Spectral Truncation Methods

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Spectral Truncation Methods
Typically prognostic equations for vorticity and
the divergence of the velocity potential,
temperature, water vapor and cloud water
vapor mixing ration and log surface pressure are
solved Nonlinear terms and
paramterizations are evaluated on a Gaussian grid
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Equations used in ECHAM3
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Governing Equations for AGCMs
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Parameterization

• Parameterization The representation of
  subgrid-scale phenomena as functions of the
  variables that are represented on the model grid.
• Goal is to make parameterizations physical,
  scale-independent, and nonempirical, but this
  goal is difficult to achieve.

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What Processes Are Parameterized?

• Radiative heating
• Radiative transfer model (terrestrial , solar,
  cloud optical properties, temperature, clouds,
  aerosols, cabon dioxide and ozone, surface
  albedo, solar angle)
• Vertical diffusion(surface flux, drags moisture
  and cloud effects,, boundary layer, kinetic
  energy dissipation
• Gravity wave drag (parameterisation of effect of
  subgrid-scale gravity waves on momentum transport)

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What Processes Are Parameterized?

• Cumulus convection (penetrative convection,
  shallow convection and midlevel convection, cloud
  properties including up- and downdraft mass
  fluxes, momentum transport by convective
  circulation)
• Stratiform clouds
• Soil processes (soil temperature, snowpack
  temperature, snow melt, sea-ice temperature, soil
  hydrology)

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How do you parameterize
Planetary boundary layer depth
Version 10
Version 10
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Parameterizations Achilles Heel?

• Considerable uncertainties surround physical
  parametrizations.
• Differences in parameterizations are likely
  responsible for much of the model-dependent
  behavior in climate change simulations.
• In many cases, physical processes are not
  adequately understood.

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How To Improve Parameterization?

• Process studies, including field experiments,
  single column modeling, etc., can lead to better
  constraints on physical processes.
• Ultimately, increased spatial resolution can
  allow more processes to be modeled explicitly.
  (But there are many orders of magnitude between
  spatial resolution of most advanced global models
  and spatial scales of cloud formation!)

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Using Atmospheric GCMs To Study Climatic Change

• Atmospheric GCMs require a set of lower boundary
  conditions.
• Land surface models are often treated as integral
  components of atmospheric GCMs.
• What to do for oceanic regions?
• Specify climatological sea surface temperature
  (SST).
• Specify climatological SST SST anomalies.

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Performance of atmospheric models El Nino
response
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Performance of atmospheric models
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Performance of atmospheric models
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Performance of atmospheric models
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COUPLED MODELS
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Is There a Better Set of Lower Boundary
Conditions?

• Yes! The lower boundary conditions for the
  atmosphere could be determined interactively in
  response to processes internal to the model.
• This goal can be achieved by coupling the
  atmosphere to an ocean model.

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Types of Coupled Models

• Atmosphere-swamp ocean
• Atmosphere-mixed layer ocean
• Atmosphere-ocean GCM
• Earth system models of intermediate complexity
  (EMICs)

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Atmosphere-Swamp Ocean

• Ocean is represented as a wet surface with zero
  heat capacity.
• Surface temperature is interactively determined.
• Albedo of swamp surface increases when
  temperature falls below freezing.

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Atmosphere-Swamp Ocean
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Atmosphere-Mixed Layer Ocean

• Ocean is represented as a shallow, motionless
  slab of water.
• Mixed layer depth is chosen to represent seasonal
  heat storage in upper ocean.
• Ocean temperature is interactively determined.
• Sea ice thermodynamics are included.

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Atmosphere-Mixed Layer Ocean
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Atmosphere-Ocean GCM

• Ocean component is a full dynamical ocean model,
  including advection, diffusion, heat storage.
• Relatively complete representation of physical
  and dynamical feedbacks between atmosphere and
  ocean.

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Atmosphere-Ocean GCM
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EMICs

• EMICs Earth System Models of Intermediate
  Complexity
• Designed to contain many feedbacks of full AOGCM
  but consume far less computer time.
• Used for climate simulations that require long
  time scales (i.e., gt1000 years).

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EMIC Example Ocean GCM with Energy Balance
Atmosphere

• Developed by A. Weaver and collaborators at Univ.
  of Victoria.
• OGCM is coupled to simple atmosphere.
• Atmospheric dynamics represented by diffusion.
• Highly simplified parameterization of atmospheric
  radiation.

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Coupling Methods

• Communication between components is an essential
  element of coupled models.
• Model component codes are often developed
  separately, so grids can be different, making
  regridding necessary.
• Frequency of communication must be managed,
  particularly given the difference in response
  times of atmosphere and ocean.

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Coupling Methods Example
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Asynchronous Coupling

• Atmosphere is run for a relatively short period
  with output archived in library.
• Ocean is run (with acceleration methods) for
  relatively long period using fluxes from
  atmospheric library.
• Cycle can be repeated indefinitely.

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Synchronous Coupling

• Conceptually simple no acceleration techniques
  are used.
• Model components may have different time steps,
  but communication occurs at a fixed interval.
• Typical interval 1x daily (models without
  diurnal variation) 8x daily (with diurnal
  variation)

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Climate Drift

• Coupled models are typically constructed from
  atmosphere and ocean components that have been
  independently developed.
• Stand-alone atmosphere and ocean components are
  tightly constrained by observed boundary
  conditions.
• When atmosphere and ocean components are coupled,
  the resulting climate will often drift away from
  a realistic state.

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Climate Drift in GFDL CM2
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Causes of Climate Drift
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Causes of Climate Drift

• Imbalances between atmosphere-ocean heat fluxes
  simulated by AGCM and OGCM when both are run with
  observed SSTs.
• Climate feedbacks triggered by flux imbalances.
  (Ex CM2_a10o2 cooling pattern in midlatitude
  N.H. ? southward shift in westerlies ? error in
  position of western boundary currents)

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Flux Corrections/Adjustments

• One ad hoc approach to reducing climate drift is
  to adjust for differences in atmospheric and
  oceanic component fluxes by adding a compensating
  flux at each grid point.
• This method is known as flux correction (Sausen
  et al. 1986) or flux adjustment (Manabe et al.
  1991).

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Flux Corrections/Adjustments
Atmosphere
Data
Data
Ocean
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Calculating Flux Adjustments

• The goal is to determine artificial heat and
  water fluxes that vary seasonally and spatially
  but do not depend on the state of the model.
• Method 1 GFDL Three-Step
• Method 2 Coupled Restore
• Method 3 Offline Flux Difference

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Method 3 Offline Flux Differences

• Step 1 Run the AGCM with climatological SSTs,
  archiving the heat and water fluxes.
• Step 2 Run the OGCM, restoring to observed T and
  S. Archive the restoring fluxes.
• Step 3 The differences between the fluxes from
  step 1 and step 2 are the flux adjustments these
  are supplied to the coupled AOGCM.

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Method 1 GFDL Three-Step

• Step 1 Run the AGCM with climatological SSTs,
  archiving the heat and water fluxes.
• Step 2 Run the OGCM with the fluxes from step 1,
  while simultaneously restoring to observed T and
  S.

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Method 1 GFDL Three-Step

• Step 1 Run the AGCM with climatological SSTs,
  archiving the heat and water fluxes.
• Step 2 Run the OGCM with the fluxes from step 1,
  while simultaneously restoring to observed T and
  S.

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Method 1 GFDL Three-Step

• Step 1 Run the AGCM with climatological SSTs,
  archiving the heat and water fluxes.
• Step 2 Run the OGCM with the fluxes from step 1,
  while simultaneously restoring to observed T and
  S.

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Method 2 Coupled Restore

• Step 1 Couple the AGCM and OGCM, then run the
  coupled models while simultaneously restoring to
  observed T and S, archiving the restoring terms
  as flux adjustments.
• Step 2 Deactivate the restoring and run the
  coupled AOGCM using the flux adjustments
  determined in step 1.

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Flux Adjustment Pros and Cons

• Cons
• Flux adjustments are nonphysical.
• There is no guarantee that coupled model biases
  are invariant over different climate states.
• Flux adjustments could distort climate feedbacks.

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Flux Adjustment Pros and Cons

• Pros
• Flux adjustments minimize climate drift that
  would distort climate feedbacks if left
  unchecked.
• Flux adjustments allow sensitivity experiments to
  be performed while better models (i.e., those
  with smaller errors) are under development.

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Design of Coupled Model Experiments

• Equilibrium The goal is to determine the climate
  that is in equilibrium with a given set of
  climate forcings. (Example What climate state is
  in equilibrium with twice the preindustrial level
  of atmospheric CO2?)
• Transient The goal is to investigate the
  time-dependent response of the climate to a given
  (often time-dependent) change. (Example How will
  the climate change in response to projected
  increases in CO2 and other human-induced climate
  forcings?)

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Types of Experiments

• Forcing-Response Impose a specific forcing and
  see how the model responds.
• Unforced Variability Allow a model to run,
  preferably for a lengthy period, and examine the
  spatiotemporal variations that are generated by
  the internal dynamics of the model.

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Design of Coupled Model Experiments Issues

• Initialization How to Start?
• Equilibration How Long to Run?
• Fidelity How Good is the Model?

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Initialization

• Not typically an important issue for
  atmosphere-only or atmosphere-mixed layer ocean
  models.
• More important for AOGCMs these can exhibit
  considerable sensitivity to initial conditions.
• Issue How to initialize time-dependent AOGCM
  simulations of past climates?

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Equilibration

• Time required varies with model type and depends
  on e-folding time of slowest component of climate
  system.
• AGCMs lt 1 year
• A-MLO models 5 years
• AOGCMs 500-1,000 years

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Equilibration

• Integration length must be adequate for sampling
  climate statistics.
• Acceleration techniques may be useful in
  ocean-only simulations, but should be used with
  caution.

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Fidelity

• How well does a model simulate the important
  processes of interest?
• Careful comparison of model simulations with the
  observed climate record are critical for
  assessments of model fidelity.
• Successful performance in such comparisons can
  increase our confidence in climate models.

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CRYOSPHERIC MODELS
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CARBON CYCLE MODELS
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VEGETATION MODELS