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A chained hydrologic-hydraulic model is implemented using predicted runoff from a large-scale hydrologic model (namely ISBA-CTRIP) as inputs to local hydrodynamic models (TELEMAC-2D) to issue forecasts of water level and flood extent. The uncertainties in the hydrological forcing and in friction parameters are reduced by an Ensemble Kalman Filter that jointly assimilates in-situ water levels and flood extent maps derived from remote sensing observations. The data assimilation framework is cycled in a real-time forecasting configuration. A cycle consists of a reanalysis and a forecast phase. Over the analysis, observations up to the present are assimilated. An ensemble is then initialized from the last analyzed states and issued forecasts for next 36 hr. Three strategies of forcing data for this forecast are investigated: (i) using CTRIP runoff for reanalysis and forecast, (ii) using observed discharge for analysis, then CTRIP runoff for forecast and (iii) using observed discharge for reanalysis and keep a persistent discharge value for forecast. It was shown that the data assimilation strategy provides a reliable reanalysis in hindcast mode. The combination of observed discharge and CTRIP runoff provides the most accurate results. For all strategies, the quality of the forecast decreases as the lead time increases. When the errors in CTRIP forcing are non-stationary, the forecast capability may be reduced. This work demonstrates that the forcing provided by a hydrologic model, while imperfect, can be efficiently used as input to a hydraulic model to issue reanalysis and forecasts, thanks to the assimilation of in-situ and remote sensing observations., Comment: 13 pages, 14 figures. Submitted to the IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

In spite of astonishing advances and developments in remote sensing technologies, meeting the spatio-temporal requirements for flood hydrodynamic modeling remains a great challenge for Earth Observation. The assimilation of multi-source remote sensing data in 2D hydrodynamic models participates to overcome such a challenge. The recently launched Surface Water and Ocean Topography (SWOT) wide-swath altimetry satellite provides a global coverage of water surface elevation at a high resolution. SWOT provides complementary observation to radar and optical images, increasing the opportunity to observe and monitor flood events. This research work focuses on the assimilation of 2D flood extent maps derived from Sentinel-1 C-SAR imagery data, and water surface elevation from SWOT as well as in-situ water level measurements. An Ensemble Kalman Filter (EnKF) with a joint state-parameter analysis is implemented on top of a 2D hydrodynamic TELEMAC-2D model to account for errors in roughness, input forcing and water depth in floodplain subdomains. The proposed strategy is carried out in an Observing System Simulation Experiment based on the 2021 flood event over the Garonne Marmandaise catchment. This work makes the most of the large volume of heterogeneous data from space for flood prediction in hindcast mode paves the way for nowcasting., Comment: Accepted for publication in IEEE 2024 International Geoscience & Remote Sensing Symposium (IGARSS 2024)

The challenges in operational flood forecasting lie in producing reliable forecasts given constrained computational resources and within processing times that are compatible with near-real-time forecasting. Flood hydrodynamic models exploit observed data from gauge networks, e.g. water surface elevation (WSE) and/or discharge that describe the forcing time-series at the upstream and lateral boundary conditions of the model. A chained hydrologic-hydraulic model is thus interesting to allow extended lead time forecasts and overcome the limits of forecast when using only observed gauge measurements. This research work focuses on comprehensively reducing the uncertainties in the model parameters, hydraulic state and especially the forcing data in order to improve the overall flood reanalysis and forecast performance. It aims at assimilating two main complementary EO data sources, namely in-situ WSE and SAR-derived flood extent observations., Comment: Copyright 2023 IEEE. Published in the IEEE 2023 International Geoscience & Remote Sensing Symposium (IGARSS 2023), scheduled for July 16 - 21, 2023 in Pasadena, California, USA

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., Comment: Copyright 2023 IEEE. Published in the IEEE 2023 International Geoscience & Remote Sensing Symposium (IGARSS 2023), scheduled for July 16 - 21, 2023 in Pasadena, California, USA. arXiv admin note: text overlap with arXiv:2304.01058

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., Comment: 19 pages, 13 figures. Submitted to the IEEE Transactions on Geoscience and Remote Sensing

Ensemble data assimilation in flood forecasting depends strongly on the density, frequency and statistics of errors associated with the observation network. This work focuses on the assimilation of 2D flood extent data, expressed in terms of wet surface ratio, in addition to the in-situ water level data. The objective is to improve the representation of the flood plain dynamics with a TELEMAC-2D model and an Ensemble Kalman Filter (EnKF). The EnKF control vector is composed of friction coefficients and corrective parameters to the input forcing. It is augmented with the water level state averaged over selected subdomains of the floodplain. This work focuses on the 2019 flood event that occurred over the Garonne Marmandaise catchment. The merits of assimilating SAR-derived flood plain data complementary to in-situ water level observations are shown in the control parameter and observation spaces with 1D and 2D assessment metrics. It was also shown that the assimilation of Wet surface Ratio in the flood plain complementary to in-situ data in the river bed brings significative improvement when a corrective term on flood plain hydraulic state is included in the control vector. Yet, it has barely no impact in the river bed that is sufficiently well described by in-situ data. We highlighted that the correction of the hydraulic state in the flood plain significantly improved the flood dynamics, especially during the recession. This proof-of-concept study paves the way towards near-real-time flood forecast, making the most of remote sensing-derived flood observations., Comment: 9 pages, 7 figures. Submitted to the 28th TELEMAC User Conference, 18-19 October 2022, Paris-Saclay, France. arXiv admin note: text overlap with arXiv:2205.08471

The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.

The aim of this paper is to investigate the numerical implementation of the Field Dislocation Mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy (2006) is recalled which permits to express the set of equations under the form of a static problem, corresponding to the determination of the local stress field for a given dislocation density distribution, complemented by an evolution problem, corresponding to the transport of the dislocation density. The static problem is solved using FFT-based techniques (Brenner et al., 2014). The main contribution of the present study is an efficient numerical scheme based on high resolution Godunov-type solvers to solve the evolution problem. Model problems of dislocation-mediated plasticity are finally considered in a simplified layer case. First, uncoupled problems with uniform velocity are considered, which permits to reproduce annihilation of dislocations and expansion of dislocation loops. Then, the FDM theory is applied to several problems of dislocation microstructures subjected to a mechanical loading.

The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically and statically admissible tensor fields, whose orthogonality and duality properties are recalled. These are endowed with specific energetic scalar products that make use of a reference and uniform elasticity tensor. The corresponding strain and stress Green's operators are introduced and interpreted as orthogonal projection operators in the admissibility spaces. In this context and as an alternative to classical minimum energy principles, two geometric variational principles are investigated with the introduction of functionals that aim at measuring the discrepancy of arbitrary test fields to the kinematic, static or material admissibility conditions of the problem. By relaxing the corresponding local equations, this study aims in particular at laying the groundwork for the homogenization of composites whose constitutive properties are only partially known or uncertain. The local fields in the composite and their macroscopic responses are computed through the minimization of the proposed geometric functionals. To do so, their gradients are computed using the Green's operators and gradient-based optimization schemes are discussed. A FFT-based implementation of these schemes is proposed and they are assessed numerically on a canonical example for which analytical solutions are available.

Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier space, and the constitutive law in real space. The methods correspond to series expansions of appropriate operators and to series expansions for the effective tensor as a function of the component moduli. It is shown that the singularity structure of this function can shed much light on the convergence properties of the iterative Fast Fourier Transform methods. We look at a model example of a square array of conducting square inclusions for which there is an exact formula for the effective conductivity (Obnosov). Theoretically some of the methods converge when the inclusions have zero or even negative conductivity. However, the numerics do not always confirm this extended range of convergence and show that accuracy is lost after relatively few iterations. There is little point in iterating beyond this. Accuracy improves when the grid size is reduced, showing that the discrepancy is linked to the discretization. Finally, it is shown that none of the three iterative schemes investigated over-performs the others for all possible microstructures and all contrasts., Comment: 41 pages, 14 figures, 1 table

We study an epidemic type change in innovations of a first order autoregressive process $ y_{n,k} = \varphi_n y_{n,k-1} + \epsilon_{k} + a_{n,k}$, where $\phi_n$ is either a constant in $(-1,1)$ or a sequence in $(0,1)$, converging to 1. For $k$ inside some unknown interval $\mathbb{I}_n^\ast=(k^\ast,k^\ast+\ell^\ast]$, $a_{n,k}=a_n$ while $a_{n,k}=0$ for $k$ outside $\mathbb{I}_n^\ast$. When $a_n\neq 0$, we have an epidemic deviation from the usual (zero) mean of innovations. Since innovations are not observed, we build uniform increments statistics on residuals $(\widehat{\epsilon}_k)$ of the process $y_{n,k}$. We assume that innovations $(\epsilon_k)$ are regularly varying with index $p \ge 2$ or satisfies integrability condition $\lim_{t \to \infty} t^p P(|\epsilon_1| > t) = 0$ for $p > 2$ and $E\epsilon_k^2 < \infty$ for $p=2$. We find the limit distributions of the tests under no change and prove consistency under short epidemics that is $\ell^\ast=O(n^\beta)$ for some $0<\beta\le 1/2$.