**Human CO2 has little effect on atmospheric CO2**

American Meteorological Society 99^{th} Annual Meeting, January 8, 2019, AMS website

(A journal is now reviewing this preprint. Copyright does not allow republishing of journal submissions. I improved Appendix A on March 19, 2019)

Edwin X Berry, Ph.D., CCM

Climate Physics LLC, Bigfork, Montana, USA

*“The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.”* – Albert Einstein

#### Abstract

A simple Physics Model makes only one assumption: outflow is proportional to the level (or concentration) of CO2 in the atmosphere. This model replicates the decay of 14CO2 after 1970 using a constant e-time of 16.5 years. This replication has significant theoretical consequences.

Human and natural CO2 inflows set independent balance levels in proportion to their inflows, independent of e-time. The total balance level is the sum of the human and natural balance levels. The CO2 level moves with e-time to its balance level until outflow equals inflow. Then the level remains constant if inflow remains constant. Continued, constant human emissions do not add more CO2 to the atmosphere. Neither human nor natural CO2 accumulate in the atmosphere. Human CO2 has not caused all the increase in atmospheric CO2 since 1750, or above 280 ppm. Present human CO2 adds only 18 ppm to the balance level. Natural CO2 adds 392 ppm.

The complex United Nations Intergovernmental Panel on Climate Change (IPCC) model cannot reproduce the decay of 14CO2 after 1970. IPCC assumes human CO2 reduced the buffer capacity of the carbonate system. However, the 14C data show e-time is constant, which means the buffer capacity has not changed.

**Keywords**: carbon dioxide, CO2, climate change, anthropogenic, accumulation

#### 1. Introduction

The United Nations *Intergovernmental Panel on Climate Change* (IPCC) [1] Executive Summary claims human emissions caused atmospheric CO2 to increase from 280 ppm in 1750, to 410 ppm in 2018, for a total increase of 130 ppm.

IPCC claims “abundant published literature” shows, with “considerable certainty,” that nature has been a “net carbon sink” since 1750, so nature could not have caused the observed rise in atmospheric carbon dioxide.

The *U.S. Global Change Research Program Climate Science Special Report* (USGCRP) [2] claims,

This assessment concludes, based on extensive evidence, that it is extremely likely that human activities, especially emissions of greenhouse gases, are the dominant cause of the observed warming since the mid-20th century.

IPCC and USGCRP claim there are “no convincing alternative explanations” other than their theory to explain the “observational evidence.”

This paper shows these IPCC and USGCRP claims are incorrect and presents a “convincing alternative explanation” that IPCC and USGCRP claim does not exist.

IPCC [3] bases all its climate conclusions on this flawed 3-step argument:

How do we know that in fact human activity has been responsible for the well documented 25% increase in atmospheric CO2 since the early 19^{th} century? Couldn’t this rise instead be the result of some long-term natural fluctuation in the natural carbon cycle? Simple arguments allow us to dismiss this possibility.

First, the observational CO2 records from ice cores … show that the maximum range of natural variability about the mean of 280 ppm during the past 1000 years was small.

Segalstad [4], Jaworowski [5], and Salby [6] present evidence that the CO2 level before 1750 was much higher than 280 ppm. Nevertheless, this paper accepts IPCC’s assumption that the CO2 level was 280 ppm in 1750. However, this paper rejects the implication that the ice-core mean of 280 ppm implies nature’s CO2 emissions did not change after 1750. IPCC continues:

Second, the observed rate of CO2 increase closely parallels the accumulated emission trends from fossil fuel combustion and from land use changes.

Proper statistics show correlation does not mean causation and time-series correlations must be detrended. Munshi [7] shows the detrended correlation of annual human emissions with annual increase in atmospheric CO2 is zero. The zero correlation proves the human contribution to the increase in atmospheric CO2 is negligible. IPCC continues:

Third, the observed isotropic trends of 13C and 14C agree qualitatively with those expected due to the CO2 emissions from fossil fuels and the biosphere, and they are quantitatively consistent with results from carbon cycle modeling.

In fact, the observed isotropic trends of 14C and 13C support the Physics Model and reject the IPCC model.

For simplicity, this paper uses levels in units of ppm (parts per million by volume in dry air) and flows in units of ppm per year. GtC (Gigatons of Carbon) units are converted into CO2 units in ppm using:

1 ppm = 2.12 GtC

Authors who conclude human CO2 adds only a minor increase in atmospheric CO2 include Revelle and Suess [8], Starr [9], Segalstad [4], [10], [11], Rorsch [12], Courtney [13], Quirk [14], Essenhigh [15], Glassman [16], Humlum [17], Salby [6], [18], [19], Pettersson [20], Harde [21], [22], and Berry [23], [24].

Authors who support the IPCC conclusion include Archer [25], Cawley [26], Joos [27], Kern and Leuenberger [28], Richardson [29], and Kohler [30].

# 2. The Physics Model

## 2.1 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 [31].

Figure 1 illustrates the system for atmospheric CO2. The system includes the level (concentration) of CO2 in the atmosphere and the inflow and outflow of CO2.

Appendix A shows the mathematical derivation of the Physics Model. It begins with the continuity equation, Equation (A.1). Then it adds one hypothesis, Equation (A.2): Outflow equals Level divided by e-time (where e-time is the e-folding time).

All other Physics Model equations are deductions from the continuity equation and the one hypothesis. For example, the balance level equals inflow multiplied by e-time, Equation (A.4).

Equation (A.8) is the analytic solution to the Physics Model rate equation when inflow and e-time are constant. It calculates the level as a function of time for any starting level, balance level, and e-time.

The Physics Model shows inflow sets a “balance level.” The level always moves towards its balance level. When the level equals the balance level, outflow equals inflow, and the level remains constant with continuing inflow.

The level of CO2 in the atmosphere behaves like the level of water in a lake where water flows into the lake and then out over a dam. Inflow sets the balance level. The lake level changes until the level equals its balance level. Then outflow equals inflow. No water “accumulates” in the lake.

The level of CO2 in the atmosphere also behaves like water in a bucket where water flows into the bucket and flows out through a hole in the bottom. As the level increases, outflow increases. When outflow equals inflow, the level remains constant. No water “accumulates” in the bucket.

The bucket analogy provides insight into e-time. If the hole in the bucket gets smaller, e-time increases. If the hole in the bucket gets larger, e-time decreases.

The Physics Model is complete. Inflow and outflow include all the effects of outside processes. If the atmosphere level were connected to external carbon reservoirs in land and ocean, the Physics Model would behave exactly as derived in this paper.

The Physics Model applies independently and in total to all definitions of CO2, for example, 14CO2, 12CO2, human CO2, and natural CO2, and their sums. The mathematics used in the Physics Model are analogous to the mathematics used to describe many engineering systems.

**Discussion**

Kohler [30] commented on Harde [21],

Harde … uses a too simplistic approach, that is based on invalid assumptions, and which leads to flawed results for anthropogenic carbon in the atmosphere. We suggest that the paper be withdrawn by the author, editor or publisher due to fundamental errors in the understanding of the carbon cycle.

Kohler [30] wants Harde [21] withdrawn. In response, the journal refused to publish Harde’s [22] rebuttal to Kohler.

Kohler claims Harde’s [21] model and therefore the Physics Model is “too simplistic.” Kohler claims a valid CO2 system must contain at least two levels.

There is no such thing as a system being “too simplistic.” A system should be as simple as possible to solve a problem. Each level of a system is isolated and connected to other levels by inflows and outflows. So long as a level includes inflow and outflow, a system is complete.

The Physics system includes the effects of outside processes. The Physics system properly computes how inflow and outflow change the level of CO2. Its equations and conclusions for the atmosphere level would not change if the atmosphere level were connected to another level. Outside processes can change inflow and outflow. The Physics system shows how inflow and outflow change the level.

Kohler claims more complex models give more correct answers. It does not work that way. One must get the physics for each level correct independent of other levels. Nothing in physics says more complexity increases validity.

## 2.2 Physics Model consequences

IPCC [1], [32] says nature emits into the atmosphere about 120 GtC from land and 90 GtC from ocean for a total of 210 GtC per year. This is equivalent to about 98 ppm per year. IPCC [32] admits its estimates of “gross fluxes generally have uncertainties of more than ±20%.”

Boden [33] shows human CO2 emissions in 2014 were 9.7 GTC per year, or 4.6 ppm per year.

Equation (A.4) shows the balance level equals the product of inflow and e-time. Using IPCC numbers, and subscripts “h” to mean human and “n” to mean natural, the balance levels of human and natural CO2 are 18.4 and 392 ppm:

*Lbh* = 4.6 (ppm/year) * 4 (years) = 18 ppm (1)

*Lbn* = 98 (ppm/year) * 4 (years) = 392 ppm (2)

Their ratio and percentage are independent of residence time,

*Lbh* / *Lbn* = 4.6 / 98 = 18 / 392 = 4.6 percent (3)

*L**bh* / (*L**bn* + *L**bh* ) = 4.6 / 102.6 = 18.4 / 410 = 4.5 percent (4)

Equation (1) shows present human emissions create a balance level of 18 ppm. This is independent of nature’s balance level. If nature’s balance level remained at 280 ppm after 1750, then present human emissions would have increased the CO2 level 18 ppm from 280 ppm to 298 ppm.

Equation (2) shows present natural emissions create a balance level of 392 ppm. The human contribution of 18 ppm brings the total balance level to 410 ppm, which is close to the level in 2018.

Equation (3) shows the ratio of human to natural CO2 in the atmosphere equals the ratio of their inflows, independent of e-time. The IPCC calls the ratio in Equation (3) the “airborne fraction.”

Equation (4) shows the percentage of human-produced CO2 in the atmosphere equals its percentage of its inflow, independent of e-time.

Equations (1) and (2) support Harde [21] and its key conclusions:

Under present conditions, the natural emissions contribute 373 ppm and anthropogenic emissions 17 ppm to the total concentration of 390 ppm (2012).

While the details are outside the scope of this paper, Appendix C, from Harde [21], shows how temperature can increase the balance level to account for the rise in atmospheric CO2 since 1750. Salby [6] and Pettersson [34] show how surface temperature determines the CO2 level. This paper shows the cause-effect path is (a) surface temperature sets CO2 inflow and (b) inflow sets the CO2 balance level.

# 3. Theories must replicate data

## 3.1 The Physics Model replicates the 14C data

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, hereinafter called 14CO2.

The 14C data are in units of D14C per mil. In D14C units, the “natural” balance level is zero, as defined by the average measured level before 1950.

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.

All valid CO2 models must replicate the 14C data after 1970. Otherwise, the model is invalid.

Hua [35] processed 14C data for both hemispheres from 1954 to 2010 using 61 mid-year data points. Turnbull [36] processed 14C data for Wellington, New Zealand, from 1954 to 2014 using 721 data points. After 1970, 14CO2 were well mixed between the hemispheres, and the 14C data from both sources are virtually identical after 1970.

Figure 2 shows the global average data for D14C [35]. Figure 3 shows the New Zealand data for D14C [36].

## 3.2 The IPCC model cannot replicate the 14C data

Maier-Reimer and Hasselmann [37] used a three-dimensional ocean circulation model connected to a one-layer atmosphere to reproduce the main features of the CO2 distribution in the surface ocean. Their model computed the exchange of carbon between the ocean and atmosphere by using a standard CO2 flux relation at the air-sea interface. Their model did not include biological sources or sinks. They found the flow of CO2 from the atmosphere into the ocean can be approximated by a sum of four exponentials with different amplitudes and time constants.

Siegenthaler and Joos [38] created the original Bern model. It contained levels for the deep and interior oceans that connected to the upper ocean, as can be seen in their Figure 1.

Archer et al. [25] compared models like the Maier-Reimer and Hasselmann model. The models “agreed that 20–35% of the CO2 remains in the atmosphere after equilibration with the ocean (2–20 centuries).” They found “a sizeable fraction of the CO2 remains in the atmosphere, awaiting a return to the solid earth by much slower weathering processes and deposition of CaCO3.”

Joos [27] uses a hypothetical pulse emission of CO2 into the atmosphere to compare the response of several atmosphere-ocean models. All models predicted a “substantial fraction” of pulse would remain in the atmosphere and ocean for millennia.

The above studies led to the coefficients and time constants in today’s Bern model. Appendix B shows IPCC’s Bern model [39]. The Bern model assumes CO2 exits the atmosphere according to a polynomial with four decay times. One decay time is infinity.

The idea to approximate the behavior of one level (the atmosphere) of a multi-level system model with a sum of exponential terms may be of general interest but it is not a substitute for correct science. It amounts to reconnecting the system model’s deep and interior ocean levels directly to the atmosphere which conflicts with reality.

Figure 4 shows how the Bern model puts human CO2 into 4 different bins, each with a different decay time.

Bern Equation (B.1) predicts 15 percent all human CO2 entering the atmosphere stays in the atmosphere forever, 25 percent stays in the atmosphere almost forever, and 28 percent stays in the atmosphere longer than 14CO2 stays in the atmosphere. Only 32 percent flows freely out of the atmosphere.

All the models reviewed by Archer [25] and by Joos [27] lack a proper Physics Model to represent the atmosphere. These models assume human CO2 caused all the rise in atmospheric CO2 since 1750.

IPCC [1] assumes the Bern model describes how CO2 flows through the atmosphere. This assumption excludes the Physics Model. Yet IPCC bases all its global warming claims on its Bern model that outrageously concludes that human CO2 sticks in the atmosphere.

The Physics Model shows how the CO2 level will rise until outflow equals inflow. It shows there is only one time constant, not four. No CO2 remains in the atmosphere forever.

The proper test is to see if the Bern model can replicate the 14CO2 data.

Figure 5 compares the Bern model with the Physics Model and with the 14CO2 data. All model calculations begin with the initial level set to 100 and the balance level set to zero.

Equation (A.8) of the Physics Model with e-time of 16.5 years replicates the 14CO2 data. Equation (A.8) with an e-time of 4 years simulates the curve for 12CO2. Equation (B.1) calculates the Bern model predictions.

The Bern model begins with a short e-time then its e-time increases. The Bern line crosses the 14C line and thus conflicts with the 14C data. The Bern model artificially constrains the outflow of CO2 from the atmosphere.

The inability of the Bern model to replicate the 14CO2 data proves the IPCC models reviewed by Joos [27] do not represent reality.

The Bern model is also an invalid model because it depends upon its history. If restarted at any point,

it cannot replicate its own prediction line. A valid model must continue its same prediction line if it is restarted at any point on its line. The Bern model is invalid because the CO2 in the atmosphere does not “know” its history. It only knows its present. The Bern model is a curve fit and not a real model.

The Bern model violates physics. IPCC [1] assumes its Bern model applies to human but not to natural CO2. That assumption is unphysical because CO2 molecules from human and natural sources are identical. All valid models must treat human and natural CO2 the same.

When applied to natural CO2, Bern Equation (B.1) predicts 100 ppm per year of natural CO2 will cause 15 ppm per year to stay in the atmosphere forever. In 1000 years, that is 15,000 ppm stuck in the atmosphere forever. This clearly invalid prediction proves the Bern model is invalid. That means IPCC’s theory and climate models produce wrong predictions.

## 3.3 The isotope 14CO2 follows 12CO2

Levin [40] concludes the C14 data provide “an invaluable tracer to gain insight into the carbon cycle dynamics.” The 12CO2 molecules participate in the same chemical reactions as 14CO2 except 12CO2 reacts faster because it is lighter than 14CO2.

RealClimate [41] agrees:

All isotopes of an element behave in a similar way chemically.

**Discussion**

Kohler [30] claims 14CO2 does not trace 12CO2 because 12CO2 is restrained by the decreased the ocean’s buffer capacity while 14CO2 is not.

As an isotope, 14CO2 will undergo the same chemical reactions as 12CO2, except slower. Both isotopes will seek their balance level according to their e-time. The 14CO2 data show e-time is constant. Therefore, buffer capacity is constant.

## 3.4 The 14C data support the Physics Model

Figure 6 shows how the predictions of the Physics and IPCC models differ.

Human fossil-fuel CO2 is “14C-free.” Inflow of human CO2 lowers the 14C balance level. IPCC [3] and Kohler [30] claim this qualitative argument proves human CO2 caused all the rise in atmospheric CO2. The numbers show otherwise.

As shown in Equation (4), the Physics Model predicts human CO2 is 4.5 percent and natural CO2 is 95.5 percent of the total. This are the same percentages as in the inflow. Therefore, the Physics Model predicts human CO2 has lowered the balance level of 14C from zero to -4.5. Appendix D shows the calculations.

Figure 7 shows the Physics Model replicates the 14C data when the balance level is -4.5.

IPCC [1] says natural CO2 is 68 percent and human CO2 is 32 percent. Therefore, the IPCC model predicts human CO2 has lowered the 14C balance level to -32.

Figure 8 shows how a balance level of -32 does not fit the 14C data.

The 14C data support the Physics Model and reject the IPCC model.

**Discussion**

Pettersson [20] shows how industrial emissions of 14C may have raised the 14C balance level and how the 12CO2 increase would lower the D14C balance level. However, Levin [40] used absolute values of 14C and still concluded the “ocean-atmosphere disequilibrium today is close to pre-industrial times.”

## 3.5 The 13C data support the Physics Model

Human CO2 has slightly less 13C than natural CO2. RealClimate [42] says the 13C/12C ratio for human CO2 is 2 percent less than for natural CO2. RealClimate says the 13C ratio in the atmosphere has declined about 0.15 percent since 1850. RealClimate says this qualitative argument proves human CO2 caused all the increase in atmospheric CO2 since 1850. The numbers show otherwise.

Using the numbers in Figure 6, the Physics Model predicts human CO2 has lowered the 13C ratio by 0.09. The IPCC model predicts human CO2 has lowered the 13C ratio by 0.64. Appendix E shows the calculations.

Figure 9 compares the Physics Model and IPCC model predictions to RealClimate’s numbers.

The 13C/12C data support the Physics Model and reject the IPCC model.

# 4. Other problems with the IPCC Model

## 4.1 IPCC’s core argument is illogical

In its core argument, IPCC [1] correctly notes that human emissions from 1750 to 2013 totaled 185 ppm while atmospheric CO2 increased by only 117 ppm. But IPCC incorrectly concludes that this proves human CO2 caused the increase.

IPCC argument omits natural CO2 which totaled about 26,000 ppm during the same period. So, the stronger logical counter-argument is that nature caused all the increase. IPCC conclusion assumes natural CO2 inflow remained exactly constant since 1750, an invalid assumption.

IPCC [1] claims “abundant published literature” shows, with “considerable certainty,” that nature has been a “net carbon sink” since 1750, so nature could not have caused the observed rise in atmospheric carbon dioxide.

Of course, nature *has* been a “net carbon sink” since 1750 because nature absorbs human CO2 emissions. But absorption of human CO2 does not prevent nature from increasing its own CO2 emissions. Inflow and outflow are two different physical processes. Nature will absorb the outflow of both human and natural CO2 because outflow is a function of level, independent of nature’s inflow.

**Discussion**

Cawley [26] is a key paper for the IPCC theory. Cawley claims to prove that human CO2 caused all the increase of atmospheric CO2 above the 280 ppm in 1750. Cawley’s proof fails.

Cawley’s Equation (3) attempts to do the same job as Equation (A.2), namely, to represent how level sets outflow. But Cawley adds to his Equation (3) a term that represents a steady-state outflow that is independent of level. Cawley’s added term is fictitious because his first term on the right side of his Equation (3) is the true source of all outflow.

So, Cawley [26] adds outflow twice. First as a level-driven outflow. Second, as a fictitious steady-state outflow. As a result, Cawley’s Equations (3), (4), (5), and his equation after (5) are wrong, which makes his whole paper wrong.

Cawley’s Equation (7) should include his Fa for human inflow. His Equations (7) and (8) should omit his arbitrary Fe for outflow and set outflow equal to level (his C) divided by his residence time. His residence time is also inaccurate.

Cawley [26] argues the ratio of human to natural CO2 in the atmosphere is a function of residence-time, which is incorrect. The Physics Model Equation (3) and common sense show the ratio is independent of e-time. Cawley equations cannot replicate the 14C data.

Kohler [30] uses Cawley [26] to “prove” the IPCC case. But since Cawley fails physics, Kohler fails physics, as does the IPCC. The IPCC model is an attempt to derive a theory by pasting together observations without addressing the underlying physics.

## 4.2 IPCC’s time constants fail physics

The only hypothesis in the Physics Model is “outflow equals level divided by e-time” as shown in Equation (A.2). E-time is not a function of inflow.

The definition of e-time is precise. The Physics Model shows e-time is the time for the level *L* to move (1 – 1/e) of the distance from *L* to its balance level, *Lb.*

IPCC’s residence, adjustment, and turnover times have confusing definitions. IPCC [43] defines “turnover time (*Tt*)” as:

The ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: Tt = M/S.

IPCC’s turnover time is not the same as e-time. Turnover time uses “total rate of removal” which is the negative difference between inflow and outflow.

IPCC [43] defines “adjustment time (*Ta*)” as:

The time-scale characterising the decay of an instantaneous pulse input into the reservoir.

Cawley [26] defines “adjustment time (*Ta*)” as:

The time taken for the atmospheric CO2 concentration to substantially recover towards its original concentration following a perturbation.

The word “substantially” indicates the definition is imprecise. IPCC’s fuzzy definition of adjustment time is necessary to allow for its fuzzy definition of residence time.

Cawley [26] follows IPCC [43] to define “residence time (*Tr*)” as:

The average length of time a molecule of CO2 remains in the atmosphere before being taken up by the oceans or terrestrial biosphere.

IPCC uses a different time constant depending upon whether the level is far from its balance level or close to its balance level:

- When the level is far from its balance level (which can be zero), IPCC thinks e-time is an adjustment time because the level is moving rapidly toward its balance level.
- When the level is close to its balance level, IPCC thinks e-time is a residence time because “molecules” are flowing in and out with little change in level.

IPCC’s time definitions do not properly model how CO2 flows through the atmosphere.

IPCC requires a decay to originate from a pulse. This is unphysical because a system does not know its history. Decay time depends only upon outflow which depends upon level. IPCC assumes decay time depends upon inflow.

Figure 10 illustrates how e-time relates to IPCC’s adjustment and residence times.

IPCC [43] claims:

In simple cases, where the global removal of the compound is directly proportional to the total mass of the reservoir, the adjustment time equals the turnover time: Ta = Tt.

The Physics Model’s replication of the 14C data shows the 14CO2 outflow is proportional to level. Therefore, by IPCC’s own definition, adjustment time equals residence time.

IPCC [43] says:

In more complicated cases, where several reservoirs are involved or where the removal is not proportional to the total mass, the equality T = Ta no longer holds.

Carbon dioxide is an extreme example. Its turnover time is only about 4 years because of the rapid exchange between atmosphere and the ocean and terrestrial biota.

Although an approximate value of 100 years may be given for the adjustment time of CO_{2 }in the atmosphere, the actual adjustment is faster initially and slower later on.

IPCC concludes 12CO2 residence time is about 4 years but claims its adjustment time is much longer. IPCC claims adjustment time is “fast initially and slower later on.” IPCC’s confusion about residence time and adjustment time is why its Bern model cannot replicate the 14C data in Figure 4.

The 14C data (Figures 2 and 3) is the upper bound for CO2 e-time. The e-time for 14CO2 is 16.5 years, not hundreds of years.

**Discussion**

Kohler [30] claims:

The IPCC summarizes the state of the art in peer-reviewed literature. Hence neither the residence time nor the adjustment time are assumptions or interpretations of the IPCC-AR5, but robust outcomes of the underlying science.

Kohler attempts to argue by authority. The implication of “Hence” is that IPCC summaries are so perfect that no one may disagree. That view violates the scientific method.

The IPCC theory makes wrong predictions. It contradicts physics. Its so-called “state of the art in peer-reviewed literature” is a repetition of inbred, invalid, protected claims.

## 4.3 IPCC’s buffer theory is invalid

IPCC theory says human but not natural emissions, reduce the “buffer capacity” of the carbonate system. There are three things wrong with this IPCC claim:

- It requires nature to treat human and natural CO2 differently, which is impossible.
- It assumes the much larger natural CO2 outflow does not reduce buffer capacity.
- It conflicts with the 14C data which show e-time is constant, which means buffer capacity has not changed.

IPCC [32] claims the reason the Bern model increases its residence time is because:

The fraction of anthropogenic CO2 that is taken up by the ocean declines with increasing CO2 concentration, due to reduced buffer capacity of the carbonate system.

IPCC’s claim requires the outflow of CO2 from the atmosphere to decrease as the level of CO2 in the atmosphere increases. That is the opposite of the Physics Model’s theory. The 14CO2 data prove the Physics Model theory is correct and the IPCC model theory is incorrect.

**Discussion**

Kohler [30] claim human emissions reduced the “buffer capacity” of the carbonate system:

the rise in atmospheric and oceanic carbon content goes along with an increase in the Revelle factor, a phenomenon which is already measurable. This implies that the oceanic uptake of anthropogenic carbon will become slower if we continue to increase anthropogenic CO2 emissions. This is already seen in all CHIMP5 model simulations.

Kohler’s last sentence illustrates the absence of logic by Kohler and the IPCC. They claim a model proves what has been fed into the model.

The 14C data are the most accurate method to measure changes in the Revelle factor and “buffer capacity.” But the 14C data (Figures 2 and 3) prove e-time has been constant since 1970. Therefore, human CO2 has not changed the buffer capacity.

## 4.4 Human CO2 does not correlate

IPCC [1] claims annual human CO2 emissions cause annual increases in the level of CO2 in the atmosphere. Cawley [26] argues,

Lastly, the rise in atmospheric carbon dioxide closely parallels the rise in anthropogenic emissions, leading to an approximately constant airborne fraction, which would be somewhat of a coincidence if the rise were essentially natural in origin!

However, proper statistics requires a detrended analysis of a time series before concluding cause and effect. Munshi [7] shows the “detrended correlation of annual emissions with annual changes in atmospheric CO2” is zero. Where there is no correlation, there is no cause and effect.

In summary, statistics show human CO2 is insignificant to the increase in atmospheric CO2.

# Conclusions

The exact replication of the 14C data by the Physics Model proves atmospheric CO2 flows out of the atmosphere in proportion to the level or concentration of CO2 in the atmosphere with a constant e-time. This fact overrides all the IPCC papers that claim outflow is not proportional to level and e-time increases with time. The consequences of this simple fact are significant.

The ratio of human to natural CO2 in the atmosphere equals the ratio of their inflows into the atmosphere, independent of e-time. Inflow sets the balance level. The level moves toward its balance level with an e-time. When the level equals its balance level, outflow equals inflow. Then, the level remains constant so long as inflow remains constant.

There are no cumulative carbon emissions. All CO2 emissions merely raise the level of CO2 in the atmosphere until outflow equals inflow. No CO2 accumulates in the atmosphere and all CO2 flows out of the atmosphere with one common e-time. Human-produced and nature-produced CO2 behave the same.

Present human CO2 inflow into the atmosphere raises the balance level by 18 ppm and present natural CO2 inflow raises the balance level by 392 ppm, for a total of 410 ppm. This conclusion is independent of e-time. Levels approach their balance levels according to the e-time.

If all human CO2 emissions stopped and natural inflow stayed constant, the CO2 level would fall to the natural balance level of 392 ppm with an e-time of about 4 years. Human CO2 does not increase atmospheric CO2 enough to change climate.

The IPCC model is pseudoscience. It cannot replicate the 14C data, it uses multiple, unphysical response times, its core arguments fail logic, and it treats human CO2 differently than it treats natural CO2.

#### Acknowledgments

The author thanks Chuck Wiese, Laurence Gould, Tom Sheahen, and Charles Camenzuli, who reviewed this paper and provided scientific critique, and Daniel Nebert, Gordon Danielson, and Valerie Berry, who provided language and grammar improvements. This research project was funded by the personal funds of Valerie and Edwin Berry.

#### Appendix A: Physics model math

We use the system definition of Section 3.1 to derive the physics model. We begin with the continuity equation:

*dL*/*dt* = *Inflow* – *Outflow* (A.1)

Where

*L* = CO2 level (concentration in ppm)

*t* = time (years)

*dL*/*dt* = the rate of change of *L *(ppm/year)

*Inflow = *the rate CO2 moves into the system (ppm/year)

*Outflow* = the rate CO2 moves out of the system (ppm/year)

Assume outflow is proportional to level,

*Outflow* = *L */ *T**e* (A.2)

where *T**e* is the “e-folding time” or simply “e-time.”

Substitute Eq. (A.2) into the continuity Eq. (A.1) to get

*dL*/*dt* = *Inflow* – *L* / *T**e* (A.3)

Define the balance level, *Lb*, as

*L**b* = Inflow * *T**e* (A.4)

Equation (A.4) shows how *Inflow* sets the balance level. Substitute Equation (A.4) for *Inflow* into Equation (A.3) to get,

*dL*/*dt* = – (*L* – *L**b*) / *T**e* (A.5)

Equation (A.5) shows how level always moves toward its balance level. At this point, 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, there is an analytic solution to Equation (A.5). Rearrange Equation (A.5) to get

*dL* / (*L* – *L**b*) = – *dt* / *T**e* (A.6)

Then integrate Eq. (A.6) from *Lo *to *L* on the left side, and from 0 to *t* on the right side, to get (Dwight, 1955),

Ln [(*L* – *L**b*) / (*L**o* – *L**b*)] = – *t* / *T**e* (A.7)

where

Ln = natural logarithm or logarithm to base e

*L**o* = Level at time zero (*t* = 0)

*L**b* = the balance level for a given inflow and *T**e*

*T**e* = time for *L* to move (1 – 1/e) of the distance to *L**b*

e = 2.7183

(The original integration of Eq. (A.6) contains two absolute functions, but they cancel each other because both *L* and *L**o* are always either above or below *L**b*.)

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

*L(t)* = *L**b* + (*L**o* – *L**b*) exp(- *t* / *T**e*) (A.8)

Equation (A.8) is the analytic solution of Eq. (A.5).

The only assumption in the physics model is Eq. (A.2), namely, outflow equals level divided by residence time. All equations after Eq. (A.2) are deductions from this assumption.

#### Appendix B: Bern model math

The Bern (2002) model is an integral equation rather than a level or rate equation. The Bern model integrates the inflow of CO2 from minus infinity to any time in the future.

To deconstruct the integral version of the Bern model, let inflow occur only in the year when “t-prime” equals zero (t’ = 0). Then the integral disappears, and the Bern model becomes a level equation.

The Bern level equation is,

*L(t)* = *Lo* [ *A _{0}* +

*A*exp(-

_{1}*t*/

*T*) +

_{1}*A*exp(-

_{2}*t*/

*T*) +

_{2}*A*exp(-

_{3}*t*/

*T*)] (B.1)

_{3}Where

*t* = time in years

*L**o *= the level of atmospheric CO2 due to inflow in year t = 0

*L(t)* = the level of atmospheric CO2 after year t = 0

where the Bern IPCC TAR standard values are,

*A _{0}* = 0.152

*A _{1}* = 0.253

*A _{2}* = 0.279

*A _{3}* = 0.319

*T _{1}* = 173 years

*T _{2}* = 18.5 years

*T _{3}* = 1.19 years

The *A*-values merely weight the four terms on the right-hand side of Eq. (B.1):

*A _{0}* +

*A*+

_{1}*A*+

_{2}*A*= 1.000

_{3}Set *t* equal to infinity. Then Eq. (B.1) becomes,

*L* = *A**o L**o* = 0.152 *L**o* (B.2)

Equation (B.2) predicts a one-year inflow that sets *L**o *to 100 ppm, followed by zero inflow forever, will cause a permanent level of 15 ppm.

#### Appendix C: How temperature increases CO2

It is outside the scope of this paper to show how the balance level of CO2 changes with surface temperature. Here is reference information.

Harde (2017a) showed how both inflow and outflow depend on surface temperature, and how this causes the balance level to be a non-linear function of surface temperature. Harde used paleoclimate data as well as modern instrumental data to show how the natural balance level of CO2 in the atmosphere depends on surface temperature.

Kohler (2017) criticize Harde’s method. However, Harde (2017b) proves Kohler is wrong. Unfortunately, the journal did not publish the Harde (2017b) reply to Kohler.

Fig. C1 shows a plot using Harde’s Eq. (17).

#### Appendix D: How the models fit the 14C data

Table D.1. Row 1 shows the natural and human 14C ratios in units of D14C. Row 2 and Row 4 show the physics and IPCC natural and human fractions. Row 3 is the product of Row 1 and Row 2. Row 5 is the product of Row 1 and Row 4.

Row | 14C Test | Natural | Human | Sum | Test |
---|---|---|---|---|---|

1 | 14C Ratio | 0 | -100 | Figs. 2 & 3 | |

2 | Physics Fraction | 0.955 | 0.045 | ||

3 | Physics Result | 0 | -4.5 | -4.5 | Pass |

4 | IPCC Fraction | .68 | .32 | ||

5 | IPCC Result | 0 | -32 | -32 | Fail |

#### Appendix E: How the models fit the 13C data

Table E.1. Row 1 shows the natural and human 13C ratios. Row 2 and Row 4 show the physics and IPCC natural and human fractions. Row 3 is the product of Row 1 and Row 2. Row 5 is the product of Row 1 and Row 4.

Row | 13C Test | Natural | Human | Sum | 100-Sum | Test |
---|---|---|---|---|---|---|

1 | 13C Ratio | 100 | 98 | -0.15 | ||

2 | Physics Fraction | 0.955 | 0.045 | |||

3 | Physics Result | 95.5 | 4.4 | 99.9 | -0.1 | Pass |

4 | IPCC Fraction | .68 | .32 | |||

5 | IPCC Result | 68.0 | 31.4 | 99.4 | -0.6 | Fail |

#### Downloads

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DMAExcellent! I think this presents your points clearly and even a layman like myself can drill into it to get the common sense heart of your position and the physics model.

An acquaintance attended last years AMS meeting and told me John Christie was the only presenter with a position differing from the IPCC. I couldn’t be right to disagree all of those scientists. I told here I felt in good company with John Christie.

I am especially glad to see your refutation of Kohler. That whole process that refused Harde a chance to defend his work was and remains repugnant.

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John A BirdExcellent article and contradictions to IPCC’s Climate Change Theory! Your article takes me a while to digest, so I must read and re-read a number of times before it becomes strikingly clear. I became interested in Climate Science once it was politicized, knowing the IPCC was typically funded by governments around the globe and these contractors would say and do anything to continue their lavish lifestyles.

M MontgomeryCongratulations for being recognized with the AMS publishing and invitation to present! Really appreciate your expert and hard work on this. And persistence!! It may be slow to payoff, but it will. And we thank you!

Colin DavidsonYou have written:

“3.2 13C data support the physics model

Let R equal the 13C/12C ratio.

RealClimate (2004b) says R for human emissions is about 98 percent of the R in natural emissions, and that R has declined about 0.15 percent since 1850. RealClimate concludes the above data prove human CO2 caused all the increase in atmospheric CO2 since 1850.

RealClimate (2004b) says R has declined about 0.15 percent since 1850 and concludes this means human CO2 caused all the increase in atmospheric CO2.” Is this last sentence redundant?

I liked your paper.

Dr. EdDear Colin,

Thank you very much for catching this error. To correct it, I have deleted the last sentence that was indeed redundant.

Ed

Ferdinand EngelbeenColin,

The problem of the origin of what resides as CO2 in the atmosphere is in the deep oceans. Vegetation and ocean surface are in fast exchange with the atmosphere and what is absorbed in one season is largely released the next season, the lag in 13C/12C (or 14C/12C) ratio change then is only a few years, which is observed in ocean surface and vegetation.

The exchange between the atmosphere and the deep oceans has a lag of about 1000 years: what goes into the deep is the isotopic composition of today, what returns the same year is the composition of ~1000 years ago, not affected by human activities.

One can calculate the residual change in 13C/12C ratio for different deep ocean – atmosphere exchanges, that gives a near constant CO2 flux between equatorial upwelling and polar sinks of about 40 GtC (20 ppmv) per year:

http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg

Independently confirmed by the faster decay rate of 14C from the bomb tests.

The discrepancy in the years before 1970 is probably from vegetation: more source than sink in that period (forest cutting?). After 1990 more sink than source: the earth is greening.

As all inorganic CO2 (oceans, volcanoes, carbonate rocks,…) is high in 13C/12C ratio and all (living and fossil) organic CO2 is (much) lower in 13C/12C ratio, there are only two main sources of low 13C CO2: vegetation and fossil fuel use. Vegetation is a proven net sink (based on O2 release), thus all reduction of the 13C/12C ratio in the atmosphere/vegetation/oceans is from the use of fossil fuels.

Based on the observed 13/12C ratio in the atmosphere, about 1/3 of all original human emissions still resides in the atmosphere, or about 10%, way above the 4% according to the physics theory.

Dr. EdDear Ferdinand,

History is irrelevant to the issue because only the present state of the land and oceans sets the inflow of CO2 into the atmosphere, and the physics model properly describes how inflow sets balance levels. By “properly” I mean the physics model is the ONLY model that explains the data. Therefore, it is the only model that we can use to explain how inflow changes level.

Before 1970, the northern hemisphere had more 14C than the southern hemisphere. It took until about 1970 for the 14C to become about equal in each hemisphere.

Thereafter, the 14CO2 show it exits the atmosphere with outflow proportional to level.

My sections 3.1 and 3.2 show how only the physics model explains the present levels of 14C and 13C in the atmosphere.

I will welcome any good explanation of why my sections 3.1 or 3.2 may be wrong. So far, your challenge does not accomplish that goal.

Colin DavidsonThe residence time is critical to your thesis. I think you need to emphasise that the residence time of 4 years for 12CO2 is constrained.

The Physics Theory requires that the residence time is constant (the basis being that this is what is expected in natural systems, and that expectation is confirmed by the measured behaviour of atmospheric 14CO2). The residence time selected for 12CO2 is derived from the passage where the IPCC says the initial “turnover time” is 4 years. (Is there a more sound basis for selecting 4 years? Are there experimental results? Why did the IPCC say 4 years?)

Perhaps you could consider this emphasis at the start of Section 4.2

Secondly, have you done a sensitivity analysis? How sensitive are your conclusions to the selected residence time?

Dr. EdDear Colin,

Thank you for your comment. The first constraint on the residence time of 12CO2 is it must be less than the 16.5 years for 14CO2.

Equation (A.4) shows Te = Level / Inflow. So we use the known recent balance level of about 400 pm and divide by the IPCC claimed inflow of about 100 ppm/year, to get a 4-year residence time.

But more important are Eqs. (3) and (4) in section 4.2. They show the ratio of human to natural balance levels is the ratio of their inflows INDEPENDENT of residence time. So, my major conclusions are independent of residence time.

Colin DavidsonThanks.

Figure 4 uses the 4 year residence time and it is discussed in Section 2. Your very clear statement above (“Equation (A.4) shows Te = Level / Inflow. So we use the known recent balance level of about 400 pm and divide by the IPCC claimed inflow of about 100 ppm/year, to get a 4-year residence time.”) could be used to justify the use of 4 years in Figure 4.

DMAColin

There is a good section on residence time analysis in Tom Segalstad’s “Carbon Cycle Modeling and Residence time of Natural and Anthropogenic CO2” where he lists about 30 tests done in the last 50 or so years using several techniques. The results varied from 2 to 20 years mostly around 4-6years.

Dr. EdThank you, DMA,

Segalstad’s paper is in my references. The link to his paper is:

http://www.co2web.info/ESEF3VO2.pdf

Ferdinand EngelbeenDr. Ed,

If your theory is right, then there should be a huge increase (30%) in natural inflow to explain the 30% increase of CO2 in the atmosphere, that means that the residence time should have remained constant over time.

If you split the table at page 13 of Segalstad’s work in half the oldest and half the newest estimates, you will see that the newer estimates (with mid-range for estimated ranges) show a slight increase in residence time over the two periods, which points to a rather stable CO2 throughput in an increasing CO2 mass of the atmosphere.

Of course, that are only estimates, but there are no indications that the carbon cycle increased near 30%.

The rest of Segalstad’s work is completely obsolete: ice core CO2 and other measurements are very reliable and atmospheric CO2 measurements are superb with very rigorous calibration procedures, of which many temperature stations can learn a lot…

Colin DavidsonI found Sections 3.1 and 3.2 hard going.

What is the Test applied in Tables 3.1 and 3.2?

Dr. EdDear Colin,

I understand your feelings. I just finished making some charts that summarize the data in Tables 1 and 2. I will add these charts to sections 3.1 and 3.1. Give me about 10 minutes and then tell me if the charts help.

OK. I added charts to sections 3.1 and 3.2. Do these charts help explain the points of these sections?The main point is the IPCC claims the 14C and 13C data support its theory. But when we insert the numbers, we find these data support the physics theory and reject the IPCC theory.

I may now move the tables to Appendices.

Colin DavidsonThanks. Much better.

It might also be improved by eliminating the shorthand “R” and substituting the word “ratio”. EG:

“RealClimate (2004b), in support of the IPCC, says the 13C/12C CO2 ratio for human emissions is about 98 percent of that in natural emissions, and that it has declined about 0.15 percent since 1850. RealClimate concludes the above data prove human CO2 caused all the increase in atmospheric CO2 since 1850. But it is important to use numbers to find the real conclusion.

The physics model assigns 95.5 percent to natural emissions and 4.5 percent to human emissions, according to Fig. 1. The IPCC model assigns 68 percent to natural emissions and 32 percent to human emissions. The physics model concludes human emissions will have lowered the 13C ratio by 0.09. The IPCC model concludes human emissions will have lowered the 13C ratio by 0.64. The calculations are shown in Appendix E”

Just a suggestion. There is a small typo in the last “ratio” in this passage, where you have “ration”.

RobKPhysicist John Reid’s article THE EMBARRASSING BOMB-TEST-CURVE covers this topic and possible mechanisms at his blog

http://blackjay.net/?p=262

Ferdinand EngelbeenEuan Mearns has a nice background article, which shows that the 14C bomb curve can’t be used to show what happens with a 12CO2 peak:

http://euanmearns.com/whats-up-with-the-bomb-model/

Dr. EdDear Ferdinand, I am presently working on an addition to my preprint that explains why Euan Mearns is wrong. Sorry, but you will have to wait until I finish that part before we can argue the details.

AlexPhysics to the rescue! Appreciate this paper so much. Brilliant use of the C14 data, who’d have known the nuclear bomb saved us again from tyranny…

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Ferdinand EngelbeenDr. Ed,

We have been there before…

As you know, I do differ in opinion as good with your theory as with the IPCC’s Bern model. Both are wrong on essential points.

1.

outflow is proportional to levelThat is only true for pressure driven processes. The largest CO2 fluxes are seasonal and temperature driven and e.g. the spring/summer uptake of CO2 by plants is entirely driven by temperature, where any extra CO2 pressure in the atmosphere plays a minor role. The uptake is estimated at about 30 ppmv/season with a similar release in fall/winter by vegetation decay. The influence of pressure in the same vegetation is about 1 ppmv/year with as result an increase in total biomass.

Temperature thus drives the residence time, which is about 5 years, not 16.5 years.

Any extra CO2 pressure above the temperature controlled dynamic equilibrium between ocean surface and atmosphere (per Henry’s law for the solubility of CO2 in seawater) gives you an extra uptake, as well as in vegetation as in the (deep) oceans. That is a much slower process, surprisingly linear over the past 60 years: about 50 years e-fold decay rate. An order of magnitude slower than the residence time.

2. About the introduction:

– The IPCC does assume that all CO2 increase in the atmosphere is caused by human emissions,

they don’t assume that all original human CO2 still resides in the atmosphereas your graph suggests, because about 20%/year of all CO2 in the atmosphere isexchangedwith CO2 from other reservoirs, especially the deep oceans which have a 14C and 13C/12C ratio of about 1,000 years ago, thus reducing the 14C and increasing the 13C/12C ratio compared to if all human CO2 should remain in the atmosphere.– The physics model shows a maximum of about 4% human CO2 in the atmosphere, while observations show a 13/12C ratio of above 9% human CO2 in the current atmosphere. Something is wrong in the model…

The essence of the discussion lies in:

outflow equals level divided by residence timeWhich is only true if all in/outflows are in the same direction at any moment of time, which is not the case.

The residence time in essence is:

residence time = level / throughputIf you have one input and one output, once in equilibrium, you can use input or output i.s.o. throughput to calculate the residence time. Or reverse, using level and residence time to calculate the outflow.

If you have many inputs and outputs, it doesn’t matter for the calculation of the residence time whatever the direction and timing is of the individual fluxes. But that has a tremendous influence on the reverse formula as used in the physics model.

In the real world the two main seasonal fluxes are opposite to each other in time:

During spring/summer some 30 ppmv is absorbed by vegetation.

In the same period, some 25 ppmv is released by the ocean surface.

Net result: -5 ppmv in the NH, near zero in the SH.

Net result over a year: -5 ppmv in spring/summer, +5 ppmv in fall/winter, about zero ppmv over a year.

With an average extra CO2 pressure of near zero in the atmosphere, there is near zero extra output caused by that pressure…

See: http://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_MLO_trend.jpg

Conclusion: you can’t use the reverse physics formula of the residence time, if the fluxes are not all in parallel at every moment in time.

Then the 14C graph. Based on the estimated fluxes in different ways, the residence time for any CO2 molecule in the atmosphere is about 5 years. The decay rate of 14C from the bomb tests is about 16 years, while the decay rate of any extra 12CO2 is about 50 years. What gives the discrepancy?

– The residence time has no connection at all with the decay rate of any extra CO2 in the atmosphere above equilibrium.

– The decay rate of any extra 14C is much faster than for any extra 12CO2 above equilibrium, as what goes into the deep oceans is the composition of any given year, what returns is the composition of ~1000 years ago. In 1960, at the height of the bomb tests, some 97.5% of all 12CO2 mass (not the same molecules!) returned the same year, while only some 45% of 14CO2 mass returned. With as result a much faster decay rate for 14CO2 than for 12CO2…

See: http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_1960.jpg

Dr. EdDear Ferdinand,

Thank you again for your comments. Here is my reply.

Indeed, temperature varies with season and the warmer growing season consumes more CO2 than the non-growing season, and seasons vary with hemisphere. However, over the year, the CO2 consumed by plants depends upon the level of CO2 in the atmosphere, just like plant growth depends on the level of CO2 in a greenhouse. So, over the year, outflow is proportional to level.

Also, instantaneously, outflow it proportional to level. Outflow is always pressure driven so long as there is a place for it to go. If there were no plants or oceans, then there would be no outflow of CO2, as well as no inflow. But that is not the situation we are trying to explain.

Regardless of the interannual cycles, the 14C data prove several things because its outflow is much greater than its inflow.

(a) Outflow = level / residence time, independent of inflow. Were this not true, the physics model would not exactly match the 14C data.

(b) The IPCC model does not match in any manner the 14C data. Therefore, the IPCC model is wrong.

(c) Because Outflow = level / residence time, even the IPCC agrees that Residence time = adjustment time.

(d) So, exchange of molecules has the same residence time as the change in level. There is no separate “e-fold” decay time. There are no slower processes that restrict the faster processes. The concept of an e-fold time that differs from residence time contradicts the 14C data. It also needlessly complicates the physics. To do good physics, we must follow Occam’s Razor: the simplest model that explains the data wins.

(e) 14CO2 has a residence time of 16.5 years. 12CO2 will have a shorter residence time, like 4 to 5 years. Rather than in its slower speed, 14CO2 follows 12CO2.

Regarding your comment about my Introduction:

(f) Nor does the physics model assume all the original human CO2 is still in the atmosphere.

(g) Arguments based upon ocean flows 1,000 years ago, or exchanges of 20 percent per year, or that original human inflow has flowed out of the atmosphere are irrelevant and serve only to confuse the physics, which is really simple:

(h) Present inflow set the present balance levels in the atmosphere. The ratio of human to natural CO2 inflows set the ratio of the human to natural CO2 balance levels in the atmosphere, independent of residence time.

(i) Similarly, the inflows of 14CO2 and 13CO2 set the balance levels 14CO2 and 13CO2, according to the physics model.

(j) Details of the processes in the oceans and land are irrelevant because only their resulting inflows affect the balance levels in the atmosphere. The physics model properly describes how inflows set the balance levels in the atmosphere.

(k) The IPCC assumes nature’s inflow has remained constant since 1750 and therefore its balance level remained constant at 280 ppm. If that assumption were true, then the level of CO2 in the atmosphere today would be nature’s contribution of 280 plus the human contribution of 18 for a total of 298 ppm.

(l) Every argument the IPCC makes to justify its claim that human CO2 added 130 ppm to the level of CO2 in the atmosphere breaks down. The only way that could be true is for the ratio of human to natural CO2 inflows to be 130/280. And that ratio contradicts the IPCC assumed data.

(m) My sections 3.1 and 3.2 show the proper calculations of how the physics model and IPCC model predictions fit the 14CO2 and 13CO2 data. Only the physics model can explain the data. The IPCC model cannot explain the data.

Regarding your other comments:

(n) The physics model is the only model that explains the 14C data.

(o) Yes, the 14CO2 has a residence time according to its data of about 16.5 years.

(p) There is no evidence that 12CO2 has or can have a longer residence time than 14CO2. There is no discrepancy in the data or in the physics model. The only discrepancy is in the incorrect IPCC model.

(q) The respective residence times measure how fast 14CO2 or 13CO2 or 12CO2 exits the atmosphere and they all exit in proportion to their levels.

(r) The approach of the level to its balance level is the same whether the level is above or below its balance level. The 14C data show the case of the level being higher than its balance level determined by natural processes.

(s) What happened 1000 years ago and what happened even last year only affects the present inflow, which sets the balance level. And the physics model properly describes how any inflow changes the level of CO2 in the atmosphere. The IPCC model cannot do this.

(t) Finally, the physics model shows the ratio of human to natural CO2 in today’s atmosphere is determined by the ratio of their inflows, independent of residence time. Nothing you have written contradicts this conclusion.

Ferdinand EngelbeenDear Dr. Ed,

To start with:

the CO2 consumed by plants depends upon the level of CO2 in the atmosphereYes, but that is not more than about 1 ppmv/year, or together with the ocean sinks about 2.5 ppmv/year. That is a “residence time” of about 50 years:

http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg

There is hardly any influence of the increased CO2 pressure in the atmosphere on the seasonal cycle, the amplitude (that is the difference between ocean release and plant uptake and reverse) hardly changed over the years, despite over 20% more CO2 in the past 60 years:

http://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_MLO_trend.jpg, only the residual change doubled, but still is only half human emissions…

Still a lot of CO2 is cycling in and out the atmosphere over the seasons, which gives the 5 years residence time, but that doesn’t make any difference in removing any extra CO2 above equilibrium.

Then:

Outflow = level / residence time, independent of inflow. Were this not true, the physics model would not exactly match the 14C data.As the definition of residence time is level/throughput, and when in balance also level/input or level/output, not reverse, I find your explanation rather questionable…

What you have proven is that the 14CO2 decay rate is linear with the extra level in the atmosphere above equilibrium, with an e-fold decay rate of about 16.5 years

But it is not because the IPCC’s Bern model is wrong, that your model is right for the right reasons…

Problem:

I don’t see how you jump from a residence time of 4 years for all CO2 to a residence time of 16.5 years to explain the 14C curve. The absorption of 14CO2 by oceans and plants is somewhat slower than for 12CO2, but that is in the % range, not a fourfold. Moreover the 14C decay rate in the ocean surface and vegetation follows the atmosphere with only a few years delay. Thus where is your 16.5 years decay rate based on and why not 4 years?

At last (gets late here):

Nothing you have written contradicts this conclusion.That is about the 13C/12C ratio in the atmosphere.

If you take the pre-industrial ratio as base, and a constant exchange with the deep oceans, then the current atmosphere contains about 10% human CO2, way above the physics model…

BTW, Fig.7 shows the 13C/12C ratio according to the IPCC model, if all original human CO2 still resides in the atmosphere, but 2/3 of that is already replaced by deep ocean CO2 at a higher 13C/12C ratio, thus even the Bern model gives about the right answer on that point: about 0.21 decrease in ratio.

Dr. EdDear Ferdinand,

“… about 2.5 ppmv/year. That is a “residence time” of about 50 years.”There is no residence time of 50 years in the data. 50-years is a belief that contradicts the data.

The 14C data are fundamental data that all models must predict. The data prove 14CO2 has a 16.5-year residence time and the outflow is equal to level / residence time. And this proves e-fold time equals residence time. There is no reason to make the picture more complicated. Simplicity that succeeds always wins.

Assuming ocean sinks consume about 2.5 ppmv/year does not prevail over the 14C data. The 14C data prove the 2.5 ppmv/year is not good data.

“There is hardly any influence of the increased CO2 pressure in the atmosphere on the seasonal cycle. Only the residual change doubled, but still is only half human emissions…”The physics model does not predict there would be any change. The comparison to the sum of human emissions is not valid because it assumes the IPCC model is correct.

The proper way to view the change of CO2 levels is to use the physics differential equation:

dL/dt = Inflow – Outflow.

This equation does not depend upon history. No valid model depends upon history.

“As the definition of residence time is level/throughput, and when in balance also level/input or level/output, not reverse, I find your explanation rather questionable…”The physics model derivation in Appendix A has only assumption: Outflow = Level/Residence time. The 14C data prove this assumption is valid. All other physics model equations are deductions, not assumptions. To prove a theory is wrong, we must show that it makes a prediction that contradicts data.

“What you have proven is that the 14CO2 decay rate is linear with the extra level in the atmosphere above equilibrium, with an e-fold decay rate of about 16.5 years.”Not true. The match of the physics model prediction to the 14C data proves the data follow the physics model that is exponential, not linear, and that e-fold time equals residence time.

“I don’t see how you jump from a residence time of 4 years for all CO2 to a residence time of 16.5 years to explain the 14C curve. The absorption of 14CO2 by oceans and plants is somewhat slower than for 12CO2, but that is in the % range, not a fourfold.”I start with 16.5 years for 14CO2 because that matches the data. Then I use 4 years for 12CO2 because IPCC uses 4 years which it calculates by dividing 400 ppm by the inflow of about 100 ppm/year. So, ask IPCC that question.

I don’t care what the 12CO2 residence time is, so long as it is less than 16.5 years. The physics model ratios are independent of residence time, and that conclusion proves the IPCC model is wrong.

“Moreover, the 14C decay rate in the ocean surface and vegetation follows the atmosphere with only a few years delay. Thus, where is your 16.5 years decay rate based on and why not 4 years?”My 16.5 years residence time for 14CO2 is a direct result of the 14C data. Data always prevails over theory.

“If you take the pre-industrial 13C/12C ratio as base, and a constant exchange with the deep oceans, then the current atmosphere contains about 10% human CO2, way above the physics model…”Not true. The current atmosphere contains about 4.5 percent human CO2 because human CO2 is about 4.5 percent of the inflow and human CO2 flows out of the atmosphere just as natural CO2 flows out of the atmosphere.

The exchange rate with the deep ocean is irrelevant to the argument because the only thing that matters is the 13C/14C ratio in the ocean surface the sends CO2 to the atmosphere.

“Fig.7 shows the 13C/12C ratio according to the IPCC model, if all original human CO2 still resides in the atmosphere, but 2/3 of that is already replaced by deep ocean CO2 at a higher 13C/12C ratio, thus even the Bern model gives about the right answer on that point: about 0.21 decrease in ratio.”The “

higher CO2 ratio” from the ocean sets the natural 13C balance level. Fig. 7 shows the deviation from the natural balance level, and it includes all effects that set the balance level. The data do not reject the physics model. Therefore, the 13C data do not prove the IPCC claim that human CO2 caused all the increase in atmospheric CO2 above 280 ppm.Thank you for your challenges.

Ferdinand EngelbeenDear Dr. Ed,

There is no residence time of 50 years in the data.There is:

Based on the definition of a linear decay rate of any process, the e-fold decay rate = disturbance / effect.

In this case, the disturbance is the extra CO2 pressure above the dynamic equilibrium for the current average ocean surface temperature, according to Henry’s law for the solubility of CO2 in seawater with temperature. The effect is the net sink rate, that is human emissions minus observed increase in the atmosphere.

In 1959: +25 ppmv, 0.5 ppmv/year, 50 years, half life time 34.7 years.

In 1988: +60 ppmv, 1.13 ppmv/year, 53 years, half life time 36.8 years.

In 2012: +110 ppmv / 2.15 ppmv/year = 51.2 years, half life time of 35.5 years.

Looks like a very simple, linear decay rate to me.

We can plot that effect over the past 60 years of good data:

http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2B.jpg

Where the calculated increase of CO2 (human emissions minus calculated sink rate with a decay rate of ~50 years) is midst the “noise” caused by Pinatubo, El Niño,…

The 14C data prove the 2.5 ppmv/year is not good data.Sorry? Data are data, as good or bad as the measurements are. All what the 14C data prove is that the decay rate of 14CO2 is different than for 12CO2. As said before, that is because the CO2 that returns from the deep oceans is firmly depleted in 14C.

dL/dt = Inflow – OutflowAgreed. In this case:

dL/dt = natural inflow + human inflow – natural outflow

In all past 60 years, natural outflow was larger than natural inflow, thus the mass balance shows that the human inflow of 1 – 4.5 ppmv/year is fully responsible for most of the 0.5 – 2.5 ppmv increase over the same period…

Simple mass balance, nothing to do with the IPCC’s Bern model.

the 14C data proves the data follow the physics model that is exponential, not linear, and that e-fold time equals residence time.The decay is exponential, but the response of the sinks is in linear ratio with the extra CO2 pressure in the atmosphere. The latter gives a “residence” time which is in fact a

change ratefor any disturbance to any process in dynamic equilibrium. That is not anexchange rate, which is what a residence time is by definition.I start with 16.5 years for 14CO2 because that matches the data. Then I use 4 years for 12CO2 because IPCC uses 4 years which it calculates by dividing 400 ppm by the inflow of about 100 ppm/year. So, ask IPCC that question.Sorry? Either use the a 16.5 years decay rate for 14CO2 and a 50 years decay rate for 12CO2 (which also matches the data for the 12CO2 decay), or use the 4 years “residence time” in both cases. The IPCC doesn’t use the 4 years residence time, as that has zero influence on the CO2 level in the atmosphere:

that is exchange, not change. Which doesn’t imply that the Bern model is right. Until now, the 12CO2 decay rate is linear without any trace of saturation that the Bern model implies.The exchange rate with the deep ocean is irrelevantBoth ocean surface and vegetation show a rapid exchange of CO2 with the atmosphere and any change in 14C/12C or 13C/12C ratio is rapidly distributed over these three reservoirs. The deep oceans exchanges are a source of 13C-rich and 14C-poor CO2, which changes the ratio in the atmosphere over longer periods, thus “dilute” the “human fingerprint”. That is very relevant.

The data do not reject the physics model.No, but don’t reject the IPCC’s Bern model either. Your graph for the IPCC shows the effect on the 13C/12C ratio if all human CO2 (as molecules) still was in the atmosphere, while the exchange with the deep oceans has already replaced 2/3 of these molecules with CO2 from the deep oceans, thus only 1/3 of the original molecules but 100% of the increase in mass is from human origin…

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Gavin Cawley“Cawley (2011) argues the ratio of human to natural CO2 in the atmosphere is a function of residence time. Equation (3) shows the ratio is independent of residence time.

Cawley’s Eqs. (3), (4), and (5) incorrectly assume that outflow depends upon its value at time zero. ”

This is factually incorrect. F_e^0 represents the outflow part steady state exchange flux between the atmosphere and the oceans and terrestrial biosphere, not it’s value at time zero. We know this steady state exchange flux exists. The most easy to understand part is the exchange flux with terrestrial plants. The plants seasonally take in CO2 for photosynthesis and subsequent primary production (e.g. growing leaves) and then emit it seasonally via decay (including soil respiration). So we know that there is a steady state exchange flux and it is that which causes residence time and adjustment time to be different. If you don’t include this in your model, then your model does not represent the actual carbon cycle as a fundamental component is missing.

“His Eqs. (7) and (8) incorrectly model human and natural CO2 differently. Therefore, all Cawley’s conclusions are wrong.”

This is factually incorrect. Both natural and anthropogenic carbon are removed according to the same constant F_e. If the physical processes taking CO2 out of the atmosphere make no distinction between anthropogenic and natural CO2, then that is essentially picking a molecule at random each time. The probability for anthropogenic carbon is then C_A/C and for natural carbon C_N/C. So in order to NOT treat anthropogenic and natural carbon differently, you need one equation for each, accounting for the difference in their atmospheric masses (mixing ratios). The only other difference is that for natural carbon there is F_i^0, which represents the influx component of the steady state exchange, which as I have already pointed out we know to exist, so if your model doesn’t include it, it doesn’t correctly represent the carbon cycle.

The basic point of my paper is that to understand the difference between residence time and adjustment time, you need to consider the effects of the steady state exchange of CO2 between the atmosphere, oceans and terrestrial biosphere. If you don’t include this steady state exchange flux, you will make exactly the same mistake that Prof. Essenhigh did.

Dr. EdDear Gavin,

First, so I don’t have to repeat myself, I refer readers to my reply to your previous comment here: https://edberry.com/blog/climate-physics/agw-hypothesis/my-poster-presentation-for-the-ams-annual-meeting-jan-8-2019/#comment-51532

Second, my physics model fully explains how CO2 flows through the atmosphere. Your model does not. Your model relies on a “steady state exchange flux” which shows you do not understand the physics.

Third, you inserted your “steady state exchange flux” in the wrong place in your math. Therefore, all your conclusions are wrong.

Gavin CawleyI note that you evade the point that you misrepresented my paper. My paper does not treat anthropogenic and natural CO2 differently. You assert that the “steady state flux is inserted in the wrong place in the math, but that is just an unsupported assertion, you haven’t actually shown it. Thus you are evading the technical criticism again. I don’t think I will bother any further, but don’t say the errors haven’t been pointed out to you. They have, but you have just ignored them.

Dr. EdDear Gavin,

You wrote in your previous comment above:

“This is factually incorrect. F_e^0 represents the outflow part steady state exchange flux between the atmosphere and the oceans and terrestrial biosphere, not it’s value at time zero. We know this steady state exchange flux exists.”

Yes, it exists but you don’t know why it exists.

Your Eq. (3) without the F0e agrees with the physics model because your ke = 1/Te.

You have incorrectly added the steady-state outflow F0e to your Eq. (3) because your keC is the source of that steady-state outflow. So, you have included the steady-state outflow twice. Your F0e does not exist by itself. It exists only because your C (the level of atmospheric CO2) drives it.

OK, I will revise my comment about your F0e being a flow at time zero, although it is a flow at time zero before you begin to account for the outflow caused by the level C.

Nevertheless, your Eqs. (3), (4), (5), and your equation after (5) are still wrong because they should not include your F0e.

Your whole paper is wrong because of this error. Finally, your paper does not prove in any way that human CO2 caused all the increase of atmospheric CO2 above the IPCC-claimed 280 ppm in 1750.

Philip MulhollandDr Ed,

The following paper may be of interest to you:-

Fergusson, G.J. 1958. Reduction of Atmospheric Radiocarbon Concentration by Fossil Fuel Carbon Dioxide and the Mean Life of Carbon Dioxide in the Atmosphere. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. Vol. 243, No. 1235 (Feb. 11, 1958), pp. 561-574 (14 pages).

https://www.jstor.org/stable/100372?seq=1#page_scan_tab_contents

H/T TdeF on Jonova’s Blog

http://joannenova.com.au/2018/12/midweek-unthreaded-53/#comment-2086709

iHansYour article provide several links, also to Harde 2017a and Harde 2017b. However, both produce the Harde Reply, where the first is supposed to link to the original Harde paper? It is on your site, as Google was able to find it.

Dr. EdDear Ihans, Thank you for bringing this to my attention. I believe these links are now fixed.

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Marcus rönningås“There is no tolerance in Kohler’s world for a contradictory opinion”

And that was shared by the publishers as well.

“Through working with the Publisher and in co-operation with the Elsevier’s Experts in Publication Ethics, we have now inspected all relevant documents, including reviews of the initial paper by Harde (2017) and the now-published Comment by Köhler et al. (2018) and the now-rejected Reply by Harde.”

https://www.sciencedirect.com/science/article/pii/S0921818117306586

Dr. EdDear Marcus, that is my point. Kohler’s world and Elsevier’s world are one and the same. What does that tell us about so-called “peer-reviewed” publications?

Marcus rönningåsYou are slightly correct in regards to the first part. The world that Kohler and Elsevier is in samoe aspect on and the same – it is called Science. Now, Elsevier might be questioned and as You probably know many institutions have left Elsevier.

And it tells us quite a lot regarding peer review, it will always be an integrated part of the scientific community. That is why it was so clear that the process failed when publishing Harde 2017.

Dr. EdDear Marcus, As my paper explains, Harde’s paper is correct and the criticism by Kohler is incorrect. Forget who did the peer review. Just follow the science.

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Char DLiang et al., 2017

https://www.nature.com/articles/s41598-017-12774-w

“Here, we analyze Δ17O data from four places (Taipei, Taiwan; South China Sea; La Jolla, United States; Jerusalem, Israel) in the northern hemisphere (with a total of 455 measurements) and find a rather narrow range (0.326 ± 0.005‰). A conservative estimate places a lower limit of 345 ± 70 PgC year−1 on the cycling flux between the terrestrial biosphere and atmosphere and infers a residence time of CO2 of 1.9 ± 0.3 years (upper limit) in the atmosphere.”

Char DThe weakness of your paper is not in its substance, but its references.

It is unlikely that a scholarly journal will agree to publish a paper that lists blog entries (i.e., from WattsUpWithThat) as sources.

And even if a journal does accept this version as is, these citations will be the initial criticism lodged by those who would prefer to dismiss than to offer a substantive counter argument.

My suggestion would be to preemptively avoid these pitfalls and not give your opposition an easy “win”.

Dr. EdDear Char, Thank you very much for your comment. I will proceed to remove such blog references. I do not need them. I only included them to show the work of others.

YonasonI’d be interested in your thoughts on this.

https://tambonthongchai.com/2018/12/19/co2responsiveness/

Basically, it seems to be saying that the human contribution to atmospheric CO2 is so little as to be undetectable, statistically.

Thanks

H/T – John Ray’s excellent “greenie watch” blog.

Dr. EdDear Yonason, The paper you linked is a good paper. It shows the increase in atmospheric CO2 does not correlate with human CO2 emissions. It shows the corresponding overall increases of human emissions with CO2 level does not prove human emissions caused the increase in the level. That is why it is necessary to detrend time series data before calculating correlations.

The paper references several papers by Munshi. My paper references the most recent paper by Munshi. Munshi has done more than anyone else on these statistical correlations.

YonasonThanks for that feedback.

GunnarI have a few questions on Te:

You calculate Te and assume it is constant at equilibrium as well as at non-equilibrium, right?

Te should be calculated and valid at the equilibrium , right? What if 400 ppm is not an equilibrium? It definitely doesn’t seem like equilibrium since the level changes by some 3 ppm per year?

Now you calculate Te at 400. What If You’d calculated Te at 280 ppm and assume that is the equilibrium You would get 275 as the natural level instead of 392?

You assume the same Te is valid for both natural and human emission, why?

Te is dependent on the partial pressure , right? shouldn’t the partial pressure of the human emission be much lower and thus the Teh be much larger?

BR,

Gunnar

Dr. EdDear

Gunnar, Thank you for your comment.

My first step was to assume Te both at and not at equilibrium. The physics model successfully replicated the 14C data using Te = constant. That did not have to happen. It could have turned out that Te changed from 1970 to 2014. So, the successful replication means Te was constant over this interval, and the interval began with 14C very far from its balance level and ended with 14C close to its balance level. Therefore, my assumption was correct.

We can calculate Te = Level / Inflow = 400 ppm / 100 ppm per year = 4 years.

That is an approximation because, as you point out, the level may not be at its balance level. Also, IPCC says its inflow numbers may be off by 20 percent.

The 14C data are much more accurate. So, the Te = 16.5 years for 14CO2 is a pretty good number. This also tells us the Te for 12CO2 will be a much smaller number and be a constant since 1970.

The reality is the level is increasing at an almost constant rate, as you note. This means the balance level is also increasing and it leads the level upward. If Te = 4 years then the level will get (1 – 1/e) closer to its balance level every 4 years. So, the level lags behind the increasing balance level by about 10 years.

The physics model tells us Inflow sets balance level: Lb = Inflow * Te

The 14C data strongly suggest that Te has remained constant from well before 1970, maybe since 1750. If this is so, then the reason the balance level was about 280 in 1750 was that inflow in 1750 was less than present inflow. Which means the reason the level has increased is that inflow has increased.

Te is the same for human and natural CO2 because their CO2 molecules are identical.

Partial pressure is proportional to level. The ratio of human to natural balance levels is shown in Eq. (3) in section 3.2 to be 4.5 percent. This ratio is independent of Te.

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