A PCA spatial pattern based downscaling approach for urban flood risk assessment
Résumé
With CPU times reduced by two to three orders of magnitude compared to shallow water models, porosity models are considered as efficient tools for the modelling of urban floods on the scale of a conurbation. However, they provide only upscaled hydraulic fields that yield unreliable estimates of the flood risk in terms of financial losses and hazard to human lives. Downscaling of the porosity model simulation outputs is thus necessary. The present work puts forward a downscaling approach based on the decomposition of microscopic hydraulic fields into linear combinations of spatial patterns. The coefficients of the linear combinations are predicted with an Artificial Neural Network (ANN) whose input is derived from macroscopic hydraulic fields. Principal Component Analysis is used both to decompose the microscopic fields into linear combinations of spatial patterns and to project the macroscopic fields into lower dimensional features that are fed to the ANN. This global downscaling approach, which reconstruct the whole microscopic field at once, is compared with a local downscaling approach that relies on a similar setup except that each cell of the microscopic field is estimated separately by a dedicated ANN and that there are as many ANNs as cells. The two downscaling approaches are evaluated and compared at estimating the water depth and the norm of the unit discharge on five synthetic urban configurations and one field-test case. The analyses in terms of absolute errors show that the global approach not only provides a valid downscaling scheme but outperforms, in almost all instances, the local approach.
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