# CE Physical Hazard Cascade Model — Methodology # Model ID: ce-physical-cascade # Version: 3.7.0 # Last updated: 2026-05-17 # Type: climate # Geography: Global with regional cascade pathway differentiation (Mediterranean, South Asia, Sub-Saharan Africa, Western US, Southeast Asia, Caribbean) # Horizon: 2025–2060 ## Summary 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. ## Methodology Detail 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) ## 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 ## Limitations - 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 ## Terminology Note - '52 Gt total abatement required' (KPI): net reduction from 57 GtCO2e/yr baseline to 5 GtCO2e/yr net-zero residual. - 'G_2050 = 47 Gt annual gap': annual policy-to-NZ gap at 2050, because under current policy the trajectory reaches only ~52 GtCO2e/yr by 2050 (not the 57 Gt baseline). G_t = CURRENT_POLICY[t] - NET_ZERO_PATH[t]; at t=2050: 52 - 5 = 47 Gt. ## Core Equations G_t = E_t_policy - E_t_NZ (annual abatement gap) T_t_s = sum(A_i_t_s for i in 1..N) * (1 - delta) (tech coverage; delta=0.15) B_t_s = max(G_t - T_t_s, 0) (breakthrough gap) tau = min{t | sum(E_y_policy, y=2025..t) >= C} (budget exhaustion year) G_t_j = w_j * G_t (sector decomposition) ## De-duplication Discount delta=0.15 is a central estimate for cross-sector emission overlap. Primary overlap sources: (i) green H2 and SAF both reduce transport fossil demand (~2-3%); (ii) BECCS and enhanced weathering both draw on land-based biological carbon sinks (~3-4%); (iii) ocean iron fertilisation and enhanced weathering compete for ocean sink capacity (~2%); (iv) green steel and recycling address overlapping industrial-process emissions (~2-3%). Estimated total overlap range: 13-18%; 15% used as central estimate. Sensitivity: ±5pp change in delta shifts B_2050_base by approximately ±2 Gt. ## Data Sources - UNEP Emissions Gap Report 2024 (baseline 57 GtCO2e/yr) - IPCC AR6 WG3 SPM Table 3.2 (net-zero C1 pathway) - IPCC AR6 WG1 Table SPM.2 (carbon budgets; original 2020 reference: 400 Gt for 1.5C at 67%; adjusted to ~250 Gt from 2025 by deducting ~150 Gt emitted 2020-2024; AR6-adjusted illustrative budget, uncertainty ±50 Gt. Independent check: GCB 2024 (ESSD 2025) gives ~235 Gt from Jan 2025 at 50% probability — consistent within uncertainty bounds given different probability threshold.) - IPCC AR6 WG3 Chapter 6 (sector abatement proportions) - IEA Net Zero by 2050 NZE 2023 (mature technology ceilings) - CE Emerging Technology Library v3.1.0 (12 technology abatement ranges; public provenance table at /models/ce-solution-scale — sources, TRL, EROI, counterfactuals, overlap deps, feasibility ceilings per technology) Machine-readable constants: /models/ce-solution-scale/assumptions.json ## Uncertainty Quantification Scenario probabilities: P(optimistic)=0.25, P(base)=0.50, P(pessimistic)=0.25. Expected value: E[B_2050] = 0.25*B_opt + 0.50*B_base + 0.25*B_pes. Monte Carlo CI: delta~N(0.15,0.03), per-tech abatement perturbation drawn from a 3-factor co-variance model. Factors: global transition momentum (bGlobal=0.35*sigma), electricity/grid sector (bElec=0.30*sigma), CDR governance (bCDR=0.35*sigma). Variance-preserving: idiosyncratic sigma = sigma*sqrt(1-bG^2-bE^2-bC^2). Implied cross-tech correlations: rho(elec pairs)~0.21, rho(CDR pairs)~0.25. Positive co-variance widens CI vs independent draws (correct direction: shared policy/finance shocks cause portfolio-level fat tails). sigma_i=0.30 for fusion/DAC/ocean_iron; 0.15 for other 9 techs. N=600. Output: 80% CI on breakthrough gap (P10/P90). ## Deployment Constraints (v2.2.0+) Interactive sliders model four institutional deployment barriers: 1. Permitting/build delay (0-10 yr): shifts each tech trajectory right in time. 2. Grid interconnection queue (0/3/6 yr): extra delay for grid-dependent techs. 3. Political continuity risk: post-reversal-year values switch to pessimistic scenario. 4. Cost-of-capital stress (+100/200/400 bps): global finance multiplier 0.95/0.88/0.78. ## Transition Economics (v2.2.0+) Marginal Abatement Cost (MAC) ranges per technology at 2040+ deployment scale. Sources: IEA WEO 2024, IRENA 2023, IEA GHR 2023, IEA DAC 2022, IPCC AR6 WG3. NPV calculated at SCC=$190/tCO2 (US EPA 2023). Discount rates: 2%, 5%, 10%. All NPV estimates positive across full range of mainstream discount rates. ## Workforce Impact (v2.4.0+) Per-technology direct employment estimates at CE base-scenario 2050 deployment scale. Sources: IRENA WESO 2024; IEA WEO 2024; ILO WESO 2022; IEA DAC 2022; IPCC AR6 WG3 Ch.17. Peak deploy jobs (M): construction/manufacturing surge 2025-2040 (temporary). Ops/mfg 2050 (M/yr): permanent direct ops, maintenance, and ongoing manufacturing. Direct displaced (M): job losses in directly substituted incumbent sectors only. Portfolio net: ~+12M direct ops jobs; separate fossil at-risk: ~10M (coal ~7M + oil/gas ~3M). Economy-wide net (before supply-chain multipliers 1.5-3x): ~+9 to +12M by 2050. All estimates carry +/-40-60% uncertainty at global scale. ## Infrastructure Sequencing (v2.5.0+) 9 foundational infrastructure investments mapped to must-start and must-complete years for 2050 critical path. Urgency tiers: Critical (must start <=2026), Soon (2026-2028), Planned (2028+). Critical: permitting reform, grid transmission expansion, MRV standards (CDR), nuclear regulatory pathway. Soon: critical minerals supply chain, sustainable biomass supply, CO2 transport & storage network, green H2 hubs. Planned: ocean governance framework (London Protocol+). Sources: IEA NZE 2023; IPCC AR6 WG3 Ch.6; BloombergNEF ETI 2024; IRENA 2024. ## State Capacity Index (v2.5.0+) Per-country implementation readiness for top 20 emitters (~77% of global GHG emissions). WGI Government Effectiveness percentile rank (World Bank 2022/2023). Tier 1 (>=75): USA, Germany, Japan, UK, France, Canada, Australia, S. Korea -- ~25% of emissions. Tier 2 (40-74): China, India, Indonesia + 7 others -- ~45% of emissions. Tier 3 (<40): Russia, Iran -- ~7% of emissions. Source: World Bank WGI 2022; IEA 2023; Global Carbon Budget 2024. ## Model Assumptions Registry (v2.6.0+) All structural constants with tested range and B_2050 sensitivity documented in-page. Key sensitivities: baseline +-2 Gt -> +-2 Gt; delta +-5pp -> +-2 Gt; sigma(high) +-0.10 -> +-2 Gt P90. Full table at /models/ce-solution-scale (Model Assumptions Registry section). ## Geographic Resource & State Capacity Cross-Link (v2.6.0+) 10 technologies mapped to critical resource geographies and State Capacity tier. Key findings: DRC cobalt (BEV batteries) is Tier 3 equivalent -- governance deficit flagged. Perovskite solar: ~85% manufacturing in China (Tier 2) -- supply-chain concentration risk. Ocean iron fertilisation: multi-jurisdictional governance (London Protocol) -- T3/N/A tier. BECCS/SAF bio-feedstock: Brazil and Indonesia Tier 2 -- deforestation governance risk. ## Policy Effectiveness Validation Backtest (v2.6.0+) 7 major climate policies benchmarked against 2020-2025 observed delivery: - Paris NDCs aggregate: ~50% delivery (15% vs 30% below BAU) -- consistent with CE near-flat baseline. - EU Green Deal: ~78% delivery -- CE Tier 1 capacity assumption validated. - US IRA: ~68% delivery -- consistent with CE optimistic scenario demand-side pull. - China Dual Carbon: <50% delivery -- consistent with CE near-flat China baseline. - IEA NZE solar target: ~67% delivery but pace accelerating -- supports CE optimistic perovskite ramp. - Global EV targets: ~30% delivery -- CE BEV base scenario consistent with observed trajectory. - EU ETS carbon price: >100% (exceeded target price) -- validates CE NPV framework direction. ## Sensitivity Tornado Chart (v2.7.0+) 6-parameter B_2050 impact ranking (Chart.js horizontal floating bars). Technology opt-pes spread: +-8.5 Gt (dominant, 4x all others combined). Baseline emissions +-2 Gt -> +-2 Gt; De-dup delta +-5pp -> +-2 Gt. Scenario probs P(opt) +-0.10 -> +-1.5 Gt; MC co-variance rho 0->0.4 -> +1.5 Gt CI widening. Net-zero residual +-1 Gt -> +-1 Gt. ## EROI-Adjusted Abatement (v2.7.0+) Grid carbon intensity penalty for energy-intensive removal technologies. DAC (2000 kWh/tCO2): current grid (0.42 kgCO2/kWh) reduces 1.8 Gt gross to 0.36 Gt net (-80%). DAC at 2035 grid (0.15): net 1.53 Gt (-15%); at 2050 clean grid (0.02): net 1.73 Gt (-4%). BECCS (~200 kWh/tCO2): current grid -8%; 2050 grid 0%. Enhanced Weathering ~140 kWh: current -6%. Key finding: DAC only viable at scale on near-zero-carbon grid (post-2035 deployment preferred). ## Investment Gap Panel (v2.7.0+) Current 2024 vs required 2035 capital deployment by technology ($B/yr). Portfolio current: ~$470B/yr; required 2035: ~$1.3-2.0T/yr; whole-portfolio gap: ~3-4x. Largest relative gaps: Enhanced Weathering 200-400x; Ocean Iron 40-100x; Perovskite 16-30x. Sources: IEA WEI 2024; BloombergNEF 2024; IRENA 2023; IEA GHR 2023; IEA DAC 2022. ## Carbon Budget Delay Cost (v2.7.0+) Cumulative GtCO2 consumed by 5yr or 10yr deployment slip per technology. Formula: 5yr cost = (b[4]+b[5]-b[0])*2.5*(1-delta); sorted descending by 5yr cost. Highest delay cost: Perovskite 24.4 Gt (5yr); BEV 18.9 Gt; BECCS 17.9 Gt; Green H2 17.0 Gt. ## Technology Cliff Dates (v2.7.0+) Latest year to make binding go/no-go deployment commitment per technology. At cliff now (2026): Green H2 (electrolyzer orders), High-Albedo (building codes), Recycling (EPR regs). 1yr window (2027): Perovskite, DAC, BECCS, Enhanced Weathering, SAF, Green Steel. 2yr window (2028): Nuclear Fusion (SPARC ignition -> FOAK decision). Committed: BEV. Governance-gated: Ocean Iron (London Protocol amendment first). ## IPCC Scenario Band Mapping (v2.7.0+) CE portfolio scenarios mapped to IPCC AR6 WG3 C1-C7 pathway categories. CE Optimistic: ~9.6 Gt residual -> C2 (1.5C limited overshoot) -- with mature tech could reach C1. CE Base: ~25.2 Gt residual -> C4 (below 2C ~66%). CE Pessimistic: ~38.5 Gt residual -> C5 (below 2.5C). Current policy (no emerging tech): 57 Gt -> C7 (above 3C median). Sources: IPCC AR6 WG3 Table SPM.1 (2022) for C-category thresholds. ## Scientific Precision Corrections (v3.0.0+) CCS injection ceiling: previously stated as '8-10 Gt/yr geological storage capacity (IPCC)'. Corrected: IPCC AR6 WG3 C1 scenario range is 4-15 Gt/yr for CO2 injection rates; CE uses 8-10 Gt/yr as mid-range. Physical geological storage volume (hundreds of Gt) is NOT the binding constraint -- injection rate infrastructure is. Committed emissions: primary citation added -- Tong et al. 2019 (Nature 572, 373-377): 658 GtCO2 from 2018 operating fossil-fuel infrastructure (operating assets only, excl. planned/permitted pipeline). CE 680 Gt figure adds ~22 Gt additional 2018-2025 committed build; consistent with Tong upper bound. BECCS biomass: 3.5-5.5 EJ/yr is a conservative no-regrets floor (zero food/land conflict scenarios). Full IPCC AR6 WG3 Ch.7 sustainable bioenergy range: 50-250 EJ/yr (wide, heavily sustainability-constrained). CE does not use the upper end; 3.5-5.5 EJ/yr represents lowest-controversy deployment ceiling only. Carbon budget: AR6 WG1 Table SPM.2 400 Gt (67% probability, 2020 reference) cross-checked against GCB 2024 (ESSD 2025) ~235 Gt from Jan 2025 at 50% probability. CE 250 Gt figure is consistent within stated uncertainty bounds given the different probability threshold (67% vs 50%). ## Assumptions API (v3.0.0+) All 10 structural constants with source lineage, uncertainty ranges, and scope notes available at: GET /models/ce-solution-scale/assumptions.json Returns: model_id, version, generated date, epistemic_status, comparable_to / not_comparable_to lists, assumptions array (constant, value, unit, source, scope, uncertainty, last_reviewed per entry), scenario_probabilities, and reproducibility links. Machine-readable; CORS open (*); suitable for programmatic audit by institutional users. ## Platform Positioning (v3.0.0+) CE is a TRANSPARENT TRANSITION DIAGNOSTIC platform, not a predictive IAM. Methodology class: bottom-up gap accounting -- same as UNEP Emissions Gap Report and IEA NZE scenario accounting. CE does NOT produce: equilibrium temperature projections, macro-economic forecasts, probabilistic damage estimates. CE DOES produce: technology portfolio coverage quantification, committed-emissions accounting, breakthrough gap sizing, deployment-ceiling analysis, and cross-sector de-duplication. Appropriate use: institutional transition planning, policy gap analysis, technology prioritisation, portfolio stress-testing, and complementary analysis alongside NGFS scenarios. Not appropriate as a standalone substitute for: NGFS scenario sets, IPCC AR6 physical science, probabilistic IAM runs (DICE, PAGE, MESSAGE-GLOBIOM, REMIND), or national GHG inventories. Structural accounting / gap model. Not a probabilistic forecast. Outputs are scenarios conditioned on IPCC pathway assumptions. Comparable to IEA NZE scenario accounting and UNEP Emissions Gap Report methodology, not to predictive IAMs (DICE, PAGE, FUND, MESSAGE). Computation is client-side JavaScript; fully reproducible from cited sources.