[Mitgcm-support] Note: November 9, 2000

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NOTES FROM THE ASSIMILATION MEETING : 09 November 2000    
     
1) BC K-filter  
--------------- 
   - Two bugs were found in the transition matrix derivation; The
     fine-to-coarse transformation used incorrect layer
     thicknesses. The time integration of displacement had an extra
     time-step.

   --> Leading (~100) eigenvalues of the corrected transition matrix
     are now nearly identical with those of MOM (JGR '99) as shown in
     this figure[1].  The leading eigenvalues are what dictate the
     asymptotic error.  Left column is eigenvalues of 1-day transition
     matrix.  Right column is same but for 3-days.  Lower figures are
     close-ups of upper figures.  Solid black is MOM.  Solid blue is
     corrected MITgcm.  Solid red is old 1-day transition matrix.
     (Dash red is red times 1.06 [See 11/02/00[2]], dash blue is 3-day
     transition matrix of 11/02/00.)  The trailing eigenvalues of MOM
     are still larger than MITgcm; Is this due to the "ringing"?

   --> The spatial structure of the time-asymptotic simulation error
     estimate (based on 1-day transition above and NCEP covariance) is
     sensible as shown in this figure[3].  (Assumed 3-day wind error
     decorrelation.) 

   --> The assimilation based on the corrected transition matrix shows
    improvements as measured by the difference between simulation
    model-data residuals and the innovation (dynamic update
    residuals).  The measure is shown as a function of time[4] and space[5].
    The green curve in the temporal skill is the simulation residual
    variance minus innovation variance.  (Blue is the same but for the
    barotropic filter.  Purple is the difference between innovation
    variance and filtered residual of the baroclinic filter.  Red is
    the same for the barotropic filter.)  The negative skill away from
    the tropical Pacific is due to sea level not being compared in the
    plot at the correct time; Simulation is based on 12-hourly outputs
    whereas assimilation is carried out every 6-hours.  Significant
    sea level variations occur over 6-hours in shallow regions that
    were not sampled in the simulation.  The negative skill east of
    Taiwan may be due to excessive model error estimates in this
    region, as seen in the simulation error estimate. 

 2) Adjoint  
----------- 
  - The data uncertainty weights based on model-data comparisons did 
    make the 3-month assimilation better after all.  This figure[6]
    compares model estimates with TAO.  Assimilation invariably is
    closer to TAO than simulation.

  - There was a bug in the flux constraint.  Instead of adding the
    cost every 10-days, the cost was added every time-step, thus
    effectively reducing the uncertainty estimate of the flux.  A
    single adjoint iteration after correcting this bug lead to a 25%
    decrease in cost.  Much larger correction and better fit is
    expected.  Will need 10 more iterations for the 3-month
    assimilation before the T/P meeting.

  - The adjoint of the new KPP package now works as well as the old
    package did.  The adjoint has run OK for at least 3-days when 
    convection and shear instability are turned off.

  3) BT filter 
------------- 
  - Comparisons between results of the barotropic filter (kf014) and
    bottom pressure gauges show improvements in coherence[7] at periods
    longer than 20-days.  The degradation at shorter periods may be
    due to the comparisons being done with the filtered results, which
    have discontinuities every 6-hours.  Better comparisons may need
    to wait until the smoother is run and/or after finer error
    calibration.

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[4] http://escher.JPL.NASA.GOV:2000/hosts/escher/escher2/medea/if/forum/t71d_1993.ps
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