PREPRINT: Contradictions to IPCC’s Climate Change Theory

CONTRADICTIONS TO IPCC’S CLIMATE CHANGE THEORY

American Meteorological Society 99th Annual Meeting
Poster Presentation 4 to 6 pm on January 8, 2019
Published on AMS website here

Edwin X Berry
Climate Physics LLC, Bigfork, Montana, USA

Abstract

Two climate theories compete to predict the 14C data from 1970 to 2014. The physics theory of atmospheric CO2 competes with the United Nations Intergovernmental Panel on Climate Change (IPCC) theory of atmospheric CO2.

The physics theory makes only one assumption: outflow is proportional to level. The physics model accurately predicts the 14C data using a constant residence time of 16.5 years. This becomes the upper bound for the residence time of 12C-CO2.

The IPCC model cannot predict how 14C-CO2 reduced its level from 1970 to 2014. Therefore, IPCC theory fails the scientific method.

IPCC theory assumes human CO2 reduced the buffer capacity of the carbonate system. But the 14C data show the residence time, and therefore the buffer capacity, have remained constant. IPCC theory assumes an adjustment time that is greater than the residence time, but the 14C data show adjustment time equals residence time. The IPCC theory treats human and natural CO2 differently, so IPCC theory is fundamentally wrong.

The physics model shows the ratio of human to natural CO2 in the atmosphere equals the ratio of their inflows, independent of residence time. It predicts human CO2 adds only 18 ppm to the atmosphere while natural CO2 adds 392 ppm.

The physics model shows CO2 inflow does not “add” to atmospheric CO2. It sets a balance level for CO2 in the atmosphere. The level moves to its balance level until outflow equals inflow. Then, if inflow remains constant, the level will remain constant. Continued, constant human emissions do not add more CO2 to the atmosphere.

1.    Introduction

The United Nations Intergovernmental Panel on Climate Change (IPCC, 2001a) 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.

The 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, 2018) agrees with the IPCC and 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.”

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

This paper presents the “convincing alternative explanation” that IPCC and USGCRP claim does not exist.

Fig. 1 illustrates the disagreement. The physics model and the IPCC model agree the annual inflow of human and natural-produced CO2 is 4.6 and 98 ppm respectively.

Levels are in units of ppm. Flows are in units of ppm per year. GtC (Gigatons of Carbon) units are converted into CO2 units in ppm (parts per million by volume in dry air), using:

1 ppm = 2.13 GtC

The physics theory predicts the ratio of human to natural CO2 in the atmosphere equals their ratio in the inflow. It predicts human CO2 produces 4.5 percent and nature produces 95.5 percent of the present level of atmospheric CO2.

The IPCC theory predicts human CO2 produces 32 percent and nature produces 68 percent of the present level of CO2.

Fig. 1. IPCC and physics theory assume human and natural annual inflow is 4.6 and 98 ppm per year respectively. The physics model predicts these inflows add 18 ppm and 392 ppm to the level of atmospheric CO2. The IPCC model predicts nature’s addition stays constant at 280 ppm while human inflow adds all the increase above 280 ppm.

Authors who conclude human emissions cause only a minor increase in the level of atmospheric CO2 include Revelle and Suess (1957), Starr (1992), Segalstad (1992, 1996, 1998), Rorsch et al. (2005), Courtney (2008), Siddons and D’Aleo (2007), Quirk (2009), Spencer (2009), MacRae (2010, 2015), Essenhigh (2009), Glassman (2010), Wilde (2012), Caryl (2013), Humlum et al. (2013), Salby (2012, 2014, 2016), Harde (2017a), and Berry (2018).

Segalstad (1998), Ball (2008, 2013, 2018), and Salby (2014) present evidence that the level in 1750 was higher than 280 ppm. Nevertheless, this paper uses IPCC data to prove the IPCC theory is wrong.

Authors who support the IPCC include Cawley (2011), Kern and Leuenberger (2013), Masters and Benestad (2013), Richardson (2013), and the Kohler et al. (2017) comment on Harde (2017a).

2.    Theories must simulate data

2.1    The 14C Data

The above-ground atomic bomb tests in the 1950s to 1960s almost doubled the concentration of 14C in the atmosphere. The 14C atoms were in the form of CO2, hereinafter called 14C-CO2.

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 14C-CO2 gradually decreased toward its natural balance level. The decrease occurred because the bomb-caused 14C inflow went to zero while the natural 14C inflow remained.

There are two good 14C data sources. Hua et al. (2013) processed 14C data for both hemispheres from 1954 to 2010 using 61 mid-year data points. Turnbull et al. (2017) processed 14C data for Wellington, New Zealand, from 1954 to 2014 using 721 data points. After 1970, 14C-CO2 were well mixed between the hemispheres, so the 14C data from both sources are virtually identical after 1970.

Fig. 2 shows the global average data for D14C (Hua et al., 2013).

Fig. 2. Global average 14C data from Hua et al. (2013) using 61 mid-year data points. The dotted red line is from the physics model.

Fig. 3 shows the New Zealand data for D14C (Turnbull et al., 2017).

Fig. 3. Wellington, New Zealand 14C data from Turnbull et al. (2013) using 721 data points. The dotted red line is from the physics model.

Figs. 2 and 3 show the physics model accurately simulates the 14C-CO2 data from 1970 to 2014. The physics model uses Eq. (A.8) with the residence time set to 16.5 years and the balance level set to zero.

Note for non-technical readers: The use of “Equation” when beginning a sentence and “Eq.” inside a sentence before “(#)” is standard terminology to reference mathematical equations.

2.2 Physics model simulates the 14C data

Section 3 and Appendix A describe the physics theory and model. The physics theory uses only one simple assumption, namely,

outflow equals level divided by residence time.

The physics theory results in mathematical equations that become the physics model. To calculate the results of the physics model in Figs. 1 and 2 using Eq. (A.8), set the starting level Lo to the measured D14C level in mid-1970, and set the balance level Lb to zero. Find the residence time Te by trial and error until the result gives a good “eyeball” fit to the data.

The physics model has no arbitrary curve-fit parameters. Once the residence time Te matches the data, the fitting is done.

The accurate match of Eq. (A.8) to the 14C data proves two things:

  1. 14C-CO2 outflow equals the level L divided by the residence time Te, and
  2. 14C-CO2 residence time remained constant at 16.5 years from 1970 to 2014.

The residence time of 16.5 years for 14C-CO2 is the upper bound for the residence time of 12C-CO2 because 12C-CO2 react and flow faster than 14C-CO2.

The physics model shows how natural 14C inflow sets a “balance level” for 14C-CO2. The level always moves towards its balance level. When the level equals the balance level, outflow equals inflow, and the level remains constant.

2.3 Physics model predicts CO2 outflow

All valid CO2 models must replicate the 14C data after 1970. According to the scientific method, it is impossible to prove a theory correct but if a prediction is wrong, the theory is wrong.

Section 4 and Appendix B describe the IPCC (2001a) theory and model. The IPCC does not derive its mathematics directly from its theory. Rather the IPCC inserted its theory into its climate models. Then the IPCC created a seven-parameter curve fit to the output of its climate models (Joos et al., 2013). The resulting curve fit is known as the “Bern model” (Bern, 2002). Therefore, the Bern model contains the mathematics for the IPCC theory.

Fig. 4 shows how Eq. (A.8) of the physics model and Eq. (B.1) of the Bern model predict how CO2 in the atmosphere will approach its balance level. All model calculations begin the simulation with the initial level set to 100 and the balance level set to zero.

In Fig. 4, because of its very close match to the 14C-CO2 data in Figs. 2 and 3, the physics model uses a residence time of 16.5 years to simulate the 14C-CO2 data and a residence time of 4 years to simulate 12C-CO2.

Fig. 4. The physics model (black line) accurately simulates the 14C-CO2 data from 1970 to 2014, using a residence time of 16.5 years. The physics model (blue line) simulates 12C-CO2 data when the residence time is 4 years. The Bern model (red lines) cannot simulate how CO2 flows out of the atmosphere.

The Bern model predicts a dramatically different change in level than the physics model does. For the first year, the Bern outflow is faster than the physics model for 12C-CO2. Then the Bern model outflow decreases while its residence time increases. The Bern model line crosses the 14C data line which is the upper bound for 12C-CO2 residence time.

The Bern model is also unphysical. The Bern model, if restarted at any point on its prediction line, cannot simulate its original Bern prediction line. A valid model must continue its same prediction line if it is restarted at any point on its line. The Bern model predicts a different future if it is restarted at any point on its curve.

2.4 Adjustment time equals residence time

IPCC (2001b) defines “turnover time (T)” the same as residence time (Te):

Turnover time (T) is 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: T = M/S.

This IPCC definition is the same as the physics model assumption that outflow [S] equals level [M] divided by residence time [T]. IPCC (2001b) defines “adjustment time (Ta)” as:

Adjustment time (Ta) is the time-scale characterising the decay of an instantaneous pulse input into the reservoir.

IPCC agrees adjustment time equals residence time when outflow is proportional to level:

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: T = Ta.

The accurate simulation of 14C-CO2 outflow by the physics model proves CO2 outflow is proportional to level. Therefore, by IPCC’s own definition, its adjustment time equals residence time.

Discussion

IPCC (2001b) agrees 12C-CO2 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,” which describes the prediction of its Bern model in Fig. 4:

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 (CO2) 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 CO2 in the atmosphere, the actual adjustment is faster initially and slower later on.

Figs. 2 and 3 show how 14C-CO2 recovered from a perturbation of human-caused inflow of 14C-CO2. Its “adjustment time” is 16.5 years, not hundreds of years. The recovery from 1970 to 2014 did not just exchange molecules. It changed the level of 14C-CO2. The level approached its balance level exactly as the physics theory predicts. According to IPCC definitions, the adjustment time of 14-CO2 equals the residence time of 16.5 years.

Kohler et al. (2017) disagree:

“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. That is not the way of science. The implication of “Hence” is that the IPCC summaries are so perfect that no one may disagree. The problem with Kohler’s claim is the IPCC model prediction disagrees with data. Therefore, the IPCC theory is wrong.

Respectfully, the IPCC theory fails the scientific method. It makes wrong predictions. It contradicts physics. Its so-called “state of the art in peer-reviewed literature” is a repetition of inbred, invalid, pampered, and protected claims. It is time for Toto to pull the curtain to reveal the wizard for the fraud that it is.

3. Data support the physics model

3.1  14C data support the physics model

Kohler et al. (2017) argue that human fossil-fuel emissions of “14C-free” CO2 lower the 14C balance level. Well, human emissions do lower the 14C balance level, but by how much?

The physics model assigns 95.5 percent to natural emissions and 4.5 percent to human emissions, as shown in Fig. 1. The IPCC model assigns 68 percent to natural emissions and 32 percent to human emissions, according to IPCC (2001a) as shown in Fig. 1.

The physics model predicts human CO2 has lowered the balance level of 14C from zero to -4.5. The IPCC model predicts human CO2 has lowered the balance level of 14C from zero to -32, or 7.2 times as much as the physics model predicts. The calculations are shown in Appendix D. 

Fig. 5 shows how the physics model plot changes when the balance level is changed from zero to -4.5.

Fig. 5. The dotted line is the physics curve fit with the balance level set to -4.5, as predicted by the physics theory. This balance level fits the data.

Fig. 6 shows how the plot changes when the balance level is set to -32.

Fig. 6. The dotted line is the physics curve fit when the balance level is set to -32, as predicted by the IPCC theory. Clearly, this balance level is too low to fit the data.

Fig. 5 shows little difference from Fig. 3 which uses a balance level of zero. This shows the physics prediction for 13C fits the data. Fig. 6 shows a significant difference from Fig. 3. This shows the IPCC prediction does not fit the data. Therefore, the 14C data support the physics model and prove the IPCC model is wrong.

3.2 13C data support the physics model

RealClimate (2004b), in support of the IPCC, says the 13C/12C ratio for human emissions is about 98 percent of the ratio in natural emissions, and the ratio 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, as shown in 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 ration by 0.64. The calculations are shown in Appendix E.

Fig. 7 compares the decrease in the 13C ratio according to RealClimate, the physics model, and the IPCC model.

Fig. 7. The IPCC 13C ratio decrease according to RealClimate, the physics model, and the IPCC model. Clearly, the physics model is the better fit to the data.

Clearly, the 13C data support the physics theory and contradict the IPCC theory.

3.3 IPCC claim of human cause does not correlate

IPCC (2001a) claims annual human CO2 emissions cause annual increases in the level of CO2 in the atmosphere.

The overall rise in atmospheric CO2 corresponds to the rise of human CO2 emissions. However, it is important to remove overall trends in any time series and then correlate the individual values in the time series.

Munshi (2017) shows the “detrended correlation analysis of annual emissions and annual changes in atmospheric CO2” is zero.

Therefore, IPCC’s claim of “considerable certainty” that human emissions increase atmospheric CO2 fails. Where there is no correlation, there is no cause and effect. Statistics show human CO2 is not responsible for most of the increase in atmospheric CO2 since 1750.

4.    The physics model

4.1 Physics model derivation

A system describes a subset of nature. A system includes levels and flows between levels. Flows are rates. Levels set the flows and the flows set the new levels (Forrester, 1968).

Fig. 8 illustrates the system for atmospheric CO2. The system includes the level (concentration) of CO2 in the atmosphere and the inflow and outflow of CO2.

Fig. 8. The system for atmospheric CO2 includes the level (concentration) of CO2 and the inflow and outflow of CO2. It applies to all definitions of CO2.

The physics theory results in mathematical equations that become the physics model. The physics model shows how natural CO2 inflow sets a “balance level” for CO2. The level always moves towards its balance level. When the level equals the balance level, outflow equals inflow, and the level remains constant.

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 inflow simply raises the lake level until 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 from a hose flows into the bucket and then 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.

Inflow and outflow include the effects of outside processes. The only way an outside process can change the level is by changing inflow or outflow.

The system and all its equations apply independently to all definitions of CO2, for example, 14C-CO2, 12C-CO2, human CO2, and natural CO2, and their sums.

The mathematics used to describe the physics model are simple and analogous to the mathematics used to describe many engineering systems.

Appendix A shows the mathematical derivation of the physics model. It begins with the continuity equation, Eq. (A.1).

Then the physics model makes one and only one assumption, namely, that the outflow is proportional to level. More specifically, outflow equals level divided by residence time, Eq. (A.2).

All other physics model equations are deductions from the continuity equation and the one assumption. For example, the balance Level equals inflow multiplied by residence time, Eq. (A.4).

Equation (A.8) is the analytic solution to the physics model rate equation. It calculates the level as a function of time, given a starting level, a balance level, and a residence time.

Discussion

The Kohler et al. (2017) comment on Harde (2017a) concludes,

“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.”

There is no tolerance in Kohler’s world for a contradictory opinion. Like the promoters of Lysenkoism, Kohler wants Harde (2017a) withdrawn. In possible response, the journal refused to publish Harde’s (2017b) rebuttal to Kohler.

Kohler claims Harde’s system, and therefore the physics system, is “too simplistic” to be valid. Kohler claims a valid atmospheric CO2 system must contain at least two levels.

Kohler is wrong. 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.

The physics system does not exclude the effects of outside processes. Outside processes change the atmosphere level by changing its inflow or outflow.

The physics system properly computes how inflow and outflow change the level of CO2 in the atmosphere. Its equations and conclusions for the atmosphere level would not change if the atmosphere level were connected to another level.

Kohler’s comments on Harde are invalid because they derive from Kohler’s misunderstanding of the system that Harde used. Kohler et al. simply do not understand systems.

Kohler can’t get the physics of the atmosphere level correct. Worse, Kohler thinks adding more levels would correct their errors in the atmosphere level. Kohler claims more complex models give correct answers. It does not work that way. One must get the physics inside each level correct independently before hooking levels together with flows.

Like software development, one must get the functions and procedures correct independently. Then one can connect the parts of the program by flows of data.

4.2 Physics model consequences

The accurate fit of the physics model to the data supports the theory in Eq. (A.2). Therefore, the deductions of the physics theory are to be trusted over the claims of the IPCC theory. Here are some deductions of the physics theory.

Eq. (A.4) shows the balance level equals the product of the inflow and the residence time. Using IPCC numbers, the balance levels of human and natural CO2 are,

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)

Lbh / (Lbn + Lbh ) = 4.6 / 102.6 = 18.4 / 410 = 4.5 percent                                            (4)

These results are indicated in Fig. 1.

Equation (1) shows present human emissions create a balance level of 18 ppm. This balance level for human emissions is independent of nature’s balance level. If nature’s balance level remained at 280 ppm as the IPCC claims it was in 1750, then the present human emissions would have increased the level of CO2 in the atmosphere by 18 ppm, for a total of 298 ppm.

Equation (2) shows present natural emissions create a balance level of 392 ppm. The addition of 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 balance ratio of human-produced to nature-produced CO2 is 4.6 percent or the ratio of their inflows, independent of residence time. The IPCC calls the ratio in Eq. (3) the “airborne fraction.”

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

Equations (1) and (2) support Harde (2017a) 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).”

The clear conclusion is human CO2 emissions have a negligible effect on the level of atmospheric CO2.

While the details are outside the scope of this paper, Appendix C (Harde, 2017a) shows how temperature can increase the balance level to account for the rise in atmospheric CO2 since 1750.

Discussion

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

4.3 Physics model significance

The physics model is simple. The continuity equation, Eq. (A.1), is a given. The only theory is Eq. (A.2) that outflow equals level divided by residence time.

Occam’s Razor says the simplest theory that explains a process is the preferred theory. Equation (A.2) is the simplest possible theory for atmospheric CO2.

The physics model shows the inflow of CO2 into the atmosphere sets a balance level for CO2 in the atmosphere. The level moves to the balance level until outflow equals inflow. Then, if inflow remains constant, the level will remain constant. Continued, constant human emissions do not add more CO2 to the atmosphere.

The physics model shows if human CO2 is 4.5 percent and natural CO2 is 96.5 percent of the inflow of CO2 into the atmosphere, then human CO2 will be 4.5 percent and natural CO2 will be 96.5 percent of the total CO2 in the atmosphere. Indeed, this result is common sense.

The physics model shows we must think in a new paradigm about how CO2 flows into and out of our atmosphere. The atmosphere is not a garbage dump for CO2. CO2 does not “accumulate” in the atmosphere.

Nothing outside the atmosphere changes the physics model’s conclusions. But the conclusions of the physics model change entirely the dominant worldview of how human emissions change the level of CO2 in our atmosphere.

5. The IPCC Model

5.1 IPCC theory contradicts nature

IPCC (2001a) argues its Bern model applies only to human CO2. However, CO2 molecules from human and natural sources are identical. Therefore, all valid models must treat human and natural CO2 the same.

IPCC’s Bern Eq. (B.1) predicts 15 percent all CO2 entering the atmosphere stays in the atmosphere forever and about 40 percent stays in the atmosphere for almost 1000 years.

Bern Eq. (B.1) applied to natural CO2 predicts 100 ppm per year for 100 years will leave 1500 ppm in the atmosphere forever. This clearly invalid prediction proves the Bern model and IPCC’s theory are wrong.

The 14C data show CO2 has a constant residence time and no CO2 stays in the atmosphere.

The Bern model is wrong because

  1. it cannot simulate the 14C data,
  2. its predictions for human and natural CO2 are wrong,
  3. it predicts a different future if it is restarted at any point on its curve, and
  4. it treats human and natural CO2 differently.

Discussion

Siegenthaler and Joos (1992) created the original Bern model. The original model contained levels for the deep and interior oceans that connected to the upper ocean, as can be seen in their Fig. 1.

IPCC reconnected the original model’s deep and interior ocean levels directly to the atmosphere level, bypassing the upper ocean level. That is why the Bern model has three residence times for the atmosphere level rather than one. Connecting flows to the wrong levels violates the principles of systems (Forrester, 1968) and will give the wrong answer.

The Bern model forces the three residence times to act in series rather than in parallel. The series connection lets a long residence-time outflow restrict a small residence-time outflow, like a small hole in a bucket restricting the flow out of a large hole. It won’t happen. Only a parallel connection would properly represent the three residence times.

Siegenthaler and Joos (1992) understood their model should reproduce the carbon-14 data and were disappointed that it did not do so.

5.2 IPCC buffer theory is wrong

IPCC theory says human CO2 emissions, but not natural emissions, reduce the “buffer capacity” of the carbonate system.

There are three things wrong with this IPCC claim:

  1. It requires nature to separate human CO2 from natural CO2, which is impossible.
  2. It assumes nature’s inflow does not increase and reduce buffer capacity.
  3. The 14C data show there has been no reduction in buffer capacity.

Discussion

IPCC’s theory is based upon its assumption that natural CO2 inflow remained constant after 1750 while human CO2 inflow caused all the CO2 increase after 1750.

IPCC (2001a) claims,

“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.”

Kohler et al. (2017) 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 illogical method used by Kohler and the IPCC. They use circular reasoning to claim a model proves what has been fed into the model.

Regarding the Revelle factor being “measurable,” the 14C data show no evidence of its effect. Reduced buffer capacity would restrict the outflow of CO2 and increase the CO2 level, which would increase the residence time. But the 14C data, shown in Figs. 2 and 3, prove the residence time has been constant while CO2 increased from 1970 to 2014.

The Bern model predicts an increase in residence time because it incorrectly assumes that human CO2 has reduced the buffer capacity. In science, data takes precedence over theory.

Ecologist Patrick Moore (2017) claims human CO2 has converted locked carbon into free carbon and upset nature’s balance. Therefore, he argues, human CO2 has caused all the increase in atmospheric CO2 above 280 ppm. He produces no numbers to support his claim.

Moore’s argument is basically the same as made by the IPCC. If Moore’s claim, that human CO2 caused all the CO2 increase, were correct, then human burning of fossil fuels would have reduced the buffer capacity of the carbonate system. It has not. Therefore, the amount of carbon released is too small to have caused CO2 to increase.

The 14C data prove there has been no decrease in buffer capacity. Therefore, IPCC theory and Patrick Moore are wrong.

5.3 14C-CO2 follow 12C-CO2

The 12C-CO2 molecules participate in the same chemical reactions as 14C-CO2 except 12C-CO2 reacts faster because it is lighter than 14C-CO2.

RealClimate (2004a) agrees:

“All isotopes of an element behave in a similar way chemically. However, because the mass of each isotope is slightly different there are certain physical processes that will discriminate (or ‘fractionate’) between them.”

However, Kohler et al. (2017) claim 14C-CO2 does not trace 12C-CO2 because 12C-CO2 is restrained by decreased the ocean’s buffer capacity while 14C-CO2 is not.

Kohler’s claim is wrong. First, there is no physical or chemical mechanism to explain Kohler’s claim. If buffer capacity decreased and slowed the flow of 12C-CO2 into the oceans, it would also slow the flow of 14C-CO2 into the oceans. Second, there is no evidence of decreased buffer capacity.

Therefore, 14C-CO2 traces how 12C-CO2 flows out of the atmosphere.

5.4 IPCC core argument is illogical

IPCC (2001a) 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.

But “abundant published literature” is irrelevant in science because votes don’t count. Claims of “extensive evidence” are irrelevant because the scientific method says if a theory makes only one false prediction the theory is wrong. And the IPCC theory makes many false predictions that prove its “abundant published literature” claims are wrong.

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

The IPCC argument omits natural CO2 which totaled about 26,000 ppm in the same period. So, the stronger logical counter-argument is that nature caused all the increase.

The IPCC also correctly notes nature is a “net absorber” because it absorbs the outflow of human CO2 emissions. But the IPCC incorrectly argues that this proves human CO2 caused all the increase.

Nature’s absorption of human CO2 outflow cannot constrain nature’s CO2 inflow. Inflow and outflow are two different physical processes. The natural inflow of 98 ppm per year shown in Fig. 1 can be any number, larger or smaller, and nature will still absorb the outflow of human CO2. The IPCC invents constraints where none exist.

6.    Conclusions

The physics model accurately simulates the fall of 14C from 1970 to 2014. The physics model accurately predicts the 14C data using a constant residence time of 16.5 years. This is the upper bound for the residence time of 12C-CO2.

The IPCC model cannot simulate the 14C data because it uses an unrealistic model that assumes the residence time increases with the level of CO2. IPCC claims human CO2 reduced the buffer capacity of the carbonate system. But the 14C data shows there has been no reduction in buffer capacity.

The IPCC assumes there is an “adjustment time” that measures the outflow of CO2 from the atmosphere. This IPCC assumption contradicts the 14C data which clearly show the IPCC “adjustment time” is the same as the residence time.

The physics model accurately predicts how human CO2 lowers the balance level of 14C and 13C in the atmosphere. The IPCC model way overpredicts how human CO2 lowers the balance level of 14C and 13C.

The physics model treats human and natural CO2 the same. The IPCC model treats human and natural CO2 differently, so IPCC theory is fundamentally wrong.

The physics model represents reality. The IPCC model represents the imagination of the IPCC.

The physics model makes only one assumption: outflow is proportional to level. It shows the ratio of human to natural CO2 in the atmosphere equals the ratio of their inflows, independent of residence time. It predicts human CO2 adds only 18 ppm to the atmosphere while natural CO2 adds 392 ppm.

The physics model shows CO2 inflow sets a balance level for CO2 in the atmosphere. The level moves to its balance level until outflow equals inflow. Then, if inflow remains constant, the level will remain constant. Continued, constant human emissions do not add more CO2 to the atmosphere.

Appendix A: Physics model math

We use the system definition of Section 4.1 to derive the physics model. We begin with the continuity equation:

dL/dt = InflowOutflow                                                                                             (A.1)

Where

L = CO2 level

dL/dt = the rate of change of L

t = time

Inflow = the rate CO2 moves into the system

Outflow = the rate CO2 moves out of the system

Assume outflow is proportional to level,

Outflow = L / Te                                                                                                        (A.2)

where Te is the 1/e residence time.

Substitute Eq. (A,2) into the continuity Eq. (A.1),

dL/dt = InflowL / Te                                                                                          (A.3)

To find an equation for Inflow, let the level equal its balance level, Lb. Then the level is constant and Eq. (A.3) becomes

Lb = Inflow * Te                                                                                                       (A.4)

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

dL/dt = – (LLb) / Te                                                                                          (A.5)

Equation (A.5) shows how level always moves toward its balance level. If inflow is zero, Lb is zero, and outflow will continue until the level goes to zero. Rearrange Eq. (A.5) to get

dL / (LLb) = – dt / Te                                                                                       (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,

Ln [(LLb) / (LoLb)] = – t / Te                                                                    (A.7)

where

Ln = natural logarithm or logarithm to base e

Lo = Level at time zero (t = 0)

Lb = the balance level for a given inflow and Te

Te = “residence time” for L to move (1 – 1/e) of the distance to Lb

e = 2.7183

(The original integration of Eq. (A.6) contains two absolute functions, 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 Eq. (A.7), to get the level as a function of time:

L(t) = Lb + (LoLb) exp(- t / Te)                                                                     (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 [ A0 + A1 exp(- t/T1) + A2 exp(- t/T2) + A3 exp(- t/T3)]              (B.1)

Where

t = time in years

Lo = 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,

A0 = 0.152

A1 = 0.253

A2 = 0.279

A3 = 0.319

T1 = 173 years

T2 = 18.5 years

T3 = 1.19 years

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

A0 + A1 + A2 + A3 = 1.000

Set t equal to infinity. Then Eq. (B.1) becomes,

L = Ao Lo = 0.152 Lo                                                                                      (B.2)

Equation (B.2) predicts a one-year inflow that sets Lo 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.

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).

Fig. C1. Curve fit to data from Harde (2017) Eq. (17). CO2 balance level increases with surface temperature exponentially.

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.

Row14C TestNaturalHumanSumTest
114C Ratio0-100Figs. 2 & 3
2Physics Fraction0.9550.045
3Physics Result0-4.5-4.5Pass
4IPCC Fraction.68.32
5IPCC Result0-32-32Fail

 

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.

Row13C TestNaturalHumanSum100-SumTest
113C Ratio10098-0.15
2Physics Fraction0.9550.045
3Physics Result95.54.499.9-0.1Pass
4IPCC Fraction.68.32
5IPCC Result68.031.499.4-0.6Fail
.

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Acknowledgments

This 8-year research project was funded by the personal funds of Edwin and Valerie Berry.

The author thanks Chuck Wiese, Laurence Gould, Tom Sheahen, and Charles Camenzuli, who provided scientific critique, and Daniel Nebert, Gordon Danielson, and Valerie Berry, who provided language and grammar improvements.

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28 thoughts on “PREPRINT: Contradictions to IPCC’s Climate Change Theory”

  1. Excellent! 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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  3. Excellent 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.

  4. Congratulations 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!

  5. You 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.

    1. Colin,

      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.

      1. Dear 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.

  6. The 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?

    1. Dear 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.

      1. Thanks.
        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.

    2. Colin
      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.

        1. Dr. 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…

    1. Dear 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.

      1. Thanks. 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”.

      1. Dear 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.

  7. Physics 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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  9. Dr. 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 level

    That 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 atmosphere as your graph suggests, because about 20%/year of all CO2 in the atmosphere is exchanged with 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 time

    Which 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 / throughput
    If 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

    1. Dear 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.

      1. Dear Dr. Ed,

        To start with:
        the CO2 consumed by plants depends upon the level of CO2 in the atmosphere

        Yes, 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.

        1. Dear 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.

        2. Dear 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 – Outflow

          Agreed. 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 rate for any disturbance to any process in dynamic equilibrium. That is not an exchange 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 irrelevant

          Both 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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