Human CO2 has small effect on atmospheric CO2
American Meteorological Society 99th Annual Meeting, January 8, 2019, AMS website
(On January 22, I sent this preprint to my first-choice journal. Copyright does not allow republishing of journal submissions.)
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
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 has significant theoretical consequences.
Human and natural CO2 inflows set independent balance levels in proportion to their inflows. The total balance level is the sum of the human and natural balance levels. The level moves to its total 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 accumulates 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 atmosphere. Natural CO2 adds 392 ppm.
The United Nations Intergovernmental Panel on Climate Change (IPCC) model cannot reproduce the decay of 14CO2 after 1970. Therefore, the IPCC model is wrong. The IPCC assumes human CO2 reduced the buffer capacity of the carbonate system. However, the 14C data combined with the physics model show e-time is constant. Therefore, the buffer capacity has not changed.
The United Nations Intergovernmental Panel on Climate Change (IPCC, 2001a, b, c) 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, 2018) 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 “observational evidence.” IPCC and USGCRP are wrong.
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 (1990) bases all its climate conclusions on this 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 19th 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 (1998), Jaworowski (2004), and Salby (2014) present evidence that the CO2 level before 1750 was much higher than 280 ppm. Therefore, IPCC’s first claim is an assumption, not fact. Nevertheless, this paper allows IPCC’s first claim because it makes no difference to this paper’s proof that the IPCC argument fails. IPCC continues:
“Second, the observed rate of CO2 increase closely parallels the accumulated emission trends from fossil fuel combustion and from land use changes.”
Section 4.5 shows (a) correlation does not mean causation, (b) time-series correlations must be detrended, and (c) the detrended correlation is zero, which proves there is no cause-effect relationship between human CO2 and the increase in atmospheric CO2. IPCC continues:
“Third, the observed isotropic trends of 13C and 14C agree qualitatively with those expected due to the CO2 emissions form fossil fuels and the biosphere, and they are quantitatively consistent with results from carbon cycle modeling.”
Sections 2.4 and 2.5 show how the observed isotropic trends of 13C and 14C support the physics model and reject the IPCC model.
In summary, this paper shows all IPCC arguments fail physics and logic, so the IPCC claim of “in fact” is invalid.
For simplicity, this paper uses levels in units of ppm, and flows 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
Boden et al. (2017) show human CO2 emissions in 2014 were 4.6 ppm per year. IPCC (2001) says nature’s CO2 emissions are 98 ppm per year. Both the physics and IPCC models use these data.
Fig. 1 illustrates the disagreement between the physics and IPCC models.
Authors who support the IPCC conclusion include Cawley (2011), Kern and Leuenberger (2013), Richardson (2013), Means (2014), and Kohler et al. (2017).
2. Theories must replicate 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 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 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.
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, 14CO2 were well mixed between the hemispheres, and the 14C data from both sources are virtually identical after 1970.
Fig. 2 shows the global average data for D14C (Hua et al., 2013).
2.2 Physics model replicates 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 e-time, Te.
Figs. 2 and 3 show the physics model Eq. (A.8) accurately replicates the 14CO2 data from 1970 to 2014 with “e-time” set to 16.5 years, balance level Lb set to zero, and starting level Lo set to the measured D14C level in mid-1970.
2.3 IPCC’s model cannot replicate the 14C data
Fig. 4 uses Eq. (A.8) of the physics model with e-time equal to 16.5 years to replicate the 14CO2 data and an e-time of 4 years to calculate the outflow curve for 12CO2. All model calculations begin with the initial level set to 100 and the balance level set to zero.
Section 4 and Appendix B describe the IPCC theory and model. Fig. 4 uses Eq. (B.1) to calculate the Bern model predictions.
The 12CO2 decay as calculated by the Bern model begins faster than the physics model for 12CO2, then decreases because its e-time increases. The Bern decay crosses the 14C line which is the upper bound for 12CO2 e-time. Therefore, the Bern calculation conflicts with the 14C data. Section 4.4 explains why the Bern model fails.
The Bern model, if restarted at any point, cannot replicate its original Bern prediction. A valid model must continue its same prediction line if it is restarted at any point on its line. The Bern model is unphysical.
2.4 The 14C data support the physics model
Human fossil-fuel CO2 is “14C-free.” So, human CO2 emissions lower the 14C balance level. IPCC (1990) and Kohler et al. (2017) claim this proves human CO2 caused all the rise in atmospheric CO2. The numbers show otherwise.
Fig. 1 shows the relative atmospheric composition predicted by the models. The physics model predicts natural CO2 is 95.5 percent and human is 4.5 percent. IPCC (2001a) says natural CO2 is 68 percent and human CO2 is 32 percent.
Appendix D shows the physics model predicts human CO2 has lowered the 14C balance level from zero to -4.5. Appendix D shows the IPCC model predicts human CO2 has lowered the 14C balance level from zero to -32.
Fig. 5 shows the physics model replicates the 14C data when the balance level is -4.5.
Fig. 6 shows the IPCC prediction does not fit the data when the balance level is set to -32.
Therefore, the 14C data support the physics model and reject the IPCC model.
Pettersson (2014b) 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 et al. (2010) used absolute values of 14C and still concluded the “ocean-atmosphere disequilibrium today is close to pre-industrial times.”
Also, the 14C data show its e-time and balance level have been constant since 1970. So any change is unobservable.
2.5 The 13C data support the physics model
RealClimate (2004b) 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 this proves human CO2 caused all the increase in atmospheric CO2 since 1850. The numbers show otherwise.
Fig. 1 shows the relative atmospheric composition of the two models. Appendix E shows the physics model predicts human emissions have lowered the 13C ratio by 0.09, and the IPCC model predicts human emissions have lowered the 13C ratio by 0.64.
Fig. 7 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.
2.6 The isotope 14CO2 follows 12CO2
Levin et al. (2010) conclude 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 (2004a) agrees:
“All isotopes of an element behave in a similar way chemically.”
Kohler et al. (2017) claim 14CO2 does not trace 12CO2 because 12CO2 is restrained by the decreased the ocean’s buffer capacity while 14CO2 is not.
There is no basis for Kohler’s claim that 14CO2 would be exempt from the effects of buffer capacity. Further, Section 4.3 shows buffer capacity has not decreased. So, Kohler’s claim is invalid.
Means (2014) claims the 14C data do not represent how 12CO2 flows out of the atmosphere:
“The CO2 [inflow] is depleted in 14C [compared to the outflow]and this gives an artificial false picture of rapid CO2 sequestration rates.”
Means has not used a proper model or calculated any numbers to prove his point. If Means’ claim were true, then the inflow would have changed the balance level of 14C. But the 14C data show no measurable change in the balance level of 14C.
3. The physics model
3.1 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 physics system for atmospheric CO2. The system includes the level (concentration) of CO2 in the atmosphere and the inflow and outflow of CO2. The system’s inflow and outflow include all the effects of outside processes. Therefore, the physics model is complete.
Appendix A shows the mathematical derivation of the physics model. It begins with the continuity equation, Eq. (A.1). Then Eq. (A2) adds one hypothesis: Outflow equals Level divided by e-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, Eq. (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 above the dam. The lake level changes until the level equals its balance level, where outflow equals inflow.
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. The level changes until the level equals its balance level, where outflow equals inflow.
The physics model applies to all definitions of CO2. For example, the physics model applies to 14CO2 and 12CO2 and their sums, and to human CO2 and natural CO2 and their sums. The mathematics used to describe the physics model are analogous to the mathematics used to describe many engineering systems.
Kohler et al. (2017) commented on Harde (2017a),
“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.”
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.” 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. So long as a level includes inflow and outflow, a system is complete.
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.
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 accuracy. And Kohler’s complexity produces invalid physics.
3.2 Physics model consequences
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 ratio of human- to nature-produced CO2 in the atmosphere equals the ratio of their inflows, independent of e-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 e-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).”
While the details are outside the scope of this paper, Appendix C, from Harde (2017a), shows how temperature can increase the balance level to account for the rise in atmospheric CO2 since 1750. Salby (2014) and Pettersson (2014a) show how the CO2 level is a consequence of temperature.
Kohler et al. rely on Cawley (2011) in their attempt to prove the IPCC is correct and Harde (2017a) is wrong. But Cawley fails. Therefore, Kohler fails.
Cawley attempts to prove that human CO2 caused all the increase of atmospheric CO2 above the IPCC-claimed 280 ppm in 1750. Cawley’s Eq. (3) intends to do the same job as Eq. (A.2), namely, to represent how level sets outflow. But Cawley adds to his Eq. (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 Eq. (3) is the true source of all outflow.
Cawley added outflow twice. First as a level-driven outflow. Second, as a fictitious steady-state outflow that does not exist independent of the level-driven outflow. As a result, Cawley’s Eqs. (3), (4), (5), and his equation after (5) are wrong, and all his conclusions are wrong.
Cawley’s Eq. (7) should include his Fa for human inflow. Cawley’s Eqs. (7) and (8) should omit his arbitrary Fe for outflow and set outflow equal to level (his C) divided by his residence time. Section 4.1 shows Cawley’s residence time is also inaccurate.
Cawley argues the ratio of human to natural CO2 in the atmosphere is a function of residence-time, which is incorrect. The physics model, Eq. (3) above, and common sense show the ratio is independent of e-time. Cawley equations cannot replicate the 14C data.
Since Cawley fails physics, Kohler also fails physics. Cawley’s failure shows how the IPCC attempts to derive a theory by pasting together observations without addressing the underlying physics.
4. The IPCC Model
4.1 IPCC’s time constants
The only hypothesis in the physics model is “outflow equals level divided by Te” as shown in Eq. (A2). The derivation of the physics model shows Te is the time for the level L to move (1 – 1/e) of the distance from L to its balance level, Lb. E-time is not a function of inflow.
IPCC’s time definitions do not properly model how CO2 flows through the atmosphere. IPCC’s residence, adjustment, and turnover times have inaccurate definitions.
IPCC (2001b) 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, or can be, the negative difference between inflow and outflow.
IPCC (2001b) defines “adjustment time (Ta)” as:
“The time-scale characterising the decay of an instantaneous pulse input into the reservoir.”
Cawley (2011) 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” shows the definition is imprecise. IPCC’s fuzzy definition of adjustment time is necessary to allow for its fuzzy definition of residence time.
Cawley (2011) follows the IPCC 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.”
The IPCC and its supporters think incorrectly that they need 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), the 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, the IPCC thinks e-time is a residence time because “molecules” are flowing in and out with little change in level.
IPCC requires a decay to originate from a pulse. This is unphysical because a system does not know its history. IPCC includes inflow in its time definitions. This is unphysical because decay time depends only upon outflow and level.
Fig. 9 illustrates the physics e-time and the IPCC adjustment and residence times.
IPCC (2001b) 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.
The IPCC 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 CO2 in the atmosphere, the actual adjustment is faster initially and slower later on.”
IPCC agrees 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,” which describes why its Bern model cannot replicate the 14C data in Fig. 4.
The 14C data (Figs. 2 and 3) show the e-time for 14CO2 is 16.5 years, not hundreds of years. The 14CO2 level approached its balance level exactly as the physics theory predicts. The IPCC does not understand how CO2 flows out of the atmosphere. That is why the IPCC’s conclusions about how human CO2 exits the atmosphere are wrong.
Kohler et al. (2017) claim:
“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 the IPCC summaries are so perfect that no one may disagree. Kohler’s problem is the IPCC model predictions disagree with data. So, they are wrong.
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.
4.2 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.
Of course, neglecting geologic time scales, nature HAS been a “net carbon sink” since 1750 because nature absorbs human CO2 emissions. But that fact does not prevent nature from increasing its own CO2 emissions.
Inflow and outflow are two different physical processes. Nature’s absorption of human CO2 outflow does not constrain nature’s CO2 inflow. The natural inflow of 98 ppm per year shown in Fig. 1 can become larger or smaller, and nature still will absorb the outflow of both human and natural CO2 because outflow is a function of level.
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 IPCC argument requires that natural CO2 inflow remained constant, which is an unmentioned and unproven assumption. IPCC’s “abundant published literature” and “extensive evidence” conclusion is invalid because it is a direct result of its assumption that nature remained constant.
4.3 IPCC buffer theory is wrong
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.
- The 14C data show buffer capacity has not changed.
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 because:
“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 Kohler’s and IPCC’s circular logic. They claim a model proves what has been fed into the model.
Reduced buffer capacity would increase e-time. But the 14C data (Figs. 2 and 3) prove e-time has been constant since 1970. Therefore, IPCC’s and Kohler et al’s. (2017) claim is wrong.
Some scientists argue human CO2 caused all the CO2 increase because human CO2 releases carbon from long-term reservoirs. If that argument were valid, then human CO2 would have increased e-time.
4.4 IPCC theory contradicts nature
Appendix B shows IPCC’s Bern model (Bern, 2002) puts human CO2 inflow into 4 different bins, as illustrated in Fig. 10. Each bin has a different decay time. One decay time is infinity. IPCC set the Bern coefficients and decay times to make the Bern model match the output of climate models (Joos et al., 2013).
IPCC’s Bern Eq. (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. IPCC’s model does not replicate the 14C data. The IPCC Bern model and IPCC’s climate models are unphysical and wrong.
Also, IPCC (2001a) assumes its Bern model applies to human but not 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 Eq. (B.1) 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 climate models are wrong.
The IPCC Bern model is wrong because
- it cannot replicate the 14C data,
- it predicts a different future if it is restarted at any time,
- it treats human and natural CO2 differently,
- it predicts nonsense for natural CO2, and
- It puts human CO2 into 4 bins, which violates physics.
Siegenthaler and Joos (1992) 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 Fig. 1.
The IPCC reconnected the original model’s deep and interior ocean levels directly to the atmosphere, bypassing the upper ocean level. That is why the Bern model has three decay times rather than one. Connecting flows to the wrong levels violates the principles of systems (Forrester, 1968) and will give the wrong answer.
Siegenthaler and Joos (1992) understood their model should reproduce the carbon-14 data and were disappointed that it did not do so.
IPCC (2007) admits its estimates of “gross fluxes generally have uncertainties of more than ±20%.” Yet the IPCC ignores the 14C data that are far more accurate than IPCC’s estimates of CO2 inflow and outflow.
4.5 Human CO2 cause does not correlate
IPCC (2001a) claims annual human CO2 emissions cause annual increases in the level of CO2 in the atmosphere. Cawley (2011) 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 (2017) shows the “detrended correlation analysis of annual emissions and 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 not responsible for most of the increase in atmospheric CO2 since 1750. IPCC’s claim of “considerable certainty” fails statistics.
The combination of the 14C data and the simple physics model proves atmospheric CO2 flows out of the atmosphere in proportion to the level or concentration of CO2 in the atmosphere. 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. Balance level follows inflow. Level moves toward its balance level with an e-time of about 4 years. When the level equals its balance level, outflow equals inflow. Then, the level remains constant so long as inflow remains constant.
Present human CO2 inflow increases the balance level by 18 ppm and present natural CO2 inflow increases the balance level by 392 ppm, for a total of 410 ppm.
If all human CO2 emissions stopped and natural inflow stayed constant, the CO2 level would fall to 392 ppm with an e-time of about 4 years. The effect of human CO2 on atmospheric CO2 is insignificant. Human CO2 does not change climate.
The IPCC model is wrong because it cannot replicate the 14C data, it uses multiple, unphysical response times, its core arguments fail logic, it makes assumptions that contradict data, and it treats human CO2 differently than it treats natural CO2. It is pseudoscience.
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)
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 “e-time.”
Substitute Eq. (A,2) into the continuity Eq. (A.1),
dL/dt = Inflow – L / 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 = – (L – Lb) / 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.
When Lb and Te are constant, there is an analytic solution to Eq. (A.5). Rearrange Eq. (A.5) to get
dL / (L – Lb) = – 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 [(L – Lb) / (Lo – Lb)] = – t / Te (A.7)
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 = 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 + (Lo – Lb) 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)
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. 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.
|1||14C Ratio||0||-100||Figs. 2 & 3|
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.
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