Marco Toffolon

Analytical description of tidal dynamics in convergent estuaries

Analytical solutions of the one-dimensional hydrodynamic equations for tidal wave propagation are now available and, in this paper, presented in explicit equations. For given topography, friction, and tidal amplitude at the downstream boundary, the velocity amplitude, the wave celerity, the tidal damping, and the phase lag can be computed. The solution is based on the full nonlinearized St. Venant equations applied to an exponentially converging channel, which may have a bottom slope. Two families of solutions exist. The first family consists of mixed tidal waves, which have a phase lag between zero and ?/2, which occur in alluvial coastal plain estuaries with almost no bottom slope; the second family consists of “apparent standing” waves, which develop in short estuaries with a steep topography. Asymptotic solutions are presented for progressive waves, frictionless waves, waves in channels with constant cross section, and waves in ideal estuaries where there is no damping or amplification. The analytical method is accurate in the downstream, marine part of estuaries and particularly useful in combination with ecological or salt intrusion models. The solutions are compared with observations in the Schelde, Elbe, and Mekong estuaries.

Modeling vegetation controls on fluvial morphological trajectories

The role of riparian vegetation in shaping river morphology is widely recognized. The interaction between vegetation growth and riverbed evolution is characterized by complex nonlinear feedbacks, which hinder direct estimates of the role of key elements on the morphological evolutionary trajectories of gravel bed rivers. Adopting a simple theoretical framework, we develop a numerical model which couples hydromorphodynamics with biomass dynamics. We perform a sensitivity analysis considering several parameters as flood intensity, type of vegetation, and groundwater level. We find that the inclusion of vegetation determines a threshold behavior, identifying two possible equilibrium configurations: unvegetated versus vegetated bars. Stable vegetation patterns can establish only under specific conditions, which depend on the different environmental and species-related characteristics. From a management point of view, model results show that relatively small changes in water availability or species composition may determine a sudden shift between dynamic unvegetated conditions to more stable, vegetated rivers.

Metal fate and effects in estuaries: A review and conceptual model for better understanding of toxicity.

Metal pollution is a global problem in estuaries due to the legacy of historic contamination and currently increasing metal emissions. However, the establishment of water and sediment standards or management actions in brackish systems has been difficult because of the inherent transdisciplinary nature of estuarine processes. According to the European Commission, integrative comprehension of fate and effects of contaminants in different compartments of these transitional environments (estuarine sediment, water, biota) is still required to better establish, assess and monitor the good ecological status targeted by the Water Framework Directive. Thus, the present study proposes a holistic overview and conceptual model for the environmental fate of metals and their toxicity effects on aquatic organisms in estuaries. This includes the analysis and integration of biogeochemical processes and parameters, metal chemistry and organism physiology. Sources of particulate and dissolved metal, hydrodynamics, water chemistry, and mechanisms of toxicity are discussed jointly in a multidisciplinary manner. It is also hypothesized how these different drivers of metal behaviour might interact and affect metal concentrations in diverse media, and the knowledge gaps and remaining research challenges are pointed. Ultimately,estuarine physicochemical gradients, biogeochemical processes, and organism physiology are jointly coordinating the fate and potential effects of metals in estuaries, and both realistic model approaches and attempts.

A new analytical framework for assessing the effect of sea‐level rise and dredging on tidal damping in estuaries

This paper explores different analytical solutions of the tidal hydraulic equations in convergent estuaries. Linear and quasi-nonlinear models are compared for given geometry, friction, and tidal amplitude at the seaward boundary, proposing a common theoretical framework and showing that the main difference between the examined models lies in the treatment of the friction term. A general solution procedure is proposed for the set of governing analytical equations expressed in dimensionless form, and a new analytical expression for the tidal damping is derived as a weighted average of two solutions, characterized by the usual linearized formulation and the quasi-nonlinear Lagrangean treatment of the friction term. The different analytical solutions are tested against fully nonlinear numerical results for a wide range of parameters, and compared with observations in the Scheldt estuary. Overall, the new method compares best with the numerical solution and field data. The new accurate relationship for the tidal damping is then exploited for a classification of estuaries based on the distance of the tidally averaged depth from the ideal depth (relative to vanishing amplification) and the critical depth (condition for maximum amplification). Finally, the new model is used to investigate the effect of depth variations on the tidal dynamics in 23 real estuaries, highlighting the usefulness of the analytical method to assess the influence of human interventions (e.g. by dredging) and global sea-level rise on the estuarine environment.

Revisiting linearized one‐dimensional tidal propagation

In this paper we extend the validity of the classical linear solution for tidal hydrodynamics including the effects of width and depth convergence. Reworking such a solution in the light of externally defined, dimensionless parameters we are able to provide simple relationships to predict the most relevant features of the tidal wave at the estuary mouth (velocity amplitude, phase lag, wavelength, and damping) and to reproduce the main dynamics of tidal wave propagation along finite and infinite length channels. We also highlight the need for an accurate treatment of the linearized bed shear stress by exploiting an iterative procedure, and we show the improvement that can be reached by subdividing the entire estuary in shorter reaches. Different versions of the analytical solution are compared with numerical results, highlighting the strengths and weaknesses of the linear model.

Thermal wave dynamics in rivers affected by hydropeaking

Release of water from reservoirs for hydropower production generates inter- mittent hydro- and thermo-peaking waves in receiving rivers which can have important ecological implications at a variety of time and spatial scales. In this paper a coupled analytical-numerical approach is used in order to grasp the relevant processes of the prop- agation of the hydrodynamic and thermal waves, within the framework of a one-dimensional mathematical model governed by the Saint Venant equations coupled with a thermal en- ergy equation. While interacting with external forcing, the waves propagate downstream with dierent celerities such that it is possible to identify a first phase of mutual over- lap and a second phase in which the two waves proceed separately. A simplified analyt- ical solution for flow depth and temperature is derived in explicit terms exploiting the typical square shape of the waves and transforming the boundary conditions into equiv- alent initial conditions. The numerical model, which retains the complete features of the problem, is solved using a second order finite volume method. The wave properties and the characteristic time scales are investigated by means of the analytical solution and compared with numerical results for some test cases. Overall, the present approach al- lows for a deeper insight into the complex dynamics that characterize the propagation of hydropeaking and thermopeaking waves.

Long‐term morphological evolution of funnel‐shape tide‐dominated estuaries

We investigate the long-term morphological evolution of a tidal channel through 1 a one-dimensional numerical model. We restrict our attention to the case of tide-dominated 2 estuaries, which are usually characterized by a funnel shape, and neglect the eect of 3 intertidal areas and river discharge, imposing a closed boundary at the landward end. 4 If the estuary is relatively short and weakly convergent the equilibrium bottom profile 5 extends over the entire length of the estuary, whereas a beach is formed inside the do- 6 main when the initial length of the channel exceeds a threshold value. Hence, it is pos- 7 sible to define an intrinsic equilibrium length as the distance between the beach and the 8 mouth. In our analysis we examine how such estuarine length, which is independent of 9 the physical dimension imposed to the system, is aected by three main parameters, namely 10 channel convergence, tidal amplitude at the mouth and friction. We show that the de- 11 gree of convergence plays a crucial role, as the analysis of real estuaries seems to con- 12 firm: a strong degree of convergence implies shorter equilibrium lengths. We also show 13 that increasing the tidal amplitude at the mouth or the channel friction produces shorter 14 equilibrium profiles. Numerical results suggest that tidal asymmetries vanish as the sys- 15 tem approaches the final equilibrium state. 16

How long are tidal channels

Do tidal channels have a characteristic length? Given the sediment characteristics, the inlet conditions and the degree of channel convergence, can we predict it? And how is this length affected by the presence of tidal flats adjacent to the channel? We answer the above questions on the basis of a fully analytical treatment, appropriate for the short channels typically observed in coastal wetlands. The equilibrium length of non-convergent tidal channels is found to be proportional to the critical flow speed for channel erosion. Channel convergence causes concavity of the bed profile. Tidal flats shorten equilibrium channels significantly. Laboratory and field observations substantiate our findings.

The role of stratification on lakes' thermal response: The case of Lake Superior

During the last several decades, the Great Lakes region has been experiencing a significant rise in temperatures, with the extraordinary summer warming that affected Lake Superior in 1998 as an example of the marked response of the lake to increasingly warmer atmospheric conditions. In this work, we combine the analysis of this exceptional event with some synthetic scenarios, to achieve a deeper understanding of the main processes driving the thermal dynamics of surface water temperature in Lake Superior. The analysis is performed by means of the lumped model air2water, which simulates lake surface temperature as a function of air temperature alone. The model provides information about the seasonal stratification dynamics, suggesting that unusual warming events can result from two factors: anomalously high summer air temperatures, and increased strength of stratification resulting from a warm spring. The relative contribution of the two factors is quantified using the model by means of synthetic scenarios, which provide a simple but effective description of the positive feedback between the thermal behavior and the stratification dynamics of the lake.

A hybrid model for river water temperature as a function of air temperature and discharge

Water temperature controls many biochemical and ecological processes in rivers, and theoretically depends on multiple factors. Here we formulate a model to predict daily averaged river water temperature as a function of air temperature and discharge, with the latter variable being more relevant in some specific cases (e.g., snowmelt-fed rivers, rivers impacted by hydropower production). The model uses a hybrid formulation characterized by a physically based structure associated with a stochastic calibration of the parameters. The interpretation of the parameter values allows for better understanding of river thermal dynamics and the identification of the most relevant factors affecting it. The satisfactory agreement of different versions of the model with measurements in three different rivers (root mean square error smaller than 1oC, at a daily timescale) suggests that the proposed model can represent a useful tool to synthetically describe medium- and long-term behavior, and capture the changes induced by varying external conditions.