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 2nd 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 Jn is for the total mass of net global CO2 in the atmosphere.  Next, we want to compare that Jn to the Jh 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.


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 GtCO2. 

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 2nd law of motion.  F = ma)

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

Jh = 0.0032 Newtons * 677 days = 2.17 Newton seconds

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


  • 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.


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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