The Physics Model Carbon Cycle for Human CO2 - with comments (Ed Berry, Simon Aegerter) by John A. Shanahan

Link: https://edberry.com/blog/climate/climate-physics/human-co2-has-little-effecton-the-carbon-cycle/?__s=fndraeko5dqnx9scih5e#comment-78292 Please see link above for original text, comments and embedded hotlinks. This article contains Ed Berry’s

PREPRINT: The Physics Model Carbon Cycle for Human CO2 November 19, 2019 and a few select comments.

Abstract The scientific basis for the effect of human carbon dioxide on atmospheric carbon dioxide rests upon correctly calculating the human carbon cycle. This paper uses the United Nations Intergovernmental Panel on Climate Change (IPCC) carbon-cycle data and allows IPCC’s assumption that the CO2 level in 1750 was 280 ppm. It derives a framework to calculate carbon cycles. It makes minor corrections to IPCC’s time constants for the natural carbon cycle to make IPCC’s flows consistent with its levels. It shows IPCC’s human carbon cycle contains significant, obvious errors. It uses IPCC’s time constants for natural carbon to recalculate the human carbon cycle. The human and natural time constants must be the same because nature must treat human and natural carbon the same. The results show human emissions have added a negligible one percent to the carbon in the carbon cycle while nature has added 3 percent, likely due to natural warming since the Little Ice Age. Human emissions through 2019 have added only 31 ppm to atmospheric CO2 while nature has added 100 ppm. If human emissions were stopped in 2020, then by 2100 only 8 ppm of human CO2 would remain in the atmosphere. Keywords: carbon dioxide, CO2, climate change, carbon cycle; climate politics; global warming

1. Introduction 1

1.1 The problem The United Nations Intergovernmental Panel on Climate Change (IPCC) [1] 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 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 [2] incorrectly claims,

With solid justification, one can describe the annual carbon budgets as products of high scientific quality with strong political relevance. The problem is to calculate the total effect of all human CO2 emitted since 1750 through 2019 on the carbon cycle and atmospheric CO2. Authors who conclude that human CO2 increases atmospheric CO2 by only a small amount include Revelle and Suess [3], Starr [4], Segalstad [5], Jaworoski [6, 7], Beck [8], Rorsch, Courtney, and Thoenes [9], Courtney [10], Quirk [11], Essenhigh [12], Glassman [13], Salby [14-17], Humlum [18], Harde [19, 20], Berry [21-23], and Munshi [24-28]. Authors who support the IPCC [1] position – that human CO2 has caused all the increase in atmospheric CO2 above about 280 ppm – include Archer et al. [29], Cawley [30], Kohler [31], and their many references. Courtney [10] (pp. 6-7) concluded in 2008,

“… 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.” IPCC [1] used different rules to calculate the human carbon cycle than it used to calculate the 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.

1.2 The solution Courtney [32] commented in his review of this paper’s Preprint, that this paper,

“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.” This paper uses the Physics model [23] with IPCC [1] data to determine the “rate constants” or “e-times” for IPCC’s natural carbon cycle. Then, this paper uses the etimes for IPCC’s natural carbon cycle to calculate the human carbon cycle. IPCC did not do this which is why IPCC got the wrong answer for the human carbon cycle. And the wrong answer has led to the incorrect public perception of the influence of human carbon emissions. The correct calculation, described herein, shows that all human carbon emissions through 2019 have increased atmospheric CO2 by only 31 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 These new carbon-cycle calculations are not complicated. Anyone competent in basic physics and in simple numerical calculations should be able to reproduce the results shown in this paper. (Some readers may wish to read the summary in Section 5.3 first.)

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.

Figure 1. The Physics model system for atmospheric carbon. Inflow and Outflow determine the rate of change in level. 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 a reservoir’s level is by changing the reservoir’s inflow, outflow, or e-time. Therefore, the Physics model INCLUDES ALL EFFECTS OF EXTERNAL PROCESSES (chemical, biological, etc.) on the level of carbon in a reservoir. 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 [23], 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 Where • • • • •

(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) 4

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) where 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 [33] processed 14C data for both hemispheres from 1954 to 2010. Turnbull [34] 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 [33, 34]. 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. [36] 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. 6

Figure 2 shows how the Physics Model replicates the 14C data.

Figure 2. The 14C data from Turnbull [29] using 721 data points. The dotted line is the Physics Model replication of the 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 Formulation “The formulation of a problem is often more essential than its solution…” – Albert Einstein

There can be no solution for the carbon cycle until there has been a formulation of the problem. IPCC does not provide a formulation to calculate the carbon cycle. The

following may be the first time the fundamental equations for the carbon cycle have been derived and presented. This paper uses IPCC [1] numbers for the carbon cycle. These numbers will change as new data becomes available. This formulation will likely endure. It provides an easy way to update these carbon cycle calculations as new data become available. 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 3. The Physics carbon-cycle model using individual flows.

Figure 4 shows net flows where the arrows can be positive or negative numbers.

Figure 4. The Physics carbon-cycle model using net flows. 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: dLg/dt = – Fga dLa/dt = Fga – Fas + Hin dLs/dt = Fas – Fsd dLd/dt = Fsd

(14) (15) (16) (17)

Now, insert the flows (11-13) into the rate equations (14-17) to get the Physics rate equations: dLg/dt = La/Tag – Lg/Tga

(18)

dLa/dt = Ls/Tsa + Lg/Tga – La/Tag – La/Tas + Hin

(19)

dLs/dt = La/Tas + Ld/Tds – Ls/Tsa – Ls/Tsd dLd/dt = Ls/Tsd – Ld/Tds

(20) (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 where: 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) 10

dLa/dt = Ksa*Ls/Ts + Lg/Tg – La/Ta + Hin

(29)

dLs/dt = Kas*La/Ta + Ld/Td – Ls/Ts dLd/dt = Ksd*Ls/Ts – Ld/Td

(30) (31)

Simplifications 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, (2427) 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 dLa/dt = Ls/2Ts + Lg/Tg – La/Ta + Hin dLs/dt = La/2Ta + Ld/Td – Ls/Ts dLd/dt = Ls/2Ts – Ld/Td

(38) (39) (40) (41)

This paper uses both the IPCC rate equations (28-31) and the Physics simplified rate equations (38-41). The Physics and IPCC results are identical when IPCC splits are set to 0.5. The Excel file used for the calculations is included in Supplemental Materials.

3. The Natural Carbon Cycle 3.1 IPCC natural carbon cycle IPCC assumes (a) the level of atmospheric CO2 in 1750 was 280 ppm and (b) human emissions caused all the increase in atmospheric CO2 above 280 ppm. Regarding (a), Segalstad [5] and Jaworowski [6, 7] present evidence that the CO2 level before 1750 was much higher than 280 ppm. Nevertheless, this paper uses assumption (a) to make the Physics carbon-cycle calculations consistent with IPCC’s natural and human carbon cycles. This paper proves assumption (b) is not compatible with IPCC data. 11

This paper uses IPCC [1] definitions for natural carbon and human carbon. Human carbon is the result of human emissions. All carbon inflow that does not result from human emissions is defined as natural carbon. IPCC calculations of the human carbon cycle attempt to “tag” every human-produced carbon atom and follow them through the whole calculation. The Physics model shows why it is best to calculate the natural and human carbon cycles independently. After the independent calculations, the human and natural carbon-cycle results can be summed to get the total result. Independent calculations automatically keep track of human carbon as it flows through the carbon cycle. IPCC [1] missed this important simplification and calculates human and natural effects together. As a result, IPCC made obvious and significant errors in its calculations. IPCC [1] Fig. 6.1 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. The IPCC natural carbon cycle from the black numbers in IPCC Fig. 6.1. 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. This paper adds IPCC’s carbon flow through marine biota of 11 PgC per year to IPCC’s flow from surface ocean to 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 12

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.

Year

Total

ppm

2300

590

900

37100

40890

278

100

2449

628

918

36896

40890

296

200

2501

638

923

36828

40890

301

270

2515

640

924

36810

40890

302

e-time

21.50

3.50

5.60

371.00

End %

6.2%

1.6%

2.3%

90.0%

100.0%

Unstable

Splits

0.64

0.36

0.40

0.60

Flows

114.62

90.08

82.09

99.40

IPCC

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.

Year

Total

ppm

2296

595

903

37096

40890

281

100

2296

595

903

37096

40890

281

200

2296

595

903

37096

40890

281

270

2296

595

903

37096

40890

281

e-time

21.10

3.50

5.90

404.00

End %

5.6%

1.5%

2.2%

90.7%

Splits

0.64

0.36

0.40

0.60

Flows

109

170

153

Stable 100.0%

Unequal

IPCC

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.

•

Year

Total

ppm

2307

594

904

37095

40900

280

100

2307

594

904

37095

40900

280

200

2307

594

904

37095

40900

280

270

2307

594

904

37095

40900

280

e-time

3.22

4.9

402

Year

End %

5.60%

1.50%

2.20%

90.70%

Splits

0.5

Flows

92.27

92.28

Total

ppm

100.00%

Best

Equal

IPCC

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.

Figure 6. The IPCC natural carbon cycle with corrected e-times and flows to keep the IPCC levels constant. 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 15

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 [1] AR5 Fig. 6.1 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.

Fig. 7. The IPCC human carbon cycle from the red numbers in IPCC Fig. 6.1. 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: 1. 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. 2. 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. 3. 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 16

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. 4. 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. 5. 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. The correct way is to model the human carbon cycle independently as this paper does.

4.2 Human carbon added to the carbon cycle This paper calculates the human carbon cycle independently from the natural carbon cycle. That eliminates the need to keep separate track of carbon from human and natural sources. These independent calculations add up to produce the same result as calculating human and natural carbon together, which is much more complicated. Boden et al. [37] provides human CO2 emissions data from 1750 to 2014. The calculations in this paper add estimates of human emissions from 2014 through 2019. Initially, the human carbon level in all reservoirs is zero. Then the calculations insert annual human carbon emissions into the atmosphere from 1750 through 2019. Each year, the calculations allow carbon to flow from the atmosphere to land and surface ocean, and from surface ocean to deep ocean. All levels must have non-negative numbers. The addition of human carbon cannot remove natural carbon from any reservoir. The surface ocean level will rise before it can flow carbon to the deep ocean. Table 4 shows the result of these calculations. All human emissions since 1750 have added 452 PgC of carbon to the natural carbon cycle. This human-carbon addition is about one percent of natural carbon. Human carbon has increased the 2020 level of atmospheric CO2 by 31 ppm. •

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.

Year

Total

ppm

1900

4.47

2.71

1.66

2.94

11.78

1.28

1950

23.08

9.24

6.63

21.75

60.70

4.36

2000

103.15

42.52

30.69

99.69

276.05

20.06

2020

165.70

66.55

48.18

171.13

451.55

31.39

2100

87.30

17.54

17.84

328.87

451.55

8.28

2020

36.7%

14.7%

10.7%

37.9%

100.0%

2100

19.3%

3.9%

72.8%

100.0%

e-time

3.22

4.9

402

Physics

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 calculated 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 8. All human carbon emissions from 1750 through 2019 have increased atmospheric CO2 by 31 ppm. The calculation sets human carbon emissions to zero beginning in 2020 to show how fast human carbon would exit the atmosphere. Figure 9 shows the combined effects of human and natural CO2 on the level of atmospheric CO2.

Figure 9. The human effect on atmospheric CO2 is seen in the area under the dotted line and above the 280-ppm horizontal line. All other atmospheric CO2 below the dashed line is caused by nature. 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.

Figure 10: Human carbon moves from the atmosphere to the land and deep ocean. 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. â&#x20AC;˘

Table 5. Results of Physics carbon-cycle model when human emissions are held constant beginning in 2020.

Year

Total

ppm

1900

1950

4.36

2000

103

100

276

20.06 21

Year

Total

ppm

2020

166

171

452

31.39

2100

383

110

677

1260

52.05

2020

36.7%

14.7%

10.7%

37.9%

100.0%

2100

30.4%

8.8%

7.2%

53.7%

100.0%

e-time

3.22

4.9

402

Physics

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 10. Continued, constant human emissions after 2019 would cause a rise in atmospheric CO2 of 52 ppm by 2100. 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 [38], represents IPCCâ&#x20AC;&#x2122;s claim that human carbon sticks in the atmosphere much longer than natural carbon. Berry [23] shows how to deconstruct [38] to get an equation to represent the results of one pulse of human CO2. The Physics carbon-cycle model uses IPCC data for the natural carbon-cycle. Figure 12 shows how the Physics carbon-cycle model and the IPCC Bern model predict the decay of a 100-ppm pulse.

Figure 12: Pulse decay shows Physics carbon cycle model predicts much faster decay than the IPCC Bern model. 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.

Figure 13. Human 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. â&#x20AC;˘

Table 6. Human carbon moves from atmosphere to land and deep ocean.

Year

Total

ppm

212

100

73.6

14.1

12.6

112

212

6.63

100

45.0

8.9

149

212

4.22

120

37.7

7.6

8.0

159

212

3.61 25

Year

Total

200

21.4

4.8

5.9

180

212

100

21.2%

4.2%

70.4%

100.0%

200

10.1%

2.2%

2.8%

84.9%

100.0%

e-time

3.22

4.9

402

ppm 2.25

Physics

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 [1] 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 entropy 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: 26

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 14. In year zero, all the carbon is in the atmosphere. 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 15. In year infinity, the L/Te are the same in all reservoirs. 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.

Figure 16. The total L/Te decreases with time as the system approaches equilibrium. 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. â&#x20AC;˘

Table 7. The L/Te values as a function of time. The total always decreases.

Year

Lg/Tg

La/2Ta

Ls/2Ts

Ld/Td

Total

ppm

0.00

32.92

0.00

32.92

100

2.94

2.18

1.28

0.28

6.69

6.63

100

1.80

1.39

0.91

0.37

4.46

4.22

Year

Lg/Tg

La/2Ta

Ls/2Ts

Ld/Td

Total

ppm

120

1.51

1.19

0.81

0.39

3.90

3.61

200

0.86

0.74

0.60

0.45

2.64

2.25

200

32.4%

28.0%

22.7%

16.9%

100.0%

e-time

3.22

4.9

402

Physics

The system seeks equilibrium because system entropy will increase as required by the Second Law of Thermodynamics.

4.6 The Principle of Least Action 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 [1], namely, Outflow = L / Te (2) The Principle of Least Action says human carbon will flow from the atmosphere to the other reservoirs in a way that reduces the system negentropy the fastest. The calculation presented in this paper may not be the least action scenario, but it is likely close.

The calculations presented here assume IPCC’s estimated values for natural levels and approximate flows are accurate. Should better estimates become available these calculations can be quickly updated using the Excel file (Supplemental Materials).

5. Discussion 5.1 Why the IPCC carbon-cycle models are wrong Archer et al. [29] 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 does not means they are correct. ALL [29] models can be equally wrong. All [29] models use different rules for human carbon than for natural carbon. Archer et al. [29] 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 [29], the decrease in atmospheric carbon dioxide has no long tail. What [29] calls a long tail is caused by the increase in the balance level of human carbon dioxide. The [29] 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. There is no physics basis to assume what nature does is “good” and what humans do is “bad.” Maybe it is “good” to restore locked carbon to the atmosphere by burning carbon fuels. There is no evidence that 1% more carbon in the carbon cycle changed the rules for the carbon cycle. 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. No such effect has been documented.

The Physics carbon-cycle model first simulates the natural carbon cycle using IPCC [1]. Then the Physics carbon cycle model uses the rules for natural carbon to calculate the human carbon cycle. The [29] models have no physics model. 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.

5.2 The effect of temperature on CO2 Salby [14-17] shows how changes in surface temperature precede CO2 changes. Harde [19, 20] shows how atmospheric carbon dioxide increases with surface temperature. 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. Tests using the Excel file (Supplemental Materials) show the only permanent way to increase atmospheric CO2 is to add new carbon to the carbon cycle. Also, the 14C data show the e-time for the atmosphere has not changed since 1970 [23].

5.3 Summary This is a summary of the fundamental information presented in this paper. Four charts show the percent distribution of natural or human carbon among the four key carbon reservoirs. These reservoirs are land, atmosphere, surface ocean, and deep ocean, in that order because that is how they connect. Carbon-cycle data is from IPCC [1] Fig. 6.1. Figure 17 shows IPCCâ&#x20AC;&#x2122;s distribution for natural carbon in 1750 when, according to IPCC, the level of natural CO2 in the atmosphere was 280 ppm. Only 1.45 percent is in the atmosphere and 90 percent is in the deep ocean.

Figure 17. IPCC natural carbon numbers for 1750, from Table 3 End%. The Figure 17 data represent the long-term equilibrium distribution for natural carbon. It is also the long-term equilibrium distribution for human carbon because natural and human carbon atoms are identical, so nature treats them the same. Figure 18 shows IPCCâ&#x20AC;&#x2122;s human carbon distribution as of about 2013. An overwhelming 66 percent of human carbon is in the atmosphere.

Figure 18. IPCC claimed results for the human carbon cycle, from Figure 7. Question: In Figure 18, how did IPCC get the 66 percent of human carbon in the atmosphere? Answer: IPCC assigned 66 percent of human carbon emissions to the atmosphere because that is the percent necessary to support IPCC’s invalid claim that human carbon emissions have caused all the increase in atmospheric CO2 above 280 ppm. IPCC simply used its assumed result rather than calculate the human carbon cycle. IPCC’s errors are obvious. IPCC shows human carbon in land is negative 8 percent. That is like having a glass of negative water. It is impossible. Also, no carbon can get to the deep ocean if there is no carbon in the surface ocean. IPCC’s human carbon cycle is clearly wrong. Yet, these IPCC errors are the basis of all climate alarmism. Figure 19 shows the physics model calculation for human carbon. The physics model simply applies IPCC’s rules for natural carbon to the human carbon cycle.

Figure 19. Physics model human carbon cycle numbers from Table 4 for 2020. Figure 19 shows less than 15 percent of all human carbon emissions from 1750 through 2019 remain in the atmosphere in 2019. About 25 percent is in the atmosphere and surface ocean. About 75 percent of human carbon has flowed to land and deep ocean. As human carbon enters the atmosphere, it simultaneously flows to land and surface ocean, and from the surface ocean to the deep ocean. Figure 20 shows the physics model distribution of human carbon in 2100 under the assumption that human carbon emissions are terminated in 2020. In 2100, less than 4 percent, or 8 ppm, of human carbon remains in the atmosphere.

Figure 20. Physics model human carbon cycle numbers from Table 4 for 2100 which assumes human emissions are terminated in 2020. In the absence of human carbon inflow, the carbon level in the atmosphere falls as carbon flows into the deep ocean. The distribution of human carbon moves toward the natural carbon equilibrium shown in Figure 17. Given enough time, the distribution of human carbon will be the same as the equilibrium distribution of natural carbon. This summary shows the result of using proper physics to calculate the natural and human carbon cycles. The result shows that human carbon is not a danger to the planet.

Conclusions This paper shows, possibly for the first time, a formulation of the carbon-cycle model and separate calculations of human and natural carbon cycles using the same time constants. IPCCâ&#x20AC;&#x2122;s own data show human emissions through 2019 have added only one percent to the carbon in the carbon cycle. During the same period, nature has added 3 percent to the carbon in the carbon cycle, likely due to natural warming since the Little Ice Age. In terms of quantity, human emissions through 2019 have added 31 ppm to atmospheric CO2 while nature has added 100 ppm. So, natural emissions have increased atmospheric 34

CO2 from 280 ppm to 380 ppm and human emissions have increased atmospheric CO2 from 380 ppm to 412 ppm. If human emissions were to stop in 2020, then by 2100, 8 ppm of human carbon would remain in the atmosphere. If nature remained constant, then stopping all human carbon emissions could not reduce atmospheric CO2 below 388 ppm. But any small changes by nature would overwhelm the decrease of 23 ppm achieved by eliminating all human carbon emissions. Human carbon emissions cause no significant long-term change to atmospheric carbon dioxide and are not the cause of climate change because human carbon flows from the atmosphere to the land and oceans as fast as natural carbon does.

Acknowledgements he 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.

Authorâ&#x20AC;&#x2122;s Contributions The author declares he is the only contributor to the research in this paper.

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Comments, Discussion Simon Aegerter January 5, 2020 at 12:58 pm Remarks on Dr. Ed Berry’s hypothesis. Before going into details, a remark. The first and foremost test of a new hypothesis is plausibility. Berry’s hypothesis fails that test on two accounts: • So, of the 134 ppm excess CO2, only 32ppm are from burning fossil fuels, the rest is natural. Where does it come from? It can not come out of the ocean, because that’s where the excess CO2 goes. What part of nature has so fundamentally changed after about 1850 that it started to spew CO2 into the atmosphere? • Since the late 1950s, that is 6 decades, scientists have measured the isotopic composition of atmospheric CO2, the changing CO2 content of the oceans, tracked the amount of carbon burned and many more relevant parameters and have come to the conclusion: of the CO2 that we spew into the atmosphere by burning fossil fuels, about half remains in the atmosphere for a while, some is taken up by a growing phytosphere and the rest is taken up by the oceans. What we observe in the atmosphere is that part that goes neither in the ocean nor in plants. Now in 2019 Dr. Berry finds that they have all been wrong. Well, that’s not impossible – remember Galileo – but that requires a very rigorous proof. Berry doesn’t deliver. The following notes are as I wrote them down while reading the paper attentively. Berrys words are in “Quotation marks”. ____________________ Physics Model: “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.” With respect to which other reservoir? The e-time has to be calculated for each pair of reservoirs. “Outflow = Level / e-time” Should read: Outflow = (Level- Balance Level) / e-time because if level = balance level, the outflow is zero. Unless there is an inflow. Hence, Equ 2 should read: Outflow = (L-Lb) / e-Time 38

Therefore (3): dL/dt = Inflow – (L-Lb) / Te And (4): Inflow = (L-Lb) / Te So equ. 5 becomes: dL/dt = (L-Lb) / Te – (L-Lb)/Te = 0 which just states the assumption that lead to equ (4) “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.” None of that can be derived from (4). It was derived under the assumption that dL/dt is 0. So, the conclusion “The response is immediate” follows from the assumption. If we increase Inflow, what happens? Either Te has to decrease or (L-Lb) has to increase what of course it does. “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.” Why? There is one carbon cycle and in the exchange between the atmosphere and the mixed layer it is one CO2-cycle. If we add something to one reservoir, we just get it out of its equilibrium and we need to calculate how fast it regains the new equilibrium. “The replication of the 14C data by the Physics Model has significant consequences. It shows hypothesis ¬(2) is correct.” That is so because the L(t) for 14CO2 is renormalized to have a Lb of 0. The Lb of total CO2 is not 0. There is another discrepancy that disallows the use of 14C data to calculate residence time of total CO2. Equ. 4, stated correctly, gives: Inflow = (L-Lb) / Te; or Te = (L-Lb) / Inflow (A) (strictly, as defined, only for the equilibrium state) Now, in the case of total CO2, the inflow is of the order of 1%, whereas in the case of 14CO2, it was almost a factor of 2 within a few years. If the Te for 14CO2 is 16.5, then Te for total CO2 can be estimated according to equ. A: L-Lb is 700 vs 412-280= 132 inflow is 0.1 vs 0.01 16.5*(132/700)/(0.01/.0.1) = 16.5*19 = 310 Years. I have not checked if that corresponds to the number that the IPCC uses but it seems to confirm the generally accepted fact that CO2 remains in the air “for many centuries”. Dec 29 2019 / SAe Reply 1.

Dr. Ed January 5, 2020 at 3:57 pm Dear Simon, Thank you for your comment. I will reply in sections to allow for separate discussion of the components of your comment.

First and foremost, you have the scientific burden of proof reversed. IPCC and its contributors claim (a) human emissions cause all the increase in atmospheric CO2 and (b) most human carbon stays in the atmosphere essentially forever. IPCC and its contributors have the burden of proof to show their claims are correct. The Null Hypothesis requires that we assume these claims are wrong until they are proven otherwise. No one has provided evidence that the IPCC claims are correct. Many have proved the IPCC claims are not correct. My preprint shows how these IPCC theories fail physics. I published my calculations so anyone can try to prove my calculations are wrong. No one has yet done this. I am prepared to defend all challenges to my calculations and arguments. You are welcome to try to defend the IPCC claims or to prove my arguments are wrong. But merely stating the past papers disagree with my preprint does not constitute proof that my calculations or arguments are wrong. Those papers agree with the IPCC claims and I have proved the IPCC claims are wrong. So, the conclusions of past papers are not valid arguments against my preprint. I show how IPCC’s natural carbon cycle is basically correct according to the Physics model. (I realize you do not understand the Physics model from your comment further below. I will address that later. For now, assume the Physics model is correct.) The fact that the Physics model shows the IPCC natural carbon cycle is basically selfconsistent, indicates the value of the Physics model to calculate the carbon cycle. The Physics model allows calculation of IPCC’s e-times inherent in IPCC’s data. The Physics model then allows the correction of IPCC’s natural carbon cycle e-times to make its levels consistent with its flows. IPCC did not do this. Then, independent of the above, I show how IPCC made obvious, significant errors in its human carbon cycle. Those obvious IPCC errors prove all the contrary claims your comment lists are invalid. Then, I show IPCC made an invalid assumption that affects all its reports. IPCC assumed nature treats human carbon differently than it treats natural carbon. That is a no-no, and it blows all the IPCC conclusions in your comment out of the water. So far, there is no math. Just simple observation. The IPCC human carbon cycle model is significantly incorrect. Yet this incorrect IPCC human carbon cycle is the basis of IPCC’s claims (a) and (b), as well as the worldwide “climate crisis” hallucination. No math and we have proved this basic IPCC claim is wrong! Also, please see my prior preprint1 here It describes the Physics model more completely that done in this preprint2. Now, to address your specific comments: • “So, of the 134-ppm excess CO2, only 32ppm are from burning fossil fuels, the rest is natural. Where does it come from? It cannot come out of the ocean, because that’s where the excess CO2 goes. What part of nature has so fundamentally changed after about 1850 that it started to spew CO2 into the atmosphere?” Reply: Who says it cannot come out of the oceans? Who says that’s where the excess CO2 goes? 40

Courtney [10] (pp. 6-7) answered your comment back in 2008: “… 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.” The earth has warmed after the Little Ice Age. The warming has released carbon formerly trapped in the oceans. This is consistent with all the data. Section 5.2 addresses the issue of how surface temperature increase causes atmospheric CO2 to increase. Please see the noted references. My preprint1 shows Harde’s conclusions for how temperature changes CO2 level in 2.4. Where are the models that supposedly prove the excess carbon cannot come out of the oceans? Where is a formulation of the carbon cycle that any previous study has used to prove the assertations in your comments? They all assume human carbon emissions have caused all the increase in atmospheric CO2 above 280 ppm. That is circular reasoning. • “Since the late 1950s, that is 6 decades, scientists have measured the isotopic composition of atmospheric CO2, the changing CO2 content of the oceans, tracked the amount of carbon burned and many more relevant parameters and have come to the conclusion: of the CO2 that we spew into the atmosphere by burning fossil fuels, about half remains in the atmosphere for a while, some is taken up by a growing phytosphere and the rest is taken up by the oceans. What we observe in the atmosphere is that part that goes neither in the ocean nor in plants.” Those are not facts. They are assumptions. Carbon isotopes data do not prove human carbon emissions caused all the rise in atmospheric CO2 above 280 ppm. My preprint1 shows how the IPCC theory does not fit the isotope data in 3.3 and 3.4. The burden of proof is upon those authors to prove their calculations are correct. Their calculations did not begin with a valid carbon cycle formulation. Then they made unwarranted assumptions. So far, your comment has not shown there is an error in my preprint’s calculations or arguments. You are welcome to try to defend the calculations made in the papers that support your comment. I will reply to the rest of your comment in another comment. Thank you again for your comment.

Dr. Ed January 5, 2020 at 5:08 pm Dear Simon, Thank you for your comment. This replies to the second part of your comment. My replies are in bold. Physics Model: “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.” With respect to which other reservoir? The e-time has to be calculated for each pair of reservoirs. “Outflow = Level / e-time” Not true. The e-time is a function of each individual reservoir: e-time = Level / Outflow. Should read: Outflow = (Level- Balance Level) / e-time because if level = balance level, the outflow is zero. Unless there is an inflow. No. Outflow is NOT a function of Balance Level. That is incorrect physics. At the Balance Level, Outflow still = Level / e-time. But when Level = Balance Level, then Outflow = Inflow. Hence, Equ 2 should read: Outflow = (L-Lb) / e-Time Therefore (3): dL/dt = Inflow – (L-Lb) / Te And (4): Inflow = (L-Lb) / Te So equ. 5 becomes: dL/dt = (L-Lb) / Te – (L-Lb)/Te = 0 which just states the assumption that lead to equ (4) No, no, no, and no! Please go back and do the physics correctly. “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.” None of that can be derived from (4). It was derived under the assumption that dL/dt is 0. So, the conclusion “The response is immediate” follows from the assumption. If we increase Inflow, what happens? Either Te has to decrease or (L-Lb) has to increase what of course it does. Lb = Inflow * Te (4) (4) was not “derived under the assumption that dL/dt is 0.” (4) is a definition, not an assumption. Nothing in the physics changes by using the definition of Balance Level, but the definition simply makes the physics easier to understand. “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.” Why? There is one carbon cycle and in the exchange between the atmosphere and the mixed layer it is one CO2-cycle. If we add something to one reservoir, we just get it out of its equilibrium, and we need to calculate how fast it regains the new equilibrium. Stop and think. (2) makes the system linear. Therefore, we can compute carbon cycles separately and add them up afterward. The answer will be the 42

same as when we calculate the cycles together. It is no different than if we calculated with half the natural carbon and then doubled the answer. And since we can do this, we should do this because it very much simplifies the calculations. Yes, IPCC did not understand this either. I may be the first to point this out. If IPCC had understood this simplification, it might have found its significant error in its human carbon cycle. Then IPCC might have corrected its error and saved the world from the climate delusion. The key point is the human and natural carbon cycles are truly independent and do not interfere with one another. And they must use the same e-times because nature cannot tell the difference between human and natural carbon atoms. “The replication of the 14C data by the Physics Model has significant consequences. It shows hypothesis (2) is correct.” That is so because the L(t) for 14CO2 is renormalized to have a Lb of 0. The Lb of total CO2 is not 0. The Lb for 14CO2 of zero is not really zero 14C. The true zero level in D14C units is -1000. The D14C zero level is defined as the normal 14C level before the bomb tests. It is 1000 D14C units above the 14C zero level. The important point is that (2) properly replicates the 14C data when Lb is set to zero and Te is set to 16.5. No IPCC model can do that. There is another discrepancy that disallows the use of 14C data to calculate residence time of total CO2. Equ. 4, stated correctly, gives: Inflow = (L-Lb) / Te; or Te = (L-Lb) / Inflow (A) (strictly, as defined, only for the equilibrium state) Those are not correct equations, as I pointed out above. Now, in the case of total CO2, the inflow is of the order of 1%, whereas in the case of 14CO2, it was almost a factor of 2 within a few years. That is irrelevant. If the Te for 14CO2 is 16.5, then Te for total CO2 can be estimated according to equ. A: L-Lb is 700 vs 412-280= 132 inflow is 0.1 vs 0.01 16.5*(132/700)/(0.01/.0.1) = 16.5*19 = 310 Years. Sorry, that is incorrect because the equations are incorrect. There is no way to estimate the Te for 12CO2 from the 14C data other than to say the Te for 12CO2 will be less than the Te for 14CO2. I have not checked if that corresponds to the number that the IPCC uses but it seems to confirm the generally accepted fact that CO2 remains in the air “for many centuries”. Sorry, it does not so confirm this. Thank you again for your comment.

carbon cycles separately and add them up afterward. The answer will be the same as when we calculate the cycles together. It is no different than if we calculated with half the natural carbon and then doubled the answer. And since we can do this, we should do this because it very much simplifies the calculations. Yes, IPCC did not understand this either. I may be the first to point this out. If IPCC had understood this simplification, it might have found its significant error in its human carbon cycle. Then IPCC might have corrected its error and saved the world from the climate delusion. The key point is the human and natural carbon cycles are truly independent and do not interfere with one another. And they must use the same e-times because nature cannot tell the difference between human and natural carbon atoms. “The replication of the 14C data by the Physics Model has significant consequences. It shows hypothesis (2) is correct.” That is so because the L(t) for 14CO2 is renormalized to have a Lb of 0. The Lb of total CO2 is not 0. The Lb for 14CO2 of zero is not really zero 14C. The true zero level in D14C units is -1000. The D14C zero level is defined as the normal 14C level before the bomb tests. It is 1000 D14C units above the 14C zero level. The important point is that (2) properly replicates the 14C data when Lb is set to zero and Te is set to 16.5. No IPCC model can do that. There is another discrepancy that disallows the use of 14C data to calculate residence time of total CO2. Equ. 4, stated correctly, gives: Inflow = (L-Lb) / Te; or Te = (L-Lb) / Inflow (A) (strictly, as defined, only for the equilibrium state) Those are not correct equations, as I pointed out above. Now, in the case of total CO2, the inflow is of the order of 1%, whereas in the case of 14CO2, it was almost a factor of 2 within a few years. That is irrelevant. If the Te for 14CO2 is 16.5, then Te for total CO2 can be estimated according to equ. A: L-Lb is 700 vs 412-280= 132 inflow is 0.1 vs 0.01 16.5*(132/700)/(0.01/.0.1) = 16.5*19 = 310 Years. Sorry, that is incorrect because the equations are incorrect. There is no way to estimate the Te for 12CO2 from the 14C data other than to say the Te for 12CO2 will be less than the Te for 14CO2. I have not checked if that corresponds to the number that the IPCC uses but it seems to confirm the generally accepted fact that CO2 remains in the air “for many centuries”. Sorry, it does not so confirm this. Thank you again for your comment.

Ision January 5, 2020 at 6:14 pm The fact is CO2, both Natural and Man-Made, have absolutely no driving influence on Earth’s climate, whatsoever. CO2 is basically meaningless, as it follows…and does not presage…climatic change. Water vapor simply overwhelms any effect CO2 might have completely. Man-made CO2 is absolutely meaningless to climate, but very important in regards to controlling humanity…and in the confiscation of wealth. John Shanahan January 6, 2020 at 5:26 pm Here is my position: 1) The website allaboutenergy.net presents over 600 articles on all sides of the manmade global warming debate so the public can access any material. I’m the editor and have uploaded all this content after studying it carefully. See here: http://allaboutenergy.net/environment 2) The conclusions about future use of fossil fuels are of the utmost importance of the modern world. They must be scientifically sound, not a politician’s or activist’s whim. 3) After carefully studying all these articles and speaking and e-mailing many of these authors, my conclusion as of January 2020 is that carbon dioxide from fossil fuels is not causing serious man-made global warming, man-made climate change, man-made climate disruption (President Obama’s Science Advisor, John Holdren’s terms). It is important that the world continue to use fossil fuels, especially with real pollution control systems and no cheating on pollution monitoring instrumentation. In following the Scientific Method, I am open to changing my position, given the necessary proof. DonR January 7, 2020 at 2:46 pm Dear John: As Dr. Ed has stated multiple times, there is no molecular difference between naturally occurring CO2 and manmade CO2 so to try to claim that manmade CO2 remains in the atmosphere longer is just plain false. Dr. Ed has proven that extensively. One question that has never been answered by any of the “Experts” is what is the perfect level of CO2 our planet should be experiencing. Can you give us an answer? Last but not least, the current alleged CO2 level in our atmosphere is supposedly around 410 PPM. Why is that bad and what should the level be? 410 PPM sounds pretty bad but when you put it into the proper context and compare it to a monetary value, that turns out to be a mere 41 cents per $1,000…………….LOL! 46

Max January 6, 2020 at 2:35 pm I think that Dr Berry should be honored to have the attention of a prestigious professor like Simon Aergerter, and I see that the discussion is becoming quite stimulating, if not exciting. Hopefully Prof Aergerter will have better points than what I’ve read here in this thread : https://www.quora.com/profile/Simon-Aegerter, by which he assumes as an apodiptic truth the fact that the entire increase of CO2 from 280 to 410 is due to humans, without even a doubt, simply because other hypothesis are not “plausible” ? With all my due respect (I am just a poor engineer that loves physics, not a professor, not a climatologist) I cannot believe that the scientific method – that was really rigorous when I was taught it by my professors a long ago – has evolved to this point.

John Shanahan January 6, 2020 at 6:21 pm Eric Jelinski has degrees in mechanical and chemical-nuclear engineering. He has a long and distinguished career working as a project manager for Canada’s nuclear power plants. He is a lecturer in nuclear engineering at the University of Toronto. In addition to all this, he is an outstanding and very observant farmer. We did not post his comments on the Ed Berry – Simon Aegerter debate about man-made carbon dioxide because we wanted everyone to see his graphics. Please see Eric Jelinski’s comments at this link: http://allaboutenergy.net/environment/item/2488-eric-jelinski-comments-on-carbondioxide-debate-between-ed-berry-and-simon-aegerter-canada-switzerland-usa Eric supports Ed Berry’s physics flow model. This is an important endorsement.

Simon Aegerter January 7, 2020 at 10:02 am Dear Ed, thank you for the extensive replies. The first one is to my argument of plausibility. You call this reversal of burden of proof. I don’t think so. If somebody challenges established knowledge the burden of proof is on him. Then the question on where the excess CO2 is coming from and the contention that it is outgassing from the ocean: In this paper: Gruber, Nicolas et al.: “The oceanic sink for anthropogenic CO2 from 1994 to 2007”, Science, 15. March 2019, (363) pg. 1193 Measurements of CO2 in the oceans have been compiled for all the oceans and the authors come to the conclusion that the total amount has increased by 125 billion tons

during these 13 years. I don’t call that outgassing. That paper was not published in some crackpot journal, but in AAASs “Science”. If the excess CO2 comes out of the ocean, then why is the excess larger in the northern hemispere and not in the southern hemisphere, where most of the oceans are? And if the excess CO2 does come out of the oceans, where are the 35 billion tons of CO2 hiding, that come out of stacks and tailpipes every year? That’s what I mean by a plausibility test. If a result looks implausible, the first thing to do is look for an error. I am convinced that the error is the use of 14CO2 to estimate the e-time of 12CO2. You think otherwise. let’s agree to disagree. I understand that the paper is submitted for publication. Let the reviewer be the judge. Best Simon Dr. Ed January 7, 2020 at 11:34 am Dear Simon, Thank you for your contribution to the discussion of my preprint. You say, “If somebody challenges established knowledge the burden of proof is on him.” Given all the challenges to the IPCC theory, the IPCC theory cannot be called “established knowledge.” The IPCC theory is not a physical law. The scientific method always puts the burden of proof on those who claim a theory is true. This means, if anyone finds an error in the theory, then the theory is false. Such errors can be an incorrect prediction or a violation of established physics in the formulation of the theory. I have shown the existence of blatant, obvious errors in IPCC’s human carbon cycle. I have shown that IPCC’s theory incorrectly assumes nature treats human and natural carbon differently. Each observation alone proves the IPCC theory is not “established knowledge.” You reference the Gerber, Nicolas et al. paper, which can be read here. Section “5.1 Why the IPCC carbon-cycle models are wrong” discusses papers reviewed by Archer [29] and shows why they are incorrect. The Gerber paper is simply another of the many papers that base their conclusions on the assumption that human emissions cause all the observed changes in the carbon cycle. Its conclusions are the result of circular reasoning.

The Gerber paper has no carbon cycle formulation or calculation. It draws conclusions that are not justified by the data. It offers no proof or even an argument to justify its conclusion that the increase in ocean carbon has been caused by human emissions. It could have been caused by nature. Gerber et al. and all the Archer [29] papers omit discussion of the natural alternative. Therefore, they cannot show how human emissions change the carbon cycle. This preprint may be the only scientific paper that properly treats both human and natural carbon cycles. You ask, “And if the excess CO2 does come out of the oceans, where are the 35 billion tons of CO2 hiding, that come out of stacks and tailpipes every year?” The carbon cycle model presented in this preprint answers that question. No one else has answered that question. Thank you again for your comments. H. Douglas Lightfoot January 7, 2020 at 5:30 pm Carbon dioxide is our good friend and not an enemy The Earth is surrounded by a blanket of atmosphere that keeps it warm and habitable. In contrast, other celestial bodies with little or no atmosphere, such as Mars and the Moon are too cold for life as we know it. Our atmosphere contains two vitally important parts—water and carbon dioxide (CO2). Energy from the Sun is necessary for both water and carbon dioxide to function. Water through evaporation, precipitation and ocean currents distributes heat from the Sun around the Earth and keeps it from becoming too hot or too cold. Through the process of photosynthesis, energy from the Sun in the presence of chlorophyll, the green color in plants, causes carbon dioxide to react with water to form food and release oxygen. The Earth has the right conditions for life as we know it to take hold and to grow and develop. We live in a wonderful world. Currently, there is widespread concern that a climate catastrophe is approaching because of rising levels of CO2 in the atmosphere. Scientists writing in the IPCC First Assessment Report for the IPCC in 1990 stated that water vapor amplified warming of the atmosphere by CO2. This led to the belief that life on Earth is headed for dangerous levels of warming. Since 1990, new information has been developed that was not available to the scientists. This is, namely, back radiation measurements and the ability to easily record air temperature and relative humidity at several places around the Earth at the same time. Applying this information proves by reproducible evidence that water vapor does not 49

amplify warming by CO2. In fact, warming by water vapor is approximately 8 to 47 times larger than that of CO2 and renders it ineffective as a warming gas. CO2 is our good friend and not our enemy. We can continue to enjoy our lives on Earth without fear of a man made climate catastrophe. Full paper and Two page summary available at: http://www.thelightfootinstitute.ca/papers.html H. Douglas Lightfoot