River, Coastal and Estuarine Morphodynamics: RCEM 2009 – Vionnet et al. (eds)
© 2010 Taylor & Francis Group, London, ISBN 978-0-415-55426-8
The importance of being coupled: Stable states, transitions and responses
to changing forcings in tidal bio-morphodynamics
M. Marani
Department of IMAGE and International Center for Hydrology, University of Padova, Padova, Italy
A. D’Alpaos
Department of Geosciences, University of Padova, Padova, Italy
C. Da Lio, L. Carniello & S. Lanzoni
Department of IMAGE and International Center for Hydrology, University of Padova, Padova, Italy
A. Rinaldo
Department of IMAGE, University of Padova, Padova, Italy
EPFL Lausanne, Lausanne, Switzerland
ABSTRACT: Changes in relative sea level, nutrient and sediment loading, and ecological characteristics expose
tidal landforms and ecosystems to responses which may or may not be reversible. Predicting such responses is
important in view of the ecological, cultural and socio-economic importance of endangered tidal environments
worldwide. Here we develop a point model of the joint evolution of tidal landforms and biota including the
dynamics of intertidal vegetation, benthic microbial assemblages, erosional and depositional processes, local
and general hydrodynamics, and relative sea-level change. Alternative stable states and punctuated equilibrium
dynamics emerge, characterized by possible sudden transitions of the system, governed by vegetation type,
disturbances of the benthic biofilm, sediment availability and marine transgressions or regressions. Multiple
equilibria are the result of the interplay of erosion, deposition and biostabilization. They highlight the importance
of the coupling between biological and sediment transport processes in determining the evolution of a tidal system
as a whole. Hysteretic switches between stable states may arise because of differences in the threshold values of
relative sea level rise inducing transitions from vegetated to unvegetated equilibria and viceversa.
1
INTRODUCTION
In times of natural and anthropogenic climate change,
tidal bio-geomorphic systems are most exposed to
possibly irreversible transformations with far-reaching
ecological and socio-economic implications (e.g.
Schneider 1997, Bohannon 2005, Day et al. 2007). It is
thus of critical importance to develop predictive models of possible evolutions to dynamically-accessible
stable states, or the lack of them, under varying
forcings.
The notion that freshwater and terrestrial ecosystems may switch abruptly to alternative stable states
as a result of feedbacks between consumers and limiting resources is widely acknowledged (Holling 1973,
May 1977, Scheffer et al. 2001, Rietkerk et al. 2004,
D’Odorico et al. 2005). On the contrary, theoretical
or observational proofs of the existence of alternative
equilibrium states in marine or intertidal ecosystems
has until recently proven to be elusive.
We believe that this circumstance, rather than being
the reflection of intrinsic properties of tidal systems,
is due to a prevalent reductionist approach, which has
until recently mostly produced either purely ecological
(e.g. Schröder et al. 2005) or purely geomorphological
models (e.g. Fagherazzi et al. 2006), while the coupled dynamics of landforms and biota in the intertidal
zone has remained largely unexplored (Fagherazzi
et al. 2004, Marani et al. 2006a, b).
Surprisingly, such a situation has occurred in spite
of a large body of observational evidence characterizing the complex interactions between intertidal
vegetation (Cronk & Fennessy 2001, Silvestri et al.
2005, Marani et al. 2006a, b), benthic microbial
assemblages (e.g., Paterson 1989), erosion and deposition processes (Allen 1990, Day et al. 1999, D’Alpaos
et al. 2005, Fagherazzi et al. 2006), hydrodynamics (e.g., Rinaldo et al. 1999a, b, Fagherazzi et al.
1999, Marani et al. 2004), eustatism and/or relative
sea-level change (Allen 1990). Indeed, few geomorphodynamic models have attempted to introduce a
coupling between geomorphological and biological
processes (Mudd et al. 2004, D’Alpaos et al. 2007,
Kirwan & Murray 2007) and when such an interaction
is accounted for, it is typically described through rigid
steady-state relations among state variables (e.g. soil
533
elevation and vegetation biomass) rather than by coupling biological and geomorphological dynamical
equations.
In a fully coupled context Marani et al. (2007) treat
topography and vegetation biomass as separate prognostic variables and describe their evolution in terms
of interacting dynamic equations leading to stable
and unstable equilibria. Here, we further develop the
model introduced in Marani et al. (2007) by accounting
for soil compaction and by exploring the full extent
of the arising alternative equilibria, their dynamic
accessibility, and the biological and physical factors controlling the possible abrupt transitions among
them. We show that alternative stable states can exist
only owing to bio-stabilization effects and we provide
evidence that the sequence of stable states produced
by marine regressions and transgressions may be
hysteretic, echoing fluvial cases (Rinaldo et al. 1995).
2
THE MODEL
The model describes the coupled time evolution of
the elevation, z(t), of a tidal platform and of the
vegetation biomass, B(t), possibly colonizing it (see
Fig. 1). In the original formulation (Marani et al. 2007,
2009) the platform is subjected to a sinusoidal tide and
to a constant forcing suspended sediment concentration, representing the available sediment due to wave
activity and possible fluvial or marine inputs. Here
we extend the model, by accounting for realistic tide
and time-varying suspended sediment availability, e.g.
from observations.
The bio-geomorphic evolution of a tidal platform is described through the two coupled dynamical
equations:
dz
QS [z, B] QT [z, B]
=
+
+ QO [B] +
dt
1−p
1−p
E[z, B, MPB(z)]
−R
−
1−p
(1)
r(z)B
dB
=
(d − B) − m(z)B
dt
d
(2)
In equation (1) the tidal platform elevation is computed with reference to the local mean sea level (MSL),
which gives rise to the rate of sea level rise term, R,
on the right-hand side including the eustatic and local
subsidence components (see Fig. 1 for notation). p is
sediment porosity (here p = 0.5), B is the vegetation
biomass, while MPB(z) indicates the dependence of
microphytobenthos (and of the associated sedimentstabilizing biofilm) on soil elevation. QS , QT and QO
are the annual average sediment settling flux, annual
average trapping rate of suspended sediment by the
canopy and annual production of organic soil due to
vegetation respectively. E is the annual average erosion
rate, mainly due to wind-induced waves (Carniello
et al. 2005).
Equation (2) describes the dynamics of vegetation
biomass in a logistic-like setting (Levins 1969), where
d is the carrying capacity of the system (biomass
density of a fully vegetated marsh). The elevationdependent reproduction and mortality rates, r(z) and
m(z), reflect the physiological responses of halophytic
species to the controlling environmental conditions,
chiefly soil water saturation, locally surrogated by
elevation (Silvestri et al. 2005, Marani et al.
2006c).
The deposition due to settling, QS , and the trapping
rate, QT , are expressed as follows
QS =
QT =
1
nY T
1
nY T
(3)
T
1
C(z, B, t) ws dt
ρs
1
C(z, B, t) αBβ dt
ρs
(4)
T
where T is the period over which averaging is performed, a suitable multiple of one year in the following. nY is the number of years in T . ws is the settling
velocity, here estimated on the basis of measured sediment size distributions (e.g. for the Venice Lagoon,
see Section 3, d50 = 50 μm, ws = 0.2 mm/s). ρs is
the sediment density (here 2650 kg/m3 ). β = 0.382
and α = 1.01 · 106 m/s (m2 /kg)β are parameters which
account for typical halophytic vegetation structure and
flow characteristics (Mudd et al. 2004, D’Alpaos et al.
2006, 2007).
C(z, B, t) is the instantaneous sediment concentration, in turn determined by solving a sediment balance
equation for the water column forced by the average
sediment concentration in lagoonal waters (Krone
1987)
Figure 1. Sketch of sediment fluxes at the surface of a tidal
platform and sediment exchanges with its surroundings. The
elevation z of the platform is computed with respect to the
local MSL.
534
d
dh
(D C) = −ws C − αBβ C + C˜
dt
dt
(5)
with
˜ B, t) =
C(z,
C0 (t)
when
C(z, B, t)
when
dh
dt
dh
dt
>0
<0
(6)
where h(t) is the instantaneous tidal elevation with
respect to local MSL, and D(t) = h(t)−z is the instantaneous water depth. The first and second terms on the
right-hand-side of eq. (5) are the instantaneous settling
and trapping fluxes, respectively, while the third term
represents the exchange of sediment between the platform and its surrounding: When the flow is toward the
platform it carries a prescribed concentration, C0 (t),
representing the available suspended sediment. When
the flow is from the platform toward the surrounding, the outgoing concentration is the instantaneous
concentration within the water column above the platform, C(z, B, t). Note that equations (5) and (6) refer to
periods of deposition, when wind-waves do not induce
any re-suspension of the bottom sediment, such that
the erosion term that should appear on the right-handside of equation (5) may be neglected. This amounts
to assuming that erosion events are relatively short (on
the annual scale) so that their effect can be represented
through the forcing concentration, C0 (t), in the estimation of the annually-averaged trapping and settling
rates, which is thus decoupled from the description of
erosion.
The production of organic matter, QO , can be
directly linked to the annually-averaged aboveground
plant dry biomass, B, as follows (Randerson 1979,
Mudd et al. 2004, D’Alpaos et al. 2006, 2007):
QO = γ B
(7)
where γ = 2.5 · 10−3 m3 /yr/kg incorporates typical vegetation characteristics and the density of the
organic soil produced.
The erosion flux, E, is computed on the basis of
the shear stress induced on the bottom by wind-waves,
which is estimated on the basis of a simple wave model
(Soulsby 1997, Carniello et al. 2005). By assuming
equilibrium conditions the energy transferred by the
wind to the water surface equals the energy dissipation by bottom friction, whitecapping, and breaking.
The effective bottom shear stress due to wind-wave
action, τ , is thus a function of water depth, D and
wind velocity, uw (Carniello et al. 2005, Fagherazzi
et al. 2006, Defina et al. 2007). The computation of
the erosion flux for a value, z, of the platform elevation is performed as follows. A value of wind velocity
is selected and the average of the bottom shear stress
over the period T is computed. The result is weighted
by the fraction of time for which the considered value
of wind velocity is observed at the anemometric station of reference. The weighted result is then summed
to the corresponding results obtained for all observed
wind velocities. This procedure produces as a result
the bottom shear stress, τ (z), averaged in time and
over the experimental wind frequency distribution and
is repeated for all values of the platform elevation of
interest. These computations finally yield the average
erosion flux, E(z, B, MPB) as:
E=
e
τ (z) − τc (MPB)
I (B)
ρs
τc (MPB)
(8)
where e is an erosion coefficient characteristic of sediment type and structure (here e = 10−4 kg/m2 /s, e.g.
van Ledden et al. 2004), I (B) is a step function, such
that I (B) = 1 if B = 0 and I (B) = 0 if B > 0 accounting for the fact that wind waves are efficiently dissipated by the presence of vegetation, which reduces
erosion to zero as it encroaches the platform (Möller
et al. 1999), τc (MPB) is the threshold bottom shear
stress for erosion, which strongly depends on the presence/absence of stabilizing polimeric biofilms produced by benthic microbes (e.g., Paterson 1989, Amos
et al. 1998) and on the presence of vegetation. Because
microphytobenthos growth is light-limited, we assume
it colonizes the platform when its elevation is such
that sufficient incoming solar irradiance for microbial
photosynthetic activity is available (MacIntyre et al.
1996). This is here assumed to occur at Mean Low
Water Level (MLWL), when the bed is freely exposed
to solar radiation for part of the tidal cycle. We further
take (Amos et al. 1998) τc = 0.4 Pa when z < −H and
τc = 0.8 Pa when z > −H . The erosion rate is now a
function of elevation and vegetation biomass alone.
It may often be assumed that vegetation adapts to
changes in elevation very quickly (i.e. on the annual
time scale) compared to typical geomorphological
time scales (often appreciable changes in local elevations occur over several years). Marani et al. (2007b)
treat in detail the solutions arising from the fully coupled dynamical system, while we will here deliberately
confine ourselves to the interesting case of ‘instantaneous’ vegetation adaptation. In this case the two
equations (1) and (2) can be decoupled, by first finding
the steady-state solution, B(z), of (2) and by substituting it back into (1). A trivial solution of dB/dt = 0
is B = 0, which cannot be observed in actual marshes
because the presence of seed banks and the continuous
input of propagules from surrounding marshes would
repopulate a marsh where vegetation had temporarily disappeared (e.g. Adam 1990, Ungar 1991). This
leaves the steady-state solution:
m(z)
Bs (z) = d 1 −
r(z)
(9)
which we recall to be valid for z ≥ 0, while Bs (z) = 0
when z < 0.
535
Two typical, and rather contrasting, relations between soil aeration and vegetation biomass may be
considered.
The first case (‘‘oxygen-limited vegetation’’) is
characterized by biomass increasing with increasing
soil elevation (between MSL, z = 0, and mean high
water level (MHWL) say z = H ) and is typical e.g.
of Mediterranean tidal environments, where several
species adapted to progressively more aerated conditions compete (Marani et al. 2004, Silvestri et al.
2005) or sites in northern continental Europe. The
second case is a Spartina spp.-dominated environment, characteristic of some North-American sites, in
which biomass is a decreasing function of elevation
between z = 0 and z = H , reflecting the adaptation of Spartina to hypoxic conditions (Morris &
Haskin 1990, Morris et al. 2002). For the sake of
brevity we will here study the oxygen-limited vegetation case, exploring dependencies on the local wind
climate, sediment availability and subsidence. A full
account of the system dynamics for the Spartinadominated case is given in Marani et al. (2009).
The oxygen-limited vegetation case is described by
assuming a reproduction rate which linearly increases
with elevation, while the mortality rate is assumed to
decrease linearly with z: r(z) = 0.5 z/H + 0.5 yr−1 ;
m(z) = −0.5 z/H + 0.5 yr−1 . We also assume each
plant to produce at most one daughter plant per year
in the most favorable conditions, i.e. r(H ) = 1 yr−1
and m(H ) = 0 yr−1 . Observations in this case indicate
that biomass is equal to zero at z = 0 and maximum at
z = H (Marani et al. 2004, Silvestri et al. 2005). We
thus take r(0) = m(0) = 0.5 yr−1 . With the above provisions the equation yielding the equilibrium platform
elevations finally has the form:
dz/dt [cm/year]
2
1.5
1 R = 7.3 mm/yr
z = 0.30 m
0.5
0
z = 0.10 m
0
dz/dt [cm/year]
2
1.5
1
z = 0.23 m
0.5
0
3
2
1
0
1
dz/dt [cm/year]
2
1.5
(c)
1
z = 0.22 m
0.5
0
2
1
0
1
z [m a.m.s.l.]
E[z, Bs (z), MPB(z)]
−R
−
1−p
3
1
(b)
3
dz
QS [z, Bs (z)] QT [z, Bs (z)]
=
+
+ QO [Bs (z)] +
dt
1−p
1−p
= F(z) − R = 0
(a)
R = 3.5 mm/yr
(10)
Figure 2. Stable equilibrium states in the oxygen-limited
vegetation case with (a) tidal observations at Murano, wind at
Tessera and suspended sediment concentration C0 (t) at Campalto; (b) same as in (a) except that the astronomic tide (i.e.
with no meteorological component) is prescribed; (c) same
as in (a) except that tidal observations at ‘‘Saline’’ are used.
RESULTS AND DISCUSSION
We explore here the stable equilibrium states arising
from the solution of 11 when observations of tidal levels, sediment concentration and wind velocities from a
network of observing stations within the Venice lagoon
are considered. To this end we take the observed 20thcentury rate of sea-level rise of 2 mm/yr (IPCC 2007,
Carbognin et al. 2004), and a local subsidence of
1.5 mm/yr (Carbognin et al. 2004), for a total R =
3.5 mm/yr. The function dz/dt = F(z) − R is plotted in Figure 2 for different combinations of forcings.
dz/dt is computed in Figure 2(a) on the basis of tidal
observations at Murano, wind regime at Tessera and
suspended sediment concentration at Campalto.
All observation stations are located within a few
kilometers from one another. Solid circles mark stable
equilibrium states, which include a subtidal platform
equilibrium, located at elevations lower than Mean
Low Water Level (MLWL), and a marsh intertidal
equilibrium located above mean sea level. These equilibria are such that a negative perturbation of elevation
produces a value dz/dt > 0, which thus brings the
system back to the original equilibrium state. On the
other hand a positive perturbation of z produces a value
536
pdf of tidal level (m–1)
1.6
1.4
(a)
Murano
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
pdf of tidal level (m–1)
1.6
1.4
0.8
1
(b)
Astronomic tide
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
1.4
0.8
1
(c)
1.6
pdf of tidal level (m–1)
dz/dt < 0 and the system is thus again pushed back
to the equilibrium state. Note that a third solution of
dz/dt = 0 exists but it corresponds to an unstable
equilibrium state, which cannot thus be observed, as
any perturbation is amplified by the system subsequent
dynamics.
Figure 2(a) shows dz/dt vs. z and the corresponding
stable equilibria for R = 3.5 mm/year (representative of local sea level rise for the 20th Century) and
for R = 7.3 mm/year, incorporating a rather extreme
IPCC projection for sea level rise in the next Century. It
is seen that expected increases in the rate of sea level
rise substantially decrease the elevations of both the
subtidal and intertidal equilibria. However, the nature
of these equilibria remains unchanged. In fact, there
is no transition from a salt marsh (vegetated) equilibrium to an unvegetated tidal flat equilibrium (z < 0 m
a.m.s.l.). The model developed allows a simple way
to explore the sensitivity of bio-morphodynamic equilibria to sea level changes, e.g. resulting from phases
of sea regressions and transgressions. For example,
a detailed inspection of Figure 2(a) allows the determination of the limit values of R for which a transition from a marsh to a tidal flat occurs (R = 10.5
mm/yr). When R is large enough such that no solution
to dz/dt = 0 (R = 16.2 mm/yr) the system makes a
transition to a marine environment, while for R = 3.2
mm/yr, a transition to a terrestrial environment occurs.
This analyses show that the available equilibrium states
are relatively insensitive to a variability in the rate of
sea level change. It should however be noted that the
model postulates that the incoming flux of suspended
sediment, i.e. the sources of C0 (t), keep on providing
the same amount of sediment, whatever change may
occur. This means that any accretion may occur only at
the expenses of other morphological structures, if no
sediment input from rivers of the sea is present (as in
the case of the Venice lagoon). In order to describe
the response of the system to large values of R further
feedbacks should thus be included in the model.
Figure 2(b) represents the accessible stable equilibria for the same forcings as in (a), except that the
astronomic tide, rather than the observed tide, was
imposed.
The exclusion of meteorological contributions to
the tide causes a general lowering of the equilibrium
elevations, due to the generally lower water levels characterizing the astronomic tide, as indicated in Figure 3.
To understand why the sub-tidal platform equilibrium
elevation is decreased one must consider that the maximum bottom shear stress as a function of water depth
occurs for intermediate depths. In fact, for very low
depths wave height is severely limited, while for large
depths the orbital velocities connected with surface
waves, and the associated bottom shear stress, become
very small close to the sediment surface. It follows
that, if frequent tidal levels are reduced, so is the elevation for which the maximum erosion occurs and thus
Saline
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
tidal level (m a.m.s.l.)
Figure 3. Tidal levels Pdf ’s for (a) observations at Murano,
(b) astronomic tide, (c) observations at ‘‘Saline’’.
the equilibrium elevation for which erosion, deposition
and sea level rise balance one another. The elevation of
the marsh equilibrium is also reduced, but the mechanism leading to this reduction does not involve the
erosion flux, as in the previous case, since erosion
over marshes is inhibited by the presence of vegetation
whatever its elevation (within the elevation interval
allowing the development of halophytic plants). In this
case a reduced frequency of high tidal levels implies
a reduced sediment deposition at high elevations and
thus a reduction of the soil elevation for which deposition, trapping and organic sediment production are
able to balance relative sea level rise.
537
The comparison of Figure 2(a) and (b) shows that
the sensitivity of the observable bio-geomorphic equilibria to changes in the tidal regimes is quite strong.
Indeed, by comparing the changes which take place in
the equilibrium states because of relatively little differences in the prevalent tidal levels to those related
to increases in R which are quite extreme within the
range of the IPCC projections, one must conclude that
the tidal system studied is potentially more exposed to
changes in the tidal regime rather than to changes in
the rate of sea level rise.
1
P [V>v]
0.8
S. Andrea
S. Leonardo
0.6
0.4
(a)
0.2
0
0
5
10
15
The strong sensitivity of system equilibria to the
characteristics of the local tide are emphasised by
Figure 2(c), which shows the results of using the same
wind and suspended sediment forcing as in Figure
2(a) and (b) and the tidal observations at the ‘‘Saline’’
tide gauge (Figure 3 for the pdf of tidal levels). The
differences between Figure 2(a) and (c) indeed show
that the local tide can decisively influence the number
and character of the available equilibrium states.
If tidal characteristics can be so important in defining the existing stable states, it is interesting to explore
the possible impacts of the local wind regime.
Figure 4 shows the different equilibrium states
obtained using time series of wind observations at
two sites. Differences can obviously occur only for
the sub-tidal equilibrium as wind-driven waves are
assumed to be completely dissipated by marsh vegetation. S. Leonardo is characterized by more frequent
high winds with respect to S. Andrea, as shown in
Figure 4(a), which in turn lead, according to intuition,
to a lower equilibrium elevation because of the greater
erosion rates. The lower elevation restores an erosion
flux which balances the fixed deposition and rate of
sea level rise.
20
v [m/s]
dz/dt [cm/year]
1
0.5
4
z=0.23 m
z=-1.62 m
0
(b)
wind at S. Andrea
0
1
dz/dt [cm/year]
1
0.5
z=0.23 m
z=-1.74 m
The model introduced here allows the exploration of
the stable equilibrium states of tidal bio-geomorphic
structures accounting for a realistic coupled dynamics of biological and physical processes forced by the
tide, the prevailing winds, the available suspended
sediment and the local sea level rise. The approach
adopted shows the importance of accounting for the
main interacting biological and physical processes in
order to obtain realistic representations of the system
dynamics. Experiments with different observed forcings in the Venice lagoon point to the following main
conclusions:
0
wind at S. Leonardo
1
(c)
0
CONCLUSIONS
1
z [m a.m.s.l.]
Figure 4. Effects of tidal regimes on the available equilibrium states. Probability of exceedance of wind velocity
according to the S. Andrea and S. Leonardo anemometers (a);
dz/dt vs. z and the associated stable equilibria on the basis of
tidal observations at Murano, suspended sediment concentration C0 (t) at Campalto, and wind velocity at S. Andrea (b)
and S. Leonardo (c).
538
i) The number and the elevation of the equilibrium
states, both in the sub-tidal and in the intertidal
zones, depend on the rate of sea level rise. Such
dependence, however, is linear and relatively mild
(at least in the Venice lagoon setting explored here)
if compared with quite extreme sea level rise IPCC
scenarios;
ii) The existence and characteristics of equilibrium
states depend quite strongly on the local tidal
regime even within the same tidal system. In particular, the tide observed at different sites within
the Venice lagoon, which differ as a result of propagation and dissipation of the tidal wave, yield
quite different equilibrium elevations. This circumstance also points to the importance of the
meteorological contribution to tidal levels, which
significantly alters the characters of the local tide,
with important bio-geomorphic implications;
iii) In the sub-tidal range the effect of tidal fluctuations
is linked to the fact that more frequent high tidal
level increase the platform elevation at which erosion by wind-waves is maximum. Consequently,
the equilibrium elevation at which erosion, deposition and sea level rise are in balance is also correspondingly increased;
iv) The effect of tidal fluctuations in the intertidal
zone are entirely due to a more effective transport of sediment at high elevations when tidal
oscillations are increased. A broader probability
distribution of tidal levels thus produces higher
marsh elevation values;
v) The local wind regime very importantly affects the
elevation of the sub-tidal equilibrium state. Subtidal equilibria resulting from wind observations
at sites separated by a few kilometers show, in
fact, important elevation differences. Salt-marsh
equilibria, on the contrary, are not affected by differences in wind regimes, as wind waves are dissipated by vegetation such that erosion does not play
a role in determining the equilibrium elevation.
The present model for the first time provides a realistic, though simplified, representation of the coupled
bio-geomorphic evolution of a tidal system and of the
ensuing equilibrium states. Further and quite immediate developments regard the inclusion of limitations
to sediment availability as a result of feedbacks, on
the scale of the entire tidal system, between erosion
by wind-waves and global elevation trends. A second important development regards the incorporation
of stochastic terms, representing disturbances, in the
biomass evolution equation to explore possible effects
on the type and resilience of equilibrium states.
ACKNOWLEDGEMENTS
This work was supported by the PRIN 2006 projects
‘‘Modelli dell’evoluzione eco-morfologica di bassifondi e barene lagunari’’ and the VECTOR-FISR 2002
project, CLIVEN research line.
REFERENCES
Allen, J.R.L. 1990. Salt-marsh growth and stratification:
A numerical model with special reference to the Severn
Estuary, southwest Britain, Mar. Geol. 95: 77–96.
Amos, C.L., Brylinsky M., Sutherland T.F., O’Brien D., Lee
S., & Cramp A. 1998. The stability of a mudflat in the
Humber estuary, South Yorkshire, UK. Geol. Soc. Spec.
Publ. 139: 25–43.
Bohannon, J. 2005. A Sinking City Yields Some Secrets.
Science 309: 1978–1980, doi: 10.1126/science.309.5743.
1978.
Carbognin, L., Teatini P., & Tosi L. 2004. Eustacy and land
subsidence in the Venice Lagoon at the beginning of the
new millennium. J. Marine Syst. 51: 345–353.
Carniello L., Defina A., Fagherazzi S., & D’Alpaos L.
2005. A combined wind wave-tidal model for the Venice
Lagoon, Italy. J. Geophys. Res. 110, F04007, doi:10.1029/
2004JF000232.
Cronk, J.K., & Fennessy M.S. 2001. Wetland Plants: Biology
and Ecology. Lewis, Boca Raton, Fla.
D’Alpaos, A., Lanzoni S., Marani M., Fagherazzi S., &
Rinaldo A. 2005. Tidal network ontogeny: channel initiation and early development. J. Geophys. Res. 110, F02001,
doi:10.1029/2004JF000182.
D’Alpaos, A., Lanzoni S., Mudd S.M., and Fagherazzi S.
2006. Modelling the influence of hydroperiod and vegetation on the cross-sectional formation of tidal channels.
Estuarine Coastal Shelf Sci. 69: 311–324, doi:10.1016/
j.ecss.2006.05.002.
D’Alpaos, A., Lanzoni S., Marani M., & Rinaldo A. 2007.
Landscape evolution in tidal embayments: Modeling
the interplay of erosion, sedimentation, and vegetation
dynamics. J. Geophys. Res. 112, F01008, doi:10.1029/
2006JF000537.
Day, J.W., Rybczyk J., Scarton F., Rismondo A., Are D., &
Cecconi G. 1999. Site accretionary dynamics, sea-level
rise and the survival of wetlands in Venice lagoon: A field
and modelling approach. Estuarine Coastal Shelf Sci. 49:
607–628.
Day, J.W. et al. 2007. Restoration of the Mississippi Delta:
Lessons from Hurricanes Katrina and Rita, Science 315
(5819): 1679-1684, doi:10.1126/science.1137030.
Defina, A., Carniello L., Fagherazzi S., & D’Alpaos L. 2007.
Self organization of shallow basins in tidal flats and salt
marshes. J. Geophys. Res.112, F03001, doi:10.1029/2006
JF000550.
D’Odorico, P., Laio F., & Ridolfi L. 2005. Noise-induced
stability in dryland plant ecosystems. Proc. Nat. Acad.
Sci. USA 102(31): 0819–10822.
Holling, C.S. 1973. Resilience and stability of ecological
systems. Annu. Rev. Ecol. Syst. 4: 1–23.
Fagherazzi, S., Marani M., & Blum L. K. 2004. The Ecogeomorphology of Tidal Marshes. AGU Coastal and Estuarine Studies, Washigton, D.C. 59: 266.
Fagherazzi, S., Carniello L., D’Alpaos L., & Defina A. 2006.
Critical bifurcation of shallow microtidal landforms in
tidal flats and salt marshes. Proc. Natl. Acad. Sci. USA.
103(22): 8337–8341.
Meehl, G.A., T.F. Stocker, W.D. Collins, P. Friedlingstein,
A.T. Gaye, J.M. Gregory, A. Kitoh, R. Knutti, J.M. Murphy, A. Noda, S.C.B. Raper, I.G. Watterson, A.J. Weaver
and Z.-C. Zhao 2007 Global Climate Projections. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report
of the Intergovernmental Panel on Climate Change, edited
by S. Solomon, D. Qin, M. Manning, Z. Chen, M.
Marquis, K.B. Averyt, M. Tignor and H.L. Miller, Cambridge University Press, Cambridge, United Kingdom
and New York, NY, USA.
Kirwan, M.L., & Murray A.B. 2007. A coupled geomorphic
and ecological model of tidal marsh evolution. Proc. Natl.
Acad. Sci. U.S.A. 104: 6118–6122.
539
Krone, R.B. 1987. A method for simulating historic marsh
elevations, in Coastal Sediments’87, edited by N.C. Krause,
pp. 316–323, ASCE, New York.
Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity for biological
control. Bull. Entomol. Soc. Am. 15: 237–240.
MacIntyre, H.L., Geiger R.J. & Miller D.C. 1996. Microphytobenthos: The ecological role of the ‘‘secret garden’’
of unvegetated, shallow-water marine habitats: 1. Distribution, abundance and primary production. Estuaries
19(2A): 186–201.
Marani, M., Lanzoni S., Silvestri S. & Rinaldo A. 2004.
Tidal landforms, patterns of halophytic vegetation and the
fate of the lagoon of Venice. J. Mar. Sys. 51: 191-210,
doi:10.1016/j.jmarsys.2004.05.012
Marani, M., Silvestri S., Belluco E., Ursino N., Comerlati A., Tosatto O. & Putti M. 2006. Spatial organization and ecohydrological interactions in oxygen-limited
vegetation ecosystems. Water Resour. Res. 42, W07S06,
doi:10.1029/2005WR004582.
Marani M., Belluco E., Ferrari S., Silvestri S., D’Alpaos A.,
Lanzoni S., Feola A. & Rinaldo A. 2006b. Analysis, synthesis and modelling of high-resolution observations of
salt-marsh ecogeomorphological patterns in the Venice
lagoon. Estuarine Coastal Shelf Sci., 69(3-4): 414-426,
doi:10.1016/j.ecss.2006.05.021.
Marani, M., Zillio T., Belluco E., Silvestri S. & Maritan A.
2006c. Nonneutral vegetation dynamics. PLoS ONE 1(1):
e78, doi:10.1371/journal.pone.0000078.
Marani, M., D’Alpaos A., Lanzoni S., Carniello L. &
Rinaldo A. 2007. Biologically—controlled multiple equilibria of tidal landforms and the fate of the Venice lagoon.
Geophys. Res. Lett. 34, L11402, doi:10.1029/2007
GL030178.
Marani, M., D’Alpaos A., Lanzoni S., Carniello L. &
Rinaldo A. 2009. The importance of being coupled: Stable states and catastrophic shifts in tidal eco-morphodynamics. submitted.
May, R.M. 1977. Thresholds and breakpoints in ecosystems
with a multiplicity of stable states. Nature 269: 471-477.
Möller, I., Spencer, T., French, J.R., Leggett, D. & Dixon, M.
1999. Wave transformation over salt marshes: A field and
numerical modelling study from North Norfolk, England,
Estuarine, Coastal and Shelf Sci., 49: 411–426.
Morris, J.T. & Haskin B. 1990, A 5-yr record of aerial primary
production and stand characteristics of Spartina alterniflora, Ecology, 7(16): 2209–2217.
Morris, J.T., Sundareshwar, P.V., Nietch, C.T., Kjerfve, B.,
& Cahoon D.R. 2002, Responses of coastal wetlands to
rising sea level, Ecology, 83: 2869–2877.
Mudd, S.M., Fagherazzi, S., Morris, J.T. and Furbish, D.J.,
2004, Flow, sedimentation, and biomass production on
a vegetated salt marsh in South Carolina: toward a predictive model of marsh morphologic and ecologic evolution, in The Ecogeomorphology of Tidal Marshes, Coastal
and Estuarine Stud., vol. 59, edited by S. Fagherazzi,
M. Marani, and L. K. Blum, pp. 165-188, AGU, Washigton, D.C.
Paterson, D.M. 1989, Short-term changes in the erodibility
of intertidal cohesive sediments related to the migratory
behaviour of epipelic diatoms, Limnol. Oceanogr., 34:
223–234.
Randerson, P.F. 1979, A simulation model of salt-marsh
development and plant ecology, in Estuarine and Coastal
Land Reclamation and Water Storage, edited by B. Knights
and A.J. Phillips, pp. 48–67, Farnborough, Saxon House.
Rietkerk, M., Dekker S.C., de Ruiter P.C. & van de Koppel J.
2004. Self-Organized Patchiness and Catastrophic Shifts
Science 305: 1926–1929, doi: 10.1126/science.1101867.
Rinaldo, A., Dietrich, W.E., Vogel, G., Rigon, R. &
I. Rodriguez-Iturbe 1995, Geomorphological signatures
of varying climate, Nature, 374: 632–636.
Rinaldo, A., Fagherazzi, S., Lanzoni, S., Marani, M. &
Dietrich W.E. 1999a, Tidal networks 2. Watershed delineation and comparative network morphology, Water
Resour. Res., 35(12): 3905–3917.
Rinaldo, A., Fagherazzi, S., Lanzoni, S., Marani, M.,
Dietrich, W.E. 1999b, Tidal networks 3. Landscapeforming discharges and studies in empirical geomorphic
relationships, Water Resour. Res., 35(12): 3919–3929.
Scheffer, M., Carpenter S., Foley J.A., Folkem C. &
Walker B. 2001. Catastrophic shifts in ecosystems. Nature
413(11): 591–596.
Schneider, S.H. 1997. The rising seas. Scientific American
3: 112–118.
Schröder, A., Persson L., & De Roos A.M. 2005. Direct
experimental evidence for alternative stable states: a
review. Oikos 110(1): 3–19.
Silvestri, S., Defina, A. & Marani M. 2005, Tidal regime,
salinity and salt marsh plant zonation, Estuarine Coastal
Shelf Sci., 62, doi:10.1016/j.ecss.2004.08.010, 119–130.
Soulsby, R.L. 1997. Dynamics of marine sands, Thomas
Telford, London.
Ungar, I.A. 1991. Ecophysiology of Vascular Halophytes,
209 pp., CRC Press, Boca Raton, Fla.
van Ledden, M., Wang, Z.B., Winterwerp, H. & de Vriend H.
2004, Sand-mud morphodynamics in a short tidal basin,
Ocean Dynamics, 54(3–4), 385–391.
540