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.
GCRI · Water Nexus
Extreme value statistics for floods and droughts
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.
01Register
Extreme value statistics for floods and droughts on the record.
Method recordSTEM method
- MethodExtreme value theory and tail risk
- StewardReinsurance and Catastrophe
- Applied inWater Nexus
- Data4 inputs
- Checks3 validation steps
- Canonical pageSTEM Commons
02Application
What extreme value theory and tail risk does here.
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.
Regional frequency analysis
Short records are pooled across hydrologically similar catchments so ungauged sites inherit a defensible frequency curve.
Compound and non-stationary extremes
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.
03Geography
Water now in the Nile Basin.
Rain, flood water and root-zone soil moisture over the Nile Basin, from NASA GIBS. Each layer carries its own date.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Water now, for this page
About this layer
- Evidence
- Estimated
- Source
- GPM IMERG (NASA GES DISC)
- Provider
- NASA GES DISC
- Licence
- NASA open data
- Vintage
- daily; Satellite estimate, near real time
- Newest at build
- 2026-10-12
- Resolution
- about 2 km grid
- Uncertainty
- Satellite estimate, near real time. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (clouds leave gaps)
- Source
- VIIRS Global Flood Product (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite detection; clouds leave gaps
- Newest at build
- 2026-10-14
- Resolution
- about 250 m grid
- Uncertainty
- Satellite detection; clouds leave gaps. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Modelled
- Source
- SMAP Level 4 (NASA NSIDC DAAC)
- Provider
- NASA NSIDC DAAC
- Licence
- NASA open data
- Vintage
- daily; Model with satellite data assimilated
- Newest at build
- 2026-10-11
- Resolution
- about 2 km grid
- Uncertainty
- Model with satellite data assimilated. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed
- Source
- VIIRS NOAA-20 corrected reflectance (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite image
- Newest at build
- 2026-10-14
- Resolution
- about 250 m grid
- Uncertainty
- Satellite image. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Modelled (latest year GIBS publishes)
- Source
- MODIS Terra and Aqua land cover (MCD12Q1) (NASA LP DAAC)
- Provider
- NASA LP DAAC
- Licence
- NASA open data
- Vintage
- yearly; Satellite classification; latest year GIBS publishes
- Newest at build
- 2024-01-01
- Resolution
- about 500 m grid
- Uncertainty
- Satellite land cover classes for the year shown, including croplands; a classification with known errors, not a farm register.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (latest month GIBS publishes)
- Source
- GRACE-FO JPL mascons (NASA JPL PO.DAAC)
- Provider
- NASA JPL PO.DAAC
- Licence
- NASA open data
- Vintage
- monthly; Satellite gravimetry; latest month GIBS publishes
- Newest at build
- 2022-07-01
- Resolution
- about 2 km grid
- Uncertainty
- Satellite gravimetry; latest month GIBS publishes. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
Keyboard, with the map focused
Hold Ctrl or ⌘ and scroll to zoom
Latest available
NASA GIBS / EOSDIS · ASTER GDEM (METI, NASA) · Blue Marble (NASA) · © OpenStreetMap contributors (ODbL) · Natural Earth
Loading the latest NASA imagery.
Drag to move. Ctrl or ⌘ and scroll, pinch or the buttons to zoom; hover for the values under the pointer; reset returns to the region.
Water now, framed on the Nile Basin.Satellite and model products as NASA publishes them, each with its own date. They are indicators, not assessments of any place.
Data: NASA GIBS · ASTER GDEM · Blue Marble · © OpenStreetMap contributors · Natural Earth · NASA EONET · NASA GPM IMERG Early · NASA JPL OPERA DIST-ALERTSources and licences
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- GPM IMERG precipitation, NASA Precipitation Processing System; distributed by the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- VIIRS near-real-time products (flood, land surface temperature, snow cover, corrected reflectance), NASA LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- SMAP Level 4 soil moisture and snow mass, NASA Global Modeling and Assimilation Office; distributed by the NASA National Snow and Ice Data Center DAAC; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- MODIS land products (vegetation indices, gross primary production, land cover), NASA LP DAAC and LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- GRACE and GRACE-FO JPL mascon solution, NASA Jet Propulsion Laboratory; distributed by the NASA Physical Oceanography DAAC (PO.DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- ASTER GDEM is a product of METI and NASA (ASTER Global Digital Elevation Model V003, NASA LP DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). Cite as: NASA/METI/AIST/Japan Spacesystems and U.S./Japan ASTER Science Team (2019). ASTER Global Digital Elevation Model V003. doi:10.5067/ASTER/ASTGTM.003. NASA open data
- Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. Public domain
- © OpenStreetMap contributors (ODbL), via NASA GIBS (coastlines, boundaries, roads and place names). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). ODbL
- Blue Marble, NASA Earth Observatory; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- Context on the globe and flat map: coastlines, boundaries, roads and place names from NASA GIBS reference layers (OpenStreetMap data, ODbL, © OpenStreetMap contributors); Blue Marble imagery as an optional base; 3D terrain and the elevation read-out from the ASTER GDEM elevation colour index (5 m to 200 m classes, exaggerated for legibility). Boundaries are drawn as published and imply no position on any territory.
- Live events: NASA Earth Observatory Natural Event Tracker (EONET); events are indicative and keep their original source links.
- Live: NASA EONET Events are indicative, not authority warnings.
- Live: NASA GPM IMERG Early. We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- Observed (EO): NASA JPL OPERA DIST-ALERT (contains modified Copernicus Sentinel data 2026). We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- NASA GIBS: We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- River discharge forecast, 30 days with range (GloFAS via Open-Meteo): Contains modified Copernicus Emergency Management Service information 2026; not a flood warning.
- Past year, daily temperature (ERA5 via Open-Meteo): Contains modified Copernicus Climate Change Service information 2026.
- Past year, daily temperature and sunshine (NASA POWER): These data were obtained from the NASA Langley Research Center (LaRC) POWER Project funded through the NASA Earth Science/Applied Science Program..
- Weather data by Open-Meteo.com (https://open-meteo.com/), licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).
- Optional layers (14 sources in the layer list: live, forecast, observed and context) print their provider credit on the map and here when switched on; forecasts are model output and derived indices are estimates.
Layers and dates
- Precipitation rate, daily mean: GPM IMERG, NASA GES DISC · 12 Oct 2026
- Flood water, 3-day composite: VIIRS Global Flood Product, NASA LANCE · 14 Oct 2026
- Root-zone soil moisture, 0 to 100 cm: SMAP Level 4, NASA NSIDC DAAC · 11 Oct 2026
- True colour: VIIRS NOAA-20 corrected reflectance, NASA LANCE · 13 Oct 2026
- Land cover type (IGBP), yearly: MODIS Terra and Aqua land cover (MCD12Q1), NASA LP DAAC · 2024
- Water storage anomaly, monthly: GRACE-FO JPL mascons, NASA JPL PO.DAAC · July 2022
04Data
What the method consumes.
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 |
05Simulator
Route a storm through a river network.
Rain becomes runoff by the curve number method, drains each sub-catchment through a linear reservoir and travels down the main stem by Muskingum routing; play it to watch the flood wave move and flatten. Teaching model with stated illustrative values, not a prediction. The map on this page shows The Nile Basin; the model itself is not tied to a place.
Controls
- Storm rainfall depth
- 120 mm
- Storm duration
- 12 h
- Curve number (soil and land cover)
- 78
- Catchment area
- 800 km²
- Reaches on the main stem
- 5
- Travel time per reach (Muskingum K)
- 6.0 h
- Muskingum X (storage weighting)
- 0.20
- Channel capacity per unit area
- 300 L/s per km²
Readouts
- Peak discharge at the outlet
- 452 m³/s
- Time to peak
- 21.6 h
- Attenuation by the channel
- 61%
- Hours over capacity
- 26.4 h
- Runoff coefficient
- 52%
Numbers, methods and sources
| Hour | Outlet (m³/s) | Unrouted (m³/s) | Upper reach (m³/s) |
|---|---|---|---|
| 2.4 | 0.0 | 678.9 | 0.0 |
| 12.0 | 308.3 | 1,151.4 | 181.8 |
| 21.6 | 452.4 | 35.1 | 73.7 |
| 31.2 | 363.3 | 1.1 | 11.1 |
| 40.8 | 198.8 | 0.0 | 1.5 |
| 50.4 | 79.3 | 0.0 | 0.2 |
| 60.0 | 25.4 | 0.0 | 0.0 |
| 69.6 | 6.9 | 0.0 | 0.0 |
| 79.2 | 1.7 | 0.0 | 0.0 |
| 88.8 | 0.4 | 0.0 | 0.0 |
| 98.4 | 0.1 | 0.0 | 0.0 |
| 108.0 | 0.0 | 0.0 | 0.0 |
| 117.6 | 0.0 | 0.0 | 0.0 |
| 127.2 | 0.0 | 0.0 | 0.0 |
| 136.8 | 0.0 | 0.0 | 0.0 |
Methods
- Curve number runoff USDA Soil Conservation Service (1972), National Engineering Handbook, Section 4: Hydrology
- Linear reservoir Nash (1957), The form of the instantaneous unit hydrograph, IAHS 45
- Muskingum channel routing McCarthy (1938); Cunge (1969), Journal of Hydraulic Research 7
- Uncertainty fan (parameter Monte Carlo) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- One-at-a-time sensitivity (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Data
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
- Rivers Natural Earth
- Lakes and reservoirs Natural Earth
- Cities Natural Earth
- Rain rate, last half hour (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
- River discharge forecast, 30 days with range (GloFAS via Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
- Surface soil moisture (SMAP) NASA SMAP · register nasa.gibs.context-live-layers
- Surface water, 30 m (OPERA DSWx-HLS) NASA JPL OPERA DSWx-HLS (contains modified Copernicus Sentinel data 2026) · register nasa.gibs.context-live-layers
- Surface water through cloud, 30 m (OPERA DSWx-S1 radar) NASA JPL OPERA DSWx-S1 (contains modified Copernicus Sentinel-1 data 2026) · register nasa.gibs.context-live-layers
Across the six pillars, led by Nexus Consortium
- Experiments Labs
- Built in Water Nexus in Foundry
- Tested at Water Nexus in Universe
- Codified in Water and Food Systems in Standards
- Published in Water Nexus in Reports
- Taught in Faculty of Earth and Environmental Sciences in Academy
06Validation
How results are checked.
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.
07Twin and cascade simulator
Model extreme value statistics for floods and droughts as a system. Run the cascade.
Assembled from the Nexus Standards area profile Water risk standards: the hazards it names, the systems and sectors that carry the loss, the controls that dampen it and the data that observe it. Choose the components, pick an initiating hazard and step through the cascade. The Map view places the run on an example geography with open data. Every coupling weight is a stated assumption you can change. A teaching model, not a forecast, an assessment or a certification. To model a place of your own choosing, open the full System Builder.
Hazards
- Flash flood
- Meteorological drought
- Groundwater depletion
- Dam failure
- Debris flow (set off downstream)
- Agricultural drought (set off downstream)
- Hydrological drought (set off downstream)
- Wildfire (set off downstream)
- Peat and underground fire (set off downstream)
- Forest dieback (set off downstream)
- Water supply shortfall (set off downstream)
- Acute food crisis (set off downstream)
- Dust storm (set off downstream)
- Land subsidence (set off downstream)
- Saltwater intrusion (set off downstream)
- River flood (set off downstream)
- Mass displacement (set off downstream)
- Amazon rainforest dieback (set off downstream)
Systems and couplings
- Water risk standards
- Energy risk standards Common driver and cascade
- Food and agriculture risk standards Cascade
- Health risk standards Cascade
- Hydrometeorological hazard standards Shared hazard records
Controls
NS-0Constitution and principlesNS-1The UNI and the artefact catalogue (grammar v0.2: domain, sector, region and environment segments)NS-3Risk record UNIs (grammar, legacy crosswalk, allocation authority)NS-3bDataset and product metadata profile (STAC, DCAT, PROV-O)NS-9Contextual UNIs (deployments, instances, programme instances)NS-10Policies and clauses (machine-readable obligations: definition, binding, evaluation and enforcement)NS-11Verification and monitoring (evidence, attestations, zero-trust conformance observation)NRS-U28Universe platform profile: Water NexusNRS-H61Hazard family: Cascading failure (NHS-1 sys.cascade)NRS-K42Domain pack profile: Cross border basins (DOMAIN-042)NRS-N1Water risk and resilienceNRS-N7Water-energy-food-health-biodiversity-infrastructure nexus couplingNRS-H62Hazard family: Compound and multi-hazard events (NHS-1 sys.compound)
Observation
- USGS Water Data APIs (listed for reference)
- GloFAS global flood forecasts and reanalysis (listed for reference)
- GRACE/GRACE-FO terrestrial water storage mascons (listed for reference)
- Aqueduct 4.0 Water Risk Atlas (listed for reference)
- CHIRPS quasi-global gridded precipitation (listed for reference)
- Level of water stress: freshwater withdrawal as a proportion of available freshwater resources
- Proportion of transboundary basin area with an operational arrangement for water cooperation
- Proportion of population using safely managed drinking water services
- Number of disruptions to basic services attributed to disasters
Example geography
- The Ganges and Brahmaputra Basin: 178 hexagonal cells
- Surface water through cloud, 30 m (OPERA DSWx-S1 radar), NASA GIBS
- Rain rate, last half hour (IMERG), NASA GIBS
- Surface soil moisture (SMAP), NASA GIBS
- Night lights tonight, outages (VIIRS Day/Night Band), NASA GIBS
08Connections
Topics that rely on this method.
09Risk and response
Coupled risk, applied response.
The sectors urban flood touches and how strongly they depend on each other: what a study has to observe and model together.
Choose a context
ACoupled risk across six sectors6 / 15 relations
Sectors · Urban floodStress
applied to
BApplied response across six pillars11 / 18 handoffs
Pillars · Urban floodKPI
In this contextDependence or handoff, heavier is strongerOutside this context
Programme yearAll phases
Context
Urban flood
Flooded streets take out substations, pumping stations and clinic access together; drinking water fails when power does.
W · E · I · F · H · B
Risk
- Sectors
- 4 of 6
- Relations
- 6 of 15
- Coupling
- 0.46 share of total
Hover a corner, a line or a row to trace it across both sides.
Route
Applied to urban flood
L · F · U · S · R · A
Response
- Pillars
- 5 of 6
- Handoffs
- 11 of 18
- Loops
- 8 closed
Expected value
- What is at stake
- $390Ba year at least, in infrastructure disruption costs to households and firms in low- and middle-income countriesWorld Bank, Lifelines, 2019
- Return on resilience
- 4 : 1benefit to costWorld Bank, Lifelines, 2019
- Avoided loss
- 30%less damage with 24 hours’ warning of a storm or heatwaveGlobal Commission on Adaptation, Adapt Now, 2019
Hover a pillar, a line or a row to read how it is applied.
A: a teaching cascade (shock 0.6, gain 0.35, four rounds) over teaching values for a typical city-region, not measurements. B: illustrative applications and the KPI each pillar answers for; values are published benchmarks, cited, not forecasts. Open events: NASA EONET, live.
10Stewardship
Who maintains the method.
Reinsurance and Catastrophe stewards extreme value theory and tail risk for the Consortium and reviews how it is applied across platforms.
11Methods and evidence
How extreme value statistics for floods and droughts is modelled, measured and tested.
The model, its assumptions, its data and its uncertainty, in the form a scientist or engineer would check. Structures follow published methods. The values drawn are illustrative, not findings.
System model
The couplings between the systems in extreme value statistics for floods and droughts: signs of influence, a reinforcing and a balancing loop, and cross-links where stress jumps.
FAIR guiding principles · GO FAIR and FORCE11W3C PROV · World Wide Web ConsortiumGuidance on consistent treatment of uncertainties · IPCCCEOS Analysis Ready Data · Committee on Earth Observation Satellites
12Connected
Where this page leads across the Consortium.
13Questions
Questions and answers.
What are the limits of extreme value theory and tail risk in this field?
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
How are results checked?
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
ReportsContribute
Contribute evidence from this page.
Reports is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.
GCRIWater NexusGlobal Sector Risk and ResilienceCountry Systems Risk and ResilienceObservatory Signal
- EmailGateway GW-GCRISend it from this pageEvidence, a correction, a case, a method, a review, a translation or profile input. It arrives tagged with this page, so the editor who owns it receives it.
- ZenodoOpen depositDeposit it and submit to the communityPublish your own record on Zenodo with your ORCID iD, then submit it to the Reports community there. Curators review it; the DOI stays yours.
- ReportsGCRISee every way to contributeThe contribution types, how each is reviewed, what credit you receive, the licence and what is never accepted.
Never send personal data, sensitive infrastructure detail or anything you have no right to share. A contribution is reviewed before use; sending it confers no authorship or editorial rights, and sponsorship never buys a finding.
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