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The phase relation between atmospheric carbon dioxide and global temperature
Ole Humlum
a,b,
⁎, Kjell Stordahl
c
, Jan-Erik Solheim
d
a
Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, N-0316 Oslo, Norway
b
Department of Geology, University Centre in Svalbard (UNIS), P.O. Box 156, N-9171 Longyearbyen, Svalbard, Norway
c
Telenor Norway, Finance, N-1331 Fornebu, Norway
d
Department of Physics and Technology, University of Tromsø, N-9037 Tromsø, Norway
abstractarticle info
Article history:
Received 25 April 2012
Accepted 25 August 2012
Available online 30 August 2012
Keywords:
Carbon dioxide
Global temperature
Sea surface temperature
Volcanic eruptions
Using data series on atmospheric carbon dioxide and global temperatures we investigate the phase relation
(leads/lags) between these for the period January 1980 to December 2011. Ice cores show atmospheric CO
2
var-
iations to lag behind atmospheric temperature changes on a century to millennium scale, but modern tempera-
ture is expected to lag changes in atmospheric CO
2
, as the atmospheric temperature increase since about 1975
generally is assumed to be caused by the modern increase in CO
2
. In our analysis we use eight well-known
datasets: 1) globally averaged well-mixed marine boundary layer CO
2
data, 2) HadCRUT3 surface air tempera-
ture data, 3) GISS surface air temperature data, 4) NCDC surface air temperature data, 5) HadSST2 sea surface
data, 6) UAH lower troposphere temperature data series, 7) CDIAC data on release of anthropogene CO
2
,and
8) GWP data on volcanic eruptions. Annual cycles are present in all datasets except 7) and 8), and to remove
the influence of these we analyze 12-month averaged data. We find a high degree of co-variation between all
data series except 7) and 8), but with changesin CO
2
always lagging changes in temperature.The maximum pos-
itive correlation between CO
2
and temperature is found for CO
2
lagging 11–12 months in relation to global sea
surface temperature, 9.5–10 months to global surface air temperature, and about 9 months to global lower tro-
pospheretemperature. The correlation betweenchanges in ocean temperatures and atmospheric CO
2
is high, but
do not explain all observed changes.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
IcecorerecordsindicatethatthegreenhousegasCO
2
co-varied
with the global temperature over several glacial–interglacial cycles,
suggesting a link between natural atmospheric greenhouse gas var-
iations and temperature on long time scales (IPCC AR4, 2007; Lüthi
et al., 2008).
Over the last 420 kyr variations in atmospheric CO
2
broadly
followed temperature according to ice cores, with a typical delay of
several centuries to more than a millennium (Lorius et al., 1990;
Mudelsee, 2001; Caillon et al., 2003). Atmospheric CO
2
is therefore
not initiating the large glacial–interglacial climate changes, and pre-
sumably these are controlled by orbital Milankovitch cycles. It has
however been suggested that the subsequent CO
2
-rise may amplify
or even in certain periods precede the global temperature increase
initiated by Milankovitch cycles, but the interpretation of the proxy
data is ambiguous with regard to this (Alley and Clarck, 1999;
Shackleton, 2000; Toggweiler and Lea, 2010; Shakun et al., 2012).
The observed time lag between atmospheric temperature and CO
2
from ice cores is thought to be caused by the slow vertical mixing that
occurs in the oceans, in association with the decrease in the solubility
of CO
2
in ocean water, as its temperature slowly increase at the end of
glacial periods (Martin et al., 2005), leading to subsequent net
out-gassing of CO
2
from the oceans (Toggweiler, 1999).
Direct measurements of temperatures and atmospheric CO
2
with
good time resolution are essential to understand empirically the effects
of CO
2
on modern global temperature changes. The first in situ continuous
measurements of atmospheric CO
2
made by a high-precision non-
dispersive infrared gas analyzer were implemented by C.D. Keeling from
the Scripps Institution of Oceanography (SIO). These measurements
were initiated in 1958 at Mauna Loa, Hawaii, located at 19°N in the Pacific
Ocean (Keeling et al., 1995). These data documented that not only was the
amount of CO
2
increasing in the atmosphere since 1958, but also that the
rise was modulated by annual cycles caused by seasonal changes in ocean
surface temperature and photosynthesis in the terrestrial biosphere.
The Mauna Loa measurements were followed by other continuous in
situ measurements at a limited number of other observation sites in both
hemispheres (Conway et al., 1994; Nakazawa et al., 1997; Langenfelds
et al., 2002). In the 1980s and 1990s, however, it was recognized that
a greater coverage of CO
2
measurements over continental areas was
required to provide the basis for estimating sources and sinks of
Global and Planetary Change 100 (2013) 51–69
⁎Corresponding author at: Department of Geosciences, University of Oslo, P.O. Box
1047 Blindern, N-0316 Oslo, Norway. Tel.: + 47 41403157.
E-mail address: Ole.Humlum@geo.uio.no (O. Humlum).
0921-8181/$ –see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.gloplacha.2012.08.008
Contents lists available at SciVerse ScienceDirect
Global and Planetary Change
journal homepage: www.elsevier.com/locate/gloplacha
Author's personal copy
atmospheric CO
2
over land as well as oceanregions, and to provide basis
for calculating a good estimate of theglobal amount of atmospheric CO
2
.
2. Modern global CO
2
and temperature
Today, an extensive network of international air sampling sites is
operated by the National Oceanic and Atmospheric Administration's
Global Monitoring Division (NOAA/GMD) in the USA. This organiza-
tion has measured carbon dioxide and other greenhouse gases for
several decades at a globally distributed network of air sampling
sites (Conway et al., 1994; IPCC AR4, 2007). A global average is
constructed by fitting a smoothed curve as a function of time to
each site, and then the smoothed value for each site is plotted as a
function of latitude for 48 equal time steps per year (IPCC AR4,
2007). A global average is calculated from the latitude plot at each
time step (Masarie and Tans, 1995), based on measurements from a
subset of network sites. Only sites where samples are predominantly
of well-mixed marine boundary layer (MBL) air representative of a
large volume of the atmosphere are considered for the global CO
2
data series (IPCC AR4, 2007). These key sites are typically at remote
marine sea level locations with prevailing onshore winds, to mini-
mize the effects of inland vegetation and industries. Measurements
from sites at higher altitude and from sites close to anthropogenic
and natural sources and sinks are excluded from the global CO
2
esti-
mate. The MBL data provide a low-noise representation of the global
trend and allows making the estimate directly from the data without
the need for applying an atmospheric transport model (IPCC AR4,
2007).
Global monthly CO
2
data (NOAA) are available from January 1980,
and is shown graphically in Fig. 1, along with the monthly global sea
surface temperature (HadSST2) and the monthly global surface air
temperature (HadCRUT3), using data published by the University of
East Anglia and the Hadley Centre, UK. In addition, in the present
study we also analyze global air temperature data from the Goddard
Institute for Space Studies (GISS) in USA, the National Climatic Data
Center (NCDC) in USA, and lower troposphere temperature data pub-
lished by the University of Alabama (UAH), Huntsville, USA. At the
end of the paper a list of URL's used to obtain the data used can be
found. All these monthly data series are now sufficiently long to
have collected a population of climate perturbations, and they are
therefore likely to reveal essentials of the coupling between atmo-
spheric CO
2
and temperature in modern time.
Global atmospheric CO
2
(Fig. 1) has increased steadily during the
entire observation period since 1980. There is, however, a pronounced
annual cyclic variation superimposed on this overall development,
caused by seasonal changes in the magnitude of sources and sinks for
CO
2
, controlled by dynamic exchanges with oceans and vegetation
(IPCC AR4, 2007). The two temperature series HadSST2 and HadCRUT3
also show an overall increase over the period, but their detailed devel-
opment is more complex than for CO
2
. In addition, they only show
small net changes since early 2002 (Scafetta, 2011).
In general, the two temperature records are seen to vary in close
concert with each other. This also applies for the three other temper-
ature records considered in this study (GISS, NCDC and UAH), but
these are not displayed in Fig. 1 to avoid visual congestion. All four
temperature records display rhythmic annual variations because of
the uneven hemispherical distribution of land and ocean, although
this is not readily apparent from the diagram, as other short-term
variations tend to dominate.
Resolving the degree of coupling between CO
2
and temperature is
not visually straightforward as illustrated by Fig. 1, but obviously re-
quires a more elaborate approach to the data series.
3. DIFF12 values
Before analyzing the monthly data, being interested in longer than
annual variations, we first removed the annual cycle from the global
atmospheric CO
2
data series by calculating a 12-month running aver-
age. This implies that we here consider the annual variation as noise
only, and instead are looking for the underlying longer signal, the
overall CO
2
increase. As the signal tends to be almost the same from
one monthly observation to nearby observations and the noise does
not, an average of several adjacent monthly observations will tend
to converge on the value of the signal alone. The most serious
Fig. 1. Monthly global atmospheric CO
2
(NOOA; green), monthly globalsea surface temperature (HadSST2; blue stippled) and monthly global surface airtemperature (HadCRUT3; red),
since January 1980. Last month shown is December 2011. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
52 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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consequence of smoothing or filtering is the shift of peaks and
troughs in the smoothed curve, relative to the original data. If several
data series are to be compared, identical filtering must therefore be
applied at all series, as spurious effects else may arise, perhaps even
inviting a false interpretation (see, e.g., discussion in Stauning, 2011).
We next calculated the difference between the average CO
2
con-
centration for the last 12 months and the average for the preceding
12 month period, referred to as DIFF12 in the following (see Fig. 1
for graphical explanation). In other words, DIFF 12 represents the
yearly net change with monthly time resolution. Technically DIFF12
values were plotted for the last month considered in the calculation.
By this we can efficiently visualize and analyze changes in the overall
atmospheric CO
2
increase since January 1980, without confounding
influence by the annual variation.
It is important to stress that the presence of a DIFF12 peak do not
indicate the presence of a concentration peak in the original CO
2
data, but instead a period with more rapid increase than else. It is
also worth emphasizing that by studying DIFF12 values we are inves-
tigating change rates in the amount of atmospheric CO
2
, and not the
total amount of CO
2
itself. However, by integrating DIFF12 values
over the observation period, changes in the total amount of CO
2
are
of cause addressed. Thus, to the degree that DIFF12 values can be
explained, changes in the total amount of atmospheric CO
2
are there-
fore also explained.
We next compared the result of the DIFF12 CO
2
calculation with
similar DIFF12 values for the global sea surface (HadSST2) and the
global surface air temperature (HadCRUT3). By this all monthly data
series were exposed to identical operations and the results are there-
fore comparable. To ensure that no spurious effects were introduced
by the data filtering we carried out a similar analysis on the unfiltered
monthly data, by calculating DIFF1
annual
,defined as the difference be-
tween 1 month and the identical month 1 yr before, e.g. January 2000
minus January 1999, etc. Finally, all DIFF1
annual
and DIFF12 series
were calculated and plotted in a time-change diagram (Fig. 2), to ob-
tain graphical overview.
From Fig. 2 it is seen that the 12-month filtering process results in
a displacement of DIFF12 peak and minimum values 12 months
ahead in time in relation to the unfiltered DIFF1
annual
values, exactly
as expected from definition of DIFF12. More important, however, it
is also seen that the relation between peaks and lows in the different
data series as to their relative timing remains unchanged. If no time
displacement of peaks and lows by filtering was important for the fol-
lowing analysis, this might have been obtained simply by changing
the plotting convention, and plotting DIFF12 at the last month in
the first 12-month interval, instead of at the last month in the second
interval. Thus, by using a 12-month filter as outlined above we ac-
quire a considerably clearer picture of the underlying signal in the in-
dividual data series (Fig. 2), compared to the unfiltered data (Fig. 1).
Fig. 2. 12-month change of global atmospheric CO
2
concentration (NOAA; green), global sea surface temperature (HadSST2; blue) and global surface air temperature (HadCRUT3;
red dotted). The upper panel shows unfiltered monthly values (e.g. January 2000 minus January 1999), while the lower panel shows filtered values (DIFF12, the difference between
the average of the last 12 month and the average for the previous 12 months for each data series). The numbers (1–9) on DIFF12 CO
2
peaks and the thin white lines refer to Table 1.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
53O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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The difference to Fig. 1 in vertical scale used for displaying DIFF12
values should be borne in mind when inspecting Fig. 2, especially for
CO
2
, but the visual impression is nevertheless instructive. The DIFF12
graph for CO
2
always remain positive, between 0.5 and 3 ppm per
year, a consequence of the steady increase in atmospheric CO
2
over
the observation period. The average DIFF12 is about 1.7 ppm/yr,
which as expected adds up to the entire overall increase of 51 ppm
in atmospheric CO
2
between 1980 and 2011. From about 2004, the
average and minimum DIFF12 values for atmospheric CO
2
are some-
what higher than before, but the data series is too short to evaluate
if this is a significant development or not.
The monthly development of DIFF12 for the two temperature re-
cords is more complicated, ranging from positive to negative values,
reflecting repeated periods of warming and cooling over time win-
dows of 12 months. However, the most conspicuous observation is
that all three DIFF12-graphs display variations in concert with each
other, suggesting internal coupling or, alternatively, the common ef-
fect of another factor, influencing all three variables.
Fig. 3 shows the result of an identical analysis, but here using glob-
al surface air temperature data from the Goddard Institute for Space
Studies (GISS), USA. The general visual impression is identical to
that conveyed by Fig. 2: all three DIFF12 graphs vary in close concert
with each other.
4. DIFF12 surface temperature analyses
A detailed inspection of Figs. 2 and 3 provides some important
clues to what appears to be an important relation between global
temperature and atmospheric CO
2
. For example, the prominent tem-
perature change peak associated with the well-known 1998 El Niño
event is seen to precede the corresponding CO
2
change peak by al-
most 1 yr, and similar lags of several months are seen for most of
the other DIFF12 CO
2
peaks. There are nine main DIFF12 atmospheric
CO
2
peaks visible in Fig. 2, and Table 1 show these nine peak values
for DIFF12 CO
2
and the corresponding nine DIFF12 values for HadSST2
and HadCRUT3. From this it is seen that DIFF12 CO
2
peak values gen-
erally are associated with negative or near zero DIFF12 values for both
HadSST2 and HadCRUT3.
One additional intriguing detail can be observed in both Figs. 2 and
3. The sea surface temperature change peaks typically occursshortly be-
fore the corresponding global surface air temperature change peak,
suggesting a characteristic sequence of events: 1) change of the global
sea surface temperature, 2) change of global surface air temperature,
and 3) change of global atmospheric CO
2
content. In other words, on
this background global temperature changes appear to be initiated at
the surface of the oceans.
Fig. 4 shows the correlation coefficient calculated for the DIFF12
surface temperature (GISS, HadCRUT3 and HadSST2) and global CO
2
data, to investigate the time lag of atmospheric CO
2
in relation to
the three different surface temperature records. The maximum posi-
tive correlation between CO
2
and temperature is found for CO
2
lag-
ging about 9.5 months after GISS, 10 months after HadCRUT3 and
11 months after HadSST2.
In other words, a change of atmospheric CO
2
typically follows about
11 months after the corresponding change of sea surface temperatures,
and 9.5–10 months later than the global surface air temperature, again
showing that changes in sea surface temperature typically occur a little
(1–1.5 months) before corresponding changes in the global surface air
temperature. The strongest positive correlation coefficient (0.45) be-
tween CO
2
and temperature is found towards the HadSST2 sea surface
temperature. However, thedifference to surface air temperatures is rel-
atively small, and the maximum positive correlation coefficient is 0.40
for HadCRUT3 and 0.43 for GISS.
5. DIFF12 land and ocean temperature analysis
The NCDC data series on surface air temperatures makes it possi-
ble to analyze the phase relation between atmospheric CO
2
and sub-
sets of surface air temperatures calculated for land, ocean, and
global surface areas, respectively. To achieve this, all three NCDC
datasets were exposed to the DIFF12 numerical procedure described
above. The result is shown in Fig. 5.
The DIFF12 NCDC data for land areas show more marked varia-
tions than the corresponding ocean and global surface air tempera-
ture records. As expected, the ocean record is showing the smallest
temperature change rates, reflecting the large difference in heat ca-
pacity between land and ocean surfaces. However, all three DIFF12
NCDC series are seen to vary in concert with each other, as well as
with the DIFF12 CO
2
series. As was the case for the previously inves-
tigated temperature series, changes in the global atmospheric CO
2
data series are seen to lag behind corresponding changes in the
NCDC temperatures.
Fig. 3. 12-month change of global atmospheric CO
2
concentration (NOAA; green), global sea surface temperature (HadSST2; blue) and global surface air temperature (GISS; red
dotted). All graphs are showing monthly values of DIFF12, the difference between the average of the last 12 months and the average for the previous 12 months for each data series.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
54 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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Table 1
Summary of peak DIFF12 CO
2
values and associated DIFF12 HadSST2 and HadCRUT3 values (Fig. 2). Underlining indicates negative values.
Peak
DIFF12 CO
2
123456789
Value DIFF12 CO
2
1.984 2.570 1.472 2.037 2.958 2.552 2.322 2.201 2.383
Value DIFF12 HadSST2 −0.004 0.005 0.038 −0.059 −0.107 0.040 −0.063 −0.123 −0.127
Value DIFF12 HadCRUT3 −0.002 0.046 0.030 −0.098 −0.072 −0.005 −0.043 −0.150 −0.139
Fig. 4. Correlation coefficients between DIFF12 monthly surface air temperatures (a: GISS; b: HadCRUT3), sea surface temperature (c: HadSST2) and global atmospheric CO
2
, for
different monthly lags of CO
2
. The maximum positive correlation is found for CO
2
lagging 9.5 months behind GISS, 10 months behind HadCRUT3 and 11 months behind HadSST2.
Numbers in parentheses show the maximum positive correlation coefficient and the associated time lag of CO
2
in months. The grey vertical arrows indicate no lag.
55O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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Fig. 6 shows statistics of the CO
2
lag in relation to the three differ-
ent NCDC surface air temperature series, when seen over the entire
study period. The maximum positive correlation (0.45) between tem-
perature and CO
2
is found for changes in atmospheric CO
2
lagging
12 months behind ocean surface air temperature. The lag is shorter
(9.5 months) in relation to land surface air temperature, with a max-
imum positive correlation coefficient of only 0.29. In relation to the
global (land and ocean) NCDC temperature atmospheric CO
2
has a
maximum positive correlation (0.39) for a lag of 10 months after cor-
responding changes in temperature.
Thus, summing up for the analysis of the NCDC data, changes in
atmospheric CO
2
is lagging 9.5–12 months behind changes in surface
air temperatures calculated for the two main types of planetary sur-
face, land and ocean, respectively. The strongest correlation (0.45)
between atmospheric CO
2
and NCDC temperature is found in rela-
tion to ocean surface air temperatures, suggesting a rather strong
coupling from changes in ocean temperature to changes in atmo-
spheric CO
2
.
6. DIFF12 troposphere temperature analyses
The above observations all suggest the ocean surface temperature
to be an initiating factor in a planetary sequence of events, coupling
temperature and atmospheric CO
2
. Therefore, maintaining a special
focus on the oceans (covering about 71% of the planetary surface),
we proceed to investigate the lag between the changes of tempera-
tures in the lower troposphere above oceans only, compared to asso-
ciated changes in global atmospheric CO
2
. This is shown in Fig. 7,
using A) data on global atmospheric CO
2
and B) data on lower tropo-
sphere temperatures above oceans (UAH). Here tropical oceans are
defined as oceans within 20 degrees north and south of the Equator.
To ensure that our analysis is comparable with the previous analysis,
all four data series were exposed to the DIFF12 yearly change proce-
dure described above.
In general, the DIFF12 temperature change peaks for these three
important ocean regions are seen to be more or less simultaneous
(Fig. 7), but with the lower troposphere temperature change above
the Northern Oceans lagging slightly behind corresponding changes
above the Southern and the Tropical Oceans. This suggests that
ocean surface temperature changes generally are initiated in the
Southern Hemisphere or near the Equator. However, notwithstanding
these comparatively small internal lags in the ocean temperature
changes as reflected in the lower troposphere, the corresponding
peaks and lows in the DIFF12 change rate of atmospheric CO
2
are
clearly lagging several months after the lower troposphere tempera-
ture change above all three main ocean regions.
Fig. 8 shows the correlation coefficient between DIFF12 for global
atmospheric CO
2
and DIFF12 for lower troposphere temperature
(UAH) over land, ocean and global, respectively, for different lags of
CO
2
in relation to temperature. The time lag is 8 months for land
areas, 10 months for oceans, and 9 months for both land and oceans.
The time lag of CO
2
is slightly shorter (1 month) than found for the
surface temperature records, but changes in atmospheric CO
2
clearly
lag the associated changes in all three lower troposphere tempera-
tures analyzed. The correlation coefficient for the global 9-month
lag is 0.48.
The overall shorter time lag of CO
2
in relation to lower tropo-
sphere temperatures, compared to surface temperatures, suggests a
typical sequence of temperature change events starting at the planet
surface and propagating to the lower troposphere with about one
month delay, given the time resolution of the data series.
7. DIFF12 hemispheric temperature analyses
The above observations suggest the ocean surface temperature to
be an initiating factor in a planetary sequence of events, coupling
temperature and atmospheric CO
2
. This motivates an analysis of the
relation between global atmospheric CO
2
and surface air temperature
in the two hemispheres separately (Fig. 9), as especially the surface of
the Southern Hemisphere is dominated by oceans, and the lower tro-
posphere temperature change above the northern oceans appears to
be lagging slightly behind corresponding changes above the southern
and the tropical oceans.
Here we show hemispherical temperatures according to NCDC, but
other temperature records (HadCRUT3 and GISS) show essential an
identical picture. The visual impression gained from Fig. 9 is similar to
what is shown by the analysis above: DIFF12 variations for atmospheric
CO
2
are tracking behind both sets of hemispherical surface air tempera-
tures. However, because of the dominance of oceans in the Southern
Hemisphere, the temperature change rates are smaller here than in the
Northern Hemisphere. An inspection of Fig. 9 reveals that each DIFF12
temperature peak for the Southern Hemisphere is followed by a corre-
sponding DIFF12 peak in global atmospheric CO
2
. Usually Northern
Hemisphere DIFF12 peaks occur in concert with Southern Hemisphere
peaks, but there are a few occasions where a Northern Hemisphere
DIFF12 temperature peak occurs independently (e.g., early 1986), and
Fig. 5. 12-month change of global atmospheric CO
2
concentration (NOAA; green), change in global surface air temperature (NCDC; blue), land surface air temperature (NCDC; yel-
low) and ocean surface air temperature (NCDC; red dotted). All graphs are showing monthly values of DIFF12, the difference between the average of the last 12 months and the
average for the previous 12 months for each data series. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
56 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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is not followed by a corresponding DIFF12 CO
2
peak. By this the visual
analysis thus favors a mainly Southern Hemisphere coupling to DIFF12
CO
2
peaks.
Fig. 10 shows the correlation coefficient between DIFF12 for global
atmospheric CO
2
and DIFF12 for Northern and Southern Hemisphere
temperature (NCDC), respectively, for different lags of CO
2
in relation
to temperature. Positive correlation is found only for DIFF12 CO
2
lag-
ging DIFF12 temperature. The maximum positive correlation is
found for DIFF12 atmospheric CO
2
lagging about 9.5 months behind
Northern Hemisphere temperature, and 11 months behind Southern
Hemisphere temperature, suggesting the Southern Hemisphere to be
leading the dynamics shown in Fig. 9. The correlation coefficient is
considerably higher (0.56) for the Southern Hemisphere than for
the Northern Hemisphere (0.26), indicating the association between
changes in hemispherical temperature and changes i n global atmospheric
CO
2
to be especially strong for the Southern Hemisphere. Thus, both anal-
yses suggest a mainly Southern Hemisphere origin of observed DIFF12
changes for atmospheric CO
2
.
Fig. 6. Correlation coefficients between DIFF12 monthly NCDC surface air temperatures (a: land; b: ocean; c: global) and global atmospheric CO
2
, for different monthly lags of CO
2
.
The maximum positive correlation is found for CO
2
lagging 9.5 months behind land surface air temperature, 12 months behind ocean surface air temperature and 10 months be-
hind the global surface air temperature. Numbers in parentheses show the maximum positive correlation coefficient and the associated time lag of CO
2
in months. The grey vertical
arrows indicate no lag.
57O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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8. DIFF12 release of CO
2
from anthropogene sources
We next investigated the degree of correlation between atmo-
spheric CO
2
and the release of CO
2
from different anthropogene
sources, using monthly data from the Carbon Dioxide Information
Analysis Center (CDIAC). DIFF12 values were calculated as above,
and the result is shown in Fig. 11. Since 2009 only annual data are
at hand, and these were therefore extrapolated on a flat average
monthly basis. The inclusion of these data in the present analysis is
important, as the increase in atmospheric CO
2
since 1958 usually is
ascribed to anthropogene release of CO
2
from anthropogene sources.
It is generally assumed that about half of the emitted anthropogene
CO
2
is absorbed by the oceans and on land by various physical and
chemical processes, leaving about the remaining half to explain the
rise in global atmospheric CO
2
.
Fig. 11 shows visually that the coupling between DIFF12 changes
in anthropogene CO
2
and DIFF12 changes in atmospheric CO
2
is
weak, especially when compared to what was the case for tempera-
tures (Figs. 2, 3, 5, 7 and 9). Several of the change rate peaks in
anthropogene CO
2
appear to lag behind peaks in atmospheric CO
2
.
In other cases, the direction of change is opposed to each other, as
is exemplified by the pronounced 1998 El Niño peak in atmospheric
CO
2
, corresponding to almost zero change in anthropogene CO
2
. The
2011 change peak for atmospheric CO
2
is another example, as this oc-
curs simultaneously with the negative change rate for anthropogene
CO
2
, caused by the recent economical crisis. A similar contrast has
previously been pointed out (Jaworowski et al., 1992) for Mauna
Loa CO
2
data during the petroleum crisis 1973–74.
As anthropogene CO
2
generally is assumed to explain the modern
rise in atmospheric CO
2
, DIFF12 for this is expected to lag somewhat
after DIFF12 for anthropogene CO
2
. In contrast to this, Fig. 11 appears
to suggest the opposite relation, if anything. This might partly be due
to the extraordinary high use of fossil fuels especially in the Northern
Hemisphere for heating purposes in relatively cold periods, which as-
sociates with DIFF12 CO
2
lows (Fig. 2). However, a detailed analysis of
this falls beyond the present investigation.
In general the coupling appears visually weak compared to the pre-
vious comparisons with temperature (Figs.2,3,5,7and9). The relation
between the two CO
2
data series also appears partly conflicting, and is
difficult to determine precisely on a visual basis alone. However, it is ev-
ident from the visual analysis that changes in atmospheric CO
2
are gen-
erally not tracking changes in anthropogene emissions, which is
contrary to expectation, if anthropogene CO
2
is the main driver for the
observed rise in global atmospheric CO
2
.
The release of CO
2
from fossil fuels into the atmosphere is
strongly asymmetrical, with the overwhelming majority being re-
leased in the Northern Hemisphere around 40°N (Fig. 12). This mo-
tivates a hemispherical analysis of the relation between changes in
anthropogene CO
2
released and changes in atmospheric CO
2
.Due
to the asymmetrical release pattern the influence of anthropogene
CO
2
would be expected to be stronger and more direct in the North-
ern Hemisphere, compared to the Southern Hemisphere.
Fig. 13 shows the relation between DIFF12 for anthropogene CO
2
and DIFF12 values for atmospheric CO
2
recorded at four different sta-
tions representing a transect from the High Arctic to the South Pole.
Here we are using the period from July 1991 to December 2006, as
data (NOAA) only are available from all four stations for this time
window. Once again, there is no direct visual coupling from the
DIFF12 values for anthropogene CO
2
to any of the four individual re-
cords, but instead the DIFF12 values for anthropogene CO
2
appears
to lag somewhat after DIFF12 values for all individual records.
Comparing the dynamic behavior of the four DIFF12 series for at-
mospheric CO
2
, a systematic sequence however stands out: peaks
and lows in DIFF12 values for Ascension Island (8°S) tend to occur
shortly before the DIFF12 values for Mauna Loa (20°N), which leads
before the DIFF12 values for the South Pole (90°S), which leads before
the DIFF12 values for Alert (82°N) in the High Arctic. From this,
changes in atmospheric CO
2
appear to be initiated near or a short dis-
tance south of the Equator, and from there spread towards the two
poles within a year or so. En route, the signal presumable is modulat-
ed by local and regional effects, as is indicated by the much larger an-
nual CO
2
variation (not shown here) in the High Arctic, compared to
that recorded at the South Pole. There is however no indications of
the main signal originating at mid-latitudes in the Northern Hemi-
sphere as would be expected from the release pattern shown in
Fig. 12. The above visual analysis might be taken further by subse-
quent analyses, but here is suffices to investigate if correlation analy-
ses between the four DIFF12 atmospheric CO
2
records and the DIFF12
anthropogene CO
2
record support the result of the visual analysis.
Fig. 14 shows the calculated correlation coefficients between
changes in anthropogene CO
2
and changes in atmospheric CO
2
for the
four stations shown in Fig. 13. In all four cases there is a negative corre-
lation from the time of release and 17–24 months later between DIFF12
changes in anthropogene CO
2
and DIFF12 changes in atmospheric CO
2
,
Fig. 7. 12-month change of global atmospheric CO
2
concentration (NOAA; green), change in lower troposphere temperature over oceans in the Northern Hemisphere (UAH; blue),
in the Southern Hemisphere (UAH; yellow) and in the Tropics (UAH; red dotted). All graphs are showing monthly values of DIFF12, the difference between the average of the last
12 months and the average for the previous 12 months for each data series. (For interpretation of the references to color in this figure legend, the reader is referred to the web
version of the article.)
58 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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showing that changes in the emission of anthropogene CO
2
are not
causing changes in atmospheric CO
2
. The strongest correlation coeffi-
cient ranges from −0.30 to −0.52, and the corresponding lag from 4
to 19 months, depending on latitude. The maximum absolute value of
the negative correlation coefficient is larger for the Southern Hemi-
sphere than for the Northern Hemisphere. On the other hand, the lag
of DIFF12 for anthropogene CO
2
in relation to DIFF12 for atmospheric
CO
2
is larger in the Northern Hemisphere than in the southern. Thus,
there is no indication of a northern mid-latitude origin for DIFF12
changes in atmospheric CO
2
. The lag is about 4 months for Ascension
(8°S), 9 months for the South Pole (90°S), 14 months for Mauna Loa
(20°N), and about 19 months for Alert (82°N) in the High Arctic.
As each station is correlated with identical values (DIFF12 for
anthropogene CO
2
) the observed lags suggest a sequence of events
starting near Equator in the Southern Hemisphere, and from there
propagating towards the two poles.
Fig. 15 (panel a) shows the calculated correlation coefficient
between changes in anthropogene CO
2
and changes in global
Fig. 8. Correlation coefficients between DIFF12 monthly lower troposphere temperatures (UAH) and global atmospheric CO
2
, for different monthly lags of CO
2
in relation to tem-
perature. The maximum positive correlation is found for CO
2
lagging 9 months after lower global troposphere temperatures, 10 months after lower troposphere temperatures over
oceans, and 8 months after lower troposphere temperatures over land. Numbers in parentheses show the maximum positive correlation coefficient and the associated time lag of
CO
2
in months. The grey vertical arrows indicate no lag.
59O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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atmospheric CO
2
for the entire period 1980–2011. It is seen that the
correlation generally is low as was suggested by the visual analysis
above, and noticeably smaller than found for correlations with tem-
peratures (Figs. 4, 6, 8 and 10). From the time of release and to
about 1 yr later there is a negative correlation between DIFF12
changes in anthropogene CO
2
and DIFF12 changes in atmospheric
CO
2
. The maximum positive correlation is found by correlating
DIFF12 changes in CO
2
from fossil fuels with atmospheric CO
2
Fig. 9. 12-monthchange of global atmosphericCO
2
concentration (NOAA; green), change in Northern Hemisphere surface air temperature(NCDC; red dotted),and Southern Hemisphere
air temperature (NCDC; blue).All graphs are showingmonthly values of DIFF12, the differencebetween the average of thelast 12 months andthe average for the previous 12 monthsfor
each data series. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 10. Correlation coefficientsbetween DIFF12 monthlysurface air temperatures in the northern (a) and the SouthernHemisphere (b)and global atmosphericCO
2
, for differen t monthly
lags of CO
2
. The maximum positive correlationis found for CO
2
lagging9.5 months behindNorthern Hemispheretemperature, and 11 months behind SouthernHemisphere temperature.
Numbers in parentheses show the maximum positive correlation coefficient and the associated time lag of CO
2
in months. The grey vertical arrows indicate no lag.
60 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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DIFF12 changes 11 months earlier. However, this is opposite to what
would be expected if changes in anthropogene CO
2
had significant
impact on changes in the amount of atmospheric CO
2
.
However, on shorter time scales the relation is highly variable as
the two panels b and c in Fig. 13 show. Dividing the entire observation
period into the two sub-periods 1980–1998 and 1998–2011 yields a
different result as to the correlation between DIFF12 changes in
anthropogene CO
2
and DIFF12 changes in global atmospheric CO
2
(panel a). For the period 1980–1998 the correlation is found to be
positive for the period at and following release, while it becomes neg-
ative for the time window 1998–2011. A positive correlation would
indeed be expected, if changes in the release of anthropogene CO
2
were controlling changes in atmospheric CO
2
. It is however contrary
to expectation that the maximum positive correlation is found
1 month before the time of release (Fig. 15, panel b).
This demonstrates that the relation between changes in the re-
lease of CO
2
from anthropogene sources and changes in atmospheric
CO
2
is not stable, but undergoes significant changes on a decadal
time scale. Had changes in the release of anthropogene CO
2
repre-
sented the main control on changes in atmospheric CO
2
,therelation
would be stable. A possible explanation for the unstable correlation
might be due to the combined El Niño–La Nino event 1997–2001,
affecting the two investigated sub periods (Fig. 15) differently. An-
other possible explanation was provided by Njau (2007), suggesting
that anthropogene CO
2
has so far been added to the atmosphere in an
amount which would have otherwise been added naturally, espe-
cially by the warming oceans, had the emission of anthropogene
CO
2
been absent. However, a detailed analysis of such and other pos-
sibilities falls beyond the present investigation, and here it suffices to
conclude that the absence of a stable, positive correlation suggests
other processes than the emission of anthropogene CO
2
to control
the main features of the observed changes in atmospheric CO
2
.
Summing up,our analysis suggests that changes in atmospheric CO
2
appear to occur largely independently of changes in anthropogene
emissions. A similar conclusion was reached by Bacastow (1976),
suggesting a coupling between atmospheric CO
2
and the Southern
Oscillation. However, by this we have not demonstrated that CO
2
re-
leased by burning fossil fuels is without influence on the amount of
atmospheric CO
2
, but merely that the effect is small compared to
the effect of other processes. Our previous analyses suggest that
such other more important effects are related to temperature, and
with ocean surface temperature near or south of the Equator
pointing itself out as being of special importance for changes in the
global amount of atmospheric CO
2
.
Fig. 11. 12-month change of global atmospheric CO
2
concentration (NOAA, green), and the change in release of CO
2
from burning of fossil fuels (CDIAC, red). Both graphs are show-
ing monthly values of DIFF12, the difference between the average of the last 12 month and the average for the previous 12 months for each data series.
Fig. 12. Latitudinal 1990 summary of CO
2
emissions from anthropogene sources. Data source: Carbon Dioxide Information Analysis Center (CDIAC).
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9. Volcanic eruptions
Volcanic eruptions are obviously relevant also to consider here, as
they may contribute not only with tephra (e.g. ash), but also with
substantial amounts of greenhouse gases such as H
2
O and CO
2
to
the atmosphere, influencing both temperature and the total amount
of greenhouse gasses. In addition, a gas like SO
2
is injected into the at-
mosphere during eruptions. Oxidation and gas-to-particle conversion
transforms SO
2
to sulphuric acid (H
2
SO
4
), which may effect cloud for-
mation. Each year several volcanic eruptions occur globally, but the
majority are small, and not significant within the present global
context.
The reported magnitude of volcanic eruptions depends much on
both the experience and vantage point of the observer. To meet the
need for a meaningful magnitude measure that can be easily applied
to eruption sizes, Newhall and Self (1982) therefore integrated quan-
titative data with the subjective descriptions of observers, resulting in
the Volcanic Explosivity Index (VEI) to provide a relative measure of
the explosiveness of volcanic eruptions. The VEI scale is a simple
0–8 index of increasing explosivity, based on volume of ejected
mass, eruption cloud height, and other qualitative observations. The
scale is logarithmic, with each interval on the scale representing a
tenfold increase in observed ejecta criteria, with the exception of be-
tween VEI 0, VEI 1 and VEI 2. The VEI-divisions indicate the amount of
tephra (volcanic ash) ejected into the atmosphere, but do not inform
directly about the amount of water vapour and CO
2
emitted, but usu-
ally the amount of these is expected to follow roughly the VEI class,
although with individual variations (see below). The most important
characteristics of the individual VEI-classes are shown in Table 2.
Here we consider only eruptions greater than VEI size class 4, as
these eruptions all are classified as large and therefore may have
ejected significant of tephra and other eruption products to high alti-
tudes, across the tropopause and into the stratosphere. The timing of
such major volcanic eruptions since 1981 is shown in Fig. 16, together
with the DIFF12 changes in the amount of atmospheric CO
2
. Data on
volcanic eruptions were obtained from the Global Volcanism Program
(GWP).
As the VEI-data are qualitatively different from all previous data
types used in the present analysis, being somewhat subjective and
representing discrete events, we shun from attempting any kind of
statistical analysis of these data, and will only consider briefly the vi-
sual impression gained from Fig. 16.
It is well known that major volcanic eruptions may influence glob-
al temperatures 4–5 yr (see, e.g., Lockwood and Fröhlich, 2008;
Thompson et al., 2009) after the culmination of the eruption, al-
though with variations reflecting the position of the volcano in rela-
tion to the Equator. The variable temperature effect of volcanic
eruptions is illustrated by comparing the timing of major eruptions
shown in Fig. 16 with the temperature graphs shown in Figs. 1, 2, 3,
5 and 7. For example, these diagrams all show global cooling after
the very large Mount Pinatubo eruption that began in earnest June
1991. However, Fig. 16 shows that this very large eruption not to
have resulted in any increase of atmospheric CO
2
. The main DIFF12
change observed is actually a period of low growth rate for atmo-
spheric CO
2
. The same observation applies for the group of 2008 erup-
tions. This effect on CO
2
may be explained by volcanic gasses/aerosols
and airborne debris affecting cloud cover, leading to cooling of the
uppermost part of the oceans and therefore increased ability to take
up atmospheric CO
2
, according to Henry's law.
Summing up, although there has been several volcanic eruptions
of at least VEI 4 during the study period, the direct effect on atmo-
spheric CO
2
in general appears to be limited on the time scale inves-
tigated, and only contributes little to explain directly observed
changes in atmospheric CO
2
within the study period. Perhaps erup-
tions larger th an VEI = 6 are r equired t o affe ct the global atmospher-
ic composition and climate significantly, but there has been no
eruptions of this magnitude during the study period. The analysis
might be taken further by also considering the type of volcanism,
Fig. 13. 12-month change of global atmospheric CO
2
concentration for Alert (NOAA; blue), Mauna Loa (NOAA; green), Ascension Island (NOAA; yellow), and the south Pole (NOAA;
purple), and the change in release of anthropogene CO
2
(CDIAC; red). All graphs show monthly values of DIFF12, the difference between the average of the last 12 months and the
average for the previous 12 months for each data series. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 14. Correlation coefficients between DIFF12 change in release of anthropogene CO
2
(CDIAC) and DIFF12 change in atmospheric CO
2
at different stations, for different lags of CO
2
in
relation to CO
2
from fossil fuel. The maximum negative correlation is found for changes in atmospheric CO
2
ranges from 4 to 19 months after changes in CO
2
release from fossil fuels.
Numbers in parentheses show the maximum absolute correlation coefficient and the associated time lag ofCO
2
in months. The grey vertical arrows indicate no lag (the time of release).
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and from which depth in the crust it originates. In general,
deep-seated volcanism is relatively rich in CO
2
, while tholeiitic erup-
tions originating from more shallow depths usually are relatively
rich in H
2
O.
As was the case for anthropogene CO
2
, we can therefore not con-
clude that volcanic activity since January 1980 is without influence on
atmospheric CO
2
, but only that the effect of eruptions in the study peri-
od apparently is small compared to other factors. On the time scale in-
vestigated here, the dominant effect of volcanic eruptions appears to
be increased removal of CO
2
from the atmosphere by the oceans, pre-
sumably caused by volcanic eruptions affecting the global cloud cover,
and thereby resulting in lower ocean surface temperature. On longer
(geological) time scales the relation may however well be different.
10. Fourier frequency analyzes
Visual inspection of Figs. 2, 3, 5, 7 and 9 suggests that some DIFF12
series may be changing according to one or several rhythmic varia-
tions. Therefore, to investigate if these records are in fact character-
ized by such periodic variations, a Fourier frequency analysis was
carried out on four key data series, 1) atmospheric CO
2
(NOAA), 2)
Fig. 15. Correlation coefficients between DIFF12 change in release of anthropogene CO
2
(CDIAC) and global atmospheric CO
2
, for different lags of atmospheric CO
2
in relation to CO
2
from fossil fuel. Numbers in parentheses show the maximum positive correlation coefficient and the associated time lag of CO
2
in months. The grey vertical arrows indicate no lag
(the time of release).
64 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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HadCRUT3, 3) HadSST2 and 4) CO
2
released by use of fossil fuels
(CDIAC). The results are shown in Fig. 17.
The DIFF12 atmospheric CO
2
record is seen to be dominated by
two periods of about 3.8 and 2.5 yr length, both with amplitude
greater than 0.25 ppm. The two DIFF12 temperature spectra are rather
similar to each other, dominated by a period of about 3.7 yr length with
amplitude greater than 0.09 °C, and both showing another important
peak around 2.4 yr. The 2.5–2.4 yr period seen in the three uppermost
records in Fig. 17 may possibly reflect the influence of the Southern
Oscillation, as suggested by both Lamb (1972);Bacastow (1976).
However, the spectrum for the DIFF12 CO
2
anthropogene record
(lowermost panel in Fig. 13) is different. In particular, there is no fre-
quency peak suggesting the existence of an important period in the
range from 3.7 to 3.8 yr, which is a principal period length in the
other three records, but the anthropogene CO
2
record does show a
less pronounced peak around 4 yr. The potential implication of this
peak will be commented later.
The significance levels shown in Fig. 17 are peak-based critical
limit significance levels, which are of particular merit in ascertaining
the significance of the largest spectral component (SeaSolve, 2003;
Humlum et al., 2012). In this type of test, one seeks to disprove the
null hypothesis postulating either a white noise signal with no auto-
correlation (AR(1)=0.0), or a red noise signal with autocorrelation
(AR(1)>0.0). Red noise is present when the background power de-
creases with increasing frequency, and the autoregressive value is a
measure of the similarity between observations in a time series as a
function of the time separation between them. All four DIFF12 series
are characterized by high autocorrelation, with AR(1) coefficients
ranging from 0.97 to 0.99.
With the background set, the peak spectral power was then com-
pared against the various critical limits. A 99% critical limit is that
level where in only 1 of 100 separate random noise signals the
highest peak would achieve this height strictly due to random chance.
Likewise, for a peak reaching the 50% critical limit there is a 50–50
probability that this could have arisen strictly from chance. The criti-
cal limit test used here is different from traditional confidence or sig-
nificance levels that apply to a single data set only. For example, a
standard 95% confidence limit would specify a level where 5% of the
points in a single spectrum would be expected to lie above this height
strictly due to random chance.
Exposed to the critical limit test all four DIFF12 series display sev-
eral frequency peaks exceeding the 95% critical limit. For that reason
the alternative null hypothesis, that the observed oscillations repre-
sent red noise only, can be rejected using a 95% peak-based critical
limit test, and the significant frequency peaks are positively worthy
of interpretation. Several peaks are seen to exceed even the 99% crit-
ical limit.
Comparing the different Fourier frequency spectra shown in
Fig. 17, the degree of similarity between the two temperature records
(HadCRUT3; HadSST2) and the atmospheric CO
2
record appears
higher than the similarity between anthropogene CO
2
and atmo-
spheric CO
2
. This lends support to the result of the previous analyzes,
that changes in atmospheric CO
2
appear to be coupled especially to
changes in temperature, and not to the same degree to changes in
CO
2
released by anthropogene sources.
The lower panel (d) in Fig. 17 indirectly shows the main rhythms of
the world economy. However, theamount of anthropogene CO
2
must to
some degree also reflect the production of heat and electricity for
heating purposes, especially during winter in the Northern Hemisphere,
as this is where most people live. Thus, it is not entirely surprising that
the prominent temperature DIFF12 peak of about 3.7 yr (HadCRUT3
and HadSST2) may find itself represented in the broad frequency peak
around 0.25 yr
−1
(4 yr) in the DIFF12 data for anthropogene CO
2
.The
visual inspection of Fig. 11 leads to a similar interpretation.
Table 2
Volcanic Explosivity Index (VEI) eruption size classes based on Newhall and Self (1982) and Simkin and Siebert (1994).
VEI class 0 1 2 3 4 5 6 7 8
Description Non-explosive Small Moderate Moderate–large Large Very large Very large Very large Very large
Tephra (m
3
)b1×10
4
b1×10
6
b1×10
7
b1×10
8
b1×10
9
b1×10
10
b1×10
11
b1×10
12
>1×10
12
Cloud height (km) b0.1 0.1–11–53–15 10–25 >25 > 25 >25 > 25
Fig. 16. 12-month change of global atmospheric CO
2
concentration (NOAA; green), and the timing of major (VEI > 3) volcanic eruptions (GWP). The CO
2
graph is showing monthly
values of DIFF12, the difference between the average of the last 12 months and the average for the previous 12 months for each data series. The DIFF12 CO
2
values have been shifted
12 months forward to correspond correctly with the time axis used for plotting the volcanic eruptions.
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11. Discussion
By the above analysis we have demonstrated that there exists a
clear phase relationship between the change of different global
temperature indices, and corresponding changes in the global
amount of atmospheric CO
2
. We have used data on CO
2
and temper-
ature with a monthly time resolution for the time window January
1980–December 2011, but instead of analyzing the monthly data,
Fig. 17. Fourier frequency spectra (Best Exact N composite algorithm; SeaSolve, 2003) for DIFF12's for changes in a) atmospheric CO
2
, b) HadCRUT3, c) HadSST2 and d) CO
2
released
by use of fossil fuels. The DIFF12 atmospheric CO
2
record is dominated by highly significant periods of about 3.8 and 2.5 yr length, while especially a period of about 3.7 yr is dom-
inant in both DIFF12 temperature records. The DIFF12 record for CO
2
from fossil fuels is characterized by a different type of spectrum, and with peaks of generally less significance
than characterizing the other records. The grey tone indicates increasing amplitude within each record. The stippled lines indicate peak-based critical limit significance levels.
66 O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
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we have removed the influence of annual cycles by analyzing DIFF12
values. The average DIFF12 CO
2
value for the entire observation peri-
od is about 1.7 ppm/yr, which adds up to the entire observed increase
of 51 ppm of atmospheric CO
2
since January 1980. Therefore, to the
degree that the observed DIFF12 atmospheric CO
2
values (Figs. 3, 5,
7 and 9) can be explained by temperature changes; the overall in-
crease of atmospheric CO
2
since January 1980 (Fig. 1) is also
explained.
The coupling from changes in atmospheric CO
2
to changes in tem-
perature appears to be weak. The rate of temperature increase often
decreases when the amount of atmospheric CO
2
increases (Figs. 2,
3, 5, 7 and 9). There are even several examples where the DIFF12 tem-
perature change becomes negative (Table 1), corresponding to de-
creasing temperatures, even though the contemporary DIFF12 CO
2
change is positive.
In general, we find that changes in atmospheric CO
2
are lagging
behind changes in any of the five different temperature records con-
sidered. The typical lag is 9.5–12 months for surface temperatures
and about 9 months for lower troposphere temperatures, suggesting
a temperature sequence of events from the surface to the lower
troposphere.
As cause always must precede effect, this observation demon-
strates that modern changes in temperatures are generally not in-
duced by changes in atmospheric CO
2
. Indeed, the sequence of
events is seen to be the opposite: temperature changes are taking
place before the corresponding CO
2
changes occur.
As the theoretical initial temperature effect of changes in atmo-
spheric CO
2
must materialize first in the troposphere, and then subse-
quently at the planet surface (land and ocean), our diagrams 2–8
reveal that the common notion of globally dominant temperature
controls exercised by atmospheric CO
2
is in need of reassessment.
Empirical observations indicate that changes in temperature general-
ly are driving changes in atmospheric CO
2
, and not the other way
around.
Numerical global climate models generally assume atmospheric
CO
2
in combination with alleged feed-back effects on atmospheric
humidity and cloud cover to have a clear net warming effect, and
that changes in atmospheric CO
2
therefore represent a main driver
for global temperature changes. For that reason changes in tempera-
ture should therefore be lagging behind corresponding changes in
CO
2
. However, Figs. 4, 6, 8 and 10 show correlation between changes
in temperature and CO
2
to be negative for negative offsets (tempera-
ture lagging CO
2
), indicating that changes towards higher concentra-
tions of atmospheric CO
2
then empirically would associate with less
rapid temperature increase or even a temperature decrease. Howev-
er, as this would invalidate the basic assumption of CO
2
having a
clear net warming effect, the perception of temperature lagging be-
hind CO
2
must therefore be rejected. A visual inspection of the data
displayed in Figs. 2, 3, 5, 7 and 9 also show the notion of temperature
lagging CO
2
to be implausible.
Thus, the simplest explanation of observed changes in DIFF12 for at-
mospheric CO
2
is that they are induced by changes in temperature, as
illustrated by Figs. 2–10. Consequently, a substantial part of the atmo-
spheric increase of CO
2
since January 1980 can be explained by associat-
ed changes in temperature,and presumably especially changes inocean
temperatures (Toggweiler, 1999; Monnin et al., 2001; Goldberg, 2008),
as this is where we find both the strongest correlation to changes in CO
2
(Figs. 4, 6 and 8), and the longest time lag.
The maximum positive correlation between ocean temperatures
and atmospheric CO
2
is within a range from 0.45 to 0.48, depending
on which dataset is considered (HadSST2, NCDC or UAH). With a sam-
ple size of 361 (number of monthly DIFF12 values) these correlation
coefficients are highly significant at the 0.05 level, and correspond
to a goodness-of-fit(r
2
) ranging from 0.20 to 0.23. This represents a
fair degree of explanation, and far bigger than achieved by any
other factor considered in the present analysis, but it also suggests
that there are other factors beyond ocean surface temperature
which have influenced observed changes in atmospheric CO
2
since
January 1980. Examples of such potential factors are changes in soil
moisture, living biomass, volcanic eruptions, geological weathering
processes, burning of fossil fuels, etc. The correlation between CO
2
re-
leased by anthropogene sources and changes in atmospheric CO
2
is not
stable (Fig. 15), and not able toexplain much of the observed increase in
atmospheric CO
2
since January 1980. A qualitatively identical conclusion
may possibly be suggested for the effect of volcanic eruptions during the
study period, but the character of the volcanic data available does not
make it possible to carry out a comparable statistical analysis on this. Ac-
tually, on the time scale investigated, the net effect of a major volcanic
eruption appears to be a reduction of the prevailing increase rate of at-
mospheric CO
2
, probably an effect of ocean cooling induced from cloud
effects.
Summing up, monthly data since January 1980 on atmospheric CO
2
and sea and air temperatures unambiguously demonstrate the overall
global temperature change sequence of events to be 1) ocean surface,
2) surface air, 3) lower troposphere, and with changes in atmospheric
CO
2
always lagging behind changes in any of these different tempera-
ture records.
A main control on atmospheric CO
2
appears to be the ocean sur-
face temperature, and it remains a possibility that a significant part
of the overall increase of atmospheric CO
2
since at least 1958 (start
of Mauna Loa observations) simply reflects the gradual warming of
the oceans, as a result of the prolonged period of high solar activity
since 1920 (Solanki et al., 2004). Based on the GISP2 ice core proxy re-
cord from Greenland it has previously been pointed out that the pres-
ent period of warming since 1850 to a high degree may be explained
by a natural c. 1100 yr periodic temperature variation (Humlum et al.,
2011).
The atmospheric CO
2
growth rate DIFF12 is seen to be at maximum
about the same time when SST DIFF12 is on the falling limb from a pre-
vious peak, indicating ocean temperature to be approaching a tempera-
ture maximum or falling after passing a peak (see, e.g., Fig. 2 and
Table 1). As the rate of CO
2
net outgassing from the ocean then is affect-
ed by reduced solubility, this offers a simple physical explanation of the
observed time lag. At least, the association between periods of maxi-
mum DIFF12 CO
2
increase and no or negative ocean surface tempera-
ture change (Table 1)isdifficult to reconcile with the notion of
atmospheric CO
2
changes controlling changes in ocean surface temper-
ature. However, more work is needed to investigate the details of
this, and it is worth noticing that atmospheric CO
2
increases over
the period considered, even when air temperatures decreases. It is
however clear from the data that emission of CO
2
from the oceans
and other natural sources plays an important role in observed
changes of atmospheric CO
2
. Independent of human emissions, this
contribution to atmospheric CO
2
is not controllable and little pre-
dictable, although the coupling to ocean surface temperature dem-
onstrated above may provide a starting basis for future prediction
attempts.
Analyses of a pole-to-pole transect of atmospheric CO
2
records
suggest that changes in atmospheric CO
2
are initiated south of the
Equator, but probably not far from the Equator, and from there
spreads towards the two poles within a year or so (Fig. 13). This ob-
servation specifically points towards the oceans at or south of the
Equator as an important source area for observed changes in atmo-
spheric CO
2
. The major release of anthropogene CO
2
is taking place
at mid-latitudes in the Northern Hemisphere (Fig. 12), but the
north–south transect investigated show no indication of the main
change signal in atmospheric CO
2
originating here. The main signal
must therefore be caused by something else. A similar conclusion,
but based on studies of the residence time of anthropogenic CO
2
in
the atmosphere, was reached by Segalstad (1998);Essenhigh (2009).
In general, the level of atmospheric CO
2
is slightly higher in the
Northern Hemisphere than in the Southern Hemisphere. This might
67O. Humlum et al. / Global and Planetary Change 100 (2013) 51–69
Author's personal copy
be seen as due to anthropogene CO
2
mainly being released in the
Northern Hemisphere (Fig. 12). However, had this being the explana-
tion, the northern mid latitudes should had been the origin for
changes in atmospheric CO
2
, which is shown not to be the case
(Figs. 13 and 14). Thus, presumably other processes are responsible
for the north–south gradient in atmospheric CO
2
, such as, e.g., respi-
ration by land-based organisms (especially Northern Hemisphere)
and ocean uptake (especially Southern Hemisphere).
Over the entire study period atmospheric CO
2
shows a continuous
increase, when annual variations are ignored. This might also be
interpreted as being the result of the release of anthropogene CO
2
,
but the observed propagation of the main atmospheric CO
2
change
signal along the pole-to-pole transect (Fig. 13) seems to argue against
such an interpretation. The signal propagation instead suggests a pos-
sible connection to especially the southern oceans and their surface
temperature, but a detailed analysis of this falls beyond the present
study.
The modern relation between temperature and CO
2
is qualitatively
identical to that demonstrated by ice cores for the Quaternary glacial–
interglacial transitions (Mudelsee, 2001; Caillon et al., 2003), although
the modern time lag between temperature and CO
2
is considerably
shorter. However, this is presumably reflecting the much coarser time
resolution provided by ice cores, displaying only changes on a
multi-decadal scale. This is partly due to sampling resolution, partly
due to gas diffusion within the ice that averages out any surfacetemper-
ature variability shorter than a few decades (Severinghaus et al., 1998).
12. Conclusions
There exist a clear phase relationship between changes of atmo-
spheric CO
2
and the different global temperature records, whether
representing sea surface temperature, surface air temperature, or lower
troposphere temperature, with changes in the amount of atmospheric
CO
2
always lagging behind corresponding changes in temperature.
(1) The overall global temperature change sequence of events ap-
pears to be from 1) the ocean surface to 2) the land surface to
3) the lower troposphere.
(2) Changes in global atmospheric CO
2
are lagging about 11–
12 months behind changes in global sea surface tempera-
ture.
(3) Changes in global atmospheric CO
2
are lagging 9.5–10 months
behind changes in global air surface temperature.
(4) Changes in global atmospheric CO
2
are lagging about 9 months
behind changes in global lower troposphere temperature.
(5) Changes in ocean temperatures appear to explain a substantial
part of the observed changes in atmospheric CO
2
since January
1980.
(6) CO
2
released from anthropogene sources apparently has little in-
fluence on the observed changes in atmospheric CO
2
,and
changes in atmospheric CO
2
are not tracking changes in human
emissions.
(7) On the time scale investigated, the overriding effect of large vol-
canic eruptions appears to be a reduction of atmospheric CO
2
,
presumably due to the dominance of associated cooling effects
from clouds associated with volcanic gases/aerosols and volca-
nic debris.
(8) Since at least 1980 changes in global temperature, and presum-
ably especially southern ocean temperature, appear to represent
a major control on changes in atmospheric CO
2
.
Acknowledgments
The present study could not have been carried out without the ex-
istence of open-access international databases on temperature and
atmospheric CO
2
. We thank one unknown referee for pointing out
the variable correlation between changes in the release of CO
2
from
anthropogene sources and changes in atmospheric CO
2
on a decadal
time scale. In addition, this referee suggested the hemispheric analy-
ses (Section 7). We are finally grateful for informal discussions in Oslo
with Drs. O.H. Ellestad, O. Engvold, and P. Brekke. Also Drs. T.V.
Segalstad and H. Yndestad have for long time been important sources
of information and inspiration.
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