Question

Create an "IPCC-like" stabilization scenario using the following simplified information. Starting in the year 2004, the concentration of CO2 in the atmosphere is 378 ppm, the global emissions of CO2 are 7.4 Gt carbon per year, the total carbon in the atmosphere is 767 Gt, and emissions are growing by 4% per year, for example, in 2005 emissions reach 7.7 Gt, 8.0 Gt in 2006, and so on. Note that concentration is given in terms of CO2, but emissions and atmospheric mass are given in Gt carbon. The oceans absorb 3 Gt net (absorbed minus emitted) each year for the indefinite future. The change or decline of emissions is influenced by "global CO2 policy" as follows: in year 2005, the emissions rate declines by 0.1 percentage points to 3.9%, and after that and up to the point that concentration stabilizes, the change is 0.1% multiplied by the ratio of the previous year's total emissions divided by 7.4 Gt, that is

 

After concentration stabilizes, emissions are 3 Gt year, so that emissions are exactly balanced by ocean absorption. To illustrate, Chg%2004 = 4% and Chg%2005 = 3.9%, and so on. Also, concentration can be calculated as 378 ppm X (total carbon in atmosphere/767 Gt).

(a) What is the maximum value of concentration reached?

(b) In what year is this value reached?

(c) What is the amount of CO2 emitted that year?

(d) Plot CO2 concentration and emissions per year on two separate graphs.

(e) The scenario in this problem is a simplification of how a carbon stabilization program might actually unfold in the future. Identify two ways in which the scenario is simplistic.

Answer 1

(a) and (b)

The approach to this problem is to understand the calculation in the first 1-year step from 2004 to 2005, and then to repeat the calculations in a spreadsheet or math software package until the concentration stabilizes.

 

In the first year, take t = 2005, t – 1 = 2004. Then total emissions in t – 1 are given as 7.4 Gt carbon per year, and the change percent value Chg%t−1 is 4.0%. We can therefore use the above formula to calculate Chg%2005:

 

Emissions for 2005 therefore increase to 7.7 Gt C. Concentration in ppm in 2005 is then the following:

 

Repeating for the transition from 2005 to 2006:

 

This process is repeated in a spreadsheet table in the following form, shown only up to year 2008 for brevity:

Year	Emits		Total in Atmosphere		Concentration		Net Emits		Change
(Gt C)		(Gt C)		(ppm)		(Gt C)		(pct)
2004	7.40		767		378		4.4		4%
2005	7.70		771.4		380.2		4.70		3.90%
2006	8.00		776.1		382.5		5.00		3.79%
2007	8.30		781.1		384.9		5.30		3.68%
2008	8.60		786.4		387.6		5.60		3.56%

 

The change percent value eventually goes into negative territory in the year 2031 and the concentration begins to taper off. In the year 2077, the concentration reaches 611.5 ppm where it stabilizes, and the change percent changes from –5.26% in year 2076 to 0% in 2077, so that emissions and uptake of CO2 are in equilibrium thereafter.

 

(c)

Emissions are 3.0 Gt in 2077, so net emissions are hence zero.

 

(d)

Graphs of net emissions per year after subtracting the uptake value:

 

Concentration value:

 

(e)

Many answers are possible. For example, the scenario stabilizes relatively quickly compared to IPCC, even though the concentration is high (610 ppm). Also, the IPCC scenarios tend to have a “smooth landing” at the tail, whereas this scenario changes abruptly.

(a) & (b).

The change percent value eventually goes into negative territory in the year 2031 and the concentration begins to taper off. In the year 2077, the concentration reaches 611.5 ppm where it stabilizes, and the change percent changes from –5.26% in year 2076 to 0% in 2077, so that emissions and uptake of CO2 are in equilibrium thereafter.