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=== 1.2.3 Definition of 1.5°C Pathways: Probability, Transience, Stabilization and Overshoot ===

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Pathways considered in this report, consistent with available literature on 1.5°C, primarily focus on the time scale up to 2100, recognising that the evolution of GMST after 2100 is also important. Two broad categories of 1.5°C pathways can be used to characterise mitigation options and impacts: pathways in which warming (defined as 30-year averaged GMST relative to pre-industrial levels, see Section 1.2.1) remains below 1.5°C throughout the 21st century, and pathways in which warming temporarily exceeds (‘overshoots’) 1.5°C and returns to 1.5°C either before or soon after 2100. Pathways in which warming exceeds 1.5°C before 2100, but might return to that level in some future century, are not considered 1.5°C pathways.

Because of uncertainty in the climate response, a ‘prospective’ mitigation pathway (see Cross-Chapter Box 1 in this chapter), in which emissions are prescribed, can only provide a level of probability of warming remaining below a temperature threshold. This probability cannot be quantified precisely since estimates depend on the method used (Rogelj et al., 2016b; Millar et al., 2017b; Goodwin et al., 2018; Tokarska and Gillett, 2018) <sup>[[#fn:r107|107]]</sup> . This report defines a ‘1.5°C pathway’ as a pathway of emissions and associated possible temperature responses in which the majority of approaches using presently available information assign a probability of approximately one-in-two to two-in-three to warming remaining below 1.5°C or, in the case of an overshoot pathway, to warming returning to 1.5°C by around 2100 or earlier. Recognizing the very different potential impacts and risks associated with high-overshoot pathways, this report singles out 1.5°C pathways with no or limited (&lt;0.1°C) overshoot in many instances and pursues efforts to ensure that when the term ‘1.5°C pathway’ is used, the associated overshoot is made explicit where relevant. In Chapter 2, the classification of pathways is based on one modelling approach to avoid ambiguity, but probabilities of exceeding 1.5°C are checked against other approaches to verify that they lie within this approximate range. All these absolute probabilities are imprecise, depend on the information used to constrain them, and hence are expected to evolve in the future. Imprecise probabilities can nevertheless be useful for decision-making, provided the imprecision is acknowledged (Hall et al., 2007; Kriegler et al., 2009; Simpson et al., 2016) <sup>[[#fn:r108|108]]</sup> . Relative and rank probabilities can be assessed much more consistently: approaches may differ on the absolute probability assigned to individual outcomes, but typically agree on which outcomes are more probable.

Importantly, 1.5°C pathways allow a substantial (up to one-in-two) chance of warming still exceeding 1.5°C. An ‘adaptive’ mitigation pathway in which emissions are continuously adjusted to achieve a specific temperature outcome (e.g., Millar et al., 2017b) <sup>[[#fn:r109|109]]</sup> reduces uncertainty in the temperature outcome while increasing uncertainty in the emissions required to achieve it. It has been argued (Otto et al., 2015; Xu and Ramanathan, 2017) <sup>[[#fn:r110|110]]</sup> that achieving very ambitious temperature goals will require such an adaptive approach to mitigation, but very few studies have been performed taking this approach (e.g., Jarvis et al., 2012) <sup>[[#fn:r111|111]]</sup> .

Figure 1.4 illustrates categories of (a) 1.5°C pathways and associated (b) annual and (c) cumulative emissions of CO <sub>2</sub> . It also shows (d) an example of a ‘time-integrated impact’ that continues to increase even after GMST has stabilised, such as sea level rise. This schematic assumes for the purposes of illustration that the fractional contribution of non-CO <sub>2</sub> climate forcers to total anthropogenic forcing (which is currently increasing, Myhre et al., 2017) <sup>[[#fn:r112|112]]</sup> is approximately constant from now on. Consequently, total human-induced warming is proportional to cumulative CO <sub>2</sub> emissions (solid line in c), and GMST stabilises when emissions reach zero. This is only the case in the most ambitious scenarios for non-CO <sub>2</sub> mitigation (Leach et al., 2018) <sup>[[#fn:r113|113]]</sup> . A simple way of accounting for varying non-CO <sub>2</sub> forcing in Figure 1.4 would be to note that every 1 W m <sup>−2</sup> increase in non-CO <sub>2</sub> forcing between now and the decade or two immediately prior to the time of peak warming reduces cumulative CO <sub>2</sub> emissions consistent with the same peak warming by approximately 1100 GtCO <sub>2</sub> , with a range of 900-1500 GtCO <sub>2</sub>  (using values from AR5: Myhre et al., 2013; Allen et al., 2018; Jenkins et al., 2018 <sup>[[#fn:r114|114]]</sup> ; Cross-Chapter Box 2 in this chapter).

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==== 1.2.3.1 Pathways remaining below 1.5°C ====

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In this category of 1.5°C pathways, human-induced warming either rises monotonically to stabilise at 1.5°C (Figure 1.4, brown lines) or peaks at or below 1.5°C and then declines (yellow lines). Figure 1.4b demonstrates that pathways remaining below 1.5°C require net annual CO <sub>2</sub> emissions to peak and decline to near zero or below, depending on the long-term adjustment of the carbon cycle and non-CO <sub>2</sub> emissions (Bowerman et al., 2013; Wigley, 2018) <sup>[[#fn:r115|115]]</sup> . Reducing emissions to zero corresponds to stabilizing cumulative CO <sub>2</sub> emissions (Figure 1.4c, solid lines) and falling concentrations of CO <sub>2</sub> in the atmosphere (panel c dashed lines) (Matthews and Caldeira, 2008; Solomon et al., 2009) <sup>[[#fn:r116|116]]</sup> , which is required to stabilize GMST if non-CO <sub>2</sub> climate forcings are constant and positive. Stabilizing atmospheric greenhouse gas concentrations would result in continued warming (see Section 1.2.4).

If emission reductions do not begin until temperatures are close to the proposed limit, pathways remaining below 1.5°C necessarily involve much faster rates of net CO <sub>2</sub> emission reductions (Figure 1.4, green lines), combined with rapid reductions in non-CO <sub>2</sub> forcing and these pathways also reach 1.5°C earlier. Note that the emissions associated with these schematic temperature pathways may not correspond to feasible emission scenarios, but they do illustrate the fact that the timing of net zero emissions does not in itself determine peak warming: what matters is total cumulative emissions up to that time. Hence every year’s delay before initiating emission reductions decreases by approximately two years the remaining time available to reach zero emissions on a pathway still remaining below 1.5°C (Allen and Stocker, 2013; Leach et al., 2018) <sup>[[#fn:r117|117]]</sup> .

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==== 1.2.3.2 Pathways temporarily exceeding 1.5°C ====

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With the pathways in this category, also referred to as overshoot pathways, GMST rises above 1.5°C relative to pre-industrial before peaking and returning to 1.5°C around or before 2100 (Figure 1.4, blue lines), subsequently either stabilising or continuing to fall. This allows initially slower or delayed emission reductions, but lowering GMST requires net negative global CO <sub>2</sub> emissions (net anthropogenic removal of CO <sub>2</sub> ; Figure 1.4b). Cooling, or reduced warming, through sustained reductions of net non-CO <sub>2</sub> climate forcing (Cross-Chapter Box 2 in this chapter) is also required, but their role is limited because emissions of most non-CO <sub>2</sub> forcers cannot be reduced to below zero. Hence the feasibility and availability of large-scale CO <sub>2</sub> removal limits the possible rate and magnitude of temperature decline. In this report, overshoot pathways are referred to as 1.5°C pathways, but qualified by the amount of the temperature overshoot, which can have a substantial impact on irreversible climate change impacts (Mathesius et al., 2015; Tokarska and Zickfeld, 2015) <sup>[[#fn:r118|118]]</sup> .

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==== 1.2.3.3 Impacts at 1.5°C warming associated with different pathways: transience versus stabilisation ====

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Figure 1.4 also illustrates time scales associated with different impacts. While many impacts scale with the change in GMST itself, some (such as those associated with ocean acidification) scale with the change in atmospheric CO <sub>2</sub> concentration, indicated by the fraction of cumulative CO <sub>2</sub> emissions remaining in the atmosphere (dotted lines in Figure 1.4c). Others may depend on the rate of change of GMST, while ‘time-integrated impacts’, such as sea level rise, shown in Figure 1.4d continue to increase even after GMST has stabilised.

Hence impacts that occur when GMST reaches 1.5°C could be very different depending on the pathway to 1.5°C. CO <sub>2</sub> concentrations will be higher as GMST rises past 1.5°C (transient warming) than when GMST has stabilized at 1.5°C, while sea level and, potentially, global mean precipitation (Pendergrass et al., 2015) <sup>[[#fn:r119|119]]</sup> would both be lower (see Figure 1.4). These differences could lead to very different impacts on agriculture, on some forms of extreme weather (e.g., Baker et al., 2018) <sup>[[#fn:r120|120]]</sup> , and on marine and terrestrial ecosystems (e.g., Mitchell et al., 2017 <sup>[[#fn:r121|121]]</sup> and Boxes 3.1 and 3.2). Sea level would be higher still if GMST returns to 1.5°C after an overshoot (Figure 1.4 d), with potentially significantly different impacts in vulnerable regions. Temperature overshoot could also cause irreversible impacts (see Chapter 3).

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'''Different 1.5°C pathways Schematic <sup>[[#fn:1|1]]</sup> illustration of the relationship between (a) global mean surface temperature (GMST) change; (b) annual rates of CO <sub>2</sub> emissions, assuming constant fractional contribution of non-CO <sub>2</sub> forcing to total human-induced warming; (c) total cumulative CO <sub>2</sub> emissions (solid lines) and the fraction thereof remaining in the atmosphere (dashed lines; these also indicates changes in atmospheric CO <sub>2</sub> concentrations); and (d) a time-integrated impact, such as sea level rise, that continues to increase even after GMST has stabilized.'''
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Different 1.5°C pathways Schematic <sup>[[#fn:1|1]]</sup> illustration of the relationship between (a) global mean surface temperature (GMST) change; (b) annual rates of CO <sub>2</sub> emissions, assuming constant fractional contribution of non-CO <sub>2</sub> forcing to total human-induced warming; (c) total cumulative CO <sub>2</sub> emissions (solid lines) and the fraction thereof remaining in the atmosphere (dashed lines; these also indicates changes in atmospheric CO <sub>2</sub> concentrations); and (d) a time-integrated impact, such as sea level rise, that continues to increase even after GMST has stabilized. Colours indicate different 1.5°C pathways. Brown: GMST remaining below and stabilizing at 1.5°C in 2100; Green: a delayed start but faster emission reductions pathway with GMST remaining below and reaching 1.5°C earlier; Blue: a pathway temporarily exceeding 1.5°C, with temperatures reduced to 1.5°C by net negative CO <sub>2</sub> emissions after temperatures peak; and Yellow: a pathway peaking at 1.5°C and subsequently declining. Temperatures are anchored to 1°C above pre-industrial in 2017; emissions–temperature relationships are computed using a simple climate model (Myhre et al., 2013; Millar et al., 2017a; Jenkins et al., 2018) <sup>[[#fn:r122|122]]</sup> with a lower value of the Transient Climate Response (TCR) than used in the quantitative pathway assessments in Chapter 2 to illustrate qualitative differences between pathways: this figure is not intended to provide quantitative information. The time-integrated impact is illustrated by the semi-empirical sea level rise model of Kopp et al. (2016) <sup>[[#fn:r123|123]]</sup> .

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