Earth and climate

Earth system models

Atmosphere, ocean, sea ice, land and the carbon cycle coupled on a global grid and run for centuries.

Question it answers: How warm does the planet get under a given path of emissions?

Leaves out: Clouds are still represented by parametrisations, the single largest source of disagreement between models.

Runs on: about 10¹⁷ FLOPS rough a large share of a national supercomputer, for months.Since: 1969 Manabe and Bryan's first coupled ocean-atmosphere climate model.In the simulations tree: Coupled ocean-atmosphere

Palaeoclimate

The same models run over ice ages and deep time, with different continents, orbits and atmospheres.

Question it answers: What set off the ice ages, and what does the past say about how sensitive climate is?

Leaves out: Ancient coastlines, ice and vegetation are reconstructed from sparse evidence, then treated as known inputs.

Runs on: about 10¹⁷ FLOPS rough similar to a modern climate run, a supercomputer share for months.Since: 1977 Manabe and Hahn's first GCM simulation of ice-age climate.

Ice sheets and sea level

Glaciers and ice sheets flowing, melting and calving into the sea.

Question it answers: How fast could the ice sheets add to sea level this century?

Leaves out: The physics of how ice suddenly fractures and slides is still poorly captured.

Runs on: about 10¹⁵ FLOPS rough a university cluster, days to weeks per simulated century.Since: 1976 Mahaffy's early finite-difference computer model of an ice sheet.

Integrated assessment models

Energy, economy, land use and climate linked in one model, used to compare policy pathways.

Question it answers: What mix of energy and land use keeps warming below a given limit, and at what cost?

Leaves out: Reduces the whole economy and climate to a handful of equations, so the answer depends heavily on the discount rate chosen.

Runs on: about 10¹² FLOPS rough a laptop; a full run takes seconds to minutes.Since: 1992 Nordhaus's DICE model, the first widely used climate-economy model.

Regional climate downscaling

A global climate model's coarse output used to drive a finer regional one over one country or mountain range.

Question it answers: What does global warming actually mean for the weather in this valley?

Leaves out: Inherits the biases of whichever global model it is nested inside, just at higher resolution.

Runs on: about 10¹⁶ FLOPS rough a national cluster, weeks for one regional projection.Since: 1989 early nested regional climate models run over a limited area.

Solar geoengineering

Climate models run with a deliberate intervention added, such as reflective particles injected into the upper atmosphere, to see what it would change.

Question it answers: Could deliberately reducing incoming sunlight offset warming, and what side effects would it have?

Leaves out: No intervention of this kind has been carried out at scale, so every result depends on how well the model represents aerosols never observed under such deployment.

Runs on: about 10¹⁷ FLOPS rough a large share of a national supercomputer, for months.Since: 1992 early climate model experiments testing a hypothetical volcanic-style intervention.

World-Earth models

Climate models coupled to simple dynamic representations of human behaviour, so that emissions, policy and social change respond to the state of the planet.

Question it answers: How do social tipping and climate feedbacks interact over centuries?

Leaves out: Behavioural rules are hypotheses, and spatial climate detail is coarse.

Runs on: about 10¹⁴ FLOPS rough Reduced-complexity models run in large ensemblesSince: 2018 Earth system modelling with complex dynamic human societies: the copan:CORE framework (2018) source

Global cloud-resolving models

Atmosphere models whose grid is fine enough, a few kilometres, to represent deep convection explicitly across the whole globe.

Question it answers: Can tropical cloud systems be simulated directly instead of through parameters?

Leaves out: Runs are short, and turbulence and cloud microphysics are still approximated.

Runs on: about 10¹⁸ FLOPS rough Weeks of simulated time on the largest machinesSince: 2007 A Madden-Julian oscillation event realistically simulated by a global cloud-resolving model (2007) sourceIn the simulations tree: Global cloud-resolving model

Superparameterisation

A small cloud-resolving model is embedded inside each column of a coarse global one to replace the usual convection scheme.

Question it answers: Can explicit cloud physics improve a climate model without a full global fine grid?

Leaves out: The embedded models are small and do not talk to neighbouring columns.

Runs on: about 10¹⁶ FLOPS rough Embedded 2D cloud models multiply cost many timesSince: 2001 Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (2001) source

Extreme-event attribution

Large ensembles of climate runs with and without human influence give the odds of a specific heatwave, flood or storm in each world.

Question it answers: How much did human emissions change the chance of this particular event?

Leaves out: Results depend on how well the model reproduces the event type at that scale.

Runs on: about 10¹⁷ FLOPS rough Hundreds to thousands of ensemble membersSince: 2004 Human contribution to the European heatwave of 2003 (2004) source

Volunteer-computed perturbed-physics ensembles

Thousands of copies of a climate model, each with slightly different physical parameters, run on donated home computers.

Question it answers: How wide is the range of warming consistent with uncertain model physics?

Leaves out: Model structure is fixed; only parameters are varied.

Runs on: about 10¹⁷ FLOPS rough Tens of thousands of model runsSince: 2005 Uncertainty in predictions of the climate response to rising levels of greenhouse gases (2005) source

Initial-condition large ensembles

A single climate model is run dozens of times from slightly different starts to separate forced change from internal variability.

Question it answers: What part of a regional trend is the climate's own noise?

Leaves out: It captures variability within one model, not differences across them.

Runs on: about 10¹⁸ FLOPS rough Dozens of centuries-long coupled runsSince: 2015 The CESM Large Ensemble Project (2015) source

Learned climate emulators

A neural network trained on climate-model output steps the atmosphere forward for decades or centuries at a tiny fraction of the cost.

Question it answers: Can a trained surrogate reproduce multi-decade climate statistics quickly?

Leaves out: It inherits the biases of its training model and may fail outside the climates it saw.

Runs on: about 10¹⁵ FLOPS rough Training on model archives, then cheap long runsSince: 2023 A fast, skillful learned global atmospheric model for climate prediction (2023) source

Earth-system digital twins

Continuously updated, high-resolution models of the planet, fed by observations and built to answer what-if questions for users.

Question it answers: What would happen to a region if a given decision or event occurred?

Leaves out: The twin is only as faithful as its models and data, and interactive scenarios are limited.

Runs on: about 10¹⁹ FLOPS rough Km-scale global models plus assimilationSince: 2021 The digital revolution of Earth-system science (2021) source

Radiative-convective climate model

A single column of atmosphere in balance between radiation and convection, used to find how much a planet warms when carbon dioxide or humidity changes.

Question it answers: How much does a column of air warm when its greenhouse gas doubles?

Leaves out: It has no winds, clouds or ocean transport, so it gives a reference warming rather than a forecast.

Runs on: about 10⁴ FLOPS rough a one-dimensional column, quick on a laptop.Since: 1967 Manabe and Wetherald's thermal equilibrium of the atmosphere with a given distribution of relative humidity. source

Energy-balance climate model

Earth reduced to latitude bands that absorb and emit heat and trade it by transport, enough to show ice-albedo feedback and tipping between climate states.

Question it answers: Could a runaway of ice cover freeze the whole planet?

Leaves out: The picture ignores dynamics and weather, so it informs but does not forecast.

Runs on: about 10³ FLOPS rough a handful of equations; seconds on any computer.Since: 1969 Sellers's global climatic model based on the energy balance of the earth-atmosphere system. source

Dynamic global vegetation and carbon-cycle modelling

Plants, soils and their carbon exchange simulated across the globe, with vegetation types competing and shifting as climate changes.

Question it answers: How much carbon will the land absorb or release as the climate warms?

Leaves out: Plant types are lumped into a few functional classes, and nutrient and disturbance feedback are crude.

Runs on: about 10¹⁴ FLOPS rough multi-century global runs, often on a coarse grid.Since: 1996 Foley and colleagues' integrated biosphere model of land surface processes, terrestrial carbon balance and vegetation dynamics. source

Coupled carbon-cycle and climate simulation

A climate model with the land and ocean carbon cycle inside it, so warming can change how much the Earth takes up and feed back on itself.

Question it answers: Will warming turn land and ocean from absorbers of carbon into sources?

Leaves out: Land carbon response varies widely between models because of soil and vegetation assumptions.

Runs on: about 10¹⁷ FLOPS rough multi-century coupled climate runs on a supercomputer.Since: 2000 Cox, Betts, Jones, Spall and Totterdell's acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model. source

Ocean ecosystem and biogeochemistry modelling

Nutrients, plankton and detritus advected and cycled through the ocean, to predict productivity and the carbon carried to the deep.

Question it answers: How much carbon does ocean life carry into the deep sea?

Leaves out: Plankton groups are a few lumped compartments with fitted rates.

Runs on: about 10¹⁵ FLOPS rough a biogeochemical module within an ocean general circulation model.Since: 1990 Fasham, Ducklow and McKelvie's nitrogen-based model of plankton dynamics in the oceanic mixed layer. source

Learned subgrid parameterisation

A neural network trained on a cloud-resolving model replaces the hand-written rules for storms and clouds that are too small for a coarse global climate model.

Question it answers: Can a coarse climate model get small-scale clouds right by learning them from a finer one?

Leaves out: The network can drift into unstable or unphysical states when the climate moves outside the conditions it was trained on.

Runs on: about 10¹⁶ FLOPS rough training on a small set of fine simulations, then cheap use inside the climate model.Since: 2018 Rasp, Pritchard and Gentine's deep-learning representation of subgrid processes in a climate model. source

Numerical weather prediction

Today’s observed atmosphere stepped forward hours to days, usually as an ensemble of slightly different starting points.

Question it answers: Will it rain here on Thursday, and how sure are we?

Leaves out: Skill collapses past about ten days, however fine the grid.

Runs on: about 10¹⁷ FLOPS rough a national weather centre's supercomputer, a few percent of it for hours.Since: 1950 Charney, Fjortoft and von Neumann's first numerical forecast.In the simulations tree: First computer forecast

Machine-learned weather

Neural networks trained on decades of past weather, producing forecasts in seconds rather than hours.

Question it answers: Can a learned emulator forecast as well as the physics it was trained on?

Leaves out: Learns the patterns in past weather, so it struggles with the kind of extreme event it has not seen before.

Runs on: about 10¹⁴ FLOPS rough a single high-end GPU; forecasts in seconds rather than hours.Since: 2022 first learned weather models to match physics-based forecast skill.

Tropical cyclones

Hurricanes and typhoons at high resolution: their tracks, intensity and rainfall.

Question it answers: Where will the storm make landfall, and how strong will it be?

Leaves out: The eye and eyewall are still smaller than most models can properly resolve.

Runs on: about 10¹⁶ FLOPS rough a national forecasting centre's cluster, run for each active storm.Since: 1969 Ooyama's early numerical model of a hurricane's development.

Air quality and dispersion

Pollutants, smoke and volcanic ash carried, mixed and chemically transformed by the wind.

Question it answers: Where does the plume go, and is the air safe to breathe or fly through?

Leaves out: Emissions inventories, the input the whole forecast depends on, are often out of date or estimated.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, hours per pollution event.Since: 1970 early computerised Gaussian plume models for smokestack pollution.

Seasonal forecasting

An ensemble of climate-length model runs, started from today's ocean and atmosphere, aimed at the odds for a whole season rather than any single day.

Question it answers: Will this winter be warmer or wetter than average?

Leaves out: Cannot say what the weather will be on any given day, only how the odds are shifted.

Runs on: about 10¹⁷ FLOPS rough a national forecasting centre's supercomputer, an ensemble of runs each season.Since: 1986 early dynamical seasonal forecasts using ocean-coupled models.

Severe convective storms

A single thunderstorm or supercell, resolved down to the scale of its updraft and downdraft, to see whether it spins up a tornado or drops large hail.

Question it answers: Will this storm produce a tornado, and where?

Leaves out: Needs a grid fine enough to see a tornado, which is too expensive to run everywhere a storm could form.

Runs on: about 10¹⁶ FLOPS rough a national cluster, hours for one storm at very high resolution.Since: 1975 early three-dimensional computer models of a single thunderstorm.

Generative ensemble weather forecasting

A diffusion model samples many plausible weather futures for the next two weeks, giving probabilities for each variable at global scale.

Question it answers: Can a learned model supply calibrated forecast uncertainty cheaply?

Leaves out: It is tied to reanalysis data and offers no physical guarantee on rare extremes.

Runs on: about 10¹⁶ FLOPS rough Training on decades of reanalysis, minutes per ensemble memberSince: 2023 GenCast: diffusion-based ensemble forecasting for medium-range weather (2023) source

Ensemble weather forecasting

A forecast run many times from slightly different starting states, so the spread shows how uncertain the weather is and how likely each outcome is.

Question it answers: How confident can a weather forecast be, and what could happen instead?

Leaves out: Starting-state perturbations only partly capture model error, so the spread is often too narrow.

Runs on: about 10¹⁶ FLOPS rough dozens of global forecasts every day, each a large run.Since: 1974 Leith's theoretical skill of Monte Carlo forecasts. source

Atmospheric reanalysis

A fixed modern forecast model run over decades of past observations, blending them into a consistent, gap-free record of the atmosphere.

Question it answers: What were the winds, temperatures and pressures at every place and time in the past?

Leaves out: Changes in the observing system over time leave artificial trends in the record.

Runs on: about 10¹⁷ FLOPS rough decades of assimilation cycles on a supercomputer.Since: 1996 Kalnay and colleagues' NCEP/NCAR 40-year reanalysis project. source

Atmospheric boundary-layer large-eddy simulation

The lowest kilometre of the atmosphere, where turbulent eddies mix heat, moisture and pollutants, with the large eddies resolved and the small ones modelled.

Question it answers: How do turbulent eddies carry heat and moisture upward from the ground?

Leaves out: Surface exchange and sub-grid mixing are parametrised, which limits accuracy near the ground.

Runs on: about 10¹⁴ FLOPS rough a few kilometres of domain at tens of metres resolution.Since: 1972 Deardorff's numerical investigation of neutral and unstable planetary boundary layers. source

Global storm-resolving simulation

A whole-planet atmosphere model at a few kilometres of resolution so that thunderstorm clusters and tropical storms appear without a convection parametrisation.

Question it answers: What does the atmosphere do when storms are resolved instead of approximated?

Leaves out: Cloud microphysics and turbulence below a few kilometres remain parametrised, and runs are too short to study climate.

Runs on: about 10¹⁹ FLOPS rough weeks on the largest machines for a few simulated months.Since: 2008 Satoh and colleagues' nonhydrostatic icosahedral atmospheric model for global cloud-resolving simulations. source

Mineral dust emission and transport

Wind lifting desert dust, carrying it across seas and depositing it, to find its effect on radiation, ocean nutrients and air quality.

Question it answers: How much desert dust enters the air and where does it go?

Leaves out: Emission thresholds depend on soil and surface properties that are poorly mapped.

Runs on: about 10¹⁴ FLOPS rough a dust module inside an atmosphere model over years.Since: 1994 Tegen and Fung's model of mineral dust in the atmosphere: sources, transport and optical thickness. source

Urban surface energy-balance modelling

Streets, roofs and walls treated as a canyon exchanging heat, moisture and momentum with the air, to predict urban heat islands and building cooling needs.

Question it answers: Why is a city hotter than the countryside around it?

Leaves out: Cities are reduced to idealised canyons, so building detail and traffic heat are approximated.

Runs on: about 10¹² FLOPS rough a canyon scheme within an atmospheric model over a metropolitan area.Since: 2000 Masson's physically-based scheme for the urban energy budget in atmospheric models. source

Thermosphere and ionosphere modelling

The upper atmosphere at 100 to 600 kilometres, heated by sunlight and particles, with winds and electric currents that change satellite drag and radio signals.

Question it answers: How does solar activity change the upper atmosphere and radio propagation?

Leaves out: The lower boundary and the energy from above are imposed from sparse data.

Runs on: about 10¹³ FLOPS rough coupled upper-atmosphere simulation over days of space weather.Since: 1988 Roble, Ridley, Richmond and Dickinson's coupled thermosphere/ionosphere general circulation model. source

Ocean circulation

Currents, eddies, heat and salt moving through the world’s oceans.

Question it answers: Could the great overturning currents of the Atlantic slow down?

Leaves out: The eddies that mix heat and carbon are mostly smaller than the grid, so their effect must be parametrised.

Runs on: about 10¹⁶ FLOPS rough a large cluster, weeks for a multi-decade run.Since: 1969 Bryan's first computer model of the global ocean circulation.

Tsunamis and storm surge

Waves raised by earthquakes or storms, crossing the ocean and running up onto the coast.

Question it answers: How high will the water reach, and which streets flood first?

Leaves out: Coastal defences and drainage are usually simplified far below the resolution of the run-up itself.

Runs on: about 10¹³ FLOPS rough a workstation; minutes for a coastal warning run.Since: 1969 Aida's early numerical experiments modelling a tsunami.

Rivers and floods

Rain falling on a catchment, soaking in or running off into streams, rivers and floodplains.

Question it answers: How big a flood does this storm make, and where?

Leaves out: Soil and land use are averaged over the catchment, hiding the one field or gully that actually floods.

Runs on: about 10¹² FLOPS rough a laptop; a catchment run takes minutes.Since: 1966 Crawford and Linsley's Stanford Watershed rainfall-runoff model.

Groundwater

Water moving slowly through soil and rock in aquifers.

Question it answers: How long can we pump this aquifer before the wells run dry?

Leaves out: Subsurface rock and soil properties are mapped from boreholes hundreds of metres apart, so most of the aquifer is inferred.

Runs on: about 10¹² FLOPS rough a laptop or workstation; minutes to hours per aquifer.Since: 1968 Pinder and Bredehoeft's early finite-difference aquifer model.

Sea ice

Floating ice on the ocean surface, cracking, ridging, drifting and melting under wind, waves and warmth.

Question it answers: How much of the Arctic Ocean will still be covered in ice by the end of summer?

Leaves out: Treats a heterogeneous field of cracked, ridged floes as a smooth continuous sheet.

Runs on: about 10¹⁵ FLOPS rough a university or national cluster, weeks coupled to an ocean run.Since: 1969 early computer models of drifting Arctic sea ice.

Ocean wave forecasting

Wind blowing over open water, generating and steering swell and chop, tracked to forecast wave height and direction for ships and coasts.

Question it answers: How rough will the sea be here tomorrow?

Leaves out: Performs poorly on the steepest, breaking crests, which matter most for maritime safety.

Runs on: about 10¹⁵ FLOPS rough a national forecasting centre's cluster, run several times a day.Since: 1956 early numerical wave forecasting following wartime swell-prediction methods.

Flood inundation modelling

Water from a river or storm spreading across a floodplain on a terrain grid, to map depth and extent for insurance and planning.

Question it answers: Which streets and fields go under water in a flood?

Leaves out: Terrain accuracy and the inflow hydrograph dominate the error, not the numerics.

Runs on: about 10¹² FLOPS rough two-dimensional shallow-water or raster models of a river basin.Since: 2000 Bates and De Roo's simple raster-based model for flood inundation simulation. source

Coastal and estuarine circulation modelling

Tides, rivers and winds moving water, salt and sediment through bays and estuaries on a terrain-following grid.

Question it answers: How do tides and rivers mix water along a coast?

Leaves out: Small-scale mixing and bathymetry errors limit the accuracy near shore.

Runs on: about 10¹² FLOPS rough three-dimensional regional model with year-long runs.Since: 1987 Blumberg and Mellor's description of a three-dimensional coastal ocean circulation model. source

Marine debris and Lagrangian drift modelling

Virtual particles carried by simulated or observed ocean currents to find where floating plastic, oil or larvae go.

Question it answers: Where do floating plastics from a coast end up?

Leaves out: Windage, wave drift and the sinking or fragmenting of particles are poorly known.

Runs on: about 10¹² FLOPS rough millions of particles advected through a year of ocean flow.Since: 2012 van Sebille, England and Froyland's origin, dynamics and evolution of ocean garbage patches from observed surface drifters. source

Petroleum and gas reservoir simulation

Oil, gas and water flowing through the pores of a rock reservoir toward wells, to plan drilling and predict how much can be recovered.

Question it answers: How much oil will a field yield, and where should the wells go?

Leaves out: Rock properties between wells are inferred from sparse data, so uncertainty is usually larger than the numerics.

Runs on: about 10¹³ FLOPS rough multiphase flow in a geological model of millions of cells.Since: 1955 Peaceman and Rachford's numerical solution of parabolic and elliptic differential equations, the basis of early reservoir simulators. source

Glacial isostatic adjustment and sea-level fingerprints

The Earth's crust rebounding as ice sheets melt and the oceans redistributing, to predict regional sea-level change and the gravity field.

Question it answers: Why does sea level fall in some places as the ice melts and rise in others?

Leaves out: Mantle viscosity beneath the plates is poorly constrained and varies from region to region.

Runs on: about 10¹² FLOPS rough viscoelastic Earth models solved on a sphere.Since: 1976 Farrell and Clark's calculation of postglacial sea level. source

Geological carbon-dioxide storage simulation

Injected carbon dioxide spreading, rising and dissolving in a saline rock formation, with trapping by caprock, capillarity and mineral reactions followed over centuries.

Question it answers: Will the gas stay underground, and where does it go?

Leaves out: The rock below the borehole is known only from a few wells and surveys, so permeability and faults are guessed with wide uncertainty.

Runs on: about 10¹⁵ FLOPS rough weeks on a cluster for a basin-scale model over thousands of years.Since: 2002 The Lawrence Berkeley intercomparison of numerical codes for geologic disposal of CO2. source

Reactive transport in the subsurface

Water carrying chemicals through rock or soil while minerals dissolve, precipitate and exchange ions, solved together with the flow.

Question it answers: How do the chemistry and the plumbing of an aquifer or repository change each other over time?

Leaves out: Reaction rates measured in a laboratory are applied to rock whose reactive surface area in the ground is unknown.

Runs on: about 10¹⁴ FLOPS rough days on a cluster for a three-dimensional field site.Since: 1985 Lichtner's continuum model for coupled chemical reactions and mass transport in hydrothermal systems. source

Mantle convection and plate tectonics

Hot rock creeping inside the planet over hundreds of millions of years, carrying the plates on top.

Question it answers: Why does Earth have plate tectonics when its neighbours do not?

Leaves out: Runs millions of simulated years at once, so it cannot also show a single earthquake.

Runs on: about 10¹⁵ FLOPS rough a university cluster, weeks for one long run.Since: 1974 McKenzie, Roberts and Weiss's first numerical mantle convection model.

Earthquakes and seismic waves

Faults rupturing and the waves spreading through the crust to shake the ground.

Question it answers: How hard will this city shake if that fault breaks?

Leaves out: The rupture's starting point and the fault's exact roughness are still assumed rather than known in advance.

Runs on: about 10¹⁶ FLOPS rough a national or university cluster, days for a large fault rupture.Since: 1968 Alterman and Karal's early finite-difference model of seismic waves.

Volcanic eruptions and lava flows

Magma rising, erupting and flowing downhill as lava, ash or fast-moving hot clouds.

Question it answers: Which villages lie in the path if the volcano erupts?

Leaves out: Cannot predict when an eruption starts, only what happens once one already has.

Runs on: about 10¹³ FLOPS rough a workstation or small cluster, hours per scenario.Since: 1980 early computer models of lava flowing downhill from a vent.

Landscape evolution

Rivers cutting valleys, hillslopes creeping and coasts eroding over thousands to millions of years.

Question it answers: How did this landscape get its shape?

Leaves out: Compresses millions of years into a run, so any single storm or rockfall is smoothed away.

Runs on: about 10¹³ FLOPS rough a workstation; days for a million-year landscape.Since: 1991 Willgoose and colleagues' early computed landscape evolution model.

Wildfire spread

Fire moving across fuel, terrain and wind, cell by cell.

Question it answers: Where will the fire front be in six hours?

Leaves out: Wind, the biggest driver of a real fire's behaviour, is usually simplified to a steady average.

Runs on: about 10¹³ FLOPS rough a workstation or laptop; minutes for a spreading fire front.Since: 1972 Rothermel's fire-spread equations, soon computerised for forecasting.

Run the interactive model

Landslides and debris flows

A slope of soil, rock or mud failing and moving downhill, tracked as it accelerates, spreads out and buries the terrain below.

Question it answers: How far will this slope travel once it fails, and how fast?

Leaves out: The moment a slope actually fails is still harder to predict than what happens once it has.

Runs on: about 10¹³ FLOPS rough a workstation or small cluster, hours per slope scenario.Since: 1980 early computer runout models for a failing slope.

Physics-based seismic hazard

Earthquake rupture and wave propagation simulations replace empirical attenuation rules to give shaking at each site.

Question it answers: How strongly would the ground shake here for each possible rupture?

Leaves out: Needs a known velocity model, and high frequencies are hard to resolve.

Runs on: about 10¹⁸ FLOPS rough Many rupture scenarios, each a 3D wave simulationSince: 2010 CyberShake: a physics-based seismic hazard model for Southern California (2010) source

Geodynamo simulation

Convection of liquid iron in Earth's core generating and sustaining the magnetic field, including its random reversals.

Question it answers: How does Earth's core make its magnetic field, and why does it flip?

Leaves out: Viscosity and conductivity values are far from real, so the flow is much smoother than inside Earth.

Runs on: about 10¹⁸ FLOPS rough months on a supercomputer for a dynamo that still runs far from Earth-like conditions.Since: 1995 Glatzmaier and Roberts's three-dimensional self-consistent simulation of a geomagnetic field reversal. source

Full-waveform seismic inversion

Seismic waves run repeatedly through a trial Earth model, which is adjusted until synthetic and recorded waves match, to image rock structure.

Question it answers: What does the rock beneath us look like, as seen by the waves that crossed it?

Leaves out: The inversion can lock onto wrong solutions unless the starting model is close.

Runs on: about 10¹⁷ FLOPS rough thousands of wave simulations inside an optimisation loop.Since: 1984 Tarantola's inversion of seismic reflection data in the acoustic approximation. source

Spectral-element seismic wave propagation

Earthquake waves propagating through a three-dimensional model of the crust or the whole Earth with high-order elements that follow topography and layers.

Question it answers: How do waves travel through the real, lumpy Earth?

Leaves out: Earth models are uncertain in small-scale structure and attenuation, so short periods are less reliable.

Runs on: about 10¹⁷ FLOPS rough whole-Earth runs resolving periods of a few seconds.Since: 1998 Komatitsch and Vilotte's spectral element method for seismic response of two- and three-dimensional structures. source

Earthquake-cycle simulation

A fault loaded slowly by plate motion, with friction that sticks and slips, simulated through many cycles of quiet buildup and sudden rupture.

Question it answers: How do earthquakes repeat on a fault over centuries?

Leaves out: The friction law is laboratory-derived and extrapolated to depths and speeds never measured.

Runs on: about 10¹⁴ FLOPS rough rate-and-state fault cycles over thousands of years.Since: 1986 Tse and Rice's crustal earthquake instability in relation to the depth variation of frictional slip properties. source

Stochastic earthquake-catalogue models

Synthetic earthquake sequences generated from a statistical model in which each shock raises the chance of aftershocks, to forecast clustering and hazard.

Question it answers: How likely are aftershocks after a large earthquake?

Leaves out: The model captures statistical clustering but has no physics of fault stress.

Runs on: about 10⁶ FLOPS rough stochastic catalogues cost little, and a long ensemble runs on a workstation.Since: 1988 Ogata's statistical models for earthquake occurrences and residual analysis for point processes. source

Land-surface model

The exchange of water, heat and carbon dioxide between soil, plants and air, written as a surface component for atmosphere and climate models.

Question it answers: How do plants and soil control the heat and water moving between ground and air?

Leaves out: Vegetation is described by a few parameters per cell, and water movement in soil is highly simplified.

Runs on: about 10¹² FLOPS rough a one-dimensional column per grid cell inside climate models.Since: 1986 Sellers, Mintz, Sud and Dalcher's simple biosphere model for use within general circulation models. source

Coupled fire and atmosphere models

A fire front and the wind it creates are solved together, so heat from the fire pulls air in, changes the flow and in turn alters how the fire spreads and throws embers and smoke.

Question it answers: How does a fire reshape the wind that drives it?

Leaves out: Combustion and fuel are represented by simple rate laws, so extreme behaviour such as crown fires and spotting is only roughly captured.

Runs on: about 10¹⁴ FLOPS rough days on a cluster for one large fire at tens-of-metres resolution.Since: 1996 Clark, Jenkins and Coen's coupled atmosphere-fire model of fire-line dynamics. source