GCRI · Systems Science and Modelling
Optimisation under uncertainty
Plans for infrastructure, reserves and portfolios must work across futures that cannot be predicted. Optimisation under uncertainty chooses decisions that perform well on average, hold up in bad cases or stay acceptable across many scenarios. This page sets out the main approaches, from stochastic to robust optimisation and decision-making under deep uncertainty, how their results are tested, and what evidence serves the planners who rely on them.
Optimisation under uncertainty on the record.
Optimisation under uncertainty: how the risk develops.
Robust and adaptive decisions when futures are deeply uncertain. The dossier below sets out how the risk develops, what is measured, where the data come from, how it is modelled and who decides.
Optimal for one future is fragile
A plan optimised for a single forecast can perform badly if the future differs. Representing uncertainty explicitly avoids this trap.
Stochastic methods use probabilities
Stochastic programming optimises expected performance across scenarios with assigned probabilities, which needs those probabilities to be credible.
Robust methods guard the worst case
Robust optimisation chooses decisions that perform acceptably for all scenarios within a set, trading average performance for protection.
Adaptive plans keep options open
Plans with decision points and triggers adapt as uncertainty resolves, avoiding commitments that lock in poor outcomes.
Hazards and exposure in North America.
Flood water, population density and daytime surface heat over North America, from NASA GIBS. Each layer carries its own date.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Hazards and exposure, for this page
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
- Estimated
- Source
- Gridded Population of the World v4.11 (NASA SEDAC (CIESIN, Columbia University))
- Provider
- NASA SEDAC (CIESIN, Columbia University)
- Licence
- CC BY 4.0
- Vintage
- null; Census-based estimate, static (2020)
- Resolution
- about 1 km grid
- Uncertainty
- Census-based estimate of people per square kilometre in 2020, shown as exposure context; not a count of people affected by any hazard.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (persistent cloud still leaves gaps)
- Source
- VIIRS NOAA-20 Level 3, 8-day (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- 8-day; Satellite 8-day composite; persistent cloud still leaves gaps
- Newest at build
- 2026-09-14
- Resolution
- about 1 km grid
- Uncertainty
- Satellite skin temperature of the ground over the 8 days ending on the date shown, a heat exposure indicator; not air temperature, heat index or a heat warning.
- 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 and overpass timing leave gaps)
- Source
- VIIRS NOAA-20 375 m (FIRMS) (NASA LANCE FIRMS)
- Provider
- NASA LANCE FIRMS
- Licence
- NASA open data
- Vintage
- daily; Satellite detection; clouds and overpass timing leave gaps
- Newest at build
- 2026-10-13
- Resolution
- about 500 m grid
- Uncertainty
- Satellite hot-spot detections for the day shown, including gas flares and industrial heat; not a confirmed fire, an incident report or a warning.
- 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.
Hazards and exposure, framed on North America.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 Survey · 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
- 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
- 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 hexagonal cells where shown (modified). doi:10.7927/H49C6VHW. CC BY 4.0
- 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
- 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 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: U.S. Geological Survey Events are indicative, not authority warnings.
- 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.
- 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 (11 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
- 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
- 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
- Active fires and thermal anomalies: VIIRS NOAA-20 375 m (FIRMS), NASA LANCE FIRMS · 13 Oct 2026
Optimisation under uncertainty supports decisions in every domain.
Findings are designed for the Methods and Technical series. Decision making under deep uncertainty (Marchau and others, 2019) sets out robust methods; owners decide.
- Case applications.
- Comparisons of robust methods.
Coupled model runner.
The screen a team would use to follow this subject: its measures, states and decisions. Names are examples and values are illustrative.
Coupled model runner
Optimisation under uncertainty · Coupled model A · Scenario set 3
Model coupling graph
nodes: models · edges: exchanged variables
Coupled components
| Hydrology | 1 day | runoff | Yes |
| Power system | 1 h | demand, outages | Yes |
| Economy | 1 quarter | output, prices | Partial |
| Population | 1 year | exposure | Yes |
Ensemble output
What is measured, and how well.
Each indicator carries its unit, its cadence, the kind of source behind it and the evidence label a value would carry. No values are shown: a programme supplies them under its own authority.
| Indicator | Unit | Cadence | Source type | Label |
|---|---|---|---|---|
| Scenarios evaluated | count | per analysis | Analysis documentation | DECLARED |
| Regret of chosen plan | difference from best plan in each scenario | per analysis | Robustness analysis | MODELLED |
| Value of the stochastic solution | difference between stochastic and deterministic plans | per analysis | Optimisation outputs | MODELLED |
| Satisficing share | percent of scenarios meeting objectives | per analysis | Robustness analysis | MODELLED |
| Adaptation triggers defined | count | per plan | Plan documentation | DECLARED |
| Out-of-sample performance | objective value on held-out scenarios | per analysis | Testing | MODELLED |
Model optimisation under uncertainty as a system. Run the cascade.
Assembled from the Nexus Standards area profile Compound and cascading hazard 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
- Natech event
- Chemical spill or leak (set off downstream)
- Emergency-response overload (set off downstream)
- Toxic gas release (set off downstream)
- Industrial fire (set off downstream)
Systems and couplings
Controls
NS-0Constitution and principlesNS-3Risk record UNIs (grammar, legacy crosswalk, allocation authority)NS-9Contextual UNIs (deployments, instances, programme instances)NS-11Verification and monitoring (evidence, attestations, zero-trust conformance observation)NRS-H61Hazard family: Cascading failure (NHS-1 sys.cascade)NRS-H62Hazard family: Compound and multi-hazard events (NHS-1 sys.compound)NRS-H60Hazard family: Supply-chain and flow disruption (NHS-1 sys.supply-chain)NRS-H94Hazard family: Systemic cyber events (NHS-1 cyber.systemic-cyber)NRS-H107Hazard family: Digital infrastructure concentration and monoculture (NHS-1 tech.digital-concentration)NRS-H7Hazard family: Large-scale circulation anomalies (NHS-1 atmo.climate-mode)
Observation
- Copernicus EMS rapid mapping activations (listed for reference)
- OpenStreetMap planet and replication (listed for reference)
- ERA5 reanalysis (Copernicus Climate Data Store) (listed for reference)
- Direct economic loss attributed to disasters in relation to global GDP
- Number of disruptions to basic services attributed to disasters
Example geography
- Bangladesh: 134 hexagonal cells
- Night lights tonight, outages (VIIRS Day/Night Band), NASA GIBS
- Carbon monoxide, smoke transport (AIRS), NASA GIBS
- Vegetation disturbance alerts, 30 m (OPERA DIST-ALERT), NASA GIBS
Where the evidence comes from.
Named public datasets and institutional records, each with its licence class. Sources by agreement are used only under their terms and never republished.
| Source | What it gives | Licence class |
|---|---|---|
| Society for Decision Making under Deep Uncertainty resources | Methods and case studies for robust and adaptive planning | Public, terms to check |
| Open-source optimisation tools such as Pyomo and JuMP | Modelling languages for stochastic and robust optimisation | Open source, BSD and MPL licences |
| EMA Workbench | Exploratory modelling and analysis toolkit | Open source, BSD licence |
| Operations research literature on stochastic programming | Methods and applications | Licence per publication |
| Published adaptive pathway plans, such as delta programmes | Applied adaptive planning | Public records, licence per government |
How optimisation under uncertainty 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.
Model, equations and assumptions
The model structure used for optimisation under uncertainty, the assumptions it makes and how each is tested.
Ri = f(Hi, Ei, Vi, Ci)hazard, exposure, vulnerability and coping capacityEAL = ∑k pk · Lkover events k with annual probability pkxt+1 = A xt + B ut + εtA carries the couplings, u the shock, ε the error| Assumption | Why it is made | How it is tested |
|---|---|---|
| Hazard and exposure are independent within an event | Keeps the loss integral tractable | Compare with a copula fit on joint records |
| Couplings are linear near the operating point | Lets shocks propagate through A | Perturb beyond the linear range and compare |
| Vulnerability curves transfer between places | Local curves are rarely available | Validate against observed losses where they exist |
- Inputs
- versioned datasets with provenance
- Outputs
- distributions, never single numbers
- Code
- released with the model card and tests
- Reproduction
- same data, code, environment and seed
Who decides, and what the evidence serves.
Systems Science and Modelling prepares evidence. The decisions below are taken by the authorities named, under their own rules, and never by the platform.
| Who decides | The question | Evidence this page serves |
|---|---|---|
| Infrastructure and resource planners | Which plans hold up across plausible futures | Robustness analyses; pathway designs |
| Analysts across Nexus platforms | Which optimisation approach suits their question | Method selection guides |
| Finance and audit bodies | Whether planning analyses considered uncertainty adequately | Analysis documentation |
Outputs this topic produces
- Method selection guides for planning under uncertainty
- Robustness and regret analyses
- Adaptive pathway designs with triggers
- Teaching material on optimisation under uncertainty
What experts ask about decisions under uncertainty.
- Is the aim to perform best on average, to avoid the worst outcomes, or to perform acceptably across many futures?
- Which uncertainties can be described with probabilities, and which cannot?
- Which decisions can be delayed, adapted or reversed as information arrives?
- How do trade-offs between objectives change across scenarios?
- What signals would indicate that a strategy needs to change?
Why optimal can be fragile.
Classical optimisation assumes a known model and known inputs. A strategy optimised for a single forecast can be finely tuned to that forecast and fragile if the future differs. In infrastructure planning, for example, a design optimised for one climate projection may fail under another.
Stochastic optimisation handles uncertainty described by probability distributions, seeking the best expected performance or managing risk measures. Robust optimisation seeks solutions that perform well across a set of possible conditions without probabilities.
Under deep uncertainty, when experts cannot agree on models or probabilities, methods such as robust decision making and adaptive pathways explore many futures, identify where strategies fail, and design plans that can change course when signposts are observed.
Methods and their limits.
- 01
Stochastic programming
Optimising expected outcomes over scenarios, using optimisation and operations research. Requires credible probabilities.
- 02
Robust optimisation
Optimising worst-case or regret across uncertainty sets. Can be conservative.
- 03
Exploratory modelling
Running models across many futures to find vulnerabilities, using decision analysis. Computationally demanding.
- 04
Adaptive pathways
Sequencing actions with triggers for change. Requires monitoring and institutional capacity.
These methods support judgement, they do not replace it. The choice of objectives and acceptable risks is a value choice for decision-makers.
How it is studied, and what the methods cannot say.
- 01Optimisation and operations researchProblem formulation guidance · Robust and stochastic comparisons · Solver benchmarkingApplied here
- 02Decision analysis under uncertaintyFraming the decision before the model · Value of information for modelsApplied here
- 03Uncertainty quantification and model validationUncertainty budgets · Surrogate models for expensive simulations · Credibility assessmentApplied here
- 04High-performance, cloud and edge computingEnsemble design within budgets · Workflow orchestration · Reproducible environmentsApplied here
Where this page’s references lead.
The bodies and documents this page is read against. Status and editions change; each link goes to the issuing body.
Questions and answers.
What is robust optimisation?
What is deep uncertainty?
What is an adaptive pathway?
Is a robust strategy always more expensive?
Does the platform choose strategies?
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