On the Dynamics of “Almost Equilibrium” Beaches in Semi-sheltered Bays Along the Southern Coast of the Gulf of Finland - The Baltic Sea Basin - page 272

Original coastline

Δ y -

Δ

y

W - W

0 y

Δ y

A D E

New
coastline

Δ V

Sediment loss

Depth of closu re h*

C

B

F

Seaward end
of the new
equilibrium profile

Seaward end
of the original
equilibrium profile

Fig. 13.8 Scheme of the calculation of the change of sand volume for small changes of the position
of the coastline

The problem of calculating sand loss for a small section of coastline has there-
fore been reduced to determination of the shift of the shoreline and the closure depth.
This approach neglects (i) the amount of sediment in the subaerial beach and (ii) a
part of sediment located between the original and the new seaward end of the equi-
librium beach profile. The first constituent of the error is small when the subaerial
beach is gently sloping. For a perfectly equilibrium profile, the second constituent,
equivalently, the error of this estimate, is smaller than 2

y tan θ and obviously can

be neglected for small coastline changes.
The resulting sand loss over a longer section of a homogeneous beach (along
which the closure depth is constant) only depends on the changes of the area of the
dry land:

h ∗

V

=

ydx . (4)

Details of the derivation of Eq. ( 4 ) and further discussion of the applications of
the method are presented in Kask et al. ( 2009 ) .
Given the calculated typical value of the closure depth for Pirita h ∗

≈

2.5 m,
Eq. ( 4 ) predicts that each square meter of gain or loss of the dry land at Pirita cor-
responds to the change of the volume of sand by 2.5 m 3 per each meter of

the beach. Realistic values representing long-term gain or loss obviously can only
be obtained for beach sections of considerable length, along which the integral in
Eq. ( 4 ) is calculated.
The accuracy of the resulting estimate with the use of Eq. ( 4 ) is the best for
beaches for which the different sand supplies and losses are almost balanced. The
relative change of the water level is equivalent to an extra loss or gain of sediment.
The relevant modification of the above estimate is presented for Pirita Beach in Kask
et al. ( 2009 ) . It is necessary to first calculate the mean slope tan

V ≈

of the equilibrium
profile, for example, using the typical grain size (defining the parameter A in the

θ