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creeks (e.g. time series as the one shown in Fig. 8.3 )
suggested that no deposition takes place for over-
marsh tides in the lowest water level class.
Therefore, D C in the lowest class of HWL -
MHWL = 0.1 m was set as 0. According to Eq. 8.12 ,
this means that:
(
)
(
)
(8.12 ¢)
αβ
=
/ 2.303
=> Δ
C
=
β
/ 2.303 ln
HWL
MHWL
+
β
; valid for
HWL
>
MHWL
(HWL)
where the physical meaning of b is D C for a high water
level of 1 m above MHWL.
Substituting Eq . 8.12 ¢ into Eq. 8.11 and adding the
result for all tidal periods in a year give D s sed for the
year in question.
In order to correct this for autocompaction, it is
necessary to know the mass depth (kg m −2 ) of the salt
marsh from the surface to the basement under the salt
marsh deposits at the specifi c location. If D s sed for the
calculated year is added to this and introduced in
Eq. 8.2 ¢, this can be solved for z , giving the salt marsh
level on top of the basement after the modelled year.
Using the procedure described above in parallel
with the model of Temmerman et al. ( 2003 ) gave a
linear relationship between D C and the overmarsh
high tide level, which indicates correspondence
between this very simple, purely empirical model
and the more complicated model based on the theo-
retical considerations of Krone ( 1987 ) . Even if the
conditions are radically changed when going from a
semitheoretical model as that of Temmerman et al.
( 2003 ) to a purely empirical model like this one, it
can be criticized for the same drawbacks as stated
above. On the other hand, if we assign the suspended
sediment a settling diameter of 25 mm in accordance
with 'normal' suspended fi ne-grained sediment in
the area around Skallingen (Bartholdy and Anthony
1998), this corresponds to a settling velocity of about
ws = 0.4 10 −3 m s −1 and a settling time for 1 m of
about 1.5 h, which is less than the expected period of
very small velocities around high water. In this envi-
ronment, the model's D C -value can therefore be
thought of as the 'full' delivery of available sediment
imported from the tidal area during a given over-
marsh tide (i.e. all the sediment in suspension will
settle out).
8.5.2
Examples of the Use of Accretion
Models
8.5.2.1 Salt Marsh Stability in Relation
to Sea-Level Rise
By means of accretion measurements over the approx-
imately 60-year period in three lines across the
Skallingen backbarrier (Nielsen 1935 ; Jakobsen 1953 ;
Bartholdy et al. 2004, 2010a ) , former and present
measurements of clay thickness corrected for auto-
compaction by means of Eq. 8.2 ¢ and sea-level data
from a nearby tide gage were used to calibrate 32
points scattered over the backbarrier for their b -value
(the deposition potential). b was found to correlate
with two variables: (1) distance to marsh edge ( X 1)
and (2) distance to creeks of second or higher order
( X 2). The distance to salt marsh edge was able to
explain 61% of the variation, and the distance to sec-
ond or higher-order creeks was able to add 10% to
this. Thus, the combined correlation explained 71% of
the variation in the deposition potential. The best cor-
relation in both cases was achieved by means of a
logarithmic relation giving the fi nal empirical equation
the following appearance:
(8.13)
()( )
()
( )
β=
4.095 ln
XX
1 ln
2
36.402 ln
X
1
32.421ln
X
2
+
288.224
By means of Eq. 8.13 , a map of the characteristic
concentration difference available for deposition for a
high water level of 1.3 m DNN was constructed as
shown in Fig. 8.17 . This high water level was chosen
as it represents the most 'effi cient' level in terms of
salt marsh deposition when frequency is also consid-
ered (Bartholdy et al. 2004 ). It is clear from Fig. 8.13
how the depositional environment refl ects the general
pattern discussed above giving rise to a salt marsh sur-
face level that accretes most rapidly in the outer part of
 
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