Transcript Slide 1
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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
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• 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.
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Climate is a Multi-scale problem
From Bob Harwood
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Modelling the Climate System
Main Message: Lots of things going on!
Karl and Trenberth 2003
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From Kevin E. Trenberth, NCAR
The Components of the Climate System
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• 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 –Stores, moves heat, fresh water, gases, –Adds delay of 10 to 100 years to response time Kevin E. Trenberth
The Components of the Climate System: Cont.
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• 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: –Huge heat capacity, long time scales (conduction) –High albedo: ice-albedo feedback –Fresh water, changes sea level – Antarctica 65 m (WAIS 4-6m), Greenland 7m, other glaciers 0.35m
Kevin E. Trenberth
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The Atmosphere
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Meteorology is (roughly) fluid dynamics on rotating sphere.
D
V
2
Ω
V
Dt
1
p
g a
F f
D Dt
t
V
+
t
(
V
) 0 Equations of motion + moisture + radiation… Continuity
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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.
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Representing the fields: Gridpoint models Represent space as a grid of regular (in long/latt co ords)
CESD Modelling Global Climate Vertical exchange between layers of momentum, heat and moisture 60 ° N 15 ° W 3.75
° 2.5
° Horizontal exchange between columns of momentum, heat and moisture Vertical exchange between layers of momentum, heat and salts by diffusion, convection and upwelling 47.5
° N 11.25
° E Vertical exchange between layers by diffusion and advection Orography, vegetation and surface characteristics included at surface on each grid box
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+ X i-1,j+1 + X i-1,j + X i-1,j-1 + X i,j+1
Derivatives
+X i+1,j+1
d dx
X i
1 ,
j
2
x X i
1 ,
j
+ X i,j + X i,j-1 + X i+1,j + X i+1,j-1
d dy
X i
,
j
1 2
y X i
,
j
1
Representing the fields: Spectal Models
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• 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
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Grid-point space Spectral transform Spectral space Advection Grid-point space Inverse Spectral transform Spectral space Linear calculations
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Computing advective terms
Eulerian vs Lagragian view of a fluid
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• 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 Dt
C
t
V
C
0
Eulerian
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DC Dt
C
t
C
t
V
C
+ +
V
C
+ + 0 + + + + + + + + + + + + + + + + + + + + For each grid point compute divergence and take dot-product with velocity field.
+ + + + + + + + + + + +
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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.
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New approaches – adaptive grids
ICOM – Imperial College Ocean Model. Grid resolution varies and changes in time
Further Reading
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ECMWF lecture notes: http://www.ecmwf.int/newsevents/training/r course_notes/index.html
ICOM http://amcg.ese.ic.ac.uk/index.php?title=IC OM
Sub-grid.
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• Recall equations of motion • Split into large scale average and residual.
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Get large-scale terms that result from sub grid scale motions…
Parameterisation
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• 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.
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Parameterized Processes
Slingo From Kevin E. Trenberth, NCAR
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What are we trying to parameterize?
What is there… How we parameterise
(Atmospheric) Modelling over-view
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• 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
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• 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
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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
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Solar radiation Snow Vegetation Wind Air temperature and humidity Thermal radiation Heat Evaporation CO 2 CH 4 Lakes Soil moisture
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Model resolution increasing with time.
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Early Visions
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More recent visions Cray Y-MP ~ 1990 HECToR – Edinburgh 2007
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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
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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…
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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
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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
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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
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• 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
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• 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
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• 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
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• 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….