Chapter 5
Climate Models
5.1 Constructing a Climate Model
5.2* Numerical representation of
atmospheric and oceanic equations
5.3 Parameterization of small scale processes
5.4 Climate simulations and climate drift
5.5** The hierarchy of climate models
5.6 Evaluation of climate model
simulations for present day climate
*Skip except mention of Fig. 5.9, **Skim
Neelin, 2011. Climate Change and Climate Modeling, Cambridge UP
5.1 Constructing a Climate Model
Typical atmospheric GCM grid
•For each grid cell, single value of
each variable (temp., vel.,…)
Finite number of equations
•Vertical coordinate follows
topography, grid spacing varies
•Transports (fluxes) of mass,
energy, moisture into grid cell
Budget involving immediate
neighbors (in balance of forces,
PGF involves neighbors)
•Effects passed from neighbor to
neighbor until global
•Budget gives change of
temperature, velocity, etc., one
time step (e.g. 15 min) later
•100yr=4million 15min steps
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Figure 5.1
5.1.b Treatment of sub-grid scale processes
Vertical column showing parameterized physics so small
scale processes within a single column in a GCM
Figure 5.2
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5.1.c Resolution and computational cost
Topography of western North America at 0.3 and 3.0 resolutions
Figure 5.3
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Supplemental: Topography of North America at 0.5 and 5.0 resolutions
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5.1.c Resolution and computational cost
• Computational time = (computer time per operation)
(operations per equation)(No. equations per grid-box)
(number of grid boxes)(number of time steps per simulation)
• Increasing resolution: # grid boxes increases & time step decreases
• Half horizontal grid size  half time step (why? See below)
twice as many time steps to simulate same number of years
• Doubling resolution in x, y & z (# grid cells)
(# of time steps)
cost increases by factor of 24 =16
• In Fig. 5.3, 5 to 0.5 degrees factor of 10 in each horizontal direction. So
even if kept vertical grid same, 1010(# grid cells)10(# of t steps)= 103
• Suppose also double vertical res. 2000 times the computational time
i.e. costs same to run low-res. model for 40 years as high res. for 1 week
• To model clouds, say 50m res. 10000 times res. in horizontal, if same in
vertical and time 1016 times the computational time … and will still have
to parameterize raindrop, ice crystal coalescence etc.
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Computational costs cont’d
• Why time step must decrease when grid size decreases:
• Time step must be small enough to accurately capture time
evolution and for smaller grid size, smaller time scales enter.
• A key time scale: time it takes wind or wave speed to cross a grid
box.
e.g., if fastest wind 50 m/s, crosses 200 km grid box in ~ 1 hour
• If time step longer, more than 1 grid box will be crossed: can yield
amplifying small scale noise until model “blows up”
(for accuracy, time step should be significantly shorter)
[See Fig. 5.9 for an example of this]
• Examples of model resolutions in IPCC (2007) report:
coarse 5 4°; typical ~2 2°; high 1° to 1.5° in lat. and longitude
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5.1.d An ocean model and ocean-atmosphere coupling
Longitude-height cross-section through an ocean model grid
Figure 5.4
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Atmosphere-ocean coupling in a GCM
via energy fluxes and wind stress
Figure 5.5
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5.1.d Land surface, snow, ice, and vegetation
Land surface types
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Figure 5.6
Summary of equations for atmosphere and ocean models
Table 5.1
Equation Name
Model
Comments
Corresp.Eq. No.
Horizontal velocity eqns.
Hydrostatic equation
Equation of state
Atm/Ocean
Atm/Ocean
Atm
Ocean
Atm
Ocean
Atm
Ocean
Atm
Ocean
Atm
Ocean
Land
Land
Land
(Ocean)
Prognostic (u, v)
Eq. 3.4, 3.5
Eq. 3.8
Eq. 3.10
Eq. 3.11
Eq. 3.20
Eq. 3.18
Eq. 3.31
Eq. 3.29
Eq. 3.35
Temperature equation
Continuity equation
Moisture equation
Salinity equation
Surface pressure eq.
Surface height eq.
Surface temperature eq.
Soil moisture equation
Snow cover equations
Sea ice equations
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Ideal gas law
Prognostic (T)
Prognostic (q)
Prognostic (S)
1 level
1 level
1 or a few levels
a few levels
1 or a few levels
ice fraction,
thickness
Eq. 3.31 3-9
Eq. 3.29 3-8
5.2 Numerical representation of atmos. and oceanic eqns.
5.2.a Finite difference versus spectral models
[Skip]
Finite differencing of a pressure field
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Figure 5.7
[Skip]
Spectral representation of a pressure field
Figure 5.8
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5.2.b Time-stepping and numerical stability
[Skim]
Simple time stepping scheme
Figure 5.9
Time step Dt must be small compared to physical time scales, here
decay time t, or extrapolating slope can give erroneous growth
T′/ t= −T′/t  (T′n+1-T′n )/Dt = −T′n/t
For advection, Dt must be small rel. to timescale to cross grid box u/Dx
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5.2.c Staggered grids
[Skip]
"C" - Staggered grid
Figure 5.10
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5.3 Parameterization of small scale processes
5.3a Mixing and surface fluxes
Vertical mixing and
fluxes of moisture
•Net flux across face of grid
box due to mixing by smaller
scale motions parameterized as
proportional to difference in q
at levels k, k-1
•Evaporation flux of surface
depends on difference between
lowest level q and saturation
value at surface
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Figure 5.11
5.3b Dry convection
[Skip]
Change in environmental lapse rate
Figure 5.12
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5.3c Moist convection
[Skip]
Parcel stability
Figure 5.13
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5.3d Land surface processes and soil moisture
Land surface model: soil moisture and evapotranspiration
Evapotranspiration
Precipitation
Aerodynamic
resistance
Canopy
Interception
Leaf
area
index
Canopy (stomatal)
resistance
Runoff
Soil capacity
Soil moisture
Figure 5.14
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5.3e Sea ice and snow
Sea ice model processes
Figure 5.15
Neelin, 2011. Climate Change and Climate Modeling, Cambridge UP
[Skip]
5.4 The hierarchy of climate models
Table 5.2
Model type
Comments
Simple models
(e.g., energy balance models)
Intermediate complexity models
Hybrid coupled models
(e.g., Cane-Zebiak model for ENSO,
EMICs)
(ocean GCM with a simple
atmosphere)
Atmospheric GCM with a mixedlayer ocean
Regional climate models
(Boundary conditions from global
climate models)
Global atmospheric GCM with a
regional ocean GCM
(e.g., tropical Pacific)
Global ocean-atmosphere GCM
Earth system model with interactive
vegetation and chemistry
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(includes interactive carbon cycle)
5.5 Climate simulations and climate drift
Climate drift
Figure 5.16
Examples of model integrations (or runs, simulations or experiments),
starting from idealized or observed initial conditions. Spin-up to
equilibrated model climatology is required (centuries for deep ocean).
Model climate differs slightly from observed (model error aka climate
drift); climate change experiments relative to model climatology.
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5.6 Evaluation of climate
model simulations for
present day climate
December-February
5.6a Atmos. model clim.
from specified SST
Atm. component of
NCAR_CCSM3 forced by
observed SST (AMIP)
Precipitation Climatology
1979-2000
with observed (CMAP)
4mm/day contour
AMIP=Atm. Model Intercomparison Project
CMAP=CPC Merged Analysis of Precip.
CPC=NOAA Climate Prediction Center
CCSM=Community Climate System Model
Figure 5.17
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June - August
December-February
Recall from Fig. 2.13
Observed (CMAP)
Precipitation Climatology
1979-2000
June - August
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5.6b Climate model simulation of climatology
December-February
4 mm/day Precipitation
climatology contour
Observed (CMAP) and
coupled/uncoupled model
NCAR_CCSM3 Coupled
simulation climatology
(20th century run, 1979-2000)
& Atmospheric component
forced by obs. SST (AMIP)
Figure 5.18
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June - August
HadCM3 simulation
precipitation climatology
(20th century run, 1961-1990)
January
July
Figure 5.19
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Observed (CMAP)
Precipitation Climatology
1979-2000
January
July
Recall Figure 2.13
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Observed (CMAP) and 5 coupled models 4 mm/day precip. contour
December-February
Coupled simulation
precipitation climatology
(20th century run, 1979-2000)
June - August
Figure 5.20
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Observed (CMAP) and 7 other coupled models 4 mm/day precip. contour
December-February
Coupled simulation
precipitation climatology
(20th century run, 1979-2000)
June - August
Supplemental Figure
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December-February
NCAR_CCSM3
coupled simulation
SST climatology
(20th century run,
1979-2000)
June - August
Figure 5.21
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January
Observed SST
climatology
Reynolds data set
(1982-2000)
July
Recall Figure 2.16
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January
HadCM3 coupled
simulation near surface air
temperature
(20th century run,
1961-1990)
July
Figure 5.22
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Regions of sea ice concentrations > 15% for Mar. & Sept.
Figure 5.23
• March (light shading/blue contour)
• September (dark shading/pink contour)
• Contours repeat observed for comparison on 2 model simulations
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5.6c Simulation of ENSO response
Precipitation anomaly (mm/day) for Dec.-Feb. for the average of
5 El Nino events minus the average of 5 La Nina events
CMAP Obs
AMIP CCSM3
AMIP MRI
Figure 5.24
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Precipitation anomaly (mm/day) for Dec.-Feb. for the average of
5 El Nino events minus the average of 5 La Nina events
CMAP Obs
AMIP CCSM3
AMIP MRI
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Shaded
where
statistically
significant
at 95%
level.
Figure 5.24
alternate
Upper tropospheric (200mb) geopotential height anomaly
(mm/day) for Dec.-Feb. for the avg of 5 El Nino events
minus the avg of 5 La Nina events
NCEP reanalysis
(observational product)
Figure 5.25
AMIP CCSM3
AMIP MRI
NCEP=National Centers for Environmental
Prediction; Reanalysis has observations
interpolated via a weather forecast model
AMIP=Atm. Model Intercomparison Project
CCSM=Community Climate System Model
Neelin, 2011. Climate Change and Climate Modeling, Cambridge UP