VERY IMPORTANT: Corrected bugs in tracer advection

[arango]

Corrected critical bug in some of the tracer advection options:

• Corrected a bug in the HSIMT advection. Previously, I fixed the issue that three ghost points are needed for this scheme. At that time, I missed making a similar change in the computation of the inverse thickness (oHz). Therefore, in step3d_t.F we need to have

        logical :: LapplySrc, Lhsimt, Lmpdata
        ...
        
        Lhsimt =ANY(Hadvection(:,ng)%HSIMT).and.                          &
       &        ANY(Vadvection(:,ng)%HSIMT)
        Lmpdata=ANY(Hadvection(:,ng)%MPDATA).and.                         &
       &        ANY(Vadvection(:,ng)%MPDATA)
        ...
        
  !
  !  Compute reciprocal thickness, 1/Hz.
  !
        IF (Lmpdata.or.Lhsimt) THEN
          DO k=1,N(ng)
            DO j=Jstrm2,Jendp2
              DO i=Istrm2,Iendp2
                oHz(i,j,k)=1.0_r8/Hz(i,j,k)
              END DO
            END DO
          END DO
        ELSE
          DO k=1,N(ng)
            DO j=Jstr,Jend
              DO i=Istr,Iend
                oHz(i,j,k)=1.0_r8/Hz(i,j,k)
              END DO
            END DO
          END DO
        END IF
  

  I have been hunting on and off for a bug in the HSIMT scheme for awhile. Many thanks to Pierre St-Laurent for ​reporting this issue. It is always helpful when another set of eyes look into a code.

• Corrected a weird bug in the tangent linear advection switches. In inp_par.F we need to have instead:

  #if defined TANGENT || defined TL_IOMS
  !
  !  Set tracer advection scheme switches for the tangent linear models
  !  (TLM and RPM) to the same values as the adjoint model.
  !
        DO ng=1,Ngrids
          DO i=1,NT(ng)
            tl_Hadvection(i,ng)%AKIMA4    = ad_Hadvection(i,ng)%AKIMA4
            tl_Hadvection(i,ng)%CENTERED2 = ad_Hadvection(i,ng)%CENTERED2
            tl_Hadvection(i,ng)%CENTERED4 = ad_Hadvection(i,ng)%CENTERED4
            tl_Hadvection(i,ng)%HSIMT     = ad_Hadvection(i,ng)%HSIMT
            tl_Hadvection(i,ng)%MPDATA    = ad_Hadvection(i,ng)%MPDATA
            tl_Hadvection(i,ng)%SPLINES   = ad_Hadvection(i,ng)%SPLINES
            tl_Hadvection(i,ng)%SPLIT_U3  = ad_Hadvection(i,ng)%SPLIT_U3
            tl_Hadvection(i,ng)%UPSTREAM3 = ad_Hadvection(i,ng)%UPSTREAM3
  !
            tl_Vadvection(i,ng)%AKIMA4    = ad_Vadvection(i,ng)%AKIMA4
            tl_Vadvection(i,ng)%CENTERED2 = ad_Vadvection(i,ng)%CENTERED2
            tl_Vadvection(i,ng)%CENTERED4 = ad_Vadvection(i,ng)%CENTERED4
            tl_Vadvection(i,ng)%HSIMT     = ad_Vadvection(i,ng)%HSIMT
            tl_Vadvection(i,ng)%MPDATA    = ad_Vadvection(i,ng)%MPDATA
            tl_Vadvection(i,ng)%SPLINES   = ad_Vadvection(i,ng)%SPLINES
            tl_Vadvection(i,ng)%SPLIT_U3  = ad_Vadvection(i,ng)%SPLIT_U3
            tl_Vadvection(i,ng)%UPSTREAM3 = ad_Vadvection(i,ng)%UPSTREAM3
          END DO
        END DO
  #endif
  

  Before, the assigment was to use the nonlinear values instead. As a consequence, the 4D-Var cost function was not decreasing correctly and the minimization failed because the broken symmetry between tangent linear (TLM) and adjoint (ADM) model operators. We need to have the same advection scheme in both TLM and ADM. Recall that in roms.in, the user specify just the values for the adjoint model.

Many thanks to Julia Levin for reporting this problem and Andy Moore for his help in debugging.