> For the complete documentation index, see [llms.txt](https://docs.therisk.global/organization/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.therisk.global/organization/model/coupled-risk.md). # Coupled risk Coupled risk: the six nexus sectors, the thirty directed relations between them, and the teaching cascade that shows how a shock in one sector is amplified through the others. **Where this fits:** all six sectors · Labs and Foundry (observation and modelling) · GCRI (evidence and methods) · Planning and readiness preparation · model page. **In brief.** The left hexagon of the model places six sectors on one figure: water, energy, infrastructure, food, health and biodiversity. Every sector depends on every other through a named mechanism, such as irrigation, hospital power or watershed regulation, and each mechanism has a strength between 0 and 1. A context, such as an urban flood, selects the sectors in play. A simple cascade then shows how the first hit spreads through the relations between them, and how much the coupling enlarges it. All strengths are **teaching values for a typical city-region, not measurements for any place**. The figure teaches what a study has to observe and model together; it does not estimate the risk of a real place. ## The six sectors | Sector | Code | What it carries in the nexus | Page | | -------------- | ---- | ----------------------------------------------------------------------------------------------- | --------------------------------------------------------------- | | Water | W | Supply, sanitation, irrigation, cooling, hydropower and the flows ecosystems need | [Water](/organization/model/sectors/water.md) | | Energy | E | Power and fuel for pumping, treatment, cold chains, hospitals, transport and telecoms | [Energy](/organization/model/sectors/energy.md) | | Infrastructure | I | The built networks (pipes, dams, grids, roads, ports and defences) that carry the other sectors | [Infrastructure](/organization/model/sectors/infrastructure.md) | | Food | F | Production, storage and distribution, and the nutrition that health depends on | [Food](/organization/model/sectors/food.md) | | Health | H | Care, public health and the workforce every other sector runs on | [Health](/organization/model/sectors/health.md) | | Biodiversity | B | Watersheds, soils, pollination, coastal buffers and the ecosystems behind them | [Biodiversity](/organization/model/sectors/biodiversity.md) | Digital, market and public infrastructure, and mental or financial health, are not nexus sectors in this model. Where they matter, they appear through the infrastructure and health sectors, or through the Foundry systems that carry data. ## The thirty directed relations Each sector depends on each of the other five, so there are thirty directed relations. A relation is read "from → to": the strength says how much a disruption in the first sector passes into the second, and the mechanism says through what. The strongest relations in the teaching set are water to food through irrigation (0.8) and energy to infrastructure through power for transport and telecoms (0.8). The weakest run through workforce and biomass (0.1). | From | To | Strength | Mechanism | | -------------- | -------------- | -------- | ------------------------------------- | | Water | Food | 0.8 | irrigation | | Water | Health | 0.7 | drinking water and sanitation | | Water | Energy | 0.6 | cooling water and hydropower | | Water | Biodiversity | 0.6 | environmental flows | | Water | Infrastructure | 0.3 | erosion and flood damage | | Energy | Infrastructure | 0.8 | power for transport and telecoms | | Energy | Water | 0.5 | pumping and treatment | | Energy | Food | 0.5 | fertiliser, machinery and cold chains | | Energy | Health | 0.5 | hospital power | | Energy | Biodiversity | 0.2 | pollution from backup fuels | | Infrastructure | Water | 0.6 | pipes, dams and treatment works | | Infrastructure | Energy | 0.6 | transmission and fuel logistics | | Infrastructure | Food | 0.5 | transport to market | | Infrastructure | Health | 0.5 | access to care | | Infrastructure | Biodiversity | 0.2 | coastal and river defences | | Food | Health | 0.7 | nutrition | | Food | Biodiversity | 0.6 | land conversion | | Food | Water | 0.3 | withdrawals and runoff | | Food | Energy | 0.2 | bioenergy feedstock | | Food | Infrastructure | 0.1 | rural roads and storage | | Health | Food | 0.3 | farm labour | | Health | Infrastructure | 0.3 | workforce for operations | | Health | Energy | 0.2 | grid workforce | | Health | Water | 0.2 | utility workforce | | Health | Biodiversity | 0.1 | conservation capacity | | Biodiversity | Food | 0.6 | pollination and soils | | Biodiversity | Water | 0.5 | watershed regulation | | Biodiversity | Health | 0.4 | zoonotic spillover and medicines | | Biodiversity | Infrastructure | 0.2 | storm surge protection | | Biodiversity | Energy | 0.1 | biomass | ## The fifteen pairs and coupling On the hexagon, each pair of sectors is drawn as one chord. Its weight is the mean of its two directions. Summed over all fifteen pairs, the teaching weights total 6.35. | Pair | First to second | Second to first | Mean | | ------------------------------- | --------------- | --------------- | ---- | | Water and energy | 0.6 | 0.5 | 0.55 | | Water and infrastructure | 0.3 | 0.6 | 0.45 | | Water and food | 0.8 | 0.3 | 0.55 | | Water and health | 0.7 | 0.2 | 0.45 | | Water and biodiversity | 0.6 | 0.5 | 0.55 | | Energy and infrastructure | 0.8 | 0.6 | 0.70 | | Energy and food | 0.5 | 0.2 | 0.35 | | Energy and health | 0.5 | 0.2 | 0.35 | | Energy and biodiversity | 0.2 | 0.1 | 0.15 | | Infrastructure and food | 0.5 | 0.1 | 0.30 | | Infrastructure and health | 0.5 | 0.3 | 0.40 | | Infrastructure and biodiversity | 0.2 | 0.2 | 0.20 | | Food and health | 0.7 | 0.3 | 0.50 | | Food and biodiversity | 0.6 | 0.6 | 0.60 | | Health and biodiversity | 0.1 | 0.4 | 0.25 | For a context that selects a set of sectors *S*, the model reports two numbers. * **Relations in play:** the number of pairs with both sectors in *S*, out of fifteen. * **Coupling:** the summed mean weight of those pairs, divided by the total of 6.35. Coupling is therefore the share of the whole system's interdependence that the context activates. It runs from 0 (one isolated sector) to 1 (all six). ## The teaching cascade The cascade shows how a first hit spreads through the relations in play. It uses three parameters. | Parameter | Value | Meaning | | ------------- | ----------------------------------------------- | ---------------------------------------------------------------------------------- | | Shock | 0.6 | Initial stress at the sectors hit first | | Gain | 0.35 | Share of a partner's stress passed on through a relation, weighted by its strength | | Rounds | 4 | Steps of propagation shown | | Amplification | total stress after the last round ÷ total shock | How much the coupling enlarges the first hit | Written out, with *s* the shock vector (0.6 for each sector hit first, 0 otherwise), *A* the matrix of directed strengths, *g* the gain and *x(t)* the stress of each sector after round *t*: > *x*ᵢ(0) = *s*ᵢ > > *x*ᵢ(*t*+1) = min(1, *s*ᵢ + *g* · Σⱼ *A*ⱼᵢ · *x*ⱼ(*t*)), for every sector *i* in *S*, summing over the other sectors *j* in *S* > > amplification = Σᵢ *x*ᵢ(4) ÷ Σᵢ *s*ᵢ Sectors outside the context carry no stress. If a context names no first-hit sector inside its set, the sector with the strongest outgoing relations in the set is taken as the first hit. In an urban flood, for example, water and infrastructure are hit first. After four rounds, water stands at 0.86, infrastructure at 0.83, health at 0.41 and energy at 0.37, and the total stress is 2.06 times the initial shock. The full table for each context is on its [scenario page](/organization/model/scenarios.md). ### How to read amplification Amplification is a teaching device for one idea: the same initial shock does more harm in a tightly coupled set of sectors than in a loosely coupled one. A drought that reaches five sectors through ten relations amplifies to ×2.89. A pollinator decline that reaches three sectors through three relations amplifies to ×1.51. The number has no units and no probability attached. It does not estimate losses, and it should never be quoted as a finding about a real place. The cascade is deliberately simple. It is linear inside a cap of 1, it runs a fixed four rounds and it ignores time, location, capacity and recovery. Each simplification has a counterpart in real analysis, which a [National Model](https://therisk.global/consortium/national/model/) adds with the country's own data: hazard and exposure maps, network topology, buffer stocks, restoration times and the uncertainty around each. See [Method and limits](/organization/model/method-and-limits.md). ## How the model relates to the research The model condenses four strands of work into a figure a minister, an engineer and a student can read together. | Strand | What it shows | What the model takes from it | | ------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------ | | Infrastructure interdependency | Infrastructures depend on one another physically, through information, through shared location and through shared logic (Rinaldi, Peerenboom and Kelly, [2001](https://doi.org/10.1109/37.969131)). Coupled networks can collapse abruptly once failure in one passes to the other (Buldyrev et al., [2010](https://doi.org/10.1038/nature08932)). | Directed relations with named mechanisms; the distinction between a first hit and the stress that arrives through the coupling | | Compound and cascading risk | Compound events, where several drivers or hazards combine, cause much of the impact that single-hazard assessments miss (Zscheischler et al., [2018](https://doi.org/10.1038/s41558-018-0156-3)). Cascades follow vulnerability paths in critical infrastructure, and secondary emergencies can exceed the primary event (Pescaroli and Alexander, [2016](https://doi.org/10.1007/s11069-016-2186-3)). Compound, interconnected, interacting and cascading risk are distinct and need one framework (Pescaroli and Alexander, [2018](https://doi.org/10.1111/risa.13128)). | Contexts defined by the sectors they activate together; amplification as the visible sign of a cascade | | Systemic risk | Strong coupling in global networks creates instabilities and cascade effects (Helbing, [2013](https://doi.org/10.1038/nature12047)). Global systemic risk is the threat that individual failures cascade through tightly coupled systems (Centeno et al., [2015](https://doi.org/10.1146/annurev-soc-073014-112317)). | Coupling as a share of the system's interdependence; the case for observing sectors together | | International assessments | Multiple climate hazards will occur together and interact with non-climatic risks, so risk compounds and cascades across sectors and regions (IPCC, [2022](https://www.ipcc.ch/report/ar6/wg2/), SPM B.5, high confidence). The Global Assessment Reports place systemic risk at the centre of risk governance (UNDRR, [2019](https://www.undrr.org/publication/global-assessment-report-disaster-risk-reduction-2019), [2022](https://www.undrr.org/gar2022-our-world-risk)) and estimate that, once cascading and ecosystem effects are counted, the total cost of disasters exceeds $2.3 trillion a year (UNDRR, [2025](https://www.undrr.org/gar/gar2025)). | The six sectors and their mechanisms as the minimum set a national risk assessment should cover together | The model also follows the policy frameworks that ask governments to treat risk this way. The Sendai Framework calls for an understanding of risk in all its dimensions and for strengthened risk governance across sectors, with a global target to reduce damage to critical infrastructure and disruption of basic services (UN General Assembly, [2015](https://www.undrr.org/publication/sendai-framework-disaster-risk-reduction-2015-2030), target d). The OECD's Recommendation on the Governance of Critical Risks opens with a comprehensive, all-hazards and transboundary approach to country risk governance (OECD, [2014](https://legalinstruments.oecd.org/en/instruments/OECD-LEGAL-0405)). The water, energy and food nexus approach of FAO ([2014](https://www.fao.org/4/bl496e/bl496e.pdf)) and the IPBES nexus assessment of biodiversity, water, food and health (IPBES, [2024](https://www.ipbes.net/nexus-assessment)) supply the sector-level evidence the relations stand for. ## What this page does not do * It does not measure or rank the risk of any country, city or asset. * It does not forecast losses. The cited values on the scenario pages are published benchmarks, each with its source. * It does not replace a national risk assessment. The responsible authority decides what to assess, with what data, and what to do about it. ## Related pages [Applied response](/organization/model/applied-response.md) · [Sectors](/organization/model/sectors.md) · [Scenarios](/organization/model/scenarios.md) · [Method and limits](/organization/model/method-and-limits.md) · [Risk convergence (doctrine)](/organization/organization/architecture/i.-thesis/ii.-risk-convergence.md) ## Sources * Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E. and Havlin, S. (2010). Catastrophic cascade of failures in interdependent networks. *Nature* 464: 1025–1028. * Centeno, M. A., Nag, M., Patterson, T. S., Shaver, A. and Windawi, A. J. (2015). The emergence of global systemic risk. *Annual Review of Sociology* 41: 65–85. * FAO (2014). *The Water-Energy-Food Nexus: A new approach in support of food security and sustainable agriculture.* Rome: FAO. * Helbing, D. (2013). Globally networked risks and how to respond. *Nature* 497: 51–59. * IPBES (2024). *Summary for Policymakers of the Thematic Assessment Report on the Interlinkages among Biodiversity, Water, Food and Health (Nexus Assessment).* * IPCC (2022). *Climate Change 2022: Impacts, Adaptation and Vulnerability.* Working Group II contribution to the Sixth Assessment Report. * OECD (2014). *Recommendation of the Council on the Governance of Critical Risks.* OECD/LEGAL/0405. * Pescaroli, G. and Alexander, D. (2016). Critical infrastructure, panarchies and the vulnerability paths of cascading disasters. *Natural Hazards* 82: 175–192. * Pescaroli, G. and Alexander, D. (2018). Understanding compound, interconnected, interacting, and cascading risks: a holistic framework. *Risk Analysis* 38(11): 2245–2257. * Rinaldi, S. M., Peerenboom, J. P. and Kelly, T. K. (2001). Identifying, understanding, and analyzing critical infrastructure interdependencies. *IEEE Control Systems Magazine* 21(6): 11–25. * UN General Assembly (2015). *Sendai Framework for Disaster Risk Reduction 2015–2030.* A/RES/69/283. * UNDRR (2019). *Global Assessment Report on Disaster Risk Reduction 2019.* * UNDRR (2022). *Global Assessment Report on Disaster Risk Reduction 2022: Our World at Risk.* * UNDRR (2025). *Global Assessment Report on Disaster Risk Reduction 2025: Resilience Pays.* * Zscheischler, J. et al. (2018). Future climate risk from compound events. *Nature Climate Change* 8: 469–477. * The model data: the "Coupled risk, applied response" section of the [GCRI home page](https://therisk.global/). --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. 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