What Humans Contribute to Atmospheric CO₂: Comparison of Carbon Cycle Models with Observations

Abstract

The Intergovernmental Panel on Climate Change assumes that the inclining atmospheric CO2 concentration over recent years was almost exclusively determined by anthropogenic emissions, and this increase is made responsible for the rising temperature over the Industrial Era. Due to the far reaching consequences of this assertion, in this contribution we critically scrutinize different carbon cycle models and compare them with observations. We further contrast them with an alternative concept, which also includes temperature dependent natural emission and absorption with an uptake rate scaling proportional with the CO2 concentration. We show that this approach is in agreement with all observations, and under this premise not really human activities are responsible for the observed CO2 increase and the expected temperature rise in the atmosphere, but just opposite the temperature itself dominantly controls the CO2 increase. Therefore, not CO2 but primarily native impacts are responsible for any observed climate changes.

Full text

Earth Sciences
2019; 8(3): 139-158
http://www.sciencepublishinggroup.com/j/earth
doi: 10.11648/j.earth.20190803.13
ISSN: 2328-5974 (Print); ISSN: 2328-5982 (Online)
What Humans Contribute to Atmospheric CO2: Comparison
of Carbon Cycle Models with Observations
Hermann Harde
Experimental Physics and Materials Science, Helmut-Schmidt-University, Hamburg, Germany
Email address:
harde@hsu-hh.de
To cite this article:
Hermann Harde. What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations. Earth Sciences.
Vol. 8, No. 3, 2019, pp. 139-158. doi: 10.11648/j.earth.20190803.13
Received: April 3, 2019; Accepted: May 11, 2019; Published: June 12, 2019
Abstract:
The Intergovernmental Panel on Climate Change assumes that the inclining atmospheric CO
2
concentration over
recent years was almost exclusively determined by anthropogenic emissions, and this increase is made responsible for the rising
temperature over the Industrial Era. Due to the far reaching consequences of this assertion, in this contribution we critically
scrutinize different carbon cycle models and compare them with observations. We further contrast them with an alternative
concept, which also includes temperature dependent natural emission and absorption with an uptake rate scaling proportional
with the CO
2
concentration. We show that this approach is in agreement with all observations, and under this premise not really
human activities are responsible for the observed CO
2
increase and the expected temperature rise in the atmosphere, but just
opposite the temperature itself dominantly controls the CO
2
increase. Therefore, not CO
2
but primarily native impacts are re-
sponsible for any observed climate changes.
Keywords:
Carbon Cycle, Atmospheric CO
2
Concentration, CO
2
Residence Time, Anthropogenic Emissions,
Fossil Fuel Combustion, Land Use Change, Climate Change
1. Introduction
Following the interpretation of the Intergovernmental
Panel on Climate Change (IPCC) the inclining atmospheric
CO
2
concentration over recent years is assumed to result
almost exclusively from anthropogenic emissions, and as a
consequence of the greenhouse effect this increase is made
responsible for the rising temperature over the Industrial Era
(see, 5th Assessment Report, AR5 [1]). These predictions are
based on more or less refined theoretical models of the
carbon cycle and their comparison with observations. But
good agreement between calculations and observations is
only a necessary, not sufficient prerequisite for reliable
simulations, they must also be in conformity with all natural
causalities. Because of the expected far reaching conse-
quences of anthropogenic carbon on future climate changes
this was motivation enough to critically scrutinize the main
assumptions used in these carbon cycle models.
In this contribution we consider three theoretical ap-
proaches, which find favor with the IPCC and predominantly
focus on the influence of human activities caused by Land
Use Change (LUC) (see e.g., Le Quéré et al. [2]; CICERO
[3]) and the Fossil Fuel Emissions (FFE) (CDIAC [4]), while
environmental effects are supposed to have been constant
over the last 270 yr. We show that the main consequence of
isolating the anthropogenic carbon cycle from the natural
cycle is to introduce a new time scale, the adjustment time,
which differs significantly from the residence time, the latter
characterizing the natural uptake of CO
2
from the atmos-
phere by extraneous reservoirs.
We compare respective simulations of these approaches
with actual observations at Mauna Loa (Keeling et al. [5];
AR5 [1] Chap.6-Fig.6.3, p. 476), and we contrast them with
our alternative description of the atmospheric carbon cycle
(Harde [6]), which is based on a first order absorption pro-
cess for the full cycle with only one time scale, the residence
time, and additionally including temperature dependent
natural variations of the emission and uptake of CO
2
.
We do not model carbon in the complete Earth-Atmos-
phere System, we only focus upon CO
2
in the atmosphere,
which is controlled by the governing Conservation Law.
Based on this fundamental relation of mass conservation
and a first order absorption process, we show that human
activities have a minor influence on the CO
2
increase in the

140 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
atmosphere, while the main contribution has to be explained
by natural effects, particularly the temperature, which is
responsible for more than 85% of the CO
2
increase since the
Industrial Revolution. Therefore, not CO
2
but primarily na-
tive impacts control any observed climate changes.
2. Physical Concept
The basis of our considerations is the balance for the influx
of CO
2
into the atmosphere and the outflux from the atmos-
phere to extraneous reservoirs, by which the CO
2
concentra-
tion C in the atmosphere is controlled. This can well be
compared with a swimming pool (see also Salby [7]) with an
influx f
in
and an outflux f
out
, for which the changing amount of
water dm
W
in the pool over the time interval dt is given by the
difference of these fluxes:
outin
W
ff
dt
dm −=
. (1)
From a simple flux consideration we get the average turn-
over or residence time τ
R
it takes to completely exchange the
water in the pool. Under steady state conditions for f
in
= f
out
then the total amount of water in the pool m
W
is exchanged
within
out
W
in
W
R
f
m
f
m==
τ
, (2)
and the other way round is this an important measure for the
outflux rate
R
W
out
m
f
τ
=
. (3)
In the same way as for the pool we can consider the balance
for atmospheric CO
2
with a total emission rate e
T
(t) of CO
2
from the surface to the atmosphere, and reversely a total ab-
sorption rate a
T
(t) of the extraneous reservoirs (Figure 1).
Generally the influx can be split into natural emissions with a
rate e
N
(t) and an additional anthropogenic emission rate e
A
(t),
which on its part results from fossil fuel emissions and land
use changes. The outflux is determined by temporary or con-
tinuing absorption of CO
2
by oceans and the land. Incidentally
the total absorption rate a
T
(t) is also separated into a fraction
a
N
(t), characterizing an uptake that can be addressed to the
amount of natural emissions, and another contribution, a
A
(t),
caused by the additional anthropogenic emissions. This results
in a total mass balance, the Conservation Law:
)()()()(
)()(
)()(
)(
tatatete
tate
dt
tdC
dt
tdC
dt
tdC
ANAN
TT
AN
−−+=
−=+=
, (4)
which governs the atmospheric CO
2
concentration.
Generally all these fluxes are changing with time and also
depend on the actual concentration C(t), which virtually may
be considered to consist of a time dependent fraction C
N
(t),
caused by native emissions, and of a time dependent anthro-
pogenic portion C
A
(t), with C(t) = C
N
(t) + C
A
(t). Thus, usually
this equation has to be solved numerically.
Figure 1. Emissions of CO
2
from the surface to the atmosphere (Red Arrows)
and absorption of CO
2
by the surface (Blue Arrows).
In analogy to the pool example it follows that an exchange
of CO
2
in the atmosphere takes the time
)(
)(
)(
)(
ta
tC
te
tC
TT
R
==
τ
, (5)
the so called residence time of CO
2
in the atmosphere, and the
absorption rate is
R
T
tC
ta
τ
)(
)(
=
. (6)
With (4) we do not model the carbon cycle in the complete
Earth-Atmosphere System (EASy). That would require a
wider analysis, accounting for processes within extraneous
systems and exchanges between them. Our analysis focuses
upon CO
2
in the atmosphere, which is controlled by the gov-
erning conservation law. Incidentally this physical law is
characterized as a flawed one-box description (see e.g., Köh-
ler et al. [8]), because a single balance equation - so the ar-
gument - does not account for details in other reservoirs, sys-
tems that are extraneous to the atmosphere. As will be shown,
such interpretation is confused. With the inclusion of surface
fluxes e
T
and a
T
, which account for influences on the atmos-
phere, the balance equation (4) entirely determines the evolu-
tion of CO
2
. Details of extraneous systems, which are largely
unobservable, are then irrelevant.
Atmospheric CO
2
is fully described by this single equation
for a reason. It follows from the 3-dimensional continuity
equation, the physical law that governs the global distribution
of atmospheric CO
2
. In flux form, the continuity equation is
given by
vv ⋅∇=⋅∇+
∂
∂
cc
t
c)(
, (7)
where the local CO
2
concentration c is transported with ve-
locity v. When integrated over the volume of the atmosphere

Earth Sciences 2019; 8(3): 139-158 141
and subjected to the divergence theorem, (7) reduces to the
governing balance equation (4) for globally averaged CO
2
.
If this would be flawed, then so would be the fundamental
physical law from which it follows.
The anthropogenic emissions e
A
(t) as the sum of the Land
Use Change (LUC) (see e.g., Le Quéré et al. [2]; CICERO [3])
and the Fossil Fuel Emissions (FFE) (CDIAC [4]) are dis-
played in Figure 2. While LUC (Red-Brown) almost stays
constant over the last 170 years, FFE (Blue) is rapidly in-
creasing over recent years.
0
1
2
3
4
5
6
1850 1880 1910 1940 1970 2000
Year
Anthropogenic Emissions e
A
(ppm/yr)
Fossil Fuel
Land Use Change
Figure 2. Total anthropogenic emissions e
A
(t) due to land use change (Red-
Brown) and fossil fuel emissions (Blue). Data from Le Quéré et al. [2] and
CDIAC [4] displayed as stacked representation.
Figure 3 shows again the total anthropogenic emissions
(Red Squares) together with the temperature anomaly
∆
T(t)
(Blue Triangles) of the global annual station temperature data
from the Goddard Institute for Space Studies (GISS) [9].
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1850 1880 1910 1940 1970 2000
Year
T-Anomaly
∆
T (°C)
0
2
4
6
8
Anthrop. Emission e
A
(ppm/yr)
T-Anomaly
Anthrop. Emission
Fit Anthrop. Emission
Figure 3. Anthropogenic emissions e
A
(t) (Red Squares) with exponential fit
(Green Graph) and global temperature anomaly (GISS-data, Blue Triangles).
The anthropogenic emissions can be well approximated by
an exponential of the form
)()(
/)(
0
0
beete
e
tt
AA
+⋅=
−
τ
(8)
with parameters: e
A0
= 0.026 ppm/yr,
τ
e
= 50 yr, t
0
= 1750 yr
and b = 4. The integral over the emission rate agrees within a
few ‰ with the integral of the estimated observations.
On first glance the almost synchronous evolution of the
fossil fuel emissions and temperature anomaly looks to be a
strong indicator for the human influence as the driving force
for a globally increasing temperature. But a closer look al-
ready reveals some systematic discrepancies, particularly
between 1940 and 1970, where the emissions are further in-
creasing, while the temperature stagnates or even slightly de-
creases. This has to be considered in some more detail, in
particular by directly comparing model calculations of the
CO
2
increase, based on the fossil fuel emissions and land use
change, with the actual observations at Mauna Loa since 1958
(Keeling et al. [5]; AR5 [1] Chap.6-Fig.6.3, p. 476).
Therefore, in this contribution we first investigate the car-
bon cycle based on the IPCC's assumptions that the human
emissions are the dominant cause of the CO
2
increase, before
we extend the balance to the full carbon cycle also including
natural variations with their temperature dependence (see also:
Harde [6]; Salby [7], [10, 11]).
3. Anthropogenic Carbon Cycles
To explain the CO
2
increase over recent years and to predict
its further progression, the IPCC assessment reports emanate
from equation (4), but they are using some restricting as-
sumptions (see AR5 [1] Chap.6), which can be summarized by
the following statements:
1. Before 1750 and in first approximation also before 1850
steady state conditions are presupposed with a CO
2
concentration of C
N0
(1750) ≈ 280 ppm, which is deter-
mined by constant natural emission and absorption rates
e
N0
= a
N0
of about 93 ppm/yr (AR5 [1] Chap.6-Fig.6.1).
2. At this concentration and with these fluxes it follows
from (5) an average residence time
τ
R
(at pre-industrial
times:
τ
R0
) of CO
2
in the atmosphere of
yr
a
C
e
C
N
N
N
N
R
0.3
0
0
0
0
0
===
τ
. (9)
Note: The same result is found from (4) for the in- and
outfluxes in equilibrium and with an absorption rate
equivalent to (6), which is scaling proportional to the
concentration C
N0
:
0
0
000000
0
R
N
NNRNNN
N
C
eCeae
dt
dC
τ
α
−=⋅−=−=
, (10)
with
α
R0
= 1/
τ
R0
as the absorptivity and
τ
R0
now as the
e-folding residence time.
3. It is assumed that an increasing CO
2
concentration over
the last 170 years is almost exclusively caused by an-
thropogenic emissions from fossil fuel combustion and
land use change, while the natural emissions over this
period are supposed to have been the same as in pre-
industrial times.
The increasing concentration is attributed to only partial
re-absorption of the anthropogenic emissions, from
which a fraction, the so-called Airborne Fraction AF =
∆
e
A
/e
A
, is assumed to remain in the atmosphere. Then
)()( teAFte
AA
⋅
=
∆
(11)

142 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
is the non-absorbed portion, which cumulates in the at-
mosphere and
)1()()()()( AFteteteta
AAAA
−
⋅
=
∆
−
=
(12)
represents the absorbed fraction of the anthropogenic
emissions. Actually the IPCC emanates from an airborne
fraction of AF = 44% (AR5 [1] Chap.6, p. 495; Le Quéré
et al. [12]).
4. To account for a changing uptake of extraneous reser-
voirs with increasing atmospheric concentration the
absorption is supposed to consist of a series of different
exponential decay terms representing the uptake of the
different reservoirs with different time constants. This
absorption is considered to be proportional to the human
emissions, not the actual concentration C (see (12)).
Based on these assumptions more or less sophisticated ap-
proaches are known to explain the increasing CO
2
concentra-
tion in the atmosphere. Three of them will be briefly charac-
terized and discussed in this contribution. They all emanate
from the same basic concept to isolate the natural carbon ex-
change between atmosphere and extraneous reservoirs and
only to consider the anthropogenic cycle.
3.1. Constant Airborne Fraction
With a constant natural emission and absorption rate over
the Industrial Era (e
N0
= a
N0
) and also a constant airborne
fraction over this period the balance equation (4) reduces to
the simple form
)()(
)( teAFte
dt
tdC
AA
⋅=∆=
(13)
and changes synchronously with e
A
(t). The concentration as a
function of time is found by simply integrating (13) over the
Industrial Era:

⋅+=
t
A
dtteAFCtC
1750
')'()1750()(
. (14)
From the carbon budget over the last 270 years we derive an
airborne fraction of AF = 42% (see Le Quéré et al. [2], Table
9). Then, with an initial concentration of C(1750) = C
N0
= 280
ppm this results in a progression as shown in Figure 4 (Green
Line), which for the last 60 yr can directly be compared with
measurements (Blue Diamonds) at Mauna Loa (Tans &
Keeling [13]). This comparison shows generally too high
concentrations, particularly for past periods. This might be
caused by a too large initial concentration in 1750, but also the
slope does not fit very well. More likely is a too large emission
rate, especially due to LUC, which anyway is only known
with an accuracy of about
±
50%.
A surprisingly good agreement can be found with an an-
thropogenic emission rate e'
A
(t), which as average over the
considered period is reduced by 0.21 ppm/yr, and using an
airborne fraction of 48% (Green Crosses), 6% larger than the
average fraction over the Industrial Era. The smooth shape of
the fits is the result of an integration over the full anthropo-
genic emissions since 1750, where the soft increase of the
curves is dominated by the 'average' emission rate, while even
larger emission events are strongly flattened.
250
280
310
340
370
400
1850 1880 1910 1940 1970 2000
Year
CO
2
Concentration C (ppm)
0
1
2
3
4
5
6
7
Anthrop. Emission e
A
(ppm/yr)
Mauna Loa
AF = 42 %
AF = 48 %; e_A - 0.21 ppm/yr
Anthrop. Emission
Figure 4. Calculated CO
2
concentration with an airborne fraction of 42%
(Green Line) compared with observations at Mauna Loa (Blue Diamonds). A
simulation with AF = 48% and reduced emissions is plotted as Green Crosses.
Also shown are the anthropogenic emissions e
A
(t) (Red Squares).
3.2. Bern Model
A more advanced approach to describe the carbon cycle, is
the so-called Bern Model of CO
2
absorption (e.g., Joos et al.
[14]), a prototype of similar treatments in other models. It
distinguishes between different sinks on different time scales
and assumes a multi-exponential decay to re-equilibrate after a
perturbation, e.g., caused by a transient spike of CO
2
added to
the atmosphere. Using the five-term fit to the Bern carbon
cycle model (Joos et al. [14]; Hansen et al. [15, 16]) the ad-
justment following a δ-pulse perturbation ∆e
P
from equilib-
rium emission e
eq
is supposed to be:
4.3/21/
70/420/
26.024.0
18.014.018.0
/))(()(
tt
tt
Peq
ee
ee
eetetR
−−
−−
⋅+⋅+ ⋅+⋅+=
∆
−
=
. (15)
0
0.2
0.4
0.6
0.8
1
1964 2014 2064 2114
2164
Year
Relat ive ∆
14
CO
2
, Pe rturb ation
Bern Model
Meas. C14 Vermunt
Meas. C14 Schauinsland
Exponential: tau = 15 yr
Figure 5. Decay of perturbation predicted by the Bern Model (Red Graph) as
calculated from (15). Also shown is the observed
14
C decay (Circles and
Triangles) and an exponential fit with a decay time
τ
= 15 yr (Dashed Blue).
Figure 5 shows the adjustment of the relative perturbation
R(t) over 200 yr (Red). Also displayed is the observed
14
CO
2
decay at Vermunt and Schauinsland (Levin et al. [17]) after the
stop of the atomic bomb tests, shown as relative fractiona-
tion-corrected ‰-deviation ∆
14
CO
2
from the Oxalic Acid
standard. This decay is well represented by a single exponen-
tial with a decay constant of only 15 yr (Dashed Blue). Almost
identical ∆
14
CO
2
decays of 16.5 yr can be found from the data

Earth Sciences 2019; 8(3): 139-158 143
of Hua et al. [18] and Turnbull et al. [19].
For calculating the atmospheric CO
2
concentration by the
Bern Model (e.g., Joos [14]), the emission of anthropogenic
CO
2
into the atmosphere is considered as a series of consecu-
tive pulse inputs. Then the atmospheric CO
2
concentration C(t)
at time t is assumed to be the sum of earlier emissions e
A
(t') at
time t' multiplied by the fraction, now a time dependent air-
borne fraction, which is still available in the atmosphere after
the time t - t' and which is given by the pulse response function
R(t - t') of (15). With an anthropogenic emission rate, which
can well be approximated by (8) (see Figure 3), it follows:
[
]
)(18.0
)(
')'()'()()(
0
/)(
4
/)(
3
/)(
2
/)(
10
/)(
00
0
40
3020
100
0
ttbec
ecec
eccecetC
dtttRtetCtC
tt
tttt
tttt
eA
t
t
A
e
−⋅⋅+⋅− ⋅−⋅− ⋅−−⋅⋅+=
⋅−⋅+=
−−
−−−−
−−−

τ
ττ
ττ
(16)
with:
4321
26.024.018.014.018.0
eeeeee
c
τττττ
⋅+⋅+⋅+⋅+⋅=
;
)26.024.018.014.0(18.0
43210
τττττ
⋅+⋅+⋅+⋅⋅−⋅= bc
e
;
)(18.0);(14.0
222111
ττττ
⋅+⋅=⋅+⋅= bcbc
ee
;
)(26.0);(24.0
444333
ττττ
⋅+⋅=⋅+⋅= bcbc
ee
;
yryr
eieieei
420;50);/(
1
==+⋅=
τττττττ
;
4;4.3;21;70
432
==== byryryr
τττ
;
This approach also presupposes an equilibrium CO
2
con-
centration C
eq
in 1750 of C
eq
= 280 ppm, and it excludes any
further variations in the natural emission rate over the Indus-
trial Era.
The calculated atmospheric CO
2
concentration as given by
(16) is displayed in Figure 6 (Solid Green). The Bern Model
shows the same tendency of too large calculated concentra-
tions as this was already found for the much simpler model of
constant airborne fraction (AF Model).
250
280
310
340
370
400
1850 1880 1910 1940 1970 2000
Year
CO2 C oncentrat ion C (ppm )
0
1
2
3
4
5
6
7
Anth rop. E mission e A (ppm /yr)
Mauna Loa
Bern Model
B-M: e_A - 0.18 ppm/yr
Anthrop. Emission
Figure 6.
Comparison of the Bern Model (Green Graph) with the Mauna Loa
data (Blue Diamonds). A simulation with reduced emission e
A
(t) - 0.18 ppm/yr
is displayed as Green Crosses. Also shown are the original data of anthro-
pogenic emissions e
A
(t) (Red Squares).
With a reduced average anthropogenic emission rate, in this
case of 0.18 ppm/yr, again a very good agreement with the
Mauna Loa data can be observed.
But from basic causalities there exist some fundamental
problems with the AF and the Bern Model:
1. Additional emissions to the atmosphere even at a con-
stant rate will never attain a new equilibrium.
2. These emissions will further accumulate in the atmos-
phere, in the Bern Model 18%, in the simple AF Model
even 48%, emissions which will stay for ever in the at-
mosphere.
3. This is a consequence of the defect, that these models
essentially add up additional emissions deviating from
pre-industrial times, and they only consider partial up-
take, which is scaling proportional with the emission rate
– and not with the concentration.
4. The Bern Model uses different time scales for the uptake,
although the
14
C-decay shows a single exponential decay
of only 15 yr or shorter.
5. Even natural year-to-year variations of only 1%, El Ni-
ños and volcanic activities comparable or even larger
than the human emissions, will cumulate in the atmos-
phere, since only additional emissions but not adequate
sinks are considered in these models.
To avoid some of these deficits another class of models uses
a first order absorption process, but applies this only to con-
centration changes C
A
(t) caused by anthropogenic emissions.
3.3. Absorption Scales with Concentration
Since the anthropogenic absorption rate a
A
(t), by presump-
tion, is proportional to the man-made emission rate e
A
(t) (see
Eq.(12)) and this rate on its part directly determines the an-
thropogenically induced fraction of the CO
2
concentration
C
A
(t), in analogy to (6) or (10) we infer:
A
A
AA
tC
AFteta
τ
)(
)1()()( −⋅=
, (17)
which converts the absorption term in (4) to a first order
process scaling proportional to the anthropogenic fraction C
A
(t)
of the concentration (for a similar approach see e.g.: Siegen-
thaler & Sarmiento [20]; Dietze [21]; Cawley [22]; Lüdecke &
Weiss [23]). For e
N0
= a
N0
this results in the balance equation:
A
N
A
A
A
A
A
CtC
te
tC
te
dt
tdC
dt
tdC
ττ
0
)(
)(
)(
)(
)(
)(
−
−=−==
(18)
with
τ
A
as the respective absorption time of molecules in the
atmosphere, which in the IPCC terminology controls the 'ad-
justment' of the atmosphere only due to anthropogenic emis-
sions. From Figure 4 and with (17) we can estimate this 'ad-
justment' time, which for C
A
= (393-280) ppm = 113 ppm, e
A
=
4.7 ppm/yr (all values averaged over 10 years from 2007-2016,
see Le Quéré et al. [2], Table 7) and the fitted AF = 48% from
Figure 4 gives

144 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
yr
AFte
tC
A
A
A
46
)1)((
)( =
−
=
τ
. (19)
Numerical integration of (18) with this 'adjustment' time,
with the given emission rate e
A
(t) and a native concentration
C
N0
= 280 ppm is shown in Figure 7 (Green Line). For a cor-
rected emission rate e'
A
(t) = e
A
(t) - 0.3 ppm/yr and the 'ad-
justment' time from (19) also this accounting scheme (Green
Crosses) gives good agreement with the observations at
Mauna Loa (Blue Diamonds). This absorption time is almost
identical with an adjustment time of 48 yr as derived from a
simple flux calculation presented in Harde [6], Eq. (9).
250
280
310
340
370
400
1850 1880 1910 1940 1970 2000
Year
CO
2
Conc entration C (pp m)
0
1
2
3
4
5
6
7
Anth rop. Emis sion e
A
(ppm /yr)
Mauna Loa
tau = 46 yr
tau = 46 yr, e_A - 0.3 ppm/yr
Anthrop. Emission
Figure 7. Calculation of the CO
2
concentration for an adjustment time
τ
A
=
46 yr (Green Line) and comparison with observations at Mauna Loa (Blue
Diamonds). A simulation with reduced emissions is displayed as Green
Crosses. Also shown are the anthropogenic emissions e
A
(t) (Red Squares).
3.4. Influence of Native Effects
So, with the right parameters all investigated approaches
can reproduce the observations at Mauna Loa very well. But
all these models are based on different hypotheses and
boundary conditions, some of them are even in contradiction
to each other. Therefore, only one or none of them may be
right. Good conformity with observations alone is not a suf-
ficient criterion for testing the validity of a model, it must also
be in agreement with basic physical principles. They alone can
give us the physically consistent explanations for a carbon
cycle, which is dominated by more than 95% of native emis-
sions and underlies continuous environmental impacts. It is
also evident that this cycle is governed by the same principles
at paleoclimatic times as today with human emissions.
Thus, for the further considerations it seems reasonable first
to concentrate on three basic questions:
1. How could nature be in equilibrium before the Industrial
Era?
Some climate scientists consider the natural carbon ex-
change as a closed cycle, which happened in this way unaf-
fected over thousands of years without larger variations. But
when looking to the glacial and interglacial periods or only to
the Holocene we have to recognize that the atmospheric CO
2
concentration was always varying over longer and shorter
periods. Slow variations per se are no sign of non-equilibrium,
they can also result from varying emission strengths over time.
But an adaptation to such natural variations is not possible,
when emissions are only cumulating, as this is assumed in the
AF and Bern Models for anthropogenic emissions, which
never come to equilibrium. Thus, an adaptation to volcanic
activities, temperature variations or even to the seasonal
variations requires an absorption process for the native cycle,
which behaves more or less proportional to the respective
concentration C
P
(t) at pre-industrial times, in a similar way as
considered in the 3rd model for the anthropogenic emissions.
So, it is close by to presuppose also a first order process for
the native cycle, and the respective balance equation for
pre-industrial times then assumes the form, analogous to (10):
RP
P
P
P
tC
te
dt
tdC
τ
)(
)(
)( −=
(20)
with e
P
(t) as the emission rate and
τ
RP
as the residence time at
pre-industrial times. Equilibrium is achieved when the left
side of (20) is zero. Then the residence time becomes
τ
RP
=
C
P
(t)/e
P
(t).
The same relation was found from the simple flux model
with a residence time
τ
R0
= 3 yr at 1750. Such a residence or
absorption time for the natural cycle is in good agreement with
the observed seasonal variations and is also supported by the
14
C-decay as will be discussed in detail in subsection 5.7.3.
When CO
2
concentrations were continuously changing in
pre-industrial times we also have to inquire:
2. Can the natural cycle really be assumed to have been
constant over the last 270 yr?
Almost every day we recognize natural phenomena and
processes in form of significant perturbations or variations,
e.g., volcanic eruptions, earthquakes, El Niño - La Niña events,
internal and external oscillations, global warming or seasonal
variations.
All these phenomena have a direct influence on the natu-
rally caused fraction C
N
(t) of CO
2
in the atmosphere. There-
fore, the balance for the natural cycle also over the Industrial
Era has to be expressed explicitly by a time dependent emis-
sion rate e
N
(t) and also a time dependent residence time
τ
R
(t).
The latter can slightly be affected by internal or external
variations, but should not significantly deviate from
pre-industrial times or 1750. Otherwise the balance must obey
the same principal relation as in pre-industrial times with:
)(
)(
)(
)(
t
tC
te
dt
tdC
R
N
N
N
τ
−=
. (21)
Finally we have to ask:
3. Can the anthropogenic cycle be considered separately
from a natural cycle?
From the preceding discussion one may conclude that the
total balance equation for the respective models looks like





−−⋅
⋅
+







−=
+=
..1/)(
)'()(
)(
)(
)(
)(
)()()(
ModOrderCte
ModelBernttRte
ModelAFAFte
t
tC
te
dt
tdC
dt
tdC
dt
tdC
AAA
A
A
R
N
N
AN
τ
τ
(22)

Earth Sciences 2019; 8(3): 139-158 145
In all cases is this equation controlled by two or more in-
dependent time scales, a fast scale with
τ
R
≈
3 yr for the ab-
sorption of natural emissions and a slow scale with an infinite
decay for 48% of emissions in the AF Model, with 5 decay
times for different sinks in the Bern Model, and an adjustment
time of 46 yr in the 3rd model, all for the adaptation of the
atmosphere to additional anthropogenic emissions.
At least here it gets obvious that naturally and human
emitted molecules cannot be treated differently. As long as no
saturation in the uptake is observed, which is not the case (see
Appendix A), an additional emission by humans must underlie
the same absorption process as the natural emissions. A sepa-
ration is in startling contradiction to the Equivalence Principle,
and as a consequence of this principle only one absorption
time, τ
R
, with the same absorption behavior for human and
native emissions must exist.
4. Complete Carbon Cycle
The preceding considerations show that a realistic analysis
of the CO
2
exchange between the atmosphere and its adjacent
reservoirs has also to include natural variations due to tempe-
rature effects or temporal events. It has also to consider a com-
mon absorption of all natural and human contributions, which
are scaling proportional to the apparent CO
2
concentration and
which are represented by one unique decay time (see also:
Essenhigh [24]; Salby [7, 10]; Harde [6]; Berry [25]).
We summarize the main deviations from the previously
discussed accounting schemes by the following fundamental
principles:
1. Changes in the natural carbon cycle, which are due to a
continuous temperature increase over the Industrial Era,
are included in the balance equation (4) by a temperature
dependent term for the natural emissions and also a term
for the temperature dependent absorption.
2. Perturbations from an equilibrium concentration C
eq
due
to natural changes or additional anthropogenic emissions
are compensated for or controlled in the carbon cycle by
an absorption rate, which changes proportional to the
actual concentration C (first order process, see Eq. (6)).
3. Molecules emitted to the atmosphere can have a number
of different sources, natural and man-made sources, but
(up to now) they have only common natural sinks in
form of the oceans and continents, which do not differ-
entiate between the native or anthropogenic origin.
4. There exists no evidence that the absorption was sud-
denly saturating and the residence time
τ
R
jumping up by
one or two orders of magnitude from
τ
R0
to
τ
A
, when the
atmospheric concentration exceeded a level of 280 ppm.
τ
R
can only have changed continuously from pre-indu-
strial to present times from 3 to 4 yr, synchronously with
the atmospheric concentration and in agreement with (5)
and (9).
5. The observed exponential decay of
14
C in the atmosphere
after the stop of the atomic bomb tests in 1963 is a strong
indication for a first order absorption process of CO
2
by
land and oceans with a unique time constant determined
by the gross flux of CO
2
from the atmosphere to the
reservoirs (see Figure 5). Only such an absorption en-
sures that the carbon cycle can stabilize and react ade-
quately on any temporal perturbations like seasonal
variations or volcanic activities.
6. For parallel absorption processes by the oceans, by the
biosphere or rock weathering the absorptivity
α
is given
as the sum of the individual channels
α
i
with
α
R
=
α
1
+
α
2
+.. +
α
N
and
τ
R
= 1/
α
R
. The uptake is not restricted by
the slowest process as assumed in the Bern Model, but by
the sum of all processes with one unique absorptivity
α
R
for all molecules. The reciprocal of
α
R
is the residence
time
τ
R
of CO
2
in the atmosphere.
These principles are incorporated in a balance equation, the
General Conservation Law, which on the one side includes
temperature dependent and, thus, time dependent natural and
anthropogenic emissions, and on the other side considers a
temperature dependent unique residence time
τ
R
, which de-
scribes the collective or net absorption of all molecules. It
does not differentiate between a residence or adjustment time:
))((
)(
)())((
)(
tT
tC
tetTe
dt
tdC
R
AN
τ
−+=
. (23)
In first order the natural emission rate and the residence
time can be assumed to increase linearly with the temperature
anomaly
∆
T:
)())((
)())((
0
0
tTtT
tTetTe
RR
eNN
∆⋅+=
∆
⋅
+
=
τ
βττ
β
. (24)
β
e
and
β
τ
are the temperature coefficients of the natural
emission and the absorption time. In the general case of a
saturating uptake by the extraneous reservoirs
τ
R
will addi-
tionally change with C. But up to now any unequivocal satu-
ration effects cannot be identified (see Appendix A).
With the temperature anomaly
∆
T(t) and the anthropogenic
emissions e
A
(t) as represented in Figure 3, Eq.(23) can be
solved numerically.
Figure 8 shows the simulated CO
2
concentration in the
atmosphere (Green Graph) over a time period 1880 - 2016, for
which reliable temperature data are available (GISS [9]),
whereas the direct CO
2
measurements at Mauna Loa (Blue
Diamonds) started not before 1958. The temperature data
were used as moving average over ±5 yr. We achieve good
agreement with the observations for a natural emission rate e
N0
= 93.3 ppm/yr,
τ
R0
= 3 yr (both in agreement with (9)) and
temperature coefficients
β
e
= 10 ppm/yr/°C and
β
τ
= 0.37
yr/°C. Similar good results are obtained with larger
β
e
(up to
24 ppm/yr/°C) and smaller
β
τ
(
→
0) or vice versa with
β
τ
(up
to 0.74 yr/°C) and smaller
β
e
(
→
0). Thus, we have to assert
that as long as the natural and anthropogenic emission rates
and at least one of the temperature coefficients are not more
accurately known, we can only determine a combination of
these parameters, not their absolute values.
Figure 8 also displays a simulation for which the anthro-
pogenic emissions were set to zero (Magenta).

146 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
260
280
300
320
340
360
380
400
1880 1900 1920 1940 1960 1980 2000 2020
Year
CO
2
Concen tration C (ppm)
Mauna Loa
T-Dep. & Anthr. Emission
Only T-Dependance
Only Anthr. Emission
17 ppm
Figure 8. Calculated CO
2
concentration with temperature-dependent emis-
sion and absorption (Green). Compared against the observed record of CO
2
from Mauna Loa (Blue Diamonds). Simulation without anthropogenic emis-
sions (Magenta), and only human activities (Blue).
The difference between both curves results from the human
activities. These graphs evidently show that, based on (23), the
anthropogenic contribution to the observed CO
2
increase over
the last 150 years is significantly less than the natural influ-
ence. So, as an average over the period 2007- 2016 the an-
thropogenic emissions were contributing not more than 4.3%
to the total concentration of 393 ppm and thus, their fraction to
the atmospheric increase since 1750 of 113 ppm is not more
than 17 ppm or 15%. The dominating contribution with 85% is
determined by natural influences, in Figure 8 represented as
difference of the Magenta Graph to the 280 ppm grid-line.
The pure anthropogenic contribution to the atmospheric
concentration, which would result without temperature effects,
is shown by the Blue Graph on a constant background of 280
ppm. With a residence time of
τ
R0
= 3 yr human emissions
cannot contribute more than 14.5 ppm, and with an increas-
ing
τ
R
over the Industrial Era due to the temperature influence
it will slightly increase to 17 ppm, as displayed by the dif-
ference between the Green and Magenta Graphs (see red ar-
row). At equilibrium the relative contribution of human ac-
tivities to the total CO
2
concentration is always determined by
the anthropogenic to the total emission rate, independent of
the actual residence time (Eq.(23); Harde [6], Eq.(14)).
Note, a simulation without anthropogenic emissions, but
slightly increased temperature coefficients (
β
τ
= 0.48 yr/°C or
β
e
= 13.3 ppm/yr/°C) lifts the Magenta curve to coincide al-
most exactly with the Green graph. Thus, the observed evo-
lution at Mauna Loa could also be reproduced without in-
volvement of e
A
(t), contrary to the IPCC interpretations.
Up to now we were only considering the seasonally aver-
aged CO
2
measurements, but it is also worthwhile to look
closer to the monthly data at Mauna Loa (see Keeling et al. [5];
AR5 [1] Chap.6-Fig.6.3, p. 476) as displayed in Figure 9
(Magenta Diamonds). The “sawtooth” curve is an obvious
indication for the direct variation of the CO
2
emission and
uptake rates, driven by the solar activity and the temperature
over the seasons. Generally this modulation is attributed to the
greater land mass on the Northern Hemisphere, where the
uptake by photosynthesis predominantly occurs during the
growing season, while CO
2
release by heterotrophic processes
is more dominant over the other seasons.
300
320
340
360
380
400
420
1958 1968 1978 1988 1998 2008 2018
Year
CO
2
Co nce ntr atio n (ppm )
10
15
20
25
30
35
Air Tem peratu re (°C )
CO2-ML
T-Air
Figure 9. Monthly time series of measured CO
2
concentration at Mauna Loa
(Magenta Diamonds) and air temperature record at Hawaii (Blue Triangles).
However, apparently also local effects have a direct influ-
ence on this record. Figure 9 shows also the monthly averaged
air temperature at Hawaii (Blue Triangles) with seasonal
variations of 3 - 4°C (NOAA [26]). Almost synchronous
changes are found for the sea surface temperature (NOAA
[27]). The CO
2
concentration follows these temperature
variations with a delay of 6 - 7 months (see also Salby [7]).
A calculation with human emissions included and using the
modulated air temperature anomaly
∆
T(t) at Hawaii (NOAA
[26]) is shown in Figure 10 (Blue Diamonds). This excellent
agreement with the monthly Mauna Loa CO
2
measurements
(Magenta Diamonds) is obtained by applying a linear response
of the natural emissions to the modulated temperature anom-
aly, and assuming a residence time with an initial value of
τ
R0
= 3
yr and an averaged slightly nonlinear temperature increase
∆
T
1.5
(t), which accounts for the nonlinear response of oceanic
emissions and the uptake of CO
2
(see Subsection 5.6). It
should be mentioned that the averaged air temperature at
Hawaii is distinguished by a quite linear increase over time.
Therefore, different to Figure 8 also smaller deviations at
about 1970 are completely disappearing.
300
320
340
360
380
400
420
1958 1968 1978 1988 1998 2008 2018
Year
CO
2
Concentration (ppm)
CO2-Measurement at ML
CO2-Simulation
τ
R0
= 3 yr
Figure 10. Monthly CO
2
concentration integrated from the balance equation
with temperature-dependent emission and absorption and an initial residence
time of 3 years (Blue Triangles). Compared against the observed record of
CO
2
from Mauna Loa (Magenta Diamonds).
A detailed analysis of the Mauna Loa curve (Salby [7, 10,
11]) and independent cross-correlation investigations of
thermally induced emission (Humlum et al. [28]) indicate that
the actual absorption time of 3-4 yr, as derived from (9) and
based on the IPCC's own estimates, may even be significantly
shorter, as short as only 8–12 months, this at least over the

Earth Sciences 2019; 8(3): 139-158 147
vegetation growths' periods on land and in oceans, but also in
areas such as the North Atlantic with cold downwelling waters.
Under such conditions, in the same way as the residence time
is getting shorter, the total emission rate gets larger (generally
the most uncertain parameter of the guessed rates). As the
admixture of human generated CO
2
is given by the percentage
of anthropogenic to total emissions, also this fraction further
decreases. So, with an absorption time of
τ
R0
= 1 yr and a total
emission rate of e
T
= 298 ppm/yr the anthropogenic emissions
of 4.7 ppm/yr do not contribute more than 1.6% or 6 ppm to
the atmospheric CO
2
. However, for a more conservative as-
sessment and in agreement with the IPCC's estimates (AR5 [1],
Chap.6-Fig. 6.1) we further emanate from conditions as de-
rived from the simulations of Figures 8 and 10 with
τ
R0
= 3 yr.
5. Discussion
All presented schemes for simulating the atmospheric CO
2
concentration are based on the balance equation considering
the fluxes from extraneous reservoirs to the atmosphere and
vice versa. However, as widely used in the literature, the ap-
proaches in Section 3 restrict these fluxes on anthropogenic
emission-absorption cycles, whereas natural emissions and
their uptake are supposed to be the same since 270 years, and
thus, any changes in these fluxes are simply disregarded in the
total balance. In addition, two of these approaches use a uni-
lateral balance for this cycle, only controlled by the influxes
and independent of the actual atmospheric concentration.
These deficits have some fatal consequences in the further
interpretation of the carbon cycle.
5.1. New Time Scale
Sole consideration of anthropogenic fluxes is identical with
the introduction of a new time scale for the uptake of man-
made emissions (see subsection 3.4). Since these emissions
and also their changes are more than one order of magnitude
too small to explain directly the observed concentration
changes over recent years, carbon-cycle models just introduce
an additional buffer factor, the 'adjustment' time. Such new
time scale ensures a sufficiently long cumulation time of the
molecules in the atmosphere to attain a concentration level,
which is in agreement with the observations. But it looks quite
dubious that 280 ppm, equivalent to the environmental frac-
tion, are exchanged with extraneous reservoirs within 3-4 yr,
and for about 45% of additional human emissions an accu-
mulation over thousands of years in the atmosphere is as-
sumed.
Effectively represents an 'adjustment' time
τ
A
nothing more
than an amplification factor for the anthropogenic emission
rate to fit with the observations. This is obvious for the ap-
proach described in subsection 3.3 (see Eqs.(18) and (19)),
where the integrated net flux is proportional to e
A
(t) and
τ
A
.
But implicitly this is also concealed in the other two schemes.
In the case of a constant airborne fraction the 'adjustment'
time for the fraction
∆
e
A
= AF
⋅
e
A
(t), cumulating in the at-
mosphere, is even infinite. Under such conditions already any
additional constant emission contributes to a linear increase of
the concentration, whereas any changes in the emission rate
only slightly affect the further shape of this increase. In such
case - with an infinite lifetime of additionally emitted mole-
cules in the atmosphere and a given emission rate for FFE
from CDIAC [4] and for LUC from Le Quéré et al. [2] (see
Figure 2) - AF is now the only free parameter controlling the
size and steepness of the concentration growth rate (see (14)).
From a simple balance of the increasing concentration and
the total emissions we derive a value for AF of 42%. A realis-
tic model then should reproduce the observations with this
airborne fraction. But our previous simulations (see Figure 4)
showed that this does not fit in size and shape. The discrep-
ancy would even further increase, when additional natural
emissions due to a globally increasing temperature have to be
considered. Good consistency can only be found with a re-
duced anthropogenic emission rate and a further adapted AF.
In the more elaborate Bern Model not only one, but even
five new time scales are introduced. This is expressed by the
response function with its five decay times (see (15)). While
the last term in (15) is similar to the decay described by the
residence time
τ
R
, the others shall represent the limited uptake
by different extraneous reservoirs with different time con-
stants, one also infinite. A simulation with this response func-
tion, which is equivalent with a time dependent airborne
fraction, reproduces quite well the general trend of the in-
creasing concentration (see Figure 6), but in direct analogy to
3.1 and 3.3 satisfactory agreement with the free-air meas-
urements at Mauna Loa is only obtained when reducing the
official anthropogenic emissions and neglecting any addi-
tional natural emissions.
5.2. First Order Absorption Process
Approaches 3.1 and 3.2 use a quite exceptional definition
for the in- and outfluxes between the atmosphere and adjacent
reservoirs. The respective absorption rates are considered to
be independent of the actual atmospheric concentration, in-
stead they are supposed to scale in direct proportion to the
emission rate either with fixed or time variable airborne frac-
tion. As long as this emission is not zero, the atmospheric
concentration further increases, independent of its actual level;
and also at constant emissions the system never reaches steady
state.
However, when such unusual correlation between emission
and absorption rates would really exist, this cannot only be
restricted to anthropogenic emissions and switched off for
native emissions. Due to the equivalence principle it should be
valid for both. Also for times before 1750 the absorption
process cannot have been completely different to that over the
Industrial Era or was suddenly changing with the first an-
thropogenic emissions.
The dramatic consequences when applying the Bern Model
to the total emissions are illustrated in Figure 11. This would
result in an exploding atmospheric CO
2
concentration (Green
Line) up to levels found 500 Mio. yr ago, and it would never
allow steady state conditions as supposed before 1750. In av-
erage such an increase over the last 270 yr is equivalent to an
AF = 35%.

148 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
0
2000
4000
6000
8000
10000
1750 1800 1850 1900 1950 2000
Year
CO
2
Co nce ntr atio n C (ppm)
Mauna Loa
B-M: e_N+e_A
B-M: e_A - 0.18 ppm/yr
Figure 11. Simulation of the CO
2
concentration based on the Bern Model
assuming the total emissions (Green). Also shown is a calculation for only
anthropogenic emissions (Green Crosses). Compared against the observed
record of CO
2
from Mauna Loa (Blue Diamonds).
An uptake process only scaling with the emission rate and
not the concentration looks completely unrealistic (see also
subsection 3.4). It must be dismissed, even when the simula-
tion for the anthropogenic emissions alone (Green Crosses)
pretends good agreement with the Mauna Loa observations
(Blue Diamonds).
A balance which only adds up net emissions, and denies an
increasing absorption rate with inclining atmospheric con-
centration, is in contradiction to real observations and hurts
fundamental physical laws. CO
2
is not a noble gas, which in-
differently accumulates in an open compartment after an
emission, but it is dissolved in oceans and converted via
photosynthesis to organic molecules. This uptake obeys a first
order absorption process and scales with the actual concen-
tration or the difference to an external reservoir
1
. It prevails as
long as its concentration C or the difference remains nonzero,
i.e., indefinitely.
Different to subsections 3.1 and 3.2 approach 3.3 already
emanates from a first order absorption process, but it is also
restricted only to anthropogenic concentration changes. Ba-
sically an 'ansatz' in (22), third case, and considering changes
relative to some reference concentration is correct, when this
also includes natural variations over the considered time pe-
riod. But the fundamental flaw in 3.3 is to introduce a new,
independent absorption constant, the adjustment time, for the
uptake of the additional emissions instead of using the same
absorption process, which already controls more than 95% of
the carbon cycle, and this - due to physical causalities - at pre-
industrial times in the same manner as over the Industrial Era.
5.3. Environment as a Net Sink
From the observations of the atmospheric concentration and
estimates of anthropogenic emissions it is widely inferred that
not natural but anthropogenic origin is responsible for the
increasing atmospheric CO
2
. Writing the global atmospheric
carbon budget in the form (see e.g., Cawley [22])
1
Diffusion processes which act proportional to the concentration difference be-
tween two reservoirs, can be assumed to consist of an outflux proportional to the
atmospheric concentration C
a
and an influx proportional to the concentration of the
reservoir C
r
.
0)( <−=−
TNA
aete
dt
dC
, (25)
it is obvious that the net environmental flux, e
N
- a
T
can quite
well be assessed without needing to know the absolute mag-
nitudes of e
N
or a
T
, quantities which on their parts are highly
uncertain. Since the concentration changes dC/dt are smaller
than the anthropogenic emission rate, the left side of (25) is
negative and thus, the environmental uptake a
T
must be larger
than the natural emissions e
N
. From this correct statement that
the environment has acted as a net sink throughout the Indus-
trial Era, however, often wrong conclusions are derived that
nature cannot be the reason for any observed CO
2
increase.
For a moment let us assume e
N
may be the emission rate at
which the system was in balance, and e
A
may represent an
additional rate of human or native emissions or of both. In
reality and in all discussed models with airborne fraction or
with first order uptake the concentration growth rate develops
slower than these additional emissions and thus, a
T
gets larger
than e
N
. So, with both sides of (25) getting negative this only
means that with additional emissions, native or humans, na-
ture also acts as a further increasing sink (compared to a pre-
vious equilibrium). As long as any arbitrary fraction of human
emission is involved, the environment is always a net sink.
This is true per definition, since up to now no artificial uptake
exists. But this does not say anything about any additional
native emissions over the Industrial Era, since emission and
uptake are largely independent processes and the absorption
does not impede nature from increasing its own emissions.
A similar strange logic is used by Richardson [29], who
considers mean values of the net atmospheric accumulation
<dC/dt> = 1.7 ppm/yr and of the human emissions <dC
A
/dt> =
e
A
(t) = 3 ppm/yr in a balance
0/// <=− dtdCdtdCdtdC
NA
, (26)
in which with <dC
A
/dt> = e
A
(t) a priori any anthropogenic
absorptions are embezzled. From this relation it is also in-
ferred that the average natural contribution <dC
N
/dt> has been
to remove CO
2
from the atmosphere, this with the same wrong
conclusion as Cawley that the long term trend of rising CO
2
could not be explained by natural causes. This argument is
disproved with Figures 8 and 10. The fact that the environ-
ment has acted as a net sink throughout the Industrial Era is a
consequence of a dynamic absorption rate, which is only
controlled by the total CO
2
concentration C = C
N
+ C
A
. So,
also with additional native emissions and/or temperature
changes in the absorptivity the total uptake always tries - with
some time delay - to compensate for the total emissions which,
of course, also include the anthropogenic fraction. In other
words: Since nature cannot distinguish between native and
human emissions, nature is always a net sink as long as human
emissions are not zero. Thus, except for shorter temporary
events like volcanic activities the environment will generally
act as a net sink even in the presence of increasing natural
emissions.
To equate <dC
A
/dt> in (26) exclusively with human emis-
sions violates conservation of mass. Only when replacing

Earth Sciences 2019; 8(3): 139-158 149
<dC
A
/dt> by <e
A
(t) - C
A
/
τ
R
>, eq.(26) satisfies the Conservation
Law, and when additionally replacing <dC
N
/dt> by <e
N
(t) -
C
N
/
τ
R
> eq.(26) converts to (23).
Again we emphasize that a separate treatment of the native
and human cycle with their respective concentrations C
A
and
C
N
is possible if and only if no contributions are missing and
the two balances are linked together in one rate equation with
only one unitary residence time.
5.4. Too Simple Model
Often climate scientists argue that changes of CO
2
in the
atmosphere cannot be understood without considering
changes in extraneous systems (see e.g., AR5 [1], Chap.6;
Köhler et al. [8]), and they characterize the Conservation Law
as a flawed 1-box description - because, a single balance
equation would not account for details in other reservoirs. In
particular, they refer to carbonate chemistry in the ocean,
where CO
2
is mostly converted to bicarbonate ions. As only
about 1% remains in the form of dissolved CO
2
, they argue
that only this small fraction could be exchanged with the at-
mosphere. Due to this so-called Revelle effect, carbonate
chemistry would sharply limit oceanic uptake of anthropo-
genic CO
2
.
In regard to understanding changes of CO
2
in the atmos-
phere, changes in extraneous systems are only qualifiedly of
interest. The governing law of CO
2
in the atmosphere (4) and
in more elaborate form (23) is self contained. With the inclu-
sion of the surface fluxes e
T
(t) and a
T
(t) = C /
τ
R
(t), which
account for influences of the adjacent reservoirs on atmos-
pheric CO
2
, details of other extraneous reservoirs of carbon
are entirely irrelevant. This feature of the governing physics is
not only powerful, but fortunate.
Concerning carbonate chemistry, it is noteworthy that, in
the Earth’s distant past, CO
2
is thought to have been almost
2000% as great as its present concentration (e.g., Royer et. al.
[30]). Most of that was absorbed by the oceans, in which
carbon today vastly exceeds that in the atmosphere. According
to the IPCC, even in modern times the oceans account for 40%
of overall absorption of CO
2
(AR5 [1], Fig.6.1). In relation to
other sinks, their absorption of CO
2
is clearly not limited (see
Appendix A). Of that 40%, over the Industrial Era anthropo-
genic CO
2
represents less than 1%. Contrasting with that
minor perturbation in absorption is oceanic emission of CO
2
.
Through upwelling of carbon-enriched water, the oceans sig-
nificantly enhance natural emission of CO
2
(Zhang [31]).
Different to our approach, which takes into account human
and also naturally varying emissions and absorptions, the
models in Section 3 emanate from such a simple and appar-
ently flawed description that over thousands of years CO
2
was
circulating like an inert gas in a closed system, and only with
the industrial revolution this closed cycle came out of control
due to the small injections by human emissions.
5.5. Different Time Constants
The different time scales introduced with the models in
Section 3 represent different absorption processes for the up-
take of atmospheric CO
2
molecules by the extraneous reser-
voirs. From physical principles it is impossible that an ab-
sorption process would differentiate between naturally and
anthropogenically emitted molecules. The temporal absorp-
tion or sequestration - except for smallest corrections due to
isotopic effects - is for all molecules identical.
The absorption also cannot decline unexpectedly by more
than one order of magnitude with the begin of the Industrial
Era or because of an additional emission rate of a few %.
Observations show that no noticeable saturation over recent
years could be found (Appendix A).
Oceans and continents consist of an endless number of
sources and sinks for CO
2
which act parallel, emitting CO
2
into the atmosphere and also absorbing it again. In the same
way as the different emission rates add up to a total emission,
the absorption rates with individual absorptivities
α
i
- and
each of them scaling proportional to the actual CO
2
concen-
tration - add up to a total uptake as a collective effect
CC
CCCa
RN
NT
⋅=⋅+++=
+
+
+
=
αααα
α
α
α
)...(
...
21
21
. (27)
Collective absorption thus leads to exponential decay of
perturbation CO
2
at a single rate
NRR
ααατα
+++== .../1
21
. (28)
This decay rate is faster than the rate of any individual sink
and it prevails as long as its concentration C or its difference to
external reservoirs remains nonzero (see: Harde [6]; Salby
[11]).
The above behavior is a consequence of the Conservation
Law and in contrast to the Bern Model, where decay proceeds
at multiple rates. A treatment of CO
2
with a multiple expo-
nential decay obeys the following:
N
t
N
tt
CCC
eCeCeCC
N
+++= +++=
−−−
...
...
21
02010
21
ααα
. (29)
Then differentiation gives:
C
CCC
eCeCeC
dt
dC
N
NN
t
NN
tt
N
⋅+++−≠ −−−=
−−−=
−−−
)...(
...
...
21
2211
0202101
21
ααα ααα
ααα
ααα
(30)
At multiple decay rates the corresponding sinks operate, not
collectively, but independently. After a couple of their decay
times, the fastest sinks become dormant. Overall decay then
continues only via the slowest sinks, which remove CO
2
gradually. It is for this reason that such a treatment leaves
atmospheric CO
2
perturbed for longer than a thousand years
(Figure 5). In contrast, the behavior required by the Conser-
vation Law decays as fast or faster than that of the fastest sink
(see (28)).
The observed decay of
14
C shows that the corresponding
absorption is determined by a single decay time and operates
on a time scale of only about one decade (see Figure 5). This

150 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
scale is the same for the natural carbon cycle as for the an-
thropogenic cycle. Therefore, it is unrealistic to differentiate
between a residence time and different adjustment times.
In this context it should be noticed that due to re-emissions
of
14
CO
2
from extraneous reservoirs the real residence time of
14
CO
2
in the atmosphere as well as that of the other isoto-
pologues of CO
2
can only be shorter, even shorter than a
decade (for details see subsection 5.7.3 and Appendix B).
5.6. Temperature Dependence
According to (9) or (10) we see that with increasing at-
mospheric concentration over the Industrial Era from 280 to
400 ppm either the residence time must be increased with
temperature from 3 to about 4 yr, or
τ
R
is considered to be
constant and the total emissions were rising from 93 to about
130 ppm/yr, synchronously increasing the concentration. Both
these limiting cases are in agreement with a temperature
anomaly of about 1.2 °C over this period (see GISS [9]), when
we assume the maximum temperature coefficients
β
τ
= 0.74
yr/°C or
β
e
= 24 ppm/yr/°C. However, generally both tem-
perature induced natural emissions as well as temperature
dependent absorptions together will dictate the inclining
concentration in the atmosphere.
In any way, as we see from Figure 8, is the CO
2
concentra-
tion dominantly empowered by the temperature increase; with
only one unique decay process not human activities but almost
only natural impacts have to be identified as the main drivers
for the observed CO
2
increase in the atmosphere and also for
the continuous climate changes over the past and present
times.
The various mechanisms, along with their dependence on
temperature and other environmental properties, could not
have remained constant during the pre-industrial era. This
inconsistency invalidates the fundamental assumption, that
natural emission and absorption during the pre-industrial pe-
riod did remain constant. Even less this is valid over the In-
dustrial Era, a period which is characterized by the IPCC as
the fastest rise in temperature over the Holocene or even the
last interglacial.
So, the CO
2
partial pressure in sea water approximately
changes with temperature as (pCO
2
)
sw
(T) = (pCO
2
)
sw
(T
0
)*
exp[0.0433*(T-T
0
)] (see: Takahashi et al. [32]) and thus, an
increase of 1°C causes a pressure change of about 18 µatm,
which amplifies the influx and attenuates the outflux. From
observations over the North Atlantic Ocean (see, Benson et al.
[33]) it can be estimated that a pressure difference
∆
pCO
2
between the atmosphere and ocean of 1 µ atm contributes to a
flux change of
δ
f
in
≈ 0.075 mol/m
2
/yr = 3.3 g/m
2
/yr. Therefore,
with an Earth's surface of 320 Mio. km
2
covered by oceans and
a pressure change of
∆
pCO
2
= 18 µatm, under conventional
conditions the native influx from oceans to the atmosphere
already increases by
∆
f
in
≈ 19 Pg/yr or 2.4 ppm/yr for an av-
erage temperature incline of 1°C. An even stronger variation
can be expected for the land vegetation with an increased
decomposition and reduced uptake of CO
2
at rising tempera-
ture (Lee [34]; Salby [11]).
Together this causes an incline of the atmospheric CO
2
level
which is larger than all apparent human activities, but its
contribution is completely neglected in the official accounting
schemes.
Also melting permafrost and emissions of volcanoes on
land and under water as well as any emissions at earthquakes
are not considered. In addition, actual estimates of dark res-
piration suggest that under global warming conditions
whole-plant respiration could be around 30% higher than ex-
isting estimates (Huntingford et al. [35]). This longer list of
different native events and effects is completely embezzled in
the favored IPCC models.
Equally inconsistent is the presumption that additional up-
take of anthropogenic CO
2
, which represents less than 1% of
the total over the Industrial Era, has, somehow, exceeded the
storage capacity of oceans and other surface and sub-surface
reservoirs, capacity which is orders of magnitude greater. A
reduced absorption is rather the consequence of global
warming than of saturation. Due to Henry's law and its tem-
perature dependence not only the partial pressure in sea water
increases, but also the solubility of CO
2
in water declines
exponentially with temperature and, thus, reduces the CO
2
uptake. Often is this effect incorrectly misinterpreted as
saturation caused by a limited buffer capacity and dependent
on the concentration level. But here we consider an uptake
changing with temperature, as this is known for chemical re-
actions, where the balance is controlled by temperature. How
strongly the biological pump (see Appendix A) and photo-
synthesis on land is also controlled by temperature, is only
incompletely known, but obviously they are also varying
slightly exponentially with temperature (Lee [34]).
Figure 12 displays a scatter plot supporting the close corre-
lation of the atmospheric CO
2
concentration with the land-
ocean temperature anomaly (GISS [9]). The latter is con-
trolled by more than 60% by the solar influence and less than
40% by CO
2
as greenhouse gas feedback (Harde [36, 37]).
y = 326 e
0.2x
R
2
= 0.89
310
330
350
370
390
410
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Land-Ocean Temperature Anomaly (°C)
Mauna Loa CO
2
Concentration C (ppm)
Figure 12. Scatter plot of Mauna Loa CO
2
concentration (Blue Diamonds)
and trend curve (Black Graph) versus land-ocean temperature anomaly.
5.7. IPCC Arguments for a Human-Made CO
2
Increase
The preceding discussion has made clear that a consistent
description of the carbon-cycle, which is in full agreement
with all observations and physical relations, can only emanate
from unitary treatment of all CO
2
molecules - native and hu-
man-caused ones. This means: the anthropogenic carbon cycle

Earth Sciences 2019; 8(3): 139-158 151
cannot be separated from the natural cycle; it exists only one
single residence time of CO
2
molecules in the atmosphere; and
the uptake of all these molecules obeys a first order principle.
But we still have to scrutinize how far this description is
really in contradiction to the key arguments (lines of evidence)
as adduced by the IPCC for a human caused CO
2
incline, or
how far these arguments also hold for our alternative ap-
proach.
In AR5 [1], Subchap.6.3.2.3 we read:
"With a very high confidence, the increase in CO
2
emissions
from fossil fuel burning and those arising from land use
change are the dominant cause of the observed increase in
atmospheric CO
2
concentration."
IPCC then lists five arguments to support this conclusion
(references in the following IPCC-citations are not listed as
additional references in this article).
5.7.1. Decrease in Atmospheric O
2
"The observed decrease in atmospheric O
2
content over
past two decades and the lower O
2
content in the northern
compared to the SH are consistent with the burning of fossil
fuels (see Figure 6.3 and Section 6.1.3.2; Keeling et al.,
1996; Manning and Keeling, 2006)".
This is barely a supporting argument for a dominantly
man-made CO
2
increase, since this 'line of evidence' is in the
same way valid for our approach, which evidently includes the
same amount of anthropogenic emissions. Burning of fossil
fuels removes oxygen from the atmosphere in a tightly defined
stoichiometric ratio dependent on the fuel carbon content.
This content is the same in our balance as in the IPCC models,
therefore, the respective O
2
decay rate and on the other hand
the CO
2
growth rate due to combustion is also the same, in-
dependent of any additional emissions of natural origin. The
fundamental difference to the IPCC's assumption is that the
anthropogenic emissions do not cumulate in the atmosphere
for longer times or for ever. They have the same residence
time as native CO
2
, in average 4 yr or shorter, and therefore
they only contribute 15% or even less to the observed increase
since 1750.
In this context it should also be clear that CO
2
and O
2
be-
have just anti-cyclic in the photosynthesis and respiration cy-
cle. Also the biochemical reactions in the atmosphere are
completely different. CO
2
is a non-reacting gas in the atmos-
phere, while O
2
preferentially oxidizes other materials and is
tied in chemical compounds. All these reactions are directly
controlled by the temperature. Compared to the atmospheric
oxygen content of about 21% a decrease of 80 ppm over 20 yr
is relatively small, it is not more than 0.4‰. As long as this O
2
cycle is not better known, an observed decline in atmospheric
oxygen gives only little evidence for a dominantly human
caused CO
2
increase. At best it can confirm the CDIAC-data,
which are the same in our approach as in the IPCC models.
5.7.2. Lower
13
C/
12
C Isotope Ratio in Fossil Fuels
"CO
2
from fossil fuels and from the land biosphere has a
lower
13
C/
12
C stable isotope ratio than the CO
2
in the at-
mosphere. This induces a decreasing temporal trend in the
atmospheric
13
C/
12
C ratio of atmospheric CO
2
concentra-
tion as well as, on annual average, slightly lower
13
C/
12
C
values in the NH (Figure 6.3). These signals are measured
in the atmosphere".
Also this is no supporting argument for a dominantly
man-made CO
2
increase, as with our approach we are also
expecting such declining
13
CO
2
concentration. The
13
C/
12
C
ratio in the atmosphere or its normalized ‰-difference
(δ
13
C)
atm
is measured at Mauna Loa and at the South Pole
atmospheric station (see AR5 [1], Figure 6.3). At Mauna Loa,
e.g., it shows an average decrease of 0.7‰ from -7.6‰ in
1980 to -8.3‰ in 2010. Over these 30 years was the anthro-
pogenic emission rate increasing by 1.8 ppm/yr from 2.5
ppm/yr in 1980 to 4.3 ppm/yr in 2010 (CDIAC [4]). With re-
spect to the total emission rate this corresponds to an increase
of 1.8 %.
Owing to the equivalence principle fossil fuel emissions
cannot cumulate in the atmosphere but will be absorbed with
the same probability like naturally emitted CO
2
molecules.
Thus, in first order the
13
C/
12
C ratio in the atmosphere can only
be diluted proportional to the leaner
13
C concentration and
proportional to the fraction of the man-made flux to the total
flux. Smaller corrections will result from the fractionation for
lighter molecules and a slightly higher emission probability
for molecules, which were just taken up (re-emission, see next
item).
Since the fossil fuel emissions have a leaner difference
(δ
13
C)
fuel-atm
= -18 ‰ compared to the atmosphere, or
(δ
13
C)
fuel-VPDB
= -25 ‰ with respect to the international VPDB
carbonate standard (Coplen [38]), the rising human emissions
over the 30 yr interval can only have contributed to a decline
of ∆ = (δ
13
C)
fuel-atm
×1.8% = -18‰×1.8% = -0.32 ‰ or a
(δ
13
C)
atm
= -7.92‰ in 2010. Thus, the difference to -8.3‰,
which is more than 50%, in any case must be explained by
other effects.
One possible explanation for a faster decline of (δ
13
C)
atm
to
-8.3‰ can be - even with oceans as source and an
13
C/
12
C ratio
in sea water greater than in air (particularly in the surface layer)
- that the lighter
12
CO
2
molecules are easier emitted at the
ocean's surface than
13
CO
2
, this with the result of a leaner
13
C
concentration in air and higher concentration in the upper
water layer (see also: Siegenthaler & Münnich [39]). From
water we also know that its isotopologues are evaporated with
slightly different rates.
Such behavior is in agreement with the observation that
with higher temperatures the total CO
2
concentration in the
atmosphere increases, but the relative
13
CO
2
concentration
decreases. This can be observed, e.g., at El Niño events (see:
M. L. Salby [40], Figure 1.14; Etheridge et al. [41]; Friedli et
al. [42]).
We also remind at the Mauna Loa curve, which shows for
the total emissions a seasonal variation with an increasing CO
2
concentration from about October till May and a decline from
June to September. The increase is driven by respiration and
decomposition mainly on the Northern Hemisphere (NH) as
well as the temperature on the Southern Hemisphere (SH) and

152 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
also local temperature effects. The (δ
13
C)
atm
value is just
anti-cyclic to the total CO
2
concentration (AR5 [1], Figure 6.3)
with a minimum at maximum CO
2
concentration and with
seasonal variations of 0.3 - 0.4‰, the same order of magnitude
as the fossil fuel effect.
An increase of
13
C in the upper strata of oceans also results
from an increased efficiency of photosynthesis for lighter CO
2
.
Plankton accumulates this form and sinks to lower layers,
where it decomposes and after longer times is emitted in
higher concentrations with stronger upwelling waters par-
ticularly in the Eastern Tropic Pacific. It is also known that the
13
C concentrations are by far not equally distributed over the
Earth's surface. Thus, it can be expected that with volcanic and
tectonic activities different ratios will be released.
So, without any doubts fossil fuel emissions will slightly
dilute the
13
CO
2
concentration in air. But presupposing regular
conditions for the uptake process (equivalence principle) they
contribute less than 50% to the observed decrease. The dif-
ference has to be explained by additional biogeochemical
processes. Particularly the seasonal cycles and events like El
Niños are clear indications for a stronger temperature con-
trolled modulation of the (δ
13
C)
atm
value. Therefore is an ob-
served decline of the
13
C/
12
C ratio over recent years by far not
a confirmation of an anthropogenic global warming (AGW)
theory.
Also the widely spread but wrong declaration that "about
half of the emissions remained in the atmosphere since 1750"
and "the removal of all the human-emitted CO
2
from the at-
mosphere by natural processes will take a few hundred thou-
sand years (high confidence)" (see AR5 [1], Chap.
6-Summary and Box 6.1) can be simply refuted by the isotope
measurements at Mauna Loa. If the 113 ppm CO
2
increase
since 1750 (28.8% of the present concentration of 393 ppm -
average between 2007 and 2016) would only result from
human impacts and would have cumulated in the atmosphere,
the actual (δ
13
C)
atm
value should have dropped by ∆ =
(δ
13
C)
fuel-atm
×28.8% = -18‰×28.8% = -5.2‰ to (δ
13
C)
atm
≈
-7‰ -5.2‰ = -12.2‰, which by far is not observed. (δ
13
C)
atm
in 1750 was assumed to have been -7‰.
5.7.3. Fossil Fuels are Devoid of Radiocarbon
"Because fossil fuel CO
2
is devoid of radiocarbon (
14
C),
reconstructions of the
14
C/C isotopic ratio of atmospheric
CO
2
from tree rings show a declining trend, as expected
from the addition of fossil CO
2
(Stuiver and Quary, 1981;
Levin et al., 2010). Yet nuclear weapon tests in the 1950s
and 1960s have been offsetting that declining trend signal
by adding
14
C to the atmosphere. Since this nuclear weapon
induced
14
C pulse in the atmosphere has been fading, the
14
C/C isotopic ratio of atmospheric CO
2
is observed to re-
sume its declining trend (Naegler and Levin, 2009; Graven
et al., 2012)".
For
14
C we can adduce almost the same comments as listed
for
13
C. Fossil CO
2
devoid of
14
C will reduce the
14
C/C ratio of
the atmosphere, this is valid for our approach in the same
manner as for the IPCC schemes. But, as no specific accu-
mulation of anthropogenic molecules is possible (equivalence
principle), this decline can only be expected proportional to
the fraction of fossil fuel emission to total emission. Before
1960 this was not more than 1% and actually it is about 4.3%.
14
C is continuously formed in the upper atmosphere from
14
N through bombardment with cosmic neutrons, and then
rapidly oxidizes to
14
CO
2
. In this form it is found in the at-
mosphere and enters plants and animals through photosyn-
thesis and the food chain. The isotopic
14
C/C ratio in air is
about 1.2⋅10
-12
, and can be derived either from the radioactiv-
ity of
14
C, which with an average half-lifetime of 5730 yr
decays back to
14
N by simultaneously emitting a beta particle,
or by directly measuring the amount of
14
C in a sample by
means of an accelerator mass spectrometer.
Fossil fuels older than several half-lives of radiocarbon are,
thus, devoid of the
14
C isotope. This influence on radiocarbon
measurements is known since the investigations of H. Suess
[43] who observed a larger
14
C decrease (about 3.5%) for trees
from industrial areas and a smaller decline for trees from un-
affected areas. This so-called Suess or Industrial effect is
important for reliable age assignments by the radiocarbon
method and is necessary for respective corrections. But for
global climate considerations it gives no new information, it
only confirms the calculations based on the human to total
emission rate (see above), and it clearly shows that an as-
sumed accumulation of anthropogenic CO
2
in the atmosphere
contradicts observations.
More important for climate investigations is that after the
stop of the nuclear bomb tests 1963
14
C could be used as a
sensitive tracer in the biosphere and atmosphere to study
temporal carbon mixing and exchange processes in the carbon
cycle. As the bomb tests produced a huge amount of thermal
neutrons and almost doubled the
14
C activity in the atmos-
phere, with the end of these tests the temporal decline of the
excess radiocarbon activity in the atmosphere can well be
studied. This decline is almost completely independent of the
radioactive lifetime, but practically only determined by the
uptake through extraneous reservoirs.
Such decline has already been displayed in Figure 5 as
fractionation-corrected ‰-deviations ∆
14
CO
2
from the Oxalic
Acid activity corrected for decay, this for a combination of
measurements at Vermunt and Schauinsland (Magenta Dots
and Green Triangles; data from Levin et al. [17]). The decay is
well represented by a single exponential with a decay constant
of about 15 yr (Dashed Blue). For similar observations see
also Hua et al. [18] and Turnbull et al. [19]. Thus, the decay
satisfies the relation
14
14
14
'
1' C
dt
dC ⋅−=
τ
, (31)
where C'
14
represents the excess concentration of radiocarbon
above a background concentration in the atmosphere. It cor-
responds to absorption that is proportional to instantaneous
concentration with an apparent absorption time
τ
14
slightly
more than a decade.
Because CO
2
is conserved in the atmosphere, it can change
only through an imbalance of the surface fluxes e
T
and a
T
. This

Earth Sciences 2019; 8(3): 139-158 153
holds for all isotopologues of CO
2
in the same way. For this
reason, its adjustment to equilibrium must proceed through
those influences. They are the same influences that determine
the removal time of CO
2
in the atmosphere. If CO
2
is per-
turbed impulsively (e.g., through a transient spike in emission),
its subsequent decay must track the removal of perturbation
CO
2
, C', which in turn is proportional to its instantaneous
concentration. Determined by the resulting imbalance be-
tween e
T
and a
T
, that decay is governed by the perturbation
form of the balance equation:
'
1' C
dt
dC
R
⋅−=
τ
, (32)
which is the same form as the observed decay of
14
C following
elimination of the perturbing nuclear source. But there is still
one important difference between these equations.
Eq.(32) is the perturbation form of (23) with a decay time
τ
R
,
the residence time, because 1/
τ
R
describes the rate at which
CO
2
is removed from the atmosphere, this as the result of the
balance between all absorption and emission processes.
In contrast to this describes (31) a decay process, which
implicitly also considers some back-pumping of radiocarbon
to the atmosphere (see Appendix B, (37)). So, from all
14
C that
is removed from the atmosphere with the time constant
τ
R
- in
the same way as all isotopes -, only some smaller fraction is
completely sequestered beneath the Earth's surface by a single
absorption process. A substantial fraction is therefore returned
to the atmosphere through re-emission (e.g., through decom-
position of vegetation which has absorbed that
14
C), and in
average it takes several absorption cycles to completely re-
move that
14
C from the atmosphere. This simply modifies the
effective absorption for radiocarbon, but with a resulting de-
cay which remains exponential (see Figure 5). Unlike any
dilution effect by fossil fuel emission, which is minor (see
Appendix B), this re-emission slows decay over what it would
be in the presence of pure absorption alone. Therefore is the
apparent absorption time - as derived from the
14
C decay curve
- longer than the actual absorption time.
In this context we emphasize that apart from some minor
influence due to fractionation all CO
2
isotopologues are in-
volved in the same multiple re-emission cycles. But in (23) or
(32) this is already considered in the total balance via the
emission rates, for which it makes no difference, if the same or
meanwhile exchanged molecules are recycled to the atmos-
phere. In contrast to this are
14
CO
2
isotopologues identified
through their radioactivity, and in the worst case without any
dilution or exchange processes in an external reservoir
τ
14
would approach the radioactive lifetime. On the other hand, at
strong diffusion, dilution or sequestration of
14
C in such res-
ervoirs
τ
14
would converge to
τ
R
. Consequently it follows from
the observed
14
C decay shown in Figure 5 that this provides an
upper bound on the actual absorption time
τ
R
, which can be
only shorter. Both are tremendously shorter than the adjust-
ment time requested by the IPCC.
The exponential decay of
14
C with only one single decay
time proves models with multiple relaxation times to be wrong.
At the same time it gives strong evidence for a first order
absorption process as considered in Section 4.
2
5.7.4. Higher Fossil Fuel Emissions in the Northern Hemi-
sphere
"Most of the fossil fuel CO
2
emissions take place in the
industrialised countries north of the equator. Consistent
with this, on annual average, atmospheric CO
2
measure-
ment stations in the NH record increasingly higher CO
2
concentrations than stations in the SH, as witnessed by the
observations from Mauna Loa, Hawaii, and the South Pole
(see Figure 6.3). The annually averaged concentration
difference between the two stations has increased in pro-
portion of the estimated increasing difference in fossil fuel
combustion emissions between the hemispheres (Figure
6.13; Keeling et al., 1989; Tans et al., 1989; Fan et al.,
1999)".
The strongest terrestrial emissions result from tropical for-
ests, not industrial areas. The strongest oceanic emissions can
be seen from the map of Takahashi et al. [32]. They are be-
tween 10°N and 10°S in the Eastern Tropic Pacific. Never-
theless, there is no doubt that industrial emissions endow their
fingerprints in the atmosphere and biosphere (Suess effect).
The influence and size of these emissions has already been
discussed above, and their different impact on the two hemi-
spheres can be estimated from Figure 6.3c of AR5 [1] indi-
cating a slightly faster decline of (δ
13
C)
atm
for the NH in
agreement with predominantly located industrial emissions in
this hemisphere. Even more distinctly this is illustrated by
Figure 6.13 of AR5 [1] for the difference in the emission rates
between the northern and SH with 8 PgC/yr, which can be
observed as a concentration difference between the hemi-
spheres of 3.8 ppm. But this is absolutely in no dissent to our
result in Section 4 that from globally 4.7 ppm/yr FFE and LUC
(average emission over 10 yr) 17 ppm or 4.3 % contribute to
the actual CO
2
concentration of 393 ppm (average). This im-
pact is of the same size as seasonal variations observed at
Mauna Loa before flattening and averaging the measurements.
5.7.5. Human Caused Emissions Grew Exponentially
"The rate of CO
2
emissions from fossil fuel burning and
land use change was almost exponential, and the rate of
CO
2
increase in the atmosphere was also almost exponen-
tial and about half that of the emissions, consistent with a
large body of evidence about changes of carbon inventory
in each reservoir of the carbon cycle presented in this
chapter".
The size and influence of FFE and LUC on the atmospheric
CO
2
concentration has extensively been discussed in the pre-
ceding sections. Only when violating fundamental physical
principles like the equivalence principle or denying basic
2
A calculation similar to Figure 8 but with a residence time of 15 yr as an upper
bound would require to reduce the natural emissions at pre-industrial times from 93
ppm/yr to 19 ppm/yr. Then the anthropogenic contribution would supply 59 ppm,
which is 15% of the total atmospheric concentration or 52% of the increase since
1850.

154 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
causalities like a first order absorption process with only a
single absorption time, the CO
2
increase can be reproduced
with anthropogenic emissions alone.
In contrast to that we could demonstrate that conform with
the rising temperature over the Industrial Era and in confor-
mity with all physical legalities the overwhelming fraction of
the observed CO
2
increase has to be explained by native im-
pacts. Such simulations reproduce almost every detail of the
observed atmospheric CO
2
increase (see Figures 8 and 10).
And from observations of natural emissions it can be seen that
they are increasing slightly exponential with temperature
(Takahashi et al. [32]; Lee [34]).
Thus, no one of the preceding lines of evidence can really
support the above statement that "fossil fuel burning and land
use change are the dominant cause of the observed increase in
atmospheric CO
2
concentration." In fact, they apply in the
same way for our concept, and thus they are useless to disfa-
vour our approach. The isotopic studies rather confirm our
ansatz of a first order absorption process with a single ab-
sorption time, which is significantly shorter than one decade,
and they refute the idea of cumulating anthropogenic emis-
sions in the atmosphere.
6. Conclusion
The increase of CO
2
over recent years can well be explained
by a single balance equation, the Conservation Law (23),
which considers the total atmospheric CO
2
cycle, consisting of
temperature and thus time dependent natural emissions, the
human activities and a temperature dependent uptake process,
which scales proportional with the actual concentration. This
uptake is characterized by a single time scale, the residence
time of about 3 yr, which over the Industrial Era slightly in-
creases with temperature. Only this concept is in complete
conformity with all observations and natural causalities. It
confirms previous investigations (Salby [7, 10]; Harde [6])
and shows the key deficits of some widespread but largely ad
hoc carbon cycle models used to describe atmospheric CO
2
,
failures which are responsible for the fatal conclusion that the
increase in atmospheric CO
2
over the past 270 years is prin-
cipally anthropogenic.
For a conservative assessment we find from Figure 8 that
the anthropogenic contribution to the observed CO
2
increase
over the Industrial Era is significantly less than the natural
influence. At equilibrium this contribution is given by the
fraction of human to native impacts. As an average over the
period 2007-2016 the anthropogenic emissions (FFE&LUC
together) donated not more than 4.3% to the total concentra-
tion of 393 ppm, and their fraction to the atmospheric increase
since 1750 of 113 ppm is not more than 17 ppm or 15%. With
other evaluations of absorption, the contribution from anthro-
pogenic emission is even smaller. Thus, not really anthropo-
genic emissions but mainly natural processes, in particular the
temperature, have to be considered as the dominating impacts
for the observed CO
2
increase over the last 270 yr and also
over paleoclimate periods.
Acknowledgements
The author thanks Prof. Murry Salby, formerly Macquarie
University Sydney, for many stimulating discussions when
preparing the paper, and Jordi López Fernández, Institute of
Environmental Assessment and Water Studies Barcelona, for
his support when searching for temperature data.
This research did not receive any specific grant from
funding agencies in the public, commercial, or not-for-profit
sectors.
Appendix
Appendix A
The absorption efficiency of extraneous reservoirs has been
claimed to have decreased, based on changes in the arbitrar-
ily-defined airborne fraction (e.g., Le Quéré et al. [12]; Ca-
nadell et al. [44]). Such claims are dubious because they rely
on the presumption that changes of CO
2
are exclusively of
anthropogenic origin. Nor are the claims supported by recent
atmospheric CO
2
data. Gloor et al. [45] found that decadal
changes of AF followed from changes in the growth of an-
thropogenic emissions - not from changes in absorption effi-
ciency, which were comparatively small. Further, uncertain-
ties in emission and absorption exceeded any changes in AF.
Ballantyne et al. [46] arrived at a similar conclusion. They
used global atmospheric CO
2
measurements and CO
2
emis-
sion inventories to evaluate changes in global CO
2
sources and
sinks during the past 50 years. Their mass balance analysis
indicates that net CO
2
uptake significantly increased, by about
0.18 Pg/yr (0.05 GtC/yr) and, between 1960 and 2010, that
global uptake actually doubled, from 8.8 to 18.4 Pg/yr. It
follows that, without quantitative knowledge of changes in
natural emission, interpretations based on AF are little more
than speculative.
The uptake and outgassing of atmospheric CO
2
by oceans is
simulated with complex marine models. How much CO
2
en-
ters or leaves the ocean surface is calculated from the differ-
ence between atmospheric and surface concentrations of CO
2
,
modified by the Revelle factor. However, most of these mod-
els involve assumptions which are not in agreement with ob-
served behavior (see, e.g., Steele [47]). They assume that the
surface layer absorbs CO
2
through equilibrium with atmos-
pheric concentration. On this premise, they calculate how
much Dissolved Inorganic Carbon (DIC) will be added to the
ocean based on increased atmospheric CO
2
since pre-indu-
strial times. In reality, the surface layer is not at equilibrium
with the atmosphere. A difference in concentration results
from conversion of CO
2
into organic carbon by photosynthesis.
Organic carbon produced then sinks into the deep ocean,
where it is sequestered. This downward transport to the deep
ocean is known as the biological pump. In the Northeastern
Atlantic basin, e.g., Benson et al. [33] report on seasonal
pressure differences between the ocean and atmosphere of
∆
pCO
2
= -70 µatm and an air-sea CO
2
flux of 220 g/m
2
/yr.
Only in those regions where strong upwelling of DIC from the
deep ocean exceeds sequestration of carbon via photosynthe-

Earth Sciences 2019; 8(3): 139-158 155
sis can CO
2
be outgassed to the atmosphere. The latter is found
primarily in the tropical oceans (Takahashi et al. [32]; Zhang
et al. [31]). Several models estimate that, without the bio-
logical pump, atmospheric CO
2
would be 200 to 300 ppm
higher than current levels (see also Evans [48]).
With increasing primary production, carbon export to depth
also grows. Arrigo et al. [49] reported that, since 1998, annual
primary production in the Arctic has increased by 30%.
Steinberg et al. [50] observed a 61% increase in meso-plank-
ton between 1994 and 2006 in the Sargasso Sea. The North
Atlantic coccolithophores have increased by 37% between
1990 and 2012 (Krumhardt et al. [51]). And Chavez et al. [52]
found a dramatic increase in primary production in the Peru
Current since the end of the Little Ice Age (LIA). Together, the
increase in primary production and downward transport of
organic carbon is sufficient to account for anthropogenic CO
2
that was absorbed from the atmosphere (Steele [47]).
Further, seasonal changes in surface CO
2
illustrate that ab-
sorption of CO
2
by the oceans and accumulation of DIC near
the surface are determined, not by the Revelle factor, but by
the biological pump. Evans et al. [48] found from buoy data
off the coast of Newport, Oregon that each spring photosyn-
thesis lowers ocean surface CO
2
to 200 ppm - far below cur-
rent atmospheric concentrations and much lower than what
would be expected from equilibrium with a pre-industrial
atmosphere. Anthropogenic CO
2
in surface water is then
quickly removed. It is also well known that higher concen-
trations of CO
2
magnify photosynthesis. At increased atmos-
pheric CO
2
, the plankton community consumed 39% more
DIC (Riebesell et al. [53]). During summer and autumn, sur-
face CO
2
can rapidly increase to 1000 ppm - more than twice
the concentration of CO
2
in the atmosphere. Surface water
then significantly enhances natural emission to the atmos-
phere. Conversely, during winter, surface CO
2
remains at
about 340 ppm. Despite reduced photosynthesis, CO
2
in sur-
face water then remains below equilibrium with the atmos-
phere, reflecting efficient removal through downward trans-
port by the biological pump. It is noteworthy that these strong
seasonal variations of CO
2
in surface water are manifest in the
record of atmospheric CO
2
(see Figures 9 and 10).
Under steady state conditions, diffusion of CO
2
into the
ocean is believed to require about 1 year to equilibrate with an
atmospheric perturbation. But, when increased sunlight en-
hances photosynthesis, such equilibration is no longer
achieved. Perturbation CO
2
is then simply transported to depth,
where it is sequestered from surface waters (McDonnell et al.
[54]). Under such conditions uptake of CO
2
is not restricted by
the Revelle factor but by the biological pump.
The foregoing processes are controlled essentially by
sunlight and temperature. There is no reason to believe that net
primary production, the biological pump, and sequestration of
CO
2
below surface waters would be the same today as 270
years ago, when temperature and atmospheric CO
2
were likely
lower.
In simulating transport of carbon in the ocean, complex
models assume behavior that is found in tracers like chloro-
fluorocarbons (CFCs). Because those species accumulate near
the ocean surface, models assume DIC does as well. But un-
like CFCs, which are inert, CO
2
entering sunlit waters is
quickly converted to organic matter by photosynthesis (Steele
[47]). Although dissolved CFCs and dissolved carbon are
passively transported in the same manner, particulate organic
carbon (alive or dead) behaves very differently. It rapidly
sinks, removing carbon from surface water through mecha-
nisms which do not operate on CFCs.
The removal of carbon from surface water depends on the
sinking velocity and also on how rapidly organic matter is
decomposed. After descending below the pycnocline (depths
of 500-1000 meters), carbon is effectively sequestered - be-
cause water at those depths does not return to the surface for
centuries (Weber et al. [55]). For the atmosphere, this
long-term sequestration translates into removal that is effec-
tively permanent. Before such carbon can return to the at-
mosphere, fossil fuel reserves will have long since been ex-
hausted.
The combination of sinking velocities and sequestration
depth suggests that a significant fraction of primary produc-
tion is sequestered in a matter of days to weeks (Steele [47]).
Therefore, increasing primary production leads to a propor-
tionate increase and rapid export of carbon to depth. If marine
productivity has increased since pre-industrial times, it will
have also sequestered the respective anthropogenic carbon
into the deeper ocean. Observations from ocean basins suggest
that, since the Little Ice Age, marine productivity and carbon
export have indeed increased as the oceans warmed (Chavez
et al. [52]; Abrantes et al. [56]).
Appendix B
The bomb radiocarbon signal in the atmosphere is a sensi-
tive tracer to study the fluxes in the carbon cycle, in particular
to determine an upper bound for the residence time of CO
2
in
the atmosphere and its uptake through extraneous reservoirs.
Carbon 14 obeys the balance equation
14
14
14
14
τ
C
e
dt
dC −=
(33)
with e
14
as the emission rate, which follows from background
emission of
14
C as well as anthropogenic emission. The decay
after the stop of the bomb tests in 1963 then satisfies the rela-
tion (see Subsection 5.7.3, (31))
14
14
14
'
1' C
dt
dC ⋅−=
τ
, (34)
where C'
14
represents the excess concentration of radiocarbon
above background concentration in the atmosphere, and
τ
14
is
the apparent absorption time of about 15 yr. Regularly not the
absolute number of
14
C but its ratio to
13
C or
12
C is measured,
either as radioactivity or by accelerator mass spectrometry.
As the total CO
2
concentration is not constant over the ob-
served decay period and this directly affects the relative
14
C
decay as well as the background level, the measured
14
C ac-
tivity has to be corrected for these variations to obtain the true

156 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
C'
14
concentration. Such corrections are important for age
dating of materials and also for atmospheric
14
C measure-
ments. Without compensating for the varying total concentra-
tion, e.g., the
14
C-decay and the background would be modi-
fied by several ten %.
Mostly the corrected data are specified as fractionation-
corrected ‰-deviations from the Oxalic Acid standard activ-
ity corrected for decay (see Stuiver&Polach [57]):
10001
14
⋅






−=∆
ABS
SN
A
A
C
(35)
with A
SN
as sampling activity normalized for isotope frac-
tionation to
13
C, and A
ABS
as the absolute international stan-
dard activity (Oxalic Acid standard). A
SN
relates to the meas-
ured sample activity A
S
as






+
−= 1000
25(2
1
13
C
AA
SSN
δ
, (36)
where δ
13
C is specified in ‰ with respect to the
13
C VPDB
standard.
This normalization procedure also accounts for fossil fuel
emissions, which are devoid of
14
C and also have a leaner
13
C
abundance. So, human emissions dilute the
14
C/
12
C and
13
C/
12
C ratio in the atmosphere. Such corrections are impor-
tant for correct age assignments, but how much does this in-
dustrial effect and the observed dilution also affect the at-
mospheric
14
C decay?
To answer this question we compare the original ∆
14
CO
2
data of Vermunt and Schauinsland shown in Figure 5, with a
hypothetical ∆
14
CO
2
-distribution, which is found for a fixed
δ
13
C-value over the full observation period, thus, assuming no
further dilution. This requires first to recalculate the sampling
activity A
S
from (35) and (36) with the known δ
13
C-record,
e.g., from Mauna Loa (AR5 [1], Chap6, Figure 6.3c, missing
data from 1964-1976 can be extrapolated from this record),
and then to simulate the decay curve with new A
S
activities,
which are derived for a constant δ
13
C(1964) = -7.4‰.
0
200
400
600
800
1964 1974 1984 1994 2004
2014
Year
∆
14
CO
2
(‰)
Measurement Vermunt
Measurem. Schauinsland
Exponential: tau = 15 yr
Delta 14C_fixed
Figure 13.
∆
14
CO
2
-evolution for Vermunt and Schauinsland (Magenta Dots
and Green Triangles), compared with a recalculated decay neglecting dilution
effects (Brown Crosses). Additionally shown is an exponential fit with an
e-folding time of 15 yr (Magenta).
Figure 13 displays the normalized ∆
14
CO
2
-values of Ver-
munt and Schauinsland (Blue Diamonds and Green Triangles;
data from Levin et al. [17]) as reproduction of Figure 5 on a
magnified scale.
It directly compares this with the hypothetical ∆
14
CO
2
de-
cay curve (Brown Crosses). Deviations over the observed time
period of 48 yr are smaller than 2‰ and the respective graphs
completely coincide on this scale. They can well be ap-
proximated by a single exponential with a decay time of 15 yr
(Magenta Line). Thus, any dilution effect of fossil fuel and
natural emissions can well be neglected for the
14
C-decay.
Far more influential is re-emission of
14
C that was absorbed
from the atmosphere. On the time scale of observed absorption,
not all
14
C is directly sequestered beneath the Earth's surface,
but needs several cycles before being removed from the at-
mosphere. This can be described by a perturbation balance,
which different to (33) now considers the regular absorption
(characterized by the residence time
τ
R
) and takes account of
an emission rate e'
14
, now for re-emitted
14
C from the upper
Earth layer (e.g., through decomposition of vegetation which
has absorbed that
14
C), before it is sequestered or distributed:
14
1414
14
14,
1414
14
14
τττττ
CC
C
CC
e
dt
Cd
R
E
RR
′
−≈
′
−








′
−
′
≈
′
−
′
=
′
. (37)
Primed quantities are now referenced against unperturbed
values before introduction of the nuclear source. From a bal-
ance for the Earth layer it follows that in good approximation
e'
14
opposes the atmospheric absorption rate C'
14
/
τ
R
minus the
sequestration rate C'
E,14
/
τ
14
, for which it is assumed that the
concentration in the upper layer C'
E,14
is almost the same as the
concentration C'
14
in the atmosphere. Thus, re-emission sim-
ply modifies the effective absorption, which for
14
C is con-
trolled by the apparent absorption time
τ
14
and not the resi-
dence time
τ
R
in agreement with (34).
Unlike the dilution effect, which is minor, this slows decay
over what it would be in the presence of absorption alone. The
apparent absorption time is therefore longer than the actual
absorption time, which must even be shorter than a decade.
Integration of (37) or (34) exactly reproduces a pure expo-
nential decay in Figure 13 with an e-folding time
τ
14
=15 yr.
References
[1] AR5, In: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M.,
Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midg-
ley, P. M. (Eds.), "Climate Change 2013: The Physical Science
Basis. Contribution of Working Group I to the Fifth Assess-
ment Report of the Intergovernmental Panel on Climate
Change", Cambridge University Press, Cambridge, United
Kingdom and New York, NY, USA, 2013.
[2] C. Le Quéré et al., "Global Carbon Budget 2017", Earth Syst.
Sci. Data Discuss., https://doi.org/10.5194/essd-2017-123,
Open Access Earth System Science Data Discussions, Manu-
script under review for journal Earth Syst. Sci. Data, 2017.
[3] CICERO, Center for International Climate Research, Oslo, R.
Andrew: http://folk.uio.no/roberan/GCP2017.shtml. 2017.
[4] CDIAC, 2017: Carbon Dioxide Information Analysis Center,
http://cdiac.ornl.gov/trends/emis/glo_2014.html.

Earth Sciences 2019; 8(3): 139-158 157
[5] C. D. Keeling, S. C. Piper, R. B. Bacastow, M. Wahlen, T. P.
Whorf, M. Heimann, H. A. Meijer, "Atmospheric CO
2
and
13
CO
2
exchange with the terrestrial biosphere and oceans from
1978 to 2000: Observations and carbon cycle implications", In:
Ehleringer, J. R., Cerling, T. E., Dearing, M. D. (Eds.), A His-
tory of Atmospheric CO2 and Its Effects on Plants, Animals,
and Ecosystems. Springer Science+Business Media, New York,
NY, USA, and Heidelberg, Germany, pp. 83–113 (actualized by
Scripps-Institutes, USA), 2005.
[6] H. Harde, "Scrutinizing the carbon cycle and CO
2
residence
time in the atmosphere", Global and Planetary Change 152, pp.
19–26, 2017.
http://dx.doi.org/10.1016/j.gloplacha.2017.02.009.
[7] M. L. Salby, "Atmospheric Carbon", Video Presentation, July
18, 2016. University College London.
https://youtu.be/3q-M_uYkpT0.
[8] P. Köhler, J. Hauck, C. Völker, D. A. Wolf-Gladrow, M. Butzin,
J. B. Halpern, K. Rice, R. E. Zeebe, Comment on “Scrutinizing
the carbon cycle and CO2 residence time in the atmosphere” by
H. Harde, Global and Planetary Change 164, pp. 67-71, 2017.
https://doi.org/10.1016/j.gloplacha.2017.09.015
[9] GISS, 2017: Goddard Institute for Space Studies:
https://data.giss.nasa.gov/gistemp/.
[10] M. L. Salby, "Relationship Between Greenhouse Gases and
Global Temperature", Video Presentation, April 18, 2013.
Helmut-Schmidt-University Hamburg
https://www.youtube.com/watch?v=2ROw_cDKwc0.
[11] M. L. Salby, "What is Really Behind the Increase of Atmos-
pheric CO
2
"? Helmut-Schmidt-University Hamburg, 10. Oc-
tober 2018, https://youtu.be/rohF6K2avtY
[12] C. Le Quéré, M. R. Raupach, J. G. Canadell, G. Marland et al.,
"Trends in the sources and sinks of carbon dioxide", Nature
Geosci., 2, pp. 831–836, 2009. doi:10.1038/ngeo689.
[13] P. Tans, NOAA/ESRL and R. Keeling, Scripps Institution of
Oceanography (scrippsco2.ucsd.edu/), 2017.
https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html.
[14] F. Joos, M. Bruno, R. Fink, U. Siegenthaler, T. F. Stocker, C. Le
Quéré, J. L. Sarmiento, "An efficient and accurate representa-
tion of complex oceanic and biospheric models of anthropo-
genic carbon uptake", Tellus B 48, pp. 397–417, 1996.
doi:10.1034/j.1600-0889.1996.t01-2-00006.x.
[15] J. Hansen, M. Sato, P. Kharecha, G. Russell, D. W. Lea, M.
Siddall, "Climate change and trace gases", Phil. Trans. R. Soc.
A 365, pp. 1925–1954, 2007. doi:10.1098/rsta.2007.2052.
[16] J. Hansen, M. Sato, G. Russell, K. Pushker, "Climate sensitivity,
sea level, and atmospheric CO
2
", Philos. Trans. R. Soc. A, 371,
20120294, 2013. doi:10.1098/rsta.2012.0294.
https://www.nasa.gov/
[17] I. Levin, B. Kromer, and S. Hammer, "Atmospheric Δ
14
CO
2
trend in Western European background air from 2000 to 2012",
Tellus B 65, pp. 1-7, 2013.
[18] Q. Hua, M. Barbetti, A. Z. Rakowski, "Atmospheric radiocar-
bon for the period 1950–2010". RADIOCARBON 55, pp.
2059–2072, (2013). Supplementary Material Table S2c,
https://doi.org/10.2458/azu_js_rc.v55i2.16177
[19] J. C. Turnbull, S. E. Mikaloff Fletcher, I. Ansell, G. W. Brails-
ford, R. C. Moss, M. W. Norris, K. Steinkamp, "Sixty years of
radiocarbon dioxide measurements at Wellington, New Zea-
land: 1954–2014", Atmos. Chem. Phys. 17, pp. 14771–14784,
2017. https://doi.org/10.5194/acp-17-14771-2017.
[20] U. Siegenthaler, J. L. Sarmiento, "Atmospheric carbon dioxide
and the ocean", Nature 365, pp. 119-125, 1993.
[21] P. Dietze, IPCC's Most Essential Model Errors, 2001.
http://www.john-daly.com/forcing/moderr.htm; (Carbon Model
Calculations, http://www.john-daly.com/dietze/cmodcalc.htm).
[22] G. C. Cawley, "On the Atmospheric Residence Time of An-
thropogenically Sourced Carbon Dioxide", Energy Fuels 25, pp.
5503–5513, 2011. dx.doi.org/10.1021/ef200914u
[23] H.-J. Lüdecke, C. O. Weiss, "Simple Model for the Anthropo-
genically Forced CO
2
Cycle Tested on Measured Quantities",
JGEESI, 8(4), pp. 1-12, 2016.
DOI: 10.9734/JGEESI/2016/30532.
[24] R. E. Essenhigh, "Potential dependence of global warming on
the residence time (RT) in the atmosphere of anthropogenically
sourced carbon dioxide", Energy Fuel 23, pp. 2773–2784, 2009.
http://pubs.acs.org/doi/abs/10.1021/ef800581r.
[25] E. Berry, "Human CO
2
has little effect on atmospheric CO
2
", 2019.
https://edberry.com/blog/climate-physics/agw-hypothesis/contradi
ctions-to-ipccs-climate-change-theory/
[26] NOAA, 2017:
https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalys
is.html
http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.G
HCN/.v2/?bbox=bb%3A-161.488%3A16.360%3A-150.062%
3A23.051%3Abb
[27] NOAA, 2018:
http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.ER
SST/.version2/.SST/index.html
http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.ER
SST/.version2/.SST/X/%28164W%29VALUES/T/%28Jan%2
01938%29%28Dec%202009%29RANGEEDGES/Y/%2819N
%29VALUES/datafiles.html
[28] O. Humlum, K. Stordahl, J. E. Solheim, "The phase relation
between atmospheric carbon dioxide and global temperature",
Global and Planetary Change 100, pp. 51-69, 2013.
[29] M. Richardson, Comment on “The phase relation between
atmospheric carbon dioxide and global temperature” by Hum-
lum, Stordahl and Solheim, Global and Planetary Change 107,
pp. 226-228, 2013.
[30] D. L. Royer, R. A. Berner, I. P. Montañez, N. J. Tabor, D. J.
Beerling, "CO
2
as a primary driver of Phanerozoic climate",
GSA Today 14, no. 3, 2004.
doi: 10.1130/1052-5173(2004)014<4:CAAPDO>2.0.CO;2.
[31] Y. G. Zhang, M. Pagani, J. Henderiks, H. Ren, "A long history
of equatorial deep-water upwelling in the Pacific Ocean", Earth
and Planetary Science Letters 467, pp. 1–9, 2017.
http://dx.doi.org/10.1016/j.epsl.2017.03.016.
[32] T. Takahashi, S. C. Sutherland, R. Wanninkhof, C. Sweeney, R.
A. Feely et al., "Climatological mean and decadal change in
surface ocean pCO
2
and net sea-air CO
2
flux over the global
oceans", Deep-Sea Res. II, 56, pp. 554–577, 2009.
doi:10.1016/j.dsr2.2008.12.009.
[33] N. U. Benson, O. O. Osibanjo, F. E. Asuquo, W. U. Anake,
"Observed trends of pCO
2
and air-sea CO
2
fluxes in the North

158 Hermann Harde: What Humans Contribute to Atmospheric CO
2
: Comparison of Carbon Cycle Models with Observations
Atlantic Ocean, Intern. J. Marine Science 4, pp. 1-7, 2014.
[34] J.-S. Lee, "Monitoring soil respiration using an automatic op-
erating chamber in a Gwangneung temperate deciduous forest",
J. Ecology & Field Biology 34(4), pp. 411-423, 2011.
[35] C. Huntingford, O. K. Atkin, A. Martinez-de la Torre, L. M.
Mercado, M. A. Heskel, A. B. Harper, K. J. Bloomfield, O. S.
O’Sullivan, P. B. Reich, K. R. Wythers, E. E. Butler, M. Chen,
K. L. Griffin, P. Meir, M. G. Tjoelker, M. H. Turnbull, S. Sitch,
A. Wiltshire, Y. Malhi, "Implications of improved representa-
tions of plant respiration in a changing climate", NATURE
COMMUNICATIONS 8, 1602, 2017.
DOI: 10.1038/s41467-017-01774-z.
[36] H. Harde, "Radiation Transfer Calculations and Assessment of
Global Warming by CO
2
", International Journal of Atmos-
pheric Sciences, Volume 2017, Article ID 9251034, pp. 1-30,
2017. https://doi.org/10.1155/2017/9251034.
[37] H. Harde, "Was tragen CO
2
und die Sonne zur globalen Er-
wärmung bei"? 12. Internationale EIKE Klima- und Energie-
konferenz und 13th International Conference on Climate
Change (ICCC-13), München, 23. u. 24. November, 2018,
https://youtu.be/ldrG4mn_KCs.
[38] T. B. Coplen, "Reporting of stable hydrogen, carbon and oxy-
gen isotopic abundances", Pure and Applied Chemistry 66, pp.
273-276, 1994.
[39] U. Siegenthaler, K. O. Münnich, "
13
C/
12
C fractionation during
CO
2
transfer from air to sea", In: Bolin, B. (Ed.): Carbon cycle
modelling (SCOPE 16), John Wiley & Sons, pp. 249-257,
1981.
[40] M. L. Salby, "Physics of the Atmosphere and Climate", Cam-
bridge University Press, Cambridge 2012. (ISBN: 978-0-521-
76718-7).
[41] D. M. Etheridge, L. P. Steele, R. L. Langenfelds, R. J. Francey,
J.-M. Barnola, V. I. Morgan, "Natural and anthropogenic changes
in atmospheric CO2 over the last 1000 years from air in Antarctic
ice and firn", J. Geophys. Res. 101, pp. 4115-4128, 1996.
[42] Friedli H., H. Lötscher, H. Oeschger, U. Siegenthaler, B.
Stauffer, 1986. Ice core record of the 13C/12C ratio of atmos-
pheric CO2 in the past two centuries, Nature 324, pp. 237-238.
[43] H. Suess, "Radiocarbon Concentration in Modern Wood",
Science 122, Issue 3166, pp. 415-417, 1955. DOI:
10.1126/science.122.3166.415-a
[44] J. G. Canadell, Le Quéré, C., Raupach, M. R., Field, C. B.,
Buitenhuis, E. T., Ciais, P., Conway, T. J., Gillett, N. P.,
Houghton, R. A., and Marland G., "Contributions to acceler-
ating atmospheric CO
2
growth from economic activity, carbon
intensity, and efficiency of natural sinks", P. Natl. Acad. USA,
104(47), 18866–18870, 2007, doi:10.1073/pnas.0702737104.
[45] M. Gloor, J. L. Sarmiento, and N. Gruber, "What can be learned
about carbon cycle climate feedbacks from the CO
2
airborne
fraction"? Atmos. Chem. Phys., 10, pp. 7739–7751, 2010.
https://www.atmos-chem-phys.net/10/7739/2010/,
doi:10.5194/acp-10-7739-2010.
[46] 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,
2012. doi:10.1038/nature11299
[47] J. Steele, "How NOAA and Bad Modeling Invented an Ocean
Acidification Icon", Part 2 – Bad Models, 2017.
https://wattsupwiththat.com/2017/03/02/how-noaa-and-bad-mo
deling-invented-an-ocean-acidification-icon-part-2-bad-models/
[48] W. Evans, B. Hales, P. G. Strut, "Seasonal cycle of surface
ocean pCO2 on the Oregon shelf", J. Geophys. Research 116,
2011, DOI: 10.1029/2010JC006625.
[49] K. R. Arrigo, G. L. van Dijken, "Continued increases in Arctic
Ocean primary production", Progress in Oceanography 136, pp.
60-70, 2015, https://doi.org/10.1016/j.pocean.2015.05.002.
[50] D. K. Steinberg, M. W. Lomas, J. S. Cope, "Long-term increase
in mesozooplankton biomass in the Sargasso Sea: Linkage to
climate and implications for food web dynamics and biogeo-
chemical cycling", Global Biogeochemical Cycle 26, 2012,
DOI: 10.1029/2010GB004026.
[51] K. M. Krumhardt, N. S. Lovenduski, N. M. Freeman, N. R.
Bates, "Apparent increase in coccolithophore abundance in the
subtropical North Atlantic from 1990 to 2014", Biogeosciences
13, pp. 1163-1177, 2016. doi:10.5194/bg-13-1163-2016,
http://www.biogeosciences.net/13/1163/2016/.
[52] F. P. Chavez, M. Messié, J. T. Pennington, "Marine Primary
Production in Relation to Climate Variability and Change",
Annu. Rev. Mar. Sci. 3, pp. 227–260, 2011,
doi:10.1146/annurev.marine.010908.163917.
[53] U. Riebesell, K. G. Schulz, R. G. J. Bellerby, M. Botros, P.
Fritsche, M. Meyerhöfer, C. Neill, G. Nondal, A. Oschlies, J.
Wohlers, E. Zöllner, "Enhanced biological carbon consumption
in a high CO
2
ocean", Nature 450, pp. 545-548, 2007,
doi:10.1038/nature06267.
[54] A. M. P. McDonnell, K. O. Buesseler, "Variability in the av-
erage sinking velocity of marine particles", Limnology and
Oceanography 55, pp. 2085–2096, 2010.
DOI:10.4319/lo.2010.55.5.2085.
[55] T. Weber, J. A. Cram, S. W. Leung, T. DeVries, C. Deutsch,
"Deep ocean nutrients imply large latitudinal variation in par-
ticle transfer efficiency", PNAS 113 no. 31, pp. 8606–8611,
2016, doi: 10.1073/pnas.1604414113.
[56] F. Abrantes, P. Cermeno, C. Lopes, O. Romero, L. Matos, J.
Van Iperen, M. Rufino, V. Magalhães, "Diatoms Si uptake ca-
pacity drives carbon export in coastal upwelling systems",
Biogeosciences 13, pp. 4099–4109, 2016,
https://doi.org/10.5194/bg-13-4099-2016
[57] M. Stuiver, H. A. Polach, "Discussion Reporting of
14
C Data",
RADIOCARBON 19, No. 3, pp. 355-363, 1977.