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SAGES
Scottish Alliance for Geoscience, Environment & Society
CESD
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.
Climate is a Multi-scale problem
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From Bob Harwood
Modelling the Climate System
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Main
Message:
Lots of
things
going on!
Karl and Trenberth 2003
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68
100
From Kevin E. Trenberth, NCAR
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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
–Stores, moves heat, fresh water, gases,
chemicals
–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
The Atmosphere
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Meteorology is (roughly) fluid
dynamics on rotating sphere.
DV
1
 2Ω  V   p  g a  Ff
Dt

D 
  V 
Dt t

 ( V )  0
t
Equations of
motion
+
thermodynamics
Continuity
+ 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 coords)
Modelling Global Climate
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Vertical exchange between layers
of momentum, heat and moisture
15° W
Horizontal exchange
between columns
of momentum,
heat and moisture
60° N
3.75°
2.5°
Vertical exchange
between layers
of momentum,
heat and salts
by diffusion,
convection
and upwelling
11.25° E
Vertical exchange between layers
by diffusion and advection
47.5° N
Orography, vegetation and surface characteristics
included at surface on each grid box
Derivatives
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+Xi-1,j+1
+Xi,j+1
+Xi+1,j+1
+Xi-1,j
+Xi,j
+Xi+1,j
+Xi-1,j-1
+Xi,j-1
+Xi+1,j-1
d
Xi  1, j  Xi  1, j

dx
2x
d
Xi , j  1  Xi , j  1

dy
2y
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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
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Grid-point
space
Advection
Spectral
transform
Spectral
space
Grid-point
space
Inverse
Spectral
transform
Linear
calculations
Spectral
space
Computing advective terms
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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 C

 V  C  0
Dt
t
Eulerian
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DC C

 V  C  0
Dt
t
C
  V  C
t
+
+
+ +
+
+
+
+
+
+
+
+ +
+ +
+ +
+
+
+
+ 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 gridpoint work out
trajectory and
where values
came from. These
places not on grid
so need to
interpolate values.
New approaches – adaptive grids
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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.
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
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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-byline 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
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Slingo
From Kevin E. Trenberth, NCAR
What are we trying to parameterize?
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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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Wind
Air temperature and humidity
Solar radiation
Thermal radiation
Heat
Evaporation
CO2
CH4
Vegetation
Snow
Soil moisture
Lakes
Model resolution increasing with time.
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Early Visions
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More recent visions
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Cray Y-MP ~
1990
HECToR –
Edinburgh 2007
Moore’s Law and Supercomputers
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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…
Projections of Future Changes in Climate
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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
Projections of Future Changes in Climate
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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://wwwpcmdi.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….