Illustrative: an ensemble of trajectories, its quantile fan and the outcome as it is observed
Risk Academy, led by the Nexus Consortium · Risk Science and Methods · Department of Quantitative Risk Analysis
Forecasts as distributions, judged by proper scoring rules
Probabilistic forecasting and verification
A risk number is a forecast, and a forecast is only as good as its verification.
- Department
- Department of Quantitative Risk Analysis
- Courses
- In preparation
- Levels
- In development
- Labs
- In development
- Probabilistic and ensemble forecasts
- Proper scoring rules (Brier, CRPS, logarithmic)
- Calibration, sharpness and reliability diagrams
- Discrimination, ROC curves and hit and false alarm rates
- Verification of categorical warnings and triggers
- Forecast value and the cost-loss model
- Post-processing and statistical calibration of ensembles
- Machine-learning weather and hazard forecasts and their verification
- Forecast combination and model averaging
Build a twin of any place
Search any place or open the world; the layers and generators follow probabilistic forecasting and verification on the planet map, the globe and in 3D.
- Terrain 24 to 2,805 m
- 3 reference earthquakes, M6.2 to M6.6
- Earthquakes M4.5 and above, past week: read live when the 3D twin opens
- USGS ShakeMap intensity contours: read live when the 3D twin opens
Drag to move, right drag or Shift with a drag to turn and tilt, Ctrl with the wheel to zoom. Keyboard: arrows move, Shift with arrows turn and tilt, + and – zoom, 0 resets, V steps through the views, Escape clears.
Flat plan of the same data: relief, the three reference epicentres with magnitude and depth, and the numbers below; the sampler's figure shows one precomputed field with its parameters. The 3D twin opens on devices that can draw it, once its data and code have been checked.
The boundaries, names and designations shown do not imply any judgement on the legal status of any territory, or any endorsement or acceptance of such boundaries. Countries: Natural Earth (public domain).
Hazards and exposure in Italy
Flood water, active fires and surface heat beside population and night-time lights, over Italy.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Hazards and exposure
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.
Hazards and exposure, framed on Italy.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 · U.S. Geological SurveySources 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 H3 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 H3 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 H3 cells where shown (modified). NASA open data
- NASA Fire Information for Resource Management System (FIRMS), VIIRS 375 m active fire product, NASA LANCE; vector tiles via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
- Center for International Earth Science Information Network (CIESIN), Columbia University. 2018. Gridded Population of the World, Version 4 (GPWv4): Population Density, Revision 11. NASA Socioeconomic Data and Applications Center (SEDAC). Licensed under CC BY 4.0. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). doi:10.7927/H49C6VHW. CC BY 4.0
- VIIRS Black Marble night-time lights, NASA Goddard Space Flight Center; distributed by the NASA Level-1 and Atmosphere Archive and Distribution System (LAADS DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 cells where shown (modified). NASA open data
- MODIS and VIIRS atmosphere products, NASA LANCE and LAADS DAAC; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 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 H3 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 H3 cells where shown (modified). ODbL
- Blue Marble, NASA Earth Observatory; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into H3 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.
- Globe: MapLibre GL JS 6.9.1, BSD-3-Clause, © MapLibre contributors.
- 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: U.S. Geological Survey Events are indicative, not authority warnings.
- 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.
- 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
- Flood water, 3-day composite: VIIRS Global Flood Product, NASA LANCE · 14 Oct 2026
- Active fires and thermal anomalies: VIIRS NOAA-20 375 m (FIRMS), NASA LANCE FIRMS · 13 Oct 2026
- Population density, 2020: Population: CIESIN, Columbia University, Gridded Population of the World v4.11 (2018), NASA SEDAC, CC BY 4.0 · static
- Land surface temperature, day, 8-day composite: VIIRS NOAA-20 Level 3, 8-day, NASA LANCE · 14 Sep 2026
- Night-time lights, daily: VIIRS Black Marble (VNP46A2), NASA LAADS DAAC · 12 Oct 2026
- Aerosol optical depth, daily: VIIRS NOAA-20 Deep Blue AOD, NASA LANCE · 13 Oct 2026
The subject, methods and measures and debates and bodies
The field and its scope
For forecasters, early warning analysts, modellers and the people who act on forecasts, who need to issue risk as a calibrated distribution and to judge forecasts fairly against what happened.
Quantities and units
Methods and their limits
Each method is listed with what it assumes and where it fails.
What the field debates
Bodies that set practice, and the data they publish
Bodies and standards are named so learners can find and apply their published work; the Academy teaches their use and links to the publisher, and no affiliation is implied.
From a probability forecast to its value for a user: hits, false alarms and the cost-loss ratio that decides
At a glance, hub, what is changing now and courses
Probabilistic forecasting and verification at a glance
risksacademy.comrisk-sciencediscipline
- Open, 0
- In preparation, 0
- Subtopics, 9
Research and tools
Research and preprints as they are published, by discipline, with the faculty's other tools.
The hub lists the newest research and preprints for Probabilistic forecasting and verification, each with its source and date. Open the research hub
What is changing now
Recent developments in probabilistic forecasting and verification, each with its source; sources checked on 16 October 2026.
- Technology
ECMWF made its machine-learning ensemble forecast operational
ECMWF's AIFS ENS became operational, producing 51-member ensemble forecasts alongside the physics-based system. It outperforms physics-based models on many measures, runs over ten times faster with far less energy, but still relies on physics-based data assimilation.
Why it matters. Hybrid physical and machine-learning ensembles change how forecast uncertainty is produced and must be validated.
Source: European Centre for Medium-Range Weather Forecasts, ECMWF's ensemble AI forecasts become operational, 1 July 2025.
Courses in this discipline
Courses for this discipline are in development; until they open, study it through the connected courses and open lessons below.
The course catalogue lists every open course of the Academy.
How Probabilistic forecasting and verification is taught, as a process you can run
Press Play to run this process from this page's own data.
Achievements, where this is practised, practised in and across the ecosystem
Achievements in this discipline
Course achievements
One for each course with this as its primary discipline, earned when you pass the course's assessed activities.
Department: Quantitative Risk Analysis
Earn two discipline achievements in the Department of Quantitative Risk Analysis. In development.
An achievement is a record of the learning completed and assessed here. How recognition works.
Where the subject is practised
A field platform page on this subject is in development.
The two Foundry systems where it is practised
- FoundryNXS-EWS systemForecasts and warnings are judged by how they verifyForecast Verification room
- NXS-LAB systemCompeting forecast methods are compared under transparent testsBenchmarks room
Foundry system pages describe what each system and its rooms are designed to do; the courses teach the methods these systems apply.
Across the ecosystem
Take part in Risk Science and Methods
Start from who you are.
Core references and where to begin
Start with Murphy, then Gneiting, then Brier.
Questions, answers and key terms
Is study here free?
What does completing a course give me?
Where do the data and the places come from?
How do I take part beyond the courses in probabilistic forecasting and verification?
Key terms
Proper scoring rule
A score that is optimised in expectation only when the forecaster reports their true probability, such as the Brier score or CRPS.
Calibration
Agreement between forecast probabilities and observed frequencies: events forecast at 30 per cent happen about that often.
Sharpness
How concentrated a forecast distribution is, judged only once calibration holds.
Continuous ranked probability score
A proper score for a forecast distribution of a continuous quantity, in the units of the quantity.
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.
Around Probabilistic forecasting and verification
Prepare with a related course
Open courses in connected disciplines teach the methods this discipline will build on.