Stefano Lanzoni

Landscape evolution in tidal embayments: Modeling the interplay of erosion, sedimentation, and vegetation dynamics

We propose an ecomorphodynamic model which conceptualizes the chief land-forming processes operating on the intertwined, long-term evolution of marsh platforms and embedded tidal networks. The rapid network incision (previously addressed by the authors) is decoupled from the geomorphological dynamics of intertidal areas, governed by sediment erosion and deposition and crucially affected by the presence of vegetation. This allows us to investigate the response of tidal morphologies to different scenarios of sediment supply, colonization by halophytes, and changing sea level. Different morphological evolutionary regimes are shown to depend on marsh ecology. Marsh accretion rates, enhanced by vegetation growth, and the related platform elevations tend to decrease with distance from the creek, measured along suitably defined flow paths. The negative feedback between surface elevation and its inorganic accretion rate is reinforced by the relation between plant productivity and soil elevation in Spartina-dominated marshes and counteracted by positive feedbacks in multispecies-vegetated marshes. When evolving under constant sea level, unvegetated and Spartina-dominated marshes asymptotically tend to mean high water level (MHWL), different from multiple vegetation species marshes, which can make the evolutionary transition to upland. Equilibrium configurations below MHWL can be reached under constant rates of sea level rise, depending on sediment supply and vegetation productivity. Our analyses on marine regressions and transgressions show that when the system is in a supply-limited regime, network retreat and expansion (associated with regressions and transgressions, respectively) tend to be cyclic. Conversely, in a transport-limited regime, network reexpansion following a regression tends to take on a new configuration, showing a hysteretic behavior. Copyright 2007 by the American Geophysical Union.

Biologically-controlled multiple equilibria of tidal landforms and the fate of the Venice lagoon

Looking across a tidal landscape, can one foresee the signs of impending shifts among different geomorphological structures? This is a question of paramount importance considering the ecological, cultural and socio-economic relevance of tidal environments and their worldwide decline. In this Letter we argue affirmatively by introducing a model of the coupled tidal physical and biological processes. Multiple equilibria, and transitions among them, appear in the evolutionary dynamics of tidal landforms. Vegetation type, disturbances of the benthic biofilm, sediment availability and marine transgressions or regressions drive the bio-geomorphic evolution of the system. Our approach provides general quantitative routes to model the fate of tidal landforms, which we illustrate in the case of the Venice lagoon (Italy), for which a large body of empirical observations exists spanning at least five centuries. Such observations are reproduced by the model, which also predicts that salt marshes in the Venice lagoon may not survive climatic changes in the next century if IPCCs scenarios of high relative sea level rise occur. Copyright 2007 by the American Geophysical Union.

On the drainage density of tidal networks

The drainage density of a network is conventionally defined as (proportional to) the ratio of its total channelized length divided by the watershed area, and in practice, it is defined by the statistical distribution and correlation structure of the lengths of unchanneled pathways. In tidal networks this requires the definition of suitable drainage directions defined by hydrodynamic (as opposed to topographic) gradients. In this paper we refine theoretically and observationally previous analyses on the drainage density of tidal networks developed within tidal marshes. The issue is quite relevant for predictions of the morphological evolution of lagoons and coastal wetlands, especially if undergoing rapid changes owing, say, to combined effects of subsidence and sea level rise. We analyze 136 watersheds within 20 salt marshes from the northern lagoon of Venice using accurate aerial photographs and field surveys taken in different years in order to study both their space and time variability. Remarkably, the tidal landforms studied show quite different physical and ecological characteristics. We find a clear tendency to develop characteristic watersheds described by exponential decays of the probability distributions of unchanneled lengths, and thereby a pointed absence of scale-free distributions which instead usually characterize fluvial settings. We further find that total channel length relates well to watershed area rather than to tidal prism, a somewhat counterintuitive result on the basis of dynamical considerations. Finally, we show that in spite of the apparent site-specific features of morphological variability, conventional measures of drainage density appear to be quite constant in space and time, indicating a similarity of form. We show that such similarity is an artifact of the Hortonian measure. Indeed, important morphological differences, most notably in stream (or link) frequency reflecting the true extent of branching innervating the marshes and the sinuosity of tidal meandering, may only be captured by introducing measures of the extent of unchanneled flow paths based on hydrodynamics rather than topography and geometry.

On tide propagation in convergent estuaries

We revisit the problem of one-dimensional tide propagation in convergent estuaries considering four limiting cases defined by the relative intensity of dissipation versus local inertia in the momentum equation and by the role of channel convergence in the mass balance. In weakly dissipative estuaries, tide propagation is essentially a weakly nonlinear phenomenon where overtides are generated in a cascade process such that higher harmonics have increasingly smaller amplitudes. Furthermore, nonlinearity gives rise to a seaward directed residual current. As channel convergence increases, the distortion of the tidal wave is enhanced and both tidal wave speed and wave lenght increase. The solution loses its wavy character when the estuary reaches its “critical convergence”; above such convergence the weakly dissipative limit becomes meaningless. Finally, when channel convergence is strong or moderate, weakly dissipative estuaries turn out to be ebb dominated. In strongly dissipative estuaries, tide propagation becomes a strongly nonlinear phenomenon that displays peaking and sharp distortion of the current profile, and that invariably leads to flood dominance. As the role of channel convergence is increasingly counteracted by the diffusive effect of spatial variations of the current velocity on flow continuity, tidal amplitude experiences a progressively decreasing amplification while tidal wave speed increases. We develop a nonlinear parabolic approximation of the full de Saint Venant equations able to describe this behaviour. Finally, strongly convergent and moderately dissipative estuaries enhance wave peaking as the effect of local inertia is increased. The full de Saint Venant equations are the appropriate model to treat this case.

Tidal networks 3. Landscape-forming discharges and studies in empirical geomorphic relationships

In this final part of our study [Fagherazzi et al., this issue; Rinaldo et al., this issue] we propose a simple model for predicting the local peak ebb and flood discharges throughout a tidal network and use this model to investigate scaling relationships between channel morphology and discharge in the Venice Lagoon. The model assumes that the peak flows are driven by spring (astronomical) tidal fluctuations (rather than precipitation-induced runoff or seiche, sea surge, or storm-induced tidal currents) and exploits the procedure presented by Fagherazzi et al. [this issue] for delineating a time-invariant drainage area to any channel cross section. The discharge is estimated using the Fagherazzi et al. model to predict water surface topography, and hence flow directions throughout the channel network and across unchanneled regions, and the assumption of flow continuity. Water surface elevation adjustment, not assumed to be instantaneous throughout the network, is defined by a suitable solution of the flow equations where significant morphological information is used and is reduced to depending on just one parameter, the Chezy resistance coefficient. For the Venice Lagoon, peak discharges are well predicted by our model. We also document well-defined power law relationships between channel width and peak discharge, watershed area, and flow, whereas curved, nonscaling relationships were found for channel cross-sectional area as a function of peak discharge. Hence our model supports the use of a power law dependency of peak discharge with drainage area in the Venice Lagoon and provides a simple means to explore aspects of morphodynamic adjustments in tidal systems.

Tidal network ontogeny: Channel initiation and early development

[1] The long-term morphological evolution of tidal landforms in response to physical and ecological forcings is a subject of great theoretical and practical importance. Toward the goal of a comprehensive theoretical framework suitable for large-scale, long-term applications, we set up a mathematical model of tidal channel network initiation and early development, which is assumed to act on timescales considerably shorter than those of other landscape-forming ecomorphodynamical processes of tidal systems. A hydrodynamic model capable of describing the key landforming features in small tidal embayments is coupled with a morphodynamic model which retains the description of the main physical processes responsible for tidal channel initiation and network ontogeny. The overall model is designed for the further direct inclusion of the chief ecomorphological mechanisms, e.g., related to vegetation dynamics. We assume that water surface elevation gradients provide key elements for the description of the processes that drive incision, in particular the exceedance of a stability (or maintenance) shear stress. The model describes tidal network initiation and its progressive headward extension within tidal flats through the carving of incised cross sections, where the local shear stress exceeds a predefined, possibly site-dependent threshold value. The model proves capable of providing complex network structures and of reproducing several observed characteristics of geomorphic relevance. In particular, the synthetic networks generated through the model meet distinctive network statistics as, among others, unchanneled length and area probability distributions. Copyright 2005 by the American Geophysical Union.

The importance of being coupled: Stable states and catastrophic shifts in tidal biomorphodynamics

We describe and apply a point model of the joint evolution of tidal landforms and biota which incorporates the dynamics of intertidal vegetation; benthic microbial assemblages; erosional, depositional, and sediment exchange processes; wind-wave dynamics, and relative sea level change. Alternative stable states and punctuated equilibria emerge, characterized by possible sudden transitions of the system state, governed by vegetation type, disturbances of the benthic biofilm, sediment availability, and marine transgressions or regressions. Multiple stable states are suggested to result from the interplay of erosion, deposition, and biostabilization, providing a simple explanation for the ubiquitous presence of the typical landforms observed in tidal environments worldwide. The main properties of accessible equilibrium states prove robust with respect to specific modeling assumptions and are thus identified as characteristic dynamical features of tidal systems. Halophytic vegetation emerges as a key stabilizing factor through wave dissipation, rather than a major trapping agent, because the total inorganic deposition flux is found to be largely independent of standing biomass under common supply-limited conditions. The organic sediment production associated with halophytic vegetation represents a major contributor to the overall deposition flux, thus critically affecting the ability of salt marshes to keep up with high rates of relative sea level rise. The type and number of available equilibria and the possible shifts among them are jointly driven and controlled by the available suspended sediment, the rate of relative sea level change, and vegetation and microphytobenthos colonization. The explicit description of biotic and abiotic processes thus emerges as a key requirement for realistic and predictive models of the evolution of a tidal system as a whole. The analysis of such coupled processes finally indicates that hysteretic switches between stable states arise because of differences in the threshold values of relative sea level rise inducing transitions from vegetated to unvegetated equilibria and vice versa.

Experiments on bar formation in a straight flume: 1. Uniform sediment

Laboratory experiments have been carried out in a large laboratory flume using a nearly uniform sand and under controlled steady flow conditions such as to ensure the development of alternate bars on a ripple and/or dune-covered bed. The interaction between small-scale and large-scale bed forms is found to enhance a modulation in time and in space of the bar pattern. Moreover, the flow depth decrease experienced by the flow field when approaching bar fronts, leading to a progressive reduction of the dimensions of small-scale bed forms, may influence appreciably the overall flow resistance. Experimental values of bar wavelength and of bar celerity are compared with the theoretical estimates obtained from a model developed within the classical framework of linear stability analysis. In particular, the model accounts for the local variability of friction coefficient and water level, for the secondary helical flow effects, and for the influence of longitudinal slope on sediment transport. Quantitatively satisfactory predictions of bar wavelength appear to be possible in spite of the fact that in various runs a correct estimation of flow resistance and flow discharge appears to be relatively difficult.

Experiments on bar formation in a straight flume: 2. Graded sediment

Laboratory experiments have been carried out in a large laboratory flume using a strongly bimodal sediment mixture in a range of flow conditions such that the initially flat bed of the flume became unstable enhancing the development of alternate bars. In order to elucidate the effect of grain sorting, the present experiments are compared with a previous set of experiments performed in the same flume under similar hydraulic conditions but using a nearly uniform sand with a mean geometric grain diameter equal to that characterizing present experiments. The comparison suggests that sediment heterogeneity may appreciably affect bed form characteristics. The development of smallscale (ripples) and mesoscale (dunes) sediment waves tended to be inhibited thus allowing a decrease in flow resistance. Owing to the bimodal character of the adopted mixture at low values of the bed shear stress a condition of partial transport was attained for which only the finer-grained portion of the mixture was observed to move, while the coarsergrained fractions remained essentially immobile throughout the experimental run. However, complete mobilization of all size fractions was observed to occur in runs carried out at higher slopes (i.e., at higher bed shear stress) in order to generate an alternate bar pattern. Selective transport of individual grain size fractions, coupled with the characteristic bar topography pattern led to an intense longitudinal sorting which accreted the coarser particles on bar crests. Furthermore, bar migration caused, through scour and fill, a significant vertical sorting. As a consequence of these sorting processes and in accordance with previous experimental observations, bar height turns out to be invariably damped with respect to uniform sediment experiments. The trend exhibited by the wavelengths is less clear and suggests that in the present experiments sorting effects do not enhance the clear shortening of bar wavelengths typically observed in other series of flume experiments carried out with weakly bimodal mixtures.

Grain sorting and bar instability

A two-dimensional model of flow and bed topography is proposed to investigate the effect of sediment heterogeneity on the development of alternate bars. Within the context of a linear stability theory the flow field, the bed topography and the grain size distribution function are perturbed leading to an integro-differential linear eigenvalue problem. It is shown that the selective transport of different grain size fractions and the resulting spatial pattern of sorting may appreciably affect the balance between stabilizing and destabilizing actions which govern bar instability. Theoretical results suggest that sediment heterogeneity leads to a damping of both growth rate and migration speed of bars, while bar wavelength is shortened with respect to the case of uniform sediment. The above findings conform, at least qualitatively, to the experimentally detected reduction of bar height, length and celerity. The observed tendency of coarser particles to pile up towards bar crests is also reproduced by theoretical results.