The importance of being coupled: Stable states, transitions and responses to changing forcings in tidal bio-morphodynamics

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1 River, Coastal and Estuarine Morphodynamics: RCEM 29 Vionnet et al. (eds) 2 Taylor & Francis Group, London, ISBN 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. 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 997, Bohannon 25, Day et al. 27). 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 973, May 977, Scheffer et al. 2, Rietkerk et al. 24, D Odorico et al. 25). 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. 25) or purely geomorphological models (e.g. Fagherazzi et al. 26), while the coupled dynamics of landforms and biota in the intertidal zone has remained largely unexplored (Fagherazzi et al. 24, Marani et al. 26a, 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 2, Silvestri et al. 25, Marani et al. 26a, b), benthic microbial assemblages (e.g., Paterson 989), erosion and deposition processes (Allen 99, Day et al. 999, D Alpaos et al. 25, Fagherazzi et al. 26), hydrodynamics (e.g., Rinaldo et al. 999a, b, Fagherazzi et al. 999, Marani et al. 24), eustatism and/or relative sea-level change (Allen 99). Indeed, few geomorphodynamic models have attempted to introduce a coupling between geomorphological and biological processes (Mudd et al. 24, D Alpaos et al. 27, Kirwan & Murray 27) and when such an interaction is accounted for, it is typically described through rigid steady-state relations among state variables (e.g. soil 533

2 elevation and vegetation biomass) rather than by coupling biological and geomorphological dynamical equations. In a fully coupled context Marani et al. (27) 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. (27) 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. 995). 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. ). In the original formulation (Marani et al. 27, 29) 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 dt = Q S[z, B] p + Q T [z, B] p + Q O[B]+ E[z, B, MPB(z)] p R () Figure. 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. db dt = r(z)b (d B) m(z)b (2) d In equation () 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. for notation). p is sediment porosity (here p =.5), B is the vegetation biomass, while MPB(z) indicates the dependence of microphytobenthos (and of the associated sedimentstabilizing biofilm) on soil elevation. Q S, Q T and Q O 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. 25). Equation (2) describes the dynamics of vegetation biomass in a logistic-like setting (Levins 969), 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. 25, Marani et al. 26c). The deposition due to settling, Q S, and the trapping rate, Q T, are expressed as follows Q S = n Y T Q T = n Y T T T ρ s C(z, B, t) w s dt (3) ρ s C(z, B, t)αb β dt (4) where T is the period over which averaging is performed, a suitable multiple of one year in the following. n Y is the number of years in T. w s is the settling velocity, here estimated on the basis of measured sediment size distributions (e.g. for the Venice Lagoon, see Section 3, d 5 = 5 μm, w s =.2 mm/s). ρ s is the sediment density (here 265 kg/m 3 ). β =.382 and α =. 6 m/s (m 2 /kg) β are parameters which account for typical halophytic vegetation structure and flow characteristics (Mudd et al. 24, D Alpaos et al. 26, 27). 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 987) d dt (DC) = w s C αb β C + C dh dt (5) 534

3 with C(z, B, t) = { C (t) when C(z, B, t) when dh dt > dh dt < (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, C (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, C (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, Q O, can be directly linked to the annually-averaged aboveground plant dry biomass, B, as follows (Randerson 979, Mudd et al. 24, D Alpaos et al. 26, 27): Q O = γ B (7) where γ = m 3 /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 997, Carniello et al. 25). 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, u w (Carniello et al. 25, Fagherazzi et al. 26, Defina et al. 27). 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) ρ s τ c (MPB) (8) where e is an erosion coefficient characteristic of sediment type and structure (here e = 4 kg/m 2 /s, e.g. van Ledden et al. 24), I(B) is a step function, such that I(B) = ifb = and I(B) = ifb > 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. 999), τ c (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 989, Amos et al. 998) 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. 996). 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. 998) τ c =.4 Pa when z < H and τ c =.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. (27b) 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 () and (2) can be decoupled, by first finding the steady-state solution, B(z), of (2) and by substituting it back into (). A trivial solution of db/dt = is B =, 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 99, Ungar 99). This leaves the steady-state solution: [ B s (z) = d m(z) ] r(z) which we recall to be valid for z, while B s (z) = when z <. (9) 535

4 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 =, 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. 24, Silvestri et al. 25) 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 = and z = H, reflecting the adaptation of Spartina to hypoxic conditions (Morris & Haskin 99, Morris et al. 22). 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. (29). 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) =.5 z/h +.5 yr ; m(z) =.5 z/h +.5 yr. We also assume each plant to produce at most one daughter plant per year in the most favorable conditions, i.e. r(h) = yr and m(h) = yr. Observations in this case indicate that biomass is equal to zero at z = and maximum at z = H (Marani et al. 24, Silvestri et al. 25). We thus take r() = m() =.5 yr. With the above provisions the equation yielding the equilibrium platform elevations finally has the form: dz dt = Q S[z, B s (z)] + Q T [z, B s (z)] + Q O [B s (z)]+ p p E[z, B s(z), MPB(z)] R p = F(z) R = () 3 RESULTS AND DISCUSSION We explore here the stable equilibrium states arising from the solution of 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 2thcentury rate of sea-level rise of 2 mm/yr (IPCC 27, Carbognin et al. 24), and a local subsidence of.5 mm/yr (Carbognin et al. 24), 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 dz/dt [cm/year] dz/dt [cm/year] dz/dt [cm/year] R = 3.5 mm/yr R = 7.3 mm/yr z =.3 m z =. m (a) (b) z =.23 m 3 2 (c) z =.22 m 3 2 z [m a.m.s.l.] Figure 2. Stable equilibrium states in the oxygen-limited vegetation case with (a) tidal observations at Murano, wind at Tessera and suspended sediment concentration C (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. 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 >, which thus brings the system back to the original equilibrium state. On the other hand a positive perturbation of z produces a value 536

5 dz/dt < and the system is thus again pushed back to the equilibrium state. Note that a third solution of dz/dt = 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 2th 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 < 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 =.5 mm/yr). When R is large enough such that no solution to dz/dt = (R = 6.2 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 C (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 pdf of tidal level (m ) pdf of tidal level (m ) pdf of tidal level (m ) Murano (a).6 (b) Astronomic tide Saline (c) 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

6 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. P [V>v] dz/dt [cm/year] dz/dt [cm/year] v [m/s].5.5 z=-.62 m wind at S. Andrea z=-.74 m z [m a.m.s.l.] S. Andrea S. Leonardo (a) z=.23 m (b) z=.23 m wind at S. Leonardo (c) 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 C (t) at Campalto, and wind velocity at S. Andrea (b) and S. Leonardo (c). 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. 4 CONCLUSIONS 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: 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 538

7 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 26 projects Modelli dell evoluzione eco-morfologica di bassifondi e barene lagunari and the VECTOR-FISR 22 project, CLIVEN research line. REFERENCES Allen, J.R.L. 99. Salt-marsh growth and stratification: A numerical model with special reference to the Severn Estuary, southwest Britain, Mar. Geol. 95: Amos, C.L., Brylinsky M., Sutherland T.F., O Brien D., Lee S., & Cramp A The stability of a mudflat in the Humber estuary, South Yorkshire, UK. Geol. Soc. Spec. Publ. 39: Bohannon, J. 25. A Sinking City Yields Some Secrets. Science 39: , doi:.26/science Carbognin, L., Teatini P., & Tosi L. 24. Eustacy and land subsidence in the Venice Lagoon at the beginning of the new millennium. J. Marine Syst. 5: Carniello L., Defina A., Fagherazzi S., & D Alpaos L. 25. A combined wind wave-tidal model for the Venice Lagoon, Italy. J. Geophys. Res., F47, doi:.29/ 24JF232. Cronk, J.K., & Fennessy M.S. 2. Wetland Plants: Biology and Ecology. Lewis, Boca Raton, Fla. D Alpaos, A., Lanzoni S., Marani M., Fagherazzi S., & Rinaldo A. 25. Tidal network ontogeny: channel initiation and early development. J. Geophys. Res., F2, doi:.29/24jf82. D Alpaos, A., Lanzoni S., Mudd S.M., and Fagherazzi S. 26. Modelling the influence of hydroperiod and vegetation on the cross-sectional formation of tidal channels. Estuarine Coastal Shelf Sci. 69: 3 324, doi:.6/ j.ecss D Alpaos, A., Lanzoni S., Marani M., & Rinaldo A. 27. Landscape evolution in tidal embayments: Modeling the interplay of erosion, sedimentation, and vegetation dynamics. J. Geophys. Res. 2, F8, doi:.29/ 26JF537. Day, J.W., Rybczyk J., Scarton F., Rismondo A., Are D., & Cecconi G Site accretionary dynamics, sea-level rise and the survival of wetlands in Venice lagoon: A field and modelling approach. Estuarine Coastal Shelf Sci. 49: Day, J.W. et al. 27. Restoration of the Mississippi Delta: Lessons from Hurricanes Katrina and Rita, Science 35 (589): , doi:.26/science.373. Defina, A., Carniello L., Fagherazzi S., & D Alpaos L. 27. Self organization of shallow basins in tidal flats and salt marshes. J. Geophys. Res.2, F3, doi:.29/26 JF55. D Odorico, P., Laio F., & Ridolfi L. 25. Noise-induced stability in dryland plant ecosystems. Proc. Nat. Acad. Sci. USA 2(3): Holling, C.S Resilience and stability of ecological systems. Annu. Rev. Ecol. Syst. 4: 23. Fagherazzi, S., Marani M., & Blum L. K. 24. The Ecogeomorphology of Tidal Marshes. AGU Coastal and Estuarine Studies, Washigton, D.C. 59: 266. Fagherazzi, S., Carniello L., D Alpaos L., & Defina A. 26. Critical bifurcation of shallow microtidal landforms in tidal flats and salt marshes. Proc. Natl. Acad. Sci. USA. 3(22): 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 27 Global Climate Projections. In Climate Change 27: 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. 27. A coupled geomorphic and ecological model of tidal marsh evolution. Proc. Natl. Acad. Sci. U.S.A. 4:

8 Krone, R.B A method for simulating historic marsh elevations, in Coastal Sediments 87, edited by N.C. Krause, pp , ASCE, New York. Levins, R Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am. 5: MacIntyre, H.L., Geiger R.J. & Miller D.C Microphytobenthos: The ecological role of the secret garden of unvegetated, shallow-water marine habitats:. Distribution, abundance and primary production. Estuaries 9(2A): Marani, M., Lanzoni S., Silvestri S. & Rinaldo A. 24. Tidal landforms, patterns of halophytic vegetation and the fate of the lagoon of Venice. J. Mar. Sys. 5: 9-2, doi:.6/j.jmarsys Marani, M., Silvestri S., Belluco E., Ursino N., Comerlati A., Tosatto O. & Putti M. 26. Spatial organization and ecohydrological interactions in oxygen-limited vegetation ecosystems. Water Resour. Res. 42, W7S6, doi:.29/25wr4582. Marani M., Belluco E., Ferrari S., Silvestri S., D Alpaos A., Lanzoni S., Feola A. & Rinaldo A. 26b. Analysis, synthesis and modelling of high-resolution observations of salt-marsh ecogeomorphological patterns in the Venice lagoon. Estuarine Coastal Shelf Sci., 69(3-4): , doi:.6/j.ecss Marani, M., Zillio T., Belluco E., Silvestri S. & Maritan A. 26c. Nonneutral vegetation dynamics. PLoS ONE (): e78, doi:.37/journal.pone.78. Marani, M., D Alpaos A., Lanzoni S., Carniello L. & Rinaldo A. 27. Biologically controlled multiple equilibria of tidal landforms and the fate of the Venice lagoon. Geophys. Res. Lett. 34, L42, doi:.29/27 GL378. Marani, M., D Alpaos A., Lanzoni S., Carniello L. & Rinaldo A. 29. The importance of being coupled: Stable states and catastrophic shifts in tidal eco-morphodynamics. submitted. May, R.M Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269: Möller, I., Spencer, T., French, J.R., Leggett, D. & Dixon, M Wave transformation over salt marshes: A field and numerical modelling study from North Norfolk, England, Estuarine, Coastal and Shelf Sci., 49: Morris, J.T. & Haskin B. 99, A 5-yr record of aerial primary production and stand characteristics of Spartina alterniflora, Ecology, 7(6): Morris, J.T., Sundareshwar, P.V., Nietch, C.T., Kjerfve, B., & Cahoon D.R. 22, Responses of coastal wetlands to rising sea level, Ecology, 83: Mudd, S.M., Fagherazzi, S., Morris, J.T. and Furbish, D.J., 24, 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 , AGU, Washigton, D.C. Paterson, D.M. 989, Short-term changes in the erodibility of intertidal cohesive sediments related to the migratory behaviour of epipelic diatoms, Limnol. Oceanogr., 34: Randerson, P.F. 979, 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 , Farnborough, Saxon House. Rietkerk, M., Dekker S.C., de Ruiter P.C. & van de Koppel J. 24. Self-Organized Patchiness and Catastrophic Shifts Science 35: , doi:.26/science.867. Rinaldo, A., Dietrich, W.E., Vogel, G., Rigon, R. & I. Rodriguez-Iturbe 995, Geomorphological signatures of varying climate, Nature, 374: Rinaldo, A., Fagherazzi, S., Lanzoni, S., Marani, M. & Dietrich W.E. 999a, Tidal networks 2. Watershed delineation and comparative network morphology, Water Resour. Res., 35(2): Rinaldo, A., Fagherazzi, S., Lanzoni, S., Marani, M., Dietrich, W.E. 999b, Tidal networks 3. Landscapeforming discharges and studies in empirical geomorphic relationships, Water Resour. Res., 35(2): Scheffer, M., Carpenter S., Foley J.A., Folkem C. & Walker B. 2. Catastrophic shifts in ecosystems. Nature 43(): Schneider, S.H The rising seas. Scientific American 3: 2 8. Schröder, A., Persson L., & De Roos A.M. 25. Direct experimental evidence for alternative stable states: a review. Oikos (): 3 9. Silvestri, S., Defina, A. & Marani M. 25, Tidal regime, salinity and salt marsh plant zonation, Estuarine Coastal Shelf Sci., 62, doi:.6/j.ecss.24.8., 9 3. Soulsby, R.L Dynamics of marine sands, Thomas Telford, London. Ungar, I.A. 99. Ecophysiology of Vascular Halophytes, 29 pp., CRC Press, Boca Raton, Fla. van Ledden, M., Wang, Z.B., Winterwerp, H. & de Vriend H. 24, Sand-mud morphodynamics in a short tidal basin, Ocean Dynamics, 54(3 4),