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 my second climate paper for your comments.

November 7, 2019: I finished all updates and improvements. Thank you all for your comments.

November 13, 2019: More updates completed.

Abstract

Copyright (c) 2019 by Edwin X Berry

Abstract

The United Nations Intergovernmental Panel on Climate Change (IPCC) has promoted the “consensus” claims that human carbon dioxide emissions have caused all the increase in atmospheric carbon dioxide since 1750 and that significant human carbon will remain in the atmosphere for thousands of years. 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 for land, atmosphere, surface ocean, and deep ocean. This may be the first correct calculation of the human carbon cycle. First, these calculations accurately replicate the IPCC data for the natural carbon cycle, which the IPCC has not done. Second, these calculations apply the same rules for the natural carbon cycle to the human carbon cycle, which the IPCC has not done. The IPCC assumes human carbon obeys different rules than natural carbon obeys, which is incorrect because nature cannot tell the difference between human and natural carbon atoms. These calculations show, contrary to the IPCC claim, that human carbon emissions have caused only about 25 percent of the increase in atmospheric carbon dioxide since 1750. Natural carbon emissions have caused about 75 percent. All human carbon through 2019 has added only one percent to the carbon in the carbon cycle. If human carbon emissions stop, human carbon will rapidly flow out of the atmosphere. Human carbon emissions cause no significant long-term change to the carbon cycle or to atmospheric carbon dioxide. These calculations provide a significant new and valuable basis for all political decisions concerning the effects of human carbon.

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) [2] 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 [3] 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 [4] incorrectly claims,

With solid justification, one can describe the annual carbon budgets as products of high scientific quality with strong political relevance.

IPCC [2] claims incorrectly,

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 [3] claims incorrectly,

The primary source of the increased atmospheric concentration of carbon dioxide since the pre-industrial period results from fossil fuel use.

The IPCC and WMO do not calculate the carbon cycle correctly. They make unwarranted assumptions about how much human carbon stays in the atmosphere. They treat human and natural carbon differently. They use circular reasoning. They violate physics and get the wrong answers.

Berry [1] described the Physics model and showed how IPCC arguments to support its climate hypothesis are wrong.

This paper uses the Physics model to calculate the total effect of all human CO2 on the carbon cycle. It includes carbon recycling. It finds that all human CO2 has increased atmospheric CO2 by only 32 ppm (parts per millions by volume in dry air ).

The IPCC and WMO do not calculate the carbon cycle correctly. They make unwarranted assumptions about how much human carbon stays in the atmosphere. They treat human and natural carbon differently. They use circular reasoning. They violate physics and get the wrong answers.

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

Authors who conclude that human CO2 increases atmospheric CO2 by only a small amount include Revelle and Suess [5], Starr [6], Segalstad [7], Jaworoski [8-9], Beck [10], Rorsch, Courtney, and Thoenes [11], Courtney [12], Quirk [13], Essenhigh [14], Glassman [15], Salby [16-19], Humlum [20], Harde [21, 22], and Berry [1, 23, 24].

Authors who support the IPCC [2] position – that human CO2 has caused all the increase in atmospheric CO2 above about 280 ppm – include Archer et al. [25], Cawley [26], and Kohler [27].

1.2. The solution

This paper applies the Physics model to the IPCC carbon cycle for the four primary reservoirs: land, atmosphere, surface ocean, and deep ocean. This paper uses IPCC [2] data and definitions to calculate how natural and human carbon move from the atmosphere to the other reservoirs. Therefore, these calculations are independent of details of ocean and surface chemistry.

The calculations show the addition of human carbon to the natural carbon cycle does not significantly increase the level of atmospheric CO2 because the human carbon rapidly flows from the atmosphere to the other reservoirs, according to IPCC data.

The calculation is not complicated. Anyone competent in fundamental physics and in simple numerical calculations should be able to reproduce the results shown in this paper. The downloadable Excel file shows all the calculations.

1.3 The Null Hypothesis

The null hypothesis is:

Nature, not human CO2 emissions, is the dominant cause of the observed increase of atmospheric CO2 above 280 ppm.

Any scientific challenge to the null hypothesis must provide evidence that the null hypothesis is wrong. Evidence means a properly structured and testable hypothesis that has not made any incorrect predictions and includes no invalid scientific assumptions.

The null hypothesis stands unchallenged. The IPCC [2] has not proved the null hypothesis is invalid. The IPCC has simply ignored the null hypothesis and assumed the following contradiction to the scientific method:

Human emissions have caused all the increase in atmospheric CO2 above 280 ppm.

Berry [1] has shown all IPCC’s arguments to support its assumption fail logic and science.

2.   The Physics Model

2.1 Physics Model description

The Physics model [1] applies independently to each carbon reservoir. The “level” of each reservoir is the amount of carbon in each reservoir. The level of carbon in the atmosphere is determined by the measurements of CO2 in the atmosphere. This paper uses e-time rather than “residence” time because there are many definitions of residence time. However, 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.

Figure 1 shows the Physics model system for carbon in the atmosphere. The carbon level 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 the four reservoirs. The only way processes in an external reservoir can change the level in a reservoir is by changing the reservoir’s inflow or e-time.

The Physics Model 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. 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.

When the Physics model is applied to multiple reservoirs, it will behave exactly as derived here for each reservoir.

2.2 Physics Model derivation

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 [1], 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)

Where

  • 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)

where

  • Lo = Level at time zero (t = 0)
  • Lb = the balance level for a given inflow and Te
  • Te = time for L to move (1 – 1/e) from L to Lb
  • e = 2.7183

The original integration of (6) contains two absolute values, but they cancel each other because both L and Lo are always either above or below Lb.

Raise e to the power of each side of (7), to get the level as a function of time:

            L(t) = Lb + (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

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 and if the level equals the balance level, outflow will equal inflow. At the balance level, continuing constant inflow will maintain a constant level of atmospheric CO2.

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.

The only way external processes can change the level is by changing the 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.

Hypothesis (2) is a linear function of level. This means the Physics model applies independently and in total to human CO2 and natural CO2. The balance levels of human CO2 and natural CO2 are independent and summable. 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 effects on the carbon cycle of human CO2 and natural CO2 simultaneously. It is better (and simpler) to compute their effects separately. The separate results can be summed to produce the total result.

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 [28] processed 14C data for both hemispheres from 1954 to 2010. Turnbull [29] processed 14C data for Wellington, New Zealand, from 1954 to 2014. After 1970, 14CO2 was well mixed between the hemispheres and 14CO2 in the stratosphere were in the troposphere. The 14C data from both sources are virtually identical after 1970.

The 14C data are in units of D14C per mil [28, 29]. The lower bound in D14C units is -1000. This value corresponds to zero 14C inflow into the atmosphere. In D14C units, the “natural” balance level, defined by the average measured level before 1950, is zero, 1000 up from -1000.

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 [29]. Because 12CO2 is a lighter molecule than 14CO2, it reacts faster than 14CO2. Therefore, the 12CO2 e-time will be shorter than the e-time for 14CO2.

Levin et al. [31] 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.

To summarize [1], 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 uses hypothesis (2) and allows only 2 parameters to be adjusted: balance level and e-time. Both are physical parameters. The Physics model is not a curve fit equation.

To perform the replication, set the Physics Model to the first data point in 1970. Then try different balance levels and e-times until the model best fits the data. Although there is room for minor differences in the fit, the best fit seems to occur when the balance level is zero and e-time is 16.5 years.

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. (See more discussion of this in Section 5.3.)

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 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?

The Physics model shows how to calculate the ultimate effect of human CO2 on atmospheric CO2. The key is to use, for each reservoir, the Physics model hypothesis: Outflow = Level / e-time.

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 IPCC model uses Figure 3. The Physics model uses Figure 4.

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 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

where:

            Kag + Kas = 1                                                                           (22)

            Ksa + Ksd = 1                                                                           (23)

IPCC’s splits are related to the Physics e-times as follows:

            Kag = Ta / Tag                                                                         (24)

            Kas = Ta / Tas                                                                          (25)

            Ksa = Ts / Tsa                                                                          (26)

            Ksd = Ts / Tsd                                                                          (27)

Substitute (24-27) into (18-21) and use (22-23) to get IPCC’s rate equations:

            dLg/dt = Kag*La/Ta – Lg/Tg                                                    (28)

            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)

Simplifications

With the above formalities, we tested and found that IPCC’s splits different from 0.5 do not give significantly different results than IPCC’s splits.  Using this simplification, (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’s [2] definitions for natural carbon and human carbon. Human carbon is the result of human CO2 emissions. These include most predominantly fossil-fuel emissions and cement production. 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 the Physics carbon-cycle calculation for IPCC’s natural carbon levels for 1750. IPCC’s flows do not maintain constant levels. Therefore, IPCC’s levels are not equilibrium values for IPCC’s flows

  • 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 claimed natural flows support a level of natural CO2 in the atmosphere of about 302 ppm rather than IPCC’s claimed 280 ppm after 1750.

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.

The reason IPCC’s flows do not produce its levels in Figure 5 is not because of the small differences in the flows between the reservoirs, e.g., 107 vs 109, or 101 vs 100. These small differences are insignificant. The reason IPCC’s flows do not produce its levels is seen in the difference in the e-times shown in Table 2 versus Table 1. The e-times for the surface ocean and deep ocean shown in Table 2 are 5% and 9% greater than the respective e-times in Table 1.

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 important numbers in Tables 1 to 3 are the “End %” of carbon in the four reservoirs. The splits do not change the End % values. These natural equilibrium percentages also represent the long-term distribution for human carbon among the four reservoirs because nature will treat human carbon the same as it treats natural carbon.

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 carbon-cycle model allowed a search for e-times that produce “corrected” flows that keep the IPCC levels constant. These corrected e-times will now be used to calculate the effect of human CO2 emissions on the carbon cycle because the e-times for human carbon must be the same as the e-times for natural carbon. The final percentages are not sensitive to split choices.

4.   The Human Carbon Cycle

4.1  IPCC’s invalid human carbon cycle

IPCC [2] AR5 Fig. 6.1 (p. 471) shows IPCC’s version of the carbon cycle. Its legend says,

Red arrows and numbers indicate annual ‘anthropogenic’ fluxes averaged over the 2000–2009 time period. These fluxes are a perturbation of the carbon cycle during Industrial Era post 1750.

Figure 7 shows IPCC’s Figure 6.1 data for the human carbon cycle. IPCC assumes nature stayed constant after 1750 and human CO2 added all the CO2 above 280 ppm. It’s no surprise that IPCC’s unrealistic result that 66% of all human CO2 is still in the atmosphere supports its assumption. IPCC used circular reasoning, not science, to achieve its desired result.

Fig. 7. The IPCC human carbon cycle from the red numbers in IPCC Fig. 6.1.

IPCC’s Fig. 6.1 for the human carbon 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.

To properly calculate the human carbon cycle, we should proceed as follows.

Initially, the level of all reservoirs is zero. Then we insert year by year human carbon emissions into the atmosphere beginning in 1750 and ending in 2009. Each year, carbon flows from the atmosphere to land and surface ocean, and from the surface ocean to the deep ocean.

As an analogy, think of these four reservoirs as water buckets of different diameters with tubes connecting them. All levels would have non-negative numbers and the surface ocean level would begin to fill before the deep ocean fills.

But here are three scientific errors in the IPCC data.

  1. The surface ocean level remains at 0 PgC, unaffected by the net 2.3 PgC inflow.
  2. The surface ocean, with zero outflow to the deep ocean, magically adds 155 PgC to the deep ocean.
  3. The net flow of 2.6 PgC per year from atmosphere to land does not add carbon to the land. 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.

Recall, the calculation of the human carbon cycle should be done separately from the calculation of the natural carbon cycle. Since human carbon can only add to the connected reservoirs, it is impossible to get a negative level.

The IPCC appears to have merged the carbon cycles for natural and human carbon into one calculation, where small errors in IPCC’s natural carbon cycle may have caused big error in IPCC’s human carbon cycle. Nowhere does the IPCC show a direct calculation of the carbon cycles as shown in this paper.

Also, IPCC’s human carbon cycle does not compare well with its natural carbon cycle. IPCC’s natural carbon cycle shows the atmosphere level at about 1.5% (Figures 5 and 6 and Tables 1, 2, and 3). But IPCC’s human carbon cycle (Figure 7) shows the atmosphere level at 65.7%.

This very significant difference in the percentages in Figures 6 and 7 indicates IPCC treats human carbon differently than it treats natural carbon. Specifically, IPCC incorrectly amplifies human carbon in the atmosphere by not allowing human carbon to flow to the other reservoirs like natural carbon. This violates physics because nature will treat human and natural carbon the same.

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.

At the end of 2019, only 14.7 percent of all human carbon remains in the atmosphere, 36.7 percent is in the land, 10.7 percent is in the surface ocean, and 37.9 percent is in the deep ocean.

Under the assumption that human emissions stopped beginning in 2020, by 2100, 3.9 percent of human carbon would remain in the atmosphere, 19.3 percent would be in the land, 3.9 percent would be in the surface ocean, and 72.8 percent 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 [33] represents IPCC’s claim that human carbon sticks in the atmosphere much longer than natural carbon. Berry [1] shows how to deconstruct [33] 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.

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 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 is the first time the carbon cycle for land, atmosphere, surface ocean, and deep ocean has been calculated correctly. The Physics model is fully derived and explained. Other investigators can use the equations shown herein to reproduce and extend the calculation shown herein.

This is the first time the human carbon cycle has been calculated independently from the natural carbon cycle. This method allows the correct calculation of human carbon recycling.

This is the first time the human carbon cycle has been calculated using the same rules and e-times for each reservoir as used for the natural carbon cycle.

This is the first time the true effect of human carbon has been calculated. The calculations show human carbon emissions have caused about 25 percent and natural carbon emissions have caused about 75 percent of the increase in atmospheric carbon dioxide since 1750.

These calculations also show that human carbon will rapidly flow out of the atmosphere if human carbon emissions stop. There is no significant long-term effect of human carbon emissions.

These calculations provide a significantly new and valuable basis for all political decisions concerning the effects of human carbon dioxide emissions.

5.2 Null Hypothesis and Statistics

Section 4.1 shows how IPCC’s numbers for the human carbon cycle are blatantly invalid. Berry shows how IPCC’s so-called “extensive evidence” fails logic and physics.

Munshi [34] shows the detrended correlation of annual human emissions and annual changes in atmospheric CO2 is zero. This result supports the null hypothesis and rejects the IPCC hypothesis.

Munshi [35] shows how the IPCC uses circular reasoning to claim human emissions cause of the increase in atmospheric CO2.

Munshi [36] shows the circular reasoning fallacy is common in climate change research. Researchers with a prior conviction to believe the IPCC hypothesis insert that hypothesis into their data analysis. Munshi shows examples of research papers, on the impact of human emissions on tropical cyclones, sea level rise, and the carbon cycle, that draw their conclusions based upon circular reasoning.

Munshi [37] shows how the IPCC [2] Fig. 6.1 ignores the fact that its 20% data accuracy cannot prove human CO2 emissions caused all the rise in atmospheric CO2. It would require 2.3% data accuracy to derive that conclusion. So, the IPCC simply assumed its desired conclusion.

Munshi’s statistical papers show there is no scientific evidence to support the IPCC hypothesis.

Archer et al. [25] support of the IPCC hypothesis consists only of concluding a consensus,

There is a strong consensus across models of global carbon cycling, as exemplified by the ones presented here, that the climate perturbations from fossil fuel CO2 release extend hundreds of thousands of years into the future.

Archer et al. make no other case that the reviewed models are valid.

5.3 Carbon isotopes in the carbon cycle

Isotopes 14C and 13C will distribute themselves in the reservoirs of the carbon cycle as natural carbon has distributed itself. The heavier isotopes 14C and 13C will have slower e-times than 12C but their distributions in the four reservoirs should resemble the distribution of natural carbon.

Berry uses numbers to prove the 13C data favor the Physics model result rather than prove the IPCC hypothesis. Munshi [38] uses statistics to prove the 13C data support the IPCC hypothesis. Munshi [39] shows the 14C data do not support the IPCC hypothesis.

5.4 The effect of temperature on CO2

This paper does not explain for how natural CO2 emissions may have caused 100 ppm of the increase in atmospheric CO2 after 1750. That subject is outside the scope of this paper.

Salby [16-19] shows how changes in surface temperature precede CO2 changes. Harde [21, 22] shows how carbon dioxide in the atmosphere increases with surface temperature.

Such an increase may have resulted in two ways: “new” carbon or constant carbon.

Scenario 1: Perhaps the Little Ice Age deposited some atmospheric carbon in limestone. Then the subsequent warming may have recovered this carbon as CO2. This process would be simulated as “new” carbon like that for the human carbon cycle but about 3-times larger.

Scenario 2: Perhaps the e-times changed to cause the increase in CO2.

The downloadable Excel file allows testing scenarios. The general Physics rate equations (18-21) may be necessary to simulate the effect of temperature on atmospheric CO2.

Conclusions

The IPCC incorrectly assumes natural CO2 emissions remained constant to support a constant atmospheric CO2 level of 280 ppm. Then, the IPCC incorrectly concluded human emissions must have caused all the increase in atmospheric CO2 since 1750.

The IPCC has never proved its human-causation assumption (Berry, 2019). In fact, it is impossible to prove a hypothesis is correct. But it is possible to prove a hypothesis is wrong. The IPCC has produced no evidence that human CO2 has caused most of the rise in atmospheric CO2. Until there is such evidence, the null hypothesis is valid.

Therefore, new ideas must be allowed to replace IPCC’s assumptions and claims.

The Physics carbon-cycle model replicates IPCC’s data for the natural carbon cycle after minor adjustments to IPCC’s inherent e-times. Then the Physics model uses the same e-times to calculate the human carbon cycle. This is the correct way to calculate the human carbon cycle.

The Physics model shows that all human carbon emitted from 1750 through 2019 has added one percent, or 452 PgC, to the carbon in the carbon cycle. In 2020, this one-percent human carbon is distributed 166 PgC to land, 48 PgC to the surface ocean, and 171 PgC to the deep ocean, leaving 67 PgC or 32 ppm in the atmosphere.  

These Physics model calculations are the first valid calculations of the human carbon cycle. They show a dramatically different result than the IPCC claims. In fact, IPCC’s own data prove IPCC’s human carbon-cycle model is invalid.

If the natural level had remained at 280 ppm as the IPCC claims, then according to IPCC’s own data, human emissions would have increased atmospheric CO2 from 280 ppm to only 312 ppm. Therefore, nature has added 100 ppm to get today’s level of 312 ppm and human CO2 is not the dominant cause of the increase in atmospheric CO2 since 1750.

The small human contribution to atmospheric CO2 would rapidly decrease if human emissions were to stop. A simulated CO2 pulse of 100 ppm decays to 15 percent in 10 years and to 4 percent in 100 years. By contrast, IPCC’s Bern model incorrectly predicts the pulse will decay to only 55 percent in 10 years, to 30 percent in 100 years, and will never go below 15 percent. Therefore, the Bern model contradicts IPCC’s own carbon-cycle data.

These results nullify all IPCC papers that are based upon IPCC’s invalid assumption that human emissions have caused all the CO2 increase above 280 ppm.

Acknowledgements

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.

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References

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51 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.
        —————————-
        Pangburn
        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.
        https://globalclimatedrivers2.blogspot.com/
        —————————–
        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.
        https://globalwarmingsolved.com/2013/11/summary-the-physics-of-the-earths-atmosphere-papers-1-3/
        utube:
        https://www.youtube.com/watch?v=XfRBr7PEawY
        ——————————
        Pat Frank
        Shows that GCM results cannot be extrapolated a few years, let alone 50 or 100.
        https://www.frontiersin.org/articles/10.3389/feart.2019.00223/full
        and
        https://wattsupwiththat.com/2019/10/15/why-roy-spencers-criticism-is-wrong/
        ———————————
        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.
        https://climateofsophistry.com/2019/10/19/the-thing-without-the-thing/

    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?
    Etc.
    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,
    Dale

    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.

    https://wattsupwiththat.com/2008/01/28/spencer-pt2-more-co2-peculiarities-the-c13c12-isotope-ratio/

    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 ( https://edberry.com/blog/climate-physics/agw-hypothesis/human-co2-emissions-have-little-effect-on-atmospheric-co2/).
        If you have time to watch videos addressing the things Potholler was trying unsuccessfully to debunk look for those by Dr. Murray Salby especially
        https://edberry.com/blog/climate-physics/agw-hypothesis/what-is-really-behind-the-increase-in-atmospheric-co2/

  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: http://www.klimatupplysningen.se/2013/10/21/%e2%88%86c14-bombprovskurvan/ 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. https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fertilization-greening-earth/ 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: http://unfccc.int/resource/brazil/carbon.html “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: https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter06_FINAL.pdf 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: http://unfccc.int/resource/brazil/carbon.html “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( https://www.youtube.com/watch?v=XfRBr7PEawY )
    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…

    http://www.woodfortrees.org/plot/esrl-co2/from:1958/mean:12/derivative/plot/hadsst3sh/from:1958/scale:0.253/offset:0.099/plot/esrl-co2/from:1958/mean:12/derivative/trend/plot/hadsst3sh/from:1958/scale:0.253/offset:0.099/trend

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

    http://www.woodfortrees.org/plot/esrl-co2/from:1958/mean:12/derivative/integral/plot/hadsst3sh/from:1958/scale:0.253/offset:0.099/integral/plot/esrl-co2/from:1958/mean:12/derivative/trend/plot/hadsst3sh/from:1958/scale:0.253/offset:0.099/trend

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

    http://www.woodfortrees.org/plot/esrl-co2/from:1958/mean:12/derivative/plot/hadsst3sh/from:1850/scale:0.253/offset:0.099/plot/esrl-co2/from:1958/mean:12/derivative/trend/plot/hadsst3sh/from:1958/scale:0.253/offset:0.099/trend

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

    http://www.woodfortrees.org/plot/hadsst3sh/from:1850/scale:0.253/offset:0.099/integral

    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…

    https://www.sealevel.info/co2.html

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

    https://i0.wp.com/i90.photobucket.com/albums/k247/dhm1353/LawMob1.png

    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 drroyspencer.com, 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?

    Regards,

    Ken Van de Burgt

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