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 268

not always apparent. This feature, not entirely typical but also not very surprising
(Dean and Dalrymple 2002 , Chap. 2.3.2), may play an important role in planning of
beach nourishment activities because material with the grain size much smaller than
the one at the waterline may be lost relatively fast. Moreover, relatively coarse and
well-sorted sand is perceived to be of the largest recreational value. In other words,
beach fill with fine sand would lead to a decrease in the beach quality.
Another basic parameter of the equilibrium beach profile is the depth of closure
h ∗ at which repeated survey profiles pinch out to a common line (Kraus 1992 ) . It
represents the maximum depth at which the breaking waves effectively adjust the
surf zone profile. Seawards from the closure depth, waves may occasionally move
bottom sediments but they are not able to maintain a specific profile. The closure
depth may be different for different sections of the beach and generally should be
treated as a function h ∗ (

of the distance x along the shoreline.
Several authors have suggested simple empirical expressions for h ∗ based on cer-
tain integral measures of the wave activity. A specific feature of wave climate in the
entire Baltic Sea is that the average wave conditions are mild, but very rough seas
may occur episodically in long-lasting, strong storms (Soomere 2008 ) . Waves in
such storms are much higher than one would estimate from the average wave con-
ditions. Moreover, the strongest storms in the Gulf of Finland tend to blow from
directions from which winds are not very frequent (Soomere and Keevallik 2003 ,
Soomere 2005 ) . As a result, the simplified estimates based on the annual mean
wave parameters substantially underestimate the closure depth (Soomere et al. 2007 ,
2008b ) . More elaborate estimates that additionally account for the duration of the
strongest storms and for the wave periods in such storms lead to adequate results.
For example, for Pirita an acceptable approximation for h ∗

x )

is (Birkemeier 1985 )

H s ,0.137
gT s

h ∗ = p 1 H s ,0.137 − p 2 , p 1 = 1.75, p 2 = 57.9, (1)

where H s ,0.137 is the threshold of the significant wave height that occurs 12 h a year,
that is, the wave height that is exceeded with a probability of 0.137%, and T s is the
peak period in such wave conditions (Soomere et al. 2007 , 2008b ) .
Although only two parameters are necessary to adequately estimate the closure
depth, the relevant information generally is not provided, nor is it in the wave atlases
or able to be extracted from the existing wave measurements (Kahma et al. 2003 ,
Pettersson 2001 ) in the northern Baltic Sea and in the Gulf of Finland. Similar
problems are frequently encountered in many regions of the world and long-term
numerical simulations are a feasible way to approach them.
The wave climate in the vicinity of Pirita Beach and in Narva Bay was estimated
on the basis of a simplified scheme for long-term wave hindcast with the use of
a triple-nested version of the WAM model (Laanearu et al. 2007 , Soomere et al.
2008b ) . This model, although constructed for open ocean conditions and for rela-
tively deep water (Komen et al. 1994 ) , gives good results in the Baltic Sea, provided
the model resolution is appropriate and the wind information is correct (Soomere
2005 ) . Since waves are relatively short in the Gulf of Finland, the innermost models