arXiv subjects

Ehouarn Simon

Publications and source records attributed to Ehouarn Simon.

5 recordsLinked to original sources

arXiv2023

A filtered multilevel Monte Carlo method for estimating the expectation of cell-centered discretized random fields

In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators have inconsistent dimensions across the multilevel hierarchy. This motivates the introduction of grid transfer operators borrowed from multigrid methods. By adapting mathematical tools from multigrid methods, we perform a theoretical spectral analysis of the MLMC estimator of the expectation of discretized random fields, in the specific case of linear, symmetric and circulant simulators. We then propose filtered MLMC (F-MLMC) estimators based on a filtering mechanism similar to the smoothing process of multigrid methods, and we show that the filtering operators improve the estimation of both the small- and large-scale components of the variance, resulting in a reduction of the total variance of the estimator. Next, the conclusions of the spectral analysis are experimentally verified with a one-dimensional illustration. Finally, the proposed F-MLMC estimator is applied to the problem of estimating the discretized variance field of a diffusion-based covariance operator, which amounts to estimating the expectation of a discretized random field. The numerical experiments support the conclusions of the theoretical analysis even with non-linear simulators, and demonstrate the improvements brought by the F-MLMC estimator compared to both a crude MC and an unfiltered MLMC estimator.

math.NA↗

arXiv2023

Dealing With Non-Gaussianity of SAR-derived Wet Surface Ratio for Flood Extent Representation Improvement

Owing to advances in data assimilation, notably Ensemble Kalman Filter (EnKF), flood simulation and forecast capabilities have greatly improved in recent years. The motivation of the research work is to reduce comprehensively the uncertainties in the model parameters, forcing and hydraulic state, and consequently improve the overall flood reanalysis and forecast capability, especially in the floodplain. It aims at assimilating SAR-derived (typically from Sentinel-1 mission) flood extent observations, expressed in terms of wet surface ratio. The non-Gaussianity of the observation errors associated with the SAR flood observations violates a major hypothesis regarding the EnKF and jeopardizes the optimality of the filter analysis. Therefore, a special treatment of such non-Gaussianity with a Gaussian anamorphosis process is thus proposed. This strategy was validated and applied over the Garonne Marmandaise catchment (Southwest of France) represented with the TELEMAC-2D hydrodynamic model, focusing on a major flood event that occurred in December 2019. The assimilation of the SAR-derived wet surface ratio observations, in complement to the in-situ water surface elevations, is illustrated to consequentially improve the flood representation.

eess.IV↗

arXiv2023

Gaussian Anamorphosis for Ensemble Kalman Filter Analysis of SAR-Derived Wet Surface Ratio Observations

Flood simulation and forecast capability have been greatly improved thanks to advances in data assimilation (DA) strategies incorporating various types of observations; many are derived from spatial Earth Observation. This paper focuses on the assimilation of 2D flood observations derived from Synthetic Aperture Radar (SAR) images acquired during a flood event with a dual state-parameter Ensemble Kalman Filter (EnKF). Binary wet/dry maps are here expressed in terms of wet surface ratios (WSR) over a number of subdomains of the floodplain. This ratio is further assimilated jointly with in-situ water-level observations to improve the flow dynamics within the floodplain. However, the non-Gaussianity of the observation errors associated with SAR-derived measurements break a major hypothesis for the application of the EnKF, thus jeopardizing the optimality of the filter analysis. The novelty of this paper lies in the treatment of the non-Gaussianity of the SAR-derived WSR observations with a Gaussian anamorphosis process (GA). This DA strategy was validated and applied over the Garonne Marmandaise catchment (South-west of France) represented with the TELEMAC-2D hydrodynamic model, first in a twin experiment and then for a major flood event that occurred in January-February 2021. It was shown that assimilating SAR-derived WSR observations, in complement to the in-situ water-level observations significantly improves the representation of the flood dynamics. Also, the GA transformation brings further improvement to the DA analysis, while not being a critical component in the DA strategy. This study heralds a reliable solution for flood forecasting over poorly gauged catchments thanks to available remote-sensing datasets.

eess.IV↗

arXiv2020

Exploiting variable precision in GMRES

We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates. Our analysis explicitly takes into account the resulting loss of orthogonality in the Arnoldi vectors. We also show how inexact matrix-vector products can be incorporated into this setting.

math.NA↗

arXiv2017

A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation

The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation problem are finally discussed.

math.NA↗