Une méthodologie de modélisation numérique de terrain pour la simulation hydrodynamique bidimensionnelle

L'article pose la problématique de la construction du Modèle Numérique de Terrain (MNT) dans le contexte d'études hydrauliques à deux dimensions, ici reliées aux inondations. La difficulté est liée à l'hétérogénéité des ensembles de données qui diffèrent en précision, en couverture spatiale, en répartition et en densité, ainsi qu'en géoréférentiation, notamment. Dans le cadre d'un exercice de modélisation hydrodynamique, toute la région à l'étude doit être documentée et l'information portée sur un support homogène. L'article propose une stratégie efficace supportée par un outil informatique, le MODELEUR, qui permet de fusionner rapidement les divers ensembles disponibles pour chaque variable qu'elle soit scalaire comme la topographie ou vectorielle comme le vent, d'en préserver l'intégrité et d'y donner accès efficacement à toutes les étapes du processus d'analyse et de modélisation. Ainsi, quelle que soit l'utilisation environnementale du modèle numérique de terrain (planification d'aménagement, conservation d'habitats, inondations, sédimentologie), la méthode permet de travailler avec la projection des données sur un support homogène de type maillage d'éléments finis et de conserver intégralement l'original comme référence. Cette méthode est basée sur une partition du domaine d'analyse par type d'information : topographie, substrat, rugosité de surface, etc.. Une partition est composée de sous-domaines et chacun associe un jeu de données à une portion du domaine d'analyse par un procédé déclaratoire. Ce modèle conceptuel forme à notre sens le MNT proprement dit. Le processus de transfert des données des partitions à un maillage d'analyse est considéré comme un résultat du MNT et non le MNT lui-même. Il est réalisé à l'aide d'une technique d'interpolation comme la méthode des éléments finis. Suite aux crues du Saguenay en 1996, la méthode a pu être testée et validée pour en démontrer l'efficacité. Cet exemple nous sert d'illustration.This article exposes the problem of constructing a Numerical Terrain Model (NTM) in the particular context of two-dimensional (2D) hydraulic studies, herein related to floods. The main difficulty is related to the heterogeneity of the data sets that differ in precision, in spatial coverage, distribution and density, and in georeference, among others. Within the framework of hydrodynamic modelling, the entire region under study must be documented and the information carried on a homogeneous grid. One proposes here an efficient strategy entirely supported by a software tool called MODELEUR, which allows to import, gather and merge together very heterogeneous data sets, whatever type they are, scalar like topography or vectorial like wind, to preserve their integrity, and provide access to them in their original form at every step of the modelling exercise. Thus, whatever the environmental purpose of the modelling exercise (enhancement works, sedimentology, conservation of habitats, flood risks analysis), the method allows to work with the projection of the data sets on a homogeneous finite element grid and to conserves integrally the original sets as the ultimate reference. This method is based on a partition of the domain under study for each data type: topography, substrates, surface roughness, etc. Each partition is composed of sub-domains and each of them associates a data set to a portion of the domain in a declarative way. This conceptual model represents formally the NTM. The process of data transfer from the partitions to the final grid is considered as a result of the NTM and not the NTM itself. It is performed by interpolation with a technique like the finite element method. Following the huge Saguenay flood in 1996, the efficiency of this method has been tested and validated successfully and this example serves here as an illustration.The accurate characteristics description of both river main channel and flood plain is essential to any hydrodynamic simulation, especially if extreme discharges are considered and if the two-dimensional approach is used.The ground altitude and the different flow resistance factors are basic information that the modeler should pass on to the simulator. For too long, this task remained "the poor relative" of the modeling process because it does not a priori seem to raise any particular difficulty. In practice however, it represents a very significant workload for the mobilisation of the models, besides hiding many pitfalls susceptible to compromise the quality of the hydraulic results. As well as the velocity and water level fields are results of the hydrodynamic model, the variables describing the terrain and transferred on the simulation mesh constitute the results of the Numerical Terrain Model (NTM). Because this is strictly speaking a modeling exercise, a validation of the results that assess the quality of the model is necessary.In this paper, we propose a methodology to integrate the heterogeneous data sets for the construction of the NTM with the aim of simulating 2D hydrodynamics of natural streams with the finite element method. This methodology is completely supported by a software, MODELEUR, developed at INRS-Eau (Secretan and Leclerc, 1998; Secretan et al., 2000). This tool, which can be assimilated to a Geographical Information System (GIS) dedicated to the applications of 2D flow simulations, allows to carry out all the steps of integrating the raw data sets for the conception of a complete NTM. Furthermore, it facilitates the application and the piloting of hydrodynamic simulations with the simulator HYDROSIM (Heniche et al., 1999).Scenarios for flow analysis require frequent and important changes in the mesh carrying the data. A return to the basis data sets is then required, which obliges to preserve them in their entirety, to have easily access to them and to transfer them efficiently on the mesh. That is why the NTM should rather put emphasis on basic data rather than on their transformed and inevitably degraded aspect after their transfer to a mesh.The data integrity should be preserved as far as possible in the sense that it is imperative to keep distinct and to give access separately to different data sets. Two measuring campaigns will not be mixed; for example, the topography resulting from digitised maps will be maintained separated from that resulting from echo-sounding campaigns. This approach allows at any time to return to the measures, to control them, to validate them, to correct them and possibly, to substitute a data set a by another one.The homogeneity of the data support with respect to the location of the data points is essential to allow the algebraic interaction between the different information layers. The operational objective which bear up ultimately the creation of the NTM in the present context is to be able to transfer efficiently the spatial basic data (measurements, geometry of civil works, etc.) each carried by diverse discretisations towards a single carrying structure.With these objectives of integrity, accessibility, efficiency and homogeneity, the proposed method consists of the following steps:1. Import of the data sets into the database, which possibly implies to digitise maps and/or to reformat the raw files to a compatible file format; 2. Construction and assembly of the NTM properly which consists, for each variable (topography, roughness, etc.), to create a partition of the domain under study, that is to subdivide it into juxtaposed sub-domains and to associate to each sub-domain the data set which describes the variable on it. More exactly, this declaratory procedure uses irregular polygons allowing to specify in the corresponding sub-domains the data source to be used in the construction of the NTM. As it is also possible to transform regions of the domain with algebraic functions to represent for example civil works in river (dikes, levees, etc.), the NTM integrates all the validated data sets and the instructions to transform them locally. From this stage, the NTM exists as entity-model and it has a conceptual character;3. Construction of a finite element mesh;4. Transfer by interpolation and assembly of the data of the different components of the NTM on the finite element mesh according to the instructions contained in the various partitions. The result is an instance of the NTM and its quality depends on the density of the mesh and the variability of the data. So, it requires a validation with respect to the original data;5. Realisation of the analysis tasks and/or hydrodynamic simulations. If the mesh should be modified for a project variant or for an analysis scenario, only tasks 3 and 4 are to be redone and task 4 is completely automated in the MODELEUR.The heterogeneity of the data sources, which constitutes one of the main difficulties of the exercise, can be classified in three groups: according to the measuring technique used; according to the format or the representation model used; according to the geographic datum and projection system.For the topography, the measuring techniques include conventional or radar satellite, airborne techniques, photogrammetry or laser scanning, ground techniques, total station or GPS station, as well as embarked techniques as the echo-sounder. These data come in the form of paper maps that have to be digitised, in the form of regular or random data points, isolines of altitude, or even as transects. They can be expressed in different datums and projections and sometime are not even georeferenced and must be first positioned.As for the bed roughness that determines the resistance to the flow, also here the data sets differ one from the other in many aspects. Data can here also have been picked as regular or random points, as homogeneous zones or as transects. Data can represent the average grain size of the present materials, the dimension of the passing fraction (D85 or D50 or median), the represented % of the surface corresponding to every fraction of the grain assemblage, etc... In absence of this basic data, the NTM can only represent the value of the friction parameter, typically n of Manning, which should be obtained by calibration for the hydrodynamic model. For the vegetation present in the flood plain or for aquatic plants, source data can be as variable as for the bed roughness. Except for the cases where data exists, the model of vegetation often consists of the roughness parameter obtained during the calibration exercise. The method was successfully applied in numerous contexts as demonstrated by the application realised on the Chicoutimi River after the catastrophic flood in the Saguenay region in 1996. The huge heterogeneity of the available data in that case required the application of such a method as proposed. So, elevation data obtained by photogrammetry, by total station or by echo-sounder on transects could be coordinated and investigated simultaneously for the purposes of hydrodynamic simulation or of sedimentary balance in zones strongly affected by the flood

An intercomparison of remote sensing river discharge estimation algorithms from measurements of river height, width, and slope

The Surface Water and Ocean Topography (SWOT) satellite mission planned for launch in 2020 will map river elevations and inundated area globally for rivers >100 m wide. In advance of this launch, we here evaluated the possibility of estimating discharge in ungauged rivers using synthetic, daily ‘‘remote sensing’’ measurements derived from hydraulic models corrupted with minimal observational errors. Five discharge algorithms were evaluated, as well as the median of the five, for 19 rivers spanning a range of hydraulic and geomorphic conditions. Reliance upon a priori information, and thus applicability to truly ungauged reaches, varied among algorithms: one algorithm employed only global limits on velocity and depth, while the other algorithms relied on globally available prior estimates of discharge. We found at least one algorithm able to estimate instantaneous discharge to within 35% relative root-mean-squared error (RRMSE) on 14/16 nonbraided rivers despite out-of-bank flows, multichannel planforms, and backwater effects. Moreover, we found RRMSE was often dominated by bias; the median standard deviation of relative residuals across the 16 nonbraided rivers was only 12.5%. SWOT discharge algorithm progress is therefore encouraging, yet future efforts should consider incorporating ancillary data or multialgorithm synergy to improve results

On the sensitivity of computed higher tidal harmonics to mesh size in a finite element model

A finite element model of the Irish and Celtic Sea regions with a range of grid resolutions is used to examine the influence of resolution upon the higher harmonics of the tide in the region. Comparisons are also made with published results from finite difference models of the area, and observations. Calculations using fine near-shore elements with non-zero water depths in coastal regions were found to be more accurate and less time consuming than those using a zero coastal water depth. A detailed examination of the spatial variability of the higher harmonics in near-shore regions of the eastern Irish Sea particularly the Solway and Morecambe Bay showed significant small-scale variability. This together with the variation in higher harmonics in the eastern Irish Sea and adjacent estuaries, clearly shows the need for an unstructured grid model of the region that can include the estuaries. To match the high resolution of the model in near-shore regions accurate high-resolution topography is require

On the modification of tides in shallow water regions by wind effects

The influence of non-linear effects upon tides in shallow coastal regions, due to the presence of a significant storm surge is examined using a two-dimensional model of the west coast of Britain. The model has an unstructured grid, designed to have a high resolution mesh in the near coastal region of the eastern Irish Sea, the area chosen as the focus of this study. The influence of tide-surge interaction upon the M2, M4 and M6 components of the tide, due to surges produced by steady uniform wind stresses is examined in detail. Calculations show that in deep regions the tide is unaffected by the surge. However, in shallow coastal regions there is significant modification of tidal elevations and currents. This arises because of changes in bottom stress, and the non-linear interaction term in the hydrodynamic equations. In addition the locations of regions that “wet and dry” are changed during the tidal cycle due to the influence of the surge. This gives rise to significant spatial variations and changes in magnitude of the tide and its higher harmonics depending upon wind stress direction and water depth. These results explain why tidal energy remains in the surge residual in shallow water when it is computed by de-tiding the total signal using a tide only calculation; an effect often found in observed surge residual

Numerical solution of the Fokker-Planck equation for fiber suspensions: Application to the Folgar-Tucker-Lipscomb model

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