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Earth Systems ScienceChapter 6

I. Modeling the Atmosphere-Ocean System

- Statistical vs physical modelsanalytical vs

numerical modelsequilibrium vs dynamical

modelsfinite difference vs spectral

modelsendogenous vs exogenous variables - Physically based climate models of different

complexities (largely review from discussion in

chapter 3) - Global Climate Models (GCMs)

Statistical v Physical Models Statistical Model

Based on observations, you identify a

relationship between two variables. You do not

necessarily understand the reason why this

relationship exists. Physical Model Based on

the rules of physics, you construct a model that

describes the relationships between different

physical phenomena.

Numerical vs Analytical Models Analytical Model

Equations are solved without the aid of the

computer, resulting in one or more equations that

allow one to calculate the answer for any time,

without calculating each time step (usually using

calculus). Complicated, highly non-linear

equations often have no analytical

solutions. Numerical Model Equations are solved

at each time step, usually by computer (STELLA

solves numerical models). Can solve any set of

equations, regardless of non-linearities.

Equilibrium vs Dynamical Models Equilibrium

Model Model that provides solution only for the

equilibrium values solution does not vary as a

function of time. Dynamical Model Model that

provides solution as a function of time (STELLA

solves dynamical models).

Finite Difference vs Spectral Models Finite

Difference Model Numerical model in which the

calculations are performed in each grid

box. Spectral Model Model that uses different

mathematical techniques, and performs

calculations using wave functions.

Endogenous vs Exogenous Variables Endogenous

Variables whose values are calculated as part of

the model Exogenous Variables whose values are

specified by the modeler Excluded Variables that

are not part of the model in any way

Physically-based climate models of different

complexities

- Many types of climate models exist. We

discuss some of the more common types, which have

different levels of complexity - Zero-dimensional radiation balance models
- 1-dimensional radiative-convective models
- 2-dimensional diffusive models
- 3-dimensional Atmospheric General Circulation

Models (AGCM) - 3-D coupled atmosphere ocean models (AOGCM)

Physically-based climate modelszero-dimensional

radiation balance model

Equilibrium modelTe (S/4s) (1-A) 0.25

Physically-based climate models1-dimensional

radiative-convective model

One-Layer Radiation Model

Physically-based climate models 1-dimensional

radiative-convective model

Convection, latent fluxes

Surface latent, sensible

Physically-based climate models 2-dimensional

climate model, or 2-d energy balance model (EBM)

Physically-based climate models 3-dimensional

Atmospheric General Circulation Model (AGCM)

surface

http//www.arm.gov/docs/documents/project/er_0441/

bkground_5/figure2.html

Physically-based climate models3-D coupled

atmosphere ocean general circulation

models(AOGCM) or Global Climate Model (GCM)

I. Global Climate Models

- processes
- Climate change experiments- equilibrium-

transient - Model resolution, subgrid-scale processes
- Dependency on initial conditions
- Results from different models

Global Climate Models (GCMs) many processes

Boundary conditions (exogenous variables) vs

modeled processes (endogenous variables)

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Climate Change Experiments

Typically, experiments are performed using

climate models (usually GCMs) to estimate the

effect of changing boundary conditions (e.g.

increasing carbon dioxide) on climate. Control

Run Model experiment simulating current climate

conditions using current boundary conditions

(e.g. CO2) Equilibrium experiments Model

experiment simulating the climate under changed

conditions by changing the boundary conditions to

what they might be at some future time (e.g.

doubled CO2, or 2xCO2) Transient Experiments

Model experiment simulating the gradual change

from current to future (e.g. increase in CO2 by

1 per year)

Transient Experiments

Figure 9.1 Global mean temperature change for

1/yr CO2 increase with subsequent stabilisation

at 2xCO2 and 4cCO2. The red curves are from a

coupled AOGCM simulation (GFDL_R15_a) while the

green curves are from a simple illustrative model

with no exchange of energy with the deep ocean.

The transient climate response, TCR, is the

temperature change at the time of CO2 doubling

and the equilibrium climate sensitivity, T2x,

is the temperature change after the system has

reached a new equilibrium for doubled CO2, i.e.,

after the additional warming commitment has

been realised.

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Model Resolution subgrid scale processes

resolution How big are the grid boxes? The larger

they are, the less realistic the model typically

1 degree lat/lon.Bigger grid boxes lower

resolutionSmaller grid boxes higher

resolution Subgrid-scale processes many physical

processes that are important for climate occur on

very small spatial scales (e.g. cloud formation).

Since the model resolution is much larger, these

processes can not be modeled physically paramete

rization a simple method, usually a statistical

model, to account for subgrid-scale processes for

which the physically-based equations can not be

included.

Dependency on Initial Conditions

Initial conditions the values of all stocks or

state variables (e.g. temperature, pressure,

etc) at each grid point must be specified in the

beginning of a model experimentThe transient

response of GCMs can change when initial

conditions are changed even slightly. This is

because the climate is a chaotic system. Ensemble

experiments the same model experiment is

performed a number of times with slightly

different initial conditions the results of the

ensemble members are averaged to get the

ensemble mean

Dependency on Initial Conditions

Figure 9.2 Three realisations of the

geographical distribution of temperature

differences from 1975 to 1995 to the first decade

in the 21st century made with the same model

(CCCma CGCM1) and the same IS92a greenhouse gas

and aerosol forcing but with slightly different

initial conditions a century earlier. The

ensemble mean is the average of the three

realisations. (Unit C).

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Results from different models

Different GCMs have many similarities, and

therefore provide, in many ways, similar results.

However, the way the different modeling groups

choose to parameterize different processes makes

the models different. Therefore, the different

models produce somewhat different results. For

example, the models agree much more closely on

temperature than on precipitation. This is

because temperature changes are more dependent on

large scale processes, which are modeled

similarly in most models. Precipitation, however,

depends on subgrid-scale processes, which are

parameterized differently by the different

modeling groups.

Results from different models

Figure 9.5 (a) The time evolution of the

globally averaged temperature change relative to

the years (1961 to 1990) of the DDC simulations

(IS92a). G greenhouse gas only (top), GS

greenhouse gas and sulphate aerosols (bottom).

The observed temperature change (Jones, 1994) is

indicated by the black line. (Unit C).

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Results from different models

Figure 9.5 (b) The time evolution of the

globally averaged precipitation change relative

to the years (1961 to 1990) of the DDC

simulations. GHG greenhouse gas only (top), GS

greenhouse gas and sulphate aerosols (bottom).

(Unit ).

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