SAGES Scottish Alliance for Geoscience, Environment & Society Modelling Climate Change Prof. Simon Tett, Chair of Earth System Dynamics & Modelling: The University of Edinburgh
Climate Modelling Climate modelling has long history first attempts made in 1950 s. Developed from numerical weather prediction Take physical laws and apply them to atmospheric motions. But now very complex. Aim of this lecture is to give you some flavour for issues. Main focus is on atmospheric modelling. Key message: Modelling approach is bottom up and emergent behaviour of model is what we are interested in.
Climate is a Multi-scale problem From Bob Harwood
Modelling the Climate System Main Message: Lots of things going on! Karl and Trenberth 2003
68 100 From Kevin E. Trenberth, NCAR
The Components of the Climate System Atmosphere: Volatile turbulent fluid, strong winds, Chaotic weather, clouds, water vapor feedback Transports heat, moisture, materials etc. Heat capacity equivalent to 3.2 m of ocean Ocean: 70% of Earth, wet, fluid, high heat capacity Kevin E. Trenberth
The Components of the Climate System: Cont. Land: Small heat capacity, small mass involved (conduction) Water storage varies: affects sensible vs latent fluxes Wide variety of features, slopes, vegetation, soils Mixture of natural and managed Vital in carbon and water cycles, ecosystems Ice: Kevin E. Trenberth Huge heat capacity, long time scales
The Atmosphere
Meteorology is (roughly) fluid dynamics on rotating sphere. DV 1 2 V = p g a F f Dt ρ D = V Dt t ρ ρv =0 t Equations of motion thermodynamics Continuity moisture radiation Continuity
Numerical Solutions No (known) analytical solutions to these equations. (Maximum Entropy Production???). Not surprising think of range of phenomenon in weather. So discretise equations of motion on a grid. (Easy to say; hard to do!) Lots of ways of doing this but two major ones at the moment. Represent as truncated sum of spherical harmonics Or as values at points/averaged over regular grid.
Representing the fields: Gridpoint models Represent space as a grid of regular (in long/latt co ords)
Modelling Global Climate Vertical exchange between layers of momentum, heat and moisture 60 N 15 W Horizontal exchange between columns of momentum, heat and moisture 3.75 2.5 Vertical exchange between layers of momentum, heat and salts by diffusion, convection and upwelling Vertical exchange between layers by diffusion and advection 11.25 E 47.5 N Orography, vegetation and surface characteristics included at surface on each grid box
Derivatives Xi 1,j1 Xi,j1 Xi1,j1 Xi 1,j Xi,j Xi1,j Xi 1,j 1 Xi,j 1 Xi1,j 1 d X i 1, j X i 1, j = dx 2x d X i, j 1 X i, j 1 = dy 2y
Representing the fields: Spectal Models Represent fields as truncated sum of spherical harmonics Derivatives easy to calculate (from analytical expression) and PDE s turn into ODE s Non linear terms become computationally hard though. So do linear & diffusive terms in spectral space then transform to grid point space to compute advective terms.
Schematic Grid point space Advection Spectral transform Spectral space Grid point space Inverse Spectral transform Linear calculations Spectral space
Computing advective terms
Eulerian vs Lagragian view of a fluid Eulerian view. Sit at a point and watch the fluid move past. Lagrangian view. Sit on a parcel of fluid and watch the world move past. For pure advection in a Lagrangian view parcel properties stay constant. DC C = V C=0 Dt t
Eulerian DC C = V C=0 Dt t C = V C t For each grid point compute divergence and take dot product with velocity field.
Semi-Lagrangian -- now used by most atmospheric models For each grid point work out trajectory and where values came from. These places not on grid so need to interpolate values.
New approaches adaptive grids ICOM Imperial College Ocean Model. Grid resolution varies and changes in time
Further Reading ECMWF lecture notes: http://www.ecmwf.int/newsevents/training/rcou ICOM http://amcg.ese.ic.ac.uk/index.php?title=icom
Sub-grid. Recall equations of motion Split into large scale average and residual. ' ' V V = V V V V = V V V ' V ' {V ' V V V ' } ' ' = V V V V Get large scale terms that result from sub grid scale motions
Parameterisation Like the closure problem for fluid dynamics. Key processes: Convection (which involves latent heat release from water vapour condensing) Clouds in general. Boundary layers. Need to simplify radiation calculations into relatively small number of broad bands and assume radiation only goes up and down. Can verify calculations through comparison with line by line calculations. Friction Many specialists work in each area. An atmospheric model (Weather) is a complex piece of software. Numerical methods for dynamics are complex as are parameterisations.
Parameterized Processes Slingo From Kevin E. Trenberth, NCAR
What are we trying to parameterize? What is there How we parameterise
(Atmospheric) Modelling overview Dynamical core solve large scale flow. Linear terms Advection Parameterisations. Act on columns so each column can be treated independently. Key for climate Codes run on parallel computers but don t scale well to hundreds of CPU s Climate problem doesn t have very high resolution as need to run ensembles and for decades to centuries.
Feedbacks Act to amplify (or decrease) warming from changes in CO2 and other greenhouse gases. Blackbody warmer planet emits more radiation. (Negative feedback) Water vapour warmer atmosphere can store more water vapour. Water vapour absorbs IR so is a GHG. Most important in the upper troposphere Warmer world will have more moisture in the atmosphere and so will trap more heat. ve feedback. Clouds ve feedback trap IR radiation ve feedback reflect back solar radiation. Ice/Albedo feedback. Ice is white and reflects lots of solar energy back to space. Melt ice and more solar radiation absorbed which in turn warms the climate..
Ocean Models Modelled Ocean circulations driven by: Wind stress Density variations (colder and saltier water is more dense) Thermohaline circulation driven by sinking of cold, salty water
Land Surface Models Wind Solar radiation Thermal radiation Heat Air temperature and humidity Evaporation CO2 CH4 Vegetation Snow Soil moisture Lakes
Model resolution increasing with time.
Early Visions
More recent visions Cray Y MP ~ 1990 HECToR Edinburgh 2007
Moore s Law and Supercomputers Doubling time of peak supercomputer performance is about 18 months. Number of transistors doubles every 2 years. But as they get smaller they go faster.
Computational requirements Computational requirements scale as (1/resolution)4. Decrease resolution means increasing the number of gridboxes in east/west, North/south and vertically as well as reducing the time step proportionally. Improved algorithms can change the constant of proportionality. So doubling the resolution increases the computational requirement by 16. Given increase in super computer performance could do the same kind of simulations as today at ½ the resolution in 10 years time
Projections of Future Changes in Climate Best estimate for low scenario (B1) is 1.8 C (likely range is 1.1 C to 2.9 C), and for high scenario (A1FI) is 4.0 C (likely range is 2.4 C to 6.4 C).
Projections of Future Changes in Climate Projected warming in 21st century expected to be greatest over land and at most high northern latitudes and least over the Southern Ocean and parts of the North Atlantic Ocean
Projections of Future Changes in Climate Precipitation increases very likely in high latitudes Decreases likely in most subtropical land regions
Some thoughts on Informatics issues Climate models getting increasingly complex and becoming Earth System models. So represent many more processes and require involvement from communities that are non operational. How to bring that software together in a useful system. How to persuade academics to produce high quality code so that others can build on their work. Social changes (metric of academic success needs to be more than a journal paper) Technological support infrastructure to support distributed software and scientific development.
Model development Earth System models are hugely complex bits of software Don t know what the outcome should be If we did then we wouldn t be building the system. But models need tuning where parameters in the various components are adjusted to give reasonable simulation of today's climate. Tuning/building Models is a very hard and laborious. Are there good ideas in the informatics community on how to do this better?
Computational issues How to effectively use massively parallel computers. Earth System models need to be run for decades to centuries with relatively low resolution. So tend not to scale very well on very large parallel computers Same issue on multi core chips where issue is memory bandwidth. Is the answer specialist Earth System computing chips???? What about data management? And data distribution see http://www pcmdi.llnl.gov/ipcc/about_ipcc.php for a good example
Summary and Conclusions Models complex but built bottom up. Uncertainties arise from imperfect knowledge of small scale processes and how to model them in terms of large scale flow. I ve mainly discussed atmospheric models Dynamical core physics. Lots of informatics issues.