Geology Reference
In-Depth Information
This is equivalent to the level rise that would be
measured down to a marker horizon if it was located
under the autocompacting salt marsh, for example in
or at the sandy base (Fig.
8.15
). Over 5 years, it adds
up to 11.4 × 10
−3
m or 1.14 cm as indicated at the top of
the salt marsh modelled in Fig.
8.14
.
Likewise, if we furthermore neglect the autocom-
paction term, we get:
−
3
−
3
−
1
Δ
E
=
4.18
×
10
+
0.2
×
10
=
4.38
×
10
m year
.
( without I and P )
ΔΔ
This is the level rise which would be measured down
to a marker horizon established on the surface the year
before the measurement. Over 5 years, it adds up to
21.9 × 10
−3
m or 2.19 cm as indicated in Fig.
8.14
.
According to Eq.
8.8
, the salt marsh level change
relative to the rising tidal frame is:
−
3
−
3
−
3
−
3
−
1
−
3
−
1
Δ= ×+×−×−×
E
4.18
10
0.2
10
2.10
10
0.5
10
m year
−×=
1.78
10
0 m year
.
rsl
Thus, the example here illustrates a salt marsh
which is in equilibrium with the stated relative sea-
level rise.
As D
P
, D
I
and D
Eu
are given properties and as D
S
org
in many cases is so small that it can be neglected, the
challenge, when trying to evaluate a salt marsh in rela-
tion to its accretion rate, mainly consists in fi nding a
way of simulating D
S
sed
(or D
S
min
as used by Allan,
1990
and Temmerman et al.
2003
) .
French (
1993
) and Temmerman et al. (
2003
)
adopted an approach to the determination of D
S
sed
based on that of Krone (
1987
) . Following Temmerman
et al. (
2003
), the temporal variation of the depth aver-
age suspended concentration is described by the fol-
lowing mass balance equation:
where h(t) is the time-dependent water level, E is the
salt marsh level, C(t) is the time-dependent depth aver-
age suspended sediment concentration in the water, w
s
is the settling velocity of the suspended sediment and
C
0
is the sediment concentration in the fl ooding water.
The left-hand side of Eq.
8.9
describes the change
in the content of suspended sediment in the water with
time as h(t)-E is the water depth which multiplied with
the depth average suspended sediment concentration
quantifi es the mass of suspended sediment over a unit
area. The fi rst term on the right-hand side describes the
result of the vertical settling of suspended sediment
and the second term on the right is supposed to describe
the lateral fl ux of sediment in water with a suspended
sediment concentration of
C
0
.
C
0
is given a specifi c
value during fl ood tide, while during ebb tide it is set
equal to
C
(
t
).
Carrying out the differentiation of the left-hand side
in Eq.
8.9
gives:
(
)
⎡
⎤
dht ECt
−
dh
⎣
⎦
(8.9)
=−
wC t
+
C
s
0
dt
dt
dht
⎡
−
E
⎤
dht
⎡
⎤
dC t
dC t
dh
⎣
⎦
⎣
⎦
(
)
(
)
ht
−
E
+
Ct
=
ht
−
E
+
Ct
= −
wCt
+
C
s
0
dt
dt
dt
dt
dt
⇒
dC t
dh t
(
)
(8.10)
⎡
⎤
ht
−
E
= −
wCt
+
C
−
Ct
⎣
⎦
s
0
dt
dt
This is the original equation suggested by Krone
(
1987
) by which the temporal variation of the depth
average suspended concentration,
C
(
t
), can be found
and multiplied by the settling velocity to give the
time-dependent sedimentation on a unit area of salt
marsh. Integrating this product over a tidal period and
adding up similar results from every tidal period in a year,
then give the combined deposition in mass per unit
