!  4DVar assimilation input parameters.
!
!svn $Id: s4dvar.in 995 2020-01-10 04:01:28Z arango $
!========================================================= Hernan G. Arango ===
!  Copyright (c) 2002-2020 The ROMS/TOMS Group                                !
!    Licensed under a MIT/X style license                                     !
!    See License_ROMS.txt                                                     !
!==============================================================================
!                                                                             !
! Input parameters can be entered in ANY order, provided that the parameter   !
! KEYWORD (usually, upper case) is typed correctly followed by "="  or "=="   !
! symbols. Any comment lines are allowed and must begin with an exclamation   !
! mark (!) in column one.  Comments may  appear to the right of a parameter   !
! specification to improve documentation.  Comments will be ignored  during   !
! reading.  Blank lines are also allowed and ignored. Continuation lines in   !
! a parameter specification are allowed and must be preceded by a backslash   !
! (\).  In some instances, more than one value is required for a parameter.   !
! If fewer values are provided, the  last value  is assigned for the entire   !
! parameter array.  The multiplication symbol (*),  without blank spaces in   !
! between, is allowed for a parameter specification.  For example, in a two   !
! grids nested application:                                                   !
!                                                                             !
!    AKT_BAK == 2*1.0d-6  2*5.0d-6              ! m2/s                        !
!                                                                             !
! indicates that the first two entries of array AKT_BAK,  in fortran column-  !
! major order, will have the same value of "1.0d-6" for grid 1,  whereas the  !
! next two entries will have the same value of "5.0d-6" for grid 2.           !
!                                                                             !
! In multiple levels of nesting and/or multiple connected domains  step-ups,  !
! "Ngrids" entries are expected for some of these parameters.  In such case,  !
! the order of the entries for a parameter is extremely important.  It  must  !
! follow the same order (1:Ngrids) as in the state variable declaration. The  !
! USER may follow the above guidelines for specifying his/her values.  These  !
! parameters are marked by "==" plural symbol after the KEYWORD.              !
!                                                                             !
!==============================================================================
!

! Number of iterations in the biconjugate gradient algorithm used to solve
! the elliptic equation for sea surface height in the error covariance
! balance operator, [1:Ngrids].

          Nbico == 200

! Parameters used to compute balanced salinity in terms of temperature using
! empirical T-S relationships in the error covariance balance operator,
! [1:Ngrids].

       dTdz_min == 0.001d0                ! minimum dT/dz (Celsius/m)
       ml_depth == 100.0d0                ! mixed-layer depth (m; positive)

! 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)

! Parameter to process the Nvct eigenvector of the stabilized representer
! matrix when computing array modes (here, Nvct=Ninner is the most important
! while Nvct=1 is the less important) OR cut-off parameter for the clipped
! analysis to disregard potentially unphysical array modes (that is, all
! the eigenvectors < Nctv are disgarded).

           Nvct =  50

! Upper bound on the relative error of the gradient for the Lanczos
! conjugate gradient algorithm.

        GradErr = 1.0d-4

! Maximum error bound on Hessian eigenvectors in the Lanczos conjugate
! gradient algorithm.  Note that even quite inaccurate eigenvectors are
! useful for pre-conditioning purposes.

       HevecErr = 1.0d-1

! Switch (T/F) to compute approximated Hessian eigenpairs in the Lanzos
! conjugate gradient algorithm.

     LhessianEV = T

! Switch (T/F) to activate hot start in weak-constraint (W4DVAR and
! W4DPSAS) algorithms of subsequent outer loops.

      LhotStart = T

! Switch (T/F) to activate IS4DVAR conjugate gradient preconditioning.
! Two types of Limited-Memory Preconditioner (LMP) are available
! (Tshimanga et al., 2008): spectral LMP and Ritz LMP.

       Lprecond = F

! Switch to activate either Ritz Limited-Memory Preconditioner (T)
! or spectral Limited-Memory Preconditioner (F) to the IS4DVAR algorithm.

          Lritz = T

! If preconditioning, specify number of eigenpairs to use. If zero,
! use HevecErr parameter to determine the number of converged eigenpairs.

        NritzEV = 0

! If weak constraint 4DVar, set number of iterations in the Lanczos
! algorithm used to estimate the posterior analysis error covariance
! matrix.

         NpostI = 50

! If observations impact or observations sensitivity, set the 4D-Var
! outer loop to process. It must be less or equal that Nouter.

        Nimpact = 1

! Number of extra-observation classes (NextraObs), observation type
! indices (ExtraIndex), and observation type names (ExtraName) to
! consider in addition to the 1-to-1 associated with the state
! variables. It is used in observation operators that require more that
! one state variable to evaluate particular observation type like
! HF radials, travel time, pressure, etc.
!
! In any application, the number of observation types is computed as:
! NobsVar = NstateVar + NextraObs.
!
! NextraObs values are expected for keywords ExtraIndex and ExtraName.
! If NextraVar > 1, enter one observation type names per line and
! use a backslash as the continuation.

      NextraObs = 0

     ExtraIndex = 20

      ExtraName = radial

! If weak constraint 4DVar, set diffusive relaxation coefficients (m2/s)
! used to relax representer tangent linear solution to privious Picard
! iteration linearized trajectory.

      tl_M2diff ==   0.0d0                ! 2D momentum
      tl_M3diff == 100.0d0                ! 3D momentum

       tl_Tdiff ==  50.0d0  50.0d0        ! NT tracers

! Switches (T/F) to create and write error covariance normalization
! factors for model, initial conditions, boundary conditions, and
! surface forcing. If TRUE, these factors are computed and written
! to NRMname(1:4) NetCDF files. If FALSE, they are read from NRMname(1:4)
! NetCDF file. The computation of these factors is very expensive and
! need to be computed only once for a particular application provided
! that grid land/sea masking, and decorrelation scales remains
! the same. Notice that four values are needed (1=initial conditions,
! 2=model, 3=boundary conditions, 4=surface forcing) per each nested
! grid, [1:4,1:Ngrids].

        LdefNRM == F F F F                ! Create a new normalization files
        LwrtNRM == F F F F                ! Compute and write normalization

! Switches to compute the correlation normalization coefficients for
! model error covariance.

 CnormM(isFsur) =  T                      ! 2D variable at RHO-points
 CnormM(isUbar) =  T                      ! 2D variable at U-points
 CnormM(isVbar) =  T                      ! 2D variable at V-points
 CnormM(isUvel) =  T                      ! 3D variable at U-points
 CnormM(isVvel) =  T                      ! 3D variable at V-points
 CnormM(isTvar) =  T T                    ! NT tracers

! Switches to compute the correlation normalization coefficients for
! initial conditions error covariance.

 CnormI(isFsur) =  T                      ! 2D variable at RHO-points
 CnormI(isUbar) =  T                      ! 2D variable at U-points
 CnormI(isVbar) =  T                      ! 2D variable at V-points
 CnormI(isUvel) =  T                      ! 3D variable at U-points
 CnormI(isVvel) =  T                      ! 3D variable at V-points
 CnormI(isTvar) =  T T                    ! NT tracers

! Switches to compute the correlation normalization coefficients for
! boundary conditions error covariance.

 CnormB(isFsur) =  T                      ! 2D variable at RHO-points
 CnormB(isUbar) =  T                      ! 2D variable at U-points
 CnormB(isVbar) =  T                      ! 2D variable at V-points
 CnormB(isUvel) =  T                      ! 3D variable at U-points
 CnormB(isVvel) =  T                      ! 3D variable at V-points
 CnormB(isTvar) =  T T                    ! NT tracers

! Switches to compute the correlation normalization coefficients for
! surface forcing error covariance.

 CnormF(isUstr) =  T                      ! surface U-momentum stress
 CnormF(isVstr) =  T                      ! surface V-momentum stress
 CnormF(isTsur) =  T T                    ! NT surface tracers flux

! Correlation normalization method:
!
!      [0] Exact, very expensive
!      [1] Approximated, randomization

        Nmethod == 0

! If randomization, select random number generation scheme:
!
!      [1] Gaussian distributed deviates, numerical recipes

        Rscheme == 1

! Number of iterations to compute correlation normalization coefficients
! via the randomization approach. A large number is required to be
! statistically meaningful and achieve zero expectation mean and unit
! variance. These factors insure that the error covariance diagonal
! elements are equal to unity.

        Nrandom =  5000

! Horizontal and vertical stability and accuracy factors (< 1) used to
! time-step discretized convolution operators below its theoretical limit.
! Notice that four values [1:4] are needed for each factor to facilitate
! the error covariance modeling: 1=initial conditions, 2=model,
! 3=boundary conditions, and 4=surface forcing.
!
!                  IC       Model    OBC      Sur For

         Hgamma =  0.5      0.5      0.5      0.5       ! horizontal operator
         Vgamma =  0.05     0.05     0.05     0.05      ! vertical operator

! Model error covariance: horizontal, isotropic decorrelation scales (m).
! This scales are only used in weak-constraint data assimilation.

HdecayM(isFsur) ==  50.0d+3                               ! free-surface
HdecayM(isUbar) ==  50.0d+3                               ! 2D U-momentum
HdecayM(isVbar) ==  50.0d+3                               ! 2D V-momentum
HdecayM(isUvel) ==  50.0d+3                               ! 3D U-momentum
HdecayM(isVvel) ==  50.0d+3                               ! 3D V-momentum
HdecayM(isTvar) ==  50.0d+3   50.0d+3                     ! 1:NT tracers

! Model error covariance: vertical, isotropic decorrelation scales (m).

VdecayM(isUvel) == 100.0d0                                ! 3D U-momentum
VdecayM(isVvel) == 100.0d0                                ! 3D V-momentum
VdecayM(isTvar) == 100.0d0   100.0d0                      ! 1:NT tracers

! Model error covariance: temporal decorrelation scales (days).
! This scales are only used in weak-constraint data assimilation.

TdecayM(isFsur) ==  1.0d0                                 ! free-surface
TdecayM(isUbar) ==  1.0d0                                 ! 2D U-momentum
TdecayM(isVbar) ==  1.0d0                                 ! 2D V-momentum
TdecayM(isUvel) ==  1.0d0                                 ! 3D U-momentum
TdecayM(isVvel) ==  1.0d0                                 ! 3D V-momentum
TdecayM(isTvar) ==  1.0d0   1.0d0                         ! 1:NT tracers

! Initial conditions error covariance: horizontal, isotropic decorrelation
! scales (m).

HdecayI(isFsur) == 100.0d+3                               ! free-surface
HdecayI(isUbar) == 100.0d+3                               ! 2D U-momentum
HdecayI(isVbar) == 100.0d+3                               ! 2D V-momentum
HdecayI(isUvel) == 100.0d+3                               ! 3D U-momentum
HdecayI(isVvel) == 100.0d+3                               ! 3D V-momentum
HdecayI(isTvar) == 100.0d+3  100.0d+3                     ! 1:NT tracers

! Initial conditions error covariance: vertical, isotropic decorrelation
! scales (m).

VdecayI(isUvel) == 100.0d0                                ! 3D U-momentum
VdecayI(isVvel) == 100.0d0                                ! 3D V-momentum
VdecayI(isTvar) == 100.0d0   100.0d0                      ! 1:NT tracers

! Boundary conditions error covariance: horizontal, isotropic decorrelation
! scales (m). A value is expected for each boundary edge in the following
! order:
!                  1: west  2: south  3: east  4: north

HdecayB(isFsur) == 100.0d+3 100.0d+3 100.0d+3 100.0d+3    ! free-surface
HdecayB(isUbar) == 100.0d+3 100.0d+3 100.0d+3 100.0d+3    ! 2D U-momentum
HdecayB(isVbar) == 100.0d+3 100.0d+3 100.0d+3 100.0d+3    ! 2D V-momentum
HdecayB(isUvel) == 100.0d+3 100.0d+3 100.0d+3 100.0d+3    ! 3D U-momentum
HdecayB(isVvel) == 100.0d+3 100.0d+3 100.0d+3 100.0d+3    ! 3D V-momentum
HdecayB(isTvar) == 4*100.0d+3  4*100.0d+3                 ! (4,1:NT) tracers

! Boundary conditions error covariance: vertical, isotropic decorrelation
! scales (m). A value is expected for each boundary edge in the following
! order:
!                 1: west  2: south  3: east  4: north

VdecayB(isUvel) == 100.0d0  100.0d0  100.0d0  100.0d0     ! 3D U-momentum
VdecayB(isVvel) == 100.0d0  100.0d0  100.0d0  100.0d0     ! 3D V-momentum
VdecayB(isTvar) == 4*100.d0  4*100.d0                     ! (4,1:NT) tracers

! Surface forcing error covariance: horizontal, isotropic decorrelation
! scales (m).

HdecayF(isUstr) == 100.0d+3                       ! surface U-momentum stress
HdecayF(isVstr) == 100.0d+3                       ! surface V-momentum stress
HdecayF(isTsur) == 100.0d+3  100.0d+3             ! 1:NT surface tracers flux

! Select flag for BackGround Quality Control (BGQC) of observations:
!
!      [1] Quality control in terms of state variable indices
!      [2] Quality control in terms of observation provenance

      bgqc_type == 1

! If BGQC is in terms of state variables, set number of standard deviations
! threshold to use in the quality control rejection of observations.
!
!   Use a large value (say, 1.0d+5) if you do not want to reject observations
!   associated with a particular state variable.
!
!   Use a small value (typically, 4 standard deviations) to perform quality
!   control of observations for a particular state variable.

 S_bgqc(isFsur) == 1.0d+5                                 ! free-surface
 S_bgqc(isUbar) == 1.0d+5                                 ! 2D U-momentum
 S_bgqc(isVbar) == 1.0d+5                                 ! 2D V-momentum
 S_bgqc(isUvel) == 1.0d+5                                 ! 3D U-momentum
 S_bgqc(isVvel) == 1.0d+5                                 ! 3D V-momentum
 S_bgqc(isTvar) == 4.0d0  4.0d0                           ! 1:NT tracers

! If BGQC is in terms of observation provenance, set number of standard
! deviations threshold to use in the quality control rejection of
! observations.
!
!   Use a small value (say, 4 standard deviations) to perform quality
!   control for the desired observation provenance(s).
!
!   Nprovenance:   Number of observation provenances to quality control
!   Iprovenance:   Observation provenance indices to process [1:Nprovenance]
!   P_bgqc:        Standard deviation threshold [1:Nprovenance]

    Nprovenance == 2
    Iprovenance == 6     7                ! ARGO Temperature and Salinity

         P_bgqc == 4.0d0 4.0d0

! If applicable, set switches (T/F) used to adjust surface tracer flux,
! [1:NT,1:Ngrids].

        Lstflux ==  T T                   ! NT tracers

! If applicable, set switches to adjust state variables at the open
! boundaries. Notice that a value is expected for each boundary segment
! per nested grid, [1:4,1:Ngrids].  The boundary order is: 1=west,
! 2=south, 3=east, and 4=north. That is, anticlockwise starting at
! the western boundary.
!
! When processing momentum, you need to activate both components. If
! processing 2D momentum, you need to activate both free-surface and
! 3D-momentum at the processing boundary.
!
!                  W   S   E   N           _____N_____
!                  e   o   a   o          |     4     |
!                  s   u   s   r          |           |
!                  t   t   t   t        1 W           E 3
!                      h       h          |           |
!                                         |_____S_____|
!                  1   2   3   4                2

  Lobc(isFsur) ==  F   F   F   F          ! free-surface
  Lobc(isUbar) ==  F   F   F   F          ! 2D U-momentum
  Lobc(isVbar) ==  F   F   F   F          ! 2D V-momentum
  Lobc(isUvel) ==  F   F   F   F          ! 3D U-momentum
  Lobc(isVvel) ==  F   F   F   F          ! 3D V-momentum

! If applicable, set switches to adjust state tracer variables at the
! open boundaries.  Notice that a value is expected for each tracer at each
! boundary segment per nested grid, [1:4,1:NT,1:Ngrids]. The boundary order
! is the same as above. Notice that the first line has the values for
! temperature boundaries, the second is salinity, and so on.

  Lobc(isTvar) ==  F   F   F   F  \
                   F   F   F   F

! Input model, initial conditions, boundary conditions, and surface forcing
! standard deviation file names, [1:Ngrids].

       STDnameM == roms_std_m.nc
       STDnameI == roms_std_i.nc
       STDnameB == roms_std_b.nc
       STDnameF == roms_std_f.nc

! Input/output model, initial conditions, boundary conditions, and surface
! forcing error covariance normalization factors file name, [1:Ngrids].

       NRMnameM == roms_nrm_m.nc
       NRMnameI == roms_nrm_i.nc
       NRMnameB == roms_nrm_b.nc
       NRMnameF == roms_nrm_f.nc

! Input/output observation file name, [1:Ngrids].

        OBSname == roms_obs.nc

! Input/output Hessian eigenvectors file name, [1:Ngrids].

        HSSname == roms_hss.nc

! Input/output Lanczos vectors file name, [1:Ngrids].

        LCZname == roms_lcz.nc

! output time-evolved Lanczos vectors file name, [1:Ngrids].

        LZEname == roms_lze.nc

! Output model data at observation locations file name, [1:Ngrids].

        MODname == roms_mod.nc

! Output posterior error covariance matrix file name, [1:Ngrids].

        ERRname == roms_err.nc

! Input forcing filenames at observation locations for computing observations
! impacts during the analysis-forecast cycle when the forecast is initialized
! with the 4D-Var analysis (OIFnameA) or the 4D-Var background (OIFnameB).

      OIFnameA == roms_oif_a.nc
      OIFnameB == roms_oif_b.nc

!
!  GLOSSARY:
!  =========
!
!------------------------------------------------------------------------------
! Error covariance matrix balance operator parameters.  These parameters are
! only used when BALANCE_OPERATOR and ZETA_ELLIPTIC are activated.
!------------------------------------------------------------------------------
!
!  Nbico          Number of iterations in the biconjugate gradient algorithm
!                 used to solve the elliptic equation for sea surface height
!                 in the error covariance balance operator, [1:Ngrids]. We
!                 need as many iterations are required to decrease the error
!                 value of the reference free-surface to 1E-8 or smaller. In
!                 some applications Nbico=200 will do the job.
!
!                   Warning: be aware that there are 4 arrays that are
!                   -------  allocated with this parameter may and its
!                            value maybe constrained by available memory:
!
!                   FOURDVAR(ng) % p_r2d (LBi:UBi,LBj:UBj,Nbico(ng))
!                   FOURDVAR(ng) % r_r2d (LBi:UBi,LBj:UBj,Nbico(ng))
!                   FOURDVAR(nd) % bp_r2d(LBi:UBi,LBj:UBj,Nbico(ng))
!                   FOURDVAR(ng) % br_r2d(LBi:UBi,LBj:UBj,Nbico(ng))
!
!                   All the iterations values are needed in the backward
!                   stepping of the adjoint.
!
!  dTdz_min       Minimum d(T)/d(z) above which the balanced salinity
!                 (deltaS_b) is computed, [1:Ngrids]:
!
!                     deltaS_b = cff * dSdT * deltaT;    dSdT = dSdz / dTdz
!
!                   where cff is a coefficient that depends on the mixed-layer
!                   depth (ml_depth):
!
!                     cff = 1.0 - EXP (z_r / ml_depth)
!
!  ml_depth       Mixed-layer depth (m; positive) used above in smoothing
!                 coefficient (cff), [1:Ngrids].
!
!  LNM_depth      Level of no motion depth (m; positive) used to compute the
!                 balanced free-surface contribution in the error covariance
!                 balance operator. It is only relevant when LNM_flag=1,
!                 balance(isFsur)=T, and ZETA_ELLIPTIC is NOT activated. It
!                 is used to integrate the non-hydrostatic equation.
!
!  LNM_flag       Level of no motion integration flag used to used to compute
!                 the balanced free-surface contribution:
!
!                   LNM_flag = 0,  integrate from local bottom to the surface
!
!                   LNM_flag = 1,  integrate from LNM_depth to surface or
!                                  integrate from local bottom if shallower
!                                  than LNM_depth
!
!  balance        Balance operator logical switches for state variables to
!                 consider in the error covariance off-diagonal 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)
!
!                 Guidelines:
!
!                   1) The salinity contribution, balance(isSalt), depends
!                      only on temperature. Notice that temperature is used
!                      establish the balanced part of the other state
!                      variables.
!
!                   2) The free-surface contribution, balance(isFsur), depends
!                      on salinity since we need to compute balanced density
!                      and integrate properly using LNM_flag and LNM_depth.
!                      This implies that balance(isSalt) needs to be TRUE too.
!                      It is independent the 2D or 3D balance velocity terms.
!
!                   3) The 3D momentum, balance(isVvel), depends on salinity
!                      since we need to compute balanced density.  This
!                      implies that balance(isSalt) needs to be TRUE too.
!
!------------------------------------------------------------------------------
!  Array modes parameter.
!------------------------------------------------------------------------------
!
!  Nvct           Either eigenvector of the stabilized representer matrix to
!                 process to computing array modes when option ARRAY_MODES is
!                 activated. In this case, Nvct =< Ninner,
!
!                   Nvct=1         less important eigenvector
!                   Nvct=Ninner    most important eigenvector
!
!                 or cut-off eigenvector for the clipped analysis when
!                 the option CLIPPING is activated to remove potentially
!                 unphysical array modes.  In this case, Nvct =< Ninner. All
!                 the eigenvectors are ordered according to their significance,
!                 Nvct=Ninner is the most important.
!
!                   Nvct:Ninner    eigenvectors will be processed
!                   1:Nvct-1       eigenvectors will be disgarded
!
!------------------------------------------------------------------------------
! Lanczos conjugate gradient algorithm parameters.
!------------------------------------------------------------------------------
!
!  GradErr        Upper bound on the relative error of the gradient.
!
!  HevecErr       Maximum error bound on Hessian eigenvectors. Note that
!                 even quite inaccurate eigenvectors are useful
!                 for pre-conditioning purposes.
!
!  LhessianEV     Switch (T/F) to compute approximated Hessian eigenvalues
!                 and eigenvectors.
!
!
!  LhotStart      Switch (T/F) to activate hot start in weak-constraint
!                 (W4DVAR and W4DPSAS) algorithms.
!
!  Lprecond       Switch (T/F) to activate preconditioning in the IS4DVAR
!                 algorithm. Two types of Limited-Memory preconditioner (LMP)
!                 are available Tshimanga et al., 2008): Spectral and Ritz.
!
!                   If Lprecond=T and Lritz=F,  Spectral LMP
!                   If Lprecond=T and Lritz=T,  Ritz LMP
!
!  Lritz          Switch to activate either Ritz Limited-Memory Preconditioner
!                 (T) or spectral Limited-Memory Preconditioner (F) to the
!                 IS4DVAR algorithm using eigenpairs approximation for the
!                 Hessian matrix.  The accuracy of the Hessian eigenvectors
!                 (HevecErr) can be used to fine tune the minimization. That
!                 is, HevecErr can be used to control number of eigenvalues
!                 of the preconditioning Hessian matrix. See Tshimanga et al.
!                 (2008) Q. J. R. Met. Soc. paper for details.
!
!  NritzEV        If preconditioning, specify number of eigenpairs to use.
!                   If zero, use HevecErr parameter to determine the number
!                   of converged eigenpairs.
!
!  NpostI         If weak constraint 4DVar (W4DPSAS or W4DVAR), set number of
!                 iterations in the Lanczos algorithm used to estimate the
!                 posterior analysis error covariance matrix.
!
!------------------------------------------------------------------------------
! Observations impact or observations sensitivity.
!------------------------------------------------------------------------------
!
!  Nimpact        Outer loop to consider in the computation of the observations
!                 impact or observation sensitivity, Nimpact =< Nouter.  This
!                 facilitates the computations with multiple outer loop 4D-Var
!                 applications.  The observation analysis needs to be computed
!                 separately for each outer loop.  The full analysis for all
!                 outer loops is combined offline.
!
!------------------------------------------------------------------------------
! Additional observation operators.
!------------------------------------------------------------------------------
!
! Currently, only one extra-observation operator has been implemented to
! process radial velocities from HF radars instruments.
!
!  NextraObs      Number of extra-observation classes to consider in addition
!                 to those associated with the state variables (one-to-one
!                 correspondence. They are used in observation operators that
!                 require more that one state variable to evaluate particular
!                 extra-observation type like HF radials, travel time,
!                 pressure, etc.
!
!                 In any application, the number of observation types is
!                 computed as:
!
!                   NobsVar(ng) = NstateVar(ng) + NextraObs
!
!                 If not processing extra-observation classes, set NextraObs
!                 to zero.
!
!  ExtraIndex     Extra-observation class identification indices, as specified
!                 in input observation NetCDF file variable "obs_type".  The
!                 index has to be a number greater than 7+2*NT, where NT is
!                 the total of active plus passive tracers. NextraObs values
!                 are expected for this Keyword. This parameter is only
!                 processed when NextraObs > 0.
!
!  ExtraName      Extra-observation class names. NextraObs values are expected.
!                 This parameter is only processed when NextraObs > 0.  Enter
!                 one class type name per line and use a backslash for
!                 continuation. For example:
!
!                   ExtraName = radials  \
!                               pressure
!
!                 Currently, however, only the radials operator is coded.
!
!------------------------------------------------------------------------------
! Diffusive relaxation coefficients.
!------------------------------------------------------------------------------
!
! If weak constraint 4DVar and RPM_RELAXATION flag is activated, this
! coefficients are use to relax the representer tangent lineas solution
! to previous outer loop linearized trajectory during the Picard
! iterations. The user may turn off relaxation on a particular variable
! by setting the coefficient to zero.
!
!  tl_M2diff      2D momentum diffusion relaxation coefficient (m2/s).
!
!  tl_M3diff      3D momentum diffusion relaxation coefficient (m2/s).
!
!  tl_Tdiff       Tracers type variables diffusion relaxation coefficients
!                 (m2/s).  NT values are expected.
!
!------------------------------------------------------------------------------
! Background/model correlation parameters.
!------------------------------------------------------------------------------
!
!  LdefNRM        Switch (T/F) to create a new normalization NetCDF file
!                 for, [4,1:Ngrids]:
!
!                      LdefNRM(1,:)   initial conditions error covariance
!                      LdefNRM(2,:)   model error covariance
!                      LdefNRM(3,:)   boundary conditions error covariance
!                      LdefNRM(4,:)   surface forcing error covariance
!
!                 The computation of the correlation normalization
!                 coefficients is very expensive and needs to be computed
!                 only once for a particular application provided that grid,
!                 land/sea masking (if any), and decorrelation scales (see
!                 below) remains the same.  The user can use this switch
!                 in conjunction with the CnormM, CnormI, CnormB, CnormF
!                 (see below) switches to compute each coefficient separately.
!                 The normalization NetCDF only needs to be created once
!                 and simultaneous runs can write to the same NetCDF.  If
!                 using this approach, compute the normalization factors
!                 with the CORRELATION CPP-option and not IS4DVAR, W4DPSAS
!                 or W4DVAR.
!
!  LwrtNRM        Switch (T/F) to write out correlation normalization factors
!                 for, [4,1:Ngrids]:
!
!                      LwrtNRM(1,:)   initial conditions error covariance
!                      LwrtNRM(2,:)   model error covariance
!                      LwrtNRM(3,:)   boundary conditions error covariance
!                      LwrtNRM(4,:)   surface forcing error covariance
!
!                 If TRUE, these factors computed and written to NRMnameI,
!                 NRMnameM, NRMnameB, and NRMnameF NetCDF file, respectively.
!                 If FALSE, they are read from NRMname NetCDF file.
!
!  CnormM         Compute (T/F) model error covariance
!                   normalization factors:
!
!                   CnormM(isFsur)                free-surface
!                   CnormM(isUbar)                2D U-momentum
!                   CnormM(isVbar)                2D V-momentum
!                   CnormM(isUvel)                3D U-momentum
!                   CnormM(isVvel)                3D V-momentum
!                   CnormM(isTvar)                tracers (1:NT)
!
!  CnormI         Compute (T/F) initial conditions error covariance
!                   normalization factors:
!
!                   CnormI(isFsur)                free-surface
!                   CnormI(isUbar)                2D U-momentum
!                   CnormI(isVbar)                2D V-momentum
!                   CnormI(isUvel)                3D U-momentum
!                   CnormI(isVvel)                3D V-momentum
!                   CnormI(isTvar)                tracers (1:NT)
!
!  CnormB         Compute (T/F) open boundary conditions error covariance
!                   normalization factors:
!
!                   CnormB(isFsur)                free-surface
!                   CnormB(isUbar)                2D U-momentum
!                   CnormB(isVbar)                2D V-momentum
!                   CnormB(isUvel)                3D U-momentum
!                   CnormB(isVvel)                3D V-momentum
!                   CnormB(isTvar)                tracers (1:NT)
!
!  CnormF         Compute (T/F) surface forcing error covariance
!                   normalization factors:
!
!                   CnormF(isTsur)                tracer flux (1:NT)
!                   CnormF(isUstr)                wind U-stress
!                   CnormF(isVstr)                wind V-stress
!
!  Nmethod        Correlation normalization method:
!
!                   [0] Exact, very expensive
!                   [1] Approximated, randomization
!
!  Rscheme        Random number generation scheme if randomization:
!
!                   [1] Gaussian distributed deviates, numerical recipes
!
!  Nrandom        Number of iterations to compute correlation normalization
!                 factors using the randomization approach of Fisher and
!                 Courtier (1995). A large number is required to be
!                 statistically meaningful and achieve zero expectation
!                 mean and unit variance, approximately. These factors insure
!                 that the error covariance diagonal elements are equal to
!                 unity.
!
!  Hgamma         Horizontal stability and accuracy factor (< 1) used to
!                 scale the time-step of the convolution operator below its
!                 theoretical limit, [1:4].  Notice that four values are
!                 needed for Hgamma to facilitate the error covariance
!                 modeling for initial conditions (1), model (2), boundary
!                 conditions (3), and surface forcing (4).
!
!  Vgamma         Vertical stability and accuracy factor (< 1) used to
!                 scale the time-step of the convolution operator below its
!                 theoretical limit,  [1:4].  Notice that four values are
!                 needed for Vgamma to facilitate the error covariance
!                 modeling for initial conditions (1), model (2), boundary
!                 conditions (3), and surface forcing (4).
!
!  HdecayM        Model error covariance, [1:Ngrids],
!                   horizontal, isotropic decorrelation scales (m):
!
!                   HdecayM(isFsur)               free-surface
!                   HdecayM(isUbar)               2D U-momentum
!                   HdecayM(isVbar)               2D V-momentum
!                   HdecayM(isUvel)               3D U-momentum
!                   HdecayM(isVvel)               3D V-momentum
!                   HdecayM(isTvar)               tracers (1:NT,1:Ngrids)
!
!  VdecayM        Model error covariance, [1:Ngrids],
!                   vertical, isotropic decorrelation scale (m):
!
!                   VdecayM(isUvel)               3D U-momentum
!                   VdecayM(isVvel)               3D V-momentum
!                   VdecayM(isTvar)               tracers (1:NT,1:Ngrids)
!
!  HdecayI        Initial conditions error covariance, [1:Ngrids],
!                   horizontal, isotropic decorrelation scales (m):
!
!                   HdecayI(isFsur)               free-surface
!                   HdecayI(isUbar)               2D U-momentum
!                   HdecayI(isVbar)               2D V-momentum
!                   HdecayI(isUvel)               3D U-momentum
!                   HdecayI(isVvel)               3D V-momentum
!                   HdecayI(isTvar)               tracers (1:NT,1:Ngrids)
!
!  VdecayI        Model error covariance, [1:Ngrids],
!                   vertical, isotropic decorrelation scale (m):
!
!                   VdecayI(isUvel)               3D U-momentum
!                   VdecayI(isVvel)               3D V-momentum
!                   VdecayI(isTvar)               tracers (1:NT)
!
!  HdecayB        Open boundary conditions error covariance, [4,1:Ngrids],
!                   horizontal, isotropic decorrelation scales (m):
!
!                   HdecayB(:,isFsur)             free-surface
!                   HdecayB(:,isUbar)             2D U-momentum
!                   HdecayB(:,isVbar)             2D V-momentum
!                   HdecayB(:,isUvel)             3D U-momentum
!                   HdecayB(:,isVvel)             3D V-momentum
!                   HdecayB(:,isTvar)             tracers (4,1:NT,1:Ngrids)
!
!                   boundary index   1: west  2: south  3: east  4: north
!
!  VdecayB        Model error covariance, [4,1:Ngrids],
!                   vertical, isotropic decorrelation scale (m):
!
!                   VdecayB(isUvel)               3D U-momentum
!                   VdecayB(isVvel)               3D V-momentum
!                   VdecayB(isTvar)               tracers (4,1:NT,1:Ngrids)
!
!                   boundary index   1: west  2: south  3: east  4: north
!
!  HdecayF        Surface forcing error covariance, [1:Ngrids],
!                   horizontal, isotropic decorrelation scales (m):
!
!                   HdecayF(isTsur)               tracers flux (1:NT,1:Ngrids)
!                   HdecayF(isUstr)               wind U-stress
!                   HdecayF(isVstr)               wind V-stress
!
!------------------------------------------------------------------------------
! Background Quality Control (BCQC) of observations parameters.
!------------------------------------------------------------------------------
!
!  bgqc_type      Flag to determine the type of background quality control:
!
!                    bgqc_type = 1    Background quality control in terms of
!                                     the state variable index (1 - MstateVar)
!                                     read from the input observation NetCDF,
!                                     variable "obs_type".
!
!                                     It is general because include all the
!                                     observation provenances for a particular
!                                     state variable. For example, all the
!                                     temperature ofservations.
!
!                    bgqc_type = 2    Background quality control in terms of
!                                     the observation provenance index read
!                                     from the input observation NetCDF,
!                                     variable "obs_provenance".
!
!                                     It is specific because only include the
!                                     observations for a particular provenance
!                                     or instrument. For example, temperature
!                                     observation from ARGO buoys.
!
!  S_bgqc         Number of standard deviations threshold to use in the quality
!                 control rejection of observations in terms of the state
!                 variable index.
!
!                    S_bgqc(isFsur)             free-surface
!                    S_bgqc(isUbar)             2D U-momentum
!                    S_bgqc(isVbar)             2D V-momentum
!                    S_bgqc(isUvel)             3D U-momentum
!                    S_bgqc(isVvel)             3D V-momentum
!                    S_bgqc(isTvar)             NT tracers (4,NT,Ngrids)
!
!                 It used when bgqc_type = 1. Use a large value (say 1.0d+5)
!                 to indicate that the observations are spread out over a wider
!                 range of background values.
!
!  Nprovenance    Number of observation provenances to consider for background
!                 quality control.  Used when bgqc_type = 2.
!
!  Iprovenance    Observation provenance index to consider for background
!                 quality control.  Use the same index value as specified
!                 in input observations NetCDF, variable "obs_provenance".
!                 1:Nprovenance values are expected for each nested grid.
!                 Used when bgqc_type = 2.
!
!  P_bgqc         Number of standard deviations threshold to use in the quality
!                 control rejection of observations in terms of the provenance
!                 index, 1:Nprovenance values are expected for each nested
!                 grid. Used when bgqc_type = 2.
!
!------------------------------------------------------------------------------
! 4DVAR adjustment switches.
!------------------------------------------------------------------------------
!
!  Lstflux        Logical switches (T/F) used to adjust surface tracer flux,
!                 including active and passive tracers, [1:NT, 1:Ngrids].
!                 These switches are used when ADJUST_STFLUX is activated.
!
!  Lobc           Logical switches (T/F) used to adjust state variables at
!                 the open boundaries. A value is expected for each boundary
!                 segment per nested grid, [1:4, 1:Ngrids].
!
!                 The boundary order is anticlockwise starting at the western
!                 edge as follows:
!
!                    1 = western  edge
!                    2 = southern edge
!                    3 = eastern  edge
!                    4 = northern edge
!
!                    Lobc(isFsur)               free-surface
!                    Lobc(isUbar)               2D U-momentum
!                    Lobc(isVbar)               2D V-momentum
!                    Lobc(isUvel)               3D U-momentum
!                    Lobc(isVvel)               3D V-momentum
!                    Lobc(isTvar)               NT tracers (4,NT,Ngrids)
!
!                WARNING: When processing momentum, you need to activate both
!                =======  components. If processing 2D momentum, you need to
!                activate both free-surface and 3D-momentum at the processing
!                boundary. The 2D momentum adjustment is computed by vertically
!                integretating the 3D momentum increments.
!
!------------------------------------------------------------------------------
!  Input/Output NetCDF files (a string with a maximum of 256 characters).
!------------------------------------------------------------------------------
!
!  STDnameM       Input model error covariance
!                   standard deviation file name.
!
!  STDnameI       Input initial conditions error covariance
!                   standard deviation file name.
!
!  STDnameB       Input open boundary conditions error covariance
!                   standard deviation file name.
!
!  STDnameF       Input surface forcing error covariance
!                   standard deviation file name.
!
!  NRMnameM       Input/output model error covariance
!                   normalization factors file name.
!
!  NRMnameI       Input/output initial conditions error covariance
!                   normalization factors file name.
!
!  NRMnameB       Input/output open boundary conditions error covariance
!                   normalization factors file name.
!
!  NRMnameF       Input/output surface forcing error covariance
!                   normalization factors file name.
!
!  OBSname        Input/Output observations data file name.
!
!  HSSname        Input/Output Hessian eigenvectors file name.
!
!  LCZname        Input/output Lanczos vectors file name.
!
!  LZEname        Output time-evolved Lanczos vectors file name.
!
!  MODname        Output model data at observations locations file name.
!
!  ERRname        Output posterior error covariance matrix file name.
!
! Input forcing filenames at observation locations for computing observations
! impacts during the analysis-forecast cycle when W4DPSAS_FCT_SENSITIVITY and
! OBS_SPACE are activated:
!
! (See www.myroms.org/wiki/Analysis-Forecast_Cycle_Observation_Impacts)
!
!  OIFnameA    Forecast initialized with 4D-Var analysis (red curve)
!
!  OIFnameB    Forecast initialized with 4D_Var background (blue curve)
!
