I was asked, “The last paper mentions the Mauna Loa measurements of CO2 and the fact that the net CO2 is about 5.5%. How do you define that this is net CO2, emissions. e.g., extra above the normal or usual one? And can you link this extra to anything? How the AGW (anthropogenic global warming) people link it to fossil fuel? Just because they model it?

The papers referenced are here:

The word “net” comes from the concept of net flux.  Net flux of CO₂ in this case describes the net amount of CO₂ which moves through a defined amount of surface area in a defined direction in a defined amount of time.  Flux is a vector directional unit.  In the case of CO₂ for the specified surface area during a specified period of time,

• Where E is the sum of all CO₂ gas diffusing in a vector direction out of earth’s surface into atmosphere from all CO₂ sources human and natural, 
• Where A is the sum of all CO₂ gas diffusing in the opposite vector direction (that is, diffusing from air into earth’s surface) by all CO₂ sinks human and natural,
• Then CO₂ net flux is E minus A

Net flux can be expressed in several different units, for example:

• Moles of CO₂ diffused per square mile per year
• Gigatonnes of CO₂ diffused per square mile per year
• Liters of CO₂ diffused per square meter per hour

Fick’s First Law describes the diffusive flux (the rate at which particles or molecules move due to diffusion) as proportional to the negative gradient of the concentration. It is the fundamental equation for the diffusive component of net flux in many contexts, including gas transport like CO₂ through porous media (e.g., soil to atmosphere) or across interfaces (e.g., air-sea).

For CO₂ specifically:

• In soil respiration or soil-to-atmosphere studies, the net CO₂ flux (often upward/out of soil) is frequently calculated using this law applied to measured vertical profiles of soil CO₂ concentration.
• Flux = -Dₛ × (ΔC / Δz), where Dₛ is the effective soil gas diffusion coefficient (accounting for soil porosity, tortuosity, and water content), and ΔC/Δz is the concentration gradient between soil depths and the surface/atmosphere.
• The negative sign means that if soil CO₂ concentration is higher than atmospheric (typical case), flux is positive upward (emission/net outflux from surface).

This describes purely diffusive transport. In real systems (e.g., ocean-atmosphere or soil-atmosphere CO₂ exchange), the total net flux may include additional terms like advection, turbulence, piston velocity (for air-sea), or biological/chemical production/consumption. However, Fick’s First Law provides the core diffusive algorithm for the concentration-driven component.  Where net flux = E – A (emissions minus absorptions over a unit of surface area in a unit of time), Fick’s law gives the diffusive mechanism by which E and A occur across the interface due to concentration differences. For example, if atmospheric CO₂ concentration exceeds surface/soil concentration, net diffusive flux would be downward (absorption dominant).

Henry’s Law informs that at phase state equilibrium for all trace (defined as <1% ) gas amounts which have not reacted with the liquid at flat or fixed surface temperature (that is, no change in surface temperature), then net flux (i.e., E minus A) will be the partition ratio known as the Henry’s Law constant for that surface temperature and for that specific combination of trace gas and liquid.  This does not mean E = A at equilibrium.  It means equilibrium results in a constant ratio of two fluxes for a specific surface temperature.

Henry’s Law derived for its temperature dependence is TH_K = c_aq/c_g, where

• T is temperature in Kelvin
• H_K is the Henry’s Law constant for the specific gas and liquid combination
• c_aq is the concentration of the unreacted trace gas in the liquid
• c_g is the concentration of the trace gas in the air or gas matrix above the liquid surface

Expressed in text form: A molar increase in concentration (or partial pressure) of the gas in atmosphere above the surface causes an offsetting increase in diffusion and absorbance (or solubility) and concentration (or partial pressure) of an equal amount the unreacted gas in the liquid surface until the Henry’s Law partition coefficient for the specified gas and liquid combination at the specified surface temperature is restored.  This assumes certain other conditions are constant or offsetting each other, for example, pH, alkalinity, salinity, winds and air and liquid currents. pH and alkalinity are partially offsetting, pH and salinity are partially offsetting.

Analogously, a molar increase in concentration (or partial pressure) of the gas in the liquid surface matrix causes an offsetting increase in diffusion (or emission) of that gas from the surface into atmosphere until the Henry’s Law partition coefficient for the specific gas and liquid combination at the specified surface temperature is restored.  This condition is commonly observed during El Ninos. 

It is critical to point out that more than 90% of CO₂ gas diffusing through the gas-liquid phase-state interface and entering the water matrix is hydrolyzed with water ions (i.e., becomes ionized), that is, the trace gas CO₂ has reacted with the liquid and is not a component to be considered in Henry’s Law coefficient.  The exact amount of CO₂ which is hydrolyzed to one of the ionic carbonate forms depends dominantly on water temperature.  The concentration (or partial pressure) of any non-ionized trace gas (e.g., aqueous CO₂ gas) in the liquid surface is inversely proportional to water temperature in the surface layer. Well known and true for all trace gases under normal conditions on Earth.

I remain skeptical of claims that 5.5% such as Veyres et al (or any specified percent) of CO₂ in atmosphere can be reliably attributed to humans (or to human burning of fossil fuels.)  Isotope ratio mass spectrometry is a very reliable technique.  However, the error and uncertainty are due to sampling not the measurement technique or instrumentation.  Sampling error rate is high in carbon, carbon isotopes or CO₂ in chaotically-mixed atmosphere. 

Net human CO₂ emission is total human CO₂ emission minus absorption of those human CO₂ emissions.  Unfortunately, we do not know with reasonable accuracy and precision the amount of net human CO₂ emission, it is not measured and only estimated or modelled.  Though media presents and many people may believe that NOAA Mauna Loa or some agencies is measuring total human CO₂ emissions, or measuring net human CO₂ emissions, or that the apparently rapidly increasing CONet human CO₂ emission is total human CO₂ emission minus absorption of those human CO₂ emissions.  Unfortunately, we do not know with reasonable accuracy and precision the amount of net human CO₂ emission, it is not measured and only estimated or modelled.  Though sloppy academics, media and many people believe that NOAA Mauna Loa or some agency is measuring total human CO₂ emissions, or measuring net human CO₂ emissions, or that the alleged rapidly increasing CO₂ trend shown ad nauseum in graphs meant to induce fear, represent human CO₂, none of that is true. Furthermore, neither do we know with reasonable accuracy and precision the amount of absorbed human CO₂.  In fact, we know neither the amount of human CO₂ emissions nor the amount of those human CO₂ emissions which are absorbed by the environment with reasonable scientific accuracy and precision; at best we have modeled estimates of estimates with high uncertainties.   

On the other hand, we do know with good accuracy and precision that annual net human emissions cannot exceed the annual increase in net CO₂, which is in recent years about 2.5 ppm per year measured at NOAA Mauna Loa.

CO₂ due to all sources minus all sinks (i.e., net CO₂) is sampled and measured routinely many times per day at Mauna Loa and is about 420 ppm; net annual increase is about 2.5 ppm. [To be clear, this is not net human CO₂ but net total CO₂ due to all CO₂ sources natural and human minus all CO₂ sinks natural and human]  Doing the arithmetic, then 2.5 ppm per year divided by 420 ppm reveals that the human proportion of the 420 ppm cannot exceed ~0.59% of net CO₂ measured at Manua Loa in that year (2020).   

Human-produced CO₂ does not additively accumulate in atmosphere; though that is how it is deceptively presented. Human-produced CO₂ and all other CO2₂ is being absorbed as it is being emitted to maintain the Henry’s Law phase-state dynamic equilibrium ratio for the local surface temperature.  No one is measuring how many times or what portion of human CO₂ is being re-cycled through the environment, that is, how many times is a human-produced CO₂ molecule repetitiously absorbed into the environment and re-emitted and in what amounts.  Human CO₂ emissions are continuously mixed with and then continuously absorbed and re-emitted along with two ~10 X larger fluxes of natural CO₂. E and A are not somehow discriminating between CO₂ molecules containing one carbon isotope or another.  The phase-state equilibrium is a pressure regime, not a isotope resolution molecular separation regime. Therefore, it is mistaken to use a highly sensitive measurement technique to analyze carbon isotope ratios and then infer from a few measurements that since CO₂ is a “well mixed gas in atmosphere” then atmosphere contains about 5.5% of human-produced CO₂.

Furthermore, as Professor Jamal Munshi’s several papers illustrate, [several can be found here on my blog by searching] as well as those of other scientists using multiple different methods, positive correlation is absent between the following two trends:

(1) the rate of change of estimated CO₂ emissions from estimated fossil fuels burned, which is a very common proxy for total human emissions [but not much >100 X smaller net human emissions] and,

(2) the rate of change of net CO₂ measured at NOAA Mauna Loa. 

The statistical signal of the largest anthropogenic source of CO₂ (i.e., estimated CO₂ from estimated fossil fuels burned by country and type of fuel) is not detectable in the trend of diligently measured net CO₂ at Mauna Loa.

Regardless of the CO₂ source, an increase in CO₂ concentration (or partial pressure) in atmosphere is offset by a proportional increase in absorption (or solubility) of CO₂ in all liquids which are in contact with the CO₂ until the partition ratio (i.e., the Henry’s Law constant) of CO₂ between atmosphere and liquid is restored for the local surface temperature.  If the partial pressure of CO₂ in atmosphere doubles, then twice as many CO₂ molecules will be colliding with the surface and twice as many will diffuse into the surface and be absorbed.  Within seconds, most (greater than 90%) of the CO₂ molecules which diffuse into the surface will be combined with water ions, thus removing those CO₂ molecules from the Henry’s Law ratio.

Again, it is a pressure regime, not a molecule-specific or isotope-specific regime.  The specific molecules which are emitted are not necessarily the same molecules which are absorbed in the partial pressure re-equilibration.  Any CO₂ molecule near a surface can be absorbed to affect re-equilibration, not necessarily the CO₂ which was emitted. The partial pressure increase is re-equilibrated to the partition ratio by absorption of any CO₂ gas molecule that happens to be near a liquid surface, any liquid surface.  This makes the measurement of carbon isotopes irrelevant and makes this 5.5% claimed human- CO₂-proportion of atmosphere also not relevant. 

Lastly, I agree with the theoretical explanation expressed in the paper Salby and Hardy-2022 (attached.)  However, I should point out an important correction that should be applied to confirmation of their theory with observations: 

Concentration of CO₂ in seawater is often expressed in scientific literature as micromoles of CO₂ gas per kilogram of seawater (µmol/kg), or elsewhere micromoles of CO₂ per liter of air, or some other unit of CO₂ per unit of volume like ppmv, or a ppm mass-based unit like µg/kg.  Salby and Hardy-2022 use ppmv, parts per million based on volume, as unfortunately do many other scientists.  These various forms of ppmv are correct in the general sense, but incorrect when used to compare with CO₂ gas measurements at NOAA Mauna Loa. Ppmv units are significantly different from the ppm units measured and reported by NOAA’s Global Monitoring Laboratory at Mauna Loa and these different units cannot converted with acceptable accuracy and precision because the amount of water vapor which was freeze-dried out of the air samples by the Mauna Loa lab is unknown, undocumented and highly variable. And, critically important, that variation dramatically changes the quantity of CO₂ in the measured air sample.  This measurement unit problem is apparently pervasive in climate and environmental studies.  For example, CO₂ in ice core samples are commonly measured wet and reported in ppmv, which is fine.  But then the problem comes when this is compared to NOAA Mauna Loa CO₂ measurement from freeze dried air samples, which are reported as micromoles of CO₂ per mole of freeze-dried air, that is, in a molar fraction measurement.  These two measurements and trends are not comparable and not convertible because there are reasonable estimates of the water vapor removed from the samples, nor of the variability of the water vapor in the samples.

NOAA’s Global Monitoring Laboratory at Mauna Loa measures and reports ppm as molar fraction for good scientific lab practice as explained in the following reference by Pieter Tans and Kirk Thoning. (2008).  In other words, the ppmv amounts in Salby & Harde 2022 and many science and media publication are not comparable with NOAA Mauna Loa ppm molar fraction units, and this difference in units cannot be reasonably converted.  This problem seems pervasive in climate and environmental literature.  If we are eventually funded to do the Henry’s Law experiment [https://budbromley.blog/2025/04/18/henrys-law-proof-experiment-for-judge-and-jury-and-scientist-with-grok-3-beta/] this difference will be critical for comparison with theoretical studies.

In the following paper published on NOAA’s website, Pieter Tans and Kirk Thoning (2008), explain how they measure CO₂ and provide a comparison of the difference between the amount of CO₂ when measured as normal “wet” samples compared to the amount of CO₂ when measured by their routine freeze-dried air sampling method, a method they have used for decades.  The difference is significant.  In their test reported in 2020, by their standard method of freeze-dried air, they measured net CO₂ at 413 ppm (micromoles of CO₂/mole of dried air) and they measured a normal wet sample at 400.6 ppm (micromoles of CO₂/mole of normal air).  The freeze-dried sample had 12.4 ppm more CO₂ than the normal wet air sample.  For 2020 versus 2019, the average annual increase NOAA measured in net CO₂ was 2.5 ppm.  Thus, NOAA’s dried sampling method results in 4.96 times higher CO₂ than the annual increase in CO₂.  Professor Harde may want to adjust his calculations to be more accurately comparable to the ppm units used by NOAA Mauna Loa.

Pieter Tans and Kirk Thoning. (2008) How we measure background CO2 levels on Mauna Loa.
NOAA Global Monitoring Laboratory, Boulder, Colorado. September, 2008. Updated December, 2016; March 2018, September 2020. Last accessed April 18, 2025. https://gml.noaa.gov/ccgg/about/co2_measurements.html