Limited Area Models

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Limited Area Models

• Adam Sobel
• Banff Summer School

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What do we mean by a limited area model?
A model whose domain is a subset of the entire
global atmosphere. Usually this is done because
higher resolution is desired, increasing the
computational expense, so reducing the domain
size compensates.
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Generic issues

• The boundaries of limited area models are
  artificial. In general there is no rigorous,
  well-posed way to formulate the boundary
  conditions (except idealized, e.g. periodic).
  This becomes more important for longer
  simulations, i.e. Regional Climate Models.
• We go to higher resolution to reduce
  parameterization issues. Yet these can in some
  respects become worse as resolution increases.
  While some processes dont need to be
  parameterized any more, others still do, and the
  parameterizations may become less justified as
  sample size of parameterized entities (clouds,
  turbulent eddies, etc.) in each grid box is
  reduced.
• Because parameterizations must change as
  resolution does, there can be no convergence, in
  the standard sense, in full-physics atmospheric
  modeling.

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Comprehensive models, what they parameterize, and
what theyre good for.

• General Circulation Models (GCMs). Cover the
  whole globe. Grid spacing typically O(200 km) in
  horizontal, 10 levels in vertical.
  Hydrostatic. Lots of physics must be
  parameterized. Used for global weather
  (including your daily forecast) and climate.
• Mesoscale/regional climate models. Cover finite
  part of globe. Grid spacing 10-100 km.
  Nowadays usually nonhydrostatic (but often not
  fully compressible). Same of parameterizations
  as GCMs, but sometimes different ones, esp. for
  convection. Used for study of individual
  synoptic-scale weather events, and regional
  climate prediction (downscaling).

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Full physics models cont.

• Cloud Resolving or Cumulus Ensemble Models.
  Grid spacing O(1 km). Nonhydrostatic.
  Convection isnt parameterized. PBL maybe, maybe
  not. Used for study of individual mesoscale
  weather events, and testing of parameterizations
  for larger-scale models.
• Large Eddy Simulation (LES). A misnomer! Grid
  spacing 10-100 m. Usually used for studies of
  PBL. The energy-containing eddies in what was
  considered small-scale turbulence (in CRM for
  example) are resolved, but lower
  inertial/dissipation range isnt. Still need to
  parameterize radiation, microphysics, and the
  really small-scale turbulence.
• Direct numerical simulation. Grid spacing at the
  Kolmogorov microscale (mm-cm). No
  parameterizations. Not practical for too many
  problems of interest.

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Mesoscale/regional climate models

• Roughly like GCMs in physics/dynamics
  partitioning (unless run at CRM resolution, in
  which case conv. scheme turned off)
• Grids can be and often are nested.
• Mesoscale model Nonhydrostatic. Used mainly
  for weather simulations (few days). Initial
  conditions are important.
• Regional climate model Usually hydrostatic.
  Longer-term simulations, e.g. for downscaling
  of global climate predictions. BCs dominate - and
  are not necessarily well-posed! Come from GCM,
  or from assimilation data set (e.g. Reanalyses)
  RCM nudged towards forcing data at boundaries.
  Usually one-way nesting.

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Example 1 Case study of a weather event using a
mesoscale model
California pineapple express flood
1996-97, Penn State/NCAR MM5 model, figure
courtesy Joe Galewsky. (Galewsky Sobel, MWR, in
press, avail. at www.columbia.edu/ahs129/home.ht
ml)
near-surface ?e and precip
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Example 2 your short-term weather forecasts
NCEP Eta model, 500 hPa forecast issued
5/2/2005. Global models are now also run
at similar resolution, erasing GCM-mesoscale
distinction.
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Example 3 A regional climate simulation
Regional climate (and GCM) simulation of tropical
Atlantic rainfall for April 1994, courtesy
Deborah Herceg. RCM domain is shown. Simulation
run for 1 month.
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Mesoscale/regional climate modeling issues

• Boundary conditions not well posed to begin
  with. More than one way of formulating them.
  Matters more for RCM.
• This leads to sensitivity to domain choice.
  Dont put boundaries near anything important.
• At 10-100 km horizontal grid spacing, basis for
  convective parameterization becomes questionable,
  as mesoscale systems start to be resolved.

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Cloud resolving models

• horizontal grid size 0.5-5 km
• no convective parameterization
• boundary layer parameterization maybe, maybe not
  now basis for this becomes questionable as
  largest PBL eddies are close to being resolved
• cloud microphysics, radiation, subgrid-scale
  turbulence parameterized
• boundary conditions can be open, for short-term
  weather simulations, or periodic, for use like an
  RCM
• In the latter case, large-scale forcings may be
  applied, as in parameterization testing mode of
  RCM
• Sometimes run in 2D, which brings up additional
  issues

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Short-term simulations usually used to understand
dynamics of mesoscale cloud systems
Radar data Houze et al., Bull. Amer. Meteor.
Soc., 1989
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3D CRM Simulation of mesoscale system
cloud (white) precipitation water (yellow)
Courtesy W.-K. Tao, NASA Goddard Mesoscale group
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CRMs in SCM mode

• E.g., for testing convective parameterizations,
  by getting realizations of distributed fields for
  same forcings
• Forced same way as SCM with large-scale
  advective terms. These do not appear in the
  mass budget (though they should).
• For forcings0, get Radiative-convective
  equilibrium
• Generally periodic BCs, to allow long simulations
  primary interest is often in statistics, rather
  than details of individual systems

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Cloud-resolving simulation
RCE, aim to understand spontaneous convective
organization (Tompkins 2001, J. Atmos. Sci. 58,
16501672)
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Same forcing issues as with SCMs

• For long-term tropical simulations with
  prescribed advective forcings, vertical advection
  term more or less determines precipitation
• Still many things meaningfully simulated (T q,
  cloud structure, radiative interactions)
• For determining large-scale controls in precip by
  e.g., SST, can use weak temperature gradient
  approach

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WTG CRM simulation (Perez et al., manuscript
submitted to JAS)

• Goddard Cumulus Ensemble Model
• 2D so mean horizontal wind strongly nudged
• No mean shear
• No horizontal advection terms (incl. moisture)
• WTG strongly relax free-tropospheric T towards
  prescribed profile (taken from RCE simulation)
  ? is then implied as that necessary so ??s/?p
  Q that ? then used in moisture equation
• Vary SST, keeping all else, including T(p) above
  PBL, fixed

MS available at www.columbia.edu/ahs129/pubs.html
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SST vs. Precip
Dashed lines are SST P of the RCE used to
derive T(p)
Right or wrong, the result at least depends
nontrivially on model physics.
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Large-Eddy Simulation

• Really about simulating small eddies resolution
  in 5-100 m range
• Mainly used for studying PBL turbulence
• Large eddies means energy-containing in the
  sense of Kolmogorov grid size should capture at
  least some of the inertial range
• Subgrid-scale (hopefully dissipation-range)
  eddies still parameterized, so this is not Direct
  Numerical Simulation
• If cloud microphysics radiation included, must
  parameterize them

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Entrainment across the inversion capping a
convective BL
Potential temperature contours delineate
the inversion
Sullivan et al. 1998, JAS, 55, pp. 30423064
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Recent developments en route to global CRMs.

• SuperParameterization (Grabowski, Randall,
  Arakawa, Khairoutdinov) put CRM on subset of
  GCM grid box, in lieu of parameterization
• DARE/RAVE (Kuang, Blossey, Bretherton,
  Pauluis) run global (or near-global CRM) but
  reduce computational cost by reducing the time
  and length scales of the large-scale flow

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Initial attempts at Super-Parameterization MJO
Original T21 GCM
GCM with Super-Param
Randall et al. 2003 BAMS 84, 15471564.
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DARE

• Diabatic Acceleration and Rescaling (Kuang et
  al. 2005, Geophys. Res. Lett., 32, L02809, doi
  10.1029/2004GL021024.)
• Reduce size of planet by factor ? increase
  rotation rate by ? also speed up all diabatic
  processes (surface radiative fluxes,
  microphysical timescales etc.) by ?. Gives a
  planet in which large-scale and convective scale
  are not as widely separated.
• Same effect can be obtained by just reducing g
  (Pauluis, Held).

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Kuang et al.s DARE simulation on an equatorial
?-plane
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Self-aggregation and sensitivity to domain size
in RCE
Bretherton et al,. An energy-balance analysis of
deep convective self-aggregation above uniform
SST, JAS, in press
Day 50
Day 6
Only happens for domains 400x400 km!
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