1. Modeling the Atmos.-Ocean System
Objectives:
Climate Models
The strengths and weaknesses of GCMs
The application of GCMs
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2. 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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3. Dynamical/physical models Using physical principles to describe the
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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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4. Climate Model – what does it do?
Starts with known physical laws – conservation of momentum, energy, & mass.
Views atmosphere, ocean, land as a continuum (i.e. all spatial scales present satisfying same laws).
Find and use 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 is very successful.
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5. Climate Model Scaling/parameterization
Need to describe details within the grid boxes
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6. 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 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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7. Scheme of a coupled atmosphere ocean model and supplementary models.
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8. Ideal gas
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9. Newton's law
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10. Navier Stokes Equations
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11. Coriolis force
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12. First law of thermodynamics
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13. Prognostic & diagnostic Eq.
u, v, T, S
w, p, 
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14. 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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15. 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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16. Model Grid:
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17. Climate Model Scaling/parameterization
Need to describe details within the grid boxes
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18. Weather forecast --------- initial value problem
Seasonal climate forecast boundary
forcing (surface
condition)
Projection of the climate change Many…
data assimilation + ensemble
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19. Types of GCM
AGCM (Atmospheric) Atmospheric GCM model the atmosphere and impose sea surface temperatures. OGCM (Ocean ) This model simulated the global sea patterns. AOGCM (Atmospheric and Ocean) Coupled atmosphere-ocean GCM is a combine models e.g. CCSM4, HadCM3, GFDL
Hardware Behind the Climate Model

20. Development of Climate Models
Taken from IPCC (modified)

21. Numerical weather forecast is one of the most significant achievements of sciences and technologies in the 20th century.
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22. 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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23. Confidence of climate projection
Confidences come from
(1) the foundation of the models;
(2) ability to reproduce observed
features of current and past climate
change
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25. Global mean near-surface temperatures from observations (black) and as obtained from 58 simulations produced by 14 different climate models driven by both natural and human-caused factors that influence climate. The mean of all these runs is also shown (thick red line). Temperature anomalies are shown relative to the 1901 to 1950 mean. Vertical grey lines indicate the timing of major volcanic eruptions.
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26. 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 ) 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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28. 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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30. 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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31. 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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32. 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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