Some may
remember the lively discussions of already several
years ago on WUWT
about the reasons why I am pretty sure that the CO_{2}
increase in the atmosphere over the past 57 years
(direct atmospheric measurements) and 165 years (ice
cores and proxies) is man-made [1] [2] [3] [4]. That did
provoke hundreds of reactions from a lot of people pro
and anti.
http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html
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 CO_{2}
rate of change variability with similar slopes:
Fig.1:
Bart's combination of T and dCO_{2}/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 CO_{2} 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 CO_{2}
rate of change.
Note: for those who know the theory behind transient
responses, it gets interesting from point
2.5 onward...
To make it clear we need to show what
happens with CO_{2}
if one varies temperature in different ways. CO_{2}
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 CO_{2}
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 CO_{2} level in the atmosphere is
reached where in and out fluxes again are equal.
In algebraic form:
dCO_{2}/dt
= k2*(k*(T-T0) - ΔpCO_{2})
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
atmosphere.
When the new equilibrium is reached, dCO_{2}/dt
= 0 and:
k*(T-T0) = ΔpCO_{2}
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-CO_{2} on a step change of temperature [10].
If the temperature has a slope, CO_{2}
will follow the slope with some delay:
Fig. 3: Response of
bio-CO_{2} on a continuous increase
of temperature [10].
A continuous increase of temperature will
induce a continuous increase of CO2 with an increasing
dCO2/dt until both increases parallel each other and dCO_{2}/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...
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-CO_{2}
on a continuous sinusoidal change in temperature [10].
It can be mathematically explained
that the lag of the CO_{2}
response is maximum pi/2 or 90° after a sinusoidal
temperature change [5]. 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 dCO_{2}/dt, that
will be clear if we plot T and dCO_{2}/dt together
in next item.
To make the temperature changes and
their result on CO_{2}
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-CO_{2}
on a continuous double sinusoidal change in
temperature [10].
As one can see, the change in CO_{2}
still follows the same form of the double sinusoid
in temperature with a lag. Plotting temperature
and dCO_{2}/dt together shows a
near 100% fit without lag, which implies that T
changes directly cause immediate dCO_{2}/dt
changes, but that still says nothing about any
influence on a trend. In fact still T changes lead
CO_{2} changes and dT/dt
changes lead dCO_{2}/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 CO_{2} from the biosphere
(that is an increasing sink with temperature over
longer term), but from the oceans with its own
amplitude:
Fig. 6: Response of Natural CO_{2}
on a continuous double sinusoid plus slope change
in temperature [10].
As one can see, again CO_{2}
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 dCO_{2}/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
dCO_{2}/dt trend, but then you
erase the amplitudes of the variability...
Thus while the variability in
temperature matches the variability in CO_{2}
rate of change, there is no influence at all from
the slope in temperature on the slope in CO_{2}
rate of change.
A linear
increase in temperature doesn't introduce a
slope in the CO_{2}
rate of change at any level.
All previous plots were about the
effect of temperature on the CO_{2}
levels in the atmosphere. Volcanoes and human
emissions are additions which are independent of
temperature and introduce an extra amount of CO_{2}
in the atmosphere above the temperature dictated
dynamic equilibrium. That has its own decay rate.
If that is slow enough, CO_{2}
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 CO_{2}
on a continuous double sinusoidal + slope change
in temperature + emissions [10].
Several important points to be
noticed:
- The variability of CO_{2}
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 CO_{2}
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 CO_{2}
rate of change is zero...
The
"match" between the_{ }slope
in temperature and the CO2 slope in rate of
change is entirely spurious.
3.1 The cause
of the
variability:
Most of the variability in CO_{2}
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 CO_{2}
releases from the oceans gives a small increase in
13C/12C ratio (δ13C) in atmospheric CO_{2},
while a similar change of CO_{2}
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 CO_{2}
measurements):
Fig. 8: 12 month averaged derivatives
from temperature and CO2/ δ13C measurements at
Mauna Loa [9].
Almost all the year by year
variability in CO_{2}
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 [5].
Over periods longer than 3 years, it is proven
from the oxygen balance that the overall biosphere
is a net, increasing sink of CO_{2},
the earth is greening [6],
[7].
Not only is the net effect of the
biological CO_{2}
rate of change completely flat as result of a
linear increasing temperature, it is even slightly
negative in offset...
The oceans show a CO_{2}
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 CO_{2} 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 CO_{2} levels. Almost all of the slope in CO_{2} rate of change is from the emissions...
The response of CO_{2} to the
temperature
variability is certainly from
vegetation, but as vegetation is a
proven small and increasing
sink for CO_{2}, that is not
the cause of the increase of CO_{2}
in the atmosphere or the slope in the CO_{2}
derivative.
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). CO_{2}
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, CO_{2}
emissions and increase in the atmosphere [9].
While the variability in temperature
is high, that is hardly visible in the CO_{2}
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 CO_{2} 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
El Niño:
Fig. 10: Influence of temperature
variability on CO_{2}
variability around the CO2 trend [9]
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 CO_{2} increase
caused by the 0.2°C ocean surface temperature
increase in that period is around 3 ppmv of the
22 ppmv measured...
The influence
of temperature on the CO_{2}
variability is quite
small: +/- 1.5 ppmv around the slope.
3.3 The response to temperature variability and human emissions:
With the theoretical transient response of CO_{2}
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:
Fig. 13: RSS and HadCRUT-SH
temperature changes compared to observed CO_{2}
rate of change and transient response of natural CO_{2} (biosphere+oceans)
rate of change [9][11].
Now
we can add human emissions into the rate of change:
For an exact match of
the slopes of RSS temperature and CO_{2}
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
CO_{2} rate
of change and the calculated rate of
change
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
CO2.
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
HadCRUT-SH temperature...
As can be seen in these
graphs, both temperature rate of change and CO_{2} 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
Niño:
Which of the two possible solutions is right is quite
easy to know, by looking which of the two matches the
observations.
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 CO_{2}
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 CO_{2}
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 CO_{2}
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 CO_{2} (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..
[1] Why the CO2 increase is man made
(part 1)
[2] Engelbeen on why he thinks the CO2
increase is man made (part 2)
[3] Engelbeen on why he thinks the CO2
increase is man made (part 3)
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.
[6]
http://esrl.noaa.gov/gmd/co2conference/pdfs/tans.pdf
Lecture of Pieter Tans at the
festivities of 50 years of Mauna Loa measurements, from
slide 11 on.
[7] http://www.sciencemag.org/content/287/5462/2467.short full text free after registration.
[8]
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
[9]
temperature trends of RSS (satellites) and HadCRUT4
(thermometer hut) and the CO2 trend and derivatives were
downloaded from Wood for
trees.
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
[10] The spreadsheet can be downloaded from:
http://www.ferdinand-engelbeen.be/klimaat/CO2_lags.xlsx