This is part 2 of a four part series
Realistically it is not possible to keep within 1.5C of global warming without the use of carbon dioxide removal from our atmosphere on a massive scale. Is it realistic to keep within a 2C limit with no carbon removal technology in face of a growing world energy demand? The mathematics of this is explored.
Realistically it is not possible to keep within 1.5C of global warming without the use of carbon dioxide removal from our atmosphere on a massive scale. Is it realistic to keep within a 2C limit with no carbon removal technology in face of a growing world energy demand? The mathematics of this is explored.
Part 1. Overview....Realism
Part 3. Where we were
at the end of 2015. 2015 progress report.
Part 2:- Calculations and Assumptions.
For a range of pathways in total energy growth and growth of
alternative (non-CO2 emitting) energy infrastructure what global temperature
anomaly will be locked in for the foreseeable future and in particular will this
meet the 2C limit as discussed at the Paris climate talks in 2015? (let alone
the 1.5C limit that would be preferable)
Information needed.
Clearly we need to have an estimate of the climate sensitivity. This can be
expressed as how much additional warming in terms of global average temperature
rise we will get if we double the CO2 concentration in the atmosphere. Since
the 2C limit refers to how much additional warming we should avoid since
preindustrial times we need to have an estimate of the pre-industrial CO2 level. We can regard these two quantities as “fixed”
measurements; meaning regardless of how accurately we know them, they have
nothing to do with our actions.
As a result of our past actions in terms of emissions (or
growth pathways), the CO2 concentrations have clearly risen. Two present day indicators that are required to make
future estimates are the CO2 atmospheric
concentration today and the rate of
increase of CO2 today. These two indicators are not only determined by our
actions but very importantly how the Earth’s atmosphere has been able to
respond. A further result of our past actions is how much of our existing
energy use comes from “alternatives”. The total
percentage alternatives can also be divided into those that we hope to be
able to increase somewhat exponentially and the rest that may not be able to
expand in this manner.
Values for the fixed estimates and other indicators.
Climate sensitivity:-
I have chosen a value 2.8C. This is
in the mid range of estimates expressed by the IPCC but perhaps a little lower
than many best estimates of 3C. When looking at assumptions later I will
explain why I have chosen a lower value. In any case this is the factor that
determines the most uncertainty for any particular pathways that outweighs any
of the simplifying assumptions and uncertainties in the other estimates.
Preindustrial levels
of CO2:- The accepted value is around 280ppm.
CO2 concentration
today:- This value of around 400ppm
for the end of 2015 can readily be
obtained from the global trend in CO2 (ignoring seasonal changes and changes
due to cycles such as the ENSO cycle). Estimates are taken from the NOAA
webpage.
Growth in CO2 concentration:- A value of 2.13ppm/year for 2015 is obtained by averaging the past ten years
in the Annual Mean Global Carbon Dioxide Growth Rates again from NOAA. (Since I
have averaged the last ten years this is likely to be an underestimate when its
value is increasing)
Total percentage
alternatives:- By alternatives here I mean sources that don’t produce net
CO2 in their operation. (Clearly to build the infrastructure will require CO2
emissions in a country that use fossil fuels to build the infrastructure but
this contribution should not be counted twice). Seasonal growth of plants burned are thus
classified as zero net CO2 emitters but if we were to burn stores of carbon
such as rainforests or peat that would not be zero net emitters of CO2. Obtaining a good estimate of this is not easy
and different sources appear to have different estimates. I have included
nuclear energy here but the reasons for whether or not humans decide to expand
or collapse our nuclear energy plant are not discussed here. The percentages I consider here relate to the
total world energy consumption per year and not just the electrical power of
the grid. These values are fairly difficult to obtain up to date estimates and
I have used information from 2013. I would like better up to date estimates of
these quantities. Sources are page 6 of an EIA 2015 report:-
and data from the world Bank:-
From all these estimates various calculations are made as
shown in the table below:-
Year ending
|
2015
|
|||||||
The
indicators
|
||||||||
Total
Ao
|
Wind
Solar
A1
|
Hydro
Nuclear
Biomass
|
||||||
Alternatives today /%
|
18.6
|
1.2
|
17.4
|
|||||
CO2 concentration/ppm
|
400
|
|||||||
..rising at/ppm per year
|
2.13
|
|||||||
Consequences
for staying
within 2C:-
(assuming a climate sensitivity of 2.8C
for doubling CO2 concentrations)
and
( pre-industrial concentration of CO2 at
280ppm)
|
||||||||
1. Years left at today’s rate of emissions
|
28
|
|||||||
2. And for the following growth pathways:-
|
||||||||
G(e)
|
g(a)
|
year decarbonised
|
Pulse:- No of years of
emissions at today’s rate
|
Overshoot factor
|
Possible T anomaly
|
|||
%
|
%
|
year
|
years/factor
|
factor
|
C
|
|||
2
|
4
|
2102
|
115
|
4.11
|
3.36
|
|||
2
|
5
|
2073
|
59
|
2.11
|
2.54
|
|||
2
|
6
|
2059
|
39
|
1.41
|
2.21
|
|||
2
|
7
|
2050
|
29
|
1.05
|
2.03
|
|||
3
|
5
|
2102
|
180
|
6.47
|
4.16
|
|||
2
|
5
|
2073
|
59
|
2.11
|
2.54
|
|||
1
|
5
|
2058
|
32
|
1.16
|
2.08
|
|||
0.7
|
5
|
2055
|
28
|
1.02
|
2.01
|
|||
0
|
5
|
2049
|
22
|
0.78
|
1.89
|
|||
0
|
4
|
2058
|
27
|
0.98
|
1.99
|
|||
G(e)
|
g(a)
|
Ao
|
A1
|
g (lin)
|
T
|
|||
1
|
15
|
18.6
|
1.2
|
2% of 0.174
|
2
|
|||
2
|
19
|
18.6
|
1.2
|
2% of 0.174
|
2
|
|||
With the factors identified we can see what assumptions lead
mathematically to these answers. Furthermore this can be evaluated and upgraded
at any time by looking at the factors to see how these have changed and
evaluate the assumptions to see how much these may alter the conclusions. In
this way this article is free of opinion and is just based on mathematics.
The Calculations and Assumptions.
1.Years left at today’s rate of emissions.
Making ONLY the further assumption that the global rise in
temperature is proportional to the logarithmic increase in CO2 then the 2C limit will be reached when the
concentration, x, reaches 459ppm.
Ln(x/280)/Ln 2 =T/2.8=2C/2.8C hence x= 280 EXP ((2C/2.8C)*ln2)
=459ppm
Making the additional assumption that the fraction of CO2
that stays in the atmosphere remains constant we can deduce the number of years
to reach 459ppm and hence a 2C rise in temperature for this level
maintained. At today’s rate of emissions this will occur in about 28 years.
{(459-400)/2.13}
2.Time taken to decarbonise.
At this point in time, td, the alternatives have reached the
growth in total energy. Assuming growth grow exponentially at a constant
percentage per year then:-
Ao(1+g(a))^td =(1+ G(e))^td
Solving gives td = ln (Ao)/ ln [(1+G(e)/(1+g(a)]
At this stage there are further simplifying assumptions
made:- I have ignored land changes affecting CO2 and potential positive carbon
feedbacks causing CO2 to be released regardless of our emissions both of which
may make my estimates optimistic.
3.Pulse of CO2 emitted while decarbonising.
If it can be
assumed that CO2 emissions are proportional to the energy produced from fossil
fuels it is a straight forward case of comparing the energy used by fossil
fuels while decarbonising and comparing to our present rate of energy from
fossil fuels, Fo, and our present rate of CO2 emissions.
The energy from fossil fuels is given by the area under the Fx
graph ( see fig 1 realism) where Fo =
the area that represents 1 year at today’s emissions and Fx = (1+G(e))^td- Ao(1+g(a))^td
So (the integral of
Fx dx)/Fo = (the integral of Fx dx)/(1-Ao) = Pulse of CO2in terms of number of
years at today’s rate.
I have assumed that the emissions per unit of energy of
fossil fuels, or emission intensity stays constant while decarbonising. The emission intensity is of course
different for different fuels with coal being twice as polluting in terms of
CO2 than natural gas. If we were to replace all our existing coal supplies with
natural gas we could reduce our emissions today by about 15%, representing a
massive saving that would provide several years advance in progress. We would
still need to reduce our gas consumption but this short term measure would give
as much needed help but this seems unlikely at the present time.
4. Overshoot Factor.
This is simply the ratio of calculation 3 to calculation 1
above and is included for simple comparison purposes.
5. Temperature anomaly locked in.
The temperature anomaly locked in, T, can be found by
rearranging the calculation as in calculation1 but first the concentration x at
the end of the CO2 pulse must be estimated.
T =2.8 *Ln(x/280)/Ln2
A simple estimate of the concentration, x, at the time of decarbonising,
but an over estimate, can be found
from assuming that the entire pulse will have the same air borne fraction as
today’s emissions. So the concentration would simple be the pulse (in terms of
emissions at today’s rate) times the rate of increase of CO2 today plus the
concentration today.
This is clearly an overestimate as the air borne fraction
will decrease as we decarbonise and particularly so if we decarbonise quickly.
However to offset this over-estimate we must consider that I have not taken
into account land changes contributions to CO2, possible positive carbon
feedbacks and have underestimated (for the purposes of these calculations) the
climate sensitivity from 3C to 2.8C for a doubling of CO2.
Let me evaluate the climate sensitivity compensation here
with the airborne fraction assumption.
If today’s CO2 level could be stabilized by a large
reduction in emissions the temperature locked in by calculation1 but for a
climate sensitivity of 3C would give;-
T =3 *Ln(400/280)/Ln2 =1.54C
(This indicates that to be fairly sure of staying
within 1.5C as hoped for in the Paris Cop21 talks we must likely have to remove
carbon from the air before the delay due to the thermal inertia provided by the
oceans kicks in.)
If we magically decarbonised our energy supplies
within a few years we may expect our atmospheric CO2 to drop to say 390ppm
producing a T anomaly locked in of 1.43C assuming 3C climate sensitivity. My
simplified approach of assuming to use the entire pulse at constant airborne
fraction but a climate sensitivity of 2.8C produces a temperature anomaly of
1.45C. The simplifications appear to be realistic.
Using these calculations.
For different growth pathways we can see the temperature
anomaly reached or certain hypothetical pathways that allow us to stay within the 2C
limit.
Realism (part1)
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