by Edwin X Berry, Ph.D., Physics
October 11, 2019: I posted the first draft of this climate paper for your comments.
November 7, 2019: I finished all updates and improvements. Thank you all for your comments.
November 19, 2019: This Preprint, slightly revised, will be submitted for publication.
Copyright (c) 2019 by Edwin X Berry
The whole scientific argument about the effect of human carbon dioxide on atmospheric carbon dioxide and climate change rests upon correctly calculating the human carbon cycle. This may be the first correct mathematical derivation and calculation of the human carbon cycle.
The calculations use United Nations Intergovernmental Panel on Climate Change (IPCC) carbon-cycle data and focus on the physics. The calculations show the IPCC natural carbon cycle data is mildly internally inconsistent. So, the calculations keep the levels and update the flows for IPCC’s natural carbon cycle to make it internally consistent.
Then the calculations simply apply the same IPCC rules for its consistent natural carbon cycle to the human carbon cycle, which IPCC has not done. IPCC’s human carbon cycle contains blatant, significant errors that prove IPCC’s fundamental conclusions are invalid.
IPCC’s own data prove all human carbon emissions since 1750 have increased atmospheric carbon dioxide by only 32 ppm, from IPCC’s 280 ppm in 1750 to 312 ppm in 2019. In the same period, natural emissions have increased atmospheric carbon dioxide by 100 ppm to produce the 2019 level of about 412 ppm.
If human emissions were to stop in 2020, then by 2100 only 4% of human carbon would remain in the atmosphere, or enough to increase atmospheric carbon dioxide by a negligible 8 ppm. IPCC’s data proves human carbon emissions cause no significant long-term change to atmospheric carbon dioxide and are not the cause of climate change.
Keywords: carbon dioxide, CO2, climate change, anthropogenic
1.1 The problem
The problem is to calculate the total effect of all human CO2 emitted since 1750 through 2019 on the carbon cycle and atmospheric CO2.
The United Nations Intergovernmental Panel on Climate Change (IPCC, 2013) incorrectly claims,
With a very high level of confidence, the increase in CO2 emissions from fossil fuel burning and those arising from land use change are the dominant cause of the observed increase in atmospheric CO2 concentration.
The removal of human-emitted CO2 from the atmosphere by natural processes will take a few hundred thousand years (high confidence).
IPCC (2007) incorrectly claims,
The primary source of the increased atmospheric concentration of carbon dioxide since the pre-industrial period results from fossil fuel use.
The United Nations World Meteorological Organization (WMO) Global Carbon Project (Candela and Carlson, 2017) incorrectly claims,
With solid justification, one can describe the annual carbon budgets as products of high scientific quality with strong political relevance.
Berry (2019b) described the Physics model and showed how IPCC arguments to support its climate hypothesis are wrong.
1.2 Prior work related to the carbon cycle
Authors who conclude that human CO2 increases atmospheric CO2 by only a small amount include Revelle and Suess(1957), Starr (1992), Segalstad (1998), Jaworoski (2003, 2007), Beck (2007), Rorsch, Courtney, and Thoenes (2005), Courtney (2008), Quirk (2009), Essenhigh (2009), Glassman (2010), Salby (2012, 2013, 2016, 2018), Humlum et al. (2013), Harde (2017, 2019), Berry (2018, 2019a, 2019b), and Munshi (2016a, 2016b, 2016c, 2016d, 2017, 2018).
Courtney (2008) (pages 6 and 7) concluded,
“… the relatively large increase of CO2concentration in the atmosphere in the twentieth century (some 30%) is likely to have been caused by the increased mean temperature that preceded it. The main cause may be desorption from the oceans. … Assessment of this conclusion requires a quantitative model of the carbon cycle, but – as previously explained – such a model cannot be constructed because the rate constants are not known for mechanisms operating in the carbon cycle.”
Courtney (November 21, 2019, comment on firstname.lastname@example.org) said this paper’s Preprint
“quantifies the anthropogenic and natural contributions to changes in atmospheric CO2 concentration without need for knowledge of rate constants for individual mechanisms. This is a breakthrough in understanding which (other authors) including myself all failed to make.”
Authors who support the IPCC position – that human CO2 has caused all the increase in atmospheric CO2 above about 280 ppm – include Archer et al. (2009), Cawley (2011), Kohler et al. (2017) and their many references.
1.3 The solution
This paper uses the Physics model (Berry, 2019b) and IPCC (2013) data to determine the “rate constants” or “e-times” for IPCC’s natural carbon cycle. Then, this paper uses the same rules and e-times for IPCC’s natural carbon cycle to calculate the true human carbon cycle.
This paper finds IPCC used significantly different rules and e-times to calculate its human carbon cycle than it used to calculate its natural carbon cycle. The correct calculation of the human carbon cycle must use the same rules as the natural carbon cycle because nature cannot distinguish between human and natural carbon atoms.
The correct calculation shows that all human CO2 from 1750 to 2020 has increased atmospheric CO2 by only 32 ppm (parts per millions by volume).
This paper converts carbon units of GtC (Gigatons of Carbon) and PgC (Petagrams of Carbon) into CO2 units of ppm (parts per million by volume in dry air) using:
1 ppm = 2.12 GtC = 2.12 PgC
The carbon-cycle calculations are not complicated. Anyone competent in fundamental physics and in simple numerical calculations should be able to reproduce the results shown in this paper and in the downloadable Excel file.
2. The Physics Model
2.1 Physics Model description
There are four key carbon reservoirs: land, atmosphere, surface ocean, and deep ocean. The Physics model (Berry, 2019b) applies independently to each carbon reservoir. The “level” of each reservoir is the mass of carbon in each reservoir.
Each reservoir has an e-time defined as the time for the level to move (1 – 1/e) of the distance from its present level to its balance level. The balance level is defined below.
Figure 1 shows the Physics model system for carbon in a reservoir. The carbon in the atmosphere is in the form of CO2.
The Physics model shows how inflow, outflow, and e-time control the level of carbon in each reservoir.
The Physics model shows how inflow, outflow, and e-time control the level of carbon in each reservoir.
The only way external processes can change the level is by changing a reservoir’s inflow or e-time. Therefore, the Physics model’s inflow and e-time INCLUDE ALL THE EFFECTS OF EXTERNAL PROCESSES on the level.
The Physics model rides above chemical processes. Chemical processes can change reservoir levels only by changing inflow, outflow, or e-time, which the Physics model includes.
2.2 Physics Model derivation
The calculation of the carbon cycle requires a theoretical base. The Physics model (Berry, 2019b) provides the base that is reviewed here.
A system describes a subset of nature. A system includes levels and flows between levels. Levels set flows and flows set new levels. The mathematics used in the Physics model are analogous to the mathematics used to describe many engineering systems.
Following Berry (2019b), the Physics model derivation begins with the continuity equation (1) which says the rate of change of level is the difference between inflow and outflow:
dL/dt = Inflow – Outflow (1)
- L = CO2 level (concentration in ppm)
- t = time (years)
- dL/dt = rate of change of L (ppm/year)
- Inflow = rate CO2 moves into the system (ppm/year)
- Outflow = rate CO2 moves out of the system (ppm/year)
The Physics model has only one hypothesis, which is outflow is proportional to level:
Outflow = L / Te (2)
where Te is the “e-folding time” or simply “e-time.” E-time is the time for the level to move (1 – 1/e) of the distance from its present level to its balance level.
Substitute (2) into (1) to get,
dL/dt = Inflow – L / Te (3)
When dL/dt is zero, the level will be at its balance level. Define the balance level, Lb, as
Lb = Inflow * Te (4)
Substitute (4) for Inflow into (3) to get,
dL/dt = – (L – Lb) / Te (5)
Equation (5) shows the level always moves toward its balance level. Both L and Lb are functions of time. Te can also be a function of time.
In the special case when Lb and Te are constant, which means Inflow is constant, there is an analytic solution to (5). Rearrange (5) to get
dL / (L – Lb) = – dt / Te (6)
Then integrate (6) from Lo to L on the left side, and from 0 to t on the right side to get
Ln [(L – Lb) / (Lo – Lb)] = – t / Te (7)
- Lo = Level at time zero (t = 0)
- Lb = the balance level for a given inflow and Te
- Te = time for L to move (1 – 1/e) from L to Lb
- e = 2.7183
The original integration of (6) contains two absolute values, but they cancel each other because both L and Lo are always either above or below Lb.
Raise e to the power of each side of (7), to get the level as a function of time:
L(t) = Lb + (Lo – Lb) exp(– t/Te) (8)
Equation (8) is the analytic solution of (5) when Lb and Te are constant.
All equations after (2) are deductions from hypothesis (2) and the continuity equation (1).
2.3 Physics Model properties
Hypothesis (2) is a linear function of level. This means the Physics model applies independently and in total to human and natural carbon. The balance levels of human and natural carbon are independent.
The Physics model also applies independently and in total to all definitions of carbon or CO2. For example, it applies independently to human CO2, natural CO2, and their sums, and to 12CO2, 13CO2, and 14CO2, and their sums.
However, if outflow were a “strictly increasing function” of level other than level to the power of one, then the Physics model would not apply independently and in total to human CO2 and natural CO2.
Because of (2), it is not necessary (or desirable) to compute the carbon cycle for human and natural carbon simultaneously. It is better (and simpler) to compute their effects separately. Just ADD ANOTHER INSTANCE of the Physics model for each carbon definition. The separate results can be summed to produce the total result.
Equation (4) shows how inflow sets a balance level. Equation (5) shows how the level moves toward the balance level with a speed determined by e-time. When the level equals the balance level, outflow will equal inflow. At the balance level, continuing constant inflow will maintain a constant level of carbon in the reservoir.
Equation (4) shows CO2 does not accumulate in the atmosphere. If inflow decreases, the balance level decreases, and the level follows the balance level. The response is immediate. When inflow to a reservoir increases the level of the reservoir, that reservoir immediately increases its outflow.
2.4 Physics Model verification
The above-ground atomic bomb tests in the 1950s and 1960s almost doubled the concentration of 14C in the atmosphere. The 14C atoms were in the form of CO2, called 14CO2.
After the cessation of the bomb tests in 1963, the concentration of 14CO2 decreased toward its natural balance level. The decrease occurred because the bomb-caused 14C inflow became zero while the natural 14C inflow continued.
Hua et al. (2013) processed 14C data for both hemispheres from 1954 to 2010. Turnbull et al. (2017) processed 14C data for Wellington, New Zealand, from 1954 to 2014. The 14C data from both sources are virtually identical after 1970. After 1970, 14CO2 molecules were well mixed between the hemispheres and 14CO2 in the stratosphere moved to the troposphere.
The 14C data are in units of D14C per mil. The lower bound in D14C units is -1000 which corresponds to zero 14C in the atmosphere. The “natural” balance level, defined by the average measured level before 1950, is zero.
A carbon atom has three isotopes, 12C, 13C, and 14C. Isotopes have the same number of protons and electrons but different numbers of neutrons. Isotopes undergo the same chemical reactions but the rates that isotopes react can differ.
Lighter isotopes form weaker chemical bonds and react faster than heavier isotopes (Wikipedia, 2019). Because 12CO2 is a lighter molecule than 14CO2, it reacts faster than 14CO2. Therefore, the 12CO2 e-time will be shorter than the 14CO2 e-time.
Levin et al. (2010) conclude the 14C data provide “an invaluable tracer to gain insight into the carbon cycle dynamics.” The 14C data trace how CO2 flows out of the atmosphere. All valid models of atmospheric CO2 must replicate the 14C data.
The Physics Model, (5) and (8), accurately replicates the 14CO2 data from 1970 to 2014 with e-time set to 16.5 years, balance level set to zero, and starting level set to the D14C level in 1970.
Figure 2 shows how the Physics Model replicates the 14C data.
The Physics model is not a curve fit equation. The Physics model uses hypothesis (2) and allows only 2 parameters to be adjusted: balance level and e-time. Both are physical parameters.
The replication of the 14C data by the Physics Model has significant consequences. It shows hypothesis (2) is correct. It shows the 14C natural balance level has remained close to zero and e-time has remained constant since 1970. If the e-time had changed since 1970, it would have required a variable e-time to make the Physics Model fit the data
The Physics model’s replication of the 14C data may be the most elegant and important fit of a hypothesis to data in climate change literature.
2.5 Physics Carbon-Cycle Model
The carbon-cycle question for climate change is:
HOW MUCH does human CO2 increase atmospheric CO2 after we account for the recycling of human carbon from the land and ocean back into the atmosphere?
There are two different ways to view the carbon-cycle system. Figure 3 shows individual outflows where the arrows are all positive numbers.
Figure 4 shows net flows where the arrows can be positive or negative numbers.
The following may be the first time the fundamental equations for the carbon cycle have been derived and presented.
The need to formalize carbon-cycle math recalls the need in the 1960’s to solve to the kinetic collection equation in atmospheric research. Berry (1967, 1968, 1969) and Berry and Reinhardt (1974 a, b, c, d) provided the first formulation and solutions to the kinetic collection equation. Other fields of science now use his general solution. In 2007, Wang et al. (2007) showed Berry’s mathematical solution to the kinetic collection equation is still the most accurate solution.
The IPCC model uses individual flows. The Physics model uses net flows because they simplify the following derivations. .
Define the Levels:
- Lg = level of carbon in the land
- La = level of carbon in the atmosphere
- Ls = level of carbon in the surface ocean
- Ld = level of carbon in the deep ocean
Define flow e-times:
- Tga = e-time for flow from land to atmosphere
- Tag = e-time for flow from atmosphere to land
- Tas = e-time for carbon to go from atmosphere to surface ocean
- Tsa = e-time for flow from surface ocean to atmosphere
- Tsd = e-time for flow from surface ocean to deep ocean
- Tds = e-time for flow from deep ocean to surface ocean
Define reservoir e-times:
- Ta = e-time for flow from atmosphere to land and surface ocean
- Ts = e-time for flow from surface ocean to atmosphere and deep ocean
Notice these relationships:
1/Ta = 1/Tag + 1/Tas (9)
1/Ts = 1/Tsa + 1/Tsd (10)
Define other variables:
- t = time in years
- Hin = Inflow of human carbon
The Physics model (2) defines the net flows in Figure 4:
Fga = Lg/Tga – La/Tag (11)
Fas = La/Tas – Ls/Tsa (12)
Fsd = Ls/Tsd – Ld/Tds (13)
The rate equations for these flows are:
dLa/dt = Fga – Fas + Hin (15)
dLs/dt = Fas – Fsd (16)
dLd/dt = Fsd (17)
Now, insert the flows (11-13) into the rate equations (14-17) to get the Physics rate equations:
dLa/dt = Ls/Tsa + Lg/Tga – La/Tag – La/Tas + Hin (19)
dLs/dt = La/Tas + Ld/Tds – Ls/Tsa – Ls/Tsd (20)
dLd/dt = Ls/Tsd – Ld/Tds (21)
Rather than use different e-times, the IPCC model specifies the “splits” to each connected reservoir.
- Kag = fraction of carbon flow from atmosphere to land = 0.64
- Kas = fraction of carbon flow from atmosphere to surface ocean = 0.36
- Ksa = fraction of carbon flow from surface ocean to atmosphere = 0.4
- Ksd = fraction of carbon flow from surface ocean to deep ocean = 0.6
Kag + Kas = 1 (22)
Ksa + Ksd = 1 (23)
IPCC’s splits are related to the Physics e-times as follows:
Kag = Ta / Tag (24)
Kas = Ta / Tas (25)
Ksa = Ts / Tsa (26)
Ksd = Ts / Tsd (27)
Substitute (24-27) into (18-21) and use (22-23) to get IPCC’s rate equations:
dLg/dt = Kag*La/Ta – Lg/Tg (28)
dLa/dt = Ksa*Ls/Ts + Lg/Tg – La/Ta + Hin (29)
dLs/dt = Kas*La/Ta + Ld/Td – Ls/Ts (30)
dLd/dt = Ksd*Ls/Ts – Ld/Td (31)
With the above formalities, we tested and found that IPCC’s splits different from 0.5 do not give significantly different results than IPCC’s splits. Using this simplification, (24-27) become:
Tag = 2 Ta (32)
Tas = 2 Ta (33)
Tsa = 2 Ts (34)
Tsd = 2 Ts (35)
Tga = Tg (36)
Tds = Td (37)
Equations (32-37) simplify the Physics rate equations (18-21) to:
dLg/dt = La/2Ta – Lg/Tg (38)
dLa/dt = Ls/2Ts + Lg/Tg – La/Ta + Hin (39)
dLs/dt = La/2Ta + Ld/Td – Ls/Ts (40)
dLd/dt = Ls/2Ts – Ld/Td (41)
The downloadable Excel spreadsheet uses both the IPCC rate equations (28-31) and the Physics rate equations (38-41). Of course, the results are identical when the IPCC splits are set to 0.5.
3. The Natural Carbon Cycle
3.1 IPCC natural carbon cycle
This paper uses IPCC (2013) definitions for natural carbon and human carbon. Human carbon is the result of human CO2 emissions. All non-human carbon inflow is defined as natural carbon.
The Physics model shows why it is possible (and best) to calculate the natural and human carbon cycles independently. After the separate calculations, the human and natural carbon-cycle results can be summed to get the total result.
A benefit of calculating the human and natural carbon cycles separately is it automatically keeps track of human carbon as it flows through the carbon cycle. No longer is it necessary to guess where the human carbon goes.
IPCC  missed this important fact and calculates human and natural effects together. As a result, IPCC made obvious and significant errors in its calculations. IPCC’s flows are not consistent with its levels.
IPCC inherently uses the Physics model (without showing it) when it claims constant natural CO2 emissions produce a constant balance level of 280 ppm.
IPCC  AR5 Fig. 6.1 (p. 471) shows IPCC’s version of the carbon cycle. Its legend says,
Black numbers and arrows indicate reservoir mass and exchange fluxes estimated for the time prior to the Industrial Era, about 1750.
Figure 5 shows the IPCC Figure 6.1 carbon cycle values for natural carbon.
Figure 5 represents the four carbon reservoirs: Land, Atmosphere, Surface Ocean, and Deep Ocean.
IPCC’s marine biota level of 3 PgC is negligible because it is 0.3 percent of IPCC’s surface ocean level of 900. IPCC’s dissolved organic carbon level of 700 PgC is negligible because it is 1.9 percent of IPCC’s deep ocean level. However, IPCC’s carbon flow through marine biota of 11 PgC per year is added to IPCC’s flow from the surface ocean to the deep ocean of 90 PgC per year to get 101 PgC per year.
IPCC’s levels and flows produce these e-times, using (2), for the natural carbon cycle:
- Tg = 2300 / 107 = 21.5 years
- Ta = 590 / 170 = 3.5 years
- Ts = 900 / 161 = 5.6 years
- Td = 37100 / 100 = 371 years
Table 1 shows selected years of the Physics carbon-cycle calculation for IPCC’s natural carbon levels for 1750. The Physics model shows IPCC’s flows do not maintain IPCC’s constant levels.
- Table 1. IPCC’s e-times and splits increase the level of atmospheric CO2 to 302 ppm rather than keep IPCC’s claimed 280 ppm. Values for levels are in PgC except for the ppm column.
IPCC’s natural flows support a natural level of CO2 in the atmosphere of about 302 ppm rather than IPCC’s claimed 280 ppm after 1750. The difference is not significant, but it shows it is possible to correct IPCC’s natural carbon cycle calculations.
3.2 Corrected IPCC natural carbon cycle model
To correct the IPCC data to be internally consistent, we use IPCC’s natural carbon levels and find e-times, and therefore flows, that make the levels constant over time.
Table 2 shows corrected e-times for IPCC splits. These e-times produce flows that maintain the atmosphere level at 280 ppm, as IPCC claims, and other levels constant.
- Table 2. Corrected e-times for IPCC splits that maintain IPCC’s levels for IPCC’s natural carbon cycle. Values for levels are in PgC except for the ppm.
Table 3 shows the corrected e-times for 0.5 splits. These e-times maintain the atmosphere level at 280 ppm and other levels constant.
- Table 3. Corrected e-times for 0.5 splits to maintain IPCC’s levels for IPCC’s natural carbon cycle. Values for levels are in PgC except for the ppm.
The flows in Tables 2 are unequal flows. The flows in Table 3 are equal.
The End % values are the same in Table 3 and Table 2. So, the End % values are independent of IPCC’s splits. These End % values represent the long-term equilibrium percentages for the natural carbon cycle.
Figure 6 shows the IPCC natural carbon cycle corrected as in Table 3.
In summary, the Physics model found e-times that properly model the IPCC natural carbon cycle. The corrected e-times slightly changed the End % in the reservoirs. IPCC’s splits produce the same result as 50-50 splits.
4. The Human Carbon Cycle
4.1 IPCC’s invalid human carbon cycle
Because human carbon atoms are identical to nature’s carbon atoms, nature will treat human carbon the same as it treats natural carbon. This is an extension of the Equivalence Principle that Einstein used to derive his theory of relativity.
According to this extended Equivalence Principle, the human carbon cycle must have the same e-times as the natural carbon cycle. Also, the human carbon long-term percentages will equal the natural long-term percentages.
IPCC (2013) AR5 Fig. 6.1 (p. 471) shows IPCC’s version of the carbon cycle. Its legend says,
Red arrows and numbers indicate annual ‘anthropogenic’ fluxes averaged over the 2000–2009 time period. These fluxes are a perturbation of the carbon cycle during Industrial Era post 1750.
Figure 7 shows IPCC’s Figure 6.1 data for the human carbon cycle.
IPCC shows 9 PgC per year (from fossil fuels, cement production, and land use change) flows into the atmosphere. IPCC shows a net 2.6 PgC per year flows from atmosphere to land, and a net 2.3 PgC per year flows from atmosphere to surface ocean. The leaves 4 PgC per year added to the atmosphere.
There are five obvious errors in IPCC’s human carbon cycle:
- The surface ocean level remains at 0 PgC, unaffected by the net 2.3 PgC inflow. That cannot happen because outflow is proportional to level, which means a level cannot go to zero so long as there is an inflow.
- The surface ocean, with zero outflow to the deep ocean, magically adds 155 PgC to the deep ocean. That cannot happen because no level can increase if its inflow is zero. And once the deep ocean level is greater than zero, carbon will flow back to the surface ocean.
- The net flow of 2.6 PgC per year from atmosphere to land does not add carbon to the land as it should. Rather it sucks carbon out of the land. This makes the land level decrease from 0 to -30 PgC. A negative level is impossible when there is only positive human carbon to fill the reservoirs. It is like having a glass filled with negative water.
- The carbon level in the atmosphere is 66%. That just happens to be the level IPCC needs to justify its assumption that human carbon caused ALL the increase in atmospheric CO2 above 280 ppm. IPCC used circular reasoning, not science, to achieve its desired result.
- IPCC’s human carbon level (Figure 7) for the atmosphere is 66% while its natural carbon level is 1.5% (Figure 6). This very significant difference shows IPCC treats human carbon differently than it treats natural carbon.
IPCC says human carbon is a “perturbation” on the natural carbon cycle. That is not the correct way to model the effect of human carbon on the carbon cycle.
4.2 Human carbon added to the carbon cycle
To calculate the human carbon cycle, we use CO2 emissions data from 1750 to 2014 compiled by Boden et al.  combined with estimates through 2019.
Table 4 shows that all human emissions since 1750 have added 452 PgC of carbon to the natural carbon cycle. This addition is about one percent. This amount has increased atmospheric CO2 by less than 32 ppm. IPCC gets a different answer because IPCC does not allow human carbon to flow out of the atmosphere as natural carbon flows out of the atmosphere.
- Table 4. The carbon-cycle model for IPCC splits shows all human CO2 emissions from 1750 to January 1, 2020, increase atmospheric CO2 by 35 ppm. The calculation sets inflow to zero on January 2, 2020, to see how fast human CO2 exits the atmosphere.
Table 4 shows, at the beginning of 2020, only 14.7% of all human carbon remains in the atmosphere, 36.7% is in the land, 10.7% is in the surface ocean, and 37.9% is in the deep ocean.
If human emissions were to stop in 2020, then by 2100, 3.9% of human carbon would remain in the atmosphere, 19.3% would be in the land, 3.9% would be in the surface ocean, and 72.8% would be in the deep ocean.
Figure 8 shows the increase in atmospheric CO2 caused by human emissions through 2019 and how this would decay if all human CO2 emissions were stopped in 2020.
Figure 9 shows the combined effects of human and natural CO2 on the level of atmospheric CO2.
Figure 10 shows how the reservoir levels change with time. Most human carbon finds its way to the deep ocean just as natural carbon finds its way to the deep ocean. The smallest amount ends up in the atmosphere.
Although human CO2 adds new carbon to the carbon cycle, human-caused CO2 increase plays a minor part in increasing the level of atmospheric CO2.
The fall of human carbon in the atmosphere after 2020, when the calculation stops human emissions, shows human carbon has little long-term effect.
4.3 Human carbon for constant emissions
Rather than set human CO2 inflow to zero in 2020, this section sets human inflow to its 2019 value from 2020 to 2100.
Table 5 shows the calculated values using the Physics carbon-cycle model.
- Table 5. Results of Physics carbon-cycle model when human emissions are held constant beginning in 2020.
Figure 11 shows the effect of continued constant human CO2 emissions after 2019. The human-caused increase is still much smaller than the increase caused by natural emissions.
Figure 11 shows the continuation of constant human emissions after 2020 would cause a total increase in atmospheric CO2 of 52 ppm by 2100.
4.4 Pulse decay: Physics versus IPCC Bern
The IPCC Bern model (Joos, 2002) represents the results of IPCC’s carbon-cycle models. Berry (2019b) shows how to deconstruct Joos (2002) to get an equation to represent the results of one pulse of human CO2.
The Physics carbon-cycle model uses IPCC natural carbon-cycle data.
Figure 12 shows how the Physics carbon-cycle model and the IPCC Bern model predict the decay of a 100-ppm pulse. The magnitude of the pulse does not matter. The percent decline will be the same for pulses of all sizes.
The Physics model shows the pulse decays to 15 ppm in 10 years and to 4 ppm in 100 years. By contrast, the IPCC Bern model predicts the pulse decays to 55 ppm in 10 years and to 30 ppm in 100 years. The incorrect Bern model says it is impossible for a pulse of human CO2 to ever decay below 15 percent.
Figure 13 shows how the carbon moves from the atmosphere to the other reservoirs.
Human carbon in the atmosphere moves rapidly to the land and the deep ocean because it flows between the reservoirs exactly like natural carbon flows. The IPCC human carbon cycle does not allow human carbon to flow like natural carbon.
Table 6 shows a summary of the pulse calculations.
- Table 6. Human carbon moves from atmosphere to land and deep ocean.
After 200 years, only 2.2% of the human pulse remains in the atmosphere and 85% is in the deep ocean. Initially, the carbon moved to the land but after 30 years, carbon from the land moved to the deep ocean.
The Bern model contradicts the IPCC  data. The IPCC Bern model is a curve fit to the calculations of IPCC’s climate models. Threfore, IPCC’s climate models do not represent the data that the IPCC puts into its own reports.
4.5 Physics carbon cycle explanation
One might ask,
Why does the carbon in a system flow to other reservoirs? What makes the system seek an equilibrium? What defines equilibrium?
In physics, entropy drives a system toward equilibrium. Left alone, the entropy of a system always increases. Equilibrium occurs when the entropy of a system is at its maximum value within the system’s constraints.
We might further ask,
What parameter of the system represents the entropy?
Equations (38-41) define the simplified Physics carbon-cycle system. Equilibrium occurs when the flows are zero. When the flows are zero, the levels are constant, and the L/Te are equal:
Lg/Tg = La/2Ta = Ls/2Ts = Ld/Td (42)
Equation (42) defines equilibrium. The sum of the L/Te’s are an inverse measure of the system’s entropy. The inverse of entropy is negentropy:
Negentropy = Lg/Tg + La/2Ta + Ls/2Ts + Ld/Td (43)
Think of negentropy as the ability to do work. Negentropy is maximum when all the carbon is in the reservoir with the smallest e-time. In year zero, all the carbon is in the atmosphere which is the reservoir with the smallest e-time. When the carbon flows to the other reservoirs, the negentropy decreases. Negentropy is at its minimum when there is no more flow which is when (42) is true.
Figure 14 illustrates the system in year zero when all the carbon is in the atmosphere. Carbon flow from A to G is defined as a negative flow for mathematical purposes.
An analogy is four water buckets connected by tubes. If all the water is in A then the system can do work, say, if turbines were in the tubes.
Figure 15 illustrates the system when the L/Te are distributed evenly between the reservoirs. At that point, the net flows between the reservoirs are zero. The entropy is maximum. If this were the analogy of four buckets, the system cannot do work.
Figure 16 shows how the L/Te levels decrease as carbon flows from the atmosphere to the other reservoirs. The total L/Te begins near 33 and decreases uniformly with time.
Table 7 shows how the L/Te values for each reservoir change with time. Some values go up but only to speed the decrease of the total L/Te that represents negentropy of the system.
- Table 7. The L/Te values as a function of time. The total always decreases.
The system seeks equilibrium because system entropy will increase as required by the Second Law of Thermodynamics.
The Principle of Least Action tells HOW the entropy will increase.
The Principle of Least Action says a system will take the path from Start to Finish that requires the least “action.”
The formal definition of “action” is the time integral of the difference between kinetic energy and potential energy. OK, that is a bit heavy for non-physicists. So, let’s make it simpler.
Action is how something moves from state A to state B. Action is the path you take to get from your home to the grocery store. The quickest or least costly way to get there is the path of least action.
The top curve in Figure 16 represents the total negentropy of the system. It trends downward smoothly because the flows between the reservoirs find the fastest way to lower negentropy and move the system to equilibrium.
In Figure 16, carbon flows into the land and surface ocean in the first 10 years because that is the fastest path to reduce negentropy of the system.
The very definitions (11-13) of the flows in the Physics carbon-cycle model are in terms of entropy levels, not of carbon levels. This definition for the flows is a result of the hypothesis of the Physics model , namely,
Outflow = L / Te (2)
Flow is defined as level divided by e-time.
The point of this discussion about entropy and the Principle of Least Action is that this calculation of the human carbon cycle shows the highest impact that human carbon dioxide can have on atmospheric carbon dioxide. It may not be the lowest impact because maybe human carbon moves toward equilibrium with the other reservoirs faster than described here. This description may not represent the least action scenario, but it is likely close.
Of course, these calculations use IPCC estimated values for natural levels and approximate flows. Should better estimates become available their data can be readily inserted into the downloadable Excel file.
In summary, these calculations prove that IPCC’s data do not support IPCC’s conclusions. Therefore, IPCC’s claims about the impact of human carbon dioxide emissions on atmospheric carbon dioxide are invalid.
This paper shows, possibly for the first time,
- the carbon cycle clearly formulated and calculated;
- the human carbon cycle calculated independently;
- the human carbon cycle calculated using the same rules as the natural carbon cycle.
This paper is a basis for other investigators to improve upon these calculations.
5.2 Why the IPCC carbon-cycle models are wrong
Archer et al. (2009) tests all IPCC carbon-cycle models and finds that all these models
“agree that 25-35% of the CO2 remains in the atmosphere after equilibrium with the ocean (2-20 centuries).”
However, the agreement among models means only that ALL the models are equally wrong.
The Archer et al. models have two major problems:
- None of the models have been tested against reality. So, they are imaginary.
- All the models use different rules for human carbon than for natural carbon.
Archer et al. conclude,
“Some CO2 from the release would remain in the atmosphere thousands of years into the future, and the atmosphere lifetime calculated at that time would be thousands of years.”
The only difference in the human carbon cycle and the equilibrium natural carbon cycle is that human carbon adds new carbon to the carbon cycle. Human carbon still flows from reservoir to reservoir as described by the Physics model.
Contrary to Archer et al., human carbon flows out of the atmosphere as described by the Physics model. The decrease in atmospheric carbon dioxide has no long tail. What Archer et al. think is a long tail, is an illusion caused by the increase in the balance level.
The Archer et al. models assume natural carbon stays balanced while human carbon, which adds only 1% to nature, throws nature out of balance. That can’t happen because nature cannot tell the difference between human and natural carbon atoms.
Furthermore, there is no evidence that 1% more carbon in the carbon cycle changed the rules. If an added 1% did change the rules, it would change the rules for natural as well as for human carbon, and the effect would be very large.
The Physics carbon-cycle model first simulates the natural carbon cycle using IPCC’s data to verify the Physics model simulates natural carbon cycle. The Archer et al. models have no such verification.
The Physics carbon cycle model correctly uses the rules for natural carbon to calculate the human carbon cycle.
Table 4 shows the human carbon level in the atmosphere never gets to 25% of total human carbon. The calculations show only 15% of all human carbon is in the atmosphere by 2020. That is because human carbon flows to the other reservoirs fast enough to keep the human carbon in the atmosphere below 25%. If human emissions were to stop in 2020, then by 2100 only 4% of all human carbon would remain in the atmosphere. There is no significant long-term effect of human carbon emissions.
Figure 12 compares a simulated pulse of human carbon with the Bern model. The Bern model, which simulates the Archer et al. models rather than IPCC data, incorrectly claims 15% of human carbon will remain in the atmosphere forever. The simulated pulse of human carbon will decrease to 15% in 10 years. Table 6 shows only 4.2% will remain after 100 years and 2.2% will remain after 200 years.
5.3 The effect of temperature on CO2
5.3 The effect of temperature on CO2
Salby (2012, 2013, 2016, 2018) shows how changes in surface temperature precede CO2 changes. Harde (2017, 2019) shows how surface temperature increases atmospheric carbon dioxide.
There are only two ways to increase atmospheric CO2: (a) add new carbon to the carbon cycle or (b) increase the e-time of the atmosphere.
The 14C data indicate the e-time for the atmosphere has not changed since 1970 (Berry, 2019b). Tests using the downloadable Excel file show the only permanent way to increase atmospheric CO2 is to add new carbon to the carbon cycle.
This paper concludes nature has added about three times as much carbon to the carbon cycle than human carbon has added since 1750.
IPCC’s own data show that natural carbon emissions have increased atmospheric carbon dioxide by 100 ppm, from IPCC’s 280 ppm in 1750 to 380 ppm in 2019. In the same period, human emissions have increased atmospheric carbon dioxide by an additional 32 ppm to produce the 2019 level of about 412 ppm.
If human emissions were to stop in 2020, then by 2100 only 4% of human carbon would remain in the atmosphere, or enough to increase atmospheric carbon dioxide by a negligible 8 ppm. Human carbon emissions cause no significant long-term change to atmospheric carbon dioxide and are not the cause of climate change.
The author thanks those who reviewed and commented on the draft of this paper: Richard Courtney, Nils-Axel Morner, Chuck Wiese, Gordon Fulks, Gordon Danielsen, Larry Lazarides, John Knipe, Ron Pritchett, Alan Falk, Leif Asbrink, Mark Harvey, Case Smit, Stephen Anderson, and Chic Bowdrie. This research project was funded by the personal funds of Valerie and Edwin Berry.
The author declares he is the only contributor to the research in this paper.
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