Extreme sea level return levels
Skew surges and tides are analysed together, or annual maxima fitted, to estimate extreme sea levels and their confidence intervals at tide gauges.
GCRI · Oceans and Coasts
Extreme value statistics for coasts
Extreme value statistics estimate rare high sea levels, waves and marine heat from limited records. In this field they give the return levels used to design coastal defences and ports, and show how sea-level rise changes their frequency.
01Contents
Extreme value statistics for coasts in five parts.
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 oceans and coasts, climate and hazards and biodiversity and nature, 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.
Amplification factors
Return levels are shifted by projected mean sea-level rise to show how much more often today’s rare levels will be reached.
Extreme wave heights
Peaks-over-threshold analysis of long wave records gives the design wave heights used for breakwaters, quays and offshore structures.
03Geography
Ocean state in Pacific Island states.
Marine heat, sea temperature and chlorophyll over Pacific Island states, from NASA GIBS. Each layer carries its own date.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Ocean state, for this page
About this layer
- Evidence
- Observed
- Source
- GHRSST MUR25 (NASA JPL PO.DAAC)
- Provider
- NASA JPL PO.DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite analysis
- Newest at build
- 2026-10-12
- Resolution
- about 2 km grid
- Uncertainty
- Satellite analysis of how far sea temperature departs from its usual value for the date shown; a marine heat indicator, not a coral bleaching alert.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed
- Source
- GHRSST MUR (NASA JPL PO.DAAC)
- Provider
- NASA JPL PO.DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite analysis
- Newest at build
- 2026-10-12
- Resolution
- about 1 km grid
- Uncertainty
- Gap-filled satellite analysis of sea surface temperature for the date shown; not a reef or species condition report.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (clouds and sun glint leave gaps)
- Source
- MODIS Aqua ocean colour (NASA OB.DAAC)
- Provider
- NASA OB.DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite retrieval; clouds and sun glint leave gaps
- Newest at build
- 2026-10-13
- Resolution
- about 1 km grid
- Uncertainty
- Satellite estimate of chlorophyll-a near the sea surface on the day shown, an indicator of plankton and ocean productivity; not a measure of fish stocks or harmful blooms.
- 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 (clouds leave gaps)
- Source
- MODIS Terra EVI (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite index; clouds leave gaps
- Newest at build
- 2026-10-13
- Resolution
- about 250 m grid
- Uncertainty
- Satellite vegetation index for the 8 days to the date shown, a habitat condition indicator; not a measure of species or biodiversity.
- 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.
Ocean state, framed on Pacific Island states.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 PACE OCI · 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
- GHRSST Level 4 MUR analyses, 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
- MODIS Aqua ocean colour, NASA Ocean Biology Processing Group; distributed by the NASA Ocean Biology DAAC (OB.DAAC); 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
- 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
- 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.
- Observed (EO): NASA PACE OCI. 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).
- 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 (10 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
- Sea surface temperature anomaly: GHRSST MUR25, NASA JPL PO.DAAC · 12 Oct 2026
- Sea surface temperature: GHRSST MUR, NASA JPL PO.DAAC · 12 Oct 2026
- Ocean chlorophyll-a concentration: MODIS Aqua ocean colour, NASA OB.DAAC · 12 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
- Enhanced vegetation index, rolling 8 days: MODIS Terra EVI, NASA LANCE · 13 Oct 2026
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 |
|---|---|---|
| GESLA tide gauge records | Extreme sea levels | OBSERVED |
| Wave hindcasts | Long wave series | MODELLED |
| Sea-level projections | Future mean | MODELLED |
05Monitor
Tail fit.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Tail fit
Oceans and coasts · Extreme value statistics · Run R-6724
Shape parameter uncertainGCRI · Oceans and Coasts
Return level curve
Method card
- Method
- Extreme value theory and tail risk
- Approach
- peaks over threshold
- Threshold
- 93th percentile
- Label
- MODELLED
Parameters
generalised Pareto fit
| Shape ξ | 0.09 | −0.04 | 0.45 | heavy tail if above zero |
| Scale σ | 3.1 | 0.9 | 6.9 | units of the variable |
| Exceedances | 138 | declustered |
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 |
|---|---|
| Record length | Return levels beyond several times the record length are flagged as extrapolation |
| Tail fit diagnostics | Fits are checked with return level plots |
| Independence of peaks | Declustering ensures events are independent |
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
07Twin and cascade simulator
Model extreme value statistics for coasts as a system. Run the cascade.
Assembled from the Nexus Standards area profile Oceans and coasts 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
- Sea-level rise
- Storm surge
- Coastal erosion
- Heatwave
- Ocean acidification
- Harmful algal bloom
- Extreme fire weather (set off downstream)
- Wildfire (set off downstream)
- Heat-driven grid stress (set off downstream)
- Agricultural drought (set off downstream)
- Flash drought (set off downstream)
- Snow drought (set off downstream)
- Ground-level ozone episode (set off downstream)
- Meteorological drought (set off downstream)
- River flood (set off downstream)
- Coastal flood (set off downstream)
- Estuary flood (set off downstream)
- Mass displacement (set off downstream)
Systems and couplings
- Oceans and coasts risk standards
- Supply chain and trade risk Cascade
- Food and agriculture risk standards Cascade
- Climate risk standards Common driver and feedback
- Cities and urban systems risk standards Exposure
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-5Figure, map and visualisation standard (with the UI/UX kit)NS-9Contextual UNIs (deployments, instances, programme instances)NS-11Verification and monitoring (evidence, attestations, zero-trust conformance observation)NRS-X3Oceans and coasts riskNRS-H11Hazard family: Coastal and sea-level hazards (NHS-1 water.coastal)NRS-H79Hazard family: Mental health crises (NHS-1 health.mental)NRS-H12Hazard family: Ocean-state extremes (NHS-1 water.ocean-state)NRS-H67Hazard family: Ocean circulation and marine tipping (NHS-1 planet.ocean-tipping)NRS-K18Domain pack profile: Oceans coastal (DOMAIN-018)
Observation
- Copernicus Marine Service ocean products (listed for reference)
- Coral Reef Watch daily 5 km heat stress products (listed for reference)
- PSMSL tide gauge mean sea level records (listed for reference)
- GEBCO global bathymetric grid (listed for reference)
- Argo float profiles (listed for reference)
- Average marine acidity (pH) measured at agreed suite of representative sampling stations
- Index of coastal eutrophication and floating plastic debris density
- Direct economic loss attributed to disasters in relation to GDP, including damage to critical infrastructure
Example geography
- Pacific Island states: 150 hexagonal cells
- Night lights tonight, outages (VIIRS Day/Night Band), NASA GIBS
- Surface water through cloud, 30 m (OPERA DSWx-S1 radar), NASA GIBS
- Rain rate, last half hour (IMERG), NASA GIBS
- Surface air temperature, daytime (AIRS), NASA GIBS
08Connections
Topics that rely on this method.
09Risk and response
Coupled risk, applied response.
The sectors coastal storm surge 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 sectors10 / 15 relations
Sectors · Coastal storm surgeStress
applied to
BApplied response across six pillars12 / 18 handoffs
Pillars · Coastal storm surgeKPI
In this contextDependence or handoff, heavier is strongerOutside this context
Programme yearAll phases
Context
Coastal storm surge
Mangroves and dunes absorb the surge; where they are gone, ports, substations and water intakes take it.
W · E · I · F · H · B
Risk
- Sectors
- 5 of 6
- Relations
- 10 of 15
- Coupling
- 0.64 share of total
Hover a corner, a line or a row to trace it across both sides.
Route
Applied to coastal storm surge
L · F · U · S · R · A
Response
- Pillars
- 5 of 6
- Handoffs
- 12 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
- $80Bflood losses avoided a yearGlobal 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 coasts 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.
Earth observation chain
How a satellite or sensor record becomes evidence on extreme value statistics for coasts, and where each step adds uncertainty.
- 01 · Acquireorbit, sensor and revisitUncertainty: gaps from cloud and orbit
- 02 · Calibrateradiometric and geometricUncertainty: sensor drift
- 03 · Correctatmosphere and terrainUncertainty: aerosol and slope assumptions
- 04 · Retrieve or classifythe variable or the classUncertainty: model and training error
- 05 · Validateagainst ground truthUncertainty: sample design and size
- 06 · Publishwith error bars and lineageUncertainty: stated, never hidden
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.
13Process
How the process runs.
Process
Extreme value statistics for coasts: Catastrophe model pipeline
Catastrophe models usually have hazard, vulnerability, exposure and financial modules, and produce loss tables, average annual loss, exceedance curves, PML and TVaR.
01 Hazard
- 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
- 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.
02 Exposure and damage
- 02ExposureDataset · Fisheries agencyThe exposure module houses the portfolio data, such as location-specific information.
- 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.
03 Financial
- 05Financial moduleModel · Fisheries agencyThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Fisheries agencyAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Fisheries agencySome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Fisheries agencyThe occurrence curve gives the chance that the largest loss in a year exceeds an amount. The aggregate curve does so for the sum of losses.
- 09AAL, PML and TVaRModel · Fisheries agencyAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Fisheries agencyThe tail metrics are used when considering a portfolio’s exposure and the level of catastrophe reinsurance an insurer requires.
Outline of an external standard or method, from its public sources. It describes what the framework says, not a record of any run. It does not show that Nexus or any partner performs, certifies or approves a step. A gate is a step of the method, never a Nexus approval.
14Questions
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.
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