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Knowledge of tidal flows in rivers and estuaries is often scarce yet vital in determining flushing properties and sediment transport rates. While many rivers still remain ungauged, methodological difficulties often arise in gauged systems, resulting in short flow records compared to historical water level data. Notwithstanding, discharge reconstructions in estuaries are possible using indirect methods based on long‐term tidal data. In this paper, we revisit the method of cubature, integrating the continuity equation for discharges at different sections. The method consists in computing temporal changes in water volume from simultaneous tidal heights readings along the river and storage width estimations. These water balance estimates remain challenging to produce, because they require spatial interpolation of gappy tidal records and an accurate representation of inundated areas over time. Improvements on the method are made by using a 1‐D nonstationary tidal harmonic model that provides continuous tidal data along the estuary, with no temporal or spatial gaps. Second, a 2‐D finite element discretization is used to compute the time‐varying wetted surface area, relying on detailed topographic data over intertidal flats. The method is applied to the St. Lawrence fluvial estuary (SLFE) and validated against discharge data collected along nine cross sections of the river, reaching relative RMSE below 4% of the diurnal tidal discharge range at downstream locations and below 9% upstream. One year reconstructions conducted in the SLFE also show the potential of the method to reproduce the tidal discharge variability along the tidal‐river continuum, for a wide range of temporal scales. Tidal discharges are computed by integration of the continuity equation, based on known water levels, upriver inflows, and river geometryImprovements include the use of temporally and spatially continuous nonstationary tidal data and computation of time‐varying wetted areasMean error ratios of modeled to observed tidal flows amount to 4.5% of the tidal discharge amplitudes in the St. Lawrence fluvial estuary

The SUPG/θ-method for applications in 2D advection–diffusion transport simulation is reviewed and it is presented in details. Spatial discretization is done with finite elements method with stabilized streamline upwind Petrov–Galerkin method, and time discretization was done with θ-stable finite difference operator. Numerical tests showed that this algorithm is general and robust and it can be applied to simulate simple problems of mass transport; for example, pure advection phenomenon in structured mesh, as well as reactive advection–diffusion transport with an unstructured mesh, and not well-behaved velocity field. The method was applied in a simulation of the transport of total phosphorus in the Lake Água Preta, and the results were validated by comparison with experimental data. The computational cost is directly associated with the value of the safety factor, introduced to assure the stability of the method.

La validation par les vitesses d’un modèle hydrodynamique montre que la variabilité du profil vertical des vitesses a une influence importante sur le résultat. Ici, cette variabilité a été introduite sous la forme d’un terme de dispersion dans un modèle hydrodynamique qui résout les équations de Saint-Venant 2D par la méthode des éléments finis. Nous tentons ensuite de la représenter à l’aide des variables du modèle (u, v, h). Le modèle appliqué à un canal courbe de 270° montre que la variabilité spatiale de la distribution des vitesses est améliorée, que ce soit par la prise en compte de la variabilité mesurée ou par le paramétrage de celle-ci. Une application est effectuée sur la rivière des Escoumins, petit cours d’eau alluvionnaire à la topographie complexe. Les résultats montrent que la modification du modèle de Saint-Venant améliore la description de l’écoulement mais ne suffit pas à représenter correctement celui-ci.

The St. Lawrence River is one of the most important large rivers in North America. This 600-km long watercourse is characterized by a high degree of physical heterogeneity, including fast moving narrow reaches separated by fluvial lakes reaching 10 km in width. The mean annual discharge from the outflow of Lake Ontario is 7500 m3/s and has been managed for hydropower and transportation since the 1960s. With the management plan currently under review an effort is being made to include criteria that take into account the impacts of regulation on the biotic components of the river ecosystem. High resolution 2D spatial modelling of river habitats and floodplains is a powerful tool to make quantitative impact assessments of the biota. Physical variables commonly used in habitat models include depth, velocity and substrate size. In addition, other abiotic variables such as wind-generated wave stress, light penetration, water temperature, sedimentation of fine particles, specific discharge and bottom slope, that define the local ’hydroperiod’ have been suggested. Our proposed approach integrates abiotic data obtained from numerical models, field measurements and biological information to overcome problems inherent in temporally and spatially heterogeneous river systems. This approach was tested with a habitat model applied to submerged aquatic vegetation, various categories of wetlands, benthic organisms and various life stages of a number offish species. Logistic regression is the statistical model currently used to synthesize the relationships between abiotic and biotic factors. The short-term objective of this modelling exercise in the St. Lawrence River is to understand the underlying links between fluvial physics and biota. A longer-term objective is to provide a real-time analysis of key variables and to quantify the links between trophic levels.

A new Eulerian approach is proposed to track the dynamic position of flow boundaries in rivers with respect to flow discharge or tides. Associated to a two dimensional (2D) transient horizontal hydrodynamic model, it allows to define the configuration of watercourses in a broad hydrological register varying from dry conditions to severe flooding. The finite element method is used to develop the numerical prediction tool. It is employed to estimate not only the classical flow variables such as water surface level and velocity field, but also the position of the shorelines. In this paper, the strategy followed for building this «drying-wetting» model consists in letting the water surface move freely, everywhere in the domain including the dry zones, allowing it to plunge under the ground. Two practical applications on rivers of Quebec (Canada) are presented. The first one deals with steady state situations on St. Marguerite River. The second one deals with the reconstitution of flood propagation on Chicoutimi River according to the extreme flooding events of July 96 in the Saguenay region.

A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection–diffusion equation for practical river surface flow simulations. Essentially, the space–time Crank–Nicolson–Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, namely Cauchy and Open, were theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on inflow, noflow and outflow boundaries where diffusion is important (diffusive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank–Nicolson–Galerkin finite element schemes gave stable and precise results for advection-dominated transport problems. Comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high-order time-stepping schemes. Diffusive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflow), and with Open conditions when the flow leaves the domain (outflow), or when it is parallel to the boundary (noflow). Although systems with mainly diffusive noflow boundaries may still be solved precisely with Open conditions, they are more susceptible to be influenced by other numerical sources of error. Moreover, the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest. © 1997 by John Wiley & Sons, Ltd.