A conservative calculation of specific impulse for CO2

Bud Bromley | June 11, 2022

Richard Feynman frequently reminded us, “If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is – if it disagrees with experiment it is wrong. That is all there is to it.” (Feynman, 1965)

In the 2 years following the June 15, 1991 eruption of the Pinatubo volcano, the natural environment removed more CO₂ than the entire increase in CO₂ concentration due to all sources, human and natural, during the entire measured daily record of the Global Monitoring Laboratory of NOAA/Scripps Oceanographic Institute (MLO) May 17, 1974 to June 15, 1991.  Then, in the 2 years after that, that CO₂ was replaced plus an additional increment of CO₂.

The Pinatubo Phase I Study (Bromley & Tamarkin, 2022) calculated the mass of net CO₂ removed from the atmosphere based on measurements taken by MLO and from those measurements then calculated the first and second time derivatives (i.e., slope and acceleration) of CO₂ concentration.  We then demonstrated a novel use of the Specific Impulse calculation, a standard physical calculation used daily in life and death decisions.  There are no theories, estimates or computer models involved in these calculations.  The following calculation is a more conservative demonstration which makes it obvious that human CO₂ is not increasing global CO₂ concentration.

The average slope of the CO₂ concentration in the pre-Pinatubo period in MLO data was 1.463 ppm/year based on the method described in Bromley and Tamarkin (2022).  Slope is the rate of change of the CO₂ concentration.  The rate of change and slope of a CO₂ concentration with respect to time elapsed are identical to the commonly known terms velocity and speed.

Converting ppm to mass of CO₂.  According to MLO, the CO₂ concentration in the atmosphere on June 15, 1991 was 358 ppm.  1 ppm CO₂ in air = 7.76 GtCO₂.  Thus 358 ppm * 7.76 GtCO₂ = 2778 Gt CO₂ in air on June 15, 1991.   The mass of CO₂ in the atmosphere on June 15, 1991 per MLO was 2778 GtCO₂.

(Note this is not GtC, i.e., gigatonnes of carbon.  GtC and GtCO₂ are not equivalent. This is GtCO₂,_, i.e., gigatonnes of CO₂.  MLO measures micromoles CO₂ per mole of dry air, which is ppm, not ppmv.  Ppm and ppmv are not equivalent. )

For avoidance of doubt about the method described in Bromley and Tamarkin (2022), slope which is calculated using only published MLO data is compared to slope calculated in Bromley & Tamarkin (2021):

MLO began reporting daily CO₂ data on May 17, 1974 and on that day reported 333 ppm.  Not including May 17, there were 6238 days between May 17, 1974 and June 15, 1991.

• MLO slope = (358 – 333 ppm)/6238 days = 0.004008 ppm per day
• Bromley & Tamarkin slope = 1.463 ppm per year / 365 days = 0.004008 ppm per day

On June 15, 1991, the velocity of 2778 Gt CO₂ = 1.463 ppm per year * 7.76 GtCO₂ per ppm = 11.35 GtCO₂ per year.  Then 11.35 GtCO₂ per year divided by 365 days per year = 0.03 GtCO₂ per day.  On June 15, 1991 net global average atmospheric CO₂ velocity was 0.03 GtCO₂ per day.

On April 22, 1993, GtCO₂ velocity was 0.62 ppm per year.  Then 0.62 * 7.76 GtCO₂ per ppm = 4.81 GtCO₂ divided by 365 days = 0.0132 GtCO2 per day.  On April 23, 1993 net global average atmospheric CO₂ velocity was 0.0132 GtCO₂ per day.  CO₂ velocity continued to decline after April 22, 1993.

June 15, 1991 was the start of the major Pinatubo volcanic eruption and April 22, 1993 was the date of maximum deceleration in net global average atmospheric CO₂ concentration after Pinatubo in the daily measurement record of MLO.

t = 677 days from June 15, 1991 to April 22, 1993 (not including April 22.)

Initial velocity u = 0.03 GtCO2 per day

Final velocity v = 0.01 GtCO2 per day

Acceleration a = (v-u)/t

a = (0.01 – 0.03)/677 days

a = -2.95 * 10^-5 GtCO₂ per day per day

The net force F on a mass equals the mass times the acceleration of the mass. (Newton’s 2^nd law of motion.  F = ma)

The net mass of CO₂ in the atmosphere on June 15, 1991 per MLO was 2778 GtCO₂.

F = 2778 GtCO₂ * – 2.95 * 10^-5GtCO₂ per day per day = – 0.082 Newtons

F = the breaking power or force the environment exerted on the net CO₂ mass in the air in response to the surface cooling that followed the Pinatubo eruption.  The negative sign indicates the vector direction of the force.  In other words, CO₂ was being removed from the atmosphere.

Impulse J = Force * time or J = Ft

J = – 0.082 Newtons * 677 days = – 55.5 Newton seconds.  Newton seconds is the standard unit for specific impulse.

The impulse calculation tells us whether a car has enough braking force to stop before hitting the wall, or enough force to take the rocket into orbit before it runs out of fuel, or, as in the analogy in the Phase Pinatubo report (Bromley & Tamarkin, 2022), enough force to accelerate the loaded 747 to liftoff velocity before reaching the end of the runway, or enough force to overcome addition of human CO₂ to air.

The above calculation for J_n is for the total mass of net global CO₂ in the atmosphere.  Next, we want to compare that J_n to the J_h for the human-produced CO₂ component.  But, unfortunately we only have estimates based on theoretical assumptions and dubious sources for the human CO₂ component.  Therefore, instead of using these theories and estimates, we will now calculate an amount of CO₂ that must be larger and is clearly larger than the human CO₂ component, that is, a not-to-exceed amount of human-CO₂.  For avoidance of doubt, this not-to-exceed amount will be more conservative than in Bromley and Tamarkin (2022).

MLO began reporting daily CO2 data on May 17, 1974.  On that day, MLO reported 333.38 ppm.  On June 15, 1991, MLO reported 358 ppm.  358 minus 333 = 25 ppm increase in CO₂.  This increase includes all CO₂ in the atmosphere from all sources, human and natural.  There is no residual human fraction.

25 ppm * 7.76 GtCO₂ per ppm = 194 GtCO₂ increase in CO₂

For this comparison, attribute that entire increase in MLO CO2 since the daily record began to humans.   This amount was measured by MLO and we know this amount exceeds the actual human CO₂ component.

The average slope for the pre-Pinatubo period in the MLO data set is 1.463 ppm per year.  Converting that to GtCO₂ we have 1.463 * 7.76 GtCO₂ per ppm = 11.35 GtCO₂.  For this comparison, assume this entire amount is due to humans.

11.35 GtCO₂ per year divided by 365 days per year = 0.031 Gt “human” CO₂ added per day.  Assume that human emissions did not slow following Pinatubo, even though total CO₂ was decelerating precipitously.

Thus:

m = 0.031 Gt “human” CO₂ per day * 677 days = 21.05 Gt “human” CO₂ added post Pinatubo.

Adding: 194 GtCO2 “human” increase + 21.05 GtCO₂ “human” added post Pinatubo = 215 GtCO₂.

Hypothetical “Human” emissions cannot exceed 215 GtCO_2. 

Then m (“human”) = 215 GtCO₂

On June 15, 1991, the velocity u of 215 GtCO2 = 1.463 ppm per year * 7.76 GtCO₂ per ppm

= 11.35 / 365 = 0.031 GtCO₂ per day.

Hypothetically, on April 22, 1993, 677 days later, final velocity v of “human” CO₂ was the same 0.031 per day.  But to be more conservative, let v = 0.041 GtCO₂ per day, that is, “human” CO₂ is growing faster even though total CO₂ is declining sharply.

Thus post-Pinatubo acceleration a of ”human” CO₂  = (v – u)/t =0.01/677 = 1.48 * 10^-5 GtCO₂ per day per day

F = ma (Newton’s 2^nd law of motion.  F = ma)

F = 215 GtCO₂ * (1.48 X 10-5 GtCO₂ per day per day) = 0.0032 Newtons

J_h = 0.0032 Newtons * 677 days = 2.17 Newton seconds

J_h = 2.17 Newton seconds is the specific impulse for our hypothetical “human” CO2 emissions.

Comparison:

• 2.17 Newton seconds for hypothetical “human” CO₂ emissions
• -55.5 Newton seconds for natural CO₂ removal from atmosphere

In this conservative calculation, based entirely on measurements (not theory, not models, and not estimates), Earth’s environment demonstrated the capacity to absorb more than 25 times the not-to-exceed amount of human CO₂ emissions at that time.

During the global cooling event in the 2 years following the Pinatubo eruption, CO₂ concentration decelerated rapidly.  Following that 2 year period, in the next 2 years CO₂ accelerated more rapidly than it had declined, reaching an average CO₂ slope which exceeded MLO-measured slope for the period prior to the June 1991 Pinatubo eruption.  The maximum force of the environment to both absorb and emit CO₂ could be much larger than the 25 times human emission and could occur much faster.  We do not know the maximum force or specific impulse.  But it is very safe to infer from this result that human CO₂ emissions are not an environmental crisis.

If a reason exists that the natural environment responds to human CO₂ in a significantly different way, e.g., the commonly asserted belief that the environment absorbs half of human CO₂, then the reader is invited to put forth that theory.  The calculations and data presented here disprove that theory.

Among other questions, the questions shouting to be answered are: where did that CO₂ go? And, where did the recovery CO₂ come from?

We are working from experiment first, sometimes called first principles.  We are looking for theory that explains the experimental result.  We reject the opposite process which is unfortunately used at great detriment to science, life, societies, and economics.  We are not looking for data to fit a priori theory, such as the IPCCs pre-conceived objective of human-caused global warming.  We are looking for theory to explain our experimental result.

The data and graphs produced by MLO also show a reduction in slope of CO₂ concentration following the June 1991 eruption of Pinatubo, and also shows the more rapid recovery of total CO₂ concentration that began about 2 years after the 1991 eruption. This graph is the annual rate of change of total atmosphere CO₂ concentration. This graph is not human CO₂.

Theoretical discussion and conclusion

These are the experiment results.  Theory must explain these results, not the other way around.

Bromley and Tamarkin (2022) suggested a theory how this very large amount of CO₂ could be absorbed so rapidly into the environment, mostly ocean surface.  This experimental result is consistent with Henry’s Law, the Law of Mass Action and Le Chatelier’s principle.  In a forthcoming addendum to Bromley and Tamarkin (2022), two additional laws, Fick’s Law and Graham’s Law are suggested additions to our theory explaining this experimental result.

There are several inorganic chemical sources in the sea surface thin layer which produce CO₂ through a series of linked reactions.  Based on theories asserted more than 60 years ago, inorganic and organic chemical sources and sinks are believed to be too small and/or too slow to explain the slope of net global average CO₂ concentration.  Our results strongly suggest that the net CO₂ absorption and net emission events that followed the Pinatubo eruption are response and recovery to a perturbation to the natural trend.  There is no suggestion in our results or in our theory that long-term warming of SST causes the slope of net global average CO₂ concentration.  We have not looked at temperatures or correlation statistics between temperature and CO₂ concentration because they are co-dependent variables, and the simultaneity bias cannot be removed with acceptable certainty.  References to 25 degrees C in Bromley and Tamarkin (2022) are only in theoretical discussion and not involved in any way in our data analysis or calculations. References to 25 degrees C are merely standard ambient temperature, part of SATP, agreed by standards organizations.

When CO₂ slope and acceleration declined post-Pinatubo, why was there a recovery to previous slope, plus and additional offset?  The decline and the recovery were certainly not due to humans or the biosphere.  As we have shown, CO₂ from humans and biosphere combined are over an order of magnitude less than the CO₂ absorbed by the environment and then re-emitted.  That alone should end fears of CO₂-caused climate crisis.  Where did the CO₂ go so rapidly and where did the CO₂ in the recovery come from?  Our data suggests that in future research we will find a series of other events, other volcanoes, El Ninos and La Ninas, etc. that have similarly disrupted the equilibrium followed by a response and recovery from the environment.

References

Bromley, B., & Tamarkin, T., 2022. Correcting Misinformation on Atmospheric Carbon Dioxide; Pinatubo Study Phase 1 Report.  ClimateCite.org. https://pinatubostudy.com/pinatuboreport.html

The Specific Impulse Calculation:  https://youtu.be/ph48Xwj_eS8

Thoning, K.W., Crotwell, A.M., & Mund, J.W. (2021). Atmospheric carbon dioxide dry air mole fractions from continuous measurements at Mauna Loa, Hawaii, Barrow, Alaska, American Samoa and South Pole. 1973-2020, Version 2021-08-09. National Oceanic and Atmospheric Administration (NOAA), Global Monitoring Laboratory (GML), Boulder, Colorado, USA https://doi.org/10.15138/yaf1-bk21 Data Set Name: co2_mlo_surface-insitu_1_ccgg_DailyData. Description: Atmospheric carbon dioxide dry air mole fractions from quasi-continuous measurements at Mauna Loa, Hawaii.

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