Development of a Global QuasiUniform Modeling Framework

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Development of a Global Quasi-Uniform Modeling
Framework
Miodrag Rancic NCEP/NOAA/SAIC ESSIC/UMD
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Content

• Authors bio-sketches
• Research background, objectives and motivation
• Methodology and approach
• Some of the results
• Potential applications
• Future development
• Acknowledgements

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Authors Bio Sketches

• Alma mater
• University of Belgrade in Serbia
• BS, Master of Science and Ph.D. in meteorology
  from the Faculty of Natural and Mathematical
  Sciences in Belgrade
• Some of best know contributors of this school
• Milutin Milankovic Theory of Climate
• Fedor Mesinger (Eta model) and Zavisa Janjic (Eta
  and WRF models)

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• Employment and Affiliations
• University of Belgrade, frmr. Yugoslavia
  (1979-1989)
• CAPS The University of Oklahoma (1989-1992)
• NCEP (1992-1997)
• Goddard Space Flight Center/UMBC (1997-2006)
• NCEP/NOAA (2006-present)
• ESSIC/UMD (2007-present)
• Research Interest
• Numerical modeling
• Data assimilation
• Atmospheric dynamics

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• Teaching record
• Numerical Modeling of Atmosphere
• Atmospheric Dynamics
• Computational Physics
• Application of Statistical Methods in Meteorology
• Weather and Climate of Yugoslavia
• Some of the scientific contributions
• A fourth-order Arakawa type advection scheme
• A first non-hydrostatic version of Eta model
• Mass conservative semi-Lagrangian schemes
• Quasi-uniform spherical grids

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Research background, objectives and motivation

• NCEP regional Eta model
• Step formulation of the terrain
• Arakawa type conservative dynamics
• Semi-staggered distribution of variables
• Full physics including explicit clouds
• Coupled with NOAH surface and subsurface
  hydrology
• Two possible directions for the development in
  mid 90s
• Nonhydrostatic version for operations beyond 10
  km
• Global version global integrations

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Global version

• Why do we need a global version
• Eta model dynamics is ideal for simulation of
  large-scale flow

Why?
Because of a strict enforcement of Arakawa
conserving constraints that should provide a
better statistical agreement between the
simulated and the real atmosphere
Because the E-grid scheme is able to properly
take care of Coriolis effect
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Motivation

• Successful long-term integrations, such as medium
  range weather forecasting ( weeks), seasonal (
  months) and global climate projections (
  decades) and coupling with other components of
  Earth climate system, have a huge potential for
  practical applications in many areas of human
  activity
• Agriculture
• Fishery
• Insurance
• Tourism
• Forestry
• ....

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Challenging science issues

• Better understanding of global warming
• Modeling of paleoclimates
• Review of historical weather and explanation of
  phenomena such as medieval warming and mini ice
  age are some of the most challenging issues
• Effects of ocean circulation and phenomena such
  as ENSO on weather patterns around the globe

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Most importantly

• There is a feeling that simulation of present day
  global climate models cannot fully describe
  signals of major climate indices (such as ENSO or
  North Atlantic Oscillation), because of the low
  resolution noise
• Thus, the idea is to build cloud scale climate
  models, which could hopefully overcome this
  problem
• One of the most serious problems in these arena
  are related to spherical geometry

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3) Method and approach
Standard longitude-latitude grid represents a
problem in global modeling
Longitude-latitude grid
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• Poles represent a problem
• How to maintain conservation of important
  integral constraints?
• How to apply polar filtering?
• Rancic and Nickovic (1988) suggested a solution
  to the first problem which was implemented by
  Wyman (1996) in a GFDL version of the Eta model
• Yet, the feeling remained that the poles
  represent a major nuisance, which came once again
  in the focus of attention with appearance of
  distributed memory computers

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• Polar filtering is a typical example of an
  excessive spatial resolution which does not
  effectively use computing resources
• (c.f., Randal et al. 1997)
• First, the areas around poles are over-resolved
  
• wasting memory
• Then, the effect of this over-resolution is
  thrown away wasting computing time
• Additionally, there is a problem of load
  balancing meaning that in principle the rest of
  the processors is idle while the processors
  assigned to deal with areas around poles are
  computing polar filtering
• And finally, polar filtering generally requires
  global operators which assume a lot of
  communications

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An alternative solution Quasi-uniform grids

• Gnomonic cube was introduced by Sadourny(1972) as
  a potential solution to the problem
• The problem that we now have 8 singular points
  and 12 singular lines

Gnomonic Cube
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Conformal-smoothed cubic grid

• Rancic et al. (1996) and Purser and Rancic (1998)
  suggested a solution to this problem
• It consists of numerically generating conformal
  coordinates thus avoiding breaking of the
  coordinate lines
• And then in the second stage smoothing of
  coordinates in order to increase resolution at
  the corners

Conformal Smoothed Cubic Grid
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Groups that use conformal cubic grid

• Climate model at MIT (John Marshal)
• An oceanic model at NCEP (Dmitry Chalikov)
• Atmospheric model of Australian Weather Bureau
  (John McGregor)
• An oceanic model at Japanese Earth Simulator
• (Motohiko Tsugawa)
• An atmospheric model associated with Japanese
  Earth Simulator (Sung-Dea Kang )

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Conformal-smoothed octagonal grid
Conformal-smoothed grid (Purser and Rancic, 1997)
was introduced with the idea to remove singular
corners out of extratropical region where
baroclinic instability is prevailing mechnanism
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Problems and advantages

• All these grids use curvilinear coordinate frame
  - which means the that fundamental conservation
  laws and the general model structure had to be
  reformulated in terms of general curvilinear
  coordinates
• Also, there is now 8 singular points, but these
  are now weak singularities on which is possible
  to preserve global conservation
• In principle, the difference between cubic and
  octagonal grids as well as other
  generalizations is only in formulation of
  communications

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• Thus we can use the same model formulation for
  all of grid topologies which allow us to refer
  to the global framework rather that to a single
  global model

Cubic Grid
Octagonal Grid
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Furthermore

• We can actually formulate such a framework in
  quite general terms as to provide its future
  application for globalization of other regional
  models (such as NMM), in which case the
  application of the Eta model is just a prototype
  for such a development
• However, dealing with the Eta alone already
  turned out to be challenging and very demanding,
  and imposed a whole set of customizations of
  model dynamics in order to achieve optimal
  performance

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Rotation of horizontal grid
B-grid
E-grid
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• Continuous Equations

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• Here
• Physics is generally defined in columns and does
  not heavily depend on underlying grid geometry

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• Curvilinear formalism

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Some results

• A long term low resolution run
• The Global Eta model is initialized using NCEP
  Global model data
• Global Eta model with global step terrain and
  full physics is run over 10 days at a very low
  resolution of about 250 km
• Only 500 hPa surface is presented in run with the
  cubic grid

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Analysis
GEF
Feb 1, 2005
Feb 1, 2005
Day 0
Feb 2, 2005
Feb 2, 2005
Analysis
GEF
Day 1
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Analysis
Feb 3, 2005
GEF
Feb 3, 2005
Day 2
Feb 4, 2005
Analysis
Feb 4, 2005
GEF
Day 3
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Analysis
GEF
Feb 11, 2005
Feb 11, 2005
Day 10
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Tests of computational Efficiency
C43 GEF Cubic grid with 10586 grid pointsO29
GEF Octagonal grid with 10978 grid pointsGFDL
FMS 144x7210368 grid pointstr running time
(sec per simulated day)tf time spend on polar
filtering
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Comparison with Regional Eta
Regional Eta 48 kmO135 Octagonal45 km C201
Cubic 45 km
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Potential Applications

• Study and simulation of tropical phenomena
  (hurricanes, El Niño, etc.) because a cubic
  version of this model has some 15 higher
  resolution around equator then long-latitude grid
  models with the same number of grid-points
• Study and simulations of polar circulation and
  phenomena (ozone, stratospheric sudden warming,
  interaction with ice, etc.) because neither cubic
  nor octagonal version has a singular polar
  problem and both provide a uniform resolution in
  polar regions

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Medium Range Weather Forecasting

• Both versions comes with a variable resolution as
  an option

Stretched Cubic Grid
Stretched Octagonal Grid
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Technique of grid stretching

• In longer integrations the concept of grid
  stretching may replace current paradigm with two
  models, regional and global, running
  successively, with the regional depending on
  global
• Grid stretching for cubic/octagonal grid was
  introduced and tested by Rancic and Hai (2005)
• The necessary numerical infrastructure, including
  domain decomposition, is also developed

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Grid topologies
Basic Cubic Grid
Cubic Grid 2
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Framework

• Thus, instead of a model operating on a single
  hardwired grid, the result here is a flexible
  framework consisting of a series of alternative
  grids that a user may chose for a particular
  application

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Further development

• A new NSF grant was recently awarded to continue
  this research
• Nonlinear advection scheme (Janjic 1984, as well
  as 4th order version of Rancic 1988) of the
  regional Eta model is written in a strong
  conservative rather then in a vector invariant
  form

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• Important property of this scheme is to
  realistically presents the nonlinear transfer of
  energy among different scales

The immediate consequence is that less noise is
allowed to affect the long scales and slowly
propagating quasi-geostrophic part of the flow
Indirectly, the effect of physical forcing is
more properly propagated up scales
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• New grid topologies

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and a series of other interesting issues

• Inclusion of 6th order conservative differencing
• A new (nu n) alternative vertical coordinate
• Merging with NMM infrastructure
• A series of new applications, including coupling
  with other components of Earth system

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Acknowledgements

• The work on this project has been sponsored by an
  NSF grant (ATM -0113037)
• Some of the material shown is prepared Dr. Hai
  Zhang, former PhD student at UMBC