Supercomputing/HPC Technology and Its Applications in Air/Sea

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On Applications of State-of-the-Art
Mathematical-Computer Models in
Oceanic-Atmospheric Environmental Sciences
Technologies.

• Le Ngoc Ly (1,2,3)
• (1)Institute of Oceanic, Atmos. Env. Technology
  (IOAET) Hanoi, Vietnam
• (2)Applied Science International (APSIN), Hanoi,
  Vietnam
• (3)Naval Postgraduate School, Monterey, CA USA
• Emails le_ASI_at_yahoo.com
  lely_at_ioaet.org
• Webs www.ioaet.orgwww.apsin.netww
  w.oc.nps.edu/lely

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Outline

• I - Introduction
• II - Supercomputing/HPC in Vietnam
• III - Basic of Atmospheric and Oceanic Models
• IV - Supercomputing/HPC with
• Data Assimilation Technique
• Numerical Grid Generation Technique
• Multi-block Grid 2-D Domain Decomposition
  Technique
• on Parallel Platforms
• V - Some Results of Hurricane Prediction Model
  With SC/HPC Technology
• VI - Conclusion

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I-Introduction

• Most complicated problems for Atm., Ocean Env.
  Modeling Complicated Physics, Numerical
  techniques, Dealing with big Data sets, Needing
  very High Resolutions (especially for Marine
  Biology modeling), very big Computing domain!
  No SC is too big, too fast for these problems!
• Typical Problems of Atmospheric, Oceanic Env.
  Sciences Weather Climate of various scales,
  Large Rain Forecasts, Hurricane Storms, Floods,
  Tide, Waves, Strom Surges, Ocean Circulation,
  Physical-Biological Coupling, Tsunami, Air/Water
  Pollutions, .Forecasts especially, Climate
  Modeling Climate Change!
• They are among 1 customers of Supercomputing
  (especially Climate Modeling, see next!).

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HPC/SU IN VIETNAM

• IOAET and now APSIN is the sole representative
  for Cray CX1 Supercomputer in Vietnam.
• We will have Cray CX1 desk supercomputer with
  HPC window2008 Red Hat Linux ROCKS by 12/2009
  in Hanoi.

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Some Advantages of Cray CX1

• Architecture vSMP using ScaleMP allows CX1
  effective as a big supercomputer (global
  memory) , while CX1 is low cost supercomputer
  as a cluster
• Desk supercomputer
• Low level of Noise and Heat to be a
  desk/personal supercomputer
• Do not need a big room for CX1
• Ideal supercomputer for a group of
  researchers/production or a U. Dept.,
  Institutions or even CX1 can be a personal
  supercomputer
• Low cost of maintenance, operating and software
  writing
• Highest level of ratio (performance/total cost)!

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III - Basic of Atmospheric/Oceanic Evm
Models

• Hydrodynamic Model with Primitive Equations.
• Full Air/Sea Boundary Layer Physics (Simplified
  BL Physics for Climate models!) Full and
  simplified Turbulence Closure.
• Numerical schemes/Methods Fine-differential
  methods with Popular Progonki/Pivotal-Condensat
  ion.
• Some most popular forecast modelWRF (atm.
  meso-scale) POM (ocean) GFDL Hurricane Model
  NCAR Climate model Physical-Biological Coupling
  Model NAM (Coupled wave-circulation model).
• Most Importance a) Micro-Physics
  Parameterizations
• b) SC/HPC
  Technology Resolutions problems and Fast with
  Large Memory to handle Forecasts/Prediction
  problems (including Economy/Financial Services)
  with Large Data Sets and Data Assimilation
  Techniques.

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IV - Supercomputing/HPC withDATA ASSIMILATION

• 1808? C. Gauss found solution for forecast
  Astronomy problem of appearing Heaven body
  based on observations.
• He formulated the problem as a minimization (or
  optimization) problem.
• Follow Gauss need to formulation the optimization
  problem as least square-fit problem. Almost all
  data assimilation schemes are based on this idea!
  
• Prof. Lev Gandin (LHMU, USSR, 1985? USA)
  formulated
• Increment (d)
  Observation - Forecast
• 
  
• 
  uij fij ? wkdk
• 
  ?ij dfij ?k
  wkdk
• Gandin finds wk so that the mean-square
  error of the estimate is minimized.
• To minimize , av(?ij .?ij), a necessary condition
  is that
• derev of av(?ij .?ij) 0 for each wk.

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• We have   T F W(T F) 
• where T Temperature estimate F
  Forecast Temp T Observation of Temp and W
  Weight.
• Then the Principle
• Estimate at Grd pnts Forecast /Guess at
  Grd pnts W Sum of d
• We have fields on grid points. With some
  model/dynamical consistency/condition adjustments
  , we have objectively analyze the data to gridded
  fields.
• Adjust the control vector (initial conditions,
  boundary conditions, other parameters) so that
  the difference between the forecast and
  observations (now in the form of estimates from
  the objective analysis) is minimized!
• We need to set up cost function(al) I of
  difference of obs and forecast. Find min by
  taking derivative of I set it to zero. Solution
  will be the optimum initial state.

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• In general, neither one of these methods are
  practical for typical problems in geophysical
  sciences. These methods require too much
  Computer Time!!!
• There are various strategies for finding Grad
  I but the most efficient is associated with the
  mathematical methodology called adjoint model.
• The adjoint model basically achieves the back
  substitution in a most efficient manner
  equivalent to 1 forward model integration.
• One of popular adjoint model of Thacker
  (Oceanographer at Atlantic Oceanographic Marine
  Lab in Miami, FL) is based on The Method of
  Lagrange Multiplier from Math Physics by
  modifying I then L (Lagrangian) is expressed in
  terms of I and forecast equations.
• Here, we would like to find Initial (guess)
  fields such that the forecasts minimize the
  squared (discrepancies d).
• That means to find minimum we need to take
  derivatives of L and then set to zero.
• Name adjoint cones from the matrix algebra!

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Kalman Filter

• In Kalman Filter we need to have Tangent Linear
  Model (TLM) for the model forecast equation.
  This can handle nonlinear dynamics though
  linearization.
• We formulating problem as
• Xn1 Fn Xn
  Weigh . Tn1 - Fn Xn
• Again in the Spirit of Gandin, we can subtract
  the True Value from both sides
• ?n1
  fn W . dTn1 - dfn1
• Need to find W so that Ave(?n1 x ?n1)
  minimized!
• Kalman permits a step by step update of the
  weight W based on previous history of the
  estimation process.
• Advantage of Kalman Filter
• a) model and observational
  errors are simultaneously accounted.
• b) weight matrix is
  automatically updated each time step.
• Disadvantage weighting matrix can be a big
  problem - a lot of matrix operations Computing
  time problem!

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Nudging Technique of DA for an Ocean Forecast
System PHYSICS - W(Mod Obs)Obs Surface
Current
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V - Supercomputing/HPC with Numerical Grid
Generation Technique

• Traditional grids Rectangular, orthogonal grids
• Non-traditional grids Curvilinear,
  nearly-orthogonal grids
• Vertical grids

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NUMERICAL GRID GENERATION

• We need more complicated grid systems than
  traditional single block grids
• Such as a) Nesting grids
• b) Curvilinear-coastal
  following (orthogonal nearly orthogonal)
  multi-block grids
• c) Moving grids
• d) Adapted grids
• Numerical Grid Generation (Jose Thompson Soni)
  International Grid Associate
• Software developed by a group of Applied Math
  people. They used properties of Elliptic
  Parabolic Equations to generate numerical grids.
  These Grid Packages are very popular in the
  world.
• Numerical Grid Generation Technique to Coastal
  Ocean Modeling.
• A New Advance in Coastal Ocean Modeling
  Application of the Grid Generation Technique.
  High Performance Computing Contributions to DoD
  Mission Success 1998

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IV - Supercomputing/HPC withMulti-Block and 2-D
Domain Decomposition (Traditional App.) on
Parallel Platforms for Coastal Ocean Modeling
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Thank You!