Fixing ROMS-JEDI LinearModel Unit Test

[hga007]

Description

This PR includes corrections and updates to several routines to fix the ROMS-JEDI LinearModel Unit Tests, guaranteeing the symmetry of the TLM/ADM operators and convergence of the 4D-Var algorithms:

• Fixed the symmetry between the tangent linear and adjoint operators to a satisfactory level in the dot product. It now passes the LinearModel unit test case and our Sanity Symmetry test:

[dot0,dot1] = tlad_dotproduct(TLname, ADname, false);             % Native ROMS interface

TL/AD date: 01-03 00:00:00 / 01-03 06:00:00, TLrec = 01, ADrec = 13, Dot Product = 112.84303514
TL/AD date: 01-03 00:30:00 / 01-03 05:30:00, TLrec = 02, ADrec = 12, Dot Product = 187.74224524
TL/AD date: 01-03 01:00:00 / 01-03 05:00:00, TLrec = 03, ADrec = 11, Dot Product = 112.04213911
TL/AD date: 01-03 01:30:00 / 01-03 04:30:00, TLrec = 04, ADrec = 10, Dot Product = 142.80619119
TL/AD date: 01-03 02:00:00 / 01-03 04:00:00, TLrec = 05, ADrec = 09, Dot Product = 132.49011272
TL/AD date: 01-03 02:30:00 / 01-03 03:30:00, TLrec = 06, ADrec = 08, Dot Product = 158.24016596
TL/AD date: 01-03 03:00:00 / 01-03 03:00:00, TLrec = 07, ADrec = 07, Dot Product = 177.18011365
TL/AD date: 01-03 03:30:00 / 01-03 02:30:00, TLrec = 08, ADrec = 06, Dot Product = 179.46528054
TL/AD date: 01-03 04:00:00 / 01-03 02:00:00, TLrec = 09, ADrec = 05, Dot Product = 192.82609918
TL/AD date: 01-03 04:30:00 / 01-03 01:30:00, TLrec = 10, ADrec = 04, Dot Product = 161.60554627
TL/AD date: 01-03 05:00:00 / 01-03 01:00:00, TLrec = 11, ADrec = 03, Dot Product = 108.95125745
TL/AD date: 01-03 05:30:00 / 01-03 00:30:00, TLrec = 12, ADrec = 02, Dot Product = 98.12076241
TL/AD date: 01-03 06:00:00 / 01-03 00:00:00, TLrec = 13, ADrec = 01, Dot Product = 112.84303514
  
Initial, dot0 = 112.84303514
Final,   dot1 = 112.84303514
    dot1-dot0 = 2.55795385e-13

[dot0,dot1] = tlad_dotproduct(TLjedi, ADjedi, false);             % ROMS-JEDI interface
  
TL/AD date: 01-03 00:00:00 / 01-03 06:00:00, TLrec = 01, ADrec = 13, Dot Product = 119.53077750
TL/AD date: 01-03 00:30:00 / 01-03 05:30:00, TLrec = 02, ADrec = 12, Dot Product = 176.32572472
TL/AD date: 01-03 01:00:00 / 01-03 05:00:00, TLrec = 03, ADrec = 11, Dot Product = 128.80173146
TL/AD date: 01-03 01:30:00 / 01-03 04:30:00, TLrec = 04, ADrec = 10, Dot Product = 140.61649865
TL/AD date: 01-03 02:00:00 / 01-03 04:00:00, TLrec = 05, ADrec = 09, Dot Product = 136.77333523
TL/AD date: 01-03 02:30:00 / 01-03 03:30:00, TLrec = 06, ADrec = 08, Dot Product = 170.12330080
TL/AD date: 01-03 03:00:00 / 01-03 03:00:00, TLrec = 07, ADrec = 07, Dot Product = 180.70557751
TL/AD date: 01-03 03:30:00 / 01-03 02:30:00, TLrec = 08, ADrec = 06, Dot Product = 183.24860942
TL/AD date: 01-03 04:00:00 / 01-03 02:00:00, TLrec = 09, ADrec = 05, Dot Product = 184.52098633
TL/AD date: 01-03 04:30:00 / 01-03 01:30:00, TLrec = 10, ADrec = 04, Dot Product = 164.24229109
TL/AD date: 01-03 05:00:00 / 01-03 01:00:00, TLrec = 11, ADrec = 03, Dot Product = 116.54522860
TL/AD date: 01-03 05:30:00 / 01-03 00:30:00, TLrec = 12, ADrec = 02, Dot Product = 112.97778545
TL/AD date: 01-03 06:00:00 / 01-03 00:00:00, TLrec = 13, ADrec = 01, Dot Product = 119.53077750
  
Initial, dot0 = 119.53077750
Final,   dot1 = 119.53077750
    dot1-dot0 = 1.57740487e-12

• The ROMS-JEDI driver jedi_roms.h was refactored to several initialization phases:

  • ROMS_initializeP1: It reads in standard input parameters. Then, allocate/initialize parameters and variables when switch LsetROMS is on. It sets TLM time-stepping parameters. The time-stepping indices are initialized as kstp=1, knew=2, krhs=3, nstp=1, nnew=2, and nrhs=nnew.
  • ROMS_initializeP2: It completes the initialization using the state vector provided by OOPS and computes depths, density, and horizontal mass fluxes.
  • ROMS_initializeP3: It computes the initial depths and level thicknesses from the initial free-surface field. Additionally, it initializes the nonlinear state variables for all time levels and applies lateral boundary conditions.

• Introduce new modules post_initial.F and associated TLM, RPM, and ADM versions that compute the initial depths and level thicknesses from the initial free-surface field, initialize the nonlinear state variables for all time levels, and apply lateral boundary conditions on the first time step in main3d.F:

 # ifndef JEDI
!
!-----------------------------------------------------------------------
! On the first timestep, it computes the initial depths and level
! thicknesses from the initial free-surface field. Additionally, it
!  initializes the nonlinear state variables for all time levels and
! applies lateral boundary conditions.
!-----------------------------------------------------------------------
!
            DO ig=1,GridsInLayer(nl)
              ng=GridNumber(ig,nl)
              IF (iic(ng).eq.ntstart(ng)) THEN
                CALL post_initial (ng, iNLM)
              END IF
            END DO
# endif

Dependencies

None.

Impact

The 4D-Var dual and primal formulations run satisfactorily in ROMS-JEDI. However, further routes are required before it can be run operationally.