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 2. Equations and assumptions used.

Part 4. Applying thisprocedure to hypothetical reports in 2025.

Part3:- 2015 progress report.

The indicators (identified within the yellow box in the table below) can be used to evaluate the progress we have to date in staying within a 2C upper limit for global temperature rise since pre-industrial times.

First we can estimate how many years we have at current rate of emissions.

Secondly we can consider how different combinations of possible growth rates both in the total energy related growth, G(e), and the alternative, g(a), or non–fossil fuel growth will affect the time taken to decarbonise and the likely eventual global temperature increase over pre-industrial levels based on these values.

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

Table 1. 2015 progress report.

For an explanation of how I have calculated these values (see part 2)

From the CO2 indicators we can conclude that we have a carbon budget of about 28 years left at our current rate.

It is seen that if our energy related economic growth, G(e), increases at 2% per annum then from 2015 we can decarbonise staying within 2C if we manage to increase on average all our alternatives by at least a massive 7% per annum for the next 35 year! See table above and figure 1 below.

Figure 1. The curves represent the energy from fossil fuels as we decarbonise for different growth rates in alternatives from a base of 18.6%. Light blue shaded area represents the energy budget from fossil fuels at todays’rate (2015) of emissions to stay within the 2C limit. The curves represent the energy from fossil fuels as we decarbonise.

The area under the curves to the axes represents the energy from fossil fuels or the CO2 emissions. For example the area under the 4% g(a) growth is 4.11 times greater than the 28 years represented by the light blue area. (4.11 x 28=115). (28 years at our current rate of emissions would be the entire carbon budget to stay within 2C as can be estimated from the indicators). This would result in an estimated 3.36C temperature anomaly based on a climate sensitivity of 2.8C for a doubling of CO2 concentration. These values are seen in the first row in the lower half of the table above.

Alternatively.

If we can only manage to have a growth in alternatives, g(a), by 5% per annum due to technical difficulties then we will have to limit our total energy related economic growth to 0.7% or less. See table above and figure 2 below.

Figure 2. The curves represent the energy from fossil fuels as we decarbonise for different growth rates in Energy related growth from a base of 18.6%. Light blue shaded area represents the energy budget from fossil fuels at todays’rate (2015) of emissions to stay within the 2C limit.

Our present day percentage of alternatives other than nuclear, biomass and waste or hydro is about 1.2%. If it is this component that can only increase exponentially then the situation is more severe. For comparison purposes and to get a mathematical statement of the extent of this problem we can assume a certain pathway and see how much the small base of 1.2% renewables that we hope to grow exponentially needs to grow. Assuming the energy related economy grows at1% per annum and the rest of the renewables can grow linearly (2% for first year and the linearly thereafter) we find that the 1.2% renewables need to grow at 15% per annum to stay within the 2C limit.

Figure 3. Graph of fossil fuel use as alternatives grow as indicated. Light blue shaded area represents the energy budget from fossil fuels at todays’rate (2015) of emissions to stay within the 2C limit.

Summary

For the CO2 concentrations and rate of increase we see today there are only about 28 years left at our current emission rates to be sure of staying within 2C. The global rate of increase of alternatives required to decarbonise to be sure of staying within the limits is greater than we have experienced. Realism shows that it is only possible if we don’t delay in growing our alternatives and minimizing our energy related growth. We still have time but it is running out.