Editing IPCC:AR6/SROCC/Chapter-4 (section)

===== 4.4.4.3.2 Using robustness criteria instead of expected utility =====

A growing literature on decision analysis of coastal adaptation advocates the use of RDM approaches instead of maximising expected utility approaches (Hallegatte et al., 2012 <sup>[[#fn:r2143|2143]]</sup> ; Haasnoot et al., 2013 <sup>[[#fn:r2144|2144]]</sup> ; Lempert et al., 2013 <sup>[[#fn:r2145|2145]]</sup> ; Wong et al., 2017 <sup>[[#fn:r2146|2146]]</sup> ). The core criterion to be considered for choosing between the two types of approaches is whether one is confronted with a situation of shallow or deep uncertainty ''(high confidence)'' (Lempert and Schlesinger, 2001 <sup>[[#fn:r2147|2147]]</sup> ; Kwakkel et al., 2010 <sup>[[#fn:r2148|2148]]</sup> ; Kwakkel et al., 2016b <sup>[[#fn:r2149|2149]]</sup> ; Hinkel et al., 2019 <sup>[[#fn:r2150|2150]]</sup> ). Uncertainty is shallow when a single unambiguous objective or subjective probability distribution can be attached to states-of-the-world. Uncertainty is deep, when this is not possible, either because there is no unambiguous method for deriving objective probabilities or the subjective probability judgements of parties involved differ (Cross-Chapter Box 4 in Chapter 1; Type 2).

Expected utility approaches can only be applied for identifying an optimal response in situations of shallow uncertainty. This is because these approaches require a probability distribution over states of the world in order to identify the optimal alternative which leads to the highest expected utility (i.e., the probability weighted sum of the utilities of all outcomes under a given alternative and all states-of-the-world; Simpson et al., 2016 <sup>[[#fn:r2151|2151]]</sup> ). A prominent example of this approach is cost-benefit analysis under risk, which assesses expected outcomes across states of the world in terms of NPV (the discounted stream of net benefits). Cost-benefit analysis has several well-known limitations, such as its sensitivity to discount rates and the difficulty to monetise ecological, cultural and other intangible benefits (Section 1.1.4) that have been widely discussed in the climate change literature (Chambwera et al., 2014 <sup>[[#fn:r2152|2152]]</sup> ; Kunreuther et al., 2014 <sup>[[#fn:r2153|2153]]</sup> ; Dennig, 2018 <sup>[[#fn:r2154|2154]]</sup> ).

In the context of coastal adaptation, uncertainty is only shallow if projected SLR does not significantly differ between low end (e.g., RCP2.6) and high end (e.g., RCP8.5) scenarios (Hinkel et al., 2019 <sup>[[#fn:r2155|2155]]</sup> ). The point in time when this is the case (i.e., time of scenario divergence) depends on what difference in expected utility matters to the particular stakeholders involved in a decision. The time of scenario divergence also differs across locations. In locations where the internal sea level variability is large as compared to relative SLR, it takes longer before the differences in sea levels under low end and high end scenarios become apparent. Figure 4.15 illustrates this effect for the ESL projections of this report (Sections 4.2.3.2 and 4.2.3.4), following the approach of Hinkel et al. (2019). Under the assumption that a 10% statistical distance between the distributions of RCP2.6 and RCP8.5 is decision relevant, scenario divergence occurs before 2050 for approximately two thirds of coastal sites with sufficient observational data, but for 7% of locations this occurs later than 2070.

In principle, a single unambiguous probability distribution on future sea levels could also be attained beyond the time of scenario divergence by attributing subjective probabilities to emission scenarios, but individuals may significantly disagree in their subjective probabilities, which again results in deep uncertainty (Lempert and Schlesinger, 2001 <sup>[[#fn:r2156|2156]]</sup> ; Stirling, 2010 <sup>[[#fn:r2157|2157]]</sup> ). For this reason, very few studies that assign subjective probabilities to emission scenarios are found in the literature (Woodward et al., 2014 <sup>[[#fn:r2158|2158]]</sup> ; Abadie, 2018 <sup>[[#fn:r2159|2159]]</sup> ). But even before the year of scenario divergence is reached, uncertainty about relative SLR can be deep, because of deep uncertainties about non-climatic contributors to relative sea level change, such as VLM during or after earthquakes and human-induced subsidence (Cross-Chapter 5 in Chapter 1; Section 4.2.2.4; Hinkel et al., 2019 <sup>[[#fn:r2160|2160]]</sup> ).

Under situations of deep uncertainty, RDM approaches aim to identify alternatives that perform reasonably well (i.e., ‘are robust’) under a wide range of states-of-the-world or scenarios and hence do not require probability assessments. These approaches include minimax or minimax regret (Savage, 1951), info gap theory (Ben-Haim, 2006 <sup>[[#fn:r2162|2162]]</sup> ), robust optimisation (Ben-Tal et al., 2009 <sup>[[#fn:r2163|2163]]</sup> ) and exploratory modelling methods that create a large ensemble of plausible future scenarios for each alternative, and then use search and visualisation techniques to extract robust alternatives (Lempert and Schlesinger, 2000 <sup>[[#fn:r2164|2164]]</sup> ). SLR examples of RDM include Brekelmans (2012) who minimise the average and maximum regret across a range of SLR scenarios for investments in dike rings in the Netherlands and Lempert et al. (2013) <sup>[[#fn:r2165|2165]]</sup> who apply RDM in Hoh-Chi-Minh City '''''.'''''

But even if SLR uncertainty is shallow, RDM are more suitable than expected utility approaches if parties involved or affected by a decision have a low uncertainty tolerance, because the goal of the uncertainty intolerant decision maker is to avoid major damages under most or all circumstances (Hinkel et al., 2019 <sup>[[#fn:r2166|2166]]</sup> ).

An adaptation strategy developed based on the maximisation of expected utility may not meet this goal, because worst case damages occurring can exceed expected damages by orders of magnitude.

The uncertainty tolerance of stakeholders is also determining how large of a SLR range needs to be considered in RDM. Stakeholders (i.e., those deciding and those affected by a decision) that have a high uncertainty tolerance (e.g., those planning for investments that can be very easily adapted) can use the combined ''likely'' range of RCP2.6 and RCP8.5 (0.29–1.10 m by 2100) for long-term adaptation decisions. For stakeholders with a low uncertainty tolerance (e.g. those planning for coastal safety in cities and long term investment in critical infrastructure) it is meaningful to also consider SLR above this range, because a 17% chance of GMSL exceeding this range under RCP8.5 is too high to be tolerated from this point of view (Ranger et al., 2013 <sup>[[#fn:r2167|2167]]</sup> ; Hinkel et al., 2015 <sup>[[#fn:r2168|2168]]</sup> ; Hinkel et al., 2019 <sup>[[#fn:r2169|2169]]</sup> ).

Independent of the debate about whether to apply expected utility or robust decision making approaches, there is an extensive literature that applies scenario-based cost-benefit analysis. For example, this approach has been applied for setting the safety standards of Dutch dike rings (Kind, 2014 <sup>[[#fn:r2170|2170]]</sup> ; Eijgenraam et al., 2016 <sup>[[#fn:r2171|2171]]</sup> ), exploring future protection alternatives for New York (Aerts et al., 2014 <sup>[[#fn:r2172|2172]]</sup> ), Ho Chi Minh City (Scussolini et al., 2017 <sup>[[#fn:r2173|2173]]</sup> ), and for many other locations. Scenario-based cost-benefit analysis differs from cost-benefit analysis under risk discussed above in that scenario-based cost-benefit analysis is not applied to rank alternatives across scenarios, but a ‘separate’ cost-benefit analysis is applied within each emission or SLR scenario considered. While this identifies the optimal alternative under each scenario, it does not formally address the problem faced by a coastal decision maker, namely to decide across scenarios (Lincke and Hinkel, 2018 <sup>[[#fn:r2174|2174]]</sup> ). Nevertheless, the results of scenario-based cost-benefit analysis (i.e., NPV of each alternative under each scenario) provide guidance for decision makers and can also be used as inputs (i.e., as attributes) to robust and flexible decision making approaches

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'''Figure 4.15 | Year of scenario divergence between extreme sea level projections for Representative Concentration Pathway (RCP)2.6 and RCP8.5 for all tide-gauge locations with sufficient observational data relative to a 1986–2005 baseline (bottom panel). Time of divergence is defined using a 10% threshold in the statistical distance between the two distributions, which can be graphically […]'''
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Figure 4.15 | Year of scenario divergence between extreme sea level projections for Representative Concentration Pathway (RCP)2.6 and RCP8.5 for all tide-gauge locations with sufficient observational data relative to a 1986–2005 baseline (bottom panel). Time of divergence is defined using a 10% threshold in the statistical distance between the two distributions, which can be graphically interpreted as the first year in which at least 10% of the area under the probability distribution function (PDF) of RCP8.5 lies outside of the area under the upper half (i.e., above the 50th percentile) of the PDF of RCP2.6. Upper panels indicate the median and 5–95% range of future extreme sea level (ESL) relative to the 1986–2005 baseline for three tide gauge locations with low variability (Papeete), medium variability (New York) and high variability (Cuxhaven). Locations with low variability have a relatively early scenario divergence.

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