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NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results

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					                        NEMOTAM status
                 Single Observation case
                   Observation field case




                NEMOTAM status
                     and
        NEMOVAR ORCA2 Intern Loop 1st results

                               F. VIGILANT
                                           Project:
                                           VODA



                                    INRIA-LJK

                                  LJK, February, 2010




1/ 25                                       F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                       NEMOTAM status
                                Single Observation case
                                  Observation field case


        plan



          1    NEMOTAM status
                 Adjoint test results
                 Tangent test results


          2    Single Observation case


          3    Observation field case




2/ 25                                                     F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                       NEMOTAM status
                                                                Adjoint test results
                                Single Observation case
                                                                Tangent test results
                                  Observation field case


        plan



          1    NEMOTAM status
                 Adjoint test results
                 Tangent test results


          2    Single Observation case


          3    Observation field case




3/ 25                                                     F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                   NEMOTAM status
                                                            Adjoint test results
                            Single Observation case
                                                            Tangent test results
                              Observation field case




        NEMOTAM is tangent and adjoint counter-part of NEMO, based on:
            NEMO v3.0
            NEMO reference configuration: GYRE, ORCA2, POMME
            selected NEMO reference options

        NEMOTAM development follows validation steps:
            adjoint test
            tangent test
            gradient test




4/ 25                                                 F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                      NEMOTAM status
                                                               Adjoint test results
                               Single Observation case
                                                               Tangent test results
                                 Observation field case




        In summary, we perform the following tests:

             Adjoint tests:

                               < Lδx , δy >                    =      < δx , L∗ δy >                             (1)

             Tangent tests:

                 M(X + p · δX , tn )         =           M(X , tn ) + L(p · δX , tn ) + O(p2 )
                                                                                                                 (2)
             gradient tests:

                       ˜ +p· ˜
                       J(X   J)                =          ˜ ) + p · || ˜ 2 + O(p2 )
                                                          J(X          J||                                       (3)


        with M the direct model, L the linear tangent model and its ajoint L∗ , ˜ the
                                                                                J
        quadratic cost function


5/ 25                                                    F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                   NEMOTAM status
                                                            Adjoint test results
                            Single Observation case
                                                            Tangent test results
                              Observation field case




        Latest main achievements:

            NEMOTAM
                adjoint tests completed for main routine (step_tam.F90) with MPP
                capability
                tangent tests implemented, not fully completed yet
            NEMOVAR (4DVar)
                gradient test implemented (E.Remy)
                exploratory results (single obs and "real case") on ORCA2




6/ 25                                                 F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                       NEMOTAM status
                                                                Adjoint test results
                                Single Observation case
                                                                Tangent test results
                                  Observation field case


        plan



          1    NEMOTAM status
                 Adjoint test results
                 Tangent test results


          2    Single Observation case


          3    Observation field case




7/ 25                                                     F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                                                              Adjoint test results
                              Single Observation case
                                                              Tangent test results
                                Observation field case




        Examples of Adjoint tests: Unitary routine and step_tam routine
        comparing: < Lδx , δy > to < δx , L∗ δy >


         Routine (L)   (L ∗ δx)T W δy           δx T LT W δy                  Rel. Err.      εmachine         Status
         dyn_spg_flt    7.9003 ∗ 1023           7.9003 ∗ 1023                    0.0         2 ∗ 10−16           ok
         tra_ldf_iso   1.5290 ∗ 1018           1.5290 ∗ 1018                    0.0         2 ∗ 10−16           ok


         Routine (L)   (L ∗ δx)T W δy          δx T LT W δy                  Rel. Err.       εmachine          Status
         step U        1.0176 ∗ 1017          1.0176 ∗ 1017                  3 ∗ 10−16      2 ∗ 10−16          warning
         step V        1.6659 ∗ 1018          1.6659 ∗ 1018                  2 ∗ 10−16      2 ∗ 10−16            ok
         step T        8.7766 ∗ 1017          8.7766 ∗ 1017                  1 ∗ 10−16      2 ∗ 10−16            ok
         step S        2.1788 ∗ 1018          2.1788 ∗ 1018                  3 ∗ 10−16      2 ∗ 10−16          warning
         step SSH      2.5607 ∗ 1018          2.5607 ∗ 1018                  2 ∗ 10−16      2 ∗ 10−16            ok
         step          1.3562 ∗ 1018          1.3562 ∗ 1018                  3 ∗ 10−16      2 ∗ 10−16          warning

                   Table: Adjoint test with δx = (δU, δV , δT , δS, δSSH)



8/ 25                                                   F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                       NEMOTAM status
                                                                Adjoint test results
                                Single Observation case
                                                                Tangent test results
                                  Observation field case


        plan



          1    NEMOTAM status
                 Adjoint test results
                 Tangent test results


          2    Single Observation case


          3    Observation field case




9/ 25                                                     F.V       NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                                                              Adjoint test results
                              Single Observation case
                                                              Tangent test results
                                Observation field case




         Validation of Tangent with Taylor expansion (eq. 2) means:

                             M(X + p · δX ) − M(X )
                                                    −→ 1                                                        (4)
                                  L(p · δX )         p


         We control the tangent and,
         if M is not linear, we control the error on the tangent:

                      M(X + p · δX ) − M(X ) − L(p · δX ) ∼ O(p2 )                                              (5)

          note that here M may be a sub-part of the model




10/ 25                                                  F.V         NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                                                              Adjoint test results
                              Single Observation case
                                                              Tangent test results
                                Observation field case


         Examples of Tangent test where we check: Linearity of the tangent,
         M(X + p · δX ) − M(X ) ∼ L(p · δX ) and residu is ∼ O(p2 )




         Figure: Tangent test graph resutst: DYNADV_CEN2 (top left), TRA_SBS
         (bottom left), EOS_BN2 (top right) and ZPS_HDE (bottom right)


11/ 25                                                  F.V         NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                      NEMOTAM status
                                                               Adjoint test results
                               Single Observation case
                                                               Tangent test results
                                 Observation field case




         Conclusion for Tangent and Adjoint tests:
            Adjoint tests
                  general: missing forcing data (emp/emps) in non-linear trajectory at
                  step "zero" (restart)
                  ORCA2: ok
                  GYRE / POMME: work to be done for balance and obs oper. tests
             Tangent tests
                  general: 2 modules with tangent test not fully succefull (residu
                  ∼ O(p) instead of ∼ O(p2 )):
                       traadv_cen2: tangent approximation ignore the finite volume part
                       (upstream) of the numerical scheme
                       dynspg_flt: root cause under investigation
                  ORCA2: DYN part of step_tam.F90 looks ok but the ’full’ testing
                  shows an offset
                  GYRE / POMME: will be used to accelerate step_tam.F90
                  validation



12/ 25                                                   F.V         NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case


     plan



         1   NEMOTAM status
               Adjoint test results
               Tangent test results


         2   Single Observation case


         3   Observation field case




13/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                    NEMOTAM status
                             Single Observation case
                               Observation field case




         Test Configuration
         We use the following configuration for the current results:

                      GRID                                     ORCA2_Z31
                      simulation window                          10 days
                      ASSIM technique                        3DFGAT - 4DVAR
                      SLA obs relative to bck                     +1.0m
                      location                                 North Atlantic
                               Table: configuration settings




14/ 25                                                 F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case




         Sea Surface height increment




            Figure: Sea surface height increments - 4DVAR(left) - 3DFGAT (right)


         4DVAR: Max value +0.23m, Min value -0.02m
         3DFGAT: Max value +0.40m, Min value : 0.0m
         in green: below 5mm in 3DFGAT case, we have the expected signal
         centered on the observation position

15/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case




         Sea Surface height increment




         Figure: Sea surface height increments profile - 4DVAR(left) - 3DFGAT (right)


         At the observation position,
         the 4DVAR-increment is weaker than 3DFGAT case but significative
         signal is spread along the south part of North Atlantic




16/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case


         Temperature increment




             Figure: Temperature profiles along z - 4DVAR(left) - 3DFGAT (right)


         Similar shape with differences:
             3DFGAT: max increment of 3.8◦ C at the 6th level
             4DVAR: max increment of 2.2◦ C at the 8th level (in other area we
             have negative increment, max −0.15◦ C )
17/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case


         Salinity increment




               Figure: Salinity profiles along z - 4DVAR(left) - 3DFGAT (right)

         Similar shape with differences:
             3DFGAT: negative increment down to −0.85 the 15th level
             4DVAR: increment between of −0.46 and 0.07 at the 15th level.
18/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case


     plan



         1   NEMOTAM status
               Adjoint test results
               Tangent test results


         2   Single Observation case


         3   Observation field case




19/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                    NEMOTAM status
                             Single Observation case
                               Observation field case




         Test Configuration
         We use the following configuration for the current results:

                         GRID                                ORCA2_Z31
                         simulation window                    10 days
                         inner loop                             10
                         subdomains settings                    1, 2
                               Table: configuration settings




20/ 25                                                 F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case




         Sea Surface height increment




            Figure: Sea surface height increments - 4DVAR(left) - 3DFGAT (right)


         4DVAR: Max value +0.57, Min value -1.59m
         3DFGAT: Max value +0.54m, Min value : -0.93m



21/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                     NEMOTAM status
                              Single Observation case
                                Observation field case




         Sea Surface temperature increment




         Figure: Sea surface temperature increments - 4DVAR(left) - 3DFGAT (right)


         4DVAR: Max value +6.69◦ C, Min value −14.3◦ C
         3DFGAT: Max value +8.84◦ C, Min value : −7.55◦ C



22/ 25                                                  F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                  NEMOTAM status
                           Single Observation case
                             Observation field case




         both 3DFGAT and 4DVAR cost function can not be compared




23/ 25                                               F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                                      NEMOTAM status
                               Single Observation case
                                 Observation field case




         Current investigation points:

             NEMOVAR (4DVar) - ORCA2
                  investigate test failure when unbalanced velocity part is included
                  into the increment
                  4DVar vs . 3DFGAT minimization results




24/ 25                                                   F.V   NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results
                         NEMOTAM status
                  Single Observation case
                    Observation field case




                 NEMOTAM status
                      and
         NEMOVAR ORCA2 Intern Loop 1st results

                                F. VIGILANT
                                            Project:
                                            VODA



                                     INRIA-LJK

                                   LJK, February, 2010




25/ 25                                         F.V     NEMOTAM status and NEMOVAR ORCA2 Intern Loop 1st results

				
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