Transcript OC-2 Wind-driven Ocean Circulation [text KKC, pp.80-85]

Modeling the Atmos-Ocean System
Objectives:
• Climate Models
– Statistical models
– 1D, 2D models
– GCM model
• the strengths and weaknesses of GCMs
• The application of GCMs
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• Statistical models:
y(t+t’) = F1(y(t))+F2(x(t));
(1) If F1 and F2 are both linear, the model is
linear statistical models. Otherwise models are
nonlinear.
(2) If F1=0, models are regression models
(3) If F2=0, models are Markov models.
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• t’ is the time interval. When t’=0, there is no
time ahead for prediction, i.e., prediction is
simultaneous.
several common statistical models:
(1) Univariate and Multiple Regression
(2) Markov models or Auto-Regression
(3) Neural Network
…………
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•
Example of Statistical models: El Nino
prediction using SLP data
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• Advantage and disadvantages of statistical models:
Advantages: simple, cheap and useful. For some
problems, statistical models are as good as the most
complicated dynamical models..
Disadvantages: (1) need a large of data set, which is
often not available.
(2) Only statistical, not physical/dynamical
(3) statistical relation may shift for different period.
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• Climate models
Use quantitative methods to simulate the
interactions of the atmosphere, oceans,
land surface, and ice.
Climate models are mainly used for
predictions and simulations.
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• Dynamical/physical models
Using physical principles to describe the
relationship among different components of
climate system in the form of mathematical
equations. These mathematical equations are called
dynamical models. By solving the
equations, we can simulate and predict the
components of the earth climate system.
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Climate Model – what does it do?
• Starts with known physical laws – conservation of
momentum, energy, & mass.
• Views atmosphere, oceans, land as a continuum (i.e. all
spatial scales present satisfying same laws).
• Find and uses numerical approximations to the continuum
physical laws.
• Integrate in time to develop climate statistics same as
observed-evaluate success by extent of agreement.
• On global scale, this agenda very successful.
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Climate
Model
Scaling/parameterization
Need to describe details
within the grid boxes
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Types of Climate models:
0-dimensional model;
(1  a) Sr  4r T
2
2
4
 S is the solar constant - the incoming solar radiation per
unit area - about 1367 W·m-2
 a is the Earth's average albedo, approximately 0.37 to 0.39
 r is Earth's radius — approximately 6.371×106m
  is the Stefan-Boltzmann constant — approximately
5.67×10-8 J·K-4·m-2·s-1
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• One dimensional model:
The only dimension represented is
variation with latitude; atmosphere is
averaged vertically and E-W. Multiple
processes of N-S heat transport by
atmosphere and oceans are usually
represented as diffusion. Such models
are useful for modeling the interaction of
heat transport feedbacks.
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Radiation energy in = Radiation
energy out + transport into another
zone :
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Two dimensional models
2D models permit more physically-based
computation of horizontal heat transport than 1D.
w'
w
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• Global climate model
These models are the most complex. The models
divide atmosphere or ocean into a horizontal grid
with a typical resolution of 2-4 degree latitude by 2-4
degree longitude and 10-20 layers in the vertical.
They directly simulate winds, ocean currents and
many other processes. Feedback processes are
simulated in the coupled atmosphere and ocean
GCMs - water vapor, clouds, seasonal snow and ice.
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Scheme of a coupled atmosphere ocean model
and supplementary models.
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• Ideal gas
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• Newton's law
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• Navier Stokes Equations
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• Coriolis force
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• First law of thermodynamics
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Prognostic & diagnostic Eq.
dT
dv
1
  p     dt    
u, v, T, S
dt
0
w
v 
0
z
p
  g
z
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dS
 
dt
   T , S , p w, p, 
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 Model Grid:
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• The derivative of a function f at a point x is
defined by the limit:
Thus, we can use finite differences to
approximate derivatives.
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 For example, consider the ordinary differential
equation
•
 The Euler method for solving this equation uses
the finite difference
•
 to approximate the differential equation by

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• Projections of future climate change
GCMs use a transient climate simulation to
project/predict future temperature changes
under various scenarios. These can be idealized
scenarios (most commonly, CO2 increasing at
1%/y).
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•
equilibrium climate simulation
greenhouse gas concentrations are suddenly changed
(typically from pre-industrial values to twice pre-industrial
values) and the model allowed to come into equilibrium
with the new forcing.
• transient climate simulation
a mode of running a global climate model in which a
period of time (typically 1850-2100) is simulated with
continuously-varying concentrations of greenhouse
gases so that the climate of the model represents a
realistic mode of possible change in the real world.
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The Intergovernmental Panel on Climate Change
(IPCC) was established in 1988 by two United
Nations organizations, the World Meteorological
Organization (WMO) and the United Nations
Environment Programme (UNEP) to assess the
"risk of human-induced climate change".
IPCC: first assessment report in 1990
second assessment report in 1995
third assessment report in 2001
fourth assessment report in 2007
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IPCC reports should be the most authoritative reports on
climate change, and are widely cited in almost any
debate related to climate change. The reports have been
influential in forming national and international responses
to climate change.
A small but vocal minority (less than 1.5%) of the
scientists involved with the report have accused the
IPCC of bias.
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The 21st century predicted by the HadCM3 climate model (one of those used
by the IPCC) if a business-as-usual scenario is assumed for economic
growth and greenhouse gas emissions. The average warming predicted by
this model is 3.0°C.
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• Time evolution of
globally averaged
temperature change
relative to the
period 1961-1990.
The top graph
shows the results of
greenhouse gas
forcing, the bottom
graph shows the
results of
greenhouse gas
forcing plus aerosol
forcing.
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• Time evolution of
globally averaged
precipitation change
relative to the
period 1961-1990.
The top graph
shows the results of
greenhouse gas
forcing, the bottom
graph shows the
results of
greenhouse gas
forcing plus aerosol
forcing.
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• Global mean
temperature
change for 1%/yr
increase with
subsequent
stabilization
2xCO2 and
4xCO2. The
colored lines
show the results
with a simplified
model that allows
no energy
exchange with
the deep ocean.
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• Accuracy of models that predict global
warming:
(1) albedo errors
(2) external factors not taken into
consideration
(3) model resolution
(4) initial conditions
(5) the role of clouds on climate changes
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What limits success of climate models?
• Processes occur on smaller scales that are
different than those resolved on the larger
scales.
• These: a) affect the large scale rules
b) change climate on scales that
humans live on.
• Have to some extent been recognized for
long time – their inclusion has been called
“parameterization” but better called “scaling”.
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• Evidence of some uncertainties:
(1) The individual models often exhibit worse agreement with
observations.
(2) All models have shortcomings in their simulations of the
present day climate of the stratosphere, which might limit the
accuracy of predictions of future climate change.
(3) There are problems in simulating natural seasonal variability.
(4) Coupled climate models do not simulate with reasonable
accuracy clouds and some related hydrological processes.
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• Evidence of model reliability:
(1) The model mean exhibits good
agreement with observations.
(2) Surface air temperature is particularly
well simulated.
(3) For nearly all models the r.m.s. error in
zonal- and annual-mean surface air
temperature is small compared with its
natural variability.
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Conclusion
=============
The majority of climatologists agree that
important climate processes are imperfectly
accounted for by the climate models but
don't think that better models would change
the conclusion.
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