosphere!

Key Distinctions (following orthodox climatology):

• Insolation: Natural variations (e.g., 11-year solar cycles) contribute negligible ERF (0.05 W/m² max since 1750). Baseline insolation (340 W/m² at TOA) enables the greenhouse effect but isn’t a “forcing” perturbation.
• Water vapor: Not a forcing agent; it’s a feedback amplifying CO₂/CH₄ effects by ~50–100% (IPCC AR6). Included here as a natural amplifier.
• CO₂ and CH₄ from all sources: Total atmospheric concentrations drive ERF, but natural emissions alone would maintain pre-industrial levels (no net change, ERF ≈ 0). The observed ERF is due to the full concentration, where human additions dominate the increase.
• CO₂ and CH₄ from human sources: ERF from anthropogenic concentration increases (nearly 100% of current forcing for these gases).

ERF Breakdown (1750–2019, per IPCC AR6 Ch. 7)

• The ratio of net warming is approximately 1.18:1 (or 118%). This reflects that:
• Human CO₂/CH₄ account for ~85% of total GHG ERF.
• Natural factors (insolation variability, water vapor feedback) contribute the remaining ~15% amplification. 
• If interpreting “all sources” as total system forcing (including feedbacks), the ratio rises to ~1.5:1, as water vapor doubles the direct GHG effect in equilibrium warming.

This above is the orthodox perturbation-based estimate; absolute natural fluxes (e.g., ~750 GtC/yr CO₂ cycle) balance without net warming, per carbon cycle analyses. Uncertainties: ±20% on individual ERFs, but ratio robust (high confidence, per IPCC AR6).

I hope you can see from this long explanation of the orthodoxy how proponents created an argument for their hypothesis by removing water vapor, water and clouds from the list of greenhouse gases (even though it is the dominant greenhouse gas). Thereby they have promoted the trace gases artificially into the position of the primary causes (in their minds, but falsely) of global warming/climate change.  By removing water vapor, water drops, clouds they conveniently and hugely diminish the role of the sun’s insolation at the surface and the huge variability in insolation at the surface due to water vapor (humidity), clouds and rain. 

Nevertheless, AGW proponents like NSF and UN IPCC fail empirical scientific experiments. Estimated trends of these trace gases which are produced by humans, (used extensively in their models, for example data from CDIAC/Oak Ridge Laboratories compiled of estimated CO2 emissions due to estimated fossil fuel use) are not correlated with the diligently measured trends of those same gases by NOAA GML labs such as Mauna Loa.  This absence of correlation is shown in the works of Demetris Koutsoyiannis, Jamal Munshi, and others. 

This is absolutely critical: 

As we know, correlation does not prove that a causal relationship exists between two variables or trends.  However, if a causal relationship is claimed to exist, as claimed by AGW proponents, then a positive correlation must exist between the two trends if the claim is true.  This positive correlation does not exist in the observed empirical experimental data. Experiments override theory. As renowned physicist Feynman said (approximately), ‘if it does not agree with experiment, it is wrong.’ As far as I know, there are no exceptions to either examples of this logic.  This is key to defeating the NSF arguments.  The technical arguments above are for your understanding and probably will never be discussed. They would only be ignored by the NSF.  It is this logic based on empirical evidence and the experiments they cannot ignore!

Here is a second experiment for judge, jury and scientists:  https://budbromley.blog/2025/09/12/second-thought-experiment-on-co2-with-grok/

For avoidance of doubt about the general applicability of Henry’s Law to all trace unreacted gases, here is the page on the website of the National Institute of Standards and Technology of the U.S. Department of Commerce (NIST) which details Henry’s Law applied to N2O (nitrous oxide) which is more rare in atmosphere than CH4 which is yet again more rare than CO2.  https://webbook.nist.gov/cgi/cbook.cgi?ID=C10024972&Mask=10#Solubility  

Henry’s Law, Fick’s Law, Ideal Gas law, etc. apply to all trace gases, not only CO2.  Henry’s Law, Fick’s Law etc are not mysterious or unknown, they are used professionally by thousands of scientists in their daily routines, but these laws are generally ignored in orthodox climatology which is mostly computer modelling.

Footnotes:

1. Footnote: Explanation of Nomenclature in the Photolysis Reactions

Molecular spectroscopy nomenclature: specifically describing electronic states during photochemical reactions in the atmosphere. These reactions are key to producing hydroxyl radicals (OH), which oxidize CH₄ as discussed earlier. Breaking it down step by step, focusing on O(¹D) and the context.

A. The Reaction Sequence

• First step: O₃ + hν → O(¹D) + O₂
  This is the photolysis (UV light-driven dissociation) of ozone (O₃). Here, hν represents a photon of ultraviolet (UV) light with energy hν (Planck’s constant × frequency, typically ~300–310 nm wavelength for this branch).

• Second step: O(¹D) + H₂O → 2OH
  The excited oxygen atom reacts with water vapor to form two OH radicals. This is a fast, exothermic reaction (~200 kJ/mol release).
• Together, they form the core of the “OH production cycle” in the troposphere, initiated by solar UV.2. Breaking Down O(¹D)

• O: This denotes a single oxygen atom (neutral, not O₂ or O₃). Oxygen atoms are transient intermediates in atmospheric chemistry.
• (¹D): This is the spectroscopic symbol for the atom’s electronic state. It specifies the atom’s energy configuration:
  • Superscript 1: Indicates singlet multiplicity (2S+1 = 1, so S=0). This means the atom’s total electron spin is zero—all electrons are paired (no unpaired spins). Singlets are often “forbidden” or higher-energy states compared to triplets.
  • Subscript D: Refers to the orbital angular momentum quantum number L=2 (D for the D subshell in atomic physics, like d-orbitals). Combined with spin, it describes the total angular momentum J via the Russell-Saunders coupling scheme: J = L + S, but for light atoms like oxygen, we often just use ²S+1L_J (here, it’s ground-state derived but excited).
• In simpler terms: O(¹D) is the first electronically excited state of the oxygen atom, 1.97 eV (190 kJ/mol) above the ground state O(³P). It’s highly reactive because the excitation puts an electron in a higher orbital, making it prone to insertion reactions (like with H₂O to break bonds and form OH).3. Why This Notation Matters Physically

• Ground vs. Excited States: Oxygen’s ground state is O(³P) (triplet, S=1, L=1), which is lower energy and less reactive—it mostly recombines or reacts slowly. O(¹D) is produced specifically by UV photolysis of O₃ in the Hartley band (200–310 nm), where the energy splits O₃ into O₂ (ground state, ³Σ_g^-) + O(¹D).
• Quantum Selection Rules: The transition to O(¹D) is allowed because the photon’s spin doesn’t flip electrons oddly. Once formed, O(¹D) has a short lifetime (~10⁻⁷ s in air) before quenching (colliding with N₂/O₂ to relax to O(³P)) or reacting.
• Notation Conventions:
  • For atoms: ²S+1L (e.g., O(³P), O(¹D), O(¹S) for higher states).
  • For molecules: Similar but with Greek letters for L (Σ, Π, Δ) and +/− for reflection symmetry (e.g., O₂(³Σ_g^-)).
  • This follows the Hund’s coupling cases in quantum chemistry, standardized in databases like NIST Atomic Spectra.

B. Broader Context

• In the atmosphere, only 10–20% of O₃ photolysis yields O(¹D) (the rest produces O(³P)); the rest quenches quickly, but enough reacts with H₂O (1–2% of air) to sustain [OH] ~10⁶ molecules/cm³ daytime. Rate constants: k(O(¹D)+H₂O) ~2×10⁻¹⁰ cm³/s (JPL/NASA kinetics, 2023). If it were O(³P), the reaction with H₂O wouldn’t occur efficiently. This nomenclature ensures precise tracking of energy levels in models like MCM (Master Chemical Mechanism). For deeper dives, see Herzberg’s Atomic Spectra and Atomic Structure or HITRAN for transition data.

2. Footnote:  Equivalent Forms of the Ideal Gas Law

The expression ½mv² = 3/2 kT is the kinetic theory derivation of the ideal gas law for translational motion in 3D—it equates the average kinetic energy per molecule (½mv², where m is molecular mass, v is root-mean-square speed) to 3/2 kT (3 degrees of freedom × ½kT each, with k = Boltzmann’s constant, T = temperature). This is microscopic and specific to monatomic gases, but it extends to polyatomics via equipartition.More Commonly Used Macroscopic Equivalents.  The standard ideal gas law is the most familiar and ubiquitous form, used in engineering, meteorology, chemistry and thermodynamics. Here are its primary equivalents, all interconvertible:

• PV = nRT (most common textbook/engineering form)
• P: Pressure (e.g., Pa or atm)
• V: Volume (e.g., m³ or L)
• n: Moles of gas
• R: Universal gas constant (8.314 J/mol·K)
• T: Temperature (K)
  Usage: Predicts behavior for bulk gases, like air parcels in the atmosphere.
• PV = NkT (statistical mechanics/atmospheric physics form)
• N: Number of molecules (Avogadro’s number × n)
• k: Boltzmann’s constant (1.381 × 10⁻²³ J/K)
  Usage: Bridges micro (your original equation) to macro; common in kinetic theory discussions.
• P = ρ (kT / m) or P = ρ R_specific T (density-based, for fluids/gases)
• ρ: Density (kg/m³)
• R_specific: Specific gas constant (R / molar mass, e.g., 287 J/kg·K for dry air)
  Usage: Hydrostatics in atmospheres, e.g., pressure scale height H = R_specific T / g.
• Quick Conversion ExampleFor 1 mole of ideal gas at 300 K and 1 atm:
• From ½mv² = 3/2 kT → average KE = 3/2 RT = ~3.74 kJ/mol.
• PV = nRT → V = (1 mol × 8.314 × 300) / 101325 Pa ≈ 0.0246 m³ (matches van der Waals corrections for real gases).
• These are all equivalent under ideal assumptions (no interactions, point particles). For real atmospheric gases like N₂ and O₂, the kinetic form holds well at room T/P, but macroscopic PV=nRT is far more practical for calculations.

References in addition to those listed above in the text.

Grok AiX. September 19, 2025

Compilation of Henry’s law constants (version 5.0.0) for water as solvent By Rolf Sander, PhD. Air Chemistry Department, Max Planck Institute of Chemistry, P.O. Box 3060, 55020 Mainz, Germany. Published: 6 October 2023.  http://www.henrys-law.org

Stumm, Werner, 1996. Aquatic Chemistry.   https://archive.org/details/aquaticchemistry0000stum/page/192/mode/2up)

Satellite and Climate Model Evidence Against Substantial Manmade Climate Change, by Roy W. Spencer, Ph.D. December 27, 2008 (last modified December 29, 2008) https://www.drroyspencer.com/research-articles/satellite-and-climate-model-evidence/