Modeling and Predicting Climate ChangeGlobal Warming: Do you believe?The dataSlide 4Predicted surface air temperature changePredicted change in annual mean precipitationComputational demandsCurrent resolution is not enoughSimulated precipitation as a function of resolutionA simulated hurricane in a climate modelSlide 11What is in a climate model?Technology limits us now.Q.Why are climate models so computationally intensive?An example of a source of computational burdenSpherical Coordinates (q,f)Slide 17Slide 18Spectral Transform MethodSlide 20Slide 21Slide 22Alternative formulationsIcosahedral meshA final creative meshPOP meshSlide 27A general modeling lesson from this example.ConclusionsEditorial commentAdditional climate model resourcesModeling and Predicting Climate ChangeMichael WehnerScientific Computing GroupComputational Research [email protected] Warming: Do you believe?Intergovernmental Panel on Climate Change 2001“An increasing body of observations gives a collective picture of a warming world and other changes in the climate system”“There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities”The dataFact: Global mean surface air temperature is increasing.Is this warming due to human factors?Can we quantify natural variability? Signal to noise.Do we understand the causes of this warming?What does the future portend?What will happen where I live?Modeling helps us address these questions.Predicted surface air temperature changeCCSM3.0Change_in_tas_decadal_mean_2090-19900 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NMIROC3.2_T42L200 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NMRI3.20 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70N-4.5-3.5-2.5-1.5-0.50.51.52.53.54.5PCM0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NPredicted change in annual mean precipitationCCSM3.0Fractional_change_daily_pr_decadal_mean0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NMIROC3.2_T42L200 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NMRI3.20 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70N-0.45-0.35-0.25-0.15-0.050.050.150.250.350.45PCM0 30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W70S50S30S10S10N30N50N70NComputational demandsHistorically, climate models have been limited by computer speed.1990 AMIP1: Many modeling groups required a calendar year to complete a 10 year integration of a stand alone atmospheric general circulation model. Typical grid resolution was T21 (64X32x10)2004 CCSM3: A fully coupled atmosphere-ocean-sea ice model achieves 5 simulated years per actual day. Typical global change simulation is 1 or 2 centuries.Control simulations are 10 centuries.Atmosphere is T85 (256X128x26)Ocean is ~1o (384X320x40)Current resolution is not enoughAtmosphereRegional climate change prediction will require horizontal grid resolution of 10km (3600X1800)Cloud physics parameterizations could exploit 100 vertical layersOceanMesoscale (~50km) eddies are thought to be crucial to ocean heat transport0.1o grid will resolve these eddies (3600X1800)Short stand-alone integrations are underway now.Ensembles of integrations are required to address issues of internal (chaotic) variability.Current practice is to make 4 realizations. 10 is better.Simulated precipitation as a function of resolutionDuffy, et al300km 75 km50 kmA simulated hurricane in a climate modelA simulated hurricane in a climate modelWhat is in a climate model?Atmospheric general circulation modelDynamicsSub-grid scale parameterized physics processesTurbulence, solar/infrared radiation transport, clouds.Oceanic general circulation modelDynamics (mostly)Sea ice modelViscous elastic plastic dynamicsThermodynamicsLand ModelEnergy and moisture budgetsBiologyChemistryTracer advection, possibly stiff rate equations.Technology limits us now. Models of atmospheric and ocean dynamics are subject to time step stability restrictions determined by the horizontal grid resolution.Adds further computational demands as resolution increasesCentury scale integrations will require of order 500Tflops (sustained).Current production speed is of order tens of Gflops in the US.Q.Why are climate models so computationally intensive?A. Lots of stuff to calculate!This is why successful climate modeling efforts are collaborations among a diverse set of scientists. Big science.But this computational burden has other causes.Fundamental cause is that interesting climate change simulations are century scale. Time steps are limited by stability criterion to minute scale.A lot of minutes in a century.An example of a source of computational burdenTask: Simulate the dynamics of the atmosphere The earth is a sphere (well, almost).Discretize the planet.Apply the equations of motionTwo dimensional Navier-Stokes equations + parameterization to represent subgrid scale phenomenaSpherical Coordinates ()Latitude-Longitude grid.Uniform in Non-uniform cell size.Convergent near the polesSingularSimple discretization of the equations of motion.Finite difference.Finite volume.Spherical Coordinates ()Two issues.Courant stability criterion on time stept < x/v x = grid spacing, v = maximum wind speedConvergence of meridians causes the time step to be overly restrictive.Accurate simulation of fluids through a singular point is difficult.Cross-polar flows will have an imprint of the mesh.Spherical Coordinates ()Solutions to time step restrictions.Recognize that the high resolution in the polar regions is false.Violate the polar Courant condition and damp out computational instabilities by filters.Works great, but…Maps poorly onto distributed memory parallel computers due to non-local communication.F`aijFiCommonly used, most notably by UK Met Office (Exeter) and the Geophysical Fluid Dynamics Laboratory (Princeton)Spectral Transform MethodThe most common solution to the “polar problem”Map the equations of motions onto spherical harmonics.M = highest Fourier wavenumberN(m) = highest associated Legendre polynomial, PResolution is
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