Annunziato Siviglia

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.

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.

Mathematical analysis of the Saint-Venant-Hirano model for mixed-sediment morphodynamics

Sediment of different size are transported in rivers under the action of flow. The first and still most popular sediment continuity model able to deal with mixed sediment is the so-called active layer model proposed by Hirano (1971, 1972). In this paper, we consider the one-dimensional hydromorphodynamic model given by the Saint-Venant equations for free-surface flow coupled with the active layer model. We perform a mathematical analysis of this model, extending the previous analysis by Ribberink (1987), including full unsteadiness and grainsize selectivity of the transported load by explicitly considering multiple sediment fractions. The presence of multiple fractions gives rise to distinct waves traveling in the downstream direction, for which we provide an analytical approximation of propagation velocity under any Froude regime. We finally investigate the role of different waves in advecting morphodynamic changes through the domain. To this aim, we implement an analytical linearized solver to analyze the propagation of small-amplitude perturbations of the bed elevation and grainsize distribution of the active layer as described by the system of governing equations. We find that initial gradients in the grainsize distribution of the active layer are able to trigger significant bed variations, which propagate in the downstream direction at faster pace than the “bed” wave arising from the unisize-sediment Saint-Venant-Exner model. We also verify that multiple “sorting” waves carry multiple associated bed perturbations, traveling at different speeds.

WAF Method and Splitting Procedure for Simulating Hydro- and Thermal-Peaking Waves in Open-Channel Flows

Hydro- and thermal-peaking waves, generated by hydroelectric power generation, have a strong impact on the ecological integrity of aquatic ecosystems. In order to reduce such effects, mitigation procedure must be studied and implemented. To this end a one-dimensional model which solves the coupling of hydrodynamics with heat transport is developed. The solution is obtained advancing simultaneously the hydrodynamic and thermal module with the same accuracy. For the numerical solution of the governing advection-reaction/diffusion problem a splitting procedure is adopted: the advection-reaction part is solved by means of the weight average flux (WAF) finite volume explicit method, while the diffusion part is solved using a nonlinear version of the implicit Crank-Nicolson method. The WAF method is extended to second-order in the presence of reaction terms. Numerical results are presented for different test examples, which demonstrate the accuracy and robustness of the scheme and its applicability in predicting temperature transport by shallow water flows. Application to the Adige River (Northern Italy) of this framework proves that the model is an effective tool for designing hydro- and thermal-peaking waves mitigation procedures.

A simple procedure for the assessment of hydropeaking flow alterations applied to several European streams

Release of water from storage hydropower plants generates rapid flow and stage fluctuations (hydropeaking) in the receiving water bodies at a variety of sub-daily time-scales. In this paper we present an approach to quantify such variations, which is easy to apply, requires stream flow data at a readily available resolution, and allows for the comparison of hydropeaking flow alteration amongst several gauged stations. Hydropeaking flow alteration is quantified by adopting a rigorous statistical approach and using two indicators related to flow magnitude and rate of change. We utilised a comprehensive stream-flow dataset of 105 gauging stations from Italy, Switzerland and Norway to develop our method. Firstly, we used a GIS approach to objectively assign the stations to one of two groups: gauges with an upstream water release from hydropower plants (peaked group) and without upstream releases (unpeaked group). Secondly, we used the datasets of the unpeaked group to calculate one threshold for each of the two indicators. Thresholds defined three different classes: absent or low pressure, medium, and high pressure, and all stations were classified according to these pressure levels. Thirdly, we showed that the thresholds can change, depending on the country dataset, the year chosen for the analysis, the number of gauging stations, and the temporal resolution of the dataset, but the outcome of the classification remains the same. Hence, the classification method we propose can be considered very robust since it is almost insensitive to the hydropeaking thresholds variability. Therefore, the method is broadly applicable to procedures for the evaluation of flow regime alterations and classification of river hydromorphological quality, and may help to guide river restoration actions.

Upwind-biased FORCE schemes with applications to free-surface shallow flows

In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple-space dimensions on structured meshes. The proposed method is an extension of the multidimensional FORCE flux developed by Toro et al. (2009) [14]. Here we introduce upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. For the linear advection equation, the proposed UFORCE method reproduces exactly the upwind Godunov method. Extension to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. Second order of accuracy in space and time on structured meshes is obtained in the framework of finite volume methods. The proposed method improves the accuracy of the solution for small Courant numbers and intermediate waves associated with linearly degenerate fields (contact discontinuities, shear waves and material interfaces). It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the schemes is assessed on a suite of test problems for the two-dimensional shallow water equations.

Simplified blood flow model with discontinuous vessel properties: Analysis and exact solutions

We formulate a simplified one-dimensional time-dependent non-linear mathematical model for blood flow in vessels with discontinuous material properties. The resulting 3 × 3 hyperbolic system is analysed and the associated Riemann problem is solved exactly, including tube collapse. Our exact solutions constitute useful reference solutions for assessing the performance of numerical methods intended for simulating more general situations. In addition the presented model may be a useful starting point for numerical calculations involving rapid and discontinuous material properties variations.

Case Study: Design of Flood Control Systems on the Vara River by Numerical and Physical Modeling

In the present paper, we investigate the effectiveness of a flood defense project based on storage reservoirs, presently under study for the Magra River and Vara River (Italy). We have focused the analysis on two detention reservoirs and studied their response to different hydrological scenarios mostly in terms of flood mitigation efficiency, leaving aside sediment transport issues. The analysis has been carried out with the aid of a physical model and one-dimensional numerical simulations. Experimental and numerical simulations have been performed spanning a wide range of hydrological conditions. Some of the results can be generalized for different applications where similar flood control systems are employed.

Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme

Abstract The purpose of this paper is twofold. First, using the Cattaneos relaxation approach, we reformulate the system of governing equations for the pollutant transport by shallow water flows over non-flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms. The proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection–diffusion models. This turns out to give a larger stability range for the choice of the time step. Second, following a flux splitting approach, we derive a novel numerical method to discretise the resulting problem. In particular, we propose a new flux splitting and study the associated two systems of differential equations, called the “hydrodynamic” and the “relaxed diffusive” system, respectively. For the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the Godunov-type. These schemes are simple to implement, robust, accurate and fast when compared with existing methods. The resulting method is implemented on unstructured meshes and is systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems including non-flat topography and wetting and drying problems. Formal second order accuracy is assessed through convergence rates studies.

Reply to comment by Cao and Hu on “Long waves in erodible channels and morphodynamic influence”

[1] We thank Cao and Hu [2008] very much for their comment. We must honestly say that at first sight, we felt that their point, reproducing that raised by Cao and Carling [2003] to challenge the formulation of the 1-D governing equations proposed by Lisle et al. [2001], had already been proven to be erroneous by Cui et al. [2005]. However, after more careful examination of the matter, we have concluded that both the final forms of the continuity equation derived by Cao and Hu [2008] (hereinafter referred to as CH) and Lanzoni et al. [2006] (hereinafter denoted as LSFS) are not wholly correct. Indeed, while the main point raised by CH is definitely correct, they reach slightly incorrect conclusions, employing a framework which ignores the distinction between bed load and suspended load. On the other hand, the LSFS derivation is also incorrect in that it will be seen to ignore the defect of water flux due to the presence of particles transported as bed load, an effect which turns out to be of the same order of magnitude as that of the retained contributions. This effect modifies the final form of the continuity equation for the fluid phase which does indeed include a sediment transport correction, whose structure will be seen to be intermediate between the one derived by LSFS and that suggested by CH. While, as shown in section 4, this modification does not affect the treatment of one-dimensional long sediment waves presented by LSFS, the issue is of conceptual importance.We are therefore grateful to CH for motivating us to provide a hopefully more conclusive clarification of the matter. We are confident that the analysis presented below will be instructive for the reader, as it was for us.