Allowable carbon emissions for medium-to-high mitigation scenarios

Figures & data

Fig. 1 Time series of allowable annual fossil fuel emissions for period 1850–2300.RCP2.6 (a), RCP4.5 (b) and SCP4.5 to 2.6 (c). The black curve is the ensemble mean, and the dark and light grey shades correspond to 68 (16–84 percentile) and 90 (5–95 percentile)% ranges respectively. The blue curve is the historical estimates of emissions (Carbon Dioxide Information Analysis Center: http://cdiac.ornl.gov/ftp/ndp030/global.1751_2009.ems). The red curves are harmonised RCP emissions (derived from MAGICC, documented in Meinshausen et al., 2011a). (d)–(f) are same as (a)–(c) but now for our constrained set of simulations using the eight observed datasets in Table 2.

Table 1  Parameters perturbed in this study and the ranges considered

Parameter	Component	Default	Perturbation range
Climate sensitivity	Atmosphere	4.7 [b]	1–6 K^†
Vertical diffusivity	Ocean	0.1–3.0 cm^2/sec*	0.3–3.0×default
Horizontal diffusivity	Ocean	1×10^7 cm^2/sec	0.5–5.0×default
Gent-McWilliams thickness parameter [a]	Ocean	7×10^6 cm^2/sec	1–20×10^6 cm^2 s^−1
Magnitude of freshwater flux adjustment	Ocean	1.0 (ratio to the values by [c])	0.5–2.0
Wind speed used in marine CO2 uptake	Marine carbon	3.3 m/s [b]	2.0–8.0 m/s
Maximum photosynthetic rate	Land carbon	8.0–13.5 µmolCO2/(m^2s)**	0.8–3.0×default
Specific leaf area	Land carbon	110–170 cm^2/(g drymatter)**	0.5–2.5×default
Minimum temperature for photosynthesis	Land carbon	−5.0–11.0°C**	−4.5–+3.0°C of default
Coefficient for temperature dependency of plant's respiration	Land carbon	2.0 (dimensionless)	1.5–3.0
A parameter of temperature dependency of soil respiration	Land carbon	46.02 K	35–55 K
Total aerosol forcing	Forcing	(RCPs)	0.0–3.0×RCPs^††

Parameters perturbed and where the symbols are: * and **: depth- and biome-dependent. ^†initially in a uniform distribution, and then weighted with a beta function (Appendix A1). ^††Weighted with combination of two Gaussian functions (Appendix A2).

[a]: Gent and McWilliams (1990).

[b]: Tachiiri et al. (2010).

[c]: Oort (1983).

Table 2  Observation data used for constraint of simulations

No.	Variables	(Average ±) SD	Assumed distribution	EES*	Reference
1	Trend of global mean air surface temperature (1906–2005)	0.74±0.11** (K/100 yr)	T	86	Trenberth et al. (2007)
2	Trend of ocean heat content for 0–700 m depth (1969–2003)	0.32±0.05 (10^22 J/yr)	T	58	[a]
3	Historical fossil fuel emission*** (1980–2008)	5.5±0.3 for 1980s, 6.4±0.4 for 1990s, 7.7±0.4 for 2000–8 (PgC/yr)	geometric mean of Gaussian weights for 3 periods	223 (RCP4.5/SCP)	Le Quéré et al. (2009)
4	Net Primary Production (1961–90, spatial 2D)	363 (gC/m^2 yr^1)^†	Gaussian	382	Zheng et al. (2003)
5	Atlantic meridional overturning circulation (after spinup for 1850)	17±2.5 (Sv)	Gaussian	220	[b]
6	Present air surface temperature (mean for 1968–96, spatial 2D)	21.8 (K)^†	Gaussian	512	Kistler et al. (2001)
7	Present sea temperature (mean for 1990–97, spatial 3D)	11.1^†/5.9^†/1.9^†/1.1^† (K)^††	geometric mean of Gaussian weights for 4 layers	485	NODC_WOA98
8	Present sea salinity (mean for 1990–97, spatial 3D)	1.5^†/0.58^†/0.27^†/0.17^† (psu)^††	geometric mean of Gaussian weights for 4 layers	510	NODC_WOA98
9	All variables	–	Product of 1–8	10	–

The symbols in the tables are:

*Effective ensemble size (EES) calculated as Σ(weights)/Σ(weights)². EES becomes large when the weights are equally distributed across many members, and small when weights are concentrated on small numbers of members. **0.18 for 90% confidence level. ***Compared with the model's allowable emission for these periods. ^†These SD values are used to calculate the weight similar to CPI (Murphy et al., 2004). ^††The values are SDs for 0–50/50–600/600–2000/2000–5500 m.

[a]: Domingues et al. (2008); Levitus et al. (2009); Ishii and Kimoto (2009).

[b]: Smethie Jr. and Fine (2001); Ganachaud (2003); Talley et al. (2003); Lumpkin and Speer (2010).

Fig. 2 Time series of cumulative allowable emissions for period 1850–2300.

RCP2.6 (a), RCP4.5 (b) and SCP4.5 to 2.6 (c). The black curve is the ensemble mean, and the dark and light grey shades correspond to 68 (16–84 percentile) and 90 (5–95 percentile)% ranges respectively. The blue curve is the historical estimates of emissions (Carbon Dioxide Information Analysis Center: http://cdiac.ornl.gov/ftp/ndp030/global.1751_2009.ems). The red curves are harmonised RCP emissions (derived from MAGICC, documented in Meinshausen et al., 2011a). (d)–(f) are same as (a)–(c) but now for our constrained set of simulations using the eight observed datasets in Table 2.

Table 3  Comparison of cumulative fossil fuel emission with CMIP5 models

		CMIP5 models*		Our result**
Unit: PgC	Obs/IAM*	mean±σ	min–max range	mean±σ	min to max range
Historical	313	303±61	194–394	314±75	−77 to 577
				320±39
RCP2.6	325	322±106	189–469	282±103	−348 to 522
2006–2100				291±63
RCP4.5	786	831±155	194–394	738±173	−2.2 to 1199
2006–2100				728±82

*Jones et al. (2013), *upper: unconstrained, lower: constrained.

Table 4  Allowable fossil-fuel emissions for 1990s and 2050s for RCP2.6

Model	1990s emissions (PgC/yr)	2050s emissions (PgC/yr)	% reduction
CMIP5*	5.76±0.8	2.92±1.8	50
Our study**	6.01±1.3	1.79±1.7	70
	6.58±0.6	1.57±1.4	76
IAM***	6.35	2.39	62
Historical****	6.4±0.4

*Jones et al. (2013), **upper: unconstrained, lower: constrained, ***van Vuuren et al. (2007), ****Le Quéré et al. (2009).

Fig. 3 The cumulative probability distribution for allowable emission thresholds when averaged over the period of years 2151–2200.

RCP2.6 (a), RCP4.5 (b) and SCP4.5 to 2.6 (c). The cumulative probability of these mean emissions being less than each threshold presented on the x-axis. Presented are the weighted probability for the unconstrained (black curve), and constrained ensembles using all variables in Table 2 (red curve).

Fig. 4 Relationship between the cumulative allowable emission (1850–2300) and variation in different parameter values.

RCP2.6 (red), RCP4.5 (black) and SCP4.5 to 2.6 (blue). Panels (1)–(12) are in the same order as Table 1. Numbers in plot areas are coefficients of correlation to parameter values (*/**/*** mean statistically significant at 90/95/99% levels). Plotted are the 512 members.

Fig. 5 Time series of global mean surface air temperature for period 1850–2300.

RCP2.6 (a), RCP4.5 (b) and SCP4.5 to 2.6 (c). The black curve is the ensemble mean, and the dark and light grey shades correspond to 68 (16–84 percentile) and 90 (5–95 percentile)% ranges respectively. The blue curve is the HadCRUT3 data (Brohan et al., 2006). Anomalies are from average of 1980–1999, and the horizontal magenta line is 2 K increase from the preindustrial (here average of 1850–1869). (d)–(f) are same as (a)–(c) but now for our constrained set of simulations using the eight observed datasets in Table 2.

Fig. 6 Carbon Climate Response.

RCP2.6 (a–c), RCP4.5 (d–f) and SCP4.5 to 2.6 (g–i). The left (a, d, g), the central (b, e, h) and right (c, f, i) columns show Carbon Climate Response (ratio of temperature rise, dT, and cumulative emission (C_E), ratio of C_A (airborne carbon) and C_E (i.e. airborne fraction) and dT/C_A, respectively. Black and red lines are the unconstrained and the constrained ensemble average.

Fig. 7 The dependence of temperature trend (warming between years 1906 to 2005), plotted against (a) climate sensitivity, (b) uncertainty in aerosol forcing. Also plotted, (c) is the cost (errors defined as absolute value of the difference) in TA trend vs climate sensitivity. Plotted are all of the 512 members. (d) and (e) are prior and posterior of climate sensitivity and aerosol forcing, in which black: unconstrained, red: constrained. Plotted are probabilities for bins of 0.1 K (d) and 0.5 W/m² (e) width.

Fig. 8 Land and ocean carbon storage.

(a)–(c) are change in land carbon storage after constraint for RCP2.6, RCP4.5 and SCP4.5 to 2.6, respectively, and where a positive value implies a gain in carbon. The dark and light grey shades correspond to 68 (16–84 percentile) and 90 (5–95 percentile)% ranges respectively. (d)–(f) are change in ocean carbon storage for the scenarios.

Fig. 9 Spatial distribution of the land carbon uptake.

Panel (a) is the weighted mean of land carbon uptake between 2010–2100 (i.e. year 2100 values minus year 2010 values), and (b) is land carbon uptake in 2100–2300. After constraint. Then panels (c) and (d) are relative uncertainty across the ensemble, calculated as SD/average in (a) and (b) respectively, presenting the extent of the consistency in the sign of change. When ∣SD/average∣ < 1, the sign of the change is considered be robust (note that the sign of ∣SD/average∣ simply presents that of average, as SD is always positive). Few grids are of robust signs for the change in 2010–2100, and even fewer grids are so in 2100–2300.

Fig. 10 Spatial distribution of the ocean carbon uptake (a): For 2010–2100, (b): 2100–2300, (c)(d): relative uncertainty (standard deviation/average). After constraint.

Fig. E1 Prior and posterior probability distribution of 12 parameters. Black: prior (unconstrained), red: posterior (after constrained by observation data). X-axis is normalised to the perturbation range (logarithmic scales for 2–4). Priors are flat for all parameters but climate sensitivity and aerosol for which non-flat distributions presented in Appendix A are used. Plotted are probabilities for bins of 0.2 (i.e. one fifth of the pertubed range) width.

Fig. F1 Spatial distribution of the change in land carbon storage for RCP2.6 and SCP4.5 to 2.6. Panel (a) is the weighted mean of land carbon uptake between 2010 and 2100 (i.e. year 2100 values minus year 2010 values), and (b) is land carbon uptake in 2100–2300 for RCP2.6. (c) is land carbon uptake in 2100–2300 for SCP4.5 to 2.6. Then panels (d)–(f) are relative uncertainty across the ensemble, calculated as SD/average in (a)–(c) respectively. After constraint.

Fig. F2 Ocean carbon uptake (a) for 2010–2100, (b) 2100–2300 for RCP2.6, (c) 2100–2300 for SCP4.5 to 2.6, (d)–(f) relative uncertainty (standard deviation/average) for (a)–(c). After constraint.

Fig. A1 The beta distribution with values B(1.8, 2.2), used to represent the asymmetric climate sensitivity's probability distribution.

Fig. A2 The distribution of aerosol represented using a combination of two normal functions.

Table B1 . Feedback parameters compared to the C4MIP models

	Unit	This study	C4MIP
α	K/ppm	0.0054±0.0013	0.0061±0.0012
βL	PgC/ppm	1.1±0.3	1.3±0.6
βO	PgC/ppm	1.2±0.3	1.1±0.2
γL	PgC/K	−97±75	−79±44
γO	PgC/K	−33±11	−31±16

Parameters presented (Friedlingstein et al., 2006), are linear transient climate sensitivity (α), sensitivity of land and ocean carbon storage to atmospheric CO₂ concentration change (β) and to temperature change (γ). “l” and “o” are land and ocean. The ± one SD of 20 members (in a small ensemble) and also for C4MIP models are presented.

Table B2 . Original parameter perturbation ranges before the tuning for the C4MIP models

Parameters	Original perturbation range
Climate sensitivity	(1–6 K)
Vertical diffusivity	0.5–2.0×default
Horizontal diffusivity	0.5–5.0×default
Gent-McWilliams thickness parameter (a)	1–10×10^6 cm^2/s
Magnitude of freshwater flux adjustment	0.5–2.0×Oort's values (b)
Wind speed used in marine CO2 uptake	1–6 m/s
Maximum photosynthetic rate	0.8–2.0×default
Specific leaf area	0.5–1.5×default
Minimum temperature for photosynthesis	−3.0~ + 3.0°C of default
Coefficient for temperature dependency of plant's respiration	1.5–3.0
A parameter of temperature dependency of soil respiration	40–60 K
Total aerosol forcing	–

Ranges are based on Tachiiri et al. (2010) Tachiiri et al. (2012). (a) Gent and McWilliams (1990). (b) Oort (1983).

Table G1 . Result of the sensitivity tests for climate sensitivity with RCP4.5

	Atmospheric temperature (K)		Allowable emission (PgC/yr)
Cut-off point	Unconstrained	Constrained	Unconstrained	Constrained
6.0 K (original)	1.2–3.4	1.3–3.3	7.4–13.7	9.9–13.0
5.5 K	1.2–3.4	1.5–3.3	7.4–13.7	9.5–12.5
5.0 K	1.2–3.3	1.5–3.3	7.7–13.9	9.8–12.5

The 5–95th percentiles for the peak periods are presented. Temperatures are anomaly from 1980 to 99.

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