Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGlobal Sensitivity Analysis with 2D Hydraulic Codes: Application on Uncertainties Related to High-Resolution Topographic Data
68
0
0.0
(
0
)
Added by
Olivier Delestre
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Authors
M Abily
Ask ChatGPT about the research
No Arabic abstract
Technologies such as aerial photogrammetry allow production of 3D topographic data including complex environments such as urban areas. Therefore, it is possible to create High Resolution (HR) Digital Elevation Models (DEM) incorporating thin above ground elements influencing overland flow paths. Even though this category of big data has a high level of accuracy, there are still errors in measurements and hypothesis under DEM elaboration. Moreover, operators look for optimizing spatial discretization resolution in order to improve flood models computation time. Errors in measurement, errors in DEM generation, and operator choices for inclusion of this data within 2D hydraulic model, might influence results of flood models simulations. These errors and hypothesis may influence significantly flood modelling results variability. The purpose of this study is to investigate uncertainties related to (i) the own error of high resolution topographic data, and (ii) the modeller choices when including topographic data in hydraulic codes. The aim is to perform a Global Sensitivity Analysis (GSA) which goes through a Monte-Carlo uncertainty propagation, to quantify impact of uncertainties, followed by a Sobol indices computation, to rank influence of identified parameters on result variability. A process using a coupling of an environment for parametric computation (Prom{e}th{e}e) and a code relying on 2D shallow water equations (FullSWOF 2D) has been developed (P-FS tool). The study has been performed over the lower part of the Var river valley using the estimated hydrograph of 1994 flood event. HR topographic data has been made available for the study area, which is 17.5 km 2 , by Nice municipality. Three uncertain parameters were studied: the measurement error (var. E), the level of details of above-ground element representation in DEM (buildings, sidewalks, etc.) (var. S), and the spatial discretization resolution (grid cell size for regular mesh) (var. R). Parameter var. E follows a probability density function, whereas parameters var. S and var. R. are discrete operator choices. Combining these parameters, a database of 2, 000 simulations has been produced using P-FS tool implemented on a high performance computing structure. In our study case, the output of interest is the maximal
rate research
Read More
Global Sensitivity Analysis (GSA) methods are useful tools to rank input parameters uncertainties regarding their impact on result variability. In practice, such type of approach is still at an exploratory level for studies relying on 2D Shallow Water Equations (SWE) codes as GSA requires specific tools and deals with important computational capacity. The aim of this paper is to provide both a protocol and a tool to carry out a GSA for 2D hydraulic modelling applications. A coupled tool between Prom{e}th{e}e (a parametric computation environment) and FullSWOF 2D (a code relying on 2D SWE) has been set up: Prom{e}th{e}e-FullSWOF 2D (P-FS). The main steps of our protocol are: i) to identify the 2D hydraulic code input parameters of interest and to assign them a probability density function, ii) to propagate uncertainties within the model, and iii) to rank the effects of each input parameter on the output of interest. For our study case, simulations of a river flood event were run with uncertainties introduced through three parameters using P-FS tool. Tests were performed on regular computational mesh, spatially discretizing an urban area, using up to 17.9 million of computational points. P-FS tool has been installed on a cluster for computation. Method and P-FS tool successfully allow the computation of Sobol indices maps. Keywords Uncertainty, flood hazard modelling, global sensitivity analysis, 2D shallow water equation, Sobol index. Analyse globale de sensibilit{e} en mod{e}lisation hydrauliqu{`e} a surface libre 2D : application dun protocole et d{e}veloppement doutils op{e}rationnels -- Les m{e}thodes danalyse de sensibilit{e} permettent de contr{^o}ler la robustesse des r{e}sultats de mod{e}lisation ainsi que didentifier le degr{e} dinfluence des param etres d entr{e}e sur le r{e}sultat en sortie dun mod ele. Le processus complet constitue une analyse globale de sensibilit{e} (GSA). Ce type dapproche pr{e}sente un grand int{e}r{^e}t pour analyser les incer-titudes de r{e}sultats de mod{e}lisation , mais est toujours a un stade exploratoire dans les etudes appliqu{e}es mettant en jeu des codes bas{e}s sur la r{e}solution bidimensionnelle des equations de Saint-Venant. En effet, l impl{e}mentation dune GSA est d{e}licate car elle
This paper presents a spatial Global Sensitivity Analysis (GSA) approach in a 2D shallow water equations based High Resolution (HR) flood model. The aim of a spatial GSA is to produce sensitivity maps which are based on Sobol index estimations. Such an approach allows to rank the effects of uncertain HR topographic data input parameters on flood model output. The influence of the three following parameters has been studied: the measurement error, the level of details of above-ground elements representation and the spatial discretization resolution. To introduce uncertainty, a Probability Density Function and discrete spatial approach have been applied to generate 2, 000 DEMs. Based on a 2D urban flood river event modelling, the produced sensitivity maps highlight the major influence of modeller choices compared to HR measurement errors when HR topographic data are used, and the spatial variability of the ranking. Highlights $bullet$ Spatial GSA allowed the production of Sobol index maps, enhancing the relative weight of each uncertain parameter on the variability of calculated output parameter of interest. 1 $bullet$ The Sobol index maps illustrate the major influence of the modeller choices, when using the HR topographic data in 2D hydraulic models with respect to the influence of HR dataset accuracy. $bullet$ Added value is for modeller to better understand limits of his model. $bullet$ Requirements and limits for this approach are related to subjectivity of choices and to computational cost.
Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture), current water height in the river, topography, nature and geometry of the river bed, etc. This data is tainted with uncertainties related to an imperfect knowledge of the field, measurement errors on the physical parameters calibrating the equations of physics, an approximation of the latter, etc. These uncertainties can lead the model to overestimate or underestimate the flow and height of the river. Moreover, complex assimilation models often require numerous evaluations of physical solvers to evaluate these uncertainties, limiting their use for some real-time operational applications. In this study, we explore the possibility of building a predictor for river height at an observation point based on drainage basin time series data. An array of data-driven techniques is assessed for this task, including statistical models, machine learning techniques and deep neural network approaches. These are assessed on several metrics, offering an overview of the possibilities related to hydraulic time-series. An important finding is that for the same hydraulic quantity, the best predictors vary depending on whether the data is produced using a physical model or real observations.
We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincare inequalities. Typically two kind of sensitivity indices are linked by a Poincare type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper to compute. This allows performing a low-cost screening of unessential variables. The efficiency of this screening then highly depends on the accuracy of the upper bounds in Poincare inequalities. The novelty in the questions concern the wide range of probability distributions involved, which are often truncated on intervals. After providing an overview of the existing knowledge and techniques, we add some theory about Poincare constants on intervals, with improvements for symmetric intervals. Then we exploit the spectral interpretation for computing exact value of Poincare constants of any admissible distribution on a given interval. We give semi-analytical results for some frequent distributions (truncated exponential, triangular, truncated normal), and present a numerical method in the general case. Finally, an application is made to a hydrological problem, showing the benefits of the new results in Poincare inequalities to sensitivity analysis.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
