Level of no motion in 4DVar Balance Operator

[arango]

The error covariance balance operator was updated to include the options for what state variable to use as a constraints (in the off-diagonal terms), and a level of no motion option when computing the balanced free-surface contribution.

Notice that the following new parameters were added to input script External/s4dvar.in:

! Balance operator level of no motion depth (m) used when computing balanced
! free-surface contribution, [1:Ngrids].

      LNM_depth == 1000.0d0               ! meters, positive

! Balance operator level of no motion flag used to compute balanced
! free-surface contribution:
!
!      [0] Integrate from local bottom to the surface
!      [1] Integrate from LNM_depth to surface or integrate from local bottom
!          if shallower than LNM_depth
!

      LNM_flag  =  0

! Balance operator logical switches for state variables to consider in the
! error covariance multivariate constraints.

balance(isSalt) =  T                      ! salinity
balance(isFsur) =  T                      ! free-sruface
balance(isVbar) =  F                      ! 2D momentum (ubar, vbar)
balance(isVvel) =  T                      ! 3D momentum (u, v)

I also cleaned few things:

• Removed the internal flag SET_ZETA. This is now the default configuration in all adjoint-based algorithm. This option was introduced a while ago during the perfect restart. The assignment of the free-surface to is its fast-time averaged value is now done by calling set_zeta in main3d and not in rhs3d. This change was supported in the adjoint-based algorithms by activating this flag. This is fully tested and we get identical solutions.

• Removed obsolete routine load_forcing from frc_adjust.F. This is not longer necessary.

• Added a new global attribute state_vector to output NetCDF file containing the variables and their order in the 4DVar state vector.