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Corrected matlab script balance_4dvar.m used to compute the balanced/unbalanced contribution for 4DVar error covariance matrix standard deviation scale. We need to use the total T and S increments when computing the density increment delta_rho, as reported in Weaver et al. (2005) balance operator in Eq (18) and (22).

Many thanks to Andy Moore for reporting this problem.

Expanded the list of timeless variables to include those with the river dimension. These are the variables describing the river positions (river_Xposition, river_Eposition), direction (river_direction), flag (river_flag), and vertical transport profile (river_Vshape).

Many thanks to Paul Mattern for reporting this ​problem.

Updated the balance operator to specify its input parameters from the s4dvar.in script:

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

Notice that we need as many Nbico iterations are required to decrease the error value of the reference free-surface to 1E-8 or smaller. In many applications Nbico=200 will do the job.

Warning: be aware that there are 4 arrays that are allocated using Nbico 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 values are needed in the backward iterations of the adjoint.

I also corrected couple of bugs. Many thanks to Andy more fore reporting and correcting these problems.