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Earth Systems Science
Chapter 6
I. Modeling the Atmosphere-Ocean System
1. Statistical vs physical models;
analytical vs numerical models;
equilibrium vs dynamical models
finite difference vs spectral models
endogenous vs exogenous variables
2. Physically based climate models of different
complexities (largely review from discussion in
chapter 3)
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 nonlinear 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 models:
zero-dimensional radiation balance model
Equilibrium model:
Te = [ (S/4s) (1-A) ]0.25
SWout
SWin
Earth’s
Energy
LWout
Physically-based climate models:
1-dimensional radiative-convective model
One-Layer Radiation Model
Physically-based climate models :
1-dimensional radiative-convective model
1-D Rad-Conv Model
S/4
(S/4)*A
Radiation Convection,
in each
latent
wavelength fluxes
band
Surface: latent, sensible
surface
Physically-based climate models :
2-dimensional climate model,
or 2-d energy balance model (EBM)
North
Pole
South
Pole
Surface
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 models:
3-D coupled atmosphere – ocean general circulation models
(AOGCM) or Global Climate Model (GCM)
Atmosphere
Flux adjustment
Ocean
I. Global Climate Models
1. processes
2. Climate change experiments
- equilibrium
- transient
3. Model resolution, subgrid-scale processes
4. Dependency on initial conditions
5. Results from different models
Global Climate Models (GCMs): many processes
Boundary conditions
(exogenous variables)
vs
modeled processes
(endogenous variables)
Included in
Climate Model
Separate Models
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
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.
Experiments
http://www.grida.no/climate/ipcc_tar/wg1/345.htm#fig91
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 resolution
Smaller 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”
parameterization 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 experiment
The 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).
http://www.grida.no/climate/ipcc_tar/wg1/346.htm#9221
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).
http://www.grida.no/climate/ipcc_tar/wg1/350.htm
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: %).
http://www.grida.no/climate/ipcc_tar/wg1/350.htm