SpaceTime Mesoscale Analysis System A sequential 3DVAR approach

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Space-Time Mesoscale Analysis SystemA sequential
3DVAR approach

• Yuanfu Xie, Steve Koch
• John McGinley and Steve Albers
• Global Systems Division
• Earth System Research Laboratory

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Space and time variational data assimilation
system

• STMAS is a three-dimensional variational
  analysis, combining horizontal spatial and
  temporal observation to provide a temporally
  consistent surface grid analysis.
• It will be developed into a full
  three-dimensional spatial and temporal analysis
  (STMAS 4D) and will be a new data assimilation
  technique.

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Resolvable Information for a Given Observation
Network
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Single solution of a 3DVAR

• It builds the grid value correlation by
  statistical estimation
• It may not resolve the frontal or boundary
  correctly that that is critical for the automatic
  front detection algorithm.

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Surface Analysis Ideal case
Left Mesonet surface stations Right An
analysis function
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Analytic functionA multi-scale frontal
propagation testing function
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Single 3DVAR approach

• A recursive filter is usually used to
  approximate the error covariance
• After selecting the parameter of recursive
  filter ?, it solves one variational problem

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A single 3DVAR with different RF ?
0.9
0.5
0.7
These analyses tend to approximate the truth
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Recursive filter version of STMAS

• A sequential 3DVAR implemented through a
  recursive filter.
• Solve the 3DVAR with large ?, e.g. 0.999
• Subtract the analysis from observation values
  used in previous 3DVAR analysis
• Reduce ? by a fraction, say ? in (0.5,1)
• Return to step 1 if it is necessary
• Add the previous analyses together.

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Comparison
Single 3DVAR With ?0.5 or 0.9
Truth
STMAS-RF
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Multigrid application in STMAS

• Replacing the recursive filter in an early
  version of STMAS, a multigrid technique is
  implemented to obtain a multiscale analysis.
• The number of grid points over a given domain
  determines the shortest wavelength allowed. A
  multigrid uses the number of grid points to
  control the wavelength.
• STMAS solves its variational problem over the
  coarsest grid and obtains observation information
  for longest waves. By gradually increasing the
  number of grid points, STMAS multigrid gains
  shorter waves by each iterations.

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An efficient analysis system

• Since the multigrid determines the wavelength,
  there is no correlation involved in STMAS
  variational analysis over a given grid.
• Only computation for the cost function is simple
  interpolations.
• A STMAS 5 km surface analysis of 6 state
  variables
• over eastern US (two-third of CONUS) using
  recursive filter spends 15 minutes A multigrid
  STMAS analysis could take about 40 seconds.

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Different Implementation of STMAS
Recursive filter
Wavelet
Multigrid
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STMAS-MG

• STMAS-MG (multigrid) is an efficient, multiscale
  grid analysis system
• It can use all possible data sources, including
  radar, satellite and so on
• It can also impose balances or constraints to
  its analysis directly
• STMAS 4D is under development.