1. Equivalence of GHG emissions
under the 2°C limit
Steve Smith1, 2
Jason Lowe2
Laila Gohar2
1UKCommittee on Climate Change
2Met Office Hadley Centre

2. Motivation
• Internationally agreed policy goal: ΔTmax < 2°C
• Climate policies are multi-gas, but only weakly linked to
ΔTmax via the GWP100
• CO2-only studies show ΔTmax is constrained by total
emissions over time (ΣECO2) 1
• GTP measures ΔT, but still relies on time horizon and
doesn’t signal need to limit ΣECO2
• So how might ΣECO2 fit into a multi-gas emissions policy?
1 Allen
et al. (2009) Warming caused by cumulative carbon emissions towards the trillionth tonne, Nature
Matthews et al. (2009) The proportionality of global warming to cumulative carbon emissions, Nature

3. Hypothesis
• On timescales relevant to
2°C, GHGs can be divided
into two baskets:
– ‘long-lived’: ΔTmax  ΣE
– ‘shorter-lived’: ΔTmax  Esustained
• Does this give a reliable
prediction for ΔTmax?
• Where is the dividing line?

4. Experimental setup
MAGICC v5.3
RCP2.6 background forcings

5. Defining long- and shorter-lived GHGs
1
HFC-32 (4.9yr)
HFC-227ea (34.2yr)
CH4 (12yr)
HFC-125 (29yr)
HFC-143a (52yr)
0.95
r2 (ΔTmax, Epeak)
HFE-125 (136yr)
N2O (114yr)
0.9 SF6 (3,200yr)
CO2
0.85
0.85 0.9 0.95 1
r2 (ΔTmax, ƩE)

6. ΔTmax vs. ΣE for long-lived GHGs
5 1
CO2 N2O (114yr)
Peak warming (°C)
Peak warming (°C)
4 0.8
3 0.6
2 0.4
1 0.2
0 0
0 1000 2000 3000 0 2000 4000 6000
Total emissions 2000-2400 (GtC) Total emissions 2000-2400 (MtN)
0.05
SF6 (3,200yr)
Peak warming (°C)
0.04
0.03
0.02 ΔTmax = (PCTx )ΣE x
0.01
0
0 500 1000 1500 2000 2500
Total emissions 2000-2400 (kt)

7. Peak Commitment Temperatures
Species Lifetime (yr) PCT (°C/kg) CO2e
CO2 - 4.32E-16 1
N2O 114 1.33E-13 309
HFC-23 270 7.43E-12 17200
HFC-236fa 240 4.83E-12 11200
SF6 3200 1.73E-11 40100
NF3 740 1.11E-11 25600
CF4 50000 6.01E-12 13900
C2 F 6 10000 9.73E-12 22500
C3 F 8 2600 6.31E-12 14600
c-C4F8 3200 7.53E-12 17400
C4F10 2600 6.37E-12 14700
C5F12 4100 6.86E-12 15900
C6F14 3200 6.68E-12 15500
C10F18 >1000 ≥4.83E-12 ≥12100
SF5CF3 800 1.11E-11 25700
HFE-125 136 6.68E-12 15400
PFPMIE 800 6.42E-12 14900

8. ΔTmax vs. Esustained for shorter-lived GHGs
dΔT (t )
τ = λΔRF(t ) - ΔT (t )
dt
For sustained emissions:
ΔTmax = ΔT (∞ )
sustained
= λαx Ax E x
sustained
ΔTmax = (SETx )E x
where: λ = climate sensitivity parameter
αx = atmospheric lifetime of gas x
Ax = radiative efficiency of gas x

9. Sustained Emission Temperatures
Species Lifetime (yr) Radiative efficiency (Wm-2ppb-1) SET (°Ckg-1yr) * CH4e
CH4† 12 3.70E-04 1.74E-12 1
HFC-32 4.9 0.11 4.66E-11 27
HFC-125 29 0.23 2.50E-10 144
HFC-134a 14 0.16 9.88E-11 57
HFC-143a 52 0.13 3.62E-10 208
HFC-152a 1.4 0.09 8.58E-12 5
HFC-227ea 34.2 0.26 2.35E-10 135
HFC-245fa 7.6 0.28 7.14E-11 41
HFC-365mfc 8.6 0.21 5.49E-11 32
HFC-43-10mee 15.9 0.4 1.14E-10 65
HFE-134 26 0.45 4.46E-10 256
HFE-143a 4.3 0.27 5.22E-11 30
HCFE-235da2 2.6 0.38 2.41E-11 14
HFE-245cb2 5.1 0.32 5.56E-11 32
HFE-245fa2 4.9 0.31 4.54E-11 26
* Values calculated for λ=0.8K(Wm-2)-1
† CH4 SET includes OH lifetime enhancement and indirect O3 & stratospheric H2O effects

10. ΔT for RCP2.6 implied by PCTs & SETs
2 0.7
Contribution to peak T from PCT (°C)
Contribution to peak T from SET (°C)
1.8
0.6
1.6
1.4 0.5
1.2 0.4
1
0.8 0.3
0.6 0.2
0.4
0.1
0.2
0 0.0
2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100
Year Year
Fossil CO2 Other CO2 N2O CH4 HFC32 HFC43_10
CF4 C2F6 C6F14 HFC125 HFC134a HFC143a
HFC23 SF6 HFC227ea HFC245fa

11. Comparison with realised ΔT
2.0
1.8
Total SET
ΔT (°C above pre-industrial)
1.6
1.4
1.2 Total PCT
1.0
0.8 RCP2.6 all
0.6
0.4 RCP2.6
0.2 GHGs only
0.0
2000 2020 2040 2060 2080 2100
Year

12. Conclusions
• For the 2°C limit GHGs could be split into two baskets:
– ‘long-lived’: committed ΔTmax = PCTx × ΣEx
– ‘shorter-lived’: future ΔTmax (if sustained) = SETx × Ex
• Sum of PCTs & SETs gives a guide to size & timing of ΔTmax
• Reduces reliance on (arbitrary) time horizons
• 2°C could be met by limiting cumulative ΣECO2e for long-lived
GHGs including N2O
• Allowable ΣECO2e depends on emissions of shorter-lived GHGs
near time of peaking only (but near-term emissions do
influence warming rate as well)