Cost-Benefit Analysis¶
The CBA module (NB08, 08_CBA_0126.ipynb) integrates all three adaptation modules on a common 25-year discounted horizon (3% annual discount rate). Present-value costs and benefits are computed separately for each standalone policy and for explicit combined scenarios.
Hazard track¶
NB08 reads the active hazard track via HAZARD_TRACK (defaulting to Track B where the city config enables extreme_hazard). All CBA outputs are interpreted within the selected track. For Track-A cities (Rome, Athens, Lisbon) the standard daily-mean workflow drives the policy analysis. For Track-B cities (Copenhagen) the extreme-event workflow is the policy-analysis track, while the standard track is kept only for cross-city comparability with policies disabled.
Benefits¶
Benefits are measured as heat-attributable deaths avoided annually relative to the current-AC baseline:
- Mortality results at the four anchor years (2020, 2030, 2040, 2050) are linearly interpolated across all intervening years to produce annual benefit streams.
- For vegetation, avoided deaths are scaled by a tree maturity function so that benefit timing tracks the biological development of planted stock.
- Gross avoided deaths → net avoided deaths via mortality displacement factors.
- Optionally weighted by residual life expectancy to produce life-years saved.
Costs¶
Costs are year-specific and incremental (attributable to the policy above the no-intervention trajectory):
| Policy | Cost components |
|---|---|
| AC | CAPEX + annual maintenance + electricity (dominant component) |
| Trees | CAPEX (distributed linearly over 25 years) + annual maintenance (scaled by maturity profile) |
| EWS | Per-capita per-warning-day operational cost (very low relative to other options) |
Standalone vs. combined bookkeeping¶
NB08 keeps standalone policy rows standalone and reports interactions explicitly, rather than silently folding co-benefits into either policy:
| Row | Meaning |
|---|---|
AC (NET) |
Standalone AC policy: CAPEX + maintenance + electricity, minus the standalone waste-heat penalty, with no tree discount |
AC (NET + trees) |
Explicit combined scenario: same AC policy but with lower operating cost because trees reduce kwh_per_user, and a reduced incremental waste-heat penalty |
Trees (base O&M) |
Standalone tree policy on direct health benefits only |
The AC waste-heat penalty is subtracted from AC benefits as an incremental negative cost (only the incremental penalty from policy-added users is charged). A marginal interaction correction factor λ_y scales that incremental penalty in the combined scenario — it corrects the policy margin only and does not re-solve background waste heat from existing AC users (for Copenhagen λ_y ≈ 0.996, so the omitted background term is negligible).
The vegetation → AC electricity co-benefit (Falchetta, De Cian & Lunghi 2026; config block electricity_feedback) is integrated directly into NB08's AC cost computation: trees lower AC electricity demand per user, reducing the AC operating cost in the combined AC + trees scenario. It is reported as a tree-owned co-benefit (on both current-AC users and all AC users in the combined scenario), not silently subtracted from either policy's standalone cost.
Equity assessment¶
Mortality benefits are stratified by: - Quintiles of the composite SVI surface (both equal-area and population-weighted). - Public vs. private cost separation — AC costs fall on private households; trees and EWS on public budgets.
Budget optimisation¶
URBADAPT-HEAT identifies Pareto-efficient adaptation portfolios across the three policy options:
- Linear combinations of the three policy scales are evaluated over a dense grid.
- The Pareto frontier is identified in (avoided deaths, present-value cost) space.
- Incremental cost-effectiveness ratios (ICERs) are reported for transitions along the frontier.
- Sensitivity of the optimal mix to budget level and discount rate is reported.
Typical cost-effectiveness ranking¶
| Policy | Cost-effectiveness | Notes |
|---|---|---|
| EWS | Most cost-effective | Very low operational cost; dominates at low budgets |
| Trees | Intermediate | Higher CAPEX/death but co-benefits (equity, amenity, cooling) not fully captured in mortality-only metric |
| AC | Highest absolute benefit | Most deaths avoided at scale; dominated by electricity costs |
All three policies lie on or near the Pareto-efficient frontier.
Output indicators¶
| Indicator | Description |
|---|---|
| Avoided deaths (gross/net) | Annual and cumulative over 25 years |
| Life-years saved | Net avoided deaths × residual life expectancy |
| PV cost | Total discounted cost over 25 years |
| NPV | PV benefits − PV costs (benefits monetised via VSL or cost-per-QALY) |
| BCR | Benefit-cost ratio |
| Cost per avoided death | PV cost / net avoided deaths |
| Cost per life-year saved | PV cost / life-years saved |
| ICER | Incremental cost per additional unit of health benefit |
| SVI-stratified benefits | Avoided deaths by vulnerability quintile |
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