remember the lively discussions of already several
years ago on WUWT
about the reasons why I am pretty sure that the CO2
increase in the atmosphere over the past 57 years
(direct atmospheric measurements) and 165 years (ice
cores and proxies) is man-made    . That did
provoke hundreds of reactions from a lot of people pro
There still is one unresolved recurring
discussion between mainly Bart/Bartemis and me about
one - and only one - alternative natural explanation:
if the natural carbon cycle is extremely huge and the
sinks are extremely fast, it is -theoretically-
possible that the natural cycle dwarfs the human
input. That is only possible if the natural cycle
increased a fourfold in the same time frame as human
emissions (for which is not the slightest indication)
and it violates about all known observations.
Nevertheless, Bart's (and Dr. Salby's) reasoning is
based on a remarkable correlation between temperature
variability and the CO2
rate of change variability with similar slopes:
Fig.1: Bart's combination of T and dCO2/dt from WoodForTrees.org
Bart (and Dr. Salby) thinks that the
match between variability and slopes (thanks to an
arbitrary factor and offset) proves beyond doubt that
temperature causes both the variability and slope of
the CO2 rate of change. The
following will show that variability and slope have
nothing in common and temperature is not the cause of
the slope in the CO2
rate of change.
Note: for those who know the theory behind transient
responses, it gets interesting from point
To make it clear we need to show what
happens with CO2
if one varies temperature in different ways. CO2
fluxes react immediately on a temperature change, but
the reaction on CO2 levels needs time, no matter if
that is by rotting vegetation or the ocean surfaces.
Moreover, increasing CO2
levels in the atmosphere reduce the CO2 pressure
difference between ocean surface and the atmosphere,
thereby reducing the average in/out flux, until a
certain CO2 level in the atmosphere is
reached where in and out fluxes again are equal.
In algebraic form:
dCO2/dt = k2*(k*(T-T0) - ΔpCO2)
Where T0 is the temperature at the start
of the change and ΔpCO2 the change in CO2 partial
pressure in the atmosphere since the start of the
temperature change, where pCO2(atm) was in equilibrium
with pCO2(aq) at T0. The transient response in rate of
change is directly proportional to the CO2 pressure
difference between the pCO2 change in water (caused by
a change in temperature) and the CO2 pressure in the
When the new equilibrium is reached, dCO2/dt = 0 and:
k*(T-T0) = ΔpCO2
Where k = ~16 ppmv/°C which is the value that Henry's law gives (4-17 ppmv/°C in the literature) for the equilibrium between seawater and the atmosphere.
In the next plot we assume the response
is from vegetation, mainly in the tropics, as that is
a short living response as will be clear from
measurements in the real world in chapter 3:
Fig. 2: Response of bio-CO2 on a step change of temperature .
If the temperature has a slope, CO2
will follow the slope with some delay:
Fig. 3: Response of bio-CO2 on a continuous increase of temperature .
A continuous increase of temperature will induce a continuous increase of CO2 with an increasing dCO2/dt until both increases parallel each other and dCO2/dt remains constant. This ends when the "fuel" (like vegetation debris) gets exhausted or the temperature slope ends. In fact, this type of reaction is more applicable to the oceans than on vegetation, but this all is more about the form of the reaction than what causes it...A typical example is the warming from the depth of a glacial period to an interglacial in the past 800,000 years: it takes about 5,000 years to reach the new maximum temperature and CO2 lags the temperature increase with some 800 +/- 600 years.
Many changes in nature are random up
and down, besides step changes and slopes. Let's
first see what happens if the temperature changes
with a nice sinus change (a sinusoid):
Fig. 4: Response of bio-CO2 on a continuous sinusoidal change in temperature .
It can be mathematically explained
that the lag of the CO2
response is maximum pi/2 or 90° after a sinusoidal
temperature change . Another mathematical
law is that by taking the derivatives, one
shifts the sinusoid forms 90° back in time. The
remarkable result in that case is that changes
in T synchronize with changes in dCO2/dt, that
will be clear if we plot T and dCO2/dt together
in next item.
To make the temperature changes and
their result on CO2
changes a little more realistic, we show here the
result of a double sinusoid where the
sinusoids have different periods. After all
natural changes are not that smooth...:
Fig. 5: Response of bio-CO2 on a continuous double sinusoidal change in temperature .
As one can see, the change in CO2
still follows the same form of the double sinusoid
in temperature with a lag. Plotting temperature
and dCO2/dt together shows a
near 100% fit without lag, which implies that T
changes directly cause immediate dCO2/dt
changes, but that still says nothing about any
influence on a trend. In fact still T changes lead
CO2 changes and dT/dt
changes lead dCO2/dt
changes, but that will be clear in next plot...
Now we are getting even more
realistic, not only we introduced a lot of
variability, we also have added a slight linear
increase in temperature. The influence of the
latter is not on CO2 from the biosphere
(that is an increasing sink with temperature over
longer term), but from the oceans with its own
Fig. 6: Response of Natural CO2 on a continuous double sinusoid plus slope change in temperature .
As one can see, again CO2 follows temperature as well for the sinusoids as for the slope. So does dCO2/dt with a lag after dT/dt, but with a zero trend, as the derivative of a linear trend is a flat line with only some offset from zero.
This proves that the trend in T is not the cause of any trend in dCO2/dt, as the latter is a flat line without a trend. No arbitrary factor can match these two lines, except (near) zero for the temperature trend to match the dCO2/dt trend, but then you erase the amplitudes of the variability...
Thus while the variability in
temperature matches the variability in CO2
rate of change, there is no influence at all from
the slope in temperature on the slope in CO2
rate of change.
A linear increase in temperature doesn't introduce a slope in the CO2 rate of change at any level.
All previous plots were about the effect of temperature on the CO2 levels in the atmosphere. Volcanoes and human emissions are additions which are independent of temperature and introduce an extra amount of CO2 in the atmosphere above the temperature dictated dynamic equilibrium. That has its own decay rate. If that is slow enough, CO2 builds up above the equilibrium and if the increase is slightly quadratic, as the human emissions are, that introduces a linear slope in the derivatives.
Fig. 7: Response of CO2 on a continuous double sinusoidal + slope change in temperature + emissions .
Several important points to be noticed:
- The variability of CO2 in the atmosphere still lags the temperature changes, no matter if taken alone or together with the result of the emissions. No distortion of amplitudes or lag times. Only simple addition of independent results of temperature and emissions.
- The slope of the natural CO2 rate of change still is zero.
- The relative amplitude of the variability is a small factor compared to the huge effect of the emissions.
- The slope and variability of temperature and CO2 rate of change is a near perfect match, despite the fact that the slope is entirely from the slightly quadratic increase of the emissions and the effect of temperature on the slope of the CO2 rate of change is zero...
"match" between the slope
in temperature and the CO2 slope in rate of
change is entirely spurious.
Most of the variability in CO2 rate of change is a response of (tropical) vegetation on (ocean) temperatures, mainly the Amazon. That the main variability is from vegetation is easily distinguished from the ocean influences, as a change in CO2 releases from the oceans gives a small increase in 13C/12C ratio (δ13C) in atmospheric CO2, while a similar change of CO2 release from vegetation gives a huge, opposite change in δ13C. Here for the period 1991-2012 (regular δ13C measurements at Mauna Loa and other stations started later than CO2 measurements):
Fig. 8: 12 month averaged derivatives
from temperature and CO2/ δ13C measurements at
Mauna Loa .
Almost all the year by year variability in CO2 rate of change is a response of (tropical) vegetation on the variability of temperature (and rain patterns). That levels off in 1-3 years either by lack of fuel (organic debris) or by an opposite temperature/moisture change . Over periods longer than 3 years, it is proven from the oxygen balance that the overall biosphere is a net, increasing sink of CO2, the earth is greening , .
Not only is the net effect of the biological CO2 rate of change completely flat as result of a linear increasing temperature, it is even slightly negative in offset...
The oceans show a CO2 increase in ratio to the temperature increase: per Henry's law about 16 ppmv/°C. That means that the ~0.6°C increase over the past 57 years is good for ~10 ppmv CO2 increase in the atmosphere that is a flat line with an offset of 0.18 ppmv/year or 0.015 ppmv/month in the above graph.
There is a non-linear component in the ocean surface equilibrium with the atmosphere for a temperature increase, but that gives not more than a 3% error on a change of 1°C at the end of the flat trend or a maximum "trend" of 0.00045 ppmv/month after 57 years. That is the only "slope" you get from the influence of temperature on CO2 levels. Almost all of the slope in CO2 rate of change is from the emissions...
The response of CO2 to the
variability is certainly from
vegetation, but as vegetation is a
proven small and increasing
sink for CO2, that is not
the cause of the increase of CO2
in the atmosphere or the slope in the CO2
Human emissions show a slightly quadratic increase over the past 115 years. In the early days more guessed than calculated, in recent decades more and more accurate, based on standardized inventories of fossil fuel sales and burning efficiency. Maybe more underestimated than overestimated, because of the human nature to avoid paying taxes, but rather accurate +/- 0.5 GtC/year or +/- 0.25 ppmv/year.
The increase in the atmosphere was measured in ice cores with an accuracy of 0.12 ppmv (1 sigma) and a resolution (smoothing) of less than a decade over the period 1850-1980 (Law Dome DE-08 cores). CO2 measurements in the atmosphere are better than 0.1 ppmv since 1958 and there is a ~20 year overlap (1960 - 1980) between the ice cores and the atmospheric measurements at Mauna Loa. That gives the following graph for the temperature - emissions - increase in the atmosphere:
Fig. 9: Temperature, CO2
emissions and increase in the atmosphere .
While the variability in temperature
is high, that is hardly visible in the CO2
variability around the trend, as the amplitudes
are not more than 4-5 ppmv/°C (maximum +/- 1.5 ppmv)
around the trend of more than 90 ppmv. To give a
better impression, here a plot of the effect of
temperature on the CO2 variability
in the period 1985-2000, where several relative
large temperature changes can be noticed like
the 1991/2 Pinatubo eruption and the 1998 super
Fig. 10: Influence of temperature variability on CO2 variability around the CO2 trend 
It is easy to recognize the 90° lag after temperature
changes, but the influence of temperature on the
variability is small, here calculated with 4
ppmv/°C. For the trend, the CO2 increase
caused by the 0.2°C ocean surface temperature
increase in that period is around 3 ppmv of the
22 ppmv measured...
of temperature on the CO2
variability is quite
small: +/- 1.5 ppmv around the slope.
With the theoretical transient response of CO2 to temperature in mind, we can calculate the response of vegetation and oceans to the increased temperature and its variability:
What does that show in the derivatives? First the transient response of the biosphere and oceans to temperature variability:
It seems that
the amplitude of the natural variability is overblown
in the RSS plot, but not in the HadCRUT-SH plot. In
both the temperature and the transient response of CO2
are equally synchronized with the observed CO2
rate of change with hardly any slope in the transient
response. Thus while all the variability is from the
transient response, there is hardly any contribution
of oceans or biosphere to the slope in CO2
rate of change.
Now we can add human emissions into the rate of change:
For an exact match of
the slopes of RSS temperature and CO2
rate of change one need to multiply
the temperature curve with a factor and add an offset. The
match of the slopes of the observed
of change and the calculated rate of
from the emissions plus the small slope of the
natural transient response needed a
very small offset to have a perfect
match in the slopes. The calculated
CO2 slope from the emissions and the
observed CO2.dt slope have a small
difference, but that is not
measurable in the total increase of
A drawback of the artificial match of the
slopes of temperature with the CO2 rate of change is
that this also affects the amplitude of the
variability as one factor is used to adjust the
slopes and the variability. As both are caused by
different processes (vegetation is dominant in the
variability, but has a zero to negative slope over
periods longer than 1-3 years), that leads to a too
low amplitude of the variability if the difference
in slope angles is large, as is the case for the
As can be seen in these
graphs, both temperature rate of change and CO2 rate of change from humans + natural
transient response show the same variability in
timing and form. That is clear if we enlarge the
graphs for the period 1987-2002, encompassing
the largest temperature changes
of the whole period, the
1991 Pinatubo eruption and the
1998 super El
Which of the two possible solutions is right is quite
easy to know, by looking which of the two matches the
The straight forward result:
- The temperature-only match violates all known observations, not at least Henry's law for the solubility of CO2 in seawater, the oxygen balance - the greening of the earth, the 13C/12C ratio, the 14C decline,... Together with the lack of a slope in the derivatives for a transient response from oceans and vegetation to a linear increase in temperature.
- The emissions + natural variability matches all observations. See: http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html
Most of the variability in the rate of change of CO2 is caused by the influence of temperature on vegetation. While the influence on the rate of change seems huge, the net effect is not more than about +/- 1.5 ppmv around the trend and zeroes out after 1-3 years.
Most of the slope in the rate of change of CO2 is caused by human emissions. That is about 110 ppmv from the 120 ppmv over the full 165 years (about 70 from the 80 ppmv over the past 57 years). The remainder is from warming oceans which changes CO2 in the atmosphere with about 16 ppmv/°C, per Henry's law, no matter if the exchanges are static or dynamic.
Yearly human emissions quadrupled
from over 1 ppmv/year in 1958 to 4.5 ppmv/year in
2013. The same quadrupling happened in the
increase rate of the atmospheric CO2 (at
average around 50% of human emissions) and in the
difference, the net sink rate.
There is not the slightest indication in any direct measurements or proxy that the natural carbon cycle or any part thereof increased to give a similar fourfold increase in exactly the same time span, which was capable to dwarf human emissions..
 Engelbeen on why he thinks the CO2 increase is man made (part 4)
Fourth comment by Paul_K, and further on in that discussion, gives a nice overview of the effect of a transient response of CO2 to temperature. Ignore the warning about the "dangerous" website if you open the referenced image.
Lecture of Pieter Tans at the festivities of 50 years of Mauna Loa measurements, from slide 11 on.
 http://www.sciencemag.org/content/287/5462/2467.short full text free after registration.
temperature trends of RSS (satellites) and HadCRUT4
(thermometer hut) and the CO2 trend and derivatives were
downloaded from Wood for
CO2 and δ13C trends are derived from the carbon tracker of NOAA: http://www.esrl.noaa.gov/gmd/dv/iadv/
CO2 emissions until 2008 from: http://cdiac.ornl.gov/trends/emis/tre_glob.html
CO2 emissions from 2009 on from: http://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=90&pid=44&aid=8
 The spreadsheet can be downloaded from:
 The spreadsheet can be downloaded
 The spreadsheet can be downloaded from:http://www.ferdinand-engelbeen.be/klimaat/RSS_Had_transient_response.xlsx