Uncertainty Analysis¶
URBADAPT-HEAT addresses uncertainty through a combination of structural and parametric sensitivity analyses, targeting each major source of uncertainty in the modelling chain.
Implementation¶
Uncertainty quantification runs in NB09 (09_uncertainty_0126_improved_fast.ipynb), a thin wrapper around cityheat.nb09_improved_fast. Relative to the original March-2026 uncertainty workflow (cityheat.nb09_improved, kept untouched), the fast/improved variant adds:
- spatially explicit daily raster modifiers for tree cooling and AC waste heat, instead of city-level scalars;
- event-level warning-day logic for EWS (warnings evaluated day-by-day rather than aggregated);
- EWS CBA uncertainty outputs alongside the impact-uncertainty outputs.
All results are written to outputs_variants/<variant>/<city>/tables/uncertainty_improved_fast/, leaving the original NB09 outputs unchanged.
Uncertainty dimensions¶
1. Impact function uncertainty¶
Source: the choice of age-specific heat-mortality dose-response family and its high-temperature extrapolation (see Impact Functions).
| Sensitivity dimension | Values examined |
|---|---|
| IF family | Masselot (main, city+age-specific) vs. Burke polynomial / power-law (sensitivity) |
| High-temperature extrapolation | Constant tail vs. log-linear tail (Masselot) |
| Anchor-point level scaling | ±50% (Burke family) |
| Reference temperature T_ref | Multiple lower threshold choices (Burke family) |
| Mortality displacement | Range of short-term displacement fractions (gross → net conversion) |
2. Climate uncertainty¶
Propagated through the low, central, and high warming-delta bands from the hazard module: - Low: P25 of GCM ensemble - Central: P50 of GCM ensemble - High: P75 of GCM ensemble
Each band generates a distinct set of annual T2M fields and corresponding mortality outcomes.
3. Parametric uncertainty¶
One-at-a-time sensitivity runs covering: - AC efficacy ranges (ε_a conservative / central / optimistic) - Vegetation cooling coefficients - Tree maturity timelines - EWS efficacy - Discount rate assumptions
4. EWS cost uncertainty¶
- Choice of cost model (per-capita vs. per-day formulation)
- Empirical range of EWS efficacy estimates from the literature
- These can yield materially different BCRs for the same mortality reduction; both are reported as sensitivity bounds.
5. Vulnerability projection uncertainty¶
- SSP scenario choice for long-run SVI evolution
- Diverging social-inequality trajectories generate different distributional profiles of avoided deaths
- Affects equity assessments and optimal targeting of spatially differentiated policies
6. Spatial uncertainty (vegetation and AC waste heat)¶
- Vegetation cooling applied through monthly cell-level cooling maps scaled by policy intensity and maturity (preserves within-city spatial heterogeneity).
- AC waste heat represented by a city-level intensity term spatially redistributed using the AC coverage pattern and added to each day's hazard field.
Global sensitivity analysis (PAWN)¶
A Monte Carlo sample is propagated through the full modelling chain and PAWN sensitivity indices are computed for key output variables:
| Output variable | Dominant sensitivity factors |
|---|---|
| Annual average impact (AAI, deaths/year) | Impact function reference temperature (T_ref) — dominant; then baseline hazard construction mode, vulnerability persistence k, GVI projection scale |
| 25-year EWS avoided deaths | EWS efficacy, AC penetration, climate scenario |
| 2050 SVI equity gap | Spatial smoothing φ₂₀₅₀, thermal retrofit rate |
AAI Monte Carlo summary (illustrative central case)¶
| Statistic | Value |
|---|---|
| Median | 0.33 deaths/year |
| P5 | 0.01 deaths/year |
| P95 | 1.92 deaths/year |
Reporting convention¶
- All main results are reported for the central climate and demographic scenario.
- Uncertainty bounds are reported as shaded bands or explicit low/central/high columns in result tables.
- Sensitivity runs are summarised in standardised diagnostic tables exported alongside main results.
- Output manifests record every configuration choice for full reproducibility.
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