HWMS answers "how much"
It integrates event magnitude over all connected grid-cell area and time.
\[HWMS=HWD\times HWMA\times HWMM\]
HPRI Method
Rank heatwave hazard without hiding the event physics
The Heatwave Physical Risk Index (HPRI) converts the DFS event-scale HWMS into a 0-100 percentile rank within an explicit reference domain and baseline. HPRI answers how unusual the physical event is. It keeps duration, area, and mean magnitude visible as diagnostics rather than adding them again as hidden score weights.
Method at a glance
Event magnitude to interpretable hazard rank
- 01DefineChoose domain and baseline
- 02MeasureUse event or local HWMS
- 03RankCalculate percentile position
- 04ExplainRead Event Signature diagnostics
01
Purpose
Why a reference-aware index is needed
HWMS is the cumulative heat load of a connected DFS event. It is scientifically meaningful, but its absolute value grows with the duration, area, and magnitude available to the event. A large continental event can therefore have a much larger raw HWMS than an exceptional event over an island or compact industrial corridor.
HPRI answers "how unusual"
It places HWMS within a catalog that is appropriate to the chosen domain and baseline.
\[HPRI=100\times PercentileRank(HWMS)\]
Reference choice is part of every HPRI score
An HPRI value without its reference domain and baseline is incomplete. The same event component can receive different percentile ranks under global, regional, or asset-local catalogs.
02
HPRI v2.0
Historical and current-event calculation
For an observed or reanalysis event \(e\), reference domain \(D\), and comparison baseline \(B\), HPRI is the percentile position of the applicable event HWMS within the comparable catalog.
Core formula
\[
\boxed{HPRI_{e,D,B}=100\times PercentileRank_{D,B}(HWMS_{e,D})}
\]
The connected DFS heatwave object being evaluated.
Global event, climate region, economic hub, or asset-local buffer.
The historical or scenario-specific catalog used for percentile ranking.
Full-event or domain-intersection HWMS, depending on the selected mode.
Lower historical rankHigher historical rank
HPRI 96
HPRI 96 means the event's HWMS exceeds approximately 96% of comparable events in the stated domain and baseline. It does not mean 96% expected loss.
| HPRI | Band | Screening interpretation |
|---|---|---|
| 0 to <60 | Monitor | Track the event and compare it with relevant asset sensitivity. |
| 60 to <75 | Elevated | Review whether vulnerable holdings overlap the event. |
| 75 to <90 | High | Quantify overlap and sector-specific transmission channels. |
| 90 to <95 | Severe | Use as a stress case and examine adaptation constraints. |
| 95 to 100 | Extreme | Review concentrated and potentially systemic physical-risk exposure. |
03
Comparable catalogs
Global, regional, and asset-local HPRI
The HPRI mode determines which part of an event is measured and which events form its reference distribution. This distinction is essential for responsible cross-region and portfolio comparison.
HPRI-GCurrent web screen
Global HPRI
Ranks full-event HWMS against the current global event database.
- Basis
- Full connected event
- Use
- Global archive ranking
HPRI-RMethod defined
Regional HPRI
Ranks only the portion of event HWMS intersecting a selected climate or economic region.
- Basis
- Event intersected with region
- Use
- Regional comparison
HPRI-LPreferred for assets
Asset-local HPRI
Ranks event magnitude inside a facility buffer, watershed, grid area, or industrial cluster.
- Basis
- Event intersected with local domain
- Use
- Portfolio asset screening
Asset-local event magnitude and rank
\[
HWMS^{local}_{e,j}=\sum_{(g,t)\in e\cap B_j}M_d(g,t)\,Area_g
\]
\[
HPRI^{local}_{e,j}=100\times PercentileRank_{B_j}\left(HWMS^{local}_{e,j}\right)
\]
\(B_j\) is the declared local reference domain for asset \(j\), not an arbitrary country-wide comparison.
04
Event explanation
Event Signature shows why an event ranks highly
HPRI uses HWMS as its score basis. The component characteristics are converted to their own percentiles and displayed beside HPRI so the event structure remains interpretable.
Diagnostic vector
\[
Event\ Signature=\left[P(HWMM),\ P(HWMA),\ P(HWD)\right]
\]
\[
CompoundTrait=\sum_{q\in\{HWMM,HWMA,HWD\}}\mathbf{1}\left[P(q)\ge90\right]
\]
Mean event magnitude is unusually high.
Mean daily affected area is unusually broad.
Event duration is unusually long.
Several high-percentile event structures occur together.
Diagnostics are not additional HPRI weights
HWD, HWMA, and HWMM already combine mathematically in HWMS. Re-weighting them inside HPRI would double count duration, footprint, or magnitude and obscure the score's meaning.
05
Interpretation boundary
HPRI is the hazard layer, not the full risk model
Physical climate risk requires more than hazard severity. Financial interpretation begins only after HPRI is joined with the location and value of exposed assets, sector sensitivity, adaptive capacity, and sourced impact evidence.
How unusual is the local physical heatwave event?
What facilities, revenue, or portfolio value overlap the event?
How strongly can heat affect operations, labor, power, water, or crops?
What buffers, redundancy, and response capacity reduce the impact?
Prototype portfolio translation
\[
Portfolio\ Heatwave\ Risk=
100\sum_j w_j\left(\frac{HPRI_j}{100}\right)V_j(1-AC_j)
\]
This is a transparent screening structure, not a calibrated loss function. Production use requires documented asset weights \(w_j\), vulnerability \(V_j\), adaptive capacity \(AC_j\), and preferably asset-local HPRI.
Not expected loss
HPRI does not directly estimate monetary loss, revenue decline, or insured loss.
Not impact probability
HPRI is not an outage, crop-failure, mortality, or supply-chain interruption probability.
Useful for screening
HPRI supports event ranking, exposure triage, stress-case selection, and transparent report discussion.
06
HPRI v2.1 framework
Dual-baseline future scenario method
Method specification
Not a live scenario product in the current website archive
Under strong future warming, a fixed historical P90 can make much of the warm season continuously active, merging distinct episodes into very large event objects. HPRI v2.1 separates event detection from historical impact comparison: use the target-period scenario climate to preserve event separability, then evaluate the same event against historical experience.
Use \(Q^{scen,W_y}_{90}\) to detect separable future event objects.
One connected event mask is retained for both magnitude calculations.
Use historical magnitude to measure stress relative to past adaptation.
Define the target climate window
For target year \(y\), use a centered 30-year window \(W_y\) when the scenario data permit.
Detect with scenario-relative P90
\[T_{max}(x,y,t)>Q^{scen,W_y}_{90}(x,y,d)\]
This mask is passed to the same DFS space-time connectivity method.
Measure historical-comparable magnitude
\[HWMS^{abs}=\sum_E M_d^{hist}(g,t)Area_g\]
This represents heat stress relative to historical adaptation conditions.
Measure scenario-relative magnitude
\[HWMS^{rel}=\sum_E M_d^{scen,W_y}(g,t)Area_g\]
This represents how unusual the event remains within the future climate state.
HPRIhist
\[HPRI^{hist}=100\times PercentileRank_{B_0,ref}(HWMS^{abs})\]
Preferred acute hazard input for financial stress testing because it retains comparison with historical experience.
HPRIscen
\[HPRI^{scen}=100\times PercentileRank_{W_y,S,ref}(HWMS^{rel})\]
Shows whether the event remains rare within the future climate state; it is not a substitute for historical-comparable impact.
When percentile scores approach 100
Future events can exceed the upper tail of the historical catalog, causing percentile ranks to saturate. Historical Exceedance Ratios preserve information about how far the event has moved beyond that catalog.
Historical exceedance ratios
\[
HER_{95}=\frac{HWMS^{abs}}{Q_{95}(HWMS_{B_0,ref})},\qquad
HER_{max}=\frac{HWMS^{abs}}{\max(HWMS_{B_0,ref})}
\]
Separate acute events from chronic heat burden
DFS represents discrete connected events. Persistent background heat above the historical threshold should be reported separately so that acute event risk is not asked to carry the full chronic warming signal.
\[CHB_{j,y,S}=\frac{1}{|W_y|}\sum_{\tau\in W_y}\sum_{g\in B_j}M_d^{hist}(g,\tau)Area_g\]
\[CHBI_{j,y,S}=100\times PercentileRank_{B_0,j}(CHB)\]
\[CHD_{j,y,S}=\text{days with }T_{max}>Q^{hist}_{90}\]
A direct count of annual or seasonal days above the historical P90 threshold.
07
Implementation and guardrails
What is available now and what remains a method framework
| Component | Status | Current interpretation |
|---|---|---|
| HPRI-G | Available | Full-event HWMS percentile against the current global event database. |
| Event Signature | Available | HWMM, HWMA, and HWD percentiles with compound-trait labels. |
| HPRI-R | Data required | Needs regional event-intersection HWMS and a declared regional catalog. |
| HPRI-L | Data required | Needs asset coordinates, local domains, and asset-local reference catalogs. |
| HPRI v2.1 future mode | Framework | Requires scenario fields, target windows, both magnitude baselines, and model provenance. |
| CHBI, HER95, HERmax | Framework | Defined for future analysis; not populated by the current historical web archive. |
| Financial loss functions | External evidence | Require sector damage functions, exposure, vulnerability, adaptation, and sourced loss data. |
Every HPRI must state its domain, baseline, and metric basis. Future scores must also state scenario, target year, target window, and threshold baseline.
Area is part of HWMS. Use regional or asset-local HPRI for cross-region portfolio discussion.
HWD, HWMA, and HWMM explain the event but are not independent score weights.
A saturated percentile only shows that an event reaches the top of the reference catalog. Exceedance ratios and a suitable extreme-value model are separate analyses.
Use HPRI for discrete DFS events and CHBI or CHD for persistent background heat burden.
Any portfolio result must retain data-quality, vulnerability, adaptation, and source-confidence notes.