A methodology to construct a numerical terrain model for two-dimensional hydrodynamic simulations
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.