Originally a guest post on 18 October 2018 at Climate Etc

A close reading of Chapters 1 and 2 of the IPCC Special Report on Global Warming of 1.5°C (SR15) reveals some interesting changes from the IPCC 5th Assessment Report (AR5), and other science-relevant statements. This article highlights statements in SR15 relating to carbon emission budgets for meeting the 1.5°C and 2°C targets.

It seems fairly extraordinary to me that the AR5 post-2010 carbon budget for 1.5°C, which was only published four years ago, has in effect been now been increased by ~700 GtCO2 – equal to 21st century emissions to date – despite SR15’s projections of future warming being based very largely on the transient climate response to cumulative emissions (TCRE) range exhibited by the models used in AR5.

Key points

  • The SR15 estimates of the carbon budgets that will allow us to remain within the 1.5°C and 2°C targets are far larger than those given in AR5 – over five times as high from end 2017 for a 66% probability of not exceeding 1.5°C warming.
  • SR15 switches the measure of past (up to 2010) warming for the 1.5°C and 2°C targets from near-surface air temperatures (SAT) everywhere (as in AR5) to a blend of near-surface air temperatures over land and sea-surface water temperatures (SST).
  • SR15 bases its estimates of the relationship of future warming to future CO2 emissions very largely on the behaviour of the current generation of Earth system models (ESMs)[i], as used for AR5. However, unlike AR5 it does not do so directly. Instead, it assumes a fixed probabilistic relationship between post-2010 cumulative CO2 emissions and the warming they cause, and derives (using simplified climate models) an allowance for warming from other causes.
  • SR15 ignores ESM simulation estimates of warming to date, instead estimating it using observational data.
  • The resulting SR15 estimate of the post-1875 cumulative CO2 emissions that would give a 50% probability of meeting the 1.5°C target is approximately 720 GtCO2 larger than per AR5, partially offset by a 210 GtCO2 increase in estimated 1876–2010 emissions, giving a net increase of 510 GtCO2 for the post-2010 carbon budget.
  • Approximately 180 GtCO2 of the ~720 GtCO2 increase in the post-1875 budget is due to lower projected post-2010 warming relative to post-2010 cumulative CO2 The lower projected warming appears to be because of two factors:
    • The TCRE value used in SR15 matches the average of the full set of ESMs in AR5; however the budgets calculated for AR5 were based on a subset of ESMs that had a higher average TCRE value.
    • Lower non-CO2 warming is projected in SR15 than in AR5

and possibly also to other, unidentified, factors.

  • The remaining 540 GtCO2 of the increase relates to changing the measure of warming up to 2010 from a model-simulation basis to an observational basis and may be allocated approximately as follows:
    • half (270 GtCO2) to the models used for the AR5 budgets warming more by 2010 than do the full set of AR5 CMIP5 models, and
    • half (270 GtCO2) to changing the measure of past warming from the globally-complete near-surface air temperature to a blend of SAT over land and SST over ocean, as measured (on a globally-incomplete basis) by the average of four observational temperature records.

SR15’s definition of warming for carbon budget purposes

In order to understand the changes in the SR15 carbon budgets from those given in AR5, it is necessary to examine the way that SR15 defines warming. The key part of SR15 here is Section 1.2.1: ‘Working definitions of 1.5°C and 2°C warming relative to pre-industrial levels’.

The SR15 report ‘adopts a working definition of “1.5°C relative to pre-industrial levels” that corresponds to global average combined land surface air and sea surface temperatures either 1.5°C warmer than the average of the 51-year period 1850–1900, 0.87°C warmer than the 20-year period 1986–2005, or 0.63°C warmer than the decade 2006–2015’. It states that these offsets are based on all available published global datasets, combined and updated.

SR15’s working definition of warming over the historical period is based on an average of the four available global datasets that are supported by peer-reviewed publications: the three datasets used in AR5 – HadCRUT4, NOAA, GISTEMP, as updated – together with the Cowtan and Way infilled version of HadCRUT4.[ii] Berkeley Earth (BEST) and JMA are not used because ‘no peer-reviewed publication is available for these global combined land–sea datasets’.

SR15 explains that ‘The IPCC has traditionally defined changes in observed global mean surface temperature (GMST) as a weighted average of near-surface air temperature (SAT) changes over land and sea surface temperature (SST) changes over the oceans’. Consistent with that, the SR15 1.5°C remaining carbon budgets are based on anthropogenic warming up to 2006–2015 of 0.87°C, which is based on surface temperature datasets that mostly combine near-surface air temperature over land and sea surface temperature over the (open) ocean.

Average global warming simulated over the historical period (1850 to date) by the ESMs used in AR5 exceeds that shown by the observational temperature records used in SR15.[iii] It is likely that part of that difference in warming is due to the ESMs using SAT as the measure of temperature over the ocean as well as land, and to incomplete global coverage of observations. The importance of this issue is reflected by SR15’s statement that ‘the use of blended SAT/SST data and incomplete coverage together can give approximately 0.2°C less warming from the 19th century to the present relative to the use of complete global-average SAT.’

However, it is doubtful that SR15’s warming measure is that far below the old one, or even by as far as the calculated 13% warming shortfall in CMIP5 models reported in SR15.[iv] Although two of the four temperature datasets used in SR15 use SST measurements for the oceans, the other two use a hybrid of SST and SAT, so the average of the four would not be expected to differ from a pure SAT dataset by as much as SR15 calculates.[v] Moreover, warming estimates for recent decades in two versions of the globally-complete ERA-interim reanalysis – one based on SAT everywhere, and one based on SAT over land but SST over ocean – differ only very marginally.[vi] In addition, one of the four datasets fully infills areas with missing data, while two others infill substantially. SR15 shows (Table 1.1) that over the long term, lack of complete infilling makes little difference: the fully infilled Cowtan and Way dataset was only 0.02°C higher over the length of the record than per the SR15 average.[vii] Moreover, over recent decades warming in the Cowtan and Way dataset matched or exceeded that in the two globally-complete reanalysis datasets featured in SR15, despite the latter using SAT everywhere while Cowtan and Way use SST over the oceans.[viii]

Although the reasons for deciding to measure warming for the purposes of the 1.5°C and 2°C targets by combining SAT over land with SST over ocean (rather than SAT everywhere, as in AR5) are not entirely clear, it is in my view a sensible decision scientifically. Surface air temperature over the ocean has been (and still is) less well measured than SST, and also has much less direct relevance to humans and the biosphere than does SST. The change has the effect of making the remaining carbon budgets larger. However, SR15 is inconsistent in applying its decision to use a weighted average of SAT and SST: it only does so in respect of past warming; future warming is in effect still projected using a fully SAT-based measure.

It is arguable that when determining warming some allowance should be made for the cooling effect of heavy volcanism during the last two decades of the 1850-1900 primary reference period. However, such cooling is likely to have been partially offset by early anthropogenic warming; the net cooling is probably small and of the same order as the excess since 1850-1900 of the GMST increase per the fastest warming observational dataset (Cowtan and Way) over the average of four datasets used in SR15.

The remaining 1.5°C carbon budget

Section 2.2.2, ‘The remaining 1.5°C carbon budget’ is particularly revealing. The key measure that affects carbon budgets is the transient climate response to cumulative emissions (TCRE), being the transient GMST change per unit cumulative CO2 emissions.[ix] Unless otherwise stated, the unit of emissions is 1000 GtC, not 1000 GtCO2 (1000 GtCO2 = 1 TtCO2 = 273 GtC).

My interest was piqued by the statement that, although:

considerably uncertainties remain, there is high agreement across various lines of evidence assessed in this report that the remaining carbon budget for 1.5°C or 2°C would be larger than the estimates at the time of the AR5.[x]

How much larger? Well, later in the section, SR15 says this:

This assessment finds a larger remaining budget from the 2006-2015 base period than the 1.5°C and 2°C remaining budgets inferred from AR5 from the start of 2011, [which were] approximately 1000 GtCO2 for the 2°C (66% of model simulations) and approximately 400 GtCO2 for the 1.5°C budget (66% of model simulations).[xi] In contrast, this assessment finds approximately 1600 GtCO2 for the 2°C (66th TCRE percentile) and approximately 860 GtCO2 for the 1.5°C budget (66th TCRE percentile) from 2011.

So, the remaining carbon budget from 1 January 2011 for a 66% probability of keeping below 1.5°C has been increased by 460 GtCO2, from 400 to 860 GtCO2 – more than doubled. Deducting the estimated 290 GtCO2 emissions during the 2011 to 2017 period,[xii] the change from 1 January 2018 is from 110 GtCO2 to 570 GtCO2 – over five times as high.

While SR15 says that the AR5 and SR15 carbon budgets are ‘not directly equivalent’, both use the same 1.5°C warming target, both measure from the 1850–1900 mean, both require the same 66% chance of meeting it (albeit derived in slightly different ways) and both allow for forcing from non-CO2 emissions.[xiii]

The SR15 carbon budgets are based on TCRE values rather than directly on climate model projections. In principle that is sensible, since the current generation of ESMs clearly have major deficiencies. However, SR15 sticks with the 0.8–2.5°C (0.22–0.68°C/TtCO2) TCRE range from AR5, which represents ‘expert judgement based on the available evidence’. This range agrees to, and appears to be largely based on, the TCRE range from CMIP5 ESMs and EMICs, and has a similar mean and median.[xiv] As a result, the best-estimate temperature response to CO2 emissions using the SR15 method should in theory be very similar to that per the AR5 ESM projections. However, in SR15, warming due to non-CO2 emissions (which is as projected by simplified ESMs) is lower than that projected by the AR5 ESMs.

As an aside, the most sophisticated TCRE study cited in AR5 was Gillett et al. (2013)[xv] – one of the two key observational-constrained, scaling-based ‘detection and attribution’ studies underlying the main AR5 human-caused warming finding.[xvi] Gillett et al. scaled CMIP5 ESM patterns of temperature responses to greenhouse gas warming so that they were consistent with the observed warming and found a TCRE range of 0.7–2.0°C, with a mean of 1.35°C. The range adopted in SR15 has a 22% higher central value and a 25% higher upper bound than this observationally-constrained range.

If one assumes a normal distribution, as SR15 does, the AR5 ‘likely’ range (taken as covering 66% probability) implies 50% (median) and 66% probability points for TCRE of 0.45°C/TtCO2 and 0.55°C/TtCO2 respectively. SR15 points out that observation-based TCRE estimates have reported log-normal distributions for TCRE, which, for a given symmetrical probability range, have a longer upper tail but a lower median than for a normal distribution. SR15 estimates that, based on its adopted 0.22–0.68°C/TtCO2 TCRE range, if it had treated the range as coming from a log-normal rather than a normal distribution – which would have implied a median TCRE of 0.38°C/TtCO2, in line with the best estimates SR15 cites from studies using observational constraints[xvii] – then the median remaining carbon budget could have been 200 GtCO2 larger.[xviii]

The median TCRE of 0.45°C/TtCO2 used in SR15 is, unsurprisingly, close to the 0.47°C/TtCO2 median TCRE of the reduced-complexity MAGICC model used in AR5 to emulate the behaviour of the set of more complex CMIP5 ESMs. SR15 introduces a new simplified ESM, the ‘Finite Amplitude Impulse Response’ (FAIR) model. The new model embodies more up to date forcing assumptions than MAGICC, which (although used in AR5) has, for instance, aerosol forcing close to the AR4 best estimate rather than to the substantially lower AR5 best estimate. FAIR is thought to produce more realistic near-term temperature trends than MAGICC. FAIR has a median TCRE of 0.38°C/TtCO2, very close to the Gillett et al. (2013) central value of 0.37°C/TtCO2. However, when calculating its carbon budgets, SR15 only uses MAGICC and FAIR (averaging their results) to project post-2010 temperature changes in response to non-CO2 emissions.

It is simple to derive the SR15 1.5°C post-2017 CO2 budgets. Subtracting the assessed anthropogenic warming up to 2006-2015 of 0.87°C from the 1.5°C target leaves allowable post-2017 warming of 0.63°C. SR15 states that ‘The mitigation pathways assessed in this report indicate that emissions of non-CO2 forcers contribute an average additional warming of around 0.15°C relative to 2006–2015 at the time of net zero CO2 emissions.’ After deducting this non-CO2 warming (more accurately, 0.155°C), the 1.5°C target allows only 0.475°C further CO2 warming. Based on the assessed 50% and 66% probability TCREs, the corresponding implied post-2017 CO2 budgets are respectively 1055 and 864 GtCO2. After deducting the 290 GtCO2 emitted during 2011–2017, and rounding to the nearest 10 GtCO2, these agree to the corresponding SR15 1.5°C post-2017 CO2 budgets at 50% and 66% probability, of 770 and 570 GtCO2 respectively.

Why is there a huge discrepancy between the AR5 and the SR15 carbon budgets, when the TCRE range used in SR15 is almost the same as the TCRE range of the ESMs used to derive the AR5 carbon budgets?

SR15 claims that Figure 2.3 (a version of which is reproduced below as Figure 1) illustrates that ‘the change since AR5 is, in very large part, due to the application of a more recent observed baseline to the historic temperature change and cumulative emissions’.

In my view this statement in SR15 lends itself to misinterpretation. A naïve interpretation of this statement is that both observed warming and observed emissions were lower than projected (by ESMs, under the RCP8.5 scenario) in AR5 over the period since then, with both of these factors contributing to an increase in the remaining carbon budgets consistent with 1.5°C or 2°C warming.

In fact, observed emissions between 2005 (the observational baseline date for emissions per the RCP scenarios) and the end of 2017 were almost identical to those per RCP8.5. And, if the ‘blended-masked’ CMIP5 models’ temperature (thin black line in Figure 1) is a fair comparison with the global temperature observations used in SR15 (thin blue line in Figure 1), then there is little difference between models and observations over that period.

Figure 1: Temperature changes from 1850-1900 versus cumulative CO2 emissions from 1876 on.  Solid lines with dots reproduce the temperature response to cumulative CO2 emissions plus non-CO2 forcers as assessed in Figure SPM10 of WGI AR5, except that points marked with years relate to a particular year. The AR5 data was derived from available ESMs for the historic observations (black) and RCP 8.5 scenario (red) and the red shaded plume shows the uncertainty range across the models as presented in AR5. The purple shaded plume and the line are indicative of the temperature response to cumulative CO2 emissions and non-CO2 warming adopted in SR15. The non-CO2 warming contribution is averaged from the MAGICC and FAIR models and the purple shaded range assumes the AR5 WGI TCRE distribution. The 2010 observations of temperature anomaly (0.87°C based on 2006-2015 mean compared to 1850-1900) and cumulative carbon dioxide emissions from 1876 to the end of 2010 of 1,930 GtCO2 is shown as a filled purple diamond. 2017 values based on the latest cumulative carbon emissions up to the end of 2017 of 2,220 GtCO2 and a temperature anomaly of 1.04°C based on an assumed temperature increase of 0.2°C per decade is shown as a hollow purple diamond. The thin blue line shows annual observations, with CO2 emissions from Le Quéré et al. (2018)[xix] and temperatures from the average of the HadCRUT4, NOAA, GISTEMP and Cowtan-Way datasets. The thin black line shows the CMIP5 models blended-masked estimates with CO2 emissions from Le Quéré et al. (2018). Dotted black lines illustrate the SR15 remaining carbon budget estimates for 1.5°C. Reproduced from SR15 Figure 2.A.3, which is a version of Figure 2.3 that additionally shows warming projections (not used in SR15) direct from the MAGICC and FAIR models.

One potential source of misunderstanding is what the change in observed baseline date involved is. It is not from 2005 to 2017, or between any other recent periods. Rather, it is from the 1850–1900 mean to the 2006–2015 mean (from 1875 to 2010 for CO2 emissions). This change in baseline date has two effects.

First, it increases cumulative CO2 emissions in both 2010 and at end 2017 by approximately 210 GtCO2, largely due to an upwards revision of pre-2000 emissions from land use change. In itself, this change reduces the remaining carbon budget by some 210 GtCO2.[xx]

As an aside, when the 2011–2017 observed emissions of 290 GtCO2 are also added, the updating of the pre-2011 emission estimate brings the post-2010 increase in the cumulative emissions estimate to 500 GtCO2. This figure exceeds the AR5 budget for a 66% probability of keeping warming below 1.5°C, of 400 GtCO2. Moreover, since 2018 emissions are expected to exceed 40 GtCO2, the 50% probability AR5 post-2010 budget of 550 GtCO2 will be breached before mid-2019. The corresponding SR15 50% probability 1.5°C budget of 1060 GtCO2 is 510 GtCO2 higher and not likely to be breached before the 2030s.

Since the effect of baseline changes on emissions estimates is to reduce the carbon budget by 210 GtCO2, it follows that the second effect of those baseline changes – the impact on historical temperature change estimates – must in large part both compensate for that reduction and give the doubling of the remaining carbon budget over AR5 estimates. The total increase in the carbon budget involved is:

  • at 66% probability, 670 GtCO2 (that is, 460 + 210 GtCO2)
  • at 50% probability, 720 GtCO2 (that is, 510 + 210 GtCO2).

A clue to the explanation lies in two observations made in SR15:

  • that ‘the use of blended SAT/SST data and incomplete coverage together can give approximately 0.2°C less warming from the 19th century to the present relative to the use of complete global-average SAT’
  • that blended-masked CMIP5 warming[xxi] from 1850–1900 to 2006–2015 is essentially identical to SR15’s measure of observed warming.[xxii]

The ‘approximately 0.2°C less warming’ referred to appears compatible with the gap of 0.24°C between:

  • CMIP5 ESMs/EMICs warming (i.e. on a fully SAT basis) of 1.11°C; and
  • CMIP5 models blended-masked warming (i.e. a blend of globally-incomplete SAT and SST) of 0.87°C.[xxiii]

for 2010 (see Figure 1).

It appears to follow that in very large part the increase in the SR15 remaining carbon budgets over those in AR5 plus an additional 210 GtCO2 – approximately 700 GtCO2 in total – is due simply to changing from using globally-complete near-surface air temperature, to incomplete temperature data – a blend of SAT and SST – as a measure of past warming. This seems remarkable, particularly as in SR15 projected future warming remains, in effect, based on AR5’s globally-complete SAT measure.[xxiv]

However, there is something odd in Figure 1 as regards warming from 1850–1900 to 2006–2015. The values for the observations and (on a blended/masked basis) for the full set of ESMs used in AR5 are essentially the same, in agreement with SR15 Table 1.1. However, the AR5 warming to 2006–2015 (red line: globally complete, SAT basis)[xxv], at 1.11°C, is 12% higher than the comparable CMIP5 figure for the same period given in SR15 Table 1.1 (0.99°C, also globally complete, SAT basis).[xxvi] This 0.12°C difference presumably arises from a different set of models being involved. It accounts for half (0.12°C / 0.24°C) of the total effect of the baseline changes on the carbon budgets.

SR15 states that the increase in carbon budgets is due ‘in very large part’ to the baseline change, indicating that it does not account for the whole of the increase. The cause of the remainder of the increase must logically be that SR15 projects lower warming relative to CO2 emissions post 2010 than does AR5. The difference between the post-2000 GtCO2 slopes of the purple and red lines in Figure 1 shows how much the median (50% probability) SR15 carbon budgets are affected by its projected warming in relation to future CO2 emissions (purple line) being lower than per the AR5 CMIP5 ESMs/EMICs (red line). The emissions producing median warming of 1°C are approximately 290 GtCO2 higher on the SR15 projections than on the AR5 projections. This difference will account for some 180 GtCO2 of the 720 GtCO2 excess of the SR15 50% probability 1.5°C budget over that in AR5 (since there is 0.63°C allowable post-2010 warming to reach 1.5°C).

Why does SR15 project lower median future warming relative to cumulative CO2 emissions post 2010 than AR5, if the TCRE range used for projections in SR15 is almost identical to that of the models used in AR5, and the AR5 CMIP5 ESMs have a similar mean and median TCRE to that used in SR15?

I believe one key reason is that the subset of ESMs actually used for the simulation runs from which the AR5 carbon budgets were derived was biased towards ESMs with a significantly higher TCRE than average. Neither SR15 nor AR5 appears to discuss this possibility, and there is only limited published information as to the TCRE values of the AR5 ESMs. However, my best estimate is that the subset of CMIP5 ESMs and EMICs used to generate the AR5 carbon budgets had a median TCRE approximately 10% higher than the 1.65°C median TCRE used for the SR15 budgets,[xxvii] which TCRE appears representative of AR5 ESMs as a whole.

Another reason for the faster future warming relative to cumulative CO2 emissions in AR5 than in SR15 appears to be that warming from changes in non-CO2 emissions is greater in AR5. This can be seen from Figure 1. The green line, which shows total warming in the MAGICC model, has a similar slope to red AR5 projections line. This is as expected, since MAGICC is set up to emulate AR5 ESMs, both as to warming from cumulative CO2 emissions and warming from non-CO2 emissions. MAGICC’s TCRE is only slightly higher than the median value used for the SR15 projections. Therefore, the excess of MAGICC over SR15 projected warming (the difference between the green and purple lines in Figure 1) should to a substantial extent be due to warming from non-CO2 emissions being greater in MAGICC (and therefore in AR5 projections) than in SR15. For SR15’s projections, the MAGICC non-CO2 warming is averaged with that in the FAIR model, which is lower (particularly in the decades following 2010).

One final point. As SR15 says, calculating carbon budgets from TCRE estimates requires the assumption that the instantaneous (actually multidecadal) warming in response to cumulative CO2 emissions equals the long-term warming or, equivalently, that the residual warming after CO2 emissions cease is negligible. That is broadly the case in CMIP5 ESMs, with the slow continuing absorption of emitted CO2 by the ocean and land biosphere as they equilibrate with higher atmospheric CO2 concentration being balanced by continuing surface warming as the sub-surface ocean gradually warms and absorbs less heat, thereby offsetting a smaller proportion of greenhouse gas etc. radiative forcing. However, if there is less difference between transient and equilibrium sensitivity in the real climate system than in current ESMs, or if CO2 uptake increases more with atmospheric concentration and/or declines less with increasing temperature in the real carbon-cycle system than in current ESMs, then GMST will fall after emissions cease. In that case – which observational evidence seems to support – TCRE will overestimate the long-term warming caused by CO2 emissions.

Conclusions

SR15 uses essentially the same range for TCRE – the warming per unit CO2 emissions – to project future warming, and hence derive carbon budgets, as those exhibited by the models used to derive the AR5 carbon budgets. And although SR15 says that it defines “1.5°C relative to pre-industrial levels” as corresponding to global average combined land surface air and sea surface temperature warming, as opposed to surface air temperature warming everywhere (as for the AR5 carbon budgets), it only applies that definition to past warming, not to projected (post-2010) warming.

Despite these close links between the SR15 and AR5 bases for deriving carbon emission budgets, the SR15 remaining carbon budgets are far higher than those in AR5. The budget for a 50% probability of meeting the 1.5°C target is 510 GtCO2 larger. SR15 says that this increase is very largely due to the updating to 2005–2016 of the early historical period observational baseline for temperature and cumulative carbon emissions. While the explanation SR15 gives for the increase in the carbon budgets since AR5 may be literally correct, it obscures the true influence of the various factors involved. The re-baselining of cumulative carbon emissions actually results in a 210 GtCO2 reduction in the remaining carbon budget, due to an upwards re-estimation of pre-2010 CO2 emissions. Therefore, changes relating to temperature account for a 720 GtCO2 increase in the SR15 50% probability 1.5°C budget over the corresponding AR5 budget. Noting SR15’s finding that the observed warming matches warming simulated by the full set of AR5 CMIP5 models when calculated on the same basis, I deduce that this 720 GtCO2 increase can be divided into:

  • approximately 180 GtCO2 due to lower projected post-2010 warming relative to post-2010 cumulative CO2 The lower projected warming appears to be due partly to AR5 having used a subset of ESMs with atypically high TCREs to derive its budgets and partly to SR15 estimating lower non-CO2 warming (and possibly also to other, unidentified, factors);
  • a balance of 540 GtCO2 relating to changing the measure of warming up to 2010 from a model-simulation basis to an observational basis, which may be allocated approximately
  • half (270 GtCO2) to the models used for the AR5 budgets warming more by 2010 than do the full set of AR5 CMIP5 models, and
  • half (270 GtCO2) to changing the measure of past warming from globally-complete near-surface air temperature to a blend of SAT over land and SST over ocean, as measured, on a globally-incomplete basis, by the average of four observational temperature records.

What’s the betting that the new SR15 carbon budgets will also turn out to be unrealistically low?

Nicholas Lewis                                                                                                       18 October 2018

[i]  Earth system models represent both the climate system and the carbon cycle, and usually some other biogeochemical cycles as well. Most current ESMs, as used in AR5 and SR15, are versions of CMIP5 3D general circulation models, but some are models of intermediate complexity (EMICs).

[ii]  To estimate changes in the NOAA and GISTEMP datasets, which start in 1880, relative to the 1850–1900 reference period, warming is computed relative to 1850–1900 using the HadCRUT4.6 dataset and scaled by the ratio of the linear trend 1880–2015 in the NOAA or GISTEMP dataset with the corresponding linear trend computed from HadCRUT4.

[iii]  Warming to date in ESMs used to derive the AR5 carbon budgets does not directly affect those derived budgets (since they are based on warming at later dates in the continuing ESM simulations), but it helps diagnose the reasons for differences in carbon budgets between AR5 and SR15.

[iv]  SR15 Table 1.1: 1850–1900 to 2006–2015 column.

[v]  NOAA and GISTEMP use ERSST ocean temperature data. Over decadal and longer periods, ERSST warming is, except in the recent part of the record, primarily tied to measurements of (night-time) SAT.

[vi]  Lewis, N. and J. Curry, 2018: The impact of recent forcing and ocean heat uptake data on estimates of climate sensitivity. Journal of Climate, 31, 6051-6071.

[vii]  Taking the change between the average over 1850–1900 and the average over 1998–2017; SR15 Table 1.1.

[viii]  SR15 Table 1.1. The reanalysis datasets involved are ERA-interim and JRA-55.

[ix] TCRE is usually measured in models as the response at the point of CO2 concentration doubling when increased by 1% per annum, taking 70 years, but it is not sensitive to the exact period or profile of CO2 increase. As the SR15 Glossary says, TCRE combines information both on the airborne fraction of cumulative CO2 emissions (the fraction of the total CO2 emitted that remains in the atmosphere, which is determined by carbon cycle processes) and on the transient climate response (TCR).

[x]  The erroneous use of “considerably” rather than “considerable” here is the IPCC’s error.

[xi] The AR5 carbon budget figures in SR15 appear to come from Table 2.2 of the IPCC AR5 Climate Change 2014 Synthesis Report, first published in 2015.

[xii] SR15 Table 2.2 note (2).

[xiii] SR15 also points out that there are some additional uncertainties that its stated probabilities don’t allow for. However, the SR15 1.5°C likely range for the remaining carbon budget is wider than that for the AR5 budget that SR15 presents for comparison, so it appears probable that the AR5 budget is also subject to these or comparable additional uncertainties. (In IPCC parlance, ‘likely’ means at least 66% probability, and a ‘likely’ range is usually interpreted as a 17%–83% probability interval.)

[xiv] AR5 WG1 section 12.5.4.2 reported a TCRE range of 0.8–2.4°C for 15 CMIP5 (full-complexity) ESMs and of 1.4–2.5°C for the EMICs used. The mean and median TCRE found for CMIP5 ESMs by Gillett et al. (2013) was close to the 1.65 K value for the TCRE distribution used in SR15 to derive its carbon budgets; the mean TCRE of the EMICs used in deriving the AR5 carbon budgets also appears to be close to 1.65°C.

[xv] Gillett, N. P., et al., 2013: Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. Journal of Climate 26.18, 6844-6858.

[xvi] Detection and attribution methods allocate observed overall changes, usually in temperature, between several factors (typically changes in greenhouse gas concentrations, in other anthropogenic climate drivers, and in natural solar and volcanic activity) by scaling the differing spatiotemporal patterns of change that each factor produces in climate models so as to obtain the best match to observed overall changes. Scaling is necessary because models vary in the magnitude of their simulated responses to the various factors; models may be too sensitive or insufficiently sensitive to individual factors and/or may over- or under-represent the magnitude of those factors.

[xvii] SR15 states that “studies using observational constraints find best estimates of 0.35–0.41°C/TtCO2, and (Table 2.A.1) that using a log-normal distribution for its TCRE range would give a median TCRE of 0.38°C/TtCO2.

[xviii] The increase would have been less (Table 2.2 indicates 100 GtCO2) at the 66% probability point.

[xix] Le Quéré, C. et al., 2018: Global Carbon Budget 2017. Earth System Science Data, 10(1), 405-448.

[xx] Comparing the RCP8.5 and latest observational estimates of cumulative emissions to 2010 and their rate of increase since then, as shown in Figure 1.

[xxi] Blended-masked CMIP5 warming is based on a weighted average of SAT over land and SST over ocean in CMIP5 models, including only grid-cells for which there were adequate observational temperature data over the historical period.

[xxii] SR15 Table 1.1; or compare thin blue and black lines in Figure 1.

[xxiii] Figure 2.A.3 of SR15, which Figure 1 reproduces, shows blended-masked CMIP5 warming in 2010 as being identical to the 0.87°C observed 2010 warming. SR15 Table 1.1 gives temperature changes to the 2006–2015 mean for these two measures of respectively 0.86°C and 0.87°C.

[xxiv] Since SR15 warming projections are based on a TCRE range that primarily reflects simulated SAT warming in climate models.

[xxv] Warming accelerates slightly between 2000 and 2020 along the red line in Figure 1, so the temperature rise averaged over 2006–2015 will if anything be very marginally higher than the 1.11°C 2010 value,

[xxvi] For the CMIP5 RCP8.5 multimodel-mean, warming to 2010 is almost identical to warming to the 2006-2015 mean.

[xxvii] The AR5 carbon budgets were computed using RCP scenario simulations by 15 CMIP5 ESMs and 4 EMICs. The average TCRE of the five of those CMIP5 ESMs that were analysed in Gillett et al (2013) was 2.1°C. Extending the estimates over the remaining CMIP5 ESMs by treating similar models to ones for which TCREs were diagnosed as having the same TCRE, and by using data from Friedlingstein et al. (2014; DOI: 10.1175/JCLI-D-12-00579.1) Table 3, brings the mean (and median) TCRE estimate for all 15 CMIP5 ESMs down to ~1.85°C. Assuming that the 5 EMICs have a mean and median TCRE in line with the 1.65 K used in SR15, the overall mean and median TCRE of the models used for the AR5 carbon budgets would be ~1.8°C.