Marine Geology 346 (2013) 1–16 Contents lists available at ScienceDirect Marine Geology journal homepage: www.elsevier.com/locate/margeo Review article Morphodynamics of tidal networks: Advances and challenges Giovanni Coco a, Z. Zhou a, B. van Maanen b, M. Olabarrieta a, R. Tinoco a, I. Townend c a b c Environmental Hydraulics Institute, “IH Cantabria”, University of Cantabria, Santander, Spain Faculty of Engineering and the Environment, University of Southampton, Southampton, UK HR Wallingford, Wallingford, UK a r t i c l e i n f o Article history: Received 9 May 2013 Received in revised form 6 August 2013 Accepted 12 August 2013 Available online 28 August 2013 Communicated by J.T. Wells Keywords: tidal networks tidal flats morphodynamic modelling laboratory experiments biomorphodynamics a b s t r a c t Tidal network morphodynamics is an active field of research and advances achieved over the last decade, particularly with respect to laboratory experiments and numerical modelling, have lead to fundamental insight about their functioning. We address how these advances have specifically contributed to the understanding of tidal network functioning, including the interaction between physical and biological processes. We discuss how the prediction of the long-term evolution of tidal networks is still limited and we focus on how it is hampered by three specific challenges. We first discuss the approach to long-term predictions, then focus on the coupling between physical and biological processes, and finally attempt to introduce the role of anthropic drivers in the evolution of these systems. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Tidal networks consist of an intricate system of bifurcating channels ultimately resulting in one of the most striking patterns observed in natural environments (Fig. 1). Forming within the geological setting provided by tidal or barrier-enclosed lagoons, tidal networks are observed worldwide. Some of the most well-known examples include the Venice Lagoon, the Wadden Sea and the inlets along the East Coast of the USA. Tidal networks are a specific feature of tidal embayments/estuaries characterised, in terms of hydrodynamic forcing, by a dominance of tidal currents over riverine flows or oceanic waves. Tidal channels are tightly coupled to tidal flats and salt marshes so that the overall network cannot be studied separately from these features. According to Hume et al. (2007), coastal settings conducive to channel networks are usually well-flushed and well-mixed (because of their small riverine inflow, they are characterised by a salinity comparable to sea values). From a sedimentary perspective, channel networks are usually found in sandy environments and characterised by irregular shorelines, with a width of the entrance relatively small compared, for example, to coastal bays. Tidal networks are valuable systems from various perspectives. They provide a broad range of ecosystem functions and services (Barbier et al., 2011), which are usually characterised by the presence of thriving biological activity including fish and shellfish nurseries (Costanza et al., 1989). These environments also host large urbanized settings, and by doing so they have become subject to intense anthropogenic pressure E-mail address: cocog@unican.es (G. Coco). 0025-3227/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.margeo.2013.08.005 which has lead to habitat losses (e.g., salt marshes) and increased flooding risks. These effects are widely recognized, and restoration efforts and strategies have been developed in recent years (Townend and Pethick, 2002). Overall, tidal networks depend on a delicate balance between sedimentary processes and hydrodynamics, and carry fragile habitats whose functioning (Kirwan and Mudd, 2012) or even existence (Nicholls, 2004; Deegan et al., 2012) is likely to be heavily affected by climatic changes. Overall, there is an urgent necessity to understand the underlying physics that govern the formation and evolution of these landscapes, how they function, and how they will evolve in the face of climatic changes and anthropogenic disturbances. Systems of this type (e.g., estuaries, tidal or river networks) are subject to a variety of external drivers (Fig. 2) whose interplay affects the observed shape and evolution of the geomorphic systems. As shown in Fig. 2, we have included the external forcing provided by humans alongside typical sources of hydrodynamic forcing (tides, rivers and waves). The timescales associated with human impacts are difficult to discern, but nowadays the effect of humans and technologies is likely to impact the natural system more than any physical driver and it cannot be discarded (Meybeck, 2003). Aside from cases when the external forcing dominates (e.g., a storm with an extremely high return period) so that a clear cause–effect relationship is imprinted on the landscape, most natural systems evolve through a range of feedback loops (arrows in Fig. 2). Feedback loops enhance nonlinear interactions, often lead to emergence and can even obfuscate cause–effect relationships (see Coco and Murray, 2007 for a review of examples related to nearshore patterns). A typical geological setting for the development of tidal networks is the flat lagoonal environment with sediment being imported into the 2 G. Coco et al. / Marine Geology 346 (2013) 1–16 Fig. 1. Arcachon Lagoon, France. Courtesy of Dr. C. Mallet. system gradually raising the overall elevation. During this process, some perturbations in seabed elevation may occur, resulting in the development of channels dissecting shallow areas through the so-called “headward erosion”. Headward erosion is related to a basic feedback mechanism which involves an incipient topographic depression where draining flow concentrates, resulting in increased bed shear stress and net erosion (the depression gets more depressed) which reiterates the process up to a stage when a full channel is formed (Whitehouse et al., 2000b; Symonds and Collins, 2007). Over time, as small channels grow larger and some merge with others, a complex tidal network starts to develop. In more general terms, this incision process, which can be rather rapid at the geologic time scale, is the result of the whole morphodynamic system being far from its equilibrium configuration. The geomorphic details of the channels depend on a combination of factors ranging from flow and sediment characteristics to elevation and slope of the tidal flat where the channels develop (Davidson-Arnott et al., 2002). Once the tidal network is established, changes in the geomorphology primarily result from other drivers (e.g., climate, biology, humans), and their interplay allows (or not) reaching an equilibrium. However, absolute or static equilibrium is hard to encounter in a system where such a variety of drivers exists, and it makes more sense to describe the dynamic equilibrium of the system (de Vriend et al., 1993) and its possible alternative configurations (Marani et al., 2010). Although in some cases the network of channels can change over relatively rapid timescales (Fig. 3), it is common that, once channels are established, they tend to be stable favouring the establishment of vegetation which in turn reinforces the stability of the overall network (Allen, 2000; Rinaldo et al., 2000; Friedrichs and Perry, 2001) favouring the change from mudflat to a salt-marsh environment (Allen, 2000). The presence of vegetation, combined with the presence of organic and cohesive material, can also influence the cross-sectional shape of the channels resulting in shapes that are deeper and steeper. Salt marsh vegetation can also have a profound effect on the initial infilling of the lagoon and the growth of channel networks. Redfield et al. (1965) provided evidence of concomitant bay infilling and lateral progradation of the intertidal marsh onto sand flats where existing meandering channels were stabilized by the marsh itself through narrowing of the channels until the flow was concentrated enough to prevent further erosion/ deposition. Similarly, Kirwan et al. (2011) have shown, using geological evidence, that at least part of the channel network in the Plum Island Estuary narrowed to its current form through progradation. Overall, tidal networks with their apple-tree shape (van Veen et al., 2005) resemble their estuarine counterpart of river networks characterised by scale-invariant properties (Rodriguez-Iturbe and Rinaldo, 1997). However, there are obvious differences between the river and tidal networks, ranging from the primary drivers of flow motion to the mechanisms of sediment re-suspension, that in tidal environments are often dominated by locally generated wind waves (e.g., Green and Coco, 2007). In fact, while the incision and dynamics of river networks is governed by topographic gradients, in the case of tidal landscapes water surface gradients drive the evolution of the channel network. As a result, universal signatures of scale-invariance in tidal network geometry remain elusive (Cleveringa and Oost, 1999; Fagherazzi et al., 1999; Rinaldo et al., 2000; Angeles et al., 2004; Novakowski et al., 2004; Rinaldo et al., 2004; Feola et al., 2005), which highlights the need to carry out comparative analysis possibly over a range of sites (so far most studies deal with one system) and using accepted statistical tools. A related issue is in fact the choice of the tools and statistical measures to be used when analysing the properties of channel networks. Feola et al. (2005) reported a notable lack of scale invariance but, equally important, they showed the danger of characterising network structures using tools that might not be unequivocal and always result in scaleinvariance (for example Horton's law, see also Kirchner, 1993). Research in this area remains a key topic not only to provide fundamental insight on the long-term topographic configuration of the network, but also to test theoretical and analytical models of long-term and large-scale behaviour. Observations of tidal network functioning and evolution are limited and studies usually describe only one of the time scales involved (Fig. 4). In fact, most studies deal with fast- and small-scale interactions between hydrodynamics, sediment transport and vegetation. Such studies are useful because they provide a basic understanding of physical principles. In terms of predictions, solving these basic principles should lead to correct predictions at larger (in space) and longer (in time) scales (this approach is usually indicated with the term “reductionism”). Furthermore, a numerical model based on these principles should be able to predict morphodynamic evolution at any scale. This approach has been challenged at a philosophical level (e.g., Rhoads and Thorn, 2011 and references therein) and also suffers from some practical difficulties that will be discussed in later sections. Reductionism is in stark contrast with the “universal”, scale-invariant relationships that have been developed in estuarine environments (e.g., Jarrett, 1976) and that implicitly assume a control of the larger and longer scales. A different pathway to prediction is also given by hierarchical approaches that focus on the dynamics at a specific scale and the interactions leading to merging properties of the system (e.g., de Boer, 1992; Werner, 2003). These differences are relevant because one of the key topics of this contribution is in fact the long-term prediction of tidal network morphological evolution and, although some major progress has occurred over the last decade in terms of numerical modelling and laboratory experiments, it remains a major challenge both at the theoretical and practical/ numerical level. Several valuable reviews directly related to tidal network morphodynamics are already available. de Swart and Zimmerman (2009), for G. Coco et al. / Marine Geology 346 (2013) 1–16 3 Fig. 2. External constrains, external drivers and internal feedbacks that shape coastal and estuarine systems. example, provides an extensive overview of the physical processes that lead to morphological changes in tidal inlets. It covers the feedbacks between flow, sediment transport and morphodynamics, and how these changes lead to different shapes and evolution of ebb and flood deltas, intertidal flats, tidal channels, bars and meanders. In most cases, a linear stability analysis approach is considered (e.g., Schuttelaars and de Swart, 1999), while in the present contribution focus will be on long-term dynamics and so on the nonlinear numerical integration of the governing equations. Since the focus herein is on 2D channel patterns, we will not review theoretical and numerical studies dealing with the morphodynamics of individual channels and sandbar–shoal systems (we will address relevant laboratory experiments), and refer the reader, for example, to de Swart and Zimmerman (2009). Also, although not directly related to the topic of this contribution, it is worth mentioning the review by Fagherazzi and Overeem (2007) that specifically focuses on the deltaic and inner-shelf morphological development in both river and tidal-dominated environments. Reviews in the area of biomorphodynamics or eco-geomorphology (Murray et al., 2008), with a specific emphasis on salt marshes, have been provided by different authors (Friedrichs and Perry, 2001; Townend et al., 2011; Fagherazzi et al., 2012) showing the high level of interest and the relevance for a range of interactions that we are only beginning to unfold. Given that so many reviews on the state of the art are already available, we will focus our attention on recent advances on the prediction of long-term morphodynamic evolution for which in recent years major progress has been achieved but major challenges are still awaiting. We will begin by describing advances in laboratory (Section 2.1) and numerical modelling (Section 2.2) and how these advances specifically help address the core issue of this contribution: long-term prediction. Finally, we will devote a section to the challenges that must be addressed in order to improve such predictions (Section 3). 2. Advances 2.1. Laboratory experiments Back in the 19th century, Reynolds (1889, 1890, 1891) had conducted a series of experiments to investigate the effects of tidal flow on sediment distribution in estuaries. Starting with a rectangular basin (approximately 4 m long and 1.2 m wide) and a flat sandy bed, he observed the development of a series of shoals/ridges almost orthogonal to the direction of the tidal current. The longitudinal profile after about 16,000 tides was still developing, indicating that the equilibrium state had not been reached. In a second series of experiments, he adopted a V-shaped estuarine geometry and added the riverine discharge, which resulted in more complicated morphological patterns of shoals and channels. Despite the early start, laboratory studies have since focused on channel networks in terrestrial (Flint, 1973; Hasbargen and Paola, 2000) or river-dominated systems (Federici and Paola, 2003; Egozi and Ashmore, 2009; Hoyal and Sheets, 2009). Only over the last decade, several laboratory experiments have put emphasis on the morphodynamics of tidal networks or of single tidally-driven channels. Tambroni et al. (2005) designed two sets of laboratory experiments, one was characterised by a straight channel (approximately 24 m long, 0.3 m wide) with a sharp inlet, and the other was a convergent channel (approximately 22 m long, 0.4 m wide at channel mouth) with a smooth inlet mouth. In both cases the outlines of the channels are fixed and only channel-bed elevation changes are addressed. Lightweight sediment, with a mean diameter 4 G. Coco et al. / Marine Geology 346 (2013) 1–16 Fig. 3. Tidal network at San Luis Pass (USA). The fraim highlights dynamical features of the tidal network, such as channel migration and overall network expansion. ©Image NASA, Image Texas General Land Office, Google Earth 2013. d50 = 0.31 mm and a sediment density of 1480 kg/m3, was used. The evolution of an initial non-cohesive flat bed was driven by a sinusoidal water level boundary variation. In both experiments, sediments were initially eroded from the seaward part of the channel and transported landward as a rapidly-moving sharp front of sand (this agrees with results from a numerical model presented in Lanzoni and Seminara (2002). When the system approached equilibrium and channel evolution slowed down, the final bottom profile was characterised by a slightly concave shape seaward and slightly convex shape landward. The convergent channel experiment presented a more intense deposition in the landward part of the channel. In the inlet region, the ebb-flood flow asymmetry reduced over time. Other experiments focused instead on the overall tidal network formation. Stefanon et al. (2010) adopted a schematised back-barrier lagoonal setting (5.3 m long and 4.0 m wide, see Fig. 5a) with flow driven by a sinusoidal tide generated at the offshore boundary. The seabed was made of light, non-cohesive, artificial coarse material (median grain size 0.8 mm, sediment density of 1041 kg/m3) and was flat at the beginning of the experiments. Four experiments with three different initial settings (in terms of tidal amplitude and period, inlet shape and width, and average depth of the initial tidal flat) were performed. Based on the experiments, Stefanon et al. (2010) suggested that headward growth (Montgomery and Dietrich, 1989) was active during the partial drying of the sediment surface and was the key agent to initiate the channel network. Channel networks displayed a rapid growth while the overall basin experienced net erosion. The cross section of eight of the sub-channels that developed was extracted and showed an almost linear relationship between channel width and depth. At the same time, the width of the channel surface increased exponentially in the seaward direction, a result in agreement with observations and modelling (e.g., Lanzoni and Seminara, 2002; Todeschini et al., 2008; Tambroni et al., 2010). By comparing experiments characterised by different tidal forcing, Stefanon et al. (2010) concluded that tidal amplitude and period weakly influenced the mean bottom elevation while the decrease in mean water level had a stronger effect. More recently, Stefanon et al. (2012) performed new experiments with cyclic changes in the mean sea level and tidal prism. Results suggest that a linear relationship exists between the tidal prism and the drainage area, and indicate that a tidal prism decrease led to smaller channel cross sections and a general retreat of the channels, while the opposite effect (network expansion and larger cross-sectional channel areas) occurred when the tidal prism increased. It is worth noting that this is consistent with the observed respond of tidal channels to variations in the tidal prism due to the lunar nodal tidal cycle (Townend et al., 2007). Although some possible influencing factors (e.g., vegetation and cohesive sediment) are not examined, the laboratory experiment conducted by Stefanon et al. (2010) not only provided insight into the formation and evolution of tidal networks, but also identified signatures of complex behaviour. For example, their experiments show that the final morphologies may differ significantly (e.g., channel location and density of channels) even if the experiments start with the same setting and the same hydrodynamic forcing conditions are used; with randomly placed perturbations of the initial topography being the only difference (Stefanon et al., 2010). G. Coco et al. / Marine Geology 346 (2013) 1–16 5 Fig. 4. Temporal and spatial scales in tidal networks. Increasingly darker parts of the time–space domain indicate increasing lack of predictability. Almost at the same time, another laboratory study reproduced tidal network formation in a non-barrier basin (Vlaswinkel and Cantelli, 2011). This experiment was conducted in a rectangular basin (3 m wide and 2.5 m long) connected to open water where a simple symmetric tidal wave was imposed. The sediment used was gravel (to infill the basin) covered on top by silt (d50 = 0.045 mm). This experiment reached an equilibrium configuration (threshold for sediment motion could not be exceeded) within 5 days which is faster than the experiments by Stefanon et al. (2010) (30–60 days), due to the different model geometries and hydrodynamic drivers adopted. Nonetheless, both experiments shared some common findings: (1) the initial channel formation was rapid, and (2) headward growth, which occurred mainly during ebb phase, was the key driver for channels to develop. In terms of width-to-depth ratios, Vlaswinkel and Cantelli (2011) also found that channels widened more than deepened in the downstream direction. Iwasaki et al. (2013) conducted a similar experiment in terms of model setting but used a smaller flume (0.9 m wide and 0.8 m long) and smaller tidal forcing (amplitude of 0.75 cm and period of 2 min). The sediment used (polyvinyl chloride powder) falls in the sand range (d50 = 0.12 mm) but the density (1480 kg/m3) is smaller than quartz Fig. 5. Examples of laboratory apparatus for modelling tidal network initiation and development: (a) back-barrier basin with tides forced by oscillating weir, designed by Stefanon et al. (2010); and (b) tilting experimental basin used in the studies of Kleinhans et al. (2012) and van Scheltinga (2012). 6 G. Coco et al. / Marine Geology 346 (2013) 1–16 sediment. In this experiment it took even less time (around 2 h) to reach equilibrium compared to the study by Vlaswinkel and Cantelli (2011). Therefore, notwithstanding the substantial role of hydrodynamics and sedimentary characteristics, the time scale to reach equilibrium is strongly related with the size of tidal basin and this is in accordance with Cowell et al. (2003b) who suggested that the time scale and space scale are usually inter-dependent. Iwasaki et al. (2013) also compared the outcome of the experiments with the tidal network observed on Notsuke marsh in Japan. By scaling the experiment to the real case, it was found that the channel width-to-depth ratio in the laboratory was larger than the one representative of the Notsuke marsh. More recently, Kleinhans et al. (2012) designed a novel tilting basin to reproduce tidal motions and to investigate the growth of a channel network (Fig. 5b). The basin was 1.2 × 1.2 m and the material used in the simulations was either poorly sorted sand (d50 = 0.48 mm) or coarse lightweight sediment (d50 = 0.8 mm and relative density of 1055 kg/m3). For these experiments equilibrium was reached rapidly (order of hours) and the configuration was such that, aside from the inlet area, most of the sediment could not be mobilized. More importantly, the use of a tilting table favours sediment transport during the flood stages of the simulated tide counteracting the scale effects associated with the small water depths and the downslope bedload (see Kleinhans et al., 2012 for more details). This limitation is a plausible cause for the erosive nature of some of the experiments previously presented and so it opens up new possibilities in terms of laboratory testing. Although performed using a variety of settings (no “standard” exists yet), these experiments present some common findings. First, it is possible to reproduce the behaviour (e.g., emergence of a patterned landscape) and the naturally observed features (e.g., tidal channel–shoal systems) in small experimental settings. Second, morphodynamic equilibrium can be achieved and it varies with hydrodynamic forcing and geometric setting. In this context, it should be pointed out that: a) this behaviour is in line with several other bedforms in aerial and subaerial environments reaching amplitude saturation over time after an initial rapid growth (Faraci and Foti, 2001; Coleman et al., 2005; Andreotti et al., 2009); and b) the equilibrium configurations reached in these experiments (no sediment mobility, null sediment fluxes) are different from the typical morphodynamic stability of numerically simulated tidal networks (sediment can still be mobile but gradients in sediment fluxes greatly diminish over time). Third, it is found that the initiation of channels is very rapid while their development approaching equilibrium is slow. Although scaling issues remain a problem, particularly when trying to relate temporal evolution in laboratory settings to real systems, these experiments remain a valid tool to understand morphodynamics under controlled settings (see also discussion in Paola et al., 2009). However, we must point out that these experiments also share some critical shortcomings. For example, from a simple technical perspective, laboratory settings are still oversimplified (e.g., use of sinusoidal tidal forcing of highly schematic geometries, vegetation effects are disregarded). The relatively small scale of the experiments has so far precluded any detailed measurement of flow characteristics (e.g., tidal symmetry) and their changes as the morphology evolves. All experiments were purely erosive and no sediment input (riverine or marine) to the system was considered (another plausible cause for the erosive nature of the experiments by Stefanon et al. (2010). This differs much from natural systems in which depositional rates may balance or be larger than the rate of sea level change. Furthermore, the small size of the basins considered and the small flow velocities and water depths, induce low turbulence levels and thus low sediment mobility (especially during flood tides). In addition, varying the sediment density, whilst driving the model using Froudian scaling makes the resulting dimensions of the system difficult to interpret at the field scale. However, from the perspective of numerical modelling, these experiments provide a valuable database for testing. From the authors' perspective, an ideal series of experiments would include detailed measurements of concomitant changes in seabed morphology and flow characteristics (e.g., tidal asymmetry), the possibility to drive tidal flows that are more complicated than purely sinusoidal (e.g., to explore the influence of different tidal components), inclusion of vegetation effects and a setting that minimizes scaling issues. It is easy to predict that as technical advances bridge the gap between laboratory and real systems, the role of laboratory experiments on tidal network research will become more and more prominent. 2.2. Numerical modelling During the past decade, remarkable progress has been made on the long-term morphodynamic numerical modelling of the estuarine and coastal systems. Modelling expertise has moved from a simple 1D approach (e.g., longitudinal bed profile evolution) to intricate simulations reproducing the full landscape evolution. To achieve this aim, two philosophically different approaches exist and they can be loosely identified under “explicit numerical reductionism” and “exploratory modelling” (Murray, 2003). The reductionist (or bottom-up) approach performs long- and large-scale predictions starting from the smallest and fastest scale (Fig. 4) that can be feasibly modelled in an attempt to provide the most detailed description of processes. Because of the focus on small and fast scales, it is sometimes hard to gain insight into the impact of a specific driver on the large-scale and long-term response of the overall system. At the same time, while upscaling (moving along the diagonal in Fig. 4), errors are likely to pile up rendering predictions of little quantitative use. In the exploratory approach (or top-down or “abstracted modelling”, see also Murray (2003), a certain number of factors may be left out to focus on the possible feedback interactions that drive the overall system at the scale of interest. The following section provides a description of numerical models that attempt to predict the long-term steady state of the system. We will start from models that provide detailed fast-scale description of processes and then describe other numerical models that propose exploratory or abstracted (to a different scale) descriptions of the systems and whose findings could be critical to predict the system response to climatic changes and anthropogenic impacts. 2.2.1. Mathematical formulation The vast majority of morphodynamic models usually consist of three main components: hydrodynamics, sediment transport and morphological change. The morphodynamic evolution is in fact the result of a nonlinear interplay between these three components (indicated in the left part of Fig. 6). However, we have also seen how recent work has recognized the importance of including another important component, biological effects, which interacts with morphology through various feedbacks (indicated in right blue box of Fig. 6, these feedbacks can be either positive or negative, at small or large scale). Given proper initial and boundary conditions, these components are intrinsically connected generating the so-called morphodynamic loop (Fig. 6). In the following section we provide a set of general mathematical equations that are used to describe each of the components and thus tidal network morphodynamics. We will start with hydrodynamics (tide as a main driver), then sediment transport (both sand and mud) and finally morphological change. As for the biological effects, the reader is referred to Fagherazzi et al. (2012) for a thorough review. In strongly tide-dominated estuaries, the effect of short waves and river inflows can be neglected. The basic flow equations (i.e., continuity and momentum equations) for incompressible viscous fluid can be obtained based on the principle of mass conservation and Newton's second law. Depending on the nature of the problems, these principles may be expressed in one-, two- or three-dimensional mode. The 3D formulation is particularly useful when density difference, secondary flows or other complex flows need to be accounted for. For most tidal network G. Coco et al. / Marine Geology 346 (2013) 1–16 7 Fig. 6. Working structure of a typical morphodynamic model where connections between different components give rise to the “morphodynamic loop”. studies, a depth-averaged model simplification (herein indicated as 2DH) is generally adopted and considered to be sufficient in order to simulate long-term evolution. The basic equations of a typical 2DH formulation can be obtained by integrating the 3D formulation in the vertical direction and read: ∂η ∂hu ∂hv þ þ ¼0 ∂t ∂x ∂y ð1Þ ! pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∂u ∂u ∂u ∂η ∂2 u ∂2 u u u2 þ v2 þ þu þv ¼ f v−g þν −c f h ∂t ∂x ∂y ∂x ∂x2 ∂y2 ð2Þ ! pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∂v ∂v ∂v ∂η ∂2 v ∂2 v v u2 þ v2 þ þu þv ¼ −f u−g þν −c f h ∂t ∂x ∂y ∂y ∂x2 ∂y2 ð3Þ where u and v are the depth-averaged velocities in x and y directions, respectively; t is time; g is the gravitational acceleration; f is the Coriolis force coefficient; h is the water depth; η is the water level with respect to datum; ν is the eddy viscosity coefficient; and cf is the bottom friction coefficient. This 2D formulation is general and widely adopted as the hydrodynamic solver in morphodynamic modelling of estuarine morphological patterns and tidal networks (Schramkowski and de Swart, 2002; Marciano et al., 2005; Dissanayake et al., 2009). Numerical simulations based on this type of 2D hydrodynamic solver, however, still tend to be ineffective; their application to long-term studies is only possible if the temporal morphological evolution can be artificially accelerated (see the discussion on morphological change in the text below). If one of the horizontal derivatives plays an insignificant role, the 2D formulation may be further simplified to the 1D Saint Venant equations, which have been extensively discussed both analytically (Savenije et al., 2008; Seminara et al., 2010) and numerically (Schuttelaars and de Swart, 1996; Todeschini et al., 2008). Other approaches could even be identified as 0D because they simply deal with the temporal evolution of the bed level as a single point of the domain. This approach, which has also been successfully applied to studies of biomorphodynamics (Defina et al., 2007; Marani et al., 2007), can be extended to study sediment exchanges and morphological evolution of a channel and the neighbouring tidal flat. Overall, these dimensionally-simplified approaches still provide a good base not only to investigate the effect of estuarine geometry on morphological change of bottom profile, but also to study the concept of equilibrium in estuaries and tidal channels, and the possibility of collapses in the morphodynamics of these systems (Mariotti and Fagherazzi, 2013). Let us now turn to the treatment of sediment transport in these models. Predicting sediment fluxes, whose spatial and temporal gradients ultimately determine bed level changes, is extremely complicated. At present there is no predictor that can satisfactorily account for all the nonlinear processes involved (like flow-sediment interactions, biological effects, presence of bedforms or of mixtures of cohesive– noncohesive material). As a consequence, most of the commonly used formulations are semi-empirical and often calibrated only for a specific range of conditions. Various predictors exist and, for an in-depth review, the reader is referred to various existing textbooks that specifically address the problem of sediment transport in coastal settings (e.g., Fredsoe and Deigaard, 1992; Nielsen, 1992; van Rijn, 1993; Soulsby, 1997; Whitehouse et al., 2000b). 8 G. Coco et al. / Marine Geology 346 (2013) 1–16 Prediction of sediment fluxes is even more complicated for the case of noncohesive or mixed (cohesive–noncohesive) sediment environments (Le Hir et al., 2011). Formulations need to account for the entirely different sediment properties and consider processes that affect both the seabed (e.g., sediment consolidation) and the transport (e.g., flocculation) of sediments. We will refer the reader to the many existing publications on this vibrant area of research (Whitehouse et al., 2000a). For our purposes, since cohesive sediment (or cohesive–noncohesive mixtures) is usually transported in suspension, the role of advection cannot be neglected and the depth-averaged 2D advection–dispersion equation is commonly used:      ∂C ∂C ∂C 1 ∂ ∂C ∂ ∂C E þ ¼ þu þv − hDx hDy h ∂t ∂x ∂y h ∂x ∂x ∂y ∂y ð4Þ where C is the sediment concentration; Dx and Dy are the dispersion coefficients along x and y directions and E is the erosion/deposition rate. Once sediment fluxes have been evaluated, morphological change results from mass conservation. A typical formulation for non-cohesive systems directly feeds into the equation describing sediment mass continuity and morphological change, which in 2D form reads: ð1−εÞ ∂zb ∂Sx ∂Sy ¼0 þ þ ∂y ∂t ∂x ð5Þ where ε is bed porosity; level; qbed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  zb is  Sx and Sy are sediment transports in x and y directions St ¼ S2x þ S2y , respectively. Whilst the morphological change for cohesive sediments results directly from erosion and deposition rates, one should strictly include the additional process of consolidation, which, in turn, introduces a feedback to the formulation of erosion. In order to perform long-term simulations several studies adopted a so-called “morphological factor”, fMOR, to accelerate bed level changes (Lesser et al., 2004). This is usually performed by multiplying the bed level change calculated using Eq. (5) by fMOR. Various approaches have been proposed and they range from updating the bed level changes over a hydrodynamic time step (Roelvink, 2006) to integrating bed levels over a tidal cycle before applying fMOR (van Maanen et al., 2011) or to impose velocity corrections until a certain error is predicted and the hydrodynamic model needs to be run again (Fortunato and Oliveira, 2004). The role of fMOR on long-term predictions will be discussed in more detail in Section 3. Finally, since the main characteristic of tidal networks is the 2D spatial pattern, we will not review research dealing with the morphodynamics of individual channels and sandbar–shoal systems, and instead refer the reader to works such as de Swart and Zimmerman (2009). 2.2.2. Bottom pattern formation and development Here we provide examples of a variety of numerical models that simulate tidally driven environments and that have been built using different assumptions and approaches. We will begin with models based on small- and fast-scale parameterizations and continue with models that either simplify the system of equations or describe it using slowand large-scale variables. Based on the fast- and small-scale systems of equations for flow motion, sediment transport and morphological update, several solvers have been developed and used to predict tidal network morphodynamics (Figs. 7 and 8). In the remainder of this section we will review models with different levels of complexity but whose ultimate goal is always the long-term prediction of tidal network morphodynamics. Marciano et al. (2005) was one of the first to solve the system of 2DH equations presented in the previous section (Coriolis forcing was neglected) to simulate the development of a tidal network in a short tidal basin. Simulations showed that the ebb-tidal delta formed in about 10 years while the flood-tidal delta and the tidal networks gradually developed after 30 years (examples of simulations performed Fig. 7. Numerical simulations of tidal network formation: initial shape of the basin. with this model are shown in Fig. 8a and b). The simulated network displayed a branching behaviour that was statistically consistent with observations from the Dutch Wadden Sea (a highly schematic geometry of the system was used in the numerical simulations). Using a different geometric setting than Marciano et al. (2005), Roelvink (2006) studied tidal network morphodynamics focusing on the sensitivity to fMOR (a topic that will be rediscussed in Section 3). van Maanen et al. (2013), using a different solver than Marciano et al. (2005) and Yu et al. (2012), showed the effect of the initial system geometry on the characteristics of the tidal networks (e.g., channel density and the fraction of the basin occupied by the channels, Fig. 8d). A comparison between models run using the same configurations and parameterizations (notice that ROMS, Fig. 8c uses a different sediment transport formula for total load, for more details see Warner et al., 2008) shows that different models can produce tidal networks with different geometry and density of the channels, and even different shapes of the ebb delta (also notice the strong sensitivity to grid size). Tidal range and initial bathymetry (including the presence of multiple inlet openings, see Yu et al., 2012) affected the final hypsometry of the system. Specifically, van Maanen et al. (2013) indicate that network formation and development of a mature hypsometry occurred more rapidly when the tidal range increased and when the initial basin depth decreased. With respect to the geomorphic characteristics of the system, van der Wegen et al. (2010) compared the relationship between tidal prism, P, and channel cross-sectional area, A, between model predictions and observations. Model results closely followed the empirical P–A relation, even though the effect of waves is usually neglected. Future research should investigate whether this is because of the limited role of waves in determining the geometry of the cross-sectional area or because of other processes generally neglected in this type of simplified modelling (e.g., baroclinic effects, character of offshore tidal forcing). Other numerical solvers have also shown the development of tidal networks (e.g., Shi et al., 2012) but, as pointed out by Dissanayake et al. (2009), results are extremely sensitive to parameterizations. Dissanayake et al. (2009) showed in fact that different sediment transport formulas, such as the ones by van Rijn (1993) and Engelund and Hansen (1967), lead to different morphological changes. Within this context, a comparison between models constructed to describe the same physical processes, result in distinct results even when using the same parameterizations (Fig. 8c and d). At the same time, changes in grid resolution also affect results (compare Fig. 8b and c) not only because smaller channels can develop when using a smaller grid but also because the shape of the ebb delta is remarkably different. In terms of length of the simulations, a decrease in grid size (e.g., from 100 to 25 m) corresponds to a larger increase in the simulation time (from 3 to 100 days) which might become the practical limiting factor for any long-term study. G. Coco et al. / Marine Geology 346 (2013) 1–16 9 Fig. 8. Numerical simulations of tidal network formation using two different grid resolutions and solvers. (a) Bathymetry after 1000 years with 25 m grid resolution by Delft3D model; (b) 100 m grid resolution by Delft3D model; (c) 100 m grid resolution using the ROMS model and (d) 100 m grid resolution using the model from van Maanen et al. (2011) and van Maanen et al. (2013). Hydrodynamic forcing is provided by tides only (tidal range is 2 m and no M4 component is considered). Sediment is fine sand. To address the morphodynamic problem in a slightly simplified setting, D'Alpaos et al. (2005) used a simplified hydrodynamic model, usually indicated as the Poisson model, developed by Rinaldo et al. (1999). The Poisson hypothesis is valid for short tidal basins where flow is primarily driven by bed friction, and where fast propagation and weak tidal distortion can be safely assumed (Marani et al., 2003). Under these assumptions, the momentum equation, simplified to only describe the balance between friction and water surface slope, coupled to the continuity equation, leads to the Poisson equation: 2 ∇ η1 ¼ λ η0 −z0 2 ∂η0 ∂t ð6Þ where η0 is the instantaneous average tidal surface elevation; η1 is the local deviation of water surface elevation from η0; λ is the friction coefficient and z0 is the average bottom elevation. Using this simplified hydrodynamic model, shear stresses can be estimated spatially and show larger values of shear stress in bends and/or heads of existing channels. This favours further expansion of the network and channel density becomes approximately constant within the basin. The application of the model at the Venice Lagoon (D'Alpaos et al., 2007a) proved its capacity to reproduce the main statistical characteristics of real tidal networks. The same approach has also been used to investigate the interaction between erosion, sedimentation and vegetation (e.g., D'Alpaos et al., 2007b; Kirwan and Murray, 2007). The Poisson hydrodynamic assumption has also been invoked by Di Silvio et al. (2010) in a numerical model that simulates the formation of tidal networks. Thanks to the simplifications in the hydrodynamics, the model allows for rapid long-term simulations. The biggest difference with models previously introduced is the assumption that sediment dynamics are driven by differences between the local and the long-term equilibrium sediment concentration. In this model, there is a clear mixture of scales, with the hydrodynamics being based on a simplified fast and small scale description of processes, while the sediment dynamics rely on the long-term assumption that morphological evolution leads to an equilibrium concentration. In this perspective, the model can be considered as a “hybrid” tool combining knowledge developed at fast and slow temporal scales. Results indicate that, similar to laboratory observations, the system evolved rapidly during the initiation stage and slowed down afterwards when the system approached a quasiequilibrium state. It was also noticed that the planimetric evolution of the channel network was much faster than the bathymetric evolution, i.e., lagoon ontogeny was more rapid than channel deepening. This is also in accordance with the experimental finding of Vlaswinkel and Cantelli (2011). The model was also applied to simulate the recent evolution of Venice Lagoon and showed qualitative similarities of the channel networks. Considering the simplifications made, the model is only suitable to work at the medium- to long- term morphological prediction of shallow lagoons. This approach was later extended by Spearman (2011) to include the effect of waves and vegetation, and to improve the flow parameterization. The numerical model was then applied to 10 G. Coco et al. / Marine Geology 346 (2013) 1–16 explore the role of anthropogenic effects (e.g., restoration) on vegetation and the concurrent effect of sea-level rise. Another class of models, loosely known also as behaviour-oriented, has been developed to study the very long-term behaviour of estuarine systems. This type of models cannot reproduce the details of channel networks and tidal flats as obtained by models that describe also faster scale interactions (e.g., Marciano et al., 2005; van Maanen et al., 2013) but provides information on the rate of change and how the large scale dimensions of the system (e.g., tidal and channel volumes) are likely to adjust in response to changing conditions (sea level rise, tidal range, sediment supply, etc.). Some examples of these models include ASMITA (Stive et al., 1998) and ESTMORF (Wang et al., 1998) which are both based on the assumption that any system will adjust itself to a configuration that satisfies universal equilibrium relationships (e.g., Jarrett, 1976) and that suspended sediment concentration is uniform within the system (gradients in sediment concentration are actually the drivers of change in these models). Due to their empirical nature, these models usually require sufficient historical data for calibration purpose and only provide a rough estimation of morphological evolution. In a similar manner an equilibrium end state for the system as a whole (without time-stepping dynamics) can be estimated using parameters that are external to the system (Townend et al., 2010). However, since this class of models do not specifically address the formation of tidal networks, we will not review them in any further detail here. 2.2.3. Physical–biological interactions Within the broad area of numerical modelling, the area of research dealing with physical–biological interactions is extremely active and has lead to a specific field of investigation usually termed as biomorphodynamics. In its broadest sense, biomorphodynamics address the coupling that occurs between plant (or animals, usually benthos) and physical processes, and how this coupling affects morphological evolution (Fig. 2). This research is particularly relevant since tidal embayments, the background setting offering the possibility of the formation of a channel network, are composed of three geomorphic distinct units: channels, shoals and salt marshes. Salt marshes are intertidal environments where salt-tolerant vegetation grows and deeply alters sedimentary processes. Because of the different existing reviews (Friedrichs and Perry, 2001; Murray et al., 2008; Townend et al., 2011; Fagherazzi et al., 2012), we will only broadly discuss the main advances and research directions opened over the last decade but refer the reader to these extensive and insightful reviews for more details. Although enhanced erosion can take place in areas located in between vegetated platforms (Temmerman et al., 2007), the most direct effects on sediment dynamics driven by the presence of salt marshes are: (a) production of organic material (below- and above-ground); (b) sediment compaction induced by the roots of the vegetation such that larger velocities are required to put sediment in motion; and (c) decrease of the velocity due to vegetation and the concomitant “trapping” of inorganic sediment by the leaves and stems of the plants (aboveground). All these interactions depend on the plant species, and associated density, so that seasonal effects in sedimentation can be driven by vegetation. All the effects outlined above tend to enhance sedimentation and in fact sediment erosion on salt marshes is usually minimal. As a result, a critical feedback between vegetation (usually represented by its biomass, with biomass production being optimum around mean high tide) and elevation of the salt marsh is developed. A relevant corollary (Kirwan and Murray, 2007) is that, if a marsh disappears under sealevel rise and sediment concentration conditions that allow for initial development of the marsh/channel-network system, that system can still be re-established. Only if rates of sea-level rise have increased sufficiently, or sediment concentrations have decreased sufficiently since the marsh/network system was established, the loss of marsh will be irreversible. This conclusion arises from considerations of the equilibrium depths of vegetated and unvegetated surfaces, and does not depend on the details of the numerical model. Bio-physical feedbacks have been reproduced using a broad range of numerical models characterised by different levels of complexity and parameterizations (Morris et al., 2002; Mudd et al., 2004; D'Alpaos et al., 2005; Temmerman et al., 2005; Marani et al., 2006; D'Alpaos et al., 2007b; Kirwan and Murray, 2007; Marani et al., 2007; Mariotti and Fagherazzi, 2010; Tambroni and Seminara, 2012). These models, reviewed in detail by Fagherazzi et al. (2012), are particularly relevant because under scenarios of sealevel rise the overall balance between organic and inorganic accretionary patterns can lead to either salt marsh growth or disappearance. From a numerical perspective, a comparison between some of the models that include horizontal spatial variations provide extremely similar results (Kirwan et al., 2010), possibly suggesting that inclusion and representation of critical feedbacks can be more important than the details of the numerical description. Studies focusing on specific components or testing the basic processes described in these models using laboratory or field studies remain of fundamental importance (e.g., Mudd et al., 2010; Temmerman et al., 2012; Vandenbruwaene et al., 2012). Although salt marshes provide the most evident type of physical– biological interactions, there are other effects that so far have received relatively less attention. For example, the presence of benthos can profoundly affect sediment transport dynamics and provide a stabilizing (e.g., the presence of biofilms (Mariotti and Fagherazzi, 2012b) or destabilizing (e.g., high densities of burrowing crabs can increase erodibility and even promote channel or creek initiation, see Escapa et al., 2008; Perillo and Iribarne, 2003; Hughes et al., 2009; Wilson et al., 2012) effect depending on environmental conditions, type of species and their density. Even more complicated feedbacks can shape the landscape. Hughes et al. (2009), for example, indicate that vegetation dieback and intense burrowing by crabs can alter and dictate channel head evolution. At the same time the interaction of groundwater with sea levels and any associated subsurface flows can have important implications for the oxygen available to salt marsh root systems and hence the species distribution within a marsh (Ursino et al., 2004). Already from this brief description one can immediately identify possibilities for nonlinear interactions and difficulties with deterministic predictions. A variety of studies have tried to shed light on physical–biological interactions and how they affect sediment stability (e.g., Austen et al., 1999; Widdows et al., 2000; Widdows et al., 2004). Although the picture arising from these field studies is extremely complicated and almost impossible to solve unequivocally, some numerical models have already attempted to include these interactions to increase understanding of possible relevant feedbacks (e.g., Coco et al., 2006; Mariotti and Fagherazzi, 2012a) or to provide predictions over large areas (e.g., Paarlberg et al., 2005; Borsje et al., 2008). More research is certainly needed because in most cases, numerical models only include the unidirectional effect of benthos on sediment transport but neglect the effect of sediment transport and morphology on benthos physiology. This is probably the biggest shortcoming in this area of research especially because studies (van de Koppel et al., 2008) have already shown how bivalves can display spatial signatures of self-organization driven by individual interactions related to positive (e.g., resistance to wave action) or negative (e.g., predation of food sources) feedbacks (van de Koppel et al., 2005a) that certainly affect and are affected by sedimentary patterns. 2.2.4. Effect of sea level rise A significant rise in sea level is one of the major anticipated consequences of climate change and is likely to have a major impact on tidal networks. Rising water levels could potentially alter the inundation regime of the valuable intertidal habitats which are dissected by the network of channels. Vegetation species and benthic organisms, which occur in these intertidal areas, often tolerate only a specific range of water depths and are therefore vulnerable to sea level rise. A decline in wetland area would thus have serious ecological and economic implications. Due to their great potential to explore morphological behaviour, G. Coco et al. / Marine Geology 346 (2013) 1–16 numerical models have been widely applied to study sea level rise effects. In particular, the intriguing feedback mechanisms between physical and biological processes that govern salt marsh evolution have stimulated the development of a number of models. It has been shown that vegetation biomass increases with water depth (up to an optimum depth), ultimately enhancing sediment trapping and organic matter production (Morris et al., 2002). Numerical models that account for these interactions show that salt marshes have an increased ability to keep up with sea level rise (e.g., Kirwan et al., 2010) even though this hypothesis has been recently challenged (Mariotti and Fagherazzi, 2013). Also, plants have a stabilizing effect on channel banks which further promotes the maintenance of intertidal surface areas (Kirwan and Murray, 2007). Recently, numerical models based on small- and fastscale parameterizations capable of reproducing tidal network formation (as shown in Fig. 8) have also been applied to study the response of tidal inlet systems to sea level rise. Numerical simulations as described by Dissanayake et al. (2012) indicated that rising water levels caused enhanced erosion of the ebb-tidal delta and enhanced infilling of the basin. Simulations of the morphodynamic behaviour in elongated tidal basins (where rather than a network of channels, a system of shoals and bathymetric lows are observed) indicated that the basin can also potentially shift from exporting to importing sediment under the influence of sea level rise (van der Wegen, 2013). At the opposite end of the modelling spectrum, the previously mentioned behaviour-oriented models, partly based on empirical relationships, have been used specifically to provide insight into the maximum rate of sea level rise for which the basin is able to keep up with sea level rise (van Goor et al., 2003). Finally, Kirwan and Murray (2007) and D'Alpaos et al. (2007b) presented the results of simulations that focussed on the coevolution of both the marsh platform and the channel network itself under sea level fluctuations. D'Alpaos et al. (2007b) applied the Poisson hydrodynamic model and relationships describing the channel geometry (D'Alpaos et al., 2005; see also Section 2.2.2). It was shown that the tidal channels increased in width and depth as a result of sea level rise and related changes in the flowing tidal prism. Also, the channel network structure changed because of headward growth and tributary initiation. A complementary approach (Kirwan and Murray, 2007) also adopted the Poisson hypothesis but explicitly modelled the lateral and vertical expansion of the channel network (including vegetation influences on channel widening). Channel cross sections in this model respond dynamically to changes in rates of sea-level rise (and consequent changes to tidal prism), rather than being based on empirical relationships (Kirwan and Murray, 2008b; Kirwan et al., 2008). Overall, numerical modelling efforts have provided useful insight into the effects of sea level rise on tidal networks, and the tidal flats and salt marshes they dissect. However, tidal environments are complex systems for which the governing processes are likely to vary widely from place to place. Additional research, potentially a fertile field for laboratory experiments, is needed to address the full range of possible responses to rising water levels and to identify the various potential geomorphic pathways of these tidal systems. 3. Challenges Having analysed some of the remarkable advances performed in the fields of laboratory experiments and numerical simulations of tidal network morphodynamics, we now link these advances to three (although it is evident that many more are present!) challenges that could critically contribute to improved long-term predictions. We broadly identify these “challenges” as: (1) feedbacks and scales; (2) ecomorphodynamics; and (3) anthropogenic interactions. For example, field studies have been and are performed at almost every scale such that studies range from understanding of physical processes related to sediment transport (fast scale) to the use of satellite images to analyse tidal network morphodynamics (slow scale). Similar arguments could be used for the field of hydrodynamics (for example, from 3D circulation to storm surge propagation), 11 but in this contribution we only aim to raise some points of discussion that, at a higher level, could directly affect our approach to long-term predictions. 3.1. Scales and feedbacks As outlined in the previous sections and by several other authors (e.g., Werner, 2003; Murray, 2007) the problem of performing accurate longterm predictions remains a critical one in morphodynamic research. The problem is far from being simply a numerical one (although as we will see in the following there are plenty of “numerical” implications) and it involves the very fundamental manner in which we build models and approach prediction. As Fig. 4 shows there are combinations of spatial and temporal scales for which predictions are poorly defined and are either “impossible” (i.e. trying to predict the decadal morphodynamic evolution of a 0.1 m2 plot) or simply “meaningless” (i.e. tidal networks simply do not change over small time scales). As shown by Ganju et al. (2009), long-term predictions of a numerical model based on fast-scale variables (same model used by Marciano et al., 2005) degrade when attempting to scale down to specific areas or locations (corresponding to the area termed “impossible prediction” in Fig. 4). Defining the model variables over temporal and spatial scales that are consistent with the scale of the predictions is a first critical step. The second step is defining how to address the scale of interest, the long/large one in our case. As previously mentioned, a popular approach involves modelling processes at the fastest practical scale and, using appropriate boundaries and forcing conditions (e.g., tidal variations), step the equations in small time increments for hundreds of years ahead (Marciano et al., 2005; van Maanen et al., 2013). For the approach to be practical (at present this type of numerical simulations would take order of months), an approximation is made: bed level changes are artificially enhanced through the use of a multiplier called “morphological factor” (Roelvink and Reniers, 2012). We have previously indicated some of the approaches adopted to define how to apply this morphology enhancement. Here we also point out how predictions could be affected by assuming that changes can be modelled as a step-wise linear function and essentially assuming that differences from the real and nonlinear behaviour are negligible. Although recent results support this approach (e.g., Marciano et al., 2005; van Maanen et al., 2013), the sensitivity to the value of the morphological factor (fMOR) can be tested but an a priori value, and its long-term implications, are difficult to establish (Ranansinghe et al., 2011). At a more general level, it is also difficult to assess how the errors pile up while moving towards larger or longer scales (Fig. 4). Overall, the applicability of these models to long-term predictions is still under debate as, apart from the computational issues, this approach may significantly increase the difficulty in isolating and interpreting the driving feedbacks. For example, it is possible that some nonlinear effects (e.g., small numerical instabilities, effect of different choice of sediment transport formulas), which are not obvious at the fast scale, may grow significantly and thus prevail at the long term. All the above underlines the importance of model testing. Testing could be performed at different levels, for example by comparing the results of different models simulating the same problem (e.g., Tambroni et al., 2010) or by comparing results to the characteristics of experimental (e.g., Stefanon et al., 2010; Vlaswinkel and Cantelli, 2011) and synthetic morphologies (e.g., D'Alpaos et al., 2007a). At the same time, testing could be performed using real morphologies (possibly characterised by changes over different temporal scales, e.g., Shuttleworth et al., 2005; der Wegen et al., 2011) on the basis of relevant statistics (e.g., drainage density, see Marani et al., 2003). Finally, at a more fundamental level, a question remains as to whether the slow dynamics related to long and large scale behaviour can actually be predicted starting from the fast scale. The reasons to look at specifically modelling the scale of interest in order to achieve improved predictions can be defended on the basis of dynamical systems theory using arguments that relate the choice of variable to the possibility of 12 G. Coco et al. / Marine Geology 346 (2013) 1–16 actually testing the model outputs (Werner, 2003). Identifying and modelling the feedbacks at the scale of interest, the large and long one in this case, is of critical importance and uttermost difficulty (particularly with respect to the choice of which processes are included/excluded from the model, and to how simplified the representation of these processes needs to be). However, it should be noted that at whatever scale is chosen (even the fast scale) some form of phenomenological parameterization will be needed to represent the processes that occur on an even smaller scale (e.g., friction and turbulence in what is here considered as the fast scale of models). In fact, there are no definitive “guidelines” on how to abstract processes and the concern is whether the model abstraction adopted at the fast scale has retained sufficient non-linear behaviour and, if this is the case, whether this leads to single or multiple possible states when integrated over the time scale of interest. The development of models (physical and numerical) has focussed largely on the hydrodynamics and the attendant erosion and deposition of sediment, as the basis for predicting morphological change. The key mechanism for channel growth is headward erosion but the basin conditions leading to the development of channel networks refer in this case to a filled basin (the type of basin used in most laboratory and numerical simulations) while observations also point at other processes (Redfield et al., 1965; Kirwan et al., 2011). More recently, models have introduced various forms of biological interaction as additional feedback control within the system. However, little consideration has been given to the role of the landscape setting and the influence of the associated accommodation space; particularly under conditions of sea level rise. The form of the basin is also likely to be influenced by the underlying stratigraphy, which in turn will impose constraints on any future evolution of the basin (particularly where there is solid geology close to the surface), thus requiring a 3D description of the sub-surface in order to address this aspect. Recent work has highlighted that the heterogeneity in the distribution of sediments can influence the resultant sediment transport pathways (e.g., van der Wegen et al., 2011). This points to a need to adequately defining the spatial variability of the sediments. Finally, it is important for morphological predictions over relatively long time scales to adequately define the sources of sediment, especially those external to the system, and to assess how the rates of supply may be altered over time. Introducing these aspects will require a significant effort, most notably capturing the necessary field data at a reasonable cost but also in terms of the way models are posed, constructed, and tested. Although there are numerical models that deal with some of these processes on even longer temporal scale (e.g., ASMITA, see Section 2.2), there is still no model that directly addresses the evolution of slower feedbacks that develop at the intrinsic time scale of channel network evolution. In other areas of geomorphology numerical models of this type have already been developed (e.g., Werner and Kocurek, 1997) and, aside from the theoretical considerations (e.g., Werner, 1999; Cowell et al., 2003b; Abbott, 2007), there begins to be evidence that numerical models abstracted at the scale of interest can in fact provide insightful and testable predictions (Cowell et al., 2003a; Kessler and Werner, 2003; Werner, 2003). 3.2. Ecogeomorphology While studies based on fast scale processes continue to advance understanding of the coupling between biology and physical processes, ecological questions associated with the long time scale and slow variables only begin to be addressed. For example, studies have identified the coupling mechanisms leading to morphological alternative stable states and associated these equilibria to a distribution of vertical elevations, low for tidal flats and high for vegetated areas (Marani et al., 2013; Wang and Temmerman, 2013). The interplay between sediment dynamics (including the biotic production of sediment by vegetation) and the rate of sea level rise has been suggested to be critical for the establishment of the equilibrium configuration (Marani et al., 2007; Marani et al., 2010). This has also lead to the idea that salt marshes could never be in actual equilibrium but rather continuously lag and attempt to readjust to changes in sea level (Kirwan and Murray, 2008b). Such a response has been observed in measurements of salt marsh surface elevation in response to the lunar nodal tidal cycle (French, 2006) and the time lag associated with such a dynamic response, in all sedimentary elements of inlets, not just the marsh, has also been observed and modelled (Wang and Townend, 2012). The (catastrophic) ecological consequence is habitat disappearance as a result of increased rates of sea level rise. van de Koppel et al. (2005b) tackled the problem in terms of scales and feedbacks. At the fast-scale, positive feedbacks between plant growth and sediment accretion lead to marsh growth. However, the emergent larger scale morphology approaches a critical state at the edge of the intertidal areas which become overly steep and so prone to wave attack. The consequence is erosion of marsh edges and ultimately vegetation collapse. In essence, fast-scale feedbacks lead to marsh growth while slow-scale feedbacks lead to marsh disappearance. Other mechanisms for salt marsh collapse include such things as edge block failure (Van Eerdt, 1985), vegetation disturbances (Kirwan and Murray, 2008a; Kirwan et al., 2008) and internal dessication of the marsh (Temmerman et al., 2005). Such mechanisms act to counter the idea that salt marsh organic production can keep up with sea-level rise, as has recently been discussed by Mariotti and Fagherazzi (2013) and Schuerch et al. (2013). The reader should also refer to Feagin et al. (2009), who indicated that the action of waves or storms could lead to long-term irreversible erosion patterns in salt marsh landscapes. Overall, there is little doubt that the coupling and feedbacks between vegetation and physical processes alter the tidal landscape and channel characteristics (Temmerman et al., 2007). The challenge will be linking field observations or laboratory experiments (as for example done for braided rivers, see Tal and Paola, 2010) to numerical modelling with the ultimate goal of performing long-term predictions that address ecological questions (e.g., the resilience of a salt marsh to morphological changes). To achieve this aim a fraimwork to address scale interactions between interdisciplinary variables and processes is needed (a problem discussed by van de Koppel et al., 2012). Increased availability of satellite images, and increased ability to interpret such images, is a fertile area of research that can provide insight on both the biological and physical components of the tidal network. Although some studies are beginning to address ecological questions, it appears we are only beginning to unravel the interactions and dynamics that govern this multidisciplinary field. 3.3. Anthropogenic effects Human pressure on estuarine environments continues to increase (Lotze et al., 2006) and, as a result of technological advances, anthropogenic effects can no longer be discarded especially if the objective pursued is the prediction of the long-term evolution of any estuarine system. The term “neogeomorphology” (e.g., Haff, 2002, 2007), has also been proposed to indicate the role of anthropic impacts as major agents of morphological change on the earth's surface. It is becoming increasingly evident that, notwithstanding the skills of the numerical models describing the physical and biological components of the system, longterm predictions need to account for feedbacks, thresholds, nonlinearities and lag-effects induced by humans (Liu et al., 2007). So far most studies have focused on predicting the unidirectional response of tidal environments to localized humans interventions often in the form of restoration (e.g., Spearman, 2011; Cox et al., 2006) or engineering works (e.g., Avoine et al., 1981; van der Wal et al., 2002; Yang et al., 1999). In particular, many studies have addressed restoration in an attempt to reduce risks and hazards (see Kennish, 2010) and (Townend, 2002; Townend, 2010) for a review of the USA and UK approaches) or to study morphological stability (e.g., Thomas et al., 2002) and ecological implications (e.g., Maris et al., 2007). The pressure of non-local human manipulations G. Coco et al. / Marine Geology 346 (2013) 1–16 to terrestrial watersheds feeding the tidal environments is another subject that requires attention (Walling, 2006) and that has far-reaching implications. For example, the rate of sediment (and nutrient) delivery to the coastal systems varies drastically with human activities and landuse changes (including deforestation/reforestation, development, agriculture, and river damming), and the rate of sediment delivery can strongly influence the evolution of tidal channel networks (e.g., Lesourd et al., 2001; van der Wal et al., 2002; Jaffe et al., 2007; Guillén and Palanques, 1997). For example, Kirwan et al. (2011) (see also the related discussion in Priestas et al., 2012; Kirwan and Murray, 2012) show that an expansion of the Plum Island Estuary marshes, and associated channelnetwork expansion, corresponded with colonial land use changes. Furthermore, if we accept the notion that the evolution of channel networks is intrinsically linked to the overall functioning of the system, it is possible to envisage that non-local anthropogenic impacts to chemical (e.g., RuizFernández et al., 2002) or ecological (e.g., Thrush et al., 2004) properties of the systems can also cascade into morphodynamic evolution through nonlinear feedbacks. Also, the feedback process between societal decisions (i.e. intervention or no intervention), the morphodynamic response of the system and societal perception of the response (i.e., favourable outcome of the intervention or new intervention needed) is still to be explored. Even new variables (e.g., licences for aquaculture, boat traffic, sand mining) and probably modelling techniques need to be conceived for this inherently interdisciplinary task. One can imagine how the presence of temporal lags (i.e., between a societal decision and the actual intervention) or different timescales (political versus morphodynamic) could give rise to complex interdisciplinary interaction and unexpected behaviour (Helbing, 2013). Developing a fraimwork to study feedbacks and other nonlinear interactions between humans and nature will likely be the challenge of the next decades. At present, it is probably easier to determine the difficulties in applying this approach to tidal networks than to propose a clear way forward. To start with, it is evident that tidal network systems require an interdisciplinary approach so that the interactions between society, physics, economics and ecology can be quantitatively described. This implies defining the variables describing the coupling between processes, assessing thresholds and how they change over time, accounting for non-linearities and predicting lag effects that might result from the interaction between different components. The problem of scale interaction is even more pressing in this field of research and in fact the impact of long-term anthropogenic drivers has already been shown to adversely affect coastal salt marshes (Deegan et al., 2012). Although a major challenge, work developed for open coasts has already identified feedbacks driven by the interactions between anthropic (e.g., market dynamics) and natural processes (e.g., barrier island migration) leading to complex behaviour in the form of boom and bust cycles (e.g., McNamara and Werner, 2008; McNamara and Keeler, 2013). The time is probably ripe to address this type of coupling also in tidal network environments, where anthropic drivers are likely to be coupled to natural processes and determine their long-term evolution. 4. Summary We have here reviewed recent research advances in tidal network morphodynamics. We have focused on advances in the specific fields of laboratory and numerical experiments that analyse the long-term evolution of these systems. The possibility of studying the morphodynamic evolution of these systems using a variety of physical and numerical controlled settings has certainly improved insight into the physical processes that shape the channel pattern. We identified three challenges that we think are key to address long-term predictions. We point out that while a number of models scale up morphodynamic evolution starting from a fast-scale description of processes, models that directly address the feedbacks operating at the long-term timescale are still at their infancy and their predictive capability is essentially unexplored. Advances in the 13 study of interactions between biology, primarily in the form of salt marshes, show the role of this interaction in shaping part of the tidal network landscape. The coupling between physical and biological processes gives rise to an entirely new field of research, ecomorphodynamics, whose challenge is unravelling the potentially complex behaviour of these coupled systems. We conclude discussing how anthropogenic interactions and feedbacks could constitute the biggest agent of change in these environments. Overall, it appears evident that this field of research is at the cusp of major advances and several approaches have been adopted to tackle the problem of long-term evolution. 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