International Journal of Atmospheric and Oceanic Sciences
2019; 3(1): 13-26
ISSN: 2640-1142 (Print); ISSN: 2640-1150 (Online)
Human CO2 Emissions Have Little Effect on Atmospheric
Edwin X Berry
Climate Physics LLC, Bigfork, USA
To cite this article:
Edwin X Berry. Human CO2 Emissions Have Little Effect on Atmospheric CO2. International Journal of Atmospheric and Oceanic Sciences.
Vol. 3, No. 1, 2019, pp. 13-26. doi: 10.11648/j.ijaos.20190301.13
Received: May 13, 2019; Accepted: June 12, 2019; Published: June 4, 2019
Abstract: The United Nations Intergovernmental Panel on Climate Change (IPCC) agrees human CO2 is only 5 percent and
natural CO2 is 95 percent of the CO2 inflow into the atmosphere. The ratio of human to natural CO2 in the atmosphere must equal
the ratio of the inflows. Yet IPCC claims human CO2 has caused all the rise in atmospheric CO2 above 280 ppm, which is now
130 ppm or 32 percent of today’s atmospheric CO2. To cause the human 5 percent to become 32 percent in the atmosphere, the
IPCC model treats human and natural CO2 differently, which is impossible because the molecules are identical. IPCC’s Bern
model artificially traps human CO2 in the atmosphere while it lets natural CO2 flow freely out of the atmosphere. By contrast, a
simple Physics Model treats all CO2 molecules the same, as it should, and shows how CO2 flows through the atmosphere and
produces a balance level where outflow equals inflow. Thereafter, if inflow is constant, level remains constant. The Physics
Model has only one hypothesis, that outflow is proportional to level. The Physics Model exactly replicates the 14C data from
1970 to 2014 with only two physical parameters: balance level and e-time. The 14C data trace how CO2 flows out of the
atmosphere. The Physics Model shows the 14 CO2 e-time is a constant 16.5 years. Other data show e-time for 12CO2 is about 4 to
5 years. IPCC claims human CO2 reduces ocean buffer capacity. But that would increase e-time. The constant e-time proves
IPCC’s claim is false. IPCC argues that the human-caused reduction of 14C and 13C in the atmosphere prove human CO2 causes
all the increase in atmospheric CO2. However, numbers show these isotope data support the Physics Model and reject the IPCC
model. The Physics Model shows how inflows of human and natural CO2 into the atmosphere set balance levels proportional to
their inflows. Each balance level remains constant if its inflow remains constant. Continued constant CO2 emissions do not add
more CO2 to the atmosphere. No CO2 accumulates in the atmosphere. Present human CO2 inflow produces a balance level of
about 18 ppm. Present natural CO2 inflow produces a balance level of about 392 ppm. Human CO2 is insignificant to the increase
of CO2 in the atmosphere. Increased natural CO2 inflow has increased the level of CO2 in the atmosphere.
Keywords: Carbon Dioxide, CO2, Climate Change, Anthropogenic
The U.S. Global Change Research Program Climate
Science Special Report (USGCRP)  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 United Nations Intergovernmental Panel on Climate
Change (IPCC)  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 and USGCRP claim there are “no convincing
alternative explanations” other than their theory to explain the
This paper presents a “convincing alternative explanation”
that explains the data. A simple physics model explains the
required first step of human-caused climate change: how
human CO2 changes atmospheric CO2.
For simplicity, this paper uses levels in units of ppm (parts
per million by volume in dry air) and flows in units of ppm per
year. GtC (Gigatons of Carbon) units are converted into CO2
units in ppm using:
Authors who support the USGCRP  and IPCC [2, 3]
14 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
include Archer et al. , Cawley , Kern and Leuenberger
, and Kohler .
Authors who conclude human CO2 increases atmospheric
CO2 as a percentage of its inflow include Revelle and Suess
, Starr , Segalstad , Jaworoski [11, 12], Beck ,
Rorsch, Courtney, and Thoenes , Courtney , Quirk
, Essenhigh , Glassman , Salby [19-22], Humlum
, Harde [24, 25], and Berry [26, 27].
2. The Science Problem
IPCC [2, 3] says nature emits about 120 GtC from land and
90 GtC from ocean for a total of 210 GtC per year. This is
equivalent to about 98 ppm per year of natural CO2 that flows
into the atmosphere. IPCC admits its estimates of “gross
fluxes generally have uncertainties of more than ±20%.”
Boden  shows human CO2 emissions in 2014 were 9.7
GTC per year, or 4.6 ppm per year. So, IPCC agrees that
human inflow is less than 5% and nature is more than 95%
of the total CO2 inflow into the atmosphere. Yet IPCC
assumes nature stayed constant since 1750 and human CO2
causes 100 percent the increase in atmospheric CO2 above
280 ppm, which today is 130 ppm or 32 percent of 410 ppm.
The Physics Model concludes the percent of human CO2 in
the atmosphere equals the percent of human CO2 in the inflow.
Figure 1 shows how the predictions of the Physics Model
and IPCC model differ regarding the composition of human
CO2 in the atmosphere.
Figure 1. The IPCC agrees the inflow of human CO2 is less than 5 percent.
The Physics Model says the percent of human CO2 in the atmosphere equals
the percent of its inflow. IPCC claims human CO2 adds all atmospheric CO2
above 280 ppm, which is now 32 percent of the total.
If the IPCC model is correct, then the effect of human CO2
emissions on atmospheric CO2 is 100 percent. If the Physics
Model is correct, then human CO2 emissions do not cause
3. The Physics Model
3.1. How CO2 Flows Through the Atmosphere
IPCC states, and much of the public believes, human
emissions “add” CO2 to the atmosphere. IPCC’s view is the
atmosphere is a garbage dump where human CO2 is deposited
and mostly stays forever.
However, nature must treat human and natural CO2 the
same because their molecules are identical. Nature has had
millions of years to “add” to atmospheric CO2. If nature’s CO2
“adds” to atmospheric CO2, the CO2 in the atmosphere would
be much higher than it is today.
Therefore, natural and human CO2 do not “add” CO2 to the
atmosphere. Both natural and human CO2 “flow through” the
atmosphere. As CO2 flows through the atmosphere, it raises
the level of atmospheric CO2 just enough so CO2 outflow
equals CO2 inflow. Nature balances CO2 in the atmosphere
when outflow equals inflow.
You pump air into a tire or inner tube that has a leak. As
you pump air into the tube, air leaks out of the tube. The
faster you pump air in, the faster air leaks out. If you pump air
into the tube at a constant rate, the air pressure in the tube will
find a level where outflow equals inflow.
River water flows into a lake or a pond and flows out over a
dam. If inflow increases, the water level increases until
outflow over the dam equals inflow from the river. Then, the
water level will remain constant so long as inflow remains
constant. The river does not “add” water to the lake. Water
“flows through” the lake and finds a balance level where
outflow equals inflow.
Similarly, human and natural CO2 flow through the
atmosphere. The inflow creates a balance level that remains
constant so long as inflow remains constant.
3.2. Physics Model System Description
Figure 2 shows a bucket of water as an analogy to CO2 in
the atmosphere. Water flows into the bucket at the top and
flows out through a hole in the bottom. An outside source
(faucet) controls the inflow.
The water level and the hole size control the outflow. No
matter what the inflow, the level and the size of the hole
control the outflow. Inflow only serves to set a balance level.
This paper uses e-time rather than “residence” time because
there are many definitions of residence time. E-time has a
precise definition: the time for the level to move (1 – 1/e) of
the distance from its present level to its balance level. The
balance level is defined below.
Figure 2. A bucket of water is an analogy to the Physics Model for
atmospheric CO2. Water flows through the bucket as CO2 flows through the
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 15
The bucket analogy provides insight into e-time. If the hole
in the bucket gets smaller, e-time increases. If the hole in the
bucket gets larger, e-time decreases. The hole is an analogy to
the ability of the oceans and land to absorb CO2 from the
Figure 3 shows the Physics Model system for atmospheric
CO2. The system includes the level (concentration) of CO2 in
the atmosphere and the inflow and outflow of CO2.
Figure 3. The Physics Model system for atmospheric CO2. Inflow and
Outflow determine the change in level. The only hypothesis is Outflow = Level
The Physics Model applies independently and in total to all
definitions of CO2, e.g., to human CO2, natural CO2, and their
sums, and to 12CO2, 13CO2, and 14CO2, and their sums.
The Physics Model is complete. It is not necessary to add
separate inflows for human and natural CO2 to the Physics
Model. Just use a copy of the Physics Model for each CO2
The Physics Model does not need to describe the details of
the external processes. Inflow, outflow, and e-time include all
the effects of outside processes. If the Physics Model were
connected to land and ocean reservoirs, it would behave
exactly as derived in this paper.
Kohler  claims Harde’s  model and therefore the
Physics Model is “too simplistic” and “leads to flawed results
for anthropogenic carbon in the atmosphere.”
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. The Physics Model shows how inflow,
outflow, and e-time affect the level of CO2 in the atmosphere.
The IPCC model cannot do this.
3.3. Physics Model Derivation
A system describes a subset of nature. A system includes
levels and flows between levels. Levels set flows and flows set
new levels. The mathematics used in the Physics Model are
analogous to the mathematics used to describe many
The Physics Model derivation begins with the continuity
equation (1) which says the rate of change of level is the
difference between inflow and outflow:
dL/dt = Inflow – Outflow (1)
L = CO2 level (concentration in ppm)
t = time (years)
dL/dt = rate of change of L (ppm/year)
Inflow = rate CO2 moves into the system (ppm/year)
Outflow = rate CO2 moves out of the system (ppm/year)
Following the idea from the bucket of water, the Physics
Model has only one hypothesis, that outflow is proportional to
Outflow = L / Te (2)
where Te is the “e-folding time” or simply “e-time.”
Substitute (2) into (1) to get,
dL/dt = Inflow – L / Te (3)
One way to replace Inflow in (3) is to set dL/dt to zero,
which means the level is constant. Then Inflow will equal a
balance level, Lb, divided by e-time. However, a more elegant
way to replace Inflow is to simply define the balance level, Lb,
Lb = Inflow * Te (4)
Equation (4) shows how Inflow and Te set the balance level.
Substitute (4) for Inflow into (3) to get,
dL/dt = – (L – Lb) / Te (5)
Equation (5) shows the level always moves toward its
balance level. At this point, both L and Lb are functions of
time. Te can also be a function of time.
In the special case when Lb and Te are constant, there is an
analytic solution to (5). Rearrange (5) to get
dL / (L – Lb) = – dt / Te (6)
Then integrate (6) from Lo to L on the left side, and from 0
to t on the right side  to get
Ln [(L – Lb) / (Lo – Lb)] = – t / Te (7)
Lo = Level at time zero (t = 0)
Lb = the balance level for a given inflow and Te
Te = time for L to move (1 – 1/e) from L to Lb
e = 2.7183
The original integration of (6) contains two absolute values,
but they cancel each other because both L and Lo are always
either above or below Lb.
Raise e to the power of each side of (7), to get the level as a
function of time:
L(t) = Lb + (Lo – Lb) exp(– t/Te) (8)
Equation (8) is the analytic solution of (5) when Lb and Te
The hypothesis (2) that outflow is proportional to level
creates a “balance level.” Equation (4) defines the balance
level in terms of inflow and e-time.
Figure 4 shows how the level always moves toward its
16 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
balance level according to (5). While outflow is always
proportional to level, inflow sets the balance level.
Figure 4. Inflow sets the balance level. The level at any time t determines the
outflow. Level always moves toward the balance level, whether the level is
above or below the balance level.
The Physics Model shows how CO2 flows through the
atmosphere. CO2 does not “stick” in the atmosphere. A higher
inflow merely raises the balance level. Then the level will rise
until outflow equals inflow, which will be at the balance level.
3.4. Physics Model Consequences
All equations after (2) are deductions from hypothesis (2)
and the continuity equation (1).
Equation (4) shows the balance level equals the product of
inflow and e-time. Using IPCC numbers, and subscripts “p” to
mean human (or people) and “n” to mean natural, the balance
levels of human and natural CO2 are 18.4 and 392 ppm:
Lbp = 4.6 (ppm/year) * 4 (years) = 18.4 ppm (9)
Lbn = 98 (ppm/year) * 4 (years) = 392 ppm (10)
The ratio of human to natural CO2 is 4.6%. The percentage
of human CO2 to total CO2 is 4.5%. Both are independent of
Lbp / Lbn = 4.6 / 98 = 4.6% (11)
Lbp / (Lbn + Lbp) = 4.6 / 102.6 = 4.5% (12)
Equation (9) shows present human emissions create a
balance level of 18 ppm, independent of nature’s balance level.
If nature’s balance level remained at 280 ppm after 1750, then
present human emissions would have increased the CO2 level
18 ppm from 280 ppm to 298 ppm.
Equation (10) shows present natural emissions create a
balance level of 392 ppm. The human contribution of 18 ppm
brings the total balance level to 410 ppm, which is close to the
level in 2018.
Equation (11) shows the ratio of human to natural CO2 in
the atmosphere equals the ratio of their inflows, independent
Equation (12) shows the percentage of human-produced
CO2 in the atmosphere equals its percentage of its inflow,
independent of e-time.
Figure 5 illustrates these Physics Model conclusions when
e-time is 4 years.
Figure 5. For an e-time of 4 years, the human inflow of 4.6 ppm per year sets
a balance level of 18 ppm, and the natural inflow of 98 ppm per year sets a
balance level of 392 ppm. When the level equals the total balance level of 410
ppm, outflow will equal inflow and level will be constant.
Equations (9) and (10) support the key conclusions of
Harde [24, 25]:
Under present conditions, the natural emissions contribute
373 ppm and anthropogenic emissions 17 ppm to the total
concentration of 390 ppm (2012).
4. The IPCC Bern Model
4.1. IPCC Bern Model Origin
In 1992, Siegenthaler and Joos  created the original
Bern model. Their Figure 1 connects the atmosphere level to
the upper ocean level, and the upper ocean level to the deep
and interior ocean levels. They used 14C data to trace the flow
of 12CO2 from the atmosphere to the upper ocean and to the
deep and interior oceans. Using some physics constraints, they
attempted without success to fit three versions of their model
to available data.
Earlier, in 1987, Maier-Reimer and Hasselmann  used
an ocean circulation model connected to a one-layer
atmosphere to reproduce the main features of the CO2
distribution in the surface ocean. They applied a mathematical
curve fit to represent their conclusions. Their curve fit used a
sum of four exponentials with different amplitudes and time
constants, as in today’s Bern model.
The use of four exponentials by  seems to result from
their reconnection of both the deep and interior ocean levels
directly to the atmosphere level. Such reconnection would be a
serious modelling mistake. Other papers followed the model
developed by .
Archer et al.  found the four-exponential models “agreed
that 20–35% of the CO2 remains in the atmosphere after
equilibration with the ocean (2–20 centuries).”
Joos et al.  compared the response of such
atmosphere-ocean models to a pulse emission of human CO2.
All the models predicted a “substantial fraction” of pulse
would remain in the atmosphere and ocean for millennia.
The conclusions of [4, 30, 31, 32] must be questioned
1. Agreement among models does not prove they are
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 17
2. All models treat human and natural CO2 differently,
which violates physics.
3. All models assume human CO2 causes all the increase
in atmospheric CO2, which violates physics.
4. All models partition human CO2 inflow into four
artificial bins, which is unphysical.
5. All models lack a valid physics model for atmospheric
Segalstad  notes that the models like  do not allow
CO2 to flow out of the atmosphere in linear proportion to the
CO2 level. Rather they use a non-linear constraint on the
outflow that contradicts physics and chemistry.
Segalstad  concludes the alleged long residence time of
500 years for carbon to diffuse to the deep ocean is inaccurate
because the 1000 GtC of suspended organic carbon in the
upper 75 meters of the ocean can sink to the deep ocean in less
than one year. That gives a residence time of 5 years rather
than 500 years.
The IPCC Bern model that evolved from models like 
artificially partitions human CO2 into four separate bins. The
separate bins prevent human CO2 in one bin from moving to a
bin with a faster e-time. This is like having three holes of
different sizes in the bottom of a bucket and claiming the
smallest hole restricts the flow through the largest hole.
The IPCC Bern model is unphysical. It begins with the
assumption that human CO2 causes all the increase in
atmospheric CO2. Then it creates a model that supports this
The Bern model fails Occam’s Razor because it is
4.2. IPCC Bern Model Derivation
The Joos  Bern model is an integral equation rather than
a level equation.
It is necessary to peer inside IPCC’s Bern model. To
deconstruct the integral version of the Bern model, let inflow
occur only in the year when “t-prime” equals zero. Then the
integral disappears, and the Bern model becomes a level
The Bern level equation is,
L(t) = Lo [A0 + A1 exp(– t/T1) + A2 exp(– t/T2) +
A3 exp (– t/T3)] (13)
t = time in years
Lo = level of atmospheric CO2 in year t = 0
L(t) = level of atmospheric CO2 in year t
and the Bern TAR standard values, derived from
curve-fitting the Bern model to the output of climate models,
A0 = 0.150
A1 = 0.252
A2 = 0.279
A3 = 0.319
T1 = 173 years
T2 = 18.5 years
T3 = 1.19 years
The A-values weight the four terms on the right-hand side of
A0 + A1 + A2 + A3 = 1.000
In (13), set t equal to infinity to get,
L = A0 Lo = 0.152 Lo (14)
Equation (14) predicts a one-year inflow that sets Lo to 100
ppm, followed by zero inflow forever, will cause a permanent
level of 15 ppm.
The four terms in (13) separate human (but not natural) CO2
into 4 bins. Each bin has a different e-time. Only one bin
allows human CO2 to flow freely out of the atmosphere. Two
bins trap human CO2 for long times. One bin has no outflow
and traps human CO2 forever.
Figure 6 shows the size of the four Bern-model bins in
percent and the amount of human CO2 that remains in the
atmosphere 8 years after an artificial pulse of human CO2
enters the atmosphere.
Figure 6. The percent of human CO2 left in each Bern model bin after 8 years.
Bern (13) predicts 15 percent all human CO2 entering the
atmosphere stays in the atmosphere forever, 25 percent stays
in the atmosphere almost forever, and only 32 percent flows
freely out of the atmosphere.
4.3. How IPCC Gets 32 Percent
The burden of proof is upon the IPCC to explain how 5
percent human inflow becomes 32 percent in the atmosphere.
IPCC cannot change the inflow. Therefore, IPCC must change
the outflow. The IPCC Bern model restricts the outflow of
human CO2 while it lets natural CO2 flow freely out of the
atmosphere. The IPCC Bern model incorrectly treats human
CO2 differently than it treats natural CO2. By doing so, it
artificially increases human CO2 in the atmosphere to 32
percent and beyond.
IPCC assumes its Bern model applies to human but not to
natural CO2. That assumption is unphysical because CO2
molecules from human and natural sources are identical. All
valid models must treat human and natural CO2 the same.
If applied to natural CO2, the Bern model predicts 15
18 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
percent of natural CO2 sticks in the atmosphere. Then in 100
years, 1500 ppm of natural CO2 sticks in the atmosphere. This
clearly has not happened. Therefore, the Bern model is
For you mathematicians:
It is simple to prove the Bern model is unphysical. Take the
derivative of (13) with respect to time. It is impossible to get
rid of the exponential terms because the Bern model has more
than one time constant in its exponentials. The Bern model
dL/dt does not correspond to a physics formulation of a
By contrast, it is straightforward to take the time derivative
of the Physics Model (8) and reproduce its dL/dt form of (5).
The Physics Model began as a rate equation, as all physics
models should. The Bern model began with a curve fit to an
imaginary scenario for a level rather than as a rate equation for
a level. The Bern model does not even include a continuity
5. Theories Must Replicate Data
5.1. The 14C Data
The above-ground atomic bomb tests in the 1950s and
1960s almost doubled the concentration of 14C in the
atmosphere. The 14C atoms were in the form of CO2, called
After the cessation of the bomb tests in 1963, the
concentration of 14CO2 decreased toward its natural balance
level. The decrease occurred because the bomb-caused 14C
inflow became zero while the natural 14C inflow continued.
The 14C data are in units of D14C per mil. The lower bound
in D14C units is -1000. This value corresponds to zero 14C
inflow into the atmosphere. In D14C units, the “natural”
balance level, defined by the average measured level before
1950, is zero, 1000 up from -1000. .
Hua  processed 14C data for both hemispheres from
1954 to 2010. Turnbull  processed 14C data for
Wellington, New Zealand, from 1954 to 2014. After 1970,
14CO2 were well mixed between the hemispheres and 14CO2
in the stratosphere were in the troposphere. The 14C data from
both sources are virtually identical after 1970.
14C is an isotope of 12C. Levin et al.  conclude the C14
data provide “an invaluable tracer to gain insight into the
carbon cycle dynamics.”
5.2. Physics Model Replicates the 14C Data
The Physics Model (8) accurately replicates the 14CO2 data
from 1970 to 2014 with e-time set to 16.5 years, balance level
set to zero, and starting level set to the D14C level in 1970.
Figure 7 shows how the Physics Model replicates the 14C
Figure 7. The 14C data from Turnbull  using 721 data points. The dotted
line is the Physics Model replication of the data.
The Physics Model is not a curve fit with many parameters
like the Bern model. The Physics model allows only 2
parameters to be adjusted: balance level and e-time, and they
are both physical parameters. It is possible that the data would
not allow replication by the Physics Model.
The replication of the 14C data begins by setting the
Physics Model to the first data point in 1970. Then it is a
matter of trying different balance levels and e-times until the
model best fits the data. Although there is room for minor
differences in the fit, the best fit seems to occur when the
balance level is zero and e-time is 16.5 years.
The replication of the 14C data by the Physics Model has
significant consequences. It shows the 14C natural balance
level has remained close to zero and e-time has remained
constant since 1970. If the e-time had changed since 1970, it
would have required a variable e-time to make the Physics
Model fit the data.
5.3. 12CO2 Reacts Faster Than 14CO2
Isotopes undergo the same chemical reactions but the rates
that isotopes react can differ. Lighter isotopes form weaker
chemical bonds and react faster than heavier isotopes .
Because 12CO2 is a lighter molecule than 14CO2, it reacts
faster than 14CO2. Therefore, its e-time will be shorter than
Equation (4) shows e-time equals Level divided by Inflow.
Using IPCC numbers, e-time for 12CO2 is about 400 ppm
divided by 100 ppm per year, or 4 years. Also, IPCC  agrees
12CO2 turnover time (e-time) is about 4 years. Segalstad 
calculated 5 years for e-time.
Figure 8 shows the Physics Model (8) simulation of 12CO2
using an e-time of 4 years. For comparison, Figure 8 shows the
14C data from Hua  and the Physics Model replication of
14CO2 data with an e-time of 16.5.
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 19
Figure 8. This plot uses the 14C data from Hua  from 1970 to 2010. Hua
data is in mid-years, so the fit begins in 1970.5. The Physics Model (dotted
line) replicates the 14CO2 data with an e-time of 16.5 years. The Physics
Model simulates 12CO2 for an e-time of 4 years (dotted line) and 5 years
5.4. IPCC Model Cannot Simulate 12CO2
The Bern model claims to predict the outflow of 12CO2.
Therefore, the Bern model should come close to predicting the
outflow of 12CO2 as calculated by the Physics Model that
replicates the 14C data.
Figure 9 shows the Bern model (13) predictions. The IPCC
Bern model begins with a short e-time, then increases its
e-time. The increased e-time causes the Bern line to cross the
14C line and thus conflicts with the 14C data. The Bern model
traps 15 percent of human CO2 in the atmosphere forever.
Figure 9. The IPCC Bern model (dashed lines) is not consistent with the
12CO2 simulation or with 14CO2 data. The Bern model includes a trap for 15
percent of human CO2.
The IPCC Bern model is not just a failure to simulate data.
The Bern model is a functional failure. It’s e-time increases
significantly with time when 14C data show e-time is constant.
The only way the Bern model can increase with time is by
using its history as a reference.
Figure 10 shows how the IPCC Bern model cannot even
replicate itself when it is restarted at any point in its
Figure 10. The Bern model (dashed lines) cannot even replicate itself after a
The IPCC Bern model cannot continue its same prediction
line if it is restarted at any point. The Bern model cannot
properly restart because it depends upon its history, which
makes it an invalid model.
A restart deletes the Bern model’s history. This forces the
Bern model to create a new history. In the real world,
molecules do not remember their history. Molecules only
know their present. Therefore, the IPCC Bern model fails the
most basic test for a physical model.
Revelle and Suess  used 14C data to calculate correctly
that human CO2 would increase atmospheric CO2 by only 1.2
percent as of 1957, based for an e-time of 5 years.
5.5. IPCC’s Buffer Theory is Invalid
IPCC  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.
Buffer capacity is the ability of the oceans to absorb CO2.
Kohler et al.  claim human (but not natural) CO2 has
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
Kohler’s last sentence exhibits circular reasoning when it
claims a model can prove what has been fed into the model.
All IPCC models use the buffer factor myth instead of
Henry’s Law to conclude human CO2 causes all the rise in
atmospheric CO2 .
The problem for Kohler and IPCC is data. Where are the
data that support their claim? They have only their models.
Models are not data. Models must make predictions that
replicate data. Their models cannot replicate data.
Ballantyne et al.  found “there is no empirical evidence”
that the ability of the land and oceans to absorb atmospheric
CO2 “has started to diminish on the global scale.”
20 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
The 14C data are the most accurate way to measure changes
in the Revelle factor and “buffer capacity.” Reduced buffer
capacity, if it existed, would increase e-time. The 14C data
prove e-time has been constant since 1970. Therefore, IPCC’s
buffer capacity has been constant.
IPCC’s buffer capacity claim is absurd because it assumes
only human CO2 reduces the buffer capacity while natural
CO2 outflow does not. IPCC treats human and natural CO2
differently, which is impossible.
Kohler  claims lower buffer capacity affects only 12CO2,
not 14CO2. That claim violates chemistry and physics. Segalstad
 previously showed Kohler’s claim is impossible because
“chemical and isotropic experiments show the equilibrium
between CO2 and water is obtained within a few hours.”
The IPCC Bern model is based upon the invalid assumption
that human CO2 decreases buffer capacity.
5.6. Isotope Data Support the Physics Model
IPCC  writes:
Third, the observed isotropic trends of 13C and 14C
agree qualitatively with those expected due to the CO2
emissions from fossil fuels and the biosphere, and they are
quantitatively consistent with results from carbon cycle
Human fossil-fuel CO2 is “14C-free” and the 14C balance
level has decreased. IPCC  and Kohler  claim this proves
human CO2 caused all the rise in atmospheric CO2.
But neither IPCC nor Kohler argue with numbers. Let’s do
the calculations to compare the results from both models with
the data. IPCC  says human CO2 comprises 32 percent of
atmospheric CO2 while the Physics Model (12) says human
CO2 is less than 5%. The question is whether the available
isotope data support or reject either of the models.
RealClimate  says the 13C/12C ratio for human CO2 is
about 98 percent of the ratio in natural CO2, and the 13C ratio
has declined about 0.15 percent since 1850. RealClimate says
this proves human CO2 caused all the increase in atmospheric
CO2 since 1850.
Human CO2 causes the new balance level of D14C and
13C/12C to be:
Lb = Ln Rn + Lh Rh (15)
Lb = the new balance level (of D14C or 13C/12C)
Ln = the natural balance level (D14C = 0; 13C/12C =
Lh = the human balance level (D14C = –1000; 13C/12C =
Rn = the fraction of natural CO2
Rh = the fraction of human CO2
The Physics Model predicts for D14C:
Lb = (0) (0.955) + (–1000) (0.045) = – 45 (16)
The IPCC model predicts for D14C:
Lb = (0) (0.68) + (–1000) (0.32) = – 320 (17)
The Physics Model predicts for 13C/12C:
Lb = (100) (0.955) + (98) (0.045) = 99.91 (18)
The IPCC model predicts for 13C/12C:
Lb = (100) (0.680) + (98) (0.320) = 99.36 (19)
The 14C data
The Physics Model (16) predicts human CO2 has lowered
the balance level of 14C from zero to –45. The IPCC model
(17) predicts human CO2 has lowered the 14C balance level to
Figure 11 compares the Physics and IPCC predicted levels
for human CO2 in the atmosphere.
Figure 11. The dotted lines show the Physics Model calculation for a balance
level of –45. The dashed line shows the Physics Model calculation for the
IPCC predicted balance level of -320.
Figure 11 shows the Physics Model result of 5 percent
human CO2 in the atmosphere matches the 14C data much
better than the IPCC model of 32 percent of human CO2 in the
In summary, the 14C data support the Physics Model and
reject the IPCC model.
The 13C data
The Physics Model (18) predicts human CO2 has lowered
the 13C ratio by 0.09. The IPCC model (19) predicts human
CO2 has lowered the 13C ratio by 0.64.
Figure 12 compares the Physics and IPCC predictions of the
13C/12C ratio to Real Climate’s numbers.
Figure 12. Real Climate  says the 13C ratio has decreased by 0.15 since
1750. Physics predicts a decrease of 0.09 and IPCC predicts a decrease of
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 21
There seem to be no error bounds in the available 13C data.
Nevertheless, even without error bounds the 13C data do not
support the IPCC model over the Physics Model. So, the IPCC
Segalstad  calculated similar results using permil units.
He concluded the isotope data show human CO2 cannot be
more than 4 percent of atmospheric CO2.
5.7. Mauna Loa Data
Some scientists argue that a viable CO2 model must replicate
the Mauna Loa CO2 data. The Physics Model can simulate the
Mauna Loa data for atmospheric CO2 as well as any other model.
Spencer  has a model that fits the Mauna Loa data.
Spencer assumes like the IPCC that the natural level of CO2 is
fixed at 280 ppm and human CO2 causes all the increase in
atmospheric CO2. His model has many variables available to
adjust so a fit to the Mauna Loa data is guaranteed.
The significance of the fit by the Physics Model is that it
comes with physical constraints that the other models do not
have. The Physics Model e-time must be 4 years and natural
CO2 must be 95 percent of atmospheric CO2.
Figure 13 shows how the Physics Model fits the Mauna Loa
Figure 13. The Physics Model replicates the Mauna Loa data with an e-time
of 4 years and the requirement that natural CO2 is 95 percent of atmospheric
In Figure 14, the total balance level is the sum of natural and
human balance levels. The balance level continues to rise.
Level follows the balance level with a lag of about 4 years (the
e-time), after the year 2000. This lag keeps the level about 10
ppm below the its balance level. Human CO2 adds to the
natural level to produce the total level, about 15 ppm above the
In 2019, the balance level in Figure 14 is artificially reset to
350 ppm to test how fast the CO2 level moves to the new
balance level. The total CO2 level falls to its new balance level
of 350 ppm in about 10 years. No CO2 remains stuck in the
5.8. Ice-core Data
IPCC claims “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
Using this invalid claim, IPCC assumes natural CO2
emissions remained constant within about one percent. IPCC’s
invalid claim about ice-core data is the basis of IPCC’s invalid
claim that human CO2 causes all the increase in atmospheric
CO2 above 280 ppm. This increase is presently 130 ppm or 32
Siegenthaler and Joos  observed that ice-core data show
natural CO2 increased by 17 ppm or 6 percent before 1900,
when human CO2 emissions totaled only 5 ppm. These
ice-core data contradict IPCC’s claim that natural CO2
emissions stayed constant after 1750.
Jaworoski  explains why ice-core data do not properly
represent past atmospheric CO2. He concludes nature
produces 97 percent of atmospheric CO2.
Proxy ice-core values for CO2 remained low for the past
650,000 years [10, 12]. If these ice-core values represent
atmospheric CO2, then atmospheric CO2 did not cause any of
the global warming in the last 650,000 years. And if CO2 did
not cause global warming in the past, then the IPCC has lost its
claim that CO2 causes present global warming .
Leaf stomata and chemical data prove the historical CO2
level was much higher than derived from ice cores . There
is no evidence that the pre-industrial CO2 level was 280 ppm
as IPCC assumes.
Beck  reconstructed CO2 from chemical data show the
level reached 440 ppm in 1820 and again in 1945.
IPCC’s claim that human CO2 produces all the increase in
atmospheric CO2 above 280 ppm is invalid. In science, when
data contradict a theory, the theory false. The IPCC, however,
ignores how its theories contradict data.
6. Theories Must Be Logical
6.1. IPCC’s Response Times Fail Physics
The Physics Model e-time has a precise definition: e-time is
the time for the level to move (1 – 1/e) of the distance to its
Segalstad  observes IPCC  uses many definitions of
lifetime — like residence time, transit time, response time,
e-folding time, and adjustment time — in its quest to prove
human CO2 remains in the atmosphere for hundreds of years.
Many investigators, from 1957 to 1992, have calculated the
e-time of atmospheric CO2 is about 5 years .
IPCC  defines “adjustment time (Ta)” as:
The time-scale characterising the decay of an
instantaneous pulse input into the reservoir.
Cawley  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” is imprecise.
Cawley follows 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
22 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
Some authors use “residence time” to mean “e-time” but
other authors, such as Cawley and IPCC, have a different
meaning for residence time. This paper uses e-time because its
definition is precise.
In summary, IPCC uses two different response times when
it should use only e-time:
1. When the level is far from its balance level (which can
be zero), IPCC thinks e-time is an adjustment time
because the level is moving rapidly toward its balance
2. When the level is close to its balance level, IPCC thinks
e-time is a residence time because “molecules” are
flowing in and out with little change in level.
Figure 14 illustrates how e-time relates to IPCC’s
adjustment and residence times.
Figure 14. E-time covers the full range of movement of level to a balance level.
IPCC  adjustment and residence times apply to only each end of the range.
IPCC 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 seems to be the same as e-time except
“removal” is not the same as outflow. Near the balance level,
IPCC sometimes interprets “removal” to mean the difference
between outflow and inflow.
IPCC says when outflow is proportional to level (the
Physics Model hypothesis) then adjustment time equals
turnover time. IPCC 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 e-time equals
IPCC says in further confusion:
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 turnover time (e-time) is about 4 years.
IPCC claims adjustment time is “fast initially and slower later
on” which is why its Bern model cannot replicate the 14C data
in Figure 9.
The 14C data show the e-time for 14CO2 is 16.5 years. This
e-time is the upper bound for 12CO2 e-time. The IPCC claim
of hundreds of years is based on IPCC’s misunderstanding of
Unfortunately, there are many different definitions of
residence time. Therefore, this paper uses e-time with its exact
6.2. IPCC’s First Core Argument Is Illogical
The IPCC  first core argument notes that human
emissions from 1750 to 2013 totaled 185 ppm while
atmospheric CO2 increased by only 117 ppm. These numbers
are OK. But IPCC claims this proves human CO2 caused all
the increase in atmospheric CO2 above 280 ppm. IPCC’s logic
Figure 15 shows the IPCC first core argument.
Figure 15. The sum of human CO2 year-by-year is larger than the increase in
However, the fact that the sum of human emissions is
greater than the increase does not prove human CO2 caused
the increase. The IPCC argument omits natural CO2 which
totaled about 6000 ppm during the same period, much larger
than the sum of human CO2.
Figure 16 shows the plot when the sum of natural CO2 is
Figure 16. The sum of natural CO2 compared to the sum of human CO2 and
the increase in CO2.
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 23
The sum of natural CO2 from 1959 to 2018 is 5700. The
sum of human CO2 over the same period is 170 ppm which is 3
percent of the natural CO2 sum. IPCC’s whole case depends
upon its incorrect assumption that nature did not vary more
that 3 percent since 1959 or since 1750. At the same time,
IPCC admits it does not know nature’s CO2 emission within
The fundamental error in this IPCC argument is discussed
in Section 3.1. The sums of inflows do not matter because
inflows do not “add” to atmospheric CO2. Inflows set balance
levels. The human effect on the total balance level is less than
6.3. IPCC’s Second Core Argument Is Illogical
IPCC  claims nature has been a “net carbon sink” since
1750, so nature could not have caused the observed rise in
atmospheric carbon dioxide. Please refer to Figure 5 that
shows the inflow and outflow of atmospheric CO2.
Of course, nature is a “net carbon sink” because nature
absorbs human CO2 emissions. However, absorption of human
CO2 has no bearing whatsoever on how much natural CO2
flows into the atmosphere. Nature can set its inflow as it pleases,
no matter how much human inflow nature absorbs. The 98-ppm
natural flow can double or reduce to one-half while nature
continues to absorb the outflow of the human addition to
atmospheric CO2. So, the IPCC argument is absurd.
The Physics Model shows how CO2 inflows set balance
levels in atmospheric CO2. At the balance level, outflow will
equal inflow. No CO2 gets trapped in the atmosphere.
6.4. Key IPCC Paper Makes Serious Errors
Kohler  uses Cawley  to “prove” the IPCC case. But
Cawley fails physics and statistics.
Cawley  is a key paper for the IPCC theory. Cawley
claims human CO2 caused all the increase of atmospheric CO2
above the 280 ppm in 1750. But Cawley’s attempted proof
Figure 17 shows three of Cawley’s equations.
Figure 17. Equations from Cawley .
Cawley’s equation (3) attempts to do the same job as
Physics Model (2), namely, to represent how level sets outflow.
But Cawley adds to his equation (3) a second term that
represents a steady-state outflow that is independent of level.
Cawley’s added term is fictitious because his first term on the
right side of his equation (3) is the true source of all outflow.
As a result, all Cawley’s equations after his (3) are wrong,
which makes his whole paper wrong.
Cawley’s equation (7) should include his Fa for human
inflow. His equations (7) and (8) should omit his arbitrary Fe
for outflow and set outflow equal to level (his C) divided by
his residence time. His residence time is also inaccurate as
shown in Section 6.1.
6.5. Statistical Correlation
Cawley  argues,
Lastly, the rise in atmospheric carbon dioxide closely
parallels the rise in anthropogenic emissions … which would
be somewhat of a coincidence if the rise were essentially
natural in origin!
IPCC  writes:
Second, the observed rate of CO2 increase closely parallels
the accumulated emission trends from fossil fuel combustion
and from land use changes.
IPCC incorrectly claims this proves human CO2 causes the
increase in atmospheric CO2.
A standard scientific test for the non-existence of cause and
effect is to show the correlation, of the assumed cause with the
assumed effect, is zero.
For the IPCC to argue that human CO2 causes climate
change, the IPCC must show that the correlation of human
emissions with the increase in atmospheric CO2 is
significantly greater than zero.
Proper statistics requires a detrended analysis of a time
series to conclude cause and effect. Munshi  shows the
“detrended correlation of annual emissions with annual
changes in atmospheric CO2” is zero. Chaamjamal 
extended Munshi’s calculations and found the correlations are
zero for time intervals from one to five years.
Therefore, the standard statistical test for cause and effect
proves human CO2 is insignificant to the increase in
The ratio of annual change in atmospheric CO2 to annual
human CO2 emissions that Munshi  tested is IPCC’s
“airborne fraction”. Therefore, IPCC’s airborne fraction has
no useful meaning.
An estimate of the airborne fraction is about 2.5 ppm/year
divided by 5 ppm/year, or 0.5. Since the increase in level is
caused by an increase in natural CO2 emissions, the airborne
fraction has little physical meaning, and it would go to infinity
if human emissions stopped.
The IPCC model and the Physics model compete to
describe how human CO2 emissions add to atmospheric CO2.
Both models agree that the CO2 inflow into the atmosphere is
less than 5 percent human CO2 and more than 95 percent
The IPCC model concludes that human CO2 causes all the
increase in atmospheric CO2 above 280 ppm; that 15 percent
of all human CO2 emissions stays in the atmosphere forever;
that 53 percent stays for hundreds of years; and only 32
percent flows freely out of the atmosphere like natural CO2.
The Physics Model treats human CO2 and natural CO2 the
24 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
same because their CO2 molecules are identical. The Physics
model makes only one hypothesis: CO2 outflow equals the
level of CO2 in the atmosphere divided by e-time.
The Physics Model concludes that inflow sets a balance
level equal to inflow multiplied by e-time, and that continuing
inflow does not continue to increase atmospheric CO2. Rather
inflow sets a balance level where outflow equals inflow and
continuing inflow will not further increase the level of
atmospheric CO2 beyond the balance level.
The proper test of two theories is not to claim the IPCC
theory explains “observational evidence.” The proper test is
the scientific method: if a prediction is wrong, the theory is
The 14C data following the cessation of the atomic bomb
tests show how the level of CO2 in the atmosphere returns to
its balance level after inflow decreases. All valid models of
atmospheric CO2 must be able to replicate the 14C data.
The Physics Model exactly replicates the 14C data after
1970. This replication shows the e-time for 14CO2 is 16.5
years and that this e-time has been constant since 1970. The
replication shows the Physics Model hypothesis — that
outflow equals level divided by e-time — is correct.
The IPCC Bern model cannot replicate the 14C data. Its
curve crosses the 14C data curve. The Bern model cannot even
replicate itself if it is restarted at any point. This failure proves
the IPCC Bern model does not have the mathematical
structure for a valid model.
If natural CO2 is inserted into the Bern model, as physics
requires, the Bern model predicts that 15 percent of natural
CO2 inflow sticks in the atmosphere forever, which
contradicts data and proves the Bern model is invalid.
The Physics Model concludes that the ratio of human to
natural CO2 in the atmosphere equals the ratio of their inflows,
independent of e-time, and that the e-times for both human
and natural CO2 are the same. Using IPCC data, the e-time for
12CO2 is about 4 years.
The ratio conclusion means human CO2 adds only about 18
ppm and natural CO2 adds about 392 ppm to today’s CO2 level
of 410 ppm. If all human CO2 emissions stopped and natural
CO2 emissions stayed constant, then the level of atmospheric
CO2 would fall only to 392 ppm in about 10 years. Nothing
would be gained by stopping human CO2 emissions. There are
no long-term effects of human CO2 emissions. Continued
constant CO2 emissions do not add more CO2 to the
atmosphere. Continued constant CO2 emissions simply
maintain the balance level.
The author thanks Chuck Wiese, Laurence Gould, Tom
Sheahen, Charles Camenzuli, and others who reviewed this
paper and provided scientific critique and suggestions. The
author thanks Daniel Nebert, Gordon Danielson, and Valerie
Berry, who provided language and grammar suggestions.
This research did not receive any grant from funding
agencies in the public, commercial, or not-for-profit sectors.
This research was funded solely by the personal funds of the
The author declares he is the only contributor to the
research in this paper.
Download supporting files.
 USGCRP, 2017: Climate Science Special Report: Fourth
National Climate Assessment, Volume I. U.S. Global Change
Research Program, Washington, DC, USA, 470 pp; 2018. doi:
 IPCC, 2001: Working Group 1: The scientific basis. The
Carbon Cycle and Atmosphere CO2.
 IPCC, 2007: Climate Change 2007: The Physical Science Basis.
 D. Archer, M. Eby, V. Brovkin, A. Ridgwell, L. Cao, U.
Mikolajewicz, et al., “Atmospheric Lifetime of Fossil Fuel
Carbon Dioxide”. Annu. Rev. Earth Planet. Sci., 37, pp. 117–
 G. C. Cawley, “On the Atmospheric residence time of
anthropogenically sourced CO2”. Energy Fuels 25, pp. 5503–
5513; 2011. http://dx.doi.org/10.1021/ef200914u
 Z. Kern, M. Leuenberger, Comment on "The phase relation
between atmospheric CO2 and global temperature" by Humlum
et al. Glob. Planet. Change 100: 51–69.: Isotopes ignored. Glob.
Planet. Chang. 109, 1–2; 2013.
 P. Kohler, J. Hauck, C. Volker, D. A. Wolf-Gladrow, M. Butzin,
J. B. Halpern, et al. Comment on “Scrutinizing the carbon cycle
andCO2residence time in the atmosphere” by H. Harde, Global
and Planetary Change; 2017.
 R. Revelle, H. Suess, “CO2 exchange between atmosphere and
ocean and the question of an increase of atmospheric CO2
during past decades”. Tellus. 9: 18-27; 1957.
 C. Starr, “Atmospheric CO2 residence time and the carbon
cycle”. Science Direct, 18, 12, pp. 1297-1310; 1992.
 T. V. Segalstad, “Carbon cycle modelling and the residence
time of natural and anthropogenic atmospheric CO2: on the
construction of the "Greenhouse Effect Global Warming"
dogma”. In: Bate, R. (Ed.): Global warming: the continuing
debate. ESEF, Cambridge, U. K. [ISBN 0952773422]: 184-219;
International Journal of Atmospheric and Oceanic Sciences 2019; 3(1): 13-26 25
 Z. Jaworowski, “Climate Change: Incorrect information on
pre-industrial CO2”. Statement written for the Hearing before
the US Senate Committee on Commerce, Science, and
 Z. Jaworowski, “CO2: The Greatest Scientific Scandal of our
Time”. 21st CENTURY Science & Technology. 2007.
 E. Beck, “180 Years of Atmospheric CO2 Gas Analysis by
Chemical Methods”. Energy & Environment. Vol 18, No. 2.
 A. Rorsch, R.S. Courtney, D. Thoenes, “The Interaction of
Climate Change and the CO2 Cycle”. Energy & Environment,
Volume 16, No 2; 2005.
 R.S. Courtney, “Limits to existing quantitative understanding
of past, present and future changes to atmospheric CO2
concentration”. International Conference on Climate Change,
New York. 2008.
 T, Quirk, “Sources and sinks of CO2”. Energy & Environment.
Volume: 20 Issue: 1, pp. 105-121. 2009.
 R. E. Essenhigh, “Potential dependence of global warming on
the residence time (RT) in the atmosphere of anthropogenically
sourced CO2”. Energy Fuel 23, pp. 2773-2784; 2009.
 J. A. Glassman, “On why CO2 is known not to have
accumulated in the atmosphere and what is happening with
CO2 in the modern era”. Rocket Scientist Journal; 2010.
 M. L. Salby, “Physics of the Atmosphere and Climate”.
Cambridge University Press. 2012. (ISBN: 978-0-521-76718-7)
 M. L. Salby, “Relationship Between Greenhouse Gases and
Global Temperature”. Video Presentation, April 18, 2013.
 M. L. Salby, “Atmosphere Carbon”. Video Presentation, July
18, 2016. University College London.
 M. L. Salby, “What is really behind the increase in atmospheric
CO2?” Video Presentation, October 10, 2018.
Helmut-Schmidt-University Hamburg, Germany.
 O. Humlum, K. Stordahl, J.E. Solheim, “The phase relation
between atmospheric CO2 and global temperatures”. Global
and Planetary Change, 100, pp 51-69, 2013.
 H. Harde, “Scrutinizing the carbon cycle and CO2 residence
time in the atmosphere”. Global and Planetary Change. 152,
 H. Harde, “What Humans Contribute to Atmospheric CO2:
Comparison of Carbon Cycle Models with Observations”.
Earth Sciences Vol. 8, No. 3, 2019, pp. 139-159. doi:
 E. X Berry, “A fatal flaw in global warming science”. Basic
Science of a Changing Climate. Porto University, Portugal. Sep
 E. X Berry, “Contradictions to IPCC’s climate change theory”.
Annual meeting of the American Meteorological Society,
 T. Boden, B. Andres, (2017) Global CO2 emissions from
fossil-fuel burning, cement manufacture, and gas flaring:
 H. B. Dwight, “Tables of Integrals and Other Mathematical
Data” Item 90.1. MacMillian Company; 1955.
 U. Siegenthaler, F. Joos, “Use of a simple model for studying
oceanic tracer distributions and the global carbon cycle”. Tellus,
44B, 186-207; 1992.
 E. Maier-Reimer, L. Hasselmann, “Transport and storage of
CO2 in the ocean – an inorganic ocean-circulation carbon cycle
model”. Climate Dynamics 2 (2):63–90; 1987. DOI:
 F. Joos, R. Roth, J. S. Fuglestvedt, G. P. Peters, I. G. Enting,
von Bloh, et al. “Carbon dioxide and climate impulse response
functions for the computation of greenhouse gas metrics: a
multi-model analysis”. Atmospheric Chemistry and Physics 13
(5), doi: 10.5194/acpd-12-19799-2012. Atmos. Chem. Phys. 13,
 F. Joos, “Parameters for tuning a simple carbon cycle model”.
 Q. Hua, M. Barbetti, A. Z. Rakowski. “Atmospheric
radiocarbon for the period 1950–2010”. RADIOCARBON, Vol
55, pp. 2059–2072. Table S2c. 2013.
26 Edwin X Berry: Human CO2 Emissions Have Little Effect on Atmospheric CO2
 J. C. Turnbull, S. E. Mikaloff Fletcher, I. Ansell, G. W.
Brailsford, R. C. Moss, Norris, et al. “Sixty years of
radiocarbon dioxide measurements at Wellington, New
Zealand: 1954–2014”. Atmos. Chem. Phys., 17, pp. 14771–
14784. 2017. https://doi.org/10.5194/acp-17-14771-2017
 I. Levin, T. Naegler, B. Kromer, M. Diehl, R. Francey, A.
Gomez-Pelaez, et al., “Observations and modelling of the
global distribution and long-term trend of atmospheric 14CO2”.
Tellus B: Chemical and Physical Meteorology. 2010.
 Wikipedia: Isotopes.
 A. P. Ballantyne, C. B. Alden, J. B. Miller, P. P. Tans, J. W. C.
White, "Increase in observed net carbon dioxide uptake by land
and oceans during the past 50 years", Nature 488, pp. 70-73,
 RealClimate, “How do we know that recent CO2 increases are
due to human activities?”. 2004.
 R. Spencer, “A simple model of the atmospheric CO2 budget”.
 J. Munshi, “Responsiveness of atmospheric CO2 to fossil fuel
emissions: Updated”. SSRN; 2017.
 Chaamjamal, “Fossil fuel emissions and atmospheric
composition”. Thongchai Thailand. 2019.