Compound Climate Hazards

Established A compound climate hazard is a combination of climate drivers or hazards whose joint arrival does the damage that neither would do alone. The research line that runs from the IPCC’s 2012 special report on extremes through Leonard and colleagues (2014) to the Zscheischler group’s 2018 agenda paper and 2020 typology sorts the combinations into four classes, and every case in this brief is one of them: preconditioned events, where one hazard prepares the ground for the next (rain on a fresh burn scar); multivariate events, where two drivers co-occur in one place (heat with drought); temporally compounding events, where hazards arrive faster than recovery (storm after storm on a weakened defence); and spatially compounding events, where correlated hazards strike distant places joined by one system (synchronised harvest failures, or one reinsurer’s book).

Established The reason the subject needs one analytical framework is arithmetic, not taxonomy. Two hazards that each carry a 1 per cent annual probability are, if independent, a 1-in-10,000-year coincidence; if they share a driver, the joint return period can shorten by orders of magnitude, and the observed correlations — hot summers are dry summers, storm surge arrives with rain, burned slopes meet the winter storms with their infiltration destroyed — are almost always in the dangerous direction. Design standards, flood maps and insurance rate filings nonetheless price hazards one at a time, not because anyone argued for independence but because each hazard has its own map, its own code committee and its own agency, and the correlation between them is nobody’s file.

Established Scope boundary. Infrastructure Resilience owns cascading failure inside engineered networks and the unmeasured restoration record; this brief supplies the correlated weather that loads those networks at several points at once. Coastal Defense Systems owns the barriers; Water Infrastructure Megaprojects owns supply; Climate Migration Planning owns moving people. What none of them owns, and this brief does, is the dependence layer: whether the correlations between climate hazards are measured, changing, modellable and priced — and what the honest answer costs when the record is shorter than the return periods at issue.

Established A sourcing note that governs every citation below. The research pass behind this brief ran with all external retrieval blocked: no journal server, agency site or news archive could be reached, including the commissioned seed article on compound hazards and infrastructure in npj Natural Hazards (2025, article s44304-025-00161-9), on which accordingly no claim here rests. The nine reading-list entries that carry URLs are bibliographic records verified in this site’s own corpus on 11 September 2026 and are reused strictly for the claims those records already carry; every other source is cited by name from the author’s own knowledge, which ends in January 2026, and the flags are set conservatively for that reason.

Established The vocabulary is young and the founding claim is quantitative. The IPCC’s SREX report gave compound events their first assessment-grade definition in 2012; Leonard and colleagues built the risk framework in 2014; and the 2018 Zscheischler paper in Nature Climate Change stated the field’s central charge: risk assessments that treat drivers and hazards separately can strongly underestimate the risk decision-makers actually face. Everything since has been an attempt to turn that charge into measured dependence, and the measurements now exist for the major pairs.

Established Heat and drought co-occur more often than they did, and the change is in the dependence, not only the margins. Mazdiyasni and AghaKouchak’s 2015 analysis of the United States found substantial increases in concurrent droughts and heatwaves between 1960–1980 and 1990–2010, largest for the most severe heatwaves — while meteorological drought frequency itself showed no comparable rise. The IPCC’s Sixth Assessment (2021) assessed with high confidence that concurrent heatwaves and droughts have become more frequent over the last century. The mechanism is not mysterious: once soil moisture is exhausted, incoming energy that would have evaporated water heats air instead, so the drought manufactures the heatwave that deepens the drought and cures the fuel that carries the fire.

Established Ignoring that dependence misprices the joint event severalfold. Zscheischler and Seneviratne showed in 2017 that the observed negative correlation between summer temperature and precipitation means the frequency of concurrent hot-dry summers is underestimated by a factor of two or more across large parts of the land surface when independence is assumed, and by much more where land-atmosphere coupling is strongest. Frontier Global mapping of co-occurring hazard pairs (Ridder and colleagues, 2020) extends the picture well beyond heat-drought, but the pairwise dependence estimates inherit every record-length problem section 4 describes.

Established Compound coastal flooding is measured, and the dependence has strengthened where it matters most. Wahl and colleagues showed in 2015 that storm surge and heavy rainfall are significantly dependent at the majority of major United States coastal cities, and that for several — New York prominent among them — the joint probability has risen over the past century, so the same defended height now faces a shorter joint return period than its design basis assumed. Frontier On the defence side, corpus-verified Dutch work finds that storm surge clusters and multi-peak storms degrade the performance of the Maeslant barrier relative to the single-storm design picture — the event the gate was certified against arrives, in practice, as several events in a row.

Established The fire-flood sequence is the cleanest preconditioned compound on record. The Thomas Fire ignited on 4 December 2017 and burned the slopes above Montecito, California; on 9 January 2018 a narrow storm cell dropped roughly 13 mm of rain in five minutes onto the fresh burn scar, and the resulting debris flows killed 23 people and damaged or destroyed more than 400 buildings, documented in detail by Kean and colleagues (2019). On unburned ground the same cell would have been an unremarkable winter storm: fire-altered, water-repellent soils and lost canopy drop the rainfall intensity needed to trigger debris flows to thresholds that common storms exceed, which is why the United States Geological Survey now issues emergency debris-flow assessments for burn scars as a standing product, with the elevated hazard persisting for roughly two to five wet seasons.

Established British Columbia ran the whole chain in five months of 2021. The late-June heat dome set Canada’s all-time temperature record at Lytton — 49.6 °C on 29 June — and the village was destroyed by fire the following day; the provincial coroner attributed 619 deaths to the heat; the fire season the heat and drought fed burned through the Interior; and in mid-November an atmospheric river severed every major highway linking Vancouver to the rest of Canada, with debris flows on summer burn scars among the failure mechanisms, flooded the Sumas Prairie, and forced the evacuation of Merritt. Established The World Weather Attribution rapid analysis judged the heat dome at least 150 times more likely with human-caused warming and still roughly a once-in-a-millennium event in the current climate — a sentence whose two halves together define the compound problem: the driver is attributably shifted, and the tail is still unsampled.

Frontier Hydroclimate whiplash compresses the sequence into one place’s few years. Los Angeles entered January 2025 with two wet winters’ grass growth cured by roughly eight rain-free months and driven by an extreme wind event; the Palisades and Eaton fires killed about thirty people and destroyed on the order of sixteen thousand structures, and the burn scars then faced ordinary winter storms as debris-flow sources. Swain and colleagues’ 2025 review names the wet-dry oscillation as a distinct and already-increasing compound driver: warming steepens both extremes of the same water year, and the whiplash itself — fuel growth, then curing, then wind — is what loaded the January fires. Frontier Published insured-loss estimates for the two fires spanned roughly 20 to 45 billion dollars across catastrophe-modelling houses while claims were still arriving — a divergence section 14 returns to.

Established Winter Storm Uri is the reference case for correlated infrastructure failure under a single meteorological driver. Over 14–17 February 2021, with ambient temperatures of 0 to −19 °C across Texas, the corpus-verified event study records 322 boil-water notices issued as power failures propagated into water treatment — the interdependency measured, not hypothesised. About 4.5 million customers lost power; the state’s official count reached 246 deaths, with excess-mortality estimates running two to three times higher, a disagreement this brief reports rather than resolves. The joint FERC-NERC inquiry counted 1,045 generating units failing 4,124 times, freezing and fuel-supply problems dominant among the causes, with gas production falling as electricity cuts shut the compressors that fed the generators that made the electricity — a circular dependency with no single-hazard name. Established The grid operator’s much-quoted margin — four minutes and thirty-seven seconds from an uncontrolled cascade — is the operator’s own figure, and the same inquiry noted that winterisation had been recommended after the freezes of 1989 and 2011 and largely not performed.

Frontier The long-record context makes the short-record problem worse, not better. Tree-ring reconstruction places 2000–2021 in southwestern North America as the driest 22-year span in at least 1,200 years, with roughly two-fifths of its severity attributed to anthropogenic forcing (Williams and colleagues) — a megadrought that is itself the precondition under the region’s fire and water-supply compounds. Frontier And the corpus-verified Russian permafrost record makes a point that generalises: bearing-capacity losses in 22 of 27 monitored settlements arrived in discrete extreme years rather than as a smooth trend. Infrastructure damage is delivered by compounding extremes on a moving baseline, which is precisely the statistic that single-hazard trend analysis is worst at.

Frontier Is the dependence itself changing, or only the marginals? A world where heatwaves worsen but their coupling to drought is fixed calls for different engineering than one where the coupling strengthens. Separating the two requires estimating a correlation trend inside an already-short record, and the honest answer for most hazard pairs is that the detection has not been made; the United States heat-drought result and the coastal surge-rain result are the exceptions, not the rule.

Frontier Do climate models get the dependence right? Model evaluation has historically scored means and marginal extremes; inter-variable and inter-site dependence is evaluated far less, and standard bias correction is univariate — it adjusts each variable’s distribution separately and can silently distort the very correlations that compound-risk projections depend on. Whether CMIP-class models reproduce observed hazard-pair dependence well enough to project its change is an active and unsettled literature.

Speculative Spatially compounding extremes through circulation patterns. The proposition that amplified planetary waves synchronise heat and drought across northern-hemisphere breadbaskets — making simultaneous harvest failure likelier than portfolio arithmetic suggests — is coherent, has published supporting analyses, and remains contested at the level of both mechanism and trend. It is the compound claim with the largest stakes and the weakest measurement.

Frontier Attribution of sequences has no agreed method. Event attribution can now state how warming shifted the odds of one heatwave or one storm; there is no settled protocol for attributing a chain — fire, then rain, then debris flow — where the second hazard’s impact is conditional on the first’s footprint. The British Columbia sequence has an attribution number for its first link only.

Frontier Does the typology predict anything? The four-class scheme organises cases. Whether it identifies systems whose risk is underpriced before the loss, rather than classifying disasters afterwards, is the fair test of the research programme, and it has not been run.

Established The binding constraint is record length against joint tails, and it is arithmetic, not funding. Estimating a univariate 100-year event from a 75-year record is already an extrapolation; estimating a joint 100-year event additionally requires the dependence between the variables at levels neither has visited often, and the effective sample for that tail dependence is a handful of points. Instrumental records run 50 to 150 years; the design and pricing questions sit at joint return periods of 100 to 10,000 years. No statistical technique manufactures the missing information: every published method buys sample size with an assumption — stationarity, spatial exchangeability, model fidelity — that the application then quietly depends on.

Established Nonstationarity forecloses the cheap fix. Pooling a century of data assumes the climate that generated 1930 still operates. Milly and colleagues’ declaration that stationarity is dead was aimed at water management in 2008, and it applies with more force to dependence parameters, which respond to warming through mechanisms — land-atmosphere coupling, sea-level rise under surge, snow-to-rain transitions — that are themselves trending.

Established Copula families agree where the data are and diverge where the decision is. The standard dependence-modelling toolkit fits parametric copulas to observed pairs; families that fit the bulk of a 60-year record near-identically can differ by large factors in the far joint tail, because tail dependence is a property the record barely samples. Finance ran this experiment at scale: the Gaussian copula’s tail independence, embedded in correlated credit pricing after Li’s 2000 formula, failed exactly in the joint tail in 2008. Frontier Hydrology’s own methodologists have said as much of environmental return periods: the multivariate ones especially are as much construction as measurement, definition-dependent — the AND, OR and survival return periods differ for the same data — and carry uncertainty bands that practice routinely drops.

Established The infrastructure side lacks its inventory. Which substations feed which water pumps, which fibre shares which duct: Infrastructure Resilience records that no audited cross-sector dependency inventory exists for any region, and without one a compound-hazard footprint cannot be converted into a predicted failure set. Established The corpus-verified grid analysis adds a caution: topological network measures correlate only mildly with physically modelled vulnerability, so the cheap abstraction does not substitute for the missing engineering data.

Established The pricing models are proprietary. Catastrophe models embed dependence assumptions — between perils, between sites, between hazard and vulnerability — that are not publicly stated and cannot be externally tested, which is why their divergence becomes observable only when a loss arrives (section 14).

Established Reanalysis is the field’s shared instrument. Globally complete, physically consistent reconstructions — ERA5 now reaching back to 1940 — are what make joint statistics computable at all outside dense gauge networks, and every dependence estimate inherits their biases, which are largest exactly for extremes.

Established Large ensembles are the only legitimate sample multiplier. The UNSEEN approach — using hundreds of model realisations of the current climate to sample events the observations have not yet produced, demonstrated for United Kingdom rainfall by Thompson and colleagues (2017) — adds tail sample without assuming stationarity, at the price of assuming the model’s dependence structure is right, which is the very thing under test.

Frontier Paleoclimate proxies extend single variables, rarely pairs. Tree rings deliver a millennium of soil moisture; joint proxy records calibrated well enough to constrain hazard-pair dependence barely exist, and this is a producible scientific result nobody currently owns.

Established The interdependency vocabulary exists and the inventories do not. Rinaldi, Peerenboom and Kelly’s 2001 taxonomy — the founding paper whose terms the infrastructure-dependence field still uses — supplies the categories; the audited regional inventories that would let a mapped hazard footprint become a predicted failure set remain unbuilt, as Infrastructure Resilience details. Established Satellite night-lights outage observation, which that brief records as the first operator-independent measure of failure extent, is equally the observable a compound-event impact record needs.

Established The decisive test needs no new instrument, and nobody has scheduled it. Fit the field’s dependence models — the copula families, the conditional models, the model-ensemble dependence structures — to the instrumental record up to a cutoff, freeze them, and score their predicted joint exceedances against the decades already observed since, region by region and hazard pair by hazard pair, with independence as the null model. The data exist; the exercise is a coordinated verification study, not a field campaign. It is decisive in both directions: if fitted dependence adds no out-of-sample skill over independence, the compound-event programme loses its central quantitative claim; if it adds large skill, then every design standard and rate filing that assumes independence is measurably wrong, with the size of the error attached.

Frontier The model-fidelity benchmark is the projection side of the same test. A standing evaluation of whether CMIP-class models reproduce observed hazard-pair dependence — not means, the dependence — would decide how much weight compound-risk projections can bear, and would discipline the univariate bias-correction practices that currently distort correlations silently.

Established One natural experiment is already running and instrumented. Every major burn scar in the American West now receives a Geological Survey debris-flow hazard assessment with explicit rainfall-intensity thresholds, and the following winters test those thresholds against observed flows — a rolling forecast-verification loop, and the best-scored compound prediction in existence. Frontier Its published skill statistics remain thin relative to the number of forecasts issued; assembling them into a public verification record is cheap and undone.

Frontier A compound load case through a standards process would be the institutional experiment. One national structural or flood standard adopting an explicit concurrent-hazard load case — burn-scar hydrology in post-fire flood mapping, joint surge-rain statistics in coastal drainage design — would generate the cost and litigation record that decides whether compound-aware design is administrable, which no amount of statistics settles.

Speculative The experiment nobody can run is the one that would settle the tail directly: observing enough joint extremes to estimate 1-in-1,000-year dependence empirically. Under stationarity that takes millennia of record; under a moving climate it is not even defined. Everything in this subject is a substitute for that impossibility and should be read as one.

Established Compound-aware engineering means designing for sequences and concurrences, and the barrier literature shows what that looks like. The corpus-verified Dutch analyses treat a storm surge barrier’s season, not its design storm: surge clusters and multi-peak storms load the machine repeatedly; a dedicated recurrence analysis exists for how often the Maeslant barrier closes and how that frequency changes; and closing more often is not free, because closure itself alters the estuary — saltwater intrusion and stratification — so rising closure frequency becomes an operating constraint independent of the structure’s condition. Protection against one hazard manufacturing a second stressor is the general pattern, not a Dutch curiosity.

Frontier The wildland-urban interface shows the single-hazard exposure basis failing at the physics level. The corpus-verified modelling of interface fire exposure to a cross-laminated-timber building found convective heating dominating over radiative at the monitored locations — a direct challenge to the radiant-heat basis on which current interface assessment rests, before any compounding with wind or drought is even considered.

Established Uri’s engineering lesson is that fuel, generation and demand form one weather-exposed system. Winterising generators while the gas gathering system freezes moves the failure rather than the load; the gas-electric loop fails as a unit and has to be hardened as one, and the same logic couples water treatment to grid islanding — the 322 boil-water notices were a water-sector consequence of an electricity-sector design basis.

Established Restoration is a shared resource that spatially compounding events exhaust. Mutual aid — line crews, pumps and generators moving toward the disaster — assumes the next region over is undamaged; a correlated multi-region event breaks the assumption that restoration capacity scales with damage. Frontier No published standard sizes restoration resources against correlated demand, a corollary of the unpublished restoration-time record Infrastructure Resilience documents.

Established This brief is the correlation layer under a cluster of siblings. Infrastructure Resilience takes the network as given and asks how it fails and recovers; this brief supplies the loading statistics. Coastal Defense Systems builds against the surge whose pairing with rainfall is measured here; Water Infrastructure Megaprojects makes and moves the water whose absence is one arm of the heat-drought-fire triangle; Arctic Engineering carries the extreme-year damage pattern this brief cites as the general signature of compounding on a trend.

Established The people side runs through Climate Migration Planning — insurance withdrawal from compound-exposed regions is already a quiet relocation instrument, unplanned and unadmitted — and the tail beyond system failure belongs to Civilization Resilience Planning. Frontier Climate Engineering is adjacent in a stranger way: an intervention that shifted the joint distribution of hazards deliberately would need exactly the dependence science this brief finds unfinished, both to promise benefit and to answer for harm.

Established No institution owns the correlation. Flood maps are drawn by flood agencies, fire codes by fire authorities, wind loads by structural committees; the United States federal flood map is a single-driver product whose 1-per-cent-annual-chance line does not see the burn scar upstream. The modelling nonprofit First Street’s national reassessment counted roughly 14.6 million properties at substantial flood risk against roughly 8.7 million designated by the official maps (modeller’s own figures). Structural standards encode joint-occurrence judgments for traditional load pairs, but no provision in mainstream structural or floodplain standards couples climate hazards sequentially — nothing prices last summer’s fire into this winter’s flood.

Established Insurance regulation has begun to move, under duress. California’s rate regulation long required catastrophe loads to be justified by a twenty-year historical average — a backward-looking rule that a trending, compounding hazard defeats by construction — and only in late 2024 did the state permit forward-looking wildfire catastrophe models in ratemaking, in exchange for coverage commitments in distressed areas. The National Flood Insurance Program’s Risk Rating 2.0, rolled out 2021–2022, replaced zone-based pricing with per-property, multi-driver modelling — the first large public pricing system to abandon the single-map abstraction. Frontier Whether either reform prices dependence, as opposed to modernising marginals, is not publicly checkable, because the models are proprietary.

Frontier The insurer-of-last-resort books are where mispriced correlation accumulates. California’s FAIR Plan carried roughly 458 billion dollars of exposure by September 2024, about triple its 2020 level (the plan’s own figures), and levied a 1-billion-dollar assessment on member insurers after the January 2025 Los Angeles fires; Canada’s insurers recorded their costliest catastrophe year in 2024 at roughly 8.5 billion Canadian dollars across four summer events (industry association figures). Established A residual market that grows as private insurers withdraw is the institutional signature of a tail someone believes is underpriced; which party is wrong is exactly the unmeasured quantity.

Established Compound events do not land evenly, and for once the inequity is measured. The corpus-verified satellite analysis of the Texas blackout found minority census block groups 1.5 to 3 times more likely to lose power — during an event whose deaths came disproportionately from hypothermia in unheated homes. Restoration priority, backup power and the ability to leave are all income-graded, so the compound tail is regressive twice: in exposure and in recovery.

Frontier Suppressed price signals are a distributional choice disguised as consumer protection. Holding insurance prices below modelled risk keeps compound-exposed housing affordable while transferring the tail to residual pools and, after the loss, to assessed policyholders and public budgets; letting prices move prices some households out of their homes. Neither option is neutral, and the choice is being made annually, mostly implicitly, in rate filings.

Established The retreat question inherits the measurement problem. Moving people off a floodplain because of a modelled joint tail asks them to bear a certain cost against an uncertain number; Climate Migration Planning documents how thin the instruments for doing that fairly are. Speculative A dependence-aware disclosure regime — telling a buyer that the burn scar upstream changes their flood odds — is draftable and nowhere drafted.

Established Correlation is the mechanism by which climate risk stops being local. Uncorrelated disasters are insurable and absorbable: the damaged region draws on the undamaged whole. Every class of compounding shortens that draw — temporal compounding exhausts local recovery, spatial compounding damages the helpers — and insured natural-catastrophe losses exceeded 100 billion United States dollars in every year from 2021 through 2024 on the reinsurance industry’s own series, with the compound-prone so-called secondary perils supplying a growing majority.

Speculative The synchronised-breadbasket scenario is the civilizational version of the claim. If circulation regimes correlate harvest failures across continents, the global food system’s buffer arithmetic — stocks, trade, substitution — rests on an independence assumption at planetary scale. The mechanism is contested and the historical sample is tiny; the stake, not the evidence, is why it appears here.

Frontier Insurance withdrawal is becoming de facto adaptation policy. Where the correlated tail cannot be priced politically, capital withdraws, asset values reprice, and settlement patterns eventually follow — an adaptation programme run by accident, with no planning instrument attached, fiscally backstopped by governments that have not booked the contingent liability. Handwave The step from there to orderly outcomes is the part nobody has shown: the claim that markets will relocate exposure smoothly works, at present, entirely by assertion.

These horizons track when dependence between climate hazards becomes a measured, verified and administered quantity rather than an assumption’s absence.

• 10 yr: Frontier The out-of-sample verification of fitted dependence models is run and published for the major hazard pairs; post-fire debris-flow forecasting acquires a public skill record; at least one national flood-mapping programme conditions on burn scars and joint surge-rain statistics. Realistic because none of it needs new hardware.
• 25 yr: Speculative Concurrent-hazard load cases appear in mainstream structural and coastal standards with litigated cost records behind them; catastrophe-model dependence assumptions become disclosable to regulators the way insurers’ capital models already are; the instrumental record’s usable length for dependence-trend detection roughly doubles simply by accumulating.
• 50 yr: Speculative Multi-century joint proxy records and mature large-ensemble archives constrain hazard-pair tails to within factors engineering can carry, and whether the twentieth century’s independence assumption caused a measurable excess of correlated failures becomes answerable from the accumulated event record.
• 100 / 250+ yr: Handwave A civilisation that plans against joint distributions as routinely as it now plans against margins. Nothing on today’s map either delivers or forbids this; the claim that it will happen because it must is an assertion about institutions, not about statistics.

• Depends on Three results on this map. From Infrastructure Resilience: the audited cross-sector dependency inventory and the published restoration-time distribution, without which a compound hazard footprint cannot be converted into predicted failures or priced recovery. From Coastal Defense Systems: the closure-frequency and multi-peak-storm operating record of the barrier fleet, the one engineered system already logging sequence effects. From Water Infrastructure Megaprojects: the storage and conveyance margins that decide whether a heat-drought compound is an inconvenience or a supply failure.
• Requires (not on this map) Five things nobody on this map produces. An out-of-sample skill record for fitted joint-tail models, because a dependence model with unverified skill is an opinion with parameters. Multi-century joint proxy records for hazard pairs, because instrumental records cannot constrain the tails design needs. Concurrent-hazard load cases in national design standards, because until a code committee owns the correlation no engineer is paid to design against it. Regulator-disclosable catastrophe-model dependence assumptions, because divergent proprietary tails cannot be audited into convergence. And risk-reflective insurance pricing that survives rate politics, because a suppressed price deletes the one signal that would otherwise carry the correlation to buyers.
• Enables Loading statistics for every resilience claim downstream: the corridor cases in Energy Corridors, the graceful-degradation premise of Infrastructure Resilience, and the retreat triggers of Climate Migration Planning all assume somebody knows how often the hazards arrive together. This brief is where that number would have to come from.
• Adjacent Civilization Resilience Planning owns the far tail; Arctic Engineering owns the thaw-driven variant; Climate Engineering would, if ever exercised, be the first deliberate intervention in the joint distribution this brief describes.

Handwave “Assuming independence is conservative.” The most consequential error in the subject, and it is backwards for climate hazards: the measured correlations — hot with dry, surge with rain, fire with the following flood — run in the direction that makes joint events more common than independence predicts, so single-hazard standards are systematically unconservative precisely where losses concentrate. Established The 2017 dependence analysis quantified the understatement for hot-dry summers at a factor of two or more over much of the land surface.

Established “The 2022 French nuclear shortfall shows heat-drought compounds crippling a grid.” Mostly false as told. The bulk of that year’s capacity loss came from stress-corrosion inspections across the reactor fleet; river-temperature discharge derates were real but have historically cost on the order of a fraction of a per cent of annual output, and 2022’s thermal derates were a small share of that year’s shortfall. The episode belongs here as a warning about attribution hygiene: a compound-shaped story attached to a mostly unrelated industrial failure. Frontier The genuinely compound part of Europe’s 2022 summer — low Rhine barge drafts, low Norwegian reservoirs and heat-driven demand coinciding — is documented but is rarely the version quoted.

Frontier “Every disaster sequence is a compound event.” Sequences also happen by chance, and a field that names every coincidence after itself will discredit its real results. Whether a given pairing reflects dependence is a statistical question requiring base rates, and for most publicised sequences the test is never run; the load-bearing cases in this brief — heat-drought, surge-rain, fire-flood — are the pairs where it has been.

Frontier “Catastrophe models already handle correlation.” They contain correlation structures; whether the structures are right is untestable from outside, and vendor estimates for the same event diverge widely while claims are still arriving — the January 2025 Los Angeles fires drew published insured-loss estimates spanning roughly 20 to 45 billion dollars across modelling houses. Divergence that wide, about a loss in progress, is not what a solved correlation problem looks like.

Established “A 100-year flood is safe to build behind for a century.” A 1-per-cent annual hazard has about a 26 per cent chance of arriving within any 30-year mortgage before any compounding and before any trend; adding a dependent second hazard shortens the joint return period further. The framing error is old, univariate and well documented; compounding makes it worse, not different.

Speculative “The record droughts and fires prove dependence is strengthening everywhere.” The paleorecord cuts both ways: the southwestern megadrought is unprecedented in 1,200 years, but pre-industrial centuries also contain compound extremes the instrumental era never sampled, so a naive reading of recent records against a 75-year baseline can overstate the change as easily as understate it. The trend-in-dependence question is open for most hazard pairs, and this brief flags it as open rather than resolving it by assertion.