Figure 8: Evolution of tidal asymmetry (\(\gamma\)). Spatially-explicit representation of\(\gamma\) in 1887 (A), 1901 (B), 1932 (C), 1970 (D), 2003 (E), 2014 (F), 2014-E25 (G), 2014-E50 (H), 2014-E75 (I), 2014-E100 (J). (K) Cumulative frequency (CDF) of \(\gamma\) for the historical configurations (1887-2014). (L) Cumulative frequency of \(\gamma\) in the hypothetical marsh erosion scenarios (2014-E25, E50, E75, E100)
5 Discussion
Our analyses highligth the difficult task of unravelling the consequences of salt-marsh loss based exclusively on numerical results obtained for the historical configurations of the Venice Lagoon, because one can hardly isolate the direct effects of marsh disappearance on the lagoon hydrodynamics from the indirect, cascade effects due to morphodynamic feedbacks triggered by marsh loss that are all globally included in each updated configuration of the lagoon. Therefore, numerical results must be interpreted based also on the conceptualized scenarios that assume additional marsh losses without any further modifying the lagoon morphology. Again, however, caution must be given when interpretating numerical results, because the simulated scenarios could be representative of non-morphodynamic equilibrium conditions.

Water Levels

How marsh disappearance affects water levels within the lagoon by modifying tide propagation is perhaps the most controversial point to debate. This is because salt marshes are most effective in regulating tide propagation at high water stages (i.e., in the upper intertidal frame) due to their characteristic topographic elevations. Conversely, at lower stages, marshes are not typically flooded and thus have limited effects on tide propagation, which indeed takes place predominantly within major tidal channels and across tidal flats.
Our simulations of hypothetical marsh-loss scenarios (E25 to E100 runs,Figure 4 L) suggest that marsh loss overall increases accommodation in the back-barrier system, thus reducing the average amplitude of tidal oscillations and, therefore, the mean tidal range (\(\overset{\overline{}}{\Delta h}\)). This observation agrees with the results of the numerical experiments carried out in other back-barrier tidal systems along the continental US coast (e.g., Donatelli et al. 2018), which demonstrated, using an approach similar to that we adopted here, that tidal amplitudes are reduced when salt marshes disappear. However, our analyses also highlight a continued increase in\(\overset{\overline{}}{\Delta h}\) (Figure 4K) observed during the last century. This is most likely a result of both the anthropogenic modifications imposed on the lagoon inlets and the reduced bottom friction due to tidal flat deepening (e.g., D’Alpaos and Martini 2005; Tambroni and Seminara 2006; Carniello et al. 2009; Ferrarin et al. 2015) (Figure 2A-F). Therefore, increasing \(\overset{\overline{}}{\Delta h}\)is only partially related, both directly and indirectly, to the observed salt-marsh loss. This is supported by enhancements of\(\overset{\overline{}}{\Delta h}\) occurred in both the northern and southern lagoon immediately after the construction of jetties at the Lido (1901, Figure 4B) and Chioggia inlet (1932, Figure 4C), respectively, together with generalized increases in\(\overset{\overline{}}{\Delta h}\) between 1932 and 1970 (Figure 4D) when pronounced deepening of tidal flats took place. Excavation of the Vittorio Emanuele and Malamocco-Marghera waterways also likely contributed to promoting the observed increase in\(\overset{\overline{}}{\Delta h},\) especially in the central part of the lagoon delimited by the Malamocco inlet to the South, the city of Venice to the North, and the industrial area of Porto Marghera to the West (Figure 4C,D). Finally, slight reductions in\(\overset{\overline{}}{\Delta h}\) between 2003 and 2014 are to be related to increased hydraulic resistance at the inlets produced by the modifications associated with the Mo.S.E. works (Figure 4K) (Matticchio et al., 2017), and are therefore not directly linked to changes in salt-marsh extent.
Similarly to \(\overset{\overline{}}{\Delta h}\), the continued increase in mean high water levels (MHWL) observed since 1887 should be only partially considered as a direct effect of shrinking marsh coverage (Figure 5 A-F). In this case, however, exploratory simulations suggest that progressive, additional loss of salt marshes would result in further MHWL increases (Figure 5 G-J). This effect is most probably related to the progressive fading of energy dissipations produced by the presence of marshes at high-water stages. Reduced energy dissipations for high-water levels magnify tidal peaks, thus enhancing MHWL. Larger MHWLpotentially bears negative consequences in terms of increased flooding risk of urban settlements (Fletcher & Spencer, 2005; Gambolati & Teatini, 2014; Rinaldo et al., 2008). One should however appreciate that marsh loss leads to differential MHWL increases across the lagoon (Figure 5 G-J), the latter being more pronounced in the innermost portions of both the northern and central-southern lagoon where marshes are still widespread nowadays. Conversely, limited changes in MHWL are observed in the proximity of the inlets as well as around the major urban settlements found within the lagoon, namely Venice city, Chioggia, and the islands of Murano, Burano, and Sant’Erasmo. For these locations, a detailed analysis of the hypothetical scenarios of additional marsh loss highlights that changes in MHWL are lower than 3% even if marshes would entirely disappear (E100 scenario), whereas even lower variations (<2%) are found when considering the maximum, rather than the mean, high-water level (\(\zeta_{\text{MAX}}\)) observed during the investigated period. Hence, the effects of salt-marsh loss on the hydrodynamics of the tidal systems which host them appears to be strongly site-specific, with significant hydrodynamic changes being observed over distances of a few kilometers even within a given tidal embayment.

Wind waves and bottom shear stresses

Differently from tidal levels, a much more straightforward interpretation can be given regarding the direct effects of marsh erosion on wind-wave fields (i.e., significant wave height\(H_{s_{\text{MAX}}}\), Figure 6 ) and on the associated bottom shear stresses (\(\tau_{\text{wc}}\), Figure 7 ) within the lagoon. Before 1932 the generation and propagation of large wind waves were hampered by the still-extensive presence of salt marshes (Figure 2A-C) that limited wind fetches, as well as by the reduced depths of tidal flats which promoted important wave-energy dissipation (Figure 6A-C). From 1970 onwards, in contrast, reduced salt-marsh coverage, coupled with pronounced tidal-flat deepening, led to the observed increase in \(H_{s_{\text{MAX}}\ }\), especially in the central and southern portions of the lagoon (Figure 6D-F) (Fagherazzi et al. 2006; Defina et al. 2007). Therefore, progressively reduced marsh extent - caused also by tidal flat deepening and expansion - favors larger\(H_{s_{\text{MAX}}}\) due to longer fetches, as confirmed also by numerical simulations involving additional marsh loss (Figure 6 G-J). The latter also suggests that the most significant increases in wave heights are to be expected in areas that are nowadays occupied by extensive salt marshes (i.e., the northern lagoon as well as the innermost portions of the central-southern lagoon, see Figure 2F), where the possible disappearance of salt marshes could reduce their wind-sheltering effect and increase the fetch length, eventually leading to the generation and propagation of larger waves (Figure 6G-J).
Larger \({H_{S}}_{\text{MAX}}\) also have negative implications from a flood-risk standpoint, as higher waves could locally increase the risk of flooding due to overtopping, especially in the more topographically depressed urban areas (Gambolati & Teatini, 2014; Mel, Carniello, et al., 2021; Mel, Viero, et al., 2021; Ruol et al., 2020). Moreover, larger waves threaten the conservation of the remaining salt-marsh ecosystems, due to the positive feedback mechanism between marsh lateral erosion and wind-wave power (Carniello et al., 2016; A. D’Alpaos et al., 2013; Finotello et al., 2020; Leonardi, Defne, et al., 2016; Marani et al., 2011; Tommasini et al., 2019). Specifically, the salt-marsh lateral retreat rate is linearly correlated to wave power (\(P_{w}\)) (Finotello et al., 2020; Leonardi, Ganju, et al., 2016; Marani et al., 2011; Tommasini et al., 2019), which in turn is a quadratic function of wave height. Hence, salt-marsh loss leads to higher, more energetic waves which in turn enhance marsh lateral retreat even further in a superlinear fashion.
Additionally, higher waves also produce larger bottom shear stresses, especially across the extensive tidal-flat areas that characterize the lagoon morphology (Figure 7 ). Indeed, our simulations demonstrate that additional losses of salt marshes would further enhance\(\tau_{\text{wc}}\) proportionally to the marsh area being lost (Figure 7G-J, L) because the wind sheltering effect typically offered by marshes would progressively be reduced, allowing for increasingly higher waves to winnow the lagoon bottom (Carniello et al., 2014, 2016; A. D’Alpaos et al., 2013; Tommasini et al., 2019). From a morphodynamic standpoint, the implications of increasing \(\tau_{\text{wc}}\) can be manifold. Unquestionably, larger \(\tau_{\text{wc}}\) will enhance the entrainment of fine sediment from the lagoon shallows, in this way leading to higher concentrations of suspended sediment (SSC) (Tognin et al., 2022). Notably, wave-driven resuspension from tidal flats represents a key source of sediment for salt marshes in sediment-starving shallow tidal embayments, where the majority of mineral sediments are delivered to the marsh surface during storm surge events concomitant with strong wave activity (Tognin et al., 2021). Thus, enhanced SSC could ensure higher resilience of salt-marsh ecosystems in the face of rising relative sea levels (Elsey-Quirk et al., 2019; Mariotti & Fagherazzi, 2010; Tognin et al., 2021). However, such a beneficial effect is likely to be offset by the above-recalled marsh loss via lateral retreat, which would reduce the total marsh area and promote fragmentation, in this way hampering the marsh’s ability to capture suspended sediment and cope with sea-level rise (Donatelli, Zhang, et al., 2020; Duran Vinent et al., 2021). Besides, enhanced SSC, coupled with the generally ebb-dominated character of tides (Figure 8 and see Section 5.3), are likely to negatively affect the lagoon net-sediment budget, leading to further tidal flat deepening and salt marsh losses.

Tidal asymmetries

Loss of salt-marsh areas appears to feedback into tidal asymmetry (\(\gamma\)) mostly in an indirect fashion, with manmade modifications on the lagoon inlet morphologies playing, in contrast, a critical role in driving tidal asymmetry changes (L. D’Alpaos, 2010; L. D’Alpaos & Martini, 2005; Matticchio et al., 2017; Tambroni & Seminara, 2006). Indeed, pronounced \(\gamma\) changes are observed after the completion of the jetties at the Lido (Figure 8B) and Chioggia inlets (Figure 8C), both of which resulted in more marked ebb dominance in the inlet surroundings. Indirect effects of salt-marsh loss on \(\gamma\) could instead arise from the positive morphodynamic feedback between marsh loss and tidal-flat deepening (Carniello et al., 2007, 2009; Defina et al., 2007), which is likely responsible for the shift from flood- to ebb-dominance observed in many portions of the lagoon between 1932 and 1970, especially in the area facing the Malamocco inlet where the Malamocco-Marghera shipway was also excavated (Ferrarin et al., 2015) (Figure 8D-E). Nonetheless, numerical simulations demonstrate that the direct effects of additional marsh losses on tidal asymmetry are potentially not negligible, with progressive marsh erosion leading to more widespread flood-dominated areas in the innermost portions of the lagoon (Figure 8G-J). This result is consistent with evidence from previous studies showing that the decrease in intertidal storage capacity associated with gradual marsh losses will re-establish flood dominance typically observed for progressive tidal waves (Dronkers, 1986; Rinaldo et al., 1999). While enhanced flood dominance associated with marsh disappearance could potentially limit sediment export to the open sea and promote marsh accretion, one should appreciate that the tidal regime in most of the lagoon is likely to remain dominated by ebb tides, especially in the surroundings of the inlets where ebb-dominance would be even further exacerbated compared to present-day conditions (Figure 8G-J). This could hardly lead to an inversion of the ongoing net sediment loss driven by ebb-dominated tides, as sediment entrained by higher, more energetic waves will likely keep on being carried in suspension by ebb-dominated tidal currents and transported outside the lagoon for the most part. Given the non-linear dependence of sediment transport processes on both tidal flow velocities and asymmetry, however, these hypotheses should be verified by ad hoc coupled hydrodynamic and sediment-transport numerical simulations to investigate how sediments will be redistributed within the basin following changes in the dominant tidal regime.

Implications for the hydrodynamics of back-barrier tidal lagoons

Our analyses highlight both direct and indirect effects of salt-marsh deterioration on the hydrodynamics of the Venice Lagoon. Despite being generally consistent with previous studies carried out in different tidal settings (e.g., Donatelli et al. 2018, 2020b, a), care should be given to generalizing the results reported here to back-barrier tidal embayments morphologically and hydrodynamically different from the study case at hand. This is a general remark which holds for previous studies and should be taken into consideration for future ones.The reasons behind this caution are manyfold, though all broadly related to the morphological and hydrodynamic peculiarities that characterize each tidal environment, as well as to the conceptualization we adopted in our numerical simulations.
First, the hydrodynamic response of a tidal system to marsh erosion depends on i) the planform geometry and hypsometry of the basin (Deb et al., 2021; Van Maanen et al., 2013); ii) the characteristics of the tidal waves, especially in terms of tidal range and progressive vs. standing character of the system (Van Maanen et al., 2013; Ward et al., 2018; Zhou et al., 2018); and iii) the wave climate, affecting both the basin hydrodynamics and its sediment transport regime (Carniello et al., 2011; A. D’Alpaos et al., 2013). Particularly important is the spatial distribution of salt marshes within the back-barrier basin. As demonstrated by Donatelli et al. (2020b), different hydrodynamic changes due to marsh loss are to be expected in back-barrier systems where most marshes fringe the mainland compared to systems characterized by the presence of extensive marsh areas detached from the mainland.
Second, in our exploratory numerical simulations, we did not account for hydrodynamic changes due to rising sea levels, and assumed that marshes are ineluctably destined to disappear. In other words, we implicitly assumed that sea-level rise will outpace vertical marsh accretion, or that, more realistically, wave-driven lateral erosion will lead to marsh disappearance. This is strictly true only if the combined rate of eustatic sea-level rise and soil subsidence is higher than the rate of marsh vertical accretion, and if no significant mineral sediment supply is available from either longshore currents or fluvial sources, which could potentially allow marshes to prevent drowning and expand laterally even in the face of rising relative sea level (Ladd et al., 2019; Roner et al., 2021). Besides, salt marshes might be less vulnerable than we hypothesized even in the absence of a significant inorganic sediment supply (Kirwan et al., 2016). Indeed, even in systems characterized by negative sediment budgets, there might potentially be a transitory regime in which sediments are supplied to marshes from the adjoining, eroding tidal flats, in this way mitigating marsh drowning (Donatelli, Kalra, et al., 2020; Kalra et al., 2021; Tognin et al., 2021).
Third, our simulated scenarios do not account for the fact that salt marshes can potentially survive sea-level rise by migrating landward (e.g., Feagin et al. 2010; Field et al. 2016; Enwright et al. 2016; Fagherazzi et al. 2019; Kirwan and Gedan 2019). While this process is hindered in the Venice Lagoon, as well as in most salt marsh ecosystems worldwide, by the presence of fixed seawalls, levees, and dikes at the interface between marshes and the upland, it cannot be disregardeda priori . Clearly, the colonization of new intertidal areas by marsh upland migration would profoundly change the hydrodynamics and sediment budget of the whole back-barrier system, since new areas would be periodically flooded by tides and additional sediment volumes would become available as marshes expand landward.
Finally, the timescale required for the system to morphodynamically adapt to changes in marsh coverage is generally difficult to quantify. This is because sediment volumes liberated by marsh lateral erosion can be redistributed within the basin by tidal currents and wind waves, thus affecting both the lagoon sediment budget and related morphological changes, besides potentially contributing to marsh vertical accretion (Donatelli, Kalra, et al., 2020; Elsey-Quirk et al., 2019; Kalra et al., 2021). In our simulations, in contrast, sediments eroded from marshes are instantaneously removed, and can no longer contribute to the lagoon morphological evolution. Moreover, although numerical simulations considering hypothetical scenarios may be useful to isolate the sole effects of salt-marsh loss on the hydrodynamics of back-barrier systems, it should be noted that salt-marsh loss seldom occurs without inducing modifications to other back-barrier landforms. This is clearly highlighted by historical field data from the Venice Lagoon, which suggest mutual feedback between marsh erosion and tidal-flat deepening. Therefore, generalizations of results obtained from hypothetical erosive scenarios should be treated with caution, since the modeled hydrodynamic changes could be mitigated or magnified by other morphodynamic adjustments induced by marsh disappearance on the tidal back-barrier system as a whole.
In view of the above, the effects of salt-marsh loss on the hydrodynamic and morphodynamics of shallow back-barrier tidal systems are likely to be extremely site-specific, and therefore difficult to generalize. Moreover, biogeomorphological feedbacks, which are key drivers of marsh spatiotemporal evolution, are likely to vary geographically as a consequence of distinct ecological assemblages of metacommunities and different climatic forcings. This further complicates predicting the morphodynamic effects of salt-marsh loss, as well as the timescales over which they would manifest themselves (Bertness & Ewanchuk, 2002; Finotello, Alpaos, et al., 2022; Pennings & He, 2021; Wilson et al., 2022).
6 Conclusions
In this study, we focused on the microtidal Venice Lagoon (Italy) to disentangle the role played by the loss of tidal wetlands on the hydrodynamics of tidal back-barrier embayments. Numerical simulations were performed considering both past morphological configurations of the lagoon dating back up to 1887 and hypothetical scenarios involving additional marsh erosion relative to the present-day conditions. This allowed us to highlight both direct and indirect effects of salt-marsh loss on the evolution of the lagoon hydrodynamics. Direct effects include enhanced mean-high water levels due to reduced energy dissipation at high-water stages, as well as the formation of higher and more powerful wind waves due to longer wind fetches promoted by reduced marsh extent. Moreover, historical data and numerical results suggest that marsh disappearance is likely to trigger tidal flat deepening, thus indirectly feeding back into hydrodynamics, leading to increased tidal ranges due to reduced energy dissipation of the lagoon, and modifying tidal asymmetries across the entire back-barrier system. We also speculated on the potential impacts of the observed hydrodynamic changes on the lagoon ecomorphodynamic evolution, as well as on the associated risk of tidal flooding in urban settlements. Although further investigations will be needed to conclusively address these hypotheses, our analyses suggest that in the absence of sea-level rise, further losses of salt marshes are unlikely to critically affect urban flooding risk, whereas it may promote additional marsh lateral erosion through positive feedback between reduced marsh extent and higher wind-wave power.
The findings of this study provide novel insights into the hydrodynamic effects of salt-marsh loss in sediment-starving, shallow tidal embayments morphodynamically dominated by wind-driven sediment transport processes, with far-reaching implications for the conservation and restoration of coastal ecosystems that extend well beyond the study case at hand. However, we stress that care should be given to generalizing the results presented here to tidal embayments that are morphologically and morphodynamically different from the Venice Lagoon. In doing so, we support the idea that the response of back-barrier systems to changing external forcing is highly dependent on site-specific morphological and ecological features, as well as on the characteristic of the local tide, wave, climate, and fluvial processes. This clearly prevents one from drawing general conclusions regarding the future of coastal back-barrier systems worldwide based on the analyses of individual study cases.
Acknowledgments
[reviewers will be acknowledged]. This scientific activity was performed in the Research Programme Venezia2021, with the contribution of the Provveditorato for the Public Works of Veneto, Trentino Alto Adige and Friuli Venezia Giulia, provided through the concessionary of State Consorzio Venezia Nuova and coordinated by CORILA, Research Line 3.2 (PI Andrea D’Alpaos).