by Edwin Berry, PhD, CCM
I submitted this preprint to an Elsevier journal. Therefore, the present copyright does not allow republication or reposting. If Elsevier accepts my preprint, I will pay the Open Access fee and post the Elsevier publication identifier here. At that time, the copyright will change to allow use as described at the end of this post.
Red text indicates edits I made since posting this preprint.
This post represents my climate research over the past year and is a significant improvement over my previous post “Why our CO2 emissions do not increase Atmosphere CO2.” I believe this post transforms the climate debate into a checkmate win for the Trump administration. – Ed
Next, I will write a version of this post for the general public, by replacing the math equations with simple explanations. – Ed
- 2. The Model
- 2.1 Derivation
- 2.2 How nature balances inflows
- 2.3 Carbon dioxide residence times
- 2.4 The Model replicates carbon-14 data
- 2.5 Human effect on carbon dioxide level
- 3. IPCC’s invalid model
- 3.1 IPCC’s core argument fails
- 3.2 IPCC manufactures climate change
- 3.3 IPCC confuses residence time
- 3.4 IPCC’s Bern model is invalid
- 3.5 IPCC’s alternative arguments fail
The United Nations Intergovernmental Panel on Climate Change (IPCC) claims human emissions raised the carbon dioxide level from 280 ppm to 410 ppm, or 130 ppm. Physics proves this claim is impossible.
The IPCC agrees today’s annual human carbon dioxide emissions are 4.5 ppm per year and nature’s carbon dioxide emissions are 98 ppm per year. Yet, the IPCC claims human emissions have caused all the increase in carbon dioxide since 1750, which is 30 percent.
How can human carbon dioxide, which is only 5 percent of natural carbon dioxide, add 30 percent to the level of atmospheric carbon dioxide? It can’t.
This paper derives a Model that shows how human and natural carbon dioxide emissions independently change the equilibrium level of atmospheric carbon dioxide. This Model should replace the IPCC’s invalid Bern model.
The Model shows the ratio of human to natural carbon dioxide in the atmosphere equals the ratio of their inflows, independent of residence time.
The model shows, contrary to IPCC claims, that human emissions do not continually add carbon dioxide to the atmosphere, but rather cause a flow of carbon dioxide through the atmosphere. The flow adds a constant equilibrium level, not a continuing increasing level, of carbon dioxide.
Present human emissions add an equilibrium level of 18 ppm, which is the product of human carbon dioxide inflow of 4.5 ppm per year multiplied by the carbon dioxide residence time of 4 years. Present natural emissions add an equilibrium level of 392 ppm, to get today’s 410 ppm.
If human emissions continue as at present, these emissions will add no additional carbon dioxide to the atmosphere. If all human emissions were stopped, and nature stayed constant, it would remove only 18 ppm. The natural level of 392 ppm would remain.
The critical questions about climate change are not about whether climate has changed. Climate always changes. The critical scientific questions about climate change are about cause-and-effect:
- How much do human emissions increase atmospheric carbon dioxide?
- How much does increased atmospheric carbon dioxide change climate?
This paper focuses on and answers the first question.
The United Nations Intergovernmental Panel on Climate Change (IPCC) agrees that annual human carbon dioxide emissions are less than 5 percent of nature’s carbon dioxide emissions. Yet, the IPCC claims human emissions have caused all the increase in carbon dioxide since 1750, which is 30 percent.
The IPCC claims abundant published literature shows, with “considerable certainty,” that nature has been a net carbon sink since 1750, so could not have caused the observed rise in atmospheric carbon dioxide. Section 3.1 shows why this IPCC argument fails.
Munshi (2017) used statistics to show “that detrended correlation analysis of annual emissions and annual changes in atmospheric carbon dioxide” is zero. Munshi proved there is no cause and effect and no “considerable certainty.”
Here are three analogies that will help you understand this paper.
Let human carbon dioxide emissions be cream and natural carbon dioxide emissions be coffee. Pour 5 parts of cream and 95 parts of coffee into a cup with a hole in the bottom. Continue to pour 5 parts of cream and 95 parts of coffee into the cup fast enough to keep the cup filled.
Question: What is the percent of cream in the cup? Answer: Clearly, it’s 5 percent.
The tea cup analogy shows, so long as you pour 5 percent cream and 95 percent coffee into the cup, you will never get more than 5 percent cream in the cup.
But the IPCC claims the cup contains 30 percent cream and 70 percent coffee, and the percent of cream in the cup will continue to increase so long as the pouring of 5 percent cream continues.
Thus, the IPCC claims the hole in the bottom of the cup magically stops over 60 percent of the cream from flowing through the hole. The IPCC further claims continually pouring this mixture into the cup will create a permanent, increasing amount of cream in the cup, that will overflow the cup.
A river flows into a lake and the lake water exits over a fixed dam. The lake level rises until outflow equals inflow. Add a new river that increases the inflow by 5 percent. The lake level will rise until, once again, outflow equals inflow.
Similarly, nature balances the inflow of carbon dioxide into the atmosphere. If human emissions increase the inflow by 5 percent, the carbon dioxide level will rise until outflow equals inflow, which will occur when the level has risen by 5 percent.
However, in this analogy, the IPCC claims if humans, not nature, created the new river, then the dam will magically stop over 60 percent of the new river’s inflow from flowing out over the dam. IPCC’s trapped inflow will raise the level of the lake without letting the trapped water flow out. The lake rise will build a vertical wall of water above the dam, held in place by nothing!
Water flows into the top of a water wheel, causes the wheel to turn, and flows out at the bottom of the wheel. More water inflow makes the wheel turn faster. The water does not get trapped in the water wheel. At equilibrium, outflow equals inflow.
This water wheel is the proper analogy to how carbon dioxide flows into and out of the atmosphere. The level of carbon dioxide in the atmosphere is like the speed of the water wheel. If the inflow increases, the level increases. The carbon dioxide never gets trapped in the atmosphere, just like water never gets trapped in the water wheel.
Continuing water inflow into a water wheel will not add to the speed of the wheel. Similarly, continuing the present human inflow of carbon dioxide into the atmosphere will not add to the level of carbon dioxide in the atmosphere.
This paper presents the physics that explains the above analogies and shows why IPCC’s climate claims are fundamentally and scientifically wrong.
Many authors have agreed that human emissions are insignificant to the level of atmospheric carbon dioxide, even though they used different methods to derive their conclusions. Revelle and Suess (1957), Star (1992), Segalstad (1992, 1996, 1998, 2009), Rorsch, Courtney, & Thoenas (2005), Courtney (2008), Siddons & D’Aleo (2007), Essenhigh (2009), Glassman (2010), Wilde (2012), Caryl (2013), Humlum et al. (2013), Salby (2012, 2015, 2016), Berry (2016), and Harde (2017) concluded that human emissions cause only a minor change in the level of atmospheric carbon dioxide.
This paper addresses the same general subject as Harde (2017) and provides additional support for Harde’s key conclusions:
Under present conditions, the natural emissions contribute 373 ppm and anthropogenic emissions 17 ppm to the total concentration of 390 ppm (2012). For the average (1/e) residence time we only find 4 years.
These results indicate that almost all … observed change of carbon dioxide during the Industrial Era followed, not from anthropogenic emission, but from changes of natural emissions.
This paper differs from Harde (2017) in its in-depth focus on the physics of carbon dioxide flows into and out of the atmosphere, and in its explanation of why the IPCC and its Bern model are fundamentally wrong.
To keep the discussion simple, this paper converts all GtC (Gigatons of Carbon) units into the equivalent carbon dioxide units of ppm (parts per million by volume in dry air), using:
1 ppm = 2.13 GtC
Swan (2017) wrote the IPCC is “generally regarded as the world’s leading authority on global warming.” Yet, the IPCC does not follow the scientific method, which says evidence can prove a theory wrong but cannot prove a theory right. The IPCC ignores that science proceeds by negating theories, not by discarding evidence that negates theories.
2. The Model
The (Berry) Model derived below describes how nature adjusts the level of atmospheric carbon dioxide until outflow equals inflow. Nature thereby balances both natural and human emissions of carbon dioxide.
The Model includes the level of atmospheric carbon dioxide and the rates of carbon dioxide inflow and outflow. The Model does not include levels for Land and Ocean because additional levels do not change the conclusions of the Model.
The Model follows the same basic structure as Berry (1967). A model is composed of levels and rates of flow between levels. Levels determine the rates and the rates set the new levels.
Fig. 1 illustrates the Model.
The Model does not include the causes of the inflow because the causes do not affect the conclusions of the Model. Therefore, Henry’s Law is not included.
The Model contains only the first power of the level. Therefore, the Model satisfies Raoult’s Law and Dalton’s Law. Dalton’s Law of partial pressures states,
The total pressure exerted in a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
Raoult’s law states about liquids,
The partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.
Therefore, the Model applies independently and in total to human-produced carbon dioxide, nature-produced carbon dioxide, carbon-14 carbon dioxide, etc.
The Model follows the Equivalence Principle. The Equivalence Principle says if data cannot tell the difference between two things then the two things are identical. The Equivalence Principle is a foundation of Einstein’s theory of general relativity. It says the inability to distinguish between gravitational and inertial forces means they are the same thing.
The Equivalence Principle applies to climate physics because nature cannot tell the difference between human-produced and nature-produced carbon dioxide in the atmosphere. Therefore, valid climate models must treat human-produced and nature-produced carbon dioxide the same.
The Model needs only two equations – the Continuity Equation and the Ideal Gas Law. The continuity equation assures that carbon atoms are conserved:
dL/dt = Inflow – Outflow (1)
L = carbon dioxide level
dL/dt = the rate of change of L
t = time
The Ideal Gas Law relates partial pressure to concentration,
p = (n/V) R T (2)
p = partial pressure
n/V = moles per volume = concentration in ppm
R = Ideal Gas Constant
T = Temperature
The partial pressure of carbon dioxide sets the rate that carbon dioxide flows out of the atmosphere. In the molecular view, a higher concentration causes more molecules per unit time to impact surfaces like plant leaves and water. The higher the rate of molecular impacts on a surface, the higher the rate of transfers into the surface.
The Ideal Gas Law says partial pressure is proportional to concentration, or level. The Ideal Gas Law causes the outflow to be proportional to the level,
Outflow = L / Te (3)
where Te is a constant that has the dimension of time. Eq. (8) reveals that Te equals the 1/e residence time of carbon dioxide in the atmosphere. Salby (2016) and Harde (2017) use a similar form of Eq. (3). The significance of Eq. (3) is it makes outflow proportional to level, which causes the level to always move toward its equilibrium level.
Substituting Eq. (3) into the Outflow in continuity equation (1), gives the Model equation
dL/dt = Inflow – L / Te (4)
To find an equation for Inflow, set the level equal to its equilibrium level, Le. Then the level does not change with time. So,
dL/dt = 0
and Eq. (4) becomes
Inflow = Le / Te (5)
Le = the equilibrium level of L
Note in passing that solving Eq. (4) for Le gives
Le = Inflow * Te (6)
Eq. (6) shows that Inflow, when multiplied by residence time, determines the equilibrium level.
Substituting Eq. (5) into Eq. (4), gives Eq. (7) which shows how the rate of change of level depends on the difference between the level and its equilibrium level, divided by residence time,
dL/dt = – (L – Le) / Te (7)
Eq. (7) shows how the Ideal Gas Law causes equilibrium. Whether the level is above or below its equilibrium level, it will always move toward its equilibrium level. Eq. (7) shows how nature balances carbon dioxide inflow whether the inflow is nature-produced or human-produced.
Rearrange Eq. (7) to get
dL / (L – Le) = – dt / Te (8)
Then integrate Eq. (8) from L0 to L on the left side, and from 0 to t on the right side, to get (Dwight, 1955, Item 90.1),
Ln [(L – Le) / (L0 – Le)] = – t / Te (9)
Ln = natural logarithm, or logarithm to base e
L0 = Level at time zero (t = 0)
Le = the equilibrium level for a given inflow and Te
Te = Residence time for level to move (1 – 1/e) of the distance from L0 to Le
e = 2.7183
(The original integration of Eq. (8) contains two absolute functions, but they cancel each other because both L and L0 are always either above or below Le.)
Raise both sides of Eq. (9) to the power of e to get the level as a function of time:
Raise e to the power of each side of Eq. (9), to get the level as a function of time:
L = Le + (L0 – Le) exp(- t / Te) (10)
Eq. (10) is the analytic solution of Eq. (7). It shows how the level approaches its equilibrium level exponentially.
2.2 How nature balances inflows
The Model equations show how the inflows of human-produced carbon dioxide and nature-produced carbon dioxide set independent equilibrium levels, and the sum of these equilibrium levels equals the total equilibrium level.
Fig. 2 shows how nature balances inflow by adjusting the level until outflow equals inflow. This applies not only to total inflow but to the inflows of each partial pressure component.
The following three previous equations describe how nature balances inflow.
Inflow sets the equilibrium level:
Le = Inflow * Te (6)
Level sets the outflow:
Outflow = L / Te (3)
Level always moves toward its equilibrium level:
dL/dt = – (L – Le) / Te (7)
If inflow is zero, then the equilibrium level is zero. So, outflow will continue until the level goes to zero according to this equation:
dL/dt = – L / Te (7a)
Notice, there is no such thing as a permanent level greater than zero when there is no inflow. Eq. (7a) proves the IPCC Bern model, discussed section 4.4, is wrong.
2.3 Carbon dioxide residence times
There are two kinds of residence times, half-life, Th, and 1/e residence time, Te. Both residence times are different measures of the same thing:
Residence time is a measure of how fast level L approaches its equilibrium level Le when inflow is constant.
In Eq. (9), when time t equals half-life Th, then the ratio,
(L – Le) / (L0 – Le) = ½
t = Th
Then Eq. (9) becomes
Ln (1/2) = – Th / Te
Ln (2) = Th / Te
Te = Th / Ln (2)
Te = 1.4427 Th (11)
Eq. (11) shows the relationship between residence half-life Th and 1/e residence time Te.
IPCC (2007) estimates the carbon dioxide flow from land to atmosphere is 56 ppm per year, and from oceans is 42 ppm per year, for a total of 98 ppm per year, or about 100 ppm per year. NOAA (2017) Mauna Loa data shows the 2015 level of atmospheric carbon dioxide is about 400 ppm.
Rearrange Eq. (5) to get,
Te = Le / Inflow (12)
Te = 400 ppm / 100 ppm per year = 4 years (13)
Eq. (13) for residence time agrees with IPCC (1990). This calculation of residence time applies to carbon dioxide levels from about 280 ppm to 1000 ppm.
2.4 The Model replicates carbon-14 data
Every valid theory must make valid predictions. Therefore, the Model must replicate the atmospheric carbon-14 data after 1963. The Bern model does not.
The atomic bomb tests in the 1960’s increased atmospheric carbon-14 by more than 80 percent. After the halt of the tests in 1963, the concentration of carbon-14 decreased exponentially toward its previous equilibrium level of 100 percent.
The Model is not a curve-fit to data. The Model is a derivation from two physical principles. The only number the Model needs to replicate the carbon-14 data is the residence time of carbon-14 carbon dioxide.
The half-life is the time for the level of carbon-14 to fall to one-half its initial level. (Not to be confused with the radioactive half-life of carbon-14 of 5730 years.)
Fig. 3 shows a plot of the carbon-14 data (Broeker et al., 1985). The data show carbon-14 lost one-half of its level above its equilibrium level every 10 years. The decrease in the level of carbon-14 carbon dioxide follows an exponential curve to its equilibrium value.
Table 1 shows data taken from Fig. 3 every ten years.
Table 1. The carbon-14 level minus 100, loses half of its value every ten years.
|Year||Level||Level – 100|
The data show the residence half-life for carbon-14 carbon dioxide is 10.0 years:
Th = 10.0 years
Therefore, using Eq. (11),
Te = 1.4428 Th = 14.4 years (14)
To test the Model, let
L0 = 180
Le = 100
Te = 14.4
Use Eq. (5) to calculate the natural inflow of carbon-14 carbon dioxide:
Inflow = Le / Te = 100 / 14.4 = 6.9 percent per year (15)
Then use either Eq. (7) or Eq. (10) to calculate the level as a function of time in years. Fig. 4, calculated in Excel, shows the result is a perfect fit to the carbon-14 data in Fig. 3.
The Model accurately predicts how the level of carbon-14 carbon dioxide approaches its equilibrium level. Therefore, the Model will also correctly predict how the levels of carbon-13 and carbon-12 carbon dioxide will approach their equilibrium levels for their residence times.
2.5 Human effect on carbon dioxide level
IPCC (2007) estimates the carbon dioxide flow from land to atmosphere is 56 ppm per year, and from oceans is 42 ppm per year, for a total of 98 ppm per year.
Data from Boden et al. (2017) show human carbon dioxide emissions from fossil-fuel burning, cement manufacturing, and gas flaring in 2014 was 4.6 ppm (9.855 GtC) per year.
Eq. (6) gives the equilibrium level for natural and human sources independently.
Using Eq. (6) for the 2014 human emissions gives,
Leh = (4.6 ppm/year) (4 years) = 18 ppm (16)
Using Eq. (6) for natural emissions gives,
Len = (98 ppm/year) (4 years) = 392 ppm (17)
Eq. (16) and Eq. (17) depend on residence time.
Eq. (16) says human emissions create an equilibrium level of 18 ppm. This means if natural emissions were zero, the level of carbon dioxide would be 18 ppm.
Eq. (17) says present natural emission create an equilibrium level of 392 ppm. This means if human emissions were zero, the level of carbon dioxide would be 392 ppm.
The total equilibrium level for human and natural emissions, using the above data for 2014, is the total of Eq. (16) and Eq. (17), or 410 ppm. This is only 10 ppm greater than the NOAA (2017) Mauna Loa data for 2015.
If human and natural emissions were to stay constant after 2014, then the carbon dioxide level would reach its equilibrium level of 410 in about 2018. NOAA (2017) for Mauna Loa data shows 404 ppm for 2016. These calculations are close enough to demonstrate the accuracy of the Model and the inaccuracy of the Bern model.
The ratio of Eq. (16) to Eq. (17) is independent of residence time,
Leh / Len = 18 / 392 = 4.6 percent (18)
Eq. (18) shows that the equilibrium level ratio of human-produced to nature-produced carbon dioxide is the ratio of their inflows.
Eq. (5) gives the natural emissions rate to produce the equilibrium level of 280 ppm in 1750,
Inflow = Le / Te = 280 ppm / 4 years = 70 ppm per year (19)
The equilibrium level increased since 1750. Rearranging Eq. (5) gives for the equilibrium level,
Le = Inflow * Te (5a)
What changed to increase the equilibrium level between 1750 and today? Either the inflow increased, or the residence time increased, or both.
Harde (2017) assumed residence time increased while inflow remained constant.
The Model concludes inflow increased while residence time remained constant. That is because Eq. (3), which defines residence time, is derived from the Ideal Gas Law which is constant.
In summary, the Model shows human emissions cause 4.4 percent of today’s 410 ppm, or only 18 ppm. Natural emissions cause the 392-ppm level. Even if ALL human emissions were stopped and nature stayed constant, atmospheric carbon dioxide would not fall below 392 ppm.
3. IPCC’s invalid model
3.1 IPCC’s core argument fails
The IPCC (2007) claims, without proof, in the third paragraph of its Executive Summary,
The present atmospheric carbon dioxide increase is caused by anthropogenic emissions of carbon dioxide.
That statement is the basis of all claims, predictions, scenarios, and conclusions of the IPCC.
The IPCC assumes the level of atmospheric carbon dioxide in 1750 was 280 ppm. Segalstad (1998) and Ball (2008) present evidence that the level in 1750 was much higher than 280 ppm. Nevertheless, this paper uses this IPCC assumption because it does not affect this paper’s conclusions.
The IPCC’s argument, described by IPCC (2007) and Pickering (2016), says,
- In 1750, the atmospheric carbon dioxide level was 280 ppm, according to ice-core data, from MacFarling Meure et al. (2006).
- In 2013, the atmospheric carbon dioxide level was 397 ppm, according to Moana Loa data, from NOAA (2017) and Olivier (2015).
- So, the atmospheric carbon dioxide level increased 117 ppm between 1750 to 2013.
- The sum of all human carbon dioxide emissions from 1750 to 2013 was 185 ppm, which is 68 ppm more than the increase in atmospheric carbon dioxide.
- Therefore, human emissions caused ALL the 117-ppm increase in atmospheric carbon dioxide, while nature absorbed the remaining 68 ppm.
- Since nature was a net absorber of carbon dioxide since 1750, nature cannot have caused the increase in atmospheric carbon dioxide.
This IPCC argument fails for the following reasons.
- Step #5 is invalid because it omits nature’s carbon dioxide emissions which are 95 percent of the data and 20 times greater than human emissions.
- Step #5 is invalid because
it is not exclusive.There are an infinite number of scenarios that satisfy Steps #1 through #4.
- Step #5 is invalid because it assumes nature’s inflow remained constant after 1750, and human outflows did not follow the Equivalence Principle.
- Step #6 is invalid because it is based on the invalid Step #5.
The Model shows, even if Steps #1 through #4 were true, that nature would have absorbed 167 ppm of the 185 ppm of human emissions from 1750 to 2013, leaving only 18 ppm of the total human emissions still in the atmosphere, and that nature, not human emissions, caused the increase from 280 ppm to 392 ppm.
Fig. 5 shows how much data the IPCC ignores to make its case. The sum of natural emissions is 20 times larger than human emissions. Natural outflow always balances all inflow, whether caused by human emissions or natural emissions. If nature did not have that flexibility then nature could not balance its own emissions.
The question is not whether nature balances human inflow. It does. The question is how much do human emissions raise the carbon dioxide level in the atmosphere to accomplish the balance. The IPCC ignores and contradicts basic physics.
3.2 IPCC manufactures climate change
IPCC (2007, Fig. 3.1a) shows for the “natural carbon cycle” that nature balances its inflows of 120 GtC (56 ppm) per year from Land, and its inflows of 90 GtC (42 ppm) per year from Ocean. So, IPCC agrees that nature balances the inflow of 98 ppm of natural carbon dioxide.
IPCC (2007, Fig. 3.1b) shows for the “human perturbation” total annual human inflows of 7.1 GtC (3.3 ppm) and outflows of 3.8 GtC (1.8 ppm), for a built-in imbalance of 1.5 ppm added to the atmosphere annually.
The IPCC claims nature is not flexible enough to include 1.5 ppm per year outflow to its natural outflow of 98 ppm per year. If nature were that rigid, nature could not balance its own inflows that change from year to year.
The IPCC does not understand how nature balances carbon dioxide inflow. Otherwise, the IPCC would not propose such an unphysical idea that nature does not balance human-caused inflow. The Model explains how nature balances all inflows.
This IPCC idea should have been rejected at its outset because it violates the Equivalence Principle.
The IPCC calls human-produced carbon dioxide a “perturbation” that nature cannot balance. That view reveals the biased mindset of the IPCC. The IPCC bases its climate models on the unscientific ethical premise that nature is good and human actions are bad.
The IPCC inserts its false idea, that nature does not balance human inflow, into its climate models. This false idea causes climate models to produce false results. Then the IPCC uses climate model results to claim human emissions cause climate change. IPCC’s climate conclusions are a result of its unscientific idea and its built-in circular reasoning.
IPCC’s false climate idea:
- Violates the Equivalence Principle.
- Violates physics because nature will always adjust the level to balance inflow.
- Adds a false “human-caused” inflow of 1.5 ppm per year into climate models.
- Causes climate models to make false claims about human-caused climate change.
- Is based on the ethical premise the nature is good and human actions are bad.
3.3 IPCC confuses residence time
IPCC (1990) properly concludes that the residence time of carbon dioxide molecules in the atmosphere is about 4 years. But the IPCC defines residence time incorrectly. The IPCC says residence time is “turnover time.” Here is a quote:
The turnover time of CO2 in the atmosphere, measured as the ratio of the content to the fluxes through it, is about 4 years. This means that on average it takes only a few years before a CO2 molecule in the atmosphere is taken up by plants or dissolved in the ocean.
This short time scale must not be confused with the time it takes for the atmospheric CO2 level to adjust to a new equilibrium if sources or sinks change.
What IPCC calls “turnover time” is the 1/e residence time.
IPCC defines two kinds of residence times: one residence time equals the average lifetime of molecule, and the other residence time equals the time for the “level to adjust to a new equilibrium” level.
But both residence times are the same thing. All definitions of residence time are the same because all definitions measure residence time according to the change in the level of carbon dioxide. No one measures how long an individual carbon dioxide molecule stays in the air.
3.4 IPCC’s Bern model is invalid
The IPCC “Bern model” (Bern, 2002) is a seven-parameter curve fit to the output of IPCC’s climate models (Joos et al., 2013). As a curve-fit to climate models, the Bern model replicates the output of IPCC’s climate models. Therefore, the Bern model includes the same false claims as the IPCC inserted into the climate models.
The IPCC changed the Bern model. The original Bern model, described by Siegenthaler and Joos (1992), connected the atmosphere level to the upper ocean level, and the upper ocean level to the deep and interior ocean levels.
The IPCC removed the Bern model levels for the deep and interior ocean, and connected their rates directly to the atmosphere level. That is why the atmosphere in the IPCC Bern model has three residence times. This is a violation of modelling principles.
IPCC (1990) acknowledges the source of the Bern model’s three residence times. The IPCC quote continues:
This adjustment time… is of the order of 50 – 200 years, determined mainly by the slow exchange of carbon between surface waters and the deep ocean.
The two curves in Figure 1.2, which represent simulations of a pulse input of CO2 into the atmosphere using atmosphere-ocean models (a box model and a General Circulation Model (GCM)), clearly show that the initial response (governed mainly by the uptake of CO2 by ocean surface waters) is much more rapid than the later response (influenced by the slow exchange between surface waters and deeper layers of the oceans).
For example, the first reduction by 50 percent occurs within some 50 years, whereas the reduction by another 50 percent (to 25 percent of the initial value) requires approximately another 250 years. The concentration will never return to its original value, but reach a new equilibrium level, about 15 percent of the total amount of CO2 emitted will remain in the atmosphere.
The IPCC applies its invalid Bern model only to human carbon dioxide emissions and not to natural emissions, which is a violation of the Equivalence Principle.
It would take a Maxwell’s Demon to prevent human-produced carbon dioxide from flowing out of the atmosphere like nature-produced carbon dioxide. The IPCC claim that nature treats human-produced and nature-produced carbon dioxide differently is impossible.
Appendix A shows how to remove the integral in the Bern model to reveal its core equation.
The Bern core equation predicts that a one-year “pulse” inflow, which sets the carbon dioxide level to 100 ppm, will cause the level to be 29 ppm after 100 years with a permanent level of 15 ppm forever.
Therefore, according to the Equivalence Principle, the Bern model must also hold for natural emissions. If natural emissions are inserted into the Bern model, it predicts that the last 1000 years of natural emissions of 100 ppm per year would have added 15 ppm per year that remains forever in the atmosphere, for a total irreversible increase of 15,000 ppm. This clearly invalid prediction proves the Bern model and all IPCC climate models are wrong.
Also, Eq. (7a) proves the IPCC Bern model is wrong. There is no permanent carbon dioxide level as the IPCC claims. The level of carbon dioxide will go to zero if there is no inflow.
The creators of the original Bern model, Siegenthaler and Joos (1992), understood that their model should reproduce the carbon-14 data and were disappointed that it did not do so. The IPCC Bern model cannot replicate the carbon-14 data.
Salby (2016) was correct to compare the Bern model output with carbon-14 data on the same plot. That comparison plot shows the Bern model is not even close to reality. The two longer residence times and one infinite residence time that the IPCC added to the Bern model prevent the Bern model from behaving like nature.
The scientific method says if a theory makes only one wrong prediction or if any of its supporting claims are wrong, then the theory is wrong. The IPCC Bern model makes invalid predictions and contains non-physical assumptions. It replicates IPCC’s climate models rather that real data. Therefore, the Bern model proves IPCC’s core claims and climate models are wrong.
3.5 IPCC’s alternative arguments fail
IPCC (2007) claims,
Carbon-13 has decreased from 1950 to 1980. Plants and fossil fuels have lower carbon-13 to carbon-12 ratio ratios than other sources of carbon dioxide. Therefore, human carbon dioxide emissions have caused all the rise in atmospheric carbon dioxide above 280 ppm.
IPCC (2007) agrees that carbon-13 decreased 18 percent from 1950 to 1980, and plant and human carbon dioxide have only 2 percent less carbon-13 than other sources.
Since human carbon dioxide emissions are only 5 percent of nature’s carbon dioxide emissions, human carbon dioxide could have caused only 2 percent of 5 percent, or 0.1 percent, decrease in carbon-13. So, human carbon dioxide cannot have caused an 18 percent decrease.
Segalstad (1992) and Spencer (2009) show why biological sources rather than human emissions caused the decrease in carbon-13.
IPCC (2007) claims the decline in atmospheric oxygen proves human emissions caused all the increase in carbon dioxide since 1750. This argument fails because a decline in the oxygen level is unrelated to the outflow of carbon dioxide from the atmosphere.
IPCC (2007) claims that the more rapid increase in carbon dioxide in the northern hemisphere proves human emissions caused all the increase in atmospheric carbon dioxide since 1750. Quirk (2009) shows how the same data imply that natural emissions, not human emissions, increase atmospheric carbon dioxide.
This paper accomplished three goals:
- It derived a simple Model that accurately computes how human and natural carbon dioxide emissions independently change the level of atmospheric carbon dioxide.
- It answered the question: “How much do human emissions increase atmospheric carbon dioxide?”
- It showed why IPCC’s claims and models are fundamentally wrong.
Contrary to IPCC claims, human emissions have not caused all the increase in carbon dioxide since 1750. Human emissions do not continually add carbon dioxide to the atmosphere, but rather cause a flow of carbon dioxide through the atmosphere. The flow adds a constant equilibrium level, not a continuing increasing level, of carbon dioxide.
The 1/e residence time of carbon-12 carbon dioxide, using IPCC data, is 4 years.
Human and natural emissions create inflows of carbon dioxide that create independent equilibrium levels of atmospheric carbon dioxide. These independent equilibrium levels add to produce a total equilibrium level of carbon dioxide in the atmosphere.
Present human emissions add an equilibrium level of 18 ppm, which is the product of human carbon dioxide inflow of 4.5 ppm per year multiplied by the carbon dioxide residence time of 4 years. Present natural emissions add an equilibrium level of 392 ppm, to get today’s 410 ppm.
If human emissions continue as at present, these emissions will add no additional carbon dioxide to the atmosphere in the future. If all human emissions were stopped, and nature stayed constant, it would remove only 18 ppm. The natural level of 392 ppm would remain.
There is no “permanent” remainder of human or natural carbon dioxide in the atmosphere. If inflow is turned off, the corresponding equilibrium level will go to zero. The level will approach zero according to the 1/e residence time of 4 years.
The ratio of human to natural carbon dioxide in the atmosphere equals the ratio of their inflows, independent of residence time.
All valid models must obey the Equivalence Principle and must replicate the carbon-14 data.
IPCC’s Bern model violates the Equivalence Principle, does not reproduce the carbon-14 data, and predicts that 1000 years of “natural emissions” will permanently increase the amount of carbon dioxide in the atmosphere by 15,000 ppm.
Since IPCC’s Bern model is a curve-fit to the output of climate models, the inaccurate and invalid Bern Model proves IPCC’s climate claims are wrong. The (Berry) Model should replace the IPCC’s invalid Bern model.
Appendix A: Bern model math
The Bern (2002) model is an integral equation rather than a rate equation. Therefore, the Bern model is not a system model. The Bern model integrates the inflow of carbon dioxide from minus infinity to any time in the future.
To deconstruct the Bern model, let inflow occur only in the year when “t-prime” equals zero (t’ = 0). Then the integral disappears and the Bern model becomes a level equation. Using the terms defined in this paper, the Bern level equation is,
L(t) = Lo [ A0 + A1 exp(- t/T1) + A2 exp(- t/T2) + A3 exp(- t/T3)] (A.1)
where the Bern IPCC TAR standard values are,
A0 = 0.152
A1 = 0.253
A2 = 0.279
A3 = 0.319
T1 = 173 years
T2 = 18.5 years
T3 = 1.19 years
The A-values merely weight the four terms on the right-hand side of Eq. (A.1):
A0 + A1 + A2 + A3 = 1.000
The IPCC assigned values to the seven arbitrary parameters by curve-fitting the Bern model to output of IPCC’s climate models. Good science would have fit the Bern model to real data, like the carbon-14 data.
Here are two easy ways to show the Bern model contradicts real-world data.
Set t equal to 100 years. Then Eq. (A.1) becomes,
L = (A0 + A1) Lo = (0.152 + 0.253*0.56) Lo = 0.29 Lo (A.2)
Set t equal to infinity. Then Eq. (A.1) becomes,
L = Ao Lo = 0.152 Lo (A.3)
Eq. (A.2) and Eq. (A.3) say if a one-year inflow sets Lo to 100 ppm and there is no other inflow forever, then the level in 100 years will be 29 ppm and the level will never fall below 15 ppm.
To get the Bern rate equation, take the time derivative of Eq. (A.1),
dL/dt = – L (A1/T1 + A2/T2 + A3/T3) (A.4)
Compare this to Eq. (7),
dL/dt = – (L – Le) / Te (7)
This comparison shows the Bern model does not include an equilibrium level or the physics that produces an equilibrium level. That is why it predicts some carbon dioxide will remain forever.
Siegenthaler and Joos (1992) designed the Bern model to connect the atmosphere with the upper ocean and the upper ocean with the deep ocean, etc., as can be seen in their Fig. 1. But the IPCC Bern model omits the separate ocean levels and simply connects their rate equations directly to the atmosphere. That is why the Bern model has three different residence times.
This research was funded by the personal funds of the author. The author thanks Daniel Nebert, Chuck Wiese, Laurence Gould, Richard Courtney, Tom Sheahen, Gordon Danielson, and Valerie Berry, who reviewed and proofread drafts of this paper.
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