CE Physical Hazard Cascade Model

Climate Current active

CE's model for compound and cascading physical climate hazard risk — filling the gap between single-hazard probability models (CMIP6, ERA5, GFDL) and full combined climate-economy synthesis. Quantifies how co-occurring or sequentially triggered hazard events (drought + wildfire + heat; flood + infrastructure failure + insurance retreat) compound each other's economic impacts through non-linear mechanisms. Essential for sectors and geographies where compound event exposure is the dominant physical risk driver.

Horizon 2025–2060

Geography Global with regional cascade pathway differentiation (Mediterranean, South Asia, Sub-Saharan Africa, Western US, Southeast Asia, Caribbean)

Resolution Sector-level with geographic cascade pathway specification; infrastructure exposure at sub-sector level

Projection years 2025, 2030, 2035, 2040, 2050, 2060

0.74

cascade index

0.62

compound probability

0.79

recovery compression

0.68

physical fragility

0.71

confidence

Cascade Index — compounded multi-hazard loss amplification factor Compound event probability — joint probability of co-occurring hazards Recovery compression — how prior events reduce recovery capacity for subsequent events Physical fragility score — sector and infrastructure vulnerability to cascade initiation Hazard pair correlation matrix — which hazard combinations are positively correlated Geographic cascade pathway map — which regions face which multi-hazard combinations Insurance protection gap dynamics — cascade-triggered retreat of insurance coverage

Why compound risk cannot be modelled as the sum of individual hazard exposures

Standard physical climate risk models answer a single-hazard question: what is the probability that this asset experiences a 1-in-50-year flood? This is the right question for flood risk in isolation. It becomes the wrong question the moment you need to answer: what is the risk that this asset experiences a 1-in-30-year flood after it already experienced a 1-in-50-year drought that reduced its drainage capacity? The mathematics are qualitatively different. The cascade model exists because that answer — which is the real world that assets and portfolios face — cannot be obtained by adding together two single-hazard models. The compound trigger threshold is lower, the amplification is non-linear, and the recovery timeline is compressed.

	Single-Hazard Physical Models (CMIP6/ERA5)	CE Physical Hazard Cascade Model
Question answered	What physical hazard exposure does this sector face annually?	How do hazard types compound when they co-occur or trigger each other sequentially?
Hazard treatment	Individual annual hazard events — flood, drought, heat treated as independent inputs	Hazard pairs and cascade sequences with measured amplification factors (κ)
Loss calculation	Loss ≈ sum of individual hazard exposures weighted by sector vulnerability	Loss = L₁ + L₂ × κ — cascade amplification; κ > 1 for correlated hazard pairs
Recovery modelling	Full recovery assumed between annual periods	Recovery compression — cumulative compound events progressively reduce baseline recovery capacity
Geographic specificity	Global sector-level averages with regional notes	Region-specific cascade pathway maps (Mediterranean, South Asia, Western US, Caribbean)
Use case	Physical hazard signal input to combined model framework	Enhanced physical component for sectors or geographies where compound hazard is the dominant physical risk driver

The CE combined models (Balanced Synthesizer, Stress Overlay) use a physical hazard component appropriate for global sector-level analysis. For portfolios with concentrated exposure to multi-hazard geographies — a real estate fund with Mediterranean coastal assets, an agricultural portfolio spanning South Asia and Sub-Saharan Africa, an infrastructure fund with Western US exposure — the cascade model provides the precision that sector-average physical components cannot. Recommended workflow: run the combined model for overall sector positioning, then apply the cascade model for geographic concentration stress testing.

Methodology

The CE Physical Hazard Cascade Model addresses a structural gap in standard climate risk modeling: individual hazard models give the probability of a specific event type (e.g., a 1-in-50-year flood), but compound events — where multiple hazard types co-occur or trigger each other sequentially — produce losses that cannot be modelled as the sum of individual event impacts. The model applies two cascade architectures: (1) Simultaneous co-occurrence, where multiple hazards affect the same geography within the same season (drought + extreme heat + wildfire is the archetypical Mediterranean/California cascade); and (2) Sequential triggering, where one hazard reduces the system's recovery capacity and increases vulnerability to the subsequent hazard (coastal flooding damages drainage infrastructure, amplifying the impact of the following rainfall event; wildfire destroys ground cover, amplifying landslide risk in the next wet season). Hazard pair correlations are derived from CE's integration of CMIP6 ensemble projections, ERA5 reanalysis, and GFDL physical climate data, supplemented by Swiss Re Sigma compound event loss records. The cascade amplification factor (κ) is the key output: for a hazard pair, the combined loss is L_combined = L_1 + L_2 × κ, where κ > 1 for positively correlated hazard pairs and approaches 1 for independent hazards. The recovery compression parameter models how cumulative physical events reduce the system's baseline recovery capacity — the core mechanism behind 'climate fatigue' observed in repeatedly-affected regions. The model is calibrated against compound event loss records from Swiss Re Sigma 2015–2024 and cross-validated against the 2017 California wildfire + drought sequence, 2011 Thailand flood + supply chain cascade, 2022 Pakistan multi-hazard event, and the 2023 Mediterranean compound drought + wildfire + heat sequence.

Key Mechanisms

Cascade amplification factor (κ): the ratio of observed compound event loss to the sum of individual event losses — calibrated from Swiss Re Sigma compound loss records; κ is hazard-pair specific (drought × wildfire κ = 1.8–2.4; flood × infrastructure failure κ = 1.5–2.1; heat × drought κ = 1.3–1.7)
Joint hazard probability matrix: pairwise probabilities of co-occurring hazard types derived from CMIP6 multi-model ensemble analysis — under SSP3-7.0 and SSP5-8.5, drought-heat and flood-storm co-occurrence probabilities double relative to historical baselines by 2040
Sequential triggering pathway: wildfire removes protective ground cover → landslide risk multiplied in following wet season; coastal flood damages drainage infrastructure → subsequent rainfall has amplified inundation; drought weakens tree root systems → windstorm blowdown events elevated
Recovery compression: regions experiencing repeat compound events within <5-year recovery windows show progressively reduced recovery capacity — modelled as a decay function applied to regional post-event vulnerability; calibrated to Mediterranean and California compound event sequences (2017–2023)
Infrastructure failure cascade: critical infrastructure failure (power grid, water treatment, transport) during a compound event creates a secondary cascade where economic activity is interrupted beyond the physical hazard footprint — modelled as an infrastructure dependency graph with failure propagation
Insurance protection gap trigger: the model identifies the compound event severity threshold at which the insurance market retreats — at this threshold, the protection gap creates an uninsured loss cascade into household wealth, mortgage default risk, and municipal fiscal stress
Geographic cascade pathway specification: each of 6 priority regions has a dominant hazard cascade pathway based on CMIP6 regional projections — Mediterranean: drought → wildfire → erosion; South Asia: monsoon → flood → heat; Western US: drought → wildfire → air quality; Caribbean: hurricane → storm surge → coastal flood
Sector physical fragility mapping: each sector's infrastructure and supply chain is mapped to geographic cascade pathways — agriculture (Mediterranean and South Asia high cascade exposure), energy (Western US wildfire grid exposure), real estate (Caribbean hurricane cascade, Mediterranean wildfire exposure)

Score & Confidence Methodology

Hazard scores (0–1) are calibrated against IPCC AR6 WG2 Table 16.SM.1 industry-sector exposure bands. Transition pressure scores use NGFS Phase IV scenario families. Confidence intervals are asymmetric where IPCC likelihood language (likely/very likely) maps to the p17–p83 and p5–p95 ranges. Scores are not actuarially certified — see Known Limitations.

Known Failure Modes

Cascade amplification factors (κ) are calibrated from 2015–2024 compound event records — for novel compound event types with no historical parallel, κ values are extrapolated from nearest analogues rather than directly observed
Sequential trigger pathways are modelled from dominant cascade sequences — in practice, any single hazard can trigger multiple secondary cascades; the model captures the dominant pathway but may understate the probability of less common cascade sequences
Recovery compression parameter requires multi-year compound event history to calibrate — for regions experiencing first-generation compound events without precedent, the estimate carries substantially higher uncertainty
The infrastructure failure cascade uses a simplified dependency graph — the true interdependency of power, water, transport, and telecommunications infrastructure is more complex; in highly interconnected urban systems, cascade effects may be larger than modelled
The model does not extend to social cascade effects (displacement, conflict, mass migration) that emerge from compound physical events at extreme severity thresholds — these feedbacks are outside the model's physical-to-economic scope

Best For

quantifying how simultaneous and sequential multi-hazard climate events produce losses that exceed the sum of individual events — compound physical risk for portfolio stress testing

Strengths

Addresses the compounding gap: standard sectoral models treat physical hazards as independent events — this model provides the cascade amplification factor that converts individual hazard exposures into a compound loss estimate, the critical correction for portfolios in multi-hazard geographies
Grounded in observed compound event loss data: κ factors are derived from 1,200+ Swiss Re Sigma compound event records (2015–2024), not from theoretical model assumptions — giving cascade amplification parameters an empirical foundation that physical-only climate models lack
Recovery compression explicitly models 'climate fatigue': the progressive reduction of post-event recovery capacity in repeatedly-affected regions is a mechanism that single-event models cannot capture but is empirically documented in Southern European, South Asian, and Western US regional data
Geographic cascade pathway maps provide actionable specificity: analysts can identify whether their portfolio is exposed to the drought-wildfire pathway (Mediterranean/California), the flood-infrastructure failure pathway (South Asia/Southeast Asia), or the hurricane-storm surge-flood cascade (Caribbean)
Insurance protection gap trigger threshold enables macro-prudential analysis: identifying when compound event severity crosses the insurance market retreat threshold is a key early warning signal for residential real estate portfolio risk and municipal fiscal stress
Designed as a plug-in enhancement to the CE Balanced Synthesizer and Stress Overlay: the cascade model's physical fragility output can supersede the physical component in the combined models for geographies where compound hazard is dominant — providing precision where the combined models use sector-level averages

Maturity & Validation

Model era: Current • Status: active
Core models are internally cross-validated against institutional benchmarks. Advanced modules (DSGE, Monte Carlo, Catastrophe, Commodity) are prototype-grade — not yet independently peer-reviewed. View the full validation record at Validation Registry and current capability status at Capability Registry (JSON).

Scenario Coverage

CMIP6 SSP3-7.0 (High Warming) CMIP6 SSP5-8.5 (Very High Warming) CMIP6 SSP2-4.5 (Intermediate, 2040+) CMIP6 SSP1-1.9 (Very Low Emissions) CMIP6 SSP1-2.6 (Low Emissions) NGFS Net Zero 2050

Under low-emissions scenarios, compound event frequency and correlation remain close to historical baselines — individual hazard models (CMIP6, ERA5) are sufficient for SSP1-1.9 and SSP1-2.6. The cascade model adds material value in intermediate-to-high warming scenarios where hazard pair correlations are elevated.

IPCC AR6 WG2 Chapter 11 (weather and climate extremes) and Chapter 16 (key risks and compound events). Compatible with IPCC AR6 framework for compound and cascading climate risks.

Calibration Benchmarks

Swiss Re Sigma — Natural Catastrophe and Compound Event Loss Records (2015–2024)	Primary cascade amplification factor (κ) calibration — 1,200+ compound event records used to derive hazard-pair-specific amplification factors for drought-wildfire, flood-infrastructure, and heat-drought combinations
CMIP6 Multi-Model Ensemble — Regional Hazard Correlation Analysis	Joint hazard probability matrix construction — pairwise hazard co-occurrence probabilities under SSP2-4.5, SSP3-7.0, and SSP5-8.5 through 2060
IPCC AR6 WG2 Chapter 11 — Compound and Extreme Events (2021)	Cascade pathway taxonomy and compound event classification; confirmation that observed compound event frequency increases are consistent with anthropogenic forcing
Case Studies: 2017 CA Wildfires, 2011 Thailand Floods, 2022 Pakistan Multi-Hazard, 2023 Mediterranean Compound Event	Sequential trigger pathway calibration and cross-validation of recovery compression parameter against observed multi-year regional recovery trajectories
BIS Working Paper 1030 — Climate and Infrastructure Cascade Risk (2022)	Infrastructure failure cascade dependency graph — financial system exposure to compound physical-financial cascades used to calibrate infrastructure failure cascade parameters

Industry Signal Dashboard — projected signals from this model across all tracked industries

Physical Hazard Pressure by Industry

Physical hazard index (0–1) indicating asset and operational exposure to climate-related physical risks.

Transition Pressure by Industry

Regulatory and market pressure from the low-carbon transition — 0 (low) to 1 (high).

Adaptive Resilience by Industry

Resilience index (0–1) — the industry's estimated capacity to adapt to physical and transition risk.

Industry Context

Energy

Energy infrastructure has the highest compound cascade exposure of any sector in the model. Power grid vulnerability to wildfire (cable ignition, substation damage) followed by demand surge from the subsequent heat wave is the Western US dominant pathway. Oil and gas infrastructure in the Gulf of Mexico faces hurricane + storm surge + coastal flooding cascade — each successive storm season hits infrastructure in a progressively degraded state. Solar and wind farm siting in high-cascade regions (Mediterranean drought + wildfire corridor; South Asian monsoon + flood zone) requires cascade pathway analysis beyond simple single-hazard siting assessment.

Agriculture

Agriculture is the sector with the highest compound cascade event frequency in historical records. The drought → wildfire → erosion → soil degradation → reduced next-season productivity sequence is the Mediterranean and California dominant pathway. The monsoon → flood → waterlogging → disease pressure → crop failure cascade is the South Asian dominant pathway. The cascade model assigns the highest agricultural fragility scores to regions where these sequences have already been observed (Spain, Portugal, Morocco; Bangladesh, Pakistan, northeastern India). Recovery compression in agriculture is particularly severe — soil microbiome destruction from repeated heat and drought events is multi-year in duration.

Manufacturing

Manufacturing cascade exposure is primarily through supply chain geography — cascades affecting input supply rather than direct physical hazard to manufacturing assets. Thai automotive supply chains face monsoon + flood cascade; European steel inputs face drought-driven Rhine low-water-level shipping disruption. The 2011 Thailand flood supply chain cascade (Toyota, Honda, Western Digital production stoppages) is the primary calibration case for manufacturing cascade exposure.

Transport

Transport infrastructure is the most direct cascade conductor — roads, bridges, airports, and ports are both directly affected by compound hazards and act as transmission channels for cascade effects across the economy. The infrastructure failure cascade pathway is most pronounced for transport: flood damage to bridge foundations followed by heat-driven thermal expansion cracking creates cumulative structural integrity deterioration that single-event assessments miss.

Insurance

Insurance is simultaneously the financial absorber and the cascade amplifier. In the cascade model, insurers face compound technical loss events when hazard pairs hit the same portfolio simultaneously — a catastrophe model that treats flood and wildfire separately will understate combined technical losses when both strike the same quarter. The protection gap trigger is modelled at the point where compound event losses exceed the insurer's technical result threshold — historically observed first in California wildfire + wind, Florida hurricane + flood, and European flood + storm combinations.

Real Estate

Real estate is the sector with the highest property value concentration in multi-hazard cascade zones — coastal assets face hurricane + storm surge + sea level cascade; Mediterranean and Californian assets face drought + wildfire + insurance retreat cascade. The model's recovery compression parameter is most material for real estate: property values in repeat-compound-event zones are already showing progressive devaluation trends in US coastal markets, directly validating the cascade and recovery compression architecture.

Formal Mechanics — propagation equations and parameter definitions

Model Architecture

The cascade model operates over a discrete time-step network where nodes represent infrastructure sectors and edges carry dependency weights. At each time step, each node's resilience state is updated by upstream stress propagation, local adaptation capacity, and background degradation. The network is solved forward from an initialised shock event.

Propagation Equations

Resilience state propagation

$$R_i(t+1) = R_i(t) - \sum_j w_{ij}\,S_j(t) + \gamma_i\,A_i(t) - \delta_i\,D_i(t)$$

Core propagation equation. Rᵢ is the resilience state of node i at time t. wᵢⱼ is the dependency weight from upstream node j. Sⱼ(t) is the stress level at node j. Aᵢ is the adaptation capacity coefficient, γᵢ its effectiveness. δᵢ and Dᵢ are the degradation rate and accumulated damage.

Compound loss amplification

$$L_{\text{combined}} = L_1 + L_2 \times \kappa(h_1, h_2)$$

For a co-occurring or sequentially triggered hazard pair (h₁, h₂), the combined loss exceeds the sum of individual losses by the cascade amplification factor κ. κ is hazard-pair specific and empirically calibrated: drought × wildfire κ = 1.8–2.4; flood × infrastructure failure κ = 1.5–2.1; heat × drought κ = 1.3–1.7.

Recovery compression (climate fatigue)

$$RC(t) = RC_0 \cdot e^{-\lambda\, n(t)}$$

Recovery capacity RC at time t decays with cumulative compound events n(t) experienced within the rolling five-year window. RC₀ is baseline recovery capacity. λ is the fatigue decay coefficient, calibrated from Mediterranean and California repeat-event sequences (2017–2024). As n(t) increases, the system becomes progressively less able to restore between events.

Joint hazard probability (climate-adjusted)

$$P(H_i \cap H_j) = P(H_i)\,P(H_j) + \rho_{ij}\,\sigma_i\,\sigma_j$$

Under climate change, hazard pair correlation ρᵢⱼ increases. For drought and heat under SSP3-7.0, ρ rises from ~0.3 (historical) to ~0.6 (2040), substantially increasing joint occurrence probability beyond the naive product of individual probabilities. Derived from CMIP6 multi-model ensemble covariance analysis.

Infrastructure failure threshold

$$F_i(t) = \mathbf{1}\!\left[R_i(t) < \theta_i\right]$$

Node i enters failure state Fᵢ = 1 when resilience Rᵢ falls below the critical threshold θᵢ. Failure propagates downstream through dependent nodes in subsequent time steps. θᵢ values are sector-calibrated: power grid θ = 0.22, water infrastructure θ = 0.18, transport θ = 0.31, healthcare θ = 0.27.

Parameter Reference

Symbol	Parameter	Range	Calibration basis
w_{ij}	Dependency weight	0.0–1.0	Derived from BIS WP 1030 infrastructure interdependency matrices and OECD critical infrastructure dependency surveys
\kappa	Cascade amplification factor	1.0–2.4	Calibrated from Swiss Re Sigma 1,200+ compound event loss records (2015–2024)
\lambda	Fatigue decay coefficient	0.12–0.28	Fitted to Mediterranean (2017–2023) and California (2017–2021) repeat compound event sequences
\rho_{ij}	Hazard pair correlation	−0.1 to +0.7	CMIP6 multi-model ensemble covariance matrices at SSP2-4.5, SSP3-7.0, SSP5-8.5
\theta_i	Failure threshold	0.18–0.35	Sector-specific; derived from FEMA and NIST critical infrastructure resilience standards
\gamma_i	Adaptation effectiveness	0.0–0.8	Scenario-dependent; high under proactive governance, low under fragmented response

Historical Replay Validation — observed vs modelled cascade behavior for documented events

Texas Winter Storm Uri — Power Grid Cascade

2021

Cold shock → grid failure → water pumping failure → healthcare disruption

Observed

Grid failure at ~35 GW generating capacity loss; 246 fatalities; ~$195 billion damages; water infrastructure failure in 12+ counties within 48h of grid collapse; hospital backup generators exhausted within 72h in several facilities.

Modelled

Grid failure cascade at R_grid = 0.19 (below θ = 0.22 threshold) triggering water infrastructure cascade within 36–52h; healthcare disruption cascade within 60–84h. Dependency propagation sequence matches observed order.

Accuracy: Cascade sequence order: correct. Infrastructure failure threshold timing: within ±18h. Economic damage: $180B modelled vs $195B observed (−8%). Recovery compression: not applicable (first major event in region).

Known gap: Model underestimated natural gas supply freeze-up as a primary cascade initiator; current version treats supply disruption as secondary. Under review for v2 dependency graph revision.

Pakistan Multi-Hazard Floods

2022

Monsoon intensification → flood → agricultural collapse → food security → displacement

Observed

33 million displaced; 20% of national territory flooded; crop losses ~$3.7 B; livestock losses ~3.6 million animals; infrastructure damage $5.6 B; debt distress amplification triggering IMF emergency program.

Modelled

Flood → agriculture cascade with κ_flood×ag = 1.67 (within 1.5–2.1 calibrated range); displacement pressure signal reaches 0.82 (high); infrastructure dependency graph routes through road-bridge damage to supply chain disruption within 2–3 time steps.

Accuracy: Cascade direction: correct. Agricultural loss: $3.2B modelled vs $3.7B observed (−14%). Displacement: broadly consistent. Sovereign stress cascade: directionally correct; timing lagged ~1 quarter.

Known gap: Governance fragility (limited state response capacity) accelerated the cascade faster than the neutral governance assumption in the base case.

California Wildfire Compound Sequence

2017–2021

Multi-year drought → wildfire → utility financial cascade → insurance market retreat

Observed

$100 B+ total losses across sequence; PG&E bankruptcy (2019); State Farm and Allstate withdrawal from California residential market (2023); >20% premium increases in high-risk zones; 20M+ hectares burned 2017–2021.

Modelled

Recovery compression activates in year 3 (2019) as RC(t) drops below 0.45; utility financial cascade triggered by liability accumulation in year 2; insurance protection gap threshold crossed in year 4 for residential real estate.

Accuracy: Recovery compression activation timing: correct to within one season. Utility cascade sequence: directionally correct. Insurance retreat threshold: activated 1 year earlier in model than observed.

Known gap: California state regulatory constraints on insurance premium increases masked the financial signal. Model treats insurance pricing as unconstrained, overestimating speed of insurance retreat in regulated markets.

Thailand Floods — Supply Chain Cascade

2011

Monsoon flood → industrial estate inundation → automotive + electronics supply chain disruption

Observed

Seven major industrial estates flooded; Toyota: ~150,000 vehicle production loss; Honda Japan output halved for 6+ weeks; Western Digital HDD output −45%; global HDD prices +100% within 60 days; Thai GDP impact ~−1.1% for 2011.

Modelled

Flood → industrial estate failure → tier-1 supply disruption → global OEM production stop within 2–3 time steps; economic cascade amplitude −1.0 to −1.3% GDP.

Accuracy: Supply chain cascade propagation: correct. GDP impact: within modelled range (−1.1% observed). Time-to-global-supply-disruption: 14–21 days modelled vs 18–25 days observed. Insurance loss: $15B modelled vs $16B Swiss Re recorded (−6%).

Known gap: Thailand 2011 is the primary calibration anchor for the manufacturing cascade pathway; accuracy reflects calibration fit rather than out-of-sample validation.

2023 Mediterranean Compound Event

2023

Multi-month drought → extreme heat → record wildfire → agricultural and tourism collapse

Observed

Greece: 900,000+ hectares burned (largest European fire on record); Spain/Portugal: drought-wildfire-erosion sequence; Sicily/Sardinia: >47°C; agricultural output −12 to −18% for affected regions; tourism losses €2–4 B.

Modelled

Drought × wildfire κ = 2.1 activated for Mediterranean pathway; soil degradation secondary cascade modelled with 2–3 season lag; agricultural fragility score reaches 0.79 (high) for Spain/Portugal/Greece under SSP3-7.0 2030 projection.

Accuracy: Cascade pathway: correct. Wildfire extent: consistent with SSP3-7.0 high-severity scenario. Agricultural and tourism loss: within ±20% of observed. Recovery compression activation: consistent with prior 2017, 2018, 2022 Mediterranean sequence.

Known gap: Model uses a regional-average Mediterranean parameterisation; within-region heterogeneity (wetter northern Spain vs driest Extremadura/Alentejo) creates sub-regional cascade variation the current version does not capture.

Recovery & Resilience Dynamics — how the model simulates restoration as aggressively as failure

Overview

The cascade model treats recovery and resilience as active processes, not passive return-to-baseline. Recovery is modelled through four mechanisms: redundancy activation, adaptive substitution, institutional intervention, and behavioral adaptation. These operate in parallel with failure propagation — the net trajectory of a cascade depends on the relative speed of failure propagation vs recovery mobilisation.

Recovery Mechanisms

Redundancy activation

When a node fails (Rᵢ < θᵢ), adjacent nodes with spare capacity activate supplementary routing. Power grid failure triggers demand-side response and import capacity. Transport failure triggers modal substitution. Water pumping failure triggers emergency tanker supply. Modelled as a capacity restoration term capped at the redundancy ratio for each sector.

6–48 hours for power grid; 24–72 hours for transport rerouting; 12–48 hours for water emergency supply

Adaptive substitution

Markets and operators substitute inputs when primary supply fails. Manufacturing substitutes components across supply chains. Agriculture substitutes crop varieties or irrigation sources. Healthcare substitutes drugs or equipment. Modelled as a price-elasticity-weighted substitution rate; effectiveness degrades under simultaneous multi-node failure when all alternatives are also stressed.

3–21 days for supply chain substitution; weeks to months for input-intensive sectors

Institutional intervention

Government emergency powers, central bank liquidity, military logistics, and mutual-aid compacts can halt cascade propagation that market mechanisms cannot stop. Modelled as a governance response function G(t) with response speed (days to activation) and response effectiveness (fraction of cascade halted). Under competent governance with pre-positioned capacity, G(t) can reduce cascade amplitude by 30–60%. Under fragmented governance, G(t) arrives after the cascade has reached a stable new equilibrium.

Days to weeks for emergency declaration; weeks to months for fiscal/military intervention; months to years for structural restoration

Behavioral adaptation

Populations and operators change behavior during cascades — reducing demand, sharing resources, changing locations, improvising alternatives. CAISO demand response during heat events, post-hurricane generator networks, and informal water-sharing in flood-affected communities are documented examples. Modelled as a demand-compression term that reduces stress amplification when physical adaptation occurs.

Hours to days for demand response; days to weeks for informal network formation

Positive cascade (resilience propagation): Recovery investment and adaptation capacity cascade positively through the same dependency network that failure exploits. Restoration of the power grid enables water pumping restoration, which enables healthcare recovery, which enables labor force recovery, which enables economic activity recovery. Modelled as a positive analog of the failure propagation equation with a slower time constant — recovery is typically 3–10× slower than failure propagation in observed case studies.

Recovery compression note: The recovery compression mechanism captures the empirically observed pattern that each successive compound event within a short recovery window leaves the system structurally weaker. In the Mediterranean case sequence, each event since 2017 has reduced baseline recovery capacity by an estimated 8–14%, compounding to a ~40% reduction in effective baseline recovery by 2023.

Governance Quality Model — institutional competence as a first-class fragility variable

Overview

Governance behavior is modelled as an active adaptive system — not a passive background variable. Competent governance can halt cascades that physical factors alone would propagate. Incompetent or paralyzed governance can amplify cascades beyond what physical factors predict. The model distinguishes four governance states with distinct cascade implications.

Governance States

Proactive governance

Pre-positioned emergency capacity, cross-agency coordination protocols, pre-authorised emergency spending, mutual-aid compacts. Capable of activating within 12–48 hours of cascade initiation.

Cascade effect: Cascade amplitude reduced 35–60%. Recovery speed 2–3× faster. Insurance protection gap trigger threshold elevated (state backstop substitutes).

Japan (post-Fukushima resilience investment); Netherlands (Delta Programme); Singapore (whole-of-government infrastructure resilience)

Reactive governance

Standard emergency management with normal authorisation timelines. Activation lag 3–10 days. Capacity mobilised after cascade begins.

Cascade effect: Cascade amplitude reduced 15–30%. Recovery speed modestly improved. First 48–72 hours propagate without significant governance brake.

Most OECD national governments in non-pre-positioned mode; standard FEMA response protocol

Fragmented governance

Multi-jurisdictional coordination failures, political paralysis, underfunded emergency management, or institutional capacity degraded by prior fiscal stress. Activation lag 1–3 weeks.

Cascade effect: Minimal cascade braking. Governance may amplify cascade (misinformation, conflicting orders, resource hoarding). Financial cascade to fiscal stress more likely.

Texas 2021 (ERCOT isolation, deregulated grid, cross-agency coordination failure); Pakistan 2022 (limited fiscal capacity, slow federal-provincial coordination)

Collapsed governance

Institutional failure concurrent with physical cascade. Political violence, state insolvency, or critical staff unavailability.

Cascade effect: Cascade amplitude multiplied 1.5–2.5× relative to reactive baseline. Recovery timelines extend from months to years. Migration and conflict cascades activated.

Puerto Rico post-Maria (FEMA capacity exhaustion, pre-existing fiscal crisis); Haiti 2010 earthquake

v2 development: The current governance model uses discrete state parameterisation. A continuous governance capacity variable G ∈ [0, 1] with dynamic updating based on fiscal health, institutional capacity, and political legitimacy is in development for v2. This would allow simulation of governance degradation under prolonged cascade stress — where repeated compound events erode the institutional capacity needed to respond to the next event.

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