where contains the unrelaxed values computed by the model and is a specified forced solution in the zone. The relaxation parameter varies from 1 at the model boundary to 0 at the end of the zone facing the interior model domain. The quality of this flow relaxation scheme depends strongly upon the quality of the specified forced solutions, , chosen for the prognostic variables.

The SUBROUTINE NCALFA computes the relaxation parameters ALPHA(LB) and ALPHAE(LB), where LB is the width of the FRS-zone, to be used for 3-D variables and 2-D variables respectively.

It may be shown, see [25], that to use this boundary conditions is equivalent to adding a Newtonian friction term of the form

to the right hand side of the equations with

where is the time step used when propagating the variable . Thus the strength of Newtonian forcing is dependent on the time step, and we are thus attempting to solve a different mathematical problem when we vary the time step. We have also seen in practice that by keeping the arrays fixed and varying the time step, different solutions may be produced. This problem is not explicitly discussed in [25].

In NCALFA we therefore first compute the arrays with one of the formulas from [25]. The formulation is normally used. We assume that this produces a reasonable Newtonian friction throughout the FRS-zone for the time step . The values of throughout the zone are computed from the above formula. Then we recompute the arrays, one for the 3-D variables that are propagated with time steps DT and one for the 2-D variables that are propagated with time steps DT/N2D, according to

The results are placed in the model variables ALPHA and ALPHAE respectively. By doing this the Newtonian friction is unaltered as the time steps are modified and we may at least hope to demonstrate convergence in time as the time step is reduced.

NCALFA may be unchanged from one application to another, but it may be advisable to test the sensitivity of the model results both to the representation of the arrays and to the choice of . As a rule of thumb choose close to the value DX / where DEPMAX is the maximum depth over the model region. If the user experiences problems at or close to the boundaries, the above options may be attempted. If the quality of the forcing field is poor, this may also reduce the quality of the model outputs and possibly cause instabilities. See [5] for a suggestion on how to produce in idealized fjord studies.