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There are two possible dimensions in which one can conduct a synthesis analysis: horizontally, across like systems, or vertically, along the causative chain. Figure 1.2 shows a simple example from Cramer et al. (2014) in which both dimensions were explicitly invoked in developing a synthesis conclusion of the detection and attribution of “increased erosion of Arctic coasts.” Vertically, synthesis assessments of individual steps in the causal chain, from “decreasing Arctic sea ice cover in summer” through “lack of sea ice protection from wind storms” were used to build the final assessment.

Alternatively, the final assessment can be seen as the horizontal synthesis across multiple like systems, in this case across the Arctic regions of Asia, Alaska, and Canada. Although the various causative steps of the regional assessments were not listed in the published report, they were necessarily implicit in the development of the regional assessments; similarly, the various Arctic‐wide assessments were developed from regional information. Thus in fact this figure should appear more as a grid, with only certain cells having published assessments.

Figure 1.2 Synthesis assessments from the IPCC AR5 concerning the attribution of increased erosion of Arctic coasts. In Cramer et al. (2014) synthesis assessments were made for various aspects of the information feeding the overall assessment. The overall assessment can be viewed as being developed through a causative chain or as aggregation across regional assessments. Confidence is given for the existence of a trend for “decreasing sea ice cover in summer” and for a “major role” in causing trends along the arrows from one box to another.

The nature of synthesis across the two dimensions differs. Sensibly, confidence along the vertical causal chain, in the existence of a trend in the first step and of causation in the last two steps, decreases as the assessment proceeds through the impact chain. Along the horizontal regional dimension, though, confidence in the Arctic‐wide assessment is the same as for the regional assessments. This is sensible enough, but what if the assessment for Asia had been for “very low confidence”? Basing the Arctic‐wide assessment on the more or less confident result would mean that the existing synthesis assessment would not be representative of the entire Arctic (Stone et al., 2013). However, taking some qualitative average (i.e., “low confidence”) would hide the existence of “medium confidence” in at least some impacts. Cramer et al. (2014) attempted to deal with this issue by adopting the practice of assigning confidence to carefully worded synthesis statements, with the explanation that “the confidence statements refer to a globally balanced assessment” (p. 1014). So for instance, the assessment of “changes in flood frequency and magnitude in non‐snowmelt‐fed rivers” referred to changes of any nature, not applicable to all non‐snowmelt‐fed rivers around the planet but rather to the existence of such changes in at least a major river in most continents.

This issue of “horizontal arithmetic” does not only apply to the confidence measure used by Cramer et al. (2014). For the binary synthesis approach previously described, Rosenzweig et al. (2007) consider if one assessment concluded no impact or an impact in the opposite sense of another region (e.g., decreased erosion for the preceding example). A high “no‐impact” count implies a lesser overall combined impact, even though this is by no means necessarily the case. However, given uncertainty in the assessments, picking the most extreme case would be biased, because it would produce a large combined impact estimate even in the absence of climate change. At the other extreme, the fact that one particular system is not being affected may have little overall relevance, and so it should not be selected as representative (Stone et al., 2013).