Title: Spectral Truncation Methods
1Spectral 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
2Equations used in ECHAM3
3Governing Equations for AGCMs
4Parameterization
- 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.
5What 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)
6What 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)
7How do you parameterize
Planetary boundary layer depth
Version 10
Version 10
8Parameterizations 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.
9How 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!)
10Using 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.
11Performance of atmospheric models El Nino
response
12Performance of atmospheric models
13Performance of atmospheric models
14Performance of atmospheric models
15COUPLED MODELS
16Is 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.
17Types of Coupled Models
- Atmosphere-swamp ocean
- Atmosphere-mixed layer ocean
- Atmosphere-ocean GCM
- Earth system models of intermediate complexity
(EMICs)
18Atmosphere-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.
19Atmosphere-Swamp Ocean
20Atmosphere-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.
21Atmosphere-Mixed Layer Ocean
22Atmosphere-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.
23Atmosphere-Ocean GCM
24EMICs
- 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).
25EMIC 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.
26Coupling 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.
27Coupling Methods Example
28Asynchronous 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.
29Synchronous 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)
30Climate 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.
31Climate Drift in GFDL CM2
32Causes of Climate Drift
33Causes 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)
34Flux 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).
35Flux Corrections/Adjustments
Atmosphere
Data
Data
Ocean
36Calculating 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
37Method 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.
38Method 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.
39Method 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.
40Method 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.
41Method 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.
42Flux 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.
43Flux 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.
44Design 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?)
45Types 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.
46Design of Coupled Model Experiments Issues
- Initialization How to Start?
- Equilibration How Long to Run?
- Fidelity How Good is the Model?
47Initialization
- 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?
48Equilibration
- 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
49Equilibration
- Integration length must be adequate for sampling
climate statistics. - Acceleration techniques may be useful in
ocean-only simulations, but should be used with
caution.
50Fidelity
- 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.
51CRYOSPHERIC MODELS
52CARBON CYCLE MODELS
53VEGETATION MODELS