PREPRINT: The Physics Model Carbon Cycle for Human CO2

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.   Introduction

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 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.

Figure 1. The Physics model system for atmospheric carbon. Inflow and Outflow determine the rate of change in level. The only hypothesis is Outflow = Level / e-time.

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 = InflowOutflow                                                                                             (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 = InflowL / 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 = – (LLb) / 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 + (LoLb) 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.

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 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 3. The Physics carbon-cycle model described as individual flows.

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

Figure 4. The Physics carbon-cycle model described as net flows.

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:

            dLg/dt = – Fga                                                                         (14)

            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:

            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                            (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 [2] 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 [2] 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. The IPCC natural carbon cycle from the black numbers in IPCC Fig. 6.1.

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.

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

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.

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 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.

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. [32] 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 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.

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 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, 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.

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.

  • 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 [2] 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 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.

  • 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 [1], 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.

5.   Discussion

5.1 Significance

This paper shows, possibly for the first time,  

  1. the carbon cycle clearly formulated and calculated;
  2. the human carbon cycle calculated independently;
  3. 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:

  1. None of the models have been tested against reality. So, they are imaginary.
  2. 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.

Author’s Contributions

The author declares he is the only contributor to the research in this paper.


Download supporting files


Archer, D., M. Eby, V. Brovkin, A. Ridgwell, L. Cao, U. Mikolajewicz, et al. 2009. Atmospheric Lifetime of Fossil Fuel Carbon Dioxide. Annu. Rev. Earth Planet. Sci., 37, pp. 117–134. CrossRef, CrossRef2

Beck, E. 2007. 180 Years of Atmospheric CO2 Gas Analysis by Chemical Methods. Energy & Environment. Vol 18, No. 2. CrossRef

Berry, E. X. 1967. Cloud droplet growth by collection. J. Atmos. Sci. 24, 688-701.  CrossRef

Berry, E. X. 1968. Comments on ‘Cloud droplet coalescence: Statistical foundations and a one-dimensional sedimentation model.’ J. Atmos. Sci. 25, 151-15. CrossRef

Berry, E. X. 1969. A mathematical framework for cloud models. J. Atmos. Sci. 26, 109-111. CrossRef

Berry, E. X. 2018. A fatal flaw in global warming science. Basic Science of a Changing Climate. Porto University, Portugal. Sep 7. CrossRef

Berry, E. X. 2019a. Contradictions to IPCC’s climate change theory. Annual meeting of the American Meteorological Society, Phoenix.  CrossRef

Berry, E. X. 2019b. Human CO2 emissions have little effect on atmospheric CO2. International Journal of Atmospheric and Oceanic Sciences. Volume 3, Issue 1, June 2019, pp 13-26. CrossRef

Berry, E. X, R.L. Reinhardt. 1974a. An analysis of cloud drop growth by collection. Part I: Double distributions. J. Atmos. Sci. 31, 1814-1824. CrossRef

Berry, E. X, R.L. Reinhardt. 1974b. An analysis of cloud drop growth by collection. Part II: Single initial distributions. J. Atmos. Sci. 31, 1825-1831. CrossRef

Berry, E. X, R.L. Reinhardt. 1974c. An analysis of cloud drop growth by collection. Part III: Accretion and self-collection. J. Atmos. Sci. 31, 2118-2126. CrossRef

Berry, E. X, R.L. Reinhardt. 1974d. An analysis of cloud drop growth by collection. Part IV: A new parameterization. J. Atmos. Sci. 31, 2127-2135. CrossRef

Boden, T., B. Andres. 2017. Global CO2 emissions from fossil-fuel burning, cement manufacture, and gas flaring: 1751-2014. CrossRef

Candela, J., D. Carlson. 2017. The annual global carbon budget. World Meteorological Organization. CrossRef

Cawley, G.C. 2011. On the Atmospheric residence time of anthropogenically sourced CO2. Energy Fuels 25, pp. 5503–5513. CrossRef

Courtney, R.S. 2008. Limits to existing quantitative understanding of past, present and future changes to atmospheric CO2 concentration. International Conference on Climate Change, New York. CrossRef

Essenhigh,R.E. 2009. Potential dependence of global warming on the residence time (RT) in the atmosphere of anthropogenically sourced CO2. Energy Fuel 23, pp. 2773-2784. CrossRef

Glassman, J.A. 2010. On why CO2 is known not to have accumulated in the atmosphere and what is happening with CO2 in the modern era. Rocket Scientist Journal. CrossRef

Harde, H. 2017: Scrutinizing the carbon cycle and CO2 residence time in the atmosphere. Global and Planetary Change. 152, 19-26. CrossRef

Harde, H. 2019. What Humans Contribute to Atmospheric CO2: Comparison of Carbon Cycle Models with Observations. International Journal of Earth Sciences Vol. 8, No. 3, pp. 139-159. CrossRef

Hua, Q., M. Barbetti, A. Z. Rakowski. 2013. Atmospheric radiocarbon for the period 1950–2010. RADIOCARBON, Vol 55, pp. 2059–2072. Table S2c. CrossRef

Humlum, O., K. Stordahl, J.E. Solheim. 2013. The phase relation between atmospheric CO2 and global temperatures. Global and Planetary Change, 100, pp 51-69. CrossRef

IPCC. 2013. Carbon and other biogeochemical cycles. CrossRef

IPCC. 2007. Climate Change 2007: The Physical Science Basis. CrossRef

Jaworowski, Z. 2003. Climate Change: Incorrect information on pre-industrial CO2. Statement written for the Hearing before the US Senate Committee on Commerce, Science, and Transportation. CrossRef

Jaworowski, Z. 2007. CO2: The greatest scientific scandal of our time. 21st CENTURY Science & Technology. CrossRef

Joos, F. 2002. Parameters for tuning a simple carbon cycle model. CrossRef

Kohler, P., J. Hauck, C. Volker, D.A. Wolf-Gladrow, M. Butzin, J.B. Halpern, et al. 2017. Comment on ‘Scrutinizing the carbon cycle and CO2 residence time in the atmosphere’ by H. Harde. Global and Planetary Change. CrossRef

Levin, I., T. Naegler, B. Kromer, M. Diehl, R. Francey, A. Gomez-Pelaez, et al. 2010. Observations and modelling of the global distribution and long-term trend of atmospheric 14CO2. Tellus B: Chemical and Physical Meteorology. CrossRef

Munshi, J. 2016a. Changes in the 13c/12c ratio of atmospheric co2 1977-2014. CrossRef

Munshi, J. 2016b. Dilution of atmospheric radiocarbon CO2 by fossil fuel emissions. CrossRef

Munshi, J. 2016c. Some methodological issues in climate science. CrossRef

Munshi, J. 2016d. Circular reasoning in climate change research. CrossRef

Munshi, J. 2017. Responsiveness of atmospheric co2 to fossil fuel emissions: updated. CrossRef

Munshi, J. 2018. Carbon Cycle Measurement Problems Solved with Circular Reasoning. 2018. Thongchai Thailand. CrossRef

Quirk, T. 2009. Sources and sinks of CO2. Energy & Environment. Volume: 20 Issue: 1, pp. 105-121. CrossRef

Revelle, R., H. Suess. 1957. CO2 exchange between atmosphere and ocean and the question of an increase of atmospheric CO2 during past decades. Tellus. 9: 18-27; 1957. CrossRef

Rorsch, A., R.S. Courtney, D. Thoenes. 2005. The Interaction of Climate Change and the CO2 Cycle. Energy & Environment, Volume 16, No 2. CrossRef

Salby, M. L. 2012. Physics of the Atmosphere and Climate. Cambridge University Press. (ISBN: 978-0-521-76718-7) CrossRef

Salby, M. L. 2013. Relationship between greenhouse gases and global temperature. Video Presentation, April 18. Helmut-Schmidt-University Hamburg. CrossRef

Salby, M. L. 2016. Atmosphere Carbon. Video Presentation, July 18. University College London. CrossRef

Salby, M. L. 2018. What is really behind the increase in atmospheric CO2? Video Presentation, October 10. Helmut-Schmidt-University Hamburg, Germany. CrossRef

Segalstad, T. V. 1998. Carbon cycle modelling and the residence time of natural and anthropogenic atmospheric CO2: on the construction of the Greenhouse Effect Global Warming dogma. In: Bate, R. (Ed.): Global warming: the continuing debate. ESEF, Cambridge, U.K. (ISBN 0952773422): 184-219; 1998. CrossRef, CrossRef2

Starr, C. 1992. Atmospheric CO2 residence time and the carbon cycle. Science Direct, 18, 12, pp. 1297-1310; 1992. CrossRef

Turnbull, J. C., S. E. Mikaloff Fletcher, I. Ansell, G. W. Brailsford, R. C. Moss, Norris, et al. 2017. Sixty years of radiocarbon dioxide measurements at Wellington, New Zealand: 1954–2014. Atmos. Chem. Phys., 17, pp. 14771–14784. CrossRef

Wang, L., Y. Xue, W.W. Grabowski. 2007. A bin integral method for solving the kinetic collection equation. Journal of Computational Physics, V605560. 2007. 10.1016/ CrossRef

Wikipedia. 2019. Isotopes.

57 thoughts on “PREPRINT: The Physics Model Carbon Cycle for Human CO2”

  1. Larry Lazarides

    Although your paper is very learned, I prefer a simpler means of disproving IPCCs alarmist predictions, as follows –

    1. The Australian Academy of Science publishes data and graphs showing temp changes over (a) the last 800,000 years and also over (b) the last 160 years. The years in (b) represents .02% of the years in (a).
    The data for (a) shows the planet’s temp has increased and decreased numerous times over a range of 16 degrees.
    The data for (b) shows temps have increased over the last 160 years and that the increases correlate with increases in CO2, however, when the (b) graph is overlain on that part of the (a) graph for the last 160 years, it can be seen that the last 160 year increases are perfectly consistent with the increases and decreases that have been occurring for thousands of years and that we are presently in an temp up cycle which will be followed by a down cycle ie temp decrease.

    2. There is 26 times the amount of CO2 in nature as there is man made. Water vapour accounts for 80% of greenhouse gas warming and CO2 less than 20%. One 26th of 20% is .7% and that is the amount which man made CO2 contributes to warming.

    3. Simple maths shows that there is simply not enough snow and ice on the planet to increase sea levels by anywhere near the amount which IPCC claims, even on their revised downward sums.

    1. Dear Larry, Thank you for your comment. I agree with your arguments but I think we need to show that every step of the climate argument is false. Step one is the IPCC claim that our CO2 is causing all the increase in atmospheric CO2. Step 2 is the IPCC claim that CO2 in the atmosphere is causing all the warming. Step 3 is the IPCC claim that warming causes bad stuff to happen. You have made good points on Steps 2 and 3.

      By the way, do you have any links to the Australian data you mention?

      1. I read all your work, but Pangburn is simpler
        IPCC Intergovernmental Panel On Climate Change
        GCM General Circulation Model (many, based on IPCC CO2 assertions)
        These six links from five authors are all you really need to understand global warming.
        My speculation: As the temperature went down into the Little Ice Age, limestone was deposited around the edges of bodies of water. As the temperature has recovered since, the limestone dissolved and added CO2 to the oceans, with a delay of 300-400 years. It was just an accident that this added CO2 coincided with our industrial revolution. Temperature creates CO2, not the other way around. There is proof of that. Read on.
        Shows that temperature change over the last 170 years is due to 3 things: 1) cycling of the ocean temperature, 2) sun variations and 3) moisture in the air. There is no significant dependence of temperature on CO2.
        Connolly father & son
        Shows the vertical temperature profile follows the ideal gas laws and is not caused by CO2. Millions of weather balloon scans and trillions of data points have been analyzed to come to these conclusions. One important conclusion is that there is no green house gas effect.
        Pat Frank
        Shows that GCM results cannot be extrapolated a few years, let alone 50 or 100.
        Joe Postma
        Shows that the “flat earth model”of the IPCC is too simple. Their real models are built into the GCMs which don’t fit the real data.

    2. I wonder if there was ever any data collected on 13CO2? There should have been an increase of 13C02 also during the testing. If the 13CO2 data showed an e-time somewhere between natural e-time and 14CO2 e-time it would be pretty compelling.

  2. At this point, I am simply “working through” your paper (no where near finished yet!). Therefore, please take my few introductory comments as more of an inquiry for clarification.
    At the beginning of your paper, a number of statements are made but not referenced for verification. Examples include: “…only 1.5 percent of human carbon is left in the atmosphere.” How do we know that?
    “…if all human emissions were to stop, that 18 ppm increase would fall to a 4-ppm increase in 20 years.”
    How can we confirm this number? Where does the 20 years come from and on what is that claim based?
    “…about 6 percent of human carbon emissions will end up on the land to increase the growth of vegetation.” 6%? How? Why?
    Please don’t take these comments in the wrong vane as I’m only trying to be sure I can understand and defend your paper, if need be.
    Thanks and good luck with the research and paper,

    1. Dear Dale, Thank you for your comment.
      The Preface I wrote is not part of my paper. It is only a brief summary of some key conclusions of my paper. You will find all the numbers I mention in the Preface derived in Sections 3 and 4 of my paper. These numbers are the result of properly calculating how human and natural carbon flow through the carbon cycle.

  3. Would part of your paper be better served if it referenced: (not my work)

    IPCC has stated that man is responsible for 40% of the total amount of the CO2 in the atmosphere since the industrial revolution (taken as 1850 on), but admits man-made CO2 only contributes 3.4% annually. This must mean nature’s 96.6% is selected by nature to be recycled but not man-made CO2 despite there being no chemical difference or process that would explain this. This is impossible without an explanation as to why the recycling process does not select natural and man-made CO2 in proportional amounts.
    One of the purported signatures of anthropogenic CO2 is the carbon isotope ratio, C13/C12. The difference between “natural” and “man-made” CO2 has a demarcation value of 1.1% C13. Above 1.1% C13 content is considered “natural”, and below is considered “man-made”.
    The concentration of C13 isn’t reported directly, it is given as “dC13”, which is computed as:

    dC13=1000*((C13/C12 Sample)/(C13/C12 STD)-1)

    If you examine the above equation, you will see that the C13 index that is reported can go down not only from decreasing C13 content, but also from an increasing C12 content (the other 98.9% of the CO2).
    We’ll fast forward through the science of analysing multi-year data trends and signals from Mauna Loa, an active volcano in Hawaii and state that no difference was found between the “natural” multiyear variability and that found for the trends, so the previous claims of all the increases of CO2 being man-made are false. Exactly what common sense would predict.

    1. Dear John, Thank you for your comment and link. Spencer makes a good argument that the decrease in dC13 does not imply a human cause. Also, in my [1], I show that d13C does not support the IPCC claim of human cause.
      However, this preprint does not need to involve 13C. This preprint simply calculates the effect of human CO2 emissions on the carbon cycle.

  4. Dear Dr. Ed,
    Your audience wants a clear, direct statement comparing annual contributions of CO2 from nature and humans. Your audience may tease the answer from:

    Lbp = 4.6 (ppm/year) * 4 (years) = 18.4 ppm (9)

    Lbn = 98 (ppm/year) * 4 (years) = 392 ppm (10)

    Consider introducing this section with: “Each year, nature produces more than 21 times the human contribution of CO2” and state sources. Thereby, you will introduce dominance of the natural CO2 contribution, supporting your models.
    Thank you!

  5. Great work. Two comments! The sexual propensitivity of Termites is also important as it is estimated that they emit from two to ten times the green house gases from mans activity. This was before finding about two million new mounds in South America.
    In 2000 Joseph O. Fletcher gave a lecture showing the heat released from the Warm Pool (sun induced) to be about ten times the then calculated estimate from green house gases. He predicted the slow down in warming at that time with a peak about 2020 then a drop.
    Clearly we are fighting a against a UN grab for power.
    Push forward because stupid laws might be passed before the cooling brings this to an end.

  6. Did I find an auto-complete typo?

    “This paper converts carbon units of GtC (Gigatons of Carbon) and PgC (Pentagrams of Carbon) into CO2 units of ppm (parts per million by volume in dry air) using:…”

    Did you mean “petagrams”?? 🙂

    And I would like to link your finished product to the ‘my website’ link, too!

  7. Introduction….
    Why mix upper case with lower case here:

    “This paper uses e-time rather than “residence” time because there are many definitions of residence time. E-time has a precise definition: 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.”

    How about “e-time” has a…
    Or “However, ‘e-time’ has a…”
    Yes, it’s the first letter of the sentence, but….

  8. 2.1 again… suggested edits… my style versus yours… SUGGESTIONS IN ALL-CAPS

    The Physics Model is ALL THAT IS REQUIRED. It is not necessary to add separate inflows for human and natural CO2 to the Physics Model. Just ADD ANOTHER INSTANCE of the Physics Model for each CO2 definition desired.

    Kohler is wrong. There is no such thing as a system being “too simplistic.” A system should be as simple as NEEDED/REQUIRED(?) to solve a problem. The Physics Model shows how inflow, outflow, and e-time affect the level of CO2 in the atmosphere. The IPCC model DOES NOT do this.

  9. 2.5…. “PER MIL”??? new term here or previously used and I missed it?

    “The 14C data are in units of D14C per mil. The lower bound in D14C units is -1000. “

  10. “The bottom line is while human emissions add carbon to the carbon cycle, human carbon that enters the atmosphere quickly finds its way to the land and deep ocean reservoirs.”.
    Ed, could you tell me how the outflow from the atmosphere of human carbon dioxide or, indeed, naturally produced carbon dioxide is measured, please? Or are the amounts just based on modelling?

  11. 2.6…
    How do the arrows, all of equal length in the figure, represent flows in petagrams per year?!
    “Figure 4. The carbon-cycle system with corrected data for the IPCC natural carbon cycle.”

    Ah, the numbers appear in figure 6…. so, in figure 4, they just represent “flows.” Hm?

    But you’re still calling them ALL “outflows” when some are outflows and some are ‘inflows,’ as indicated by the directions of the arrows! Sounds like ‘flows’ is still a better term…

      1. Heidi
        Nearly all of Potholler’s assertions have been adequately refuted in Dr. Ed’s Co2 paper at (
        If you have time to watch videos addressing the things Potholler was trying unsuccessfully to debunk look for those by Dr. Murray Salby especially

  12. The bomb test curve essentially shows the C14/C12 ratio compared to a reference ratio valid for year 1950. The ∆C14 value is among other things affected by human emissions of C14-free CO2 from fossil burning. The ratio we would have had today if the bomb tests were never done is of course unknown, but we can correct for the effects of human C12 emissions. Here is a paper showing the result: Fig 1, red dots. The reason for the C14 not to go to zero can be emissions from the nuclear power industry and also emissions from the biosphere which stored C14 enriched carbon ever since 1960. I do not know in what way the correction would affect your application of the physical model, but it seems you should mention this correction. Another thing, the increased CO2 concentration has caused greening of the planet with up to 30% increase of biomass production per year. That has obviously increased the flow of CO2 into the biosphere but the release back into the atmosphere from e.g. Amazonas will be delayed for a long time. It seems to me one could estimate this memory effect of the biosphere and perhaps neglect it after showing that it is small. Only long-lived plants will contribute, of course. This memory effect is a very good thing – it makes life on earth easier for humanity and all other animals that depend on plants for their living.

  13. Ed,

    I like the concept and am still studying the detail. My first observation (and probably my only one) is that your mass unit, pentagrams, shouldn’t that be petagrams?

    Mark Harvey

  14. Hi Ed,
    1. You may have defined it somewhere in the paper, but to me “human emissions” are the exhalations of us people.
    2. I view the matter of atmospheric carbon dioxide very simply. The partial pressure of CO2 in the atmosphere is the same as the partial pressure of CO2 in our oceans (possibly with some delay although there is intimate contact between the two). As the oceans warm after the Little Ice Age, so the partial pressure of the contained CO2 rises – this will be balanced by the atmospheric CO2.

    1. Reason I ask is because he comes to approximately the same percentage as Archer utilizing a different method but promotes this view of climate carbon feedback from the ocean that resists ocean being a sink-i.e the sink is acting as a positive feedback instead of a sink.

      1. Dear Stephen, my preprint considers the ocean as a reservoir for carbon. Carbon flows in and carbon flows out. The rate of change of level is the difference between inflow and outflow.

  15. In Sweden, where I live, about 70% of the land is covered by forests. That is 28 million hectares or 280000 square kilometers. 75 % of that is cultivated with an average time to felling of about 80 years. The Swedish forests bind about 0.14 GTCO2 per year. After felling a large part will become CO2 within a couple of years while roots will stay in the forest and give away CO2 during a long time. It seems reasonable to assume that the carbon stored in a forest will essentially be back in the atmosphere after 150 years. We can assume that
    CO2 from a single event like the C-14 from the bomb tests that is stored in a forest will be given back to the atmosphere as a delayed, wide peak with a long tail.

    In the period 1982 to 2015 the leaf area in Swedish forests has increased by about 25% on the average. According to the site about 70% of the increase is because of CO2 fertilization. From 1982 to 2015 CO2 has increased from 341 to 400 ppm. If we assume that the increased leaf area results in a proportionally bigger growth, the binding of CO2 per year would have increased by 0.025 GTCO2 each year. This is of course good – but it means
    that the increase of CO2 we see today will cause an increase with a maximum maybe 80 years from now. That increase will in turn cause increased storage in threes that would be released another maybe 80 years into the future. Sweden with 0.7% of all forests stores 0.025 GTCO2 extra in 2015 relative to 1982. The entire world, if similar, would store 3.6 GTCO2 but that is with 341 ppm CO2 as the baseline. As compared to pre-industrial levels,
    280 ppm, assuming a linear dependence the extra long-lived storage in the biosphere should be in the order of 7 GTCO2 or 2GTC or 4 ppm. Now, assuming the world as whole has the same growth rate of forests as the Swedish forest industry is most probably seriously wrong, more realistic would probably be to assume that the extra stored CO2 is an order of magnitude smaller. IPCC, 2007, states that the exchange between atmosphere and biosphere is about 120 GTC/year. Most of that is very fast because the life span of most plants is short. There is however a small fraction that goes into long lived threes.

    The point of this posting is that indeed there is a tail on the response curve for a single CO2 emission like the bomb tests. How large it is and how long it lasts should be possible to estimate far more accurately by professionals on forestry. My very rough estimate was just intended to inspire someone to do it better.

    Worldwide forests have a much wider life span so a computation for the entire world would presumably give something similar to a slow exponential fall-off. An exponential never falls to exactly zero so the statement from IPCC that a carbon emission to the atmosphere will change the atmospheric CO2 for thousands of years is mathematically correct. The way the political spokesmen for IPCC present this to the public is however most inappropriate. This is not a dooms day thing. An increased amount of long-lived biomass on the planet is a good thing. Mankind can make good use of it.

    Based on the above I suggest that you mention the effects of long storage times in the biosphere and explain why you neglect them completely. Alternatively add one more reservoir that connects to the atmosphere with an appropriately guessed very long
    e-time and size. This tail shows up in IPCC models as several long e-times in the bern model.

    The big controversy, as I see it is that IPCC makes models under the assumption that the temperature would have stayed constant at the pre-industrial level if there would have been no antropogenic CO2. This means that IPCC assumes that the heating due to CO2 is the reason for for the oceans to give off more CO2 causing an increased heating – with an additional amplification from water vapor. That means they model our climate as a system with a very large feedback. To me that seems very unlikely because a large positive feedback should have made the climate very unstable – and that is not what we can learn from climate history.

    The e-time from the bomb test curve is about 16.5 years. I do not understand why you use an e-time from IPCC. They use multiple e-times in a complicated model. I can not see any reason why the e-time should depend on the isotope. If you use a different time from 16.5 years there is at minimum a need for a precise reference so we can read what IPCC is saying that the time stands for – and how they arrived at it.

    IPCC attributes all heating to antropogenic emissions and consequently they attribute the CO2 from the oceans due to a higher temperature to antropogenic CO2. In your model heating is external and causes a natural increase of CO2. With a 16.5 year time constant I think you would find that about 50% of CO2 is natural while 50% is antropogenic. Assuming external heating means that the radiative forcing of CO2 has to be much lower than the 3.7 W/m2 assumed by IPCC. (There are many papers that arrive at lower values.)

    1. Dear Leif, Thank you for your comment. The NASA article repeats the incorrect IPCC claim that half of human CO2 emissions cause of all the rise in atmospheric CO2 and the remainder adds to the ocean and plants:

      “Every year, about half of the 10 billion tons of carbon emitted into the atmosphere from human activities remains temporarily stored, in about equal parts, in the oceans and plants.”

      The calculations in my preprint show human CO2 distributes itself in the same percentages as natural CO2 distributes itself, namely, 6% to land, 1.4% to the atmosphere, 2.2% to surface ocean, and 90.7% to deep ocean.

      You are, of course, correct that the e-time for land is a composition of different e-times for the plants.

      My paper [1] shows the e-time for 14CO2 is 16.5 years. The only place my preprint uses the IPCC e-time of 4 years is in Section 2.4 but that use is for illustration purposes only. Equation (11) shows that the ratio of human to natural CO2 in the atmosphere is independent of e-time.

      Section 2.5 explains why the e-time for 12CO2 is smaller than for 14CO2. It is because the lighter isotopes react faster.

      1. Dear ED, as we know, a CO2 molecule does not have any memory so it is obvious that molecules of human origin and natural origin behave the same. The statement from NASA that you refer to must be ill-written, neither NASA nor IPCC can believe molecules have memory. I, therefore, rephrase their statement like this: “Every year, when 10 billion tons of carbon is emitted into the atmosphere from human activities, about 5 billion tons is temporarily stored, in about equal parts, in the oceans and plants while 5 billion tons remain in the atmosphere. (forever?)” I think it is even more clear how absurd the statement is. Further, it is in clear disagreement with IPCC models.

        This link: “A preindustrial background (CO2 around 280 ppm, zero emissions) was used and a pulse of 40 GtC was released instantaneously into the model atmosphere”

        The graph shows the response of IPCC models. The paper fits parameters to the IPCC-TAR curve: 15% or 6 GtC will stay forever in the atmosphere. I have seen arguments that the parameter a(0) must be identically zero. Now, that is false but we can estimate a(0) from 40 GtC in relation to all the carbon: (Approximate in GtC: 40000 sea, 2300 biosphere, and 780 atmosphere.)

        After many thousand years reservoirs have evened out the extra CO2 in the atmosphere so a(0) could be 0.009 maximum. The somewhat higher CO2 level might increase the permanent storage of calcium carbonate at the sea bottom causing a(0) to be a bit smaller. The graph reaches 50% in about 20 years. The equivalent e-time is obviously very much longer than 4 years.

        You write: “The IPCC [2] estimates the e-time for natural CO2 is 4 years. It takes an e-time of 4 years to make the IPCC’s flow estimates equal to the IPCC’s level of atmospheric CO2.”

        There must be a misunderstanding here. The graph they show from the 40GtC sudden exposure is not consistent at all with an e-time of 4 years.

        A remark: Your ref [2] does not have any figure 6.1. I did, however, find a figure 6.1 here: so I suggest you change the reference.

        Your figure 5 with 90 down and 100 up from deep ocean does not agree with IPCC figure 6.1. When you ignore “Marine biota” and “dissolved organic carbon” you must move those boxes into the two ones you have. That means that from surface ocean to deep ocean IPCC has a flow of 103 down and 100 up. That makes more sense, if you would incorporate decimals you would find that the net flow into the ocean (surface+deep) is zero and to the sediments 1,75. The net flow into the atmosphere is 0,4 instead of zero, but that is well within error limits.

        To me, it is obvious that the e-time for the atmosphere can not be 2.95 years. It has to be very close to the C14 e-time. Your ref. [29] states that the isotope effect is small. A factor of 5.6 is absurd. Exchange rates have to be seriously wrong since the amount of CO2 in the atmosphere should be fairly accurate.

        Maybe you need one more box for the biosphere with a flow of maybe 80 in and 80 out and an e-time of 1 year representing the one year plant season. The amplitude of the 1-year variation of CO2 at Mauna Loa is in the order of 6 ppm. Maybe also another box for the surface of the sea where CO2 gas dissolves in water and releases again with a small e-time while 16.5 years is for carbon to get into “Surface Ocean.”

        1. Dear Leif,

          Thank you for your comment.

          Regarding: “Every year, when 10 billion tons of carbon is emitted into the atmosphere from human activities, about 5 billion tons is temporarily stored, in about equal parts, in the oceans and plants while 5 billion tons remain in the atmosphere. (forever?)”

          Even the IPCC Figure 6.1 data show this is not the case. When I extract the e-times from the IPCC data and apply them to human CO2, I calculate that human CO2 flows to the other reservoirs fast enough to keep the amount of human carbon in the atmosphere below about 15 percent. There is no calculation that shows it is 50 percent.

          Regarding the link: “A preindustrial background (CO2 around 280 ppm, zero emissions) was used and a pulse of 40 GtC was released instantaneously into the model atmosphere.”

          My previous paper [1] references that link to the Bern model and discusses the Bern model. I am considering showing in this paper how the Berm model prediction compares with the Physics model prediction.

          Regarding: “The IPCC [2] estimates the e-time for natural CO2 is 4 years. It takes an e-time of 4 years to make the IPCC’s flow estimates equal to the IPCC’s level of atmospheric CO2.”

          The IPCC does say the e-time is about 4 years and, indeed, the Bern model disagrees. I am adding a new section to my preprint that shows how the Physics model calculates an e-time of about 6 years based, of course, on IPCC’s data for the levels.

          Regarding the link to figure 6.1: thank you for checking. I have corrected the link.

          Regarding: “Marine biota” and “dissolved organic carbon”. I consider these reservoirs negligible. The amounts in these levels are in the noise level of the carbon-cycle calculation.

          Regarding e-time: As mentioned above, I am adding a section to my preprint that will show how to get an e-time of about 6.5 year using IPCC’s data.

          Regarding “one more box for the biosphere: Perhaps but I think it is outside what I can include in this paper. I have enough to handle just sticking with IPCC’s for major levels.

          Thanks again.

        2. Leif what I don’t understand is how they can assume only 50% of human emission is absorbed every year. Only 50% absorbed in 1750. Only 50% absorbed in 1800, in 1850, in 1900, in 1950, in 2000. How is that possible?

        3. Stephen,
          The way it’s done is to assume that natural emissions have not increased at all since preindustrial times. Next, assume that all natural emissions are absorbed first followed by the human emissions. Voila! 50% of the human emissions corresponds to roughly 100% of the rise in atmospheric CO2.

        4. Chic,
          I’m a Louis L’amour fan too by the way. But they believe it was 50% in 1750 and then also 50% in say for instance 1950 when anthropogenic emission was much greater. I understand they need that scenario for their math to work but it defies all logic.

  16. Off topic but very substantial finding supporting Dr. Ed’s contention of small effect from human CO2.
    See( )
    The Connolly’s analysis of 20 million radiosondes “categorically shows that there is no greenhouse effect in our atmosphere.” Conclusion is that increased radiative gasses will absorb more but simultaneously emit the same amount and cause no warming.

  17. Here is the definitive argument that the atmospheric carbon dioxide growth rate is driven by temperature (and not by human emissions):

    First we’ll compare the carbon dioxide growth rate with the SSTs of the southern ocean going back to 1958…

    Next we’ll compare the integrals of both data sets…

    Then we’ll compare the carbon dioxide growth rate and temperature again, but this time extending temperature all the way back to 1850…

    And then we’ll take the integral of the temperature data set from 1850…

    Note the increase of about 125ppm. Ice cores tell us that the carbon dioxide level was 287ppm in 1850. Add 125ppm to that and we get 412ppm. Let’s see how we did…

    Not bad(!) Lastly lets compare the carbon dioxide levels in ice cores with the moberg temperature reconstruction…

    Note that for the past five hundred years the temperature relationship with the carbon dioxide growth rate still holds true. Low temperatures produce flat or falling carbon dioxide levels. Relatively high temperatures produce rising carbon dioxide levels. (and the higher the temps, the faster the rise)…

    So, there you have it folks. The definitive argument that it is temperature that causes carbon dioxide levels to rise in the atmosphere. (a 500 year correlation !!!)

  18. I applaud your efforts in taking on Big Climate. “It’s a dirty job, but somebody has to do it” comes to mind. I’ve been defending your model on, so some of my comments will only be the devil’s advocate variety.

    My first point involves the title. This paper extends your argument from the previous paper “Human CO2 emissions have little effect on atmospheric CO2” by showing how the Physics model also applies to the other CO2 reservoirs involved in the carbon cycle. While the previous title addresses the accounting of the CO2 budget appropriately for the atmosphere, I do not think the current title is best for this paper. A seemingly small effect on the carbon cycle budget may translate into a large detrimental effect on the ecosystem in terms of ocean acidification and carbonate depletion. I agree that the IPCC climate cycle budget is in error. Would you consider changing the title to reflect your correction of the IPCC’s numerical accounting thus avoiding criticisms you may get from the title as is?

    Furthermore, the effect of fossil fuel emissions on the increase in atmospheric CO2 is one thing. What about the effects of land use changes that contribute to changes in the carbon cycle, even potentially positive ones? A need for third paper perhaps?

    The penultimate paragraph in your abstract contains sentences that invite criticism of the body of the paper. “The Physics carbon-cycle model shows if all human CO2 emissions stopped in 2020, the increase caused by human CO2 would fall by 78 percent in 20 years.” This presumes something about the future of natural emissions. You will already be challenged about the lack of data on past natural emissions. By my calculation, the fall would be 55%.

    “Stopping all human emissions cannot lower the level of atmospheric CO2 below the level set by natural emissions which is about 390 ppm.” Isn’t 390 your model’s estimate of natural emissions? You will be challenged to cite actual data to back it up.

    “In the long-term, only 1.5 percent of human carbon emissions will end up in the atmosphere.” Again this assumes some prediction about future emissions. Stopping human emissions would make it virtually 0%, holding both human and natural emissions constant at present levels would be more like 4%. The former is impossible and the latter very unlikely.

    The model development sections seem to be mostly word for word from your previous paper. A brief summary with a reference would suffice. The thrust of this paper begins at section 2.6.

    The caption for Figure 4 describes corrected data which you put in a later figure, not 4.

    I agree with Lief that your IPCC Figure 6.1 numbers are wrong. The Physics carbon-cycle model still shows that IPCC flows don’t produce IPCC levels. But you can easily get the right levels by much more modest adjustment of their flows (109 for land to air and 105 for deep ocean to surface ocean).

    You have 12 as the land to air flow in Figure 7. I sum all anthro emissions to 20.5 PgC/yr. That would explain the negative 30 PgC for the land reservoir. Again this doesn’t make the IPCC model right, just less wrong.

    I’ll stop at this point to see if we are still on the same page, before proceeding to your other models.

    1. Dear Chic,

      Thank you very much for your extended comment. I will consider all of your suggestions as I edit my preprint.

      Change title: yes.

      Effects of land use changes? Well, the IPCC adds these into its numbers for human emissions. For this paper, I need to stick with IPCC’s numbers for the levels and human inflows.

      Regarding: “The Physics carbon-cycle model shows if all human CO2 emissions stopped in 2020, the increase caused by human CO2 would fall by 78 percent in 20 years.”

      Check again. It says the increase “caused by human CO2.” I think this makes the sentence independent of natural CO2.

      Regarding: “Stopping all human emissions cannot lower the level of atmospheric CO2 below the level set by natural emissions which is about 390 ppm.”
      You are correct. I need to justify the 390 ppm.

      Regarding: “In the long-term, only 1.5 percent of human carbon emissions will end up in the atmosphere.”

      I need to be sure this sentence is based on the assumption that all human CO2 emissions stop. If stopped, then that 1.5 percent is caused by the new carbon put into the carbon cycle by human CO2. It can never go to zero in the less than a million-year time frame.

      Holding human emissions constant after 2020 would still increase the amount of human CO2 in the atmosphere, according to my latest calculations.

      Since I am introducing additional equations in this paper, I choose to include the derivation of the Physics model. Perhaps I can reduce my descriptions and focus on the equations.

      Thanks for catching my error in Figure 4, etc.

      To correct the IPCC Figure 6.1 numbers, it takes more than simply adjusting the flows. It takes calculations of the equilibrium state where chosen e-times produce constant levels over time. This calculation can be done only with a carbon-cycle model.

      No matter what, it is impossible to get a negative level. I will explain this more in my next edits but consider human carbon as water in four buckets connected by tubes. We add water to the atmosphere bucket, and it flows out into the other buckets. There is no way to get negative water in any of the buckets. Water will flow between buckets until all have the same water levels.

  19. So far, so good until IPCC Figure 6.1. Check the arrows involving “Marine biota” and “dissolved organic carbon”. There is a net transfer of 13 PgC/yr from surface to deep ocean. This should be added to the 90 PgC/yr giving about 103 total. This constitutes a crucial error in your Figure 5 which will continue to cause you unnecessary further criticism if left uncorrected, IMO.

    Regarding the IPCC flows and e-times, I believe I created a reasonable facsimile of your spreadsheet which uses ratios of flows divided by sums of flows to get the Ki “splits” as you call them. The method used to calculate IPCC e-times from Figure 5 are not consistent with the way you derive your e-times in Table 2. Is anyone else confused about this? Perhaps it would be more clear what you are doing with a link to your spreadsheet.

    Splits are not very physically meaningful to me. They seem to be related to rate constants which are not arbitrary in nature. The Mauna Loa data seems to indicate the removal rate of CO2 is about 0.28 equivalent to an e-time of 3.6 years which is consistent with your model.

    The bottom line is not how the IPCC preindustrial numbers don’t fit a model properly. The improper treatment of human emissions is the problem you should be emphasizing, not the IPCC preindustrial numbers.

    1. Dear Chic,
      Thank you very much for your helpful comment.

      I changed Figure 5 and nearby text to include the flow through the marine biota, as you suggested. You are correct. This required a change to Table 1. It did not change anything else in my paper.

      I will put my spreadsheet online so you can download it at the link I will put under downloads.

      Of course, my overall goal is to calculate the effect of human emissions. But I must begin with the IPCC data if I am to refute the IPCC claims. That is why I use IPCC level data to derive equilibrium e-times that I can then use to calculate the human effect. The IPCC equilibrium levels are preindustrial by IPCC’s definition.

  20. Dear Ed,

    Regarding: “Marine biota” and “dissolved organic carbon”. You consider these reservoirs negligible. Yes, but ignoring them makes your figure 5 open for criticism since it implies that the IPCC figure 6.1has a source of 10 PgC in the deep ocean while they actually have a sink of 2 PgC. I suggest you just change 90 to 102 for the flow into the Deep Ocean. Then you represent 6.1 correctly and I do not think it would change anything of your basic results.
    The e-time for CO2 is about 16 years. I find it ridiculous to assume isotopic effects could change that significantly. You have taken flows from IPCC 6.1 that sum up to 169 PgC/year for the atmosphere. With the correct e-time the summed flows into land and sea has to be about 36 PgC/year. To be consistent with the physical model all flows have to be reduced by the factor 169/36=4.7. In figure 5 the flow from the atmosphere to the biosphere is 109 PgC/year. This number, actually 123 (minus 14.1 for the increased growth today due to the fertilization effect of CO2.) The number comes from Beer et al. 2010. Here is table 1 in the paper:
    Tropical forests 40.8
    Temperate forests 9.9
    Boreal forests 8.3
    Tropical savannahs and grasslands 31.3
    Temperate grasslands and shrublands 8.5
    Deserts 6.4
    Tundra 1.6
    Croplands 14.8
    Total 121.7

    As stated by IPCC “carbon can be released back into the atmosphere … on a very wide range of time scales (seconds to millennia)” I think croplands savannahs and grasslands have an e-time of not much more than 1 year. Threes in the rain forest several hundred years. To me this seems to be a show stopper. I do not think you can use IPCC data to split the outflow from the atmosphere between sea and land. Also the sea is complicated somewhere I have seen that the equilibrium between CO2 in the atmosphere and dissolved CO2 in a thin laminar layer, less than 1 mm, is very fast. mixing with deeper layers and forming bicarbonate and other ions is much slower and mixing with deep water is presumably associated with the 16 year time constant. The biosphere is presumably essentially one reservoir with a very short e-time that we can include in the atmosphere and another with a much longer e-time that we can associate with threes. Had the biosphere e-time been similar to the sea e-time we should have seen a distortion on the bomb test curve as plants with twice the normal C-14 concentration would rotten and send out C14 to bend up the tail. The sea is a container of almost infinite size. We know that organisms that live in the sea seem to have an age of 500 to 1000 years when analyzed for the C14 content.

    From the bomb-test curve we know the time constant and with only two containers, the atmosphere and “all the rest” it is possible to compute the contribution to the atmospheric CO2 from human emissions as you do in [1] while the rest of the CO2 is “natural.” That “natural” is essentially from the oceans that have become warmer. IPCC would argue that the warmer oceans are due to the heating effect of CO2 and argue they are not natural, but caused by humans! In case you would correct the e-time to 16.5 years and apply to the model in [1] you should find that about 50% of CO2 is human and 50% is natural. IPCC would of course still argue that what you attribute to natural, which is outgassing from the sea, is the greenhouse effect caused by humans, but it could equally well be caused by phenomena on the sun – and considering historical temperature data I personally find it most likely that the sun is responsible for a large part.

    1. Dear Leif,
      Thank you very much once again for your helpful comment.

      I changed Figure 5 and nearby text to include the flow through the marine biota, as you suggested. You are correct. This required a change to Table 1. It did not change anything else in my paper.

      Let’s review what I am attempting to do in my paper. I do not assign e-times from external information. I find e-times that support the IPCC data for natural levels at equilibrium. The IPCC claims (incorrectly) that nature remained constant after 1750 so it would support the level of 280 ppm. Therefore, I do not include information outside of the IPCC data.

      If data exists for additional levels, then they would be easy to add to my calculations. For example, what I and the IPCC call land, could be separated into sublevels, as you describe. But that step is outside the scope of my present paper.

      Yesterday, I made several other changes to my paper that will require a new read.
      Regarding e-times, please note that the Physics model calculates an e-time for the atmosphere and surface ocean that is 2 times the IPCC model e-time.

      The scope of my paper is to use IPCC data to show the IPCC claims are wrong, and to use IPCC data to calculate that human emissions since 1750 have increased atmospheric CO2 by only 32 ppm. Then, by default, nature has caused all the rest of the increase above 280 ppm … which, of course, is due to the increase in surface temperature.

      1. Dr. Ed Berry,

        I just started reading a book by Dr. J. Marvin Herndon, Ph.D.. Dr Herndon states that we should not assume “constant Earth-heat production” but “one should consider and investigate Earth-heat variability. The fundamental implication of Earth-heat variability is ocean temperature variability which directly affects atmospheric CO2 variability.” Dr. Herndon is questioning with scientific evidence the assumption that Earth-heat is constant. If there is a warmer ocean there will be more CO2 and a cooler ocean there will be less CO2.

        As a lay person, I thought that Dr. Herndon’s information should be examined and might be beneficial in the study of atmospheric CO2. I’m not sure if this fits in with your paper on AGW.

        “Herndon’s Earth and the Dark Side of Science”

        Dan Dewey

  21. You stated in one of the responses “The scope of my paper is to use IPCC data to show the IPCC claims are wrong, and to use IPCC data to calculate that human emissions since 1750 have increased atmospheric CO2 by only 32 ppm. Then, by default, nature has caused all the rest of the increase above 280 ppm … which, of course, is due to the increase in surface temperature.”

    I am trying to figure out where the 100 ppm increase in atmosphere is coming from if it is not due to human activity adding Carbon Dioxide to the Carbon Cycle.

    Are you saying there would be 100 ppm increase absent human activity just because the global temperature anomaly has increased by ~ 0.8C since 1880? Are you sure the increase in total atmospheric CO2 isn’t due to the increase in total carbon dioxide in the carbon cycle? My understanding is ice core data suggest CO2 was about 280 ppm during Roman and Medieval warm periods … so why would the modern warm period be having a different effect?


    Ken Van de Burgt

  22. Dear Ed B. – will this be published? Is it going to be peer reviewed? Where are your other articles published?


  23. A lot of things I don’t understand your work. But what I would like to say is thank you for being there for all people and giving me a voice I trust.

  24. Why do you trust a voice you don’t understand? Ed Berry’s work is nonsense and his misconceptions have been pointed put by myself and others. Do you just not want to face the truth?

    1. Dear David, you have not pointed out any errors in my paper. You are delusional. You have lost the scientific argument. That is why you are incapable of discussing physics.

Leave a Comment

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.