Return-period flows and rainfall
Generalised extreme-value or peaks-over-threshold distributions are fitted to annual maxima, with confidence intervals reported alongside the point estimate.
The Global Centre for Risk and Innovation (GCRI)
Extreme-value statistics gives the return period its meaning: how rare a flow, a rainfall depth or a dry spell is, and how uncertain that estimate is when the record is short.
Water NexusWireframe of the working environment, not a live screen. Names and values are placeholders.
Extreme value theory and tail risk study the behaviour of rare, high-impact events. They provide methods to estimate the magnitude and frequency of extremes beyond the range of observed data. In water, climate and hazards and critical infrastructure, extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different systems tend to occur together. The canonical description is on the STEM Commons.
Generalised extreme-value or peaks-over-threshold distributions are fitted to annual maxima, with confidence intervals reported alongside the point estimate.
Short records are pooled across hydrologically similar catchments so ungauged sites inherit a defensible frequency curve.
Dependence between rainfall and surge, or drought and heat, is modelled with copulas; trends in the record are tested and, where present, the frequency curve is allowed to move.
Where this page’s subject sits in the world: boundaries and context now, the field layers when the interactive map loads.
MapWorld map in the Equal Earth projection, land and boundaries from Natural Earth (public domain). The interactive map loads through the Nexus Foundry plugin (globe or flat view).
Data from the source register feeds the methods; calibration and an independent test gate the estimate and its limits; the decision stays with the competent authority.
Fig. 01Nodes carry their type, metrics and state; connectors show what feeds what; the gates are the validation steps; the timeline is one application. Design of the method’s use, not a record of a run.
Datasets and records used by extreme value theory and tail risk on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| Annual maximum series | Distribution fitting | OBSERVED |
| Peaks over threshold | Distribution fitting | OBSERVED |
| Regional catchment descriptors | Pooling groups | ESTIMATED |
| Climate model projections | Non-stationary scenarios | MODELLED |
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
| Check | How it is done |
|---|---|
| Goodness of fit | Several distributions are compared; the choice and its effect on the estimate are reported |
| Bootstrap uncertainty | Confidence intervals are resampled, not assumed |
| Stationarity tests | Trend and change-point tests precede any quoted return period |
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
Reinsurance and Catastrophe stewards extreme value theory and tail risk for the Consortium and reviews how it is applied across platforms.
| Link | Relationship | Why |
|---|---|---|
| Extreme value theory and tail risk | Canonical method page | Platform application links to the canonical method page. |
| Extreme value theory and tail risk in reinsurance and catastrophe | Steward platform | Reinsurance and Catastrophe stewards this method. |
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