Figure 5: Evolution of mean-high water level (MHWL). Spatially-explicit representation of MHWL 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 MHWL for the historical configurations (1887-2014). (L) Cumulative frequency ofMHWL in the hypothetical marsh erosion scenarios (2014-E25, E50, E75, E100)
.More in detail, the cumulative frequency of water levels for the selected study period is the closest to the average distribution observed between 2000 and 2020 (Figure 3 C). Moreover, the study period is characterized by two relatively strong Bora wind events (Figure 3 A) that are typical of the wind climate observed in the Venice Lagoon (Figure 3 D). Thus, the selected study period allows us to focus both on characteristic tides as well as significant wind-wave events.
The hydrodynamic effects of morphological changes at the whole lagoon scale will be investigated by considering different parameters (e.g., local tidal range, mean high water level, wave height) related to both tides and wind waves. The parameters of interest are computed for each element of the computational grid, and will be presented both in a spatially-explicit fashion as well as in the form of cumulative frequency distributions (CDF) for all the analyzed morphological configurations of the lagoon, to provide a synthetic description of their changes through time and in the four scenarios characterized by different degrees of marsh-area loss assumed as possible future configurations of the lagoon.
4 Results

Water Levels

Concerning water levels within the lagoon, we first focused on the mean tidal range (\(\overset{\overline{}}{\Delta h}\), Figure 4 ), computed as the average of the local difference \(\Delta h\) between two consecutive high- and low-tide water levels. Overall, results show a continued increase of \(\overset{\overline{}}{\Delta h}\) from 1887 to 2003, though spatially-explicit representations suggest that such an increase is not spatially homogeneous. Increases in\(\overset{\overline{}}{\Delta h}\) between 1887 and 1901 are mostly limited to the northern lagoon (Figure 4 A,B), whereas between 1901 and 1932 enhanced \(\overset{\overline{}}{\Delta h}\) values are observed especially in the southern lagoon and in the surroundings of Venice City (Figure 4 B,C). The most pronounced and generalized increase in \(\overset{\overline{}}{\Delta h}\) is however observed between 1932 and 1970 (Figure 4 D), as a result of extensive loss of marshlands, the disappearance of many minor branches of tidal channel networks, and generalized tidal-flat deepening (seeFigure 2 D). In contrast, only minor changes are observed from 1970 onwards (Figure 4 D,E,F), with probability distributions suggesting only a slight increase in \(\overset{\overline{}}{\Delta h}\)between 1970 and 2003 followed by a reduction between 2003 and 2014 (Figure 4 K). Numerical simulations involving additional loss of salt-marsh areas suggest that slight \(\overset{\overline{}}{\Delta h}\)reductions may occur proportional to the percentage of marsh area being lost (Figure 4 L).
Following its definition, the mean tidal range (\(\overset{\overline{}}{\Delta h}\)) can only be used to quantify the mean absolute amplitude of tidal oscillations, whereas it does not embed any information regarding possible changes in high water levels due to modifications of tide propagation as a consequence of morphological changes at the basin scale. Therefore, aiming to better characterize changes in the tidal regime, we also investigated how modifications of the lagoon morphology affected the Mean High Water Level (MHWL). The MHWL is defined as the average of all the water levels maxima observed during the study period and thus it represents a meaningful proxy to estimate changes in flooding risk in urban areas within the lagoon. Overall, a generalized increase inMHWL occurred during the study period (Figure 5 A-F). A slight attenuation of MHWL is observed between 1901 and 1932 (Figure 5 K), which is nonetheless followed by a pronouncedMHWL increase between 1932 and 1970 (Figure 5 K), when more than half of the total marsh area was already lost (seeFigure 2 K) and the lagoon underwent significant morphological changes (see Figure 2 C,D). After 1970, only minor increases inMHWL are observed until 2014 (Figure 5 K). However, exploratory simulations suggest that progressive, additional loss of salt marshes could result in further MHWL increases relative to the values observed in 2014 (Figure 5 ).

Wind waves and bottom shear stresses

Besides tides, wind waves play a fundamental role in the hydrodynamics and morphodynamics of shallow tidal systems, in general (e.g., Green and Coco 2014), and of the Venice Lagoon, in particular (Carniello et al., 2011). To quantify changes in wind-wave fields through time, we focus here on the maximum significant wave height (\(H_{s_{\text{MAX}}}\),Figure 6 ). \(H_{s_{\text{MAX}}}\) invariably increases through time in all the considered historical configurations, but only minor changes occurred before 1932 (Figure 6 A,B,C,K). Conversely, between 1932 and 1970, pronounced increases in \(H_{s_{\text{MAX}}}\)are observed, especially in the central and southern portions of the lagoon, which are the areas most exposed to the action of Bora winds (Figure 6 D). Although after 1970 the distribution of\(H_{s_{\text{MAX}}}\) does not display substantial changes until 2014 (Figure 6E,F,K), numerical simulations considering additional loss of salt marshes suggest that \(H_{s_{\text{MAX}}}\) will increase further proportionally to the percentage of salt-marsh area being lost (Figure 6G-J and L). The most important increases in \(H_{s_{\text{MAX}}}\) are to be expected in areas that are nowadays occupied by extensive salt marshes (Figure 6 G-J), that is, in the whole northern lagoon as well as the most landward portions of the central-southern lagoon (seeFigure 2 F).
The key role exerted by wind waves on the lagoon morphodynamics is related to their ability to determine sediment resuspension from shallow tidal-flat areas, a process whose intensity depends nonlinearly on the wave characteristics. Specifically, wind waves produce large bottom shear stresses (\(\tau_{\text{ww}}\)), which compound the bottom shear stresses induced by tidal currents (\(\tau_{b}\)) and determine the total shear stresses (\(\tau_{\text{wc}}\)) that eventually lead to sediment resuspension when \(\tau_{\text{wc}}\) exceeds the critical threshold for erosion (Carniello et al. 2012; see section 3.1). Numerical results suggest that within channels, where \(\tau_{b}\) is typically dominant, only minor increases in \(\tau_{\text{wc}}\) maxima occurred over time (Figure 7 A-F). In contrast, across shallow tidal flat areas, where the wave-induced bottom shear stress component (\(\tau_{\text{ww}}\)) is predominant, the maximum values of\(\tau_{\text{wc}}\) invariably increases from 1887 to 2014 (Figure 7 A-F). This process, which is consistent with changes in maximum wave heights (\(H_{s_{\text{MAX}}}\)), eventually leads to a generalized increase of \(\tau_{\text{wc}}\) across the entire lagoon, especially between 1932 and 1970 (Figure 7 K). Numerical simulations with additional losses of salt marshes suggest that\(\tau_{\text{wc}}\) maxima will be further enhanced proportionally to the marsh area being lost (Figure 7 G-J, L), in agreement also with the modelled increase in maximum wave height (Figure 6 L).