Computation of ALADIN singular vectors: very first results

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Computation of ALADIN singular vectors very
first results

• Presented by András HORÁNYI
• On behalf of Edit HÁGEL
• Hungarian Meteorological Service

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Outline of the talk

• The singular vector technique
• Test of the tangent linear and adjoint code
• First tests with ALADIN SVs, a case study
• Future work

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The singular vector technique (1)

• Problem search for the most rapidly growing
  perturbations to a given atmospheric state
• Solution singular vector technique
• Fastest growth perturbations which maximize
• To solve this problem some assumptions and
  choices (degrees of freedom) are needed

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The singular vector technique (2)

• Main assumption
• perturbations grow linearly in time ( ? use of
  the tangent linear model)
• Choices
• how to measure the size of a perturbation (choice
  of norms at initial and final time)
• what region(s) to focus on (optimization areas)
• between which two model layers to allow the
  perturbations to grow
• how long to allow the perturbations to grow for
  (optimization time)

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The singular vector technique (3)

• The SV computation requires the use of the
  tangent linear (TL) and the adjoint (AD) code
• First necessary steps
• Test of the tangent linear code conf. 501 in
  ALADIN
• Test of the adjoint code conf. 401 in ALADIN

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Test of the tangent linear (conf. 501)

• The following should be true (Taylor formula)
• where ?10-b and b is an integer going from 0 to
  10
• M is the nonlinear model
• L is the tangent linear model
• Using cycle 30 the TL code works well

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Test of the tangent linear (conf. 501)

• ALFA 1.0E-10 RAT 0.1002425599276024E01
• ALFA 1.0E-09 RAT 0.9993331534012678E00
• ALFA 1.0E-08 RAT 0.1000065662569316E01
• ALFA 1.0E-07 RAT 0.1000000064146868E01
• ALFA 1.0E-06 RAT 0.1000000267929838E01
• ALFA 1.0E-05 RAT 0.1000000343874977E01
• ALFA 1.0E-04 RAT 0.1000002775468967E01
• ALFA 1.0E-03 RAT 0.1000027748189749E01
• ALFA 1.0E-02 RAT 0.1000277468132422E01
• ALFA 1.0E-01 RAT 0.1002773551970114E01
• ALFA 1.0E00 RAT 0.1027650625584925E01
• Parameter Vorticity, wavenumber 4372

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Test of the tangent linear (conf. 501)
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Test of the adjoint (conf. 401)

• Testing the adjoint code in the 3D primitive
  equations hydrostatic model by comparing two
  scalar products
• The two scalar products S1 and S2 must be equal
  (adjoint equality)!

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Test of the adjoint (conf. 401)

• Tests were done with cy28t3 both on HMS IBM and
  Météo-France Fujitsu supercomputer
• The two scalar products (S1 and S2) did not
  agree, dependency on the number of processors was
  found!
• After some discussion with French colleagues new
  tests were performed with cycle 30
• TEST OF THE ADJOINT
• 12345678901234567890
• lt F(X) , Y gt 0.32056706261337210000E00
• lt X , F(Y) gt 0.32056706261337200000E00
• THE DIFFERENCE IS 1.560 TIMES THE ZERO OF
  THE MACHINE

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First tests with ALADIN SVs (conf. 601)

• SV code in ALADIN is maintained but has not been
  really used in the last couple of years ? careful
  tests are needed!
• Lack of detailed and updated documentation is
  also a problem
• The most recent documentation about SV
  computation is provided by ECMWF for cycle 25R1
  (perhaps a more recent internal documentation
  exists?)
• On ARPEGE/ALADIN side the last available
  (detailed) documentation is for cycle 22T2
• For the experiments we were using cycle30 which
  is not even the newest one

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First tests with ALADIN SVs (conf. 601)

• To compute SVs, certain choices have to be made
• Norms used at initial and final times
• Optimization area(s)
• Optimization time
• Vertical optimization
• Other important issues
• What resolution should be used for SV
  computation?
• How many SVs should be computed?
• How many iterations are necessary for that?
• LBC Coupling frequency?

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First tests with ALADIN SVs (conf. 601)

• Our choices for the first tests
• Norms total energy norm (initial and final time)
• Optimization area 55.78N/33.67S/1.83W/39.79E
• Optimizationt time 12 hours
• Vertical optimization between level 1 and 46
  (all levels)
• Resolution 20 km
• LBC Coupling every 3 hours

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How many iterations are necessary?
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Total CPU time required
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Total memory required
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Case study 28 June 2006, 12 UTC
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Case study

• ARPEGE and ALADIN SVs were computed and compared
• Same target area and target time (12 hours)
• Truncation in case of ARPEGE T95
• Resolution in case of ALADIN 20 km
• Animations
• First singular vector
• Temperature on model levels
• Contour interval 0.01

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Case study ARPEGE SVs
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Case study ALADIN SVs
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How to continue?

• Study the ALADIN SVs carefully
• Compare them with high resolution ARPEGE (and
  possibly ECMWF) SVs
• Application of simplified physics
• Perform EPS experiments where the ICs are
  perturbed using the ALADIN SVs (contribution to
  GLAMEPS)
• Questions to be answered in this case
• How to build the perturbations from the SVs?
• What to use as LBCs for such a forecasts?

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Thanks to many people for their help, especially
to

• Martin Leutbecher from ECMWF
• Jan Barkmeijer from KNMI
• Claude Fischer from Météo-France

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Thank you for listening!