(5)

which is equivalent to the closure assumption invoked in the coastal inlet Reservoir Model

(Kraus 2000).

To proceed, the apportionment of *q *must be known. For this purpose, partitioning

coefficients *a *are introduced, where the *a*'s are numbers or, more generally, functions of

the ambient conditions (which can be expressed as decimal fractions of unity or

percentages). A subscript denotes the association or coupling to the input transport rate.

Thus,

(6)

These coefficients obey the constraint:

(7)

The constraint expresses one equation in three unknowns, requiring two additional

equations. To proceed, in the absence of process-based estimates, one can, for example,

specify *a*b and *a*d as inputs and solve for *a*s as *a*s = 1 - *a*b - *a*d . The determination of the

coupling coefficients in terms of the time dependent coastal processes at the site is the

subject of future work. At the moment, values are specified based on experience gained

with the model (see the examples below).

For the channel bottom, the continuity equation gives a change in bottom elevation ∆*z*

in time interval ∆*t *as,

(*W*0 - *x*)∆*z *= ( qd - *q*r ) ∆*t *= qd -

which becomes:

=

1 - q,

(8)

Similarly, for infilling by growth of the side channel, continuity gives,

∆*x *( z0 - *z *) = *q*b∆*t *= *a*b q∆*t*

which becomes:

Kraus and Larson

5

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