Transcript Slide 1

Atmospheric General
Circulation Modeling
Anthony J. Broccoli
Dept. of Environmental Sciences
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Today’s Lecture
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•
•
•
•
•
Modeling principles
Hierarchy of atmospheric models
Governing equations for AGCMs
Grid vs. spectral
Parameterization
Using AGCMs to study climatic change
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Why Do We Use Models?
• To gain quantitative insights into the
behavior of the Earth system.
• A climate model is a mathematical
representation of the physical processes
that determine climate.
• Models are a natural extension of theory.
Theory: analytical solutions.
Models: numerical solutions
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Models: Complex or Simple?
• “…all models are wrong some are useful.
Accepting this principle, the job is not so
much the search for the true model but to
select one model that is appropriate for the
problem in hand.” (G. E. P. Box, 1976)
• “A useful model is not one that is ‘true’ or
‘realistic’ but one that is parsimonious,
plausible and informative.” (M. Feldstein,
1982)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Models: Complex or Simple?
• Models are simplifications of the
complexity of nature.
• Models should be carefully matched to the
problems they attempt to solve.
• “As simple as possible, but no simpler.”
(A. Einstein, unknown)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Example: Earth’s Orbit
• A very good approximation of the timing of
the seasons can be obtained by
considering only the gravitational effects of
Earth and Sun.
• However, effects of other planets (Jupiter
and Saturn) are necessary to explain the
slow variations in the shape of Earth’s
orbit that are responsible for the ice ages.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Hierarchy of Atmospheric Models
Zero-dimensional
model of global
energy balance:
Q1     T
4
P
Accounts for exchange of radiation between Earth
system and space.
Q = incoming solar radiation
 = planetary albedo of Earth
TP = effective blackbody temperature of Earth-atmosphere system
 = Stefan-Boltzmann constant
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Hierarchy of Atmospheric Models
One-dimensional models
Examples:
• Energy balance model (e.g., MAGICC)
• Single column model (e.g., radiativeconvective model)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Hierarchy of Atmospheric Models
Two-dimensional models
Example: Zonally averaged model
1. Express prognostic variables in “primitive
equations” as sum of zonal mean and eddy
terms.
2. Zonally average the equations.
3. Either set eddies to zero (axially symmetric
model), specify them from data, or use some
other closure method.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
•
•
“Primitive equations” are used in most
AGCMs.
The following processes are
represented:
–
–
–
–
–
conservation of momentum
conservation of thermodynamic energy
conservation of mass
conservation of water vapor
equation of state
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
 T T  Qrad Qcon
T
 
 V  T   


 DH
t
cp
 p p  c p
q
q
  V  q  
 E  C  Dq
t
p

   V
p

RT

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
momentum eq.
 T T  Qrad Qcon
T
 
 V  T   


 DH
t
cp
 p p  c p
q
q
  V  q  
 E  C  Dq
t
p

   V
p

RT

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
 T T  Qrad Qcon
T
 
 V  T   


 DH
t
cp
 p p  c p
q
q
  V  q  
 E  C  Dq
t
p

   V
p

RT

p
p
February 24, 2003
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Modeling of Climate Change
momentum eq.
thermodynamic eq.
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
momentum eq.
 T T  Qrad Qcon
T
 
 V  T   


 DH thermodynamic eq.
t
cp
 p p  c p
q
q
conservation of water vapor
  V  q  
 E  C  Dq
t
p

   V
p

RT

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
momentum eq.
 T T  Qrad Qcon
T
 
 V  T   


 DH thermodynamic eq.
t
cp
 p p  c p
q
q
conservation of water vapor
  V  q  
 E  C  Dq
t
p

conservation of mass
   V
p

RT

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
momentum eq.
 T T  Qrad Qcon
T
 
 V  T   


 DH thermodynamic eq.
t
cp
 p p  c p
q
q
conservation of water vapor
  V  q  
 E  C  Dq
t
p

conservation of mass
   V
p

RT
hydrostatic eq.

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Numerical Methods in AGCMs
• Finite difference methods: Derivatives appearing
in the governing equations are approximated
using differences in dependent variables over
finite space and time intervals.
f ( x0  x)  f ( x0  x)
d
f ( x0 )  lim
dx
2x
x 0
Example: First-order centered difference.
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Numerical Methods in AGCMs
• Spectral transform method: Use a spherical
harmonic basis for horizontal expansion of scalar
fields
T (l ,  j ) 
M
N m 
 T
m M n  m
P ( j )e
m m
n
n
iml
In the spectral transform method, model variables are
represented by truncated series of spherical harmonics
and grid point values.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Spectral Transform Method
Advantages:
• Analytic representation of derivatives
improves numerical accuracy.
• Semi-implicit time differencing
implemented easily.
• Absence of “pole problem.”
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Spectral Transform Method
Disadvantages:
• Representation of topography
(smoothness, Gibbs ripples).
• Computational overhead at high
resolution.
• Less intuitive mapping onto scalable
computer architecture.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Spectral Truncation Methods
10
R
9
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
8
7
6
R = Rhomboidal
n
5
R
R
R
R
R
T = Triangular
4
R
R
R
R
R
B = Both
3
R
R
R
R
2
R
R
R
1
R
R
0
R
R5
0
1
2
3
4
5
6
7
8
9
10
m
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Spectral Truncation Methods
10
9
8
7
T
T
T
T
T
T
T
6
T
T
T
T
T
T
T
5
T
T
T
T
T
T
T = Triangular
4
T
T
T
T
T
B = Both
3
T
T
T
T
2
T
T
T
1
T
T
0
T
R = Rhomboidal
T7
n
0
1
2
3
4
5
6
T
7
8
9
10
m
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Spectral Truncation Methods
10
R
9
8
R
R
R
R
R
7
T
T
B
B
B
B
T
6
T
B
B
B
B
B
T
5
B
B
B
B
B
B
T = Triangular
4
B
B
B
B
B
B = Both
3
B
B
B
B
2
B
B
B
1
B
B
0
B
R = Rhomboidal
n
0
1
2
3
T
R5 and T7 have
same number of
degrees of
freedom.
4
5
6
7
8
9
10
m
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
 T T  Qrad Qcon
T
 
 V  T   


 DH
t
cp
 p p  c p
q
q
  V  q  
 E  C  Dq
t
p

   V
p

RT

p
p
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Governing Equations for AGCMs
V
V
  V  V  
 fk  V     D M
t
p
 T T  Qrad Qcon
T
 
 V  T   


 DH
t
cp
 p p  c p
q
q
  V  q  
 E  C  Dq
t
p

These terms involve
   V
processes that occur
p
on scales unresolved
by the model.

RT

p
p
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Parameterization
• Parameterization: The representation of
subgrid-scale phenomena as functions of
the variables that are represented on the
model grid.
• Goal is to make parameterizations
physical, scale-independent, and
nonempirical, but this goal is difficult to
achieve.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
What Processes Are
Parameterized?
• Atmospheric radiative transfer (solar and
longwave radiation)
• Moist convective processes.
• Stable precipitation.
• Planetary boundary layer.
• Cloud formation and radiative interactions.
• Mechanical dissipation of kinetic energy.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Parameterizations: Achilles’ Heel?
• Considerable uncertainties surround
physical parametrizations.
• Differences in parameterizations are likely
responsible for much of the modeldependent behavior in climate change
simulations.
• In many cases, physical processes are not
adequately understood.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
How To Improve Parameterization?
• Process studies, including field experiments,
single column modeling, etc., can lead to better
constraints on physical processes.
• Ultimately, increased spatial resolution can allow
more processes to be modeled explicitly. (But
there are many orders of magnitude between
spatial resolution of most advanced global
models and spatial scales of cloud formation!)
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Using Atmospheric GCMs To
Study Climatic Change
• Atmospheric GCMs require a set of lower
boundary conditions.
• Land surface models are often treated as
integral components of atmospheric
GCMs.
• What to do for oceanic regions?
– Specify climatological sea surface
temperature (SST).
– Specify climatological SST + SST anomalies.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Atmospheric Response To
ENSO Variability
• Experimental design: Prescribe timevarying SSTs (global, tropical Pacific only,
etc.) and identify atmospheric response.
• This experimental design has been widely
used, and forms the basis for the
Atmospheric Model Intercomparison
Project (AMIP) protocol.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
ENSO Response in Western Pacific
Near-surface circulation
changes: El Niño minus
La Niña (courtesy of N.-C.
Lau, GFDL)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Interannual Variations in Water Vapor
Temporal variations in tropical-mean precipitable water: Simulated vs. observed
(courtesy of B. J. Soden, GFDL)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Limitations of Prescribing SSTs
• Prescribed SST anomaly (i.e., AMIP-type)
experiments are most effective when the ocean
is primarily forcing the atmosphere. (Tropical
surface heating → anomalous convection →
atmospheric teleconnection patterns.)
• Prescribed SST experiments are also useful in
isolating purely internal atmospheric variability
(i.e., the variability that would occur even in the
absence of external forcing or coupled air-sea
interactions)
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Arctic Oscillation
In the real world, the positive
phase of the AO features an
enhanced SLP gradient over
the high-latitude North
Atlantic Ocean.
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli
Arctic Oscillation
The enhanced westerlies
increase the advection of
cold air across offshore,
cooling the sea surface.
Over Europe, the
onshore flow is
strengthened, which
causes a warming.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Simulation of Arctic Oscillation
If one were to prescribe the
SST pattern that
accompanies the positive
phase of the AO, would
Europe experience positive
temperature anomalies?
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Simulation of Arctic Oscillation
Probably not! Cooler than
normal water upstream
would probably lead to
negative anomalies over
Europe. Why doesn’t the
response match the real
world? Because the SST
anomalies in the real world
arise primarily as an oceanic
response to atmospheric
forcing.
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Limitations of Prescribing SSTs
• One may be interested in using a climate
model to study processes that will alter the
sea surface temperature.
• Examples: What is the response of climate
to major volcanic eruption? How will
increasing greenhouse gases affect future
climate?
February 24, 2003
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Modeling of Climate Change
Anthony J. Broccoli
Is There a Better Set of Lower
Boundary Conditions?
• Yes! The lower boundary conditions for the
atmosphere could be determined
interactively in response to processes
internal to the model.
• This goal can be achieved by coupling the
atmosphere to an ocean model.
February 24, 2003
16:375:544
Modeling of Climate Change
Anthony J. Broccoli