Incorrectly coded option UV_PSOURCE in step2d_LF_AM3.h

[arango]

I have been hunting for an adjoint bug in tl_step2d_LF_AM3.h and ad_step2d_LF_AM3.h for two days. It occurs when the mass point sources UV_PSOURCE option is activated. It turns out the the bug was in the nonlinear code step2d_LF_AM3.h:

      DO is=1,Nsrc
        i=Isrc(is)
        j=Jsrc(is)
        IF (((IstrR.le.i).and.(i.le.IendR)).and.                        &
     &      ((JstrR.le.j).and.(j.le.JendR))) THEN
          IF (INT(Dsrc(is)).eq.0) THEN
            cff=1.0_r8/(on_u(i,j)*                                      &
     &                  0.5_r8*(zeta(i-1,j,knew)+h(i-1,j)+              &
     &                          zeta(i  ,j,knew)+h(i  ,j)))
            ubar(i,j,knew)=Qbar(is)*cff
#  ifdef SOLVE3D
            DU_avg1(i,j)=Qbar(is)
#  endif
          ELSE
            cff=1.0_r8/(om_v(i,j)*                                      &
     &                  0.5_r8*(zeta(i,j-1,knew)+h(i,j-1)+              &
     &                          zeta(i,j  ,knew)+h(i,j  )))
            vbar(i,j,knew)=Qbar(is)*cff
#  ifdef SOLVE3D
            DV_avg1(i,j)=Qbar(is)
#  endif
          END IF
        END IF
      END DO

The override of variables DU_av1 and DV_avg1 is completely incorrect here and should be done separately after all the barotropic time-steps have been carry-out. That is, when

      IF ((iif(ng).eq.(nfast(ng)+1)).and.PREDICTOR_2D_STEP(ng)) THEN
#  ifdef UV_PSOURCE
        DO is=1,Nsrc
          i=Isrc(is)
          j=Jsrc(is)
          IF (((IstrR.le.i).and.(i.le.IendR)).and.                      &
     &        ((JstrR.le.j).and.(j.le.JendR))) THEN
            IF (INT(Dsrc(is)).eq.0) THEN
              DU_avg1(i,j)=Qbar(is)
            ELSE
              DV_avg1(i,j)=Qbar(is)
            END IF
          END IF
        END DO
#  endif
        ...
      END IF

This generated a nasty bug in the adjoint codes. There cannot be redundant operations in the adjoint model... This bug have been in the adjoint codes since the beginning. In the nonlinear model is it a minor correction and not identical results can be achived after this update.