Earth System Models - Maths of Planet Earth

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Earth System Models: Tools for understanding
climate variability and change
www.cawcr.gov.au
Julie Arblaster
(with thanks to colleagues at NCAR and BoM)
Climate Change Science Team, Bureau of Meteorology
Climate Change Prediction group, NCAR
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Outline
  Why do we need to model the climate system
  Brief history and make-up of earth system models
  State-of-the-art in climate simulation
- the Antarctic ozone hole and SH rainfall
  Some key issues for improvement
Why model the climate system?
Australia's climate is variable
Wettest spring on record in 2010
Extreme heat in January 2013
http://www.bom.gov.au/climate
Why model the climate system?
Why model the climate system?
Projections are based primarily on climate models as extrapolations
or analogues from the past are unlikely to represent the future
Modelling the climate system
Requires understanding of
•  atmospheric predictability/basic
fluid dynamics
•  physics/dynamics of phase
change
•  radiative transfer (aerosols,
chemical constituents, etc.)
•  interactions between the
atmosphere and ocean (El Nino,
etc.) and sea-ice
•  solar physics and chemistry
(solar-terrestrial interactions,
solar impact on ozone, etc.)
•  impacts of anthropogenic and
other biological activity
Earth System Model ‘Evolution’
2000
!
2005
Ice sheets
Human
interactions
Cloud
resolving
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Climate vs Numerical Weather Prediction
• NWP:
• Initial state is CRITICAL
• Don’t really care about whole PDF, just probable phase
space
• Non-conservation of mass/energy to match observed
state
• Climate
• Get rid of any dependence on initial state
• Conservation of mass & energy critical
• Want to know the PDF of all possible states
• Really want to know tails (extreme events)
Conceptual Framework for Modeling
•  Can’t resolve all scales, so have to represent them
•  Energy Balance / Reduced Models
•  Mean State of the System
•  Energy Budget, conservation, Radiative transfer
•  Dynamical Models
•  Finite element representation of system
•  Fluid Dynamics on a rotating sphere
•  Basic equations of motion
•  Advection of mass, trace species
•  Physical Parameterizations for moving energy
Meteorological Primitive Equations
•  Applicable to wide scale of motions; > 1hour, >100km
Global Climate Model Physics
Terms F, Q, and Sq represent physical processes
•  Equations of motion, F
•  turbulent transport, generation, and dissipation of momentum
•  Thermodynamic energy equation, Q
•  convective-scale transport of heat
•  convective-scale sources/sinks of heat (phase change)
•  radiative sources/sinks of heat
•  Water vapor mass continuity equation
•  convective-scale transport of water substance
•  convective-scale water sources/sinks (phase change)
Grid Discretizations
Equations are distributed on a sphere
•  Different grid approaches:
•  Rectilinear (lat-lon)
•  Reduced grids
•  ‘equal area grids’: icosahedral, cubed sphere
•  Different numerical methods for solution:
•  Spectral Transforms
•  Finite element
•  Lagrangian (semi-lagrangian)
•  Spectral element
•  Vertical Discretization
•  Terrain following (sigma)
•  Pressure
•  Isentropic
•  Hybrid Sigma-pressure (most common)
BoM (2003)
Physical Parameterization
Many physical processes occur on scales below the
numerical truncation limit and need to be parameterized
•  Physical parameterization
•  express unresolved physical processes by simplified
mathematical relationships to resolved processes
•  generally empirical techniques, limited by observational record
•  Examples of parameterized physics
•  dry and moist convection
•  cloud amount/cloud optical properties
•  radiative transfer
•  planetary boundary layer transports
•  surface energy exchanges
•  horizontal and vertical dissipation processes e.g. gravity wave
drag
•  ...
Basic Logic in a GCM (Time-step Loop)
For a grid of atmospheric columns:
1.  ‘Dynamics’: Iterate Basic Equations
Horizontal momentum, Thermodynamic energy,
Mass conservation, Hydrostatic equilibrium,
Water vapor mass conservation
2.  Transport ‘constituents’ (water vapor, aerosol, etc)
3.  Calculate physics terms for each column
Clouds & Precipitation, Radiation, etc
4.  Update dynamics fields with physics forcings
5.  Gravity Waves, Diffusion
6.  Next time step (repeat)
Internal and external ‘forcings’
Coupled modelling framework
CO2, volcanic
eruptions, solar
cycle, ozone hole
Land
Land ice
Atmosphere
Coupler
Ocean
Sea Ice
Modelling the climate system
surface air temperature
Global annual mean surface air temperature
Modelling the climate system
Animation of surface air temperatures from 1850-2100
http://www.cgd.ucar.edu/ccr/strandwg/animations/
CCSM3_A1B_800x600_60fps.mov
Courtesy Gary Strand, Department of Energy/National Center
for Atmospheric Research
Modelling the climate system
surface air temperature
Diversity of equally
plausible approaches to
modelling the climate
system => no best model
Numerous modelling
centres worldwide
40+ models participated in
most recent coupled model
intercomparison
Attempts to link model performance to projections, for the most
part, have not been very successful so use multimodel means
Modelling the climate system
seasonal mean precipitation
IPCC 2007
Have GCMs actually been getting any better?
Reichler et al., 2008, BAMS
SST Biases (Pre-Industrial)
CCSM3
mean = -0.76oC
rms = 1.57oC
CCSM4 (2º)
CCSM4 (1º)
o
mean = 0.07 C
rms = 1.11oC
mean = 0.30oC
rms = 1.46oC
Overall reduction
SST bias, all basins
El Niño−Southern Oscillation
Observations
CCSM3
El Niño−Southern Oscillation
Observations
CCSM4
ENSO and temperature extremes
Arblaster & Alexander (2012)
Tropical Land Precipitation
(Frequency of Daily Rate)
CCSM3: too few
strong rainfall events
CCSM4: more
realistic extremes
Arctic winter sea ice cover (late 20th Century)
CCSM3
(%)
CCSM4
Extent
SSM/I
(m)
Thickness
CCSM4-CCSM3
September Arctic Sea Ice Extent
Antarctic sea ice cover (late 20th Century)
JAS
CCSM4
JFM
(%)
Too extensive, similar to CCSM3
Some current developments
1) Higher Resolution
2) Improved external forcings
3) Improved parametrisations, new processes
Increases in global model resolution
~1.4°
~0.5°
~1°
~1/8°
Forcings: variations in ozone
⇒  Ozone depletion over
Antarctica of more than 50%
compared to 1980 levels
⇒  Predominantly in spring
months, impact on surface
climate in summer
⇒  Recovery of the ozone
hole projected by mid-late
21st Century
⇒  Stratospheric ozone has
only a minor impact on
global surface temperatures
NASA!
Ozone depletion and Southern Hemisphere
atmospheric circulation
Depletion =>
cooling in
Antarctic
stratosphere =>
changes in
atmospheric
circulation and
rainfall
WET
DRY
recent research suggests jet has moved poleward by ~2° latitude since 1979
Son et al 2010!
Ozone depletion and the Southern Hemisphere
atmospheric circulation
1950-1999 sea level pressure trends
Arblaster and Meehl 2006!
Impacts on surface climate
Impacts of strengthening and poleward shift in summertime
circulation (~ozone depletion)
surface temperature & wind
sea surface temperature & wind
Thompson et al. Nature Geosciences, 2011!
Impacts on summer surface climate
temperature
rainfall
Impacts of increasing
and poleward shift in
summertime
circulation (~ozone
depletion)
⇒  Warm over New
Zealand, dry in west,
wet in east
rainfall
⇒  Wet and cool over
southern Australia
Thompson et al. Nature Geosciences, 2011!
Climate model experiments
Recent studies show these
impacts can be captured by
climate models
⇒  observed summer
rainfall change from
1979-2000
⇒  climate model summer
rainfall change driven by
ozone depletion
Kang et al., Science, 2011!
How will our climate change in the future?
Our future climate depends on
both the response of the Earth
system and the technological
and economic choices we
make
No crystal ball to gaze into the
future and know which choices
will be made
⇒  instead use a scenario
approach where the climate
impacts from a variety of
potential pathways are
examined
Moss et al 2010!
Representative Concentration Pathways
(RCPs)
For the first time in 12 years, new scenarios have been developed
Meehl et al 2012!
Temperature projections
Warming in the near-term
is scenario independent
⇒  Adaption problem
Warming in the long-term
is scenario dependent
=> Mitigation can
influence the outcome
Meehl et al. J Climate 2012!
Future scenarios and SH climate
  a poleward shift in the
SH extratropical
circulation (westerly jet,
SAM) is one of the most
robust responses to
global warming
  ozone recovery will
offset this shift in austral
summer to some extent
  which forcing
dominates is scenario
and model dependent
Perlwitz, 2011!
⇒  implications for rainfall, carbon uptake and ice sheets
Tropical rainfall biases linked to Southern Ocean
Observations
Models
Rainfall
SW
radiation
bias
Hwang and Frierson (2013)!
Climate sensitivity
Equilibrium
climate sensitivity
(the response of
the climate
system to a
doubling of CO2)
estimates today
are similar to
ranges estimated
in the 1970s
Knutti and Hegerl (2008)!
Summary
  Climate models are essential for future projections
  Significant successes, ever evolving and improving
  Some remaining challenges & areas of focus
- increased resolution
- improved estimates of forcing
- improved processes (e.g. Southern Ocean clouds)
- constraining climate sensitivity
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Julie Arblaster
Climate Change Science Team, CAWCR
Climate Change Prediction group, NCAR
With thanks to David Lawrence, Gary Strand and Andrew Gettelman, NCAR
Thank you
www.cawcr.gov.au
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