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 271

a magnitude R , which usually is a small fraction of the transport rate I t ) and by
unsorted material abraded from the cliff at the northern end of the sandy strip. The
erosion of the cliff has been mapped by several topographic surveys. The cliff sedi-
ments comprise roughly 1/3 of sand and gravel. If the amount of M is abraded from
the cliff, the beach receives about

1

3 M of material. Also, at times a certain amount
of sand S is eroded from the dune scarp and berm along the sandy beach. The lat-
ter quantity has been estimated as S 400 m 3 /year in 1997-2006 from the results

of subsequent topographic surveys (Soomere et al. 2007 ) . The earlier observations
suggest that the sand volume of the beach was more or less unchanged before the
1970s (Soomere et al. 2007 ) . The balance equation for the sand volume was thus

≈

1
3 M

Q = R + + S − D = 0, (3)

where D is the net loss of sand volume to the deeper areas. There are no lateral
loss terms in Eq. ( 2 ) , because (i) the Pirita Harbour completely stops the littoral
drift and (ii) the southwards drift overwhelmingly dominates at the northern border
of the beach. Assuming that the beach was in equilibrium in the past, this balance
equation can be used to calculate the flux R in the past provided the contemporary
average rate D of net sand loss from the beach to offshore is known.

13.5.2 Sediment Loss from Almost Equilibrium Beaches

To obtain an accurate estimate of the net sand loss normally requires long-term
measurements of sediment transport, or sediment trapped at a groin, or historical
geomorphic and bathymetric changes, and thus is time-consuming and costly. A
simple method is proposed by Kask et al. ( 2009 ) for rapid estimation of this quan-
tity for beaches where the sediment loss or gain is almost balanced by the land
uplift or downsinking. The method consists of inverting the Bruun Rule (Bruun
1962 ) . The sediment loss or gain is expressed in terms of the changes of the dry
land area, the width of the equilibrium beach profile, and the uplift or downsinking
rate. The method essentially relies on the existence of a more or less persistent beach
profile.
Usually, the Bruun Rule is expressed as the linear relation S tan

=− θ

y

between the shift y of the shoreline and the relative water level rise S , where the

proportionality coefficient is the inverse mean slope tan of the equilibrium profile.

This relation is valid for any shape of the equilibrium profile with the mean slope
tan

θ

.
Consider now a situation in which a certain loss of sand has occurred from the
equilibrium profile and the entire profile has been shifted shoreward (Fig. 13.8 ) . For
small changes of the shoreline position the slope of the dry beach can be ignored.
The curved regions ABD and 0EC are obviously identical. To a first approximation,
the cross-section of the entire profile has been shifted to the left and the volume of
lost sand is

θ

h ∗ y , where h ∗ is the closure depth. V ≈