z
qr =
qd
(5)
z0
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,
qb = ab q
qd = ad q
(6)
qs = as q
These coefficients obey the constraint:
ab + ad + as = 1
(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 ab and ad as inputs and solve for as as as = 1 - ab - ad . 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).
in time interval ∆t as,
z
z
(W0 - x)∆z = ( qd - qr ) ∆t = qd -
qd ∆t = ad q 1 - ∆t
z0
z0
which becomes:
ad
z
dz
=
1 - q,
z(0) = 0
(8)
dt W0 - x z0
Similarly, for infilling by growth of the side channel, continuity gives,
∆x ( z0 - z ) = qb∆t = ab q∆t
which becomes:
Kraus and Larson
5
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