Search

Your search keyword '"Jerome Monnier"' showing total 53 results
Start Over Author "Jerome Monnier"
53 results on '"Jerome Monnier"'

1. A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission

Author

Michael Durand, Colin J. Gleason, Tamlin M. Pavelsky, Renato Prata De Moraes Frasson, Michael Turmon, Cédric H. David, Elizabeth H. Altenau, Nikki Tebaldi, Kevin Larnier, Jerome Monnier, Pierre Olivier Malaterre, Hind Oubanas, George H. Allen, Brian Astifan, Craig Brinkerhoff, Paul D. Bates, David Bjerklie, Stephen Coss, Robert Dudley, Luciana Fenoglio, Pierre-André Garambois, and Augusto Getirana

Subjects
Earth Resources and Remote Sensing, Meteorology and Climatology
Abstract

The Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products (available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two-thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage-constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.

Published
2023
Full Text
View/download PDF

2. A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission

Author

Michael Durand, Colin J. Gleason, Tamlin M. Pavelsky, Renato Prata de Moraes Frasson, Michael Turmon, Cédric H. David, Elizabeth H. Altenau, Nikki Tebaldi, Kevin Larnier, Jerome Monnier, Pierre Olivier Malaterre, Hind Oubanas, George H. Allen, Brian Astifan, Craig Brinkerhoff, Paul D. Bates, David Bjerklie, Stephen Coss, Robert Dudley, Luciana Fenoglio, Pierre‐André Garambois, Augusto Getirana, Peirong Lin, Steven A. Margulis, Pascal Matte, J. Toby Minear, Aggrey Muhebwa, Ming Pan, Daniel Peters, Ryan Riggs, Md Safat Sikder, Travis Simmons, Cassie Stuurman, Jay Taneja, Angelica Tarpanelli, Kerstin Schulze, Mohammad J. Tourian, Jida Wang, Ohio State University [Columbus] (OSU), School of Earth Sciences [Columbus], University of Massachusetts [Amherst] (UMass Amherst), University of Massachusetts System (UMASS), University of North Carolina [Chapel Hill] (UNC), University of North Carolina System (UNC), California Institute of Technology (CALTECH), CS Group - SI Toulouse [France] (C-S Group), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Gestion de l'Eau, Acteurs, Usages (UMR G-EAU), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Bureau de Recherches Géologiques et Minières (BRGM) (BRGM)-Institut de Recherche pour le Développement (IRD)-AgroParisTech-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut Agro Montpellier, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Virginia Polytechnic Institute and State University [Blacksburg], NOAA National Weather Service (NWS), University of Bristol [Bristol], U.S Geological Survey, Institut für Geodäsie und Geoinformationstechnik, Technical University of Berlin / Technische Universität Berlin (TU), Universität Bonn = University of Bonn, Risques, Ecosystèmes, Vulnérabilité, Environnement, Résilience (RECOVER), Aix Marseille Université (AMU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), NASA Goddard Space Flight Center (GSFC), Peking University [Beijing], Department of Civil and Environmental Engineering [UCLA - Los Angeles], University of California [Los Angeles] (UCLA), University of California (UC)-University of California (UC), Environment and Climate Change Canada, University of Colorado [Boulder], Kansas State University, University of California [San Diego] (UC San Diego), University of California (UC), Texas A&M University [College Station], California Institute of Technology, Pasadena, CA, 91125, USA, Research Institute for the Geo-Hydrological Protection, National Research Council (CNR), Perugia, and University of Stuttgart

Subjects
remote sensing, discharge, [SDE]Environmental Sciences, inverse problem, SWOT mission, hydrology, Water Science and Technology
Abstract

International audience; The Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products (available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two-thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage-constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.Plain Language Summary The Surface Water and Ocean Topography (SWOT) satellite mission was launched on 15 December 2022. SWOT is designed to produce estimates of river discharge on many rivers where no in situ discharge measurements are currently available. This paper describes how SWOT discharge estimates will be created, and their expected accuracy. SWOT discharge will be estimated using simple flow laws that combine SWOT measurements of river water elevation above sea level, river width, and river slope, with ancillary data such as river bathymetry. We expect that discharge uncertainty will be less than 30% for two-thirds of global reaches and will be dominated by a systematic bias. Temporal variations in river discharge time series are expected to be estimated within 15% for nearly all reaches, thus capturing the response of river discharge to rainfall and snowmelt events, including in basins that are currently ungaged, and providing a new capability for scientists to better track the flows of freshwater water through the Earth system.

Published
2023

3. Physically-constrained data-driven inversions to infer the bed topography beneath glaciers flows. Application to East Antarctica

Author

Jiamin Zhu, Jerome Monnier, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Laboratoire Jacques-Louis Lions (LJLL), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
surface data, 010504 meteorology & atmospheric sciences, Inverse transform sampling, [INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], 010502 geochemistry & geophysics, 01 natural sciences, bed inference, Data assimilation, topography, Interferometric synthetic aperture radar, Variational data assimilation, [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology, Computers in Earth Sciences, Conservation of mass, Physics::Atmospheric and Oceanic Physics, [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS], 0105 earth and related environmental sciences, reduced flow model, inference, geography, Hydrogeology, geography.geographical_feature_category, Elevation, deep learning, Glacier, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Geodesy, Computer Science Applications, Computational Mathematics, Computational Theory and Mathematics, Antarctica, glaciers, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Ice sheet, Geology
Abstract

A method for infering bed topography beneath glaciers from surface measurements (elevation from altimetry and velocity from InSAR) and sparse thickness measurements is developed and evaluated. The method is based on an original non-isothermal Reduced Uncertainty (RU) version of the Shallow Ice Approximation (SIA) equation that natively incorporates the surface measurements. The flow model has a single dimensionless multi-physics parameter γ. This parameter takes into account the basal slipperiness and the variable vertical rate factor profiles, thus the vertical thermal variations. The inversions are based on three steps involving: an Artificial Neural Network (ANN) and two Variational Data Assimilation (VDA) processes. The ANN-based stage aims at estimating the multi-physics number γ from the thickness measurements; the resulting estimator is remarkably robust. The full inversion method is valid for half-sheared flows (presenting a moderate basal slipperiness): it can be applied to inland ice-sheets areas. Also these estimates connect continuously with estimates from mass conservation only, i.e. with areas of sliding flows. Numerical results are presented for areas of the East Antarctica Ice Sheet where bed elevation can be very uncertain (Bedmap2 values). Estimates are valid for wavelengths longer than $\sim 10 \bar h$ (due to the long wave assumption, shallow flow model) with resolution at $\sim \bar h$ ( $\bar h$ a characteristic thickness value).

Published
2021

4. River discharge and bathymetry estimation from SWOT altimetry measurements

Author

Jerome Monnier, Jonas Verley, Pierre-André Garambois, and Kévin Larnier

Subjects
Meteorology, Discharge, Applied Mathematics, General Engineering, 010103 numerical & computational mathematics, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Hydrology (agriculture), Data assimilation, Bathymetry, Altimeter, 0101 mathematics, Data flow model, SWOT analysis, Inverse method, Geology
Abstract

An inverse method to estimate the discharge of rivers observed by satellite altimetry is developed and assessed. The flow model relies on the Saint-Venant equations combined with a dedicated algebr...

Published
2020

5. Exploring the Factors Controlling the Error Characteristics of the Surface Water and Ocean Topography Mission Discharge Estimates

Author

Peirong Lin, Pierre-André Garambois, Mark Hagemann, Renato Prata de Moraes Frasson, David M. Bjerklie, Konstantinos M. Andreadis, Kevin Larnier, Robert W. Dudley, Hind Oubanas, Michael Durand, Cédric H. David, Colin J. Gleason, Jerome Monnier, Tamlin M. Pavelsky, Pierre-Olivier Malaterre, C. B. Brinkerhoff, California Institute of Technology (CALTECH), Ohio State University [Columbus] (OSU), School of Earth Sciences [Columbus], CS Corporation, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), University of Massachusetts [Amherst] (UMass Amherst), University of Massachusetts System (UMASS), EAB: Education Technology, Services, and Research, Richmond, U.S Geological Survey, Gestion de l'Eau, Acteurs, Usages (UMR G-EAU), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut de Recherche pour le Développement (IRD)-AgroParisTech-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut Agro - Montpellier SupAgro, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Risques, Ecosystèmes, Vulnérabilité, Environnement, Résilience (RECOVER), Aix Marseille Université (AMU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Princeton University, University of North Carolina [Chapel Hill] (UNC), University of North Carolina System (UNC), and NASA SWOT Science Team funding (NNX16AH82G)

Subjects
[SDV]Life Sciences [q-bio], hydrology, Inverse problem, Ocean surface topography, remote sensing, Hydrology (agriculture), Remote sensing (archaeology), discharge, Environmental science, inverse problem, ZABR, Surface water, Water Science and Technology, Remote sensing
Abstract

International audience; The Surface Water and Ocean Topography (SWOT) satellite mission will measure river width, water surface elevation, and slope for rivers wider than 50–100 m. SWOT observations will enable estimation of river discharge by using simple flow laws such as the Manning-Strickler equation, complementing in situ streamgages. Several discharge inversion algorithms designed to compute unobserved flow law parameters (e.g., friction coefficient and bathymetry) have been proposed, but to date, a systematic assessment of factors controlling algorithm performance has not been conducted. Here, we assess the performance of the five algorithms that are expected to be used in the construction of the SWOT product. To perform this assessment, we used synthetic SWOT observations created with hydraulic model output corrupted with SWOT-like error. Prior information provided to the algorithms was purposefully limited to an estimate of mean annual flow (MAF), designed to produce a “worst case” benchmark. Prior MAF error was an important control on algorithm performance, but discharge estimates produced by the algorithms are less biased than the MAF; thus, the discharge algorithms improve on the prior. We show for the first time that accuracy and frequency of remote sensing observations are less important than prior bias, hydraulic variability among reaches, and flow law accuracy in governing discharge algorithm performance. The discharge errors and error sensitivities reported herein are a bounding benchmark, representing worst possible expected errors and error sensitivities. This study lays the groundwork to develop predictive power of algorithm performance, and thus map the global distribution of worst-case SWOT discharge accuracy.Measurements of river flow are essential for the allocation of water resources, flood and drought forecast and mitigation efforts, and others. Access to local measurements is not ubiquitous and is particularly difficult for rivers flowing in remote locations or across country borders. Measurements taken by satellites such as the upcoming Surface Water and Ocean Topography (SWOT) mission will offer freely available global data and methods to estimate discharge using such data have been in development. We conducted a comprehensive assessment of the accuracy and precision of five SWOT discharge inversion algorithms under three conditions: (a) ideal, that is if the measurements were available once a day and contained no error; (b) with no measurement error but changing how frequently the measurements were taken, and (c) under different levels of measurement error. We found that the methods consistently improved over the initial estimates of discharge and we identified river hydraulic properties that increase the chances of successful parameter estimation. We also found that despite the use of very similar discharge equations, the subtle differences in equations among the methods can be important. Finally, we found that at least two methods can work well with the expected amount of measurement error and frequency.

Published
2021

6. Inference of the bottom topography in anisothermal mildly-sheared shallow ice flows

Author

Jiamin Zhu, Jerome Monnier, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], [ SDU.STU.GL ] Sciences of the Universe [physics]/Earth Sciences/Glaciology, Computational Mechanics, General Physics and Astronomy, Geometry, 010103 numerical & computational mathematics, 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Data assimilation, Thermal, Interferometric synthetic aperture radar, Newtonian fluid, [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology, Gravimetry, 0101 mathematics, Mechanical Engineering, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], Inverse problem, Computer Science Applications, 010101 applied mathematics, Boundary layer, Mechanics of Materials, [ SPI.MECA.MEFL ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Geology, Dimensionless quantity
Abstract

This study proposes a new inverse method to estimate the bed topography elevation beneath glaciers flows from surface observations (altimetry elevations and InSAR velocities) and (very) sparse depth measurements (e.g. acquired during airborne campaigns). To do so an original form of depth-integrated flow equations (long-wave assumption) is derived. The latter are valid for highly to mildly-sheared regimes hence including moderately fast flows; varying internal thermal profiles are taken into account. The inverse problem is particularly challenging since the surface signatures integrate the bottom features (bed elevation and friction–slip amount) plus the internal deformation. The first key ingredient of the inverse method is the derivation of this non-isothermal Reduced Uncertainty (RU) version of the classical SIA equation (lubrication type model for generalised Newtonian fluids) by intrinsically integrating the surface measurements in the formulation. This resulting multi-physics RU-SIA equation contains a unique uncertain dimensionless parameter only (the parameter γ ). The next key ingredient is an advanced Variational Data Assimilation (VDA) formulation combined with a purely data-driven extension of γ based on the trend observed in the (sparse) depth measurements (e.g. along the flight tracks). The resulting inverse method provides the first physical-based depth estimations in mildly-sheared mildly-slippery shallow flows. In poorly monitored ice-sheet areas (e.g. in Antarctica), the resulting estimations are noticeably less uncertain than the current ones (in particular compared to those obtained by gravimetry inversions). The present numerical experiments and experimental sensitivity analyses demonstrate the reliability of this new RU-SIA equation and the robustness of the inverse method. In other respect, the RU-SIA equation may provide a-posteriori estimations of the thermal boundary layer at bottom.

Published
2019

7. Estimating River Discharge With Swath Altimetry: A Proof of Concept Using AirSWOT Observations

Author

Mark Hagemann, Michael Durand, Jerome Monnier, Pierre-André Garambois, Kévin Larnier, Mark A. Fonstad, S. Tuozzolo, Brandon T. Overstreet, Joseph F. Mangano, Renato Prata de Moraes Frasson, and Greg D. Lind

Subjects
Geophysics, Remote sensing (archaeology), Discharge, Proof of concept, General Earth and Planetary Sciences, Environmental science, Altimeter, Remote sensing
Published
2019

8. Double-scale diffusive wave model dedicated to spatial river observation and associated covariance kernel for variational data assimilation

Author

Jerome Monnier and Thibault Malou

Subjects
Wave model, Data assimilation, Scale (ratio), Kernel (statistics), Statistical physics, Covariance, Mathematics
Abstract

The spatial altimetry provides an important amount of water surface height data from multi-missions satellites (especially Jason-3, Sentinel-3A/B and the forthcoming NASA-CNES SWOT mission). To exploit at best the potential of spatial altimetry, the present study proposes on the derivation of a model adapted to spatial observations scale; a diffusive-wave type model but adapted to a double scale [1].Moreover, Green-like kernel can be employed to derived covariance operators, therefore they may provide an approximation of the covariance kernel of the background error in Variational Data Assimilation processes. Following the derivation of the aforementioned original flow model, we present the derivation of a Green kernel which provides an approximation of the covariance kernel of the background error for the bathymetry (i.e. the control variable) [2].This approximation of the covariance kernel is used to infer the bathymetry in the classical Saint-Venant’s (Shallow-Water) equations with better accuracy and faster convergence than if not introducing an adequate covariance operator [3].Moreover, this Green kernel helps to analyze the sensitivity of the double-scale diffusive waves (or even the Saint-Venant’s equations) with respect to the bathymetry.Numerical results are analyzed on real like datasets (derived from measurements of the Rio Negro, Amazonia basin).The double-scale diffusive wave provide more accurate results than the classical version. Next, in terms of inversions, the derived physically-based covariance operators enable to improve the inferences, compared to the usual exponential one.[1] T. Malou, J. Monnier "Double-scale diffusive wave equations dedicated to spatial river observations". In prep.[2] T. Malou, J. Monnier "Physically-based covariance kernel for variational data assimilation in spatial hydrology". In prep.[3] K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Inv. Pb. Sc. Eng (2020).

Published
2021

15. Hybrid Neural Network – Variational Data Assimilation algorithm to infer river discharges from SWOT-like data

Author

Kevin Larnier and Jerome Monnier

Subjects
Hybrid neural network, Data assimilation, Artificial neural network, Computer science, Bathymetry, Inversion (meteorology), Altimeter, Algebraic number, Inverse problem, Algorithm, Physics::Atmospheric and Oceanic Physics, Physics::Geophysics
Abstract

A new algorithm to estimate river discharges from altimetry measurements only is designed. A first estimation is obtained by an artificial neural network trained from the altimetry large scale water surface measurements plus drainage area information. The combination of this purely data-based estimation and a dedicated algebraic flow model provides a first physically-consistent estimation. The latter is next employed as the first guess of an advanced variational data assimilation formulation. The final estimation is highly accurate for rivers presenting features within the learning partition; for rivers far outside the learning partition, the space-time variations of discharge remain accurately approximated however the global estimation presents a potential bias. Indeed, it is shown that if the estimation is based on the hydrodynamics models only, the inverse problem may be well-defined but up to a bias only (the bias scales the global estimation). This bias is removed thanks to the ANN but for rivers in the learning partition only. For rivers outside the learning partition, any mean value (eg. annual, seasonal) enables to remove the bias. Finally, the present hybrid and hierarchical inversion strategy seems to provide much more accurate estimations compared to the state-of-the-art for the considered 29 heterogeneous river portions.

Published
2020

16. Discharge and bathymetry estimations of rivers from altimetry and datasets by hybrid computational methods

Author

Kevin Larnier, Pierre-André Garambois, and Jerome Monnier

Subjects
Bathymetry, Altimeter, Geology, Remote sensing
Abstract

We present the Hierarchical Variational Discharge Inference (HiVDI) algorithm [1,2] and its capabilities to estimate the discharge and bathymetry of rivers from altimetry measurement, more particularly from the forthcoming SWOT space mission. The last version algorithm is based on hierarchical flow models and hybrid computational approaches : 1) a dedicated satellite-scale low-complexity model relating the discharge Q(x,t), the bathymetry b(x) and the friction parameter K [2]; 2) an advanced Variational Data Assimilation (VDA) formulation based on a relatively complete physics (Saint-Venant’s equations) [2,4] ; 3) deep neural networks based estimations obtained from recently enriched databases [1]. The resulting algorithm turns out to be robust and relatively accurate. Passed the assimilation of a hydrological cycle (~ 1 year variations, considered as a “learning period) the identified parameters (b(x), K) are identified; next given newly acquired satellite measurements, the low complexity model enables to estimate Q(x,t) in real-time [1,2].Numerical results on numerous river datasets are analyzed in detail including for relatively complex flows and multi-satellite datasets [1,2,3].References[1] K. Larnier, J. Monnier. "Hybrid data assimilation - deep learning approaches to estimate rivers discharges from altimetry". Submitted.[2] K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Revised (nov. 2019).[3] P.-A. Garambois, K. Larnier, J. Monnier, P. Finaud-Guyot, J. Verley, A. Montazem, S. Calmant. "Variational inference of effective channel and ungauged anabranching river discharge from multi-satellite water heights of different spatial sparsity". J. of Hydrology 2019.[4] P. Brisset, J. Monnier, P.-A. Garambois, H. Roux. "On the assimilation of altimetry data in 1D Saint-Venant river models". Adv. Water Ress. 2018. [5] "DassFlow: Data Assimilation for Free Surface Flows", open-source computational software. INSA - IMT, CNRS, CNES, CS group. http://www.math.univ-toulouse.fr/DassFlow

Published
2020

17. Estimation of Inflows and Effective Channel from Satellite Observations: From Local to Hydrographic Network Scale

Author

Kévin Larnier, Sylvain Biancamaria, Jerome Monnier, Daniel Medeiros Moreira, Stéphane Calmant, Léo Pujol, Pascal Finaud-Guyot, Pierre-André Garambois, Robert Mosé, and Adrien Paris

Subjects
Estimation, Meteorology, Scale (ratio), Environmental science, Satellite, Hydrographic network, Communication channel
Abstract

With the upcoming SWOT satellite mission, which should provide spatially dense river surface elevations, widths and slopes observations globally, comes the need to pertinently use such data into hydrodynamic models, from the reach to hydrographic network scales. Based on the HiVDI (Hierarchical Variational Discharge Inversion) modeling strategy ([1,2], DassFlow software1), this work tackles the forward and inverse modeling capabilities of distributed channel parameters and inflows (in the 1D Saint-Venant model) from multisatellite observations of river surface. Several synthetic cases are designed to study fluvial and torrential flows signatures and assess the inference capabilities of model parameters (inflows, bathymetry, friction) given different observation patterns. Accurate inferences of both inflows and distributed channel parameters (bathymetry-friction) is achievable even with a minimum spatial observability between inflows. A sensitivity analysis of the inferences to prior hydraulic parameter values and to regularization parameters is performed. Next a real case is studied: 871km of the Negro river (Amazon basin) including complex multichannel reaches, 21 tributaries and backwater controls from major confluences. An effective modeling approach is proposed using (i) WS elevations from ENVISAT observations and dense in situ GPS flow lines, (ii) average river top widths from optical imagery, (iii) upstream and lateral flows from the MGB large-scale hydrological model [3]. The calibrated effective hydraulic model closely fits satellite altimetry observations of WS signatures and contains real-like spatial variabilities and flood wave propagations (frequential features analyzed with identifiability maps [2]). Synthetic SWOT observations are generated from the simulated flowlines and the identifiability of model parameters (579 bathymetry points, 17 friction patches and 22 upstream and lateral hydrographs) is tested using the HiVDI computational inverse method and given hydraulically coherent prior guesses and regularization parameter values. Inferences of channel parameters carried out on this fine hydraulic model applied at large scale give satisfying results considering the challenging inverse problems solved globally in space and time, even with noisy SWOT data. Inferences of spatially distributed temporal parameters (lateral inflows) give satisfying results as well, with even small scale hydrograph variations being infered accurately. This study brings insights in: the hydraulic visibility of multiple inflows hydrographs signature at large scale with SWOT; the simultaneous identifiability of spatially distributed channel parameters and inflows by assimilation of satellite altimetry data; the need to further taylor and scale hydrodynamic models and assimilation methods to improve potential information feedbacks to hydrological modules in integrated chains. References: [1] Larnier, Monnier, Garambois, Verley. (2019) River discharge and bathymetry estimations from SWOT altimetry measurements.[2] Brisset, Monnier, Garambois, Roux. (2018) On the assimilation of altimetric data in 1d Saint-Venant river flow models. AWR, doi: 10.1016/j.advwatres.2018.06.004.[3] Paiva, Buarque, Collischonn, et al. Large-scale hydrologic and hydrodynamic modeling of the amazon river basin. WRR, doi: 10.1002/wrcr.20067.

Published
2020

18. Variational estimation of effective channel and ungauged anabranching river discharge from multi-satellite water heights of different spatial sparsity

Author

Pierre-André Garambois, Pascal Finaud-Guyot, Jonas Verley, Jerome Monnier, Kévin Larnier, Amanda Samine Montazem, Stéphane Calmant, Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA), Risques, Ecosystèmes, Vulnérabilité, Environnement, Résilience (RECOVER), Aix Marseille Université (AMU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES), Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Littoral, Environment: MOdels and Numerics (LEMON), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'études en Géophysique et océanographie spatiales (LEGOS), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), and Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)

Subjects
010504 meteorology & atmospheric sciences, Flow (psychology), 0207 environmental engineering, Hydrograph, 02 engineering and technology, Hydraulic visibility, 01 natural sciences, Piecewise linear function, Anabranching river, Bathymetry, Satellite altimetry, Time series, 020701 environmental engineering, Geomorphology, Scaling, 0105 earth and related environmental sciences, Water Science and Technology, Variational assimilation, Discharge, [SDE.IE]Environmental Sciences/Environmental Engineering, [PHYS.MECA]Physics [physics]/Mechanics [physics], Inverse problem, SWOT, 6. Clean water, Ungauged river, 13. Climate action, 1D hydraulic model, Geology
Abstract

Multi-satellite sensing of continental water surfaces (WS) represents an unprecedented and increasing potential for studying ungauged hydrological and hydraulic processes from their signatures, especially on complex flow zones such as anabranching rivers. However the estimation of discharge from WS observations only is a very challenging, ill-posed, inverse problem due to unknown bathymetry and friction in ungauged rivers, measurements nature, quality and spatio-temporal resolutions regarding the flow (model) scales. This paper proposes an effective 1D hydraulic modeling approach of sufficient complexity to describe anabranching river flows from sparse multisatellite observations using the HiVDI inverse method presented in Larnier et al. (2019) with an augmented control vector including a spatially distributed friction law K ( x , h ) depending on the flow depth h. It is shown on 71 km of the Xingu River (anabranching, Amazon basin) with altimetric water height timeseries that a fairly accurate upstream discharge hydrograph and effective patterns of channel bathymetry and friction can be inferred simultaneously. The coherence between the sparse observation grid and the fine hydraulic model grid is ensured in the optimization process by imposing a piecewise linear bathymetry profile b ( x ) , which is consistent with the hydraulic visibility ofWS signatures (Garambois et al., 2017; Montazem et al., 2019). The discharge hydrograph Q(t) at observation times and effective bathymetry-friction b ( x ) , K ( x , h ) patterns are retrieved from 8 years of satellite altimetry (ENVISAT) at 6 virtual stations (VS) along flow. Next, the potential of the forthcoming SWOT data, dense in space, is highlighted by inferring a discharge hydrograph and dense patterns of effective river bathymetry and friction; a physically consistent scaling of friction by reaches enables to consider more dense bathymetry controls. Finally a numerical analysis shows: (i) the importance of an unbiased prior information in the inference of a triplet Q , b ( x ) , K ( x , h ) from WS observations; (ii) the clear signatures of river bottom slope break in low flows and width variations in high flows, through the analysis of the friction slope term, which is consistent with the findings of Montazem et al. (2019) from WS curvature analysis.

Published
2020

19. Generation and analysis of stage-fall-discharge laws from coupled hydrological-hydraulic river network model integrating sparse multi-satellite data

Author

Adrien Paris, Kévin Larnier, Pierre-André Garambois, T. Malou, Jerome Monnier, Risques, Ecosystèmes, Vulnérabilité, Environnement, Résilience (RECOVER), Aix Marseille Université (AMU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), ANRT, Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Collecte Localisation Satellites (CLS), Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Centre National d'Études Spatiales [Toulouse] (CNES), and OceanNext

Subjects
River networks, 010504 meteorology & atmospheric sciences, [SDE.IE]Environmental Sciences/Environmental Engineering, Stage-fall-discharge laws, 0207 environmental engineering, Sampling (statistics), 02 engineering and technology, 01 natural sciences, 6. Clean water, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Current (stream), Data assimilation, Multisatellite altimetry, Law, Nadir, Bathymetry, Variational data assimilation, Stage (hydrology), Altimeter, Hydrological-hydraulic modeling, 020701 environmental engineering, Visibility, Geology, 0105 earth and related environmental sciences, Water Science and Technology
Abstract

Current and forthcoming altimetry satellites provide increasing hydraulic visibility of river surface variabilities. However, due to unobservable river bathymetry and friction, as well as the sampling and quality of remote sensing data, discharge estimation remains a challenging problem. This paper proposes a new rigorous methodology to estimate stage-fall-discharge laws at any point of a hydrographic network including backwater affected reaches. This methodology is adapted to operational estimation of discharge from multi-mission satellite altimetry data. The cornerstone of the method is to take advantage of meaningful hydraulic signatures, including water surface slopes, simulated by a river network model optimally combined with multi-satellite noisy observations. This optimal combination of heterogeneous multi-source data with a river network model is achieved through variational data assimilation performed using the DassFlow-HiVDI hydraulic model inflowed by MGB regional hydrological model. It is newly applied to the large and complex Negro-Branco River network in the Amazon basin. An effective model is obtained by variational calibration using Jason-3 and Sentinel-3A and -3B altimetry observations between February 2016 and May 2019. A fairly good fit bellow 1 m for 80 % of the altimetric observations is obtained. Using this hydrodynamic model as a fine spatio-temporal extrapolator of hydraulic quantities, and in particular of multi-scale water surface slope signatures, the parameters of a general SFD law, as well as the uncertainties estimations, can be constrained at any location within the river network domain using a Bayesian optimization method. This methodology is tested over 4 virtual stations representing various hydraulic complexities. Accurate discharge estimates and meaningful SFD parameters are obtained compared to those of the reference low Froude model at these locations. Analyses are also performed on a reference case with fine-scale bathymetry data of the Garonne River, France. The strength of the method lies in its applicability to noisy multi-satellite data while ensuring physical consistency. It should be applicable in real time to any river basin, using nadir altimetry only or combined to the forthcoming SWOT satellite data. Moreover, the method allows to take full advantage, via the hydrodynamic model, of variable water masks observations and physical segmentations of river networks. The method is implemented in the open source hydrodynamic data assimilation platform DassFlow.

Published
2021

20. Hydraulic visibility: Using satellite altimetry to parameterize a hydraulic model of an ungauged reach of a braided river

Author

Amanda Samine Montazem, Pierre-André Garambois, Pascal Finaud-Guyot, Stéphane Calmant, Joecila Santos da Silva, Hélène Roux, Jerome Monnier, and Adrien Paris

Subjects
Hydrology, geography, geography.geographical_feature_category, 010504 meteorology & atmospheric sciences, Water flow, Hydraulics, 0208 environmental biotechnology, 02 engineering and technology, Sciences de l'ingénieur [physics]/Autre, 01 natural sciences, 6. Clean water, 020801 environmental engineering, Water level, law.invention, Current (stream), Ocean surface topography, law, Tributary, Bathymetry, Surface water, Geomorphology, Geology, 0105 earth and related environmental sciences, Water Science and Technology
Abstract

What hydraulic information can be gained from remotely sensed observations of a river's surface? In this study, we analyze the relationship between river bed undulations and water surfaces for an ungauged reach of the Xingu River, a first‐order tributary of the Amazon river. This braided reach is crosscut more than 10 times by a ENVISAT (ENVironmental SATellite) track that extends over 100 km. Rating curves based on a modeled discharge series and altimetric measurements are used, including the zero‐flow depth Z0 parameter, which describes river's bathymetry. River widths are determined from JERS (Japanese Earth Ressources Satellite) images. Hydrodynamic laws predict that irregularities in the geometry of a river bed produce spatial and temporal variations in the water level, as well as in its slope. Observation of these changes is a goal of the Surface Water and Ocean Topography satellite mission, which has a final objective of determining river discharge. First, the concept of hydraulic visibility is introduced, and the seasonality of water surface slope is highlighted along with different flow regimes and reach behaviors. Then, we propose a new single‐thread effective hydraulic approach for modeling braided rivers flows, based on the observation scales of current satellite altimetry. The effective hydraulic model is able to reproduce water surface elevations derived by satellite altimetry, and it shows that hydrodynamical signatures are more visible in areas where the river bed morphology varies significantly and for reaches with strong downstream control. The results of this study suggest that longitudinal variations of the slope might be an interesting criteria for the analysis of river segmentation into elementary reaches for the Surface Water Ocean Topography mission that will provide continuous measurements of the water surface elevations, the slopes, and the reach widths.

Published
2016

21. Wavelet‐Based River Segmentation Using Hydraulic Control‐Preserving Water Surface Elevation Profile Properties

Author

Pascal Finaud-Guyot, A. Samine Montazem, Stéphane Calmant, D. Medeiros Moreira, J. T. Minear, Pierre-André Garambois, Jerome Monnier, Sylvain Biancamaria, Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), GOHS, Laboratoire d'études en Géophysique et océanographie spatiales (LEGOS), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées, and Finaud-Guyot, Pascal

Subjects
Surface (mathematics), Hydraulic control, 010504 meteorology & atmospheric sciences, 0207 environmental engineering, Elevation, 02 engineering and technology, 01 natural sciences, 6. Clean water, [SDU] Sciences of the Universe [physics], Geophysics, Wavelet, [SDU]Sciences of the Universe [physics], [SDU.STU.HY] Sciences of the Universe [physics]/Earth Sciences/Hydrology, General Earth and Planetary Sciences, Segmentation, [SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology, 020701 environmental engineering, Geomorphology, Geology, ComputingMilieux_MISCELLANEOUS, 0105 earth and related environmental sciences
Abstract

International audience

Published
2019

22. Multi-regime shallow free surface laminar flow models for quasi-Newtonian fluids

Author

Jean-Paul Vila, Marc Boutounet, and Jerome Monnier

Subjects
Physics, Coordinate system, Prandtl number, General Physics and Astronomy, Laminar flow, Slip (materials science), Mechanics, 01 natural sciences, Power law, 010305 fluids & plasmas, Physics::Fluid Dynamics, 010101 applied mathematics, symbols.namesake, Free surface, 0103 physical sciences, Newtonian fluid, symbols, Boundary value problem, 0101 mathematics, Mathematical Physics
Abstract

The mathematical modeling of thin free-surface laminar flows for quasi-Newtonian fluids (power-law rheology) is addressed with a particular attention to geophysical flows (e.g. ice or lava flows). Asymptotic thin-layer flow models (one-equation and two-equation models) consistent with various viscous regimes, corresponding to different basal boundary conditions (from adherence to pure slip), are derived. The challenge being to derive models consistent from slip to no-slip basal boundary condition, though at the price of balancing small friction by small mean slope. Starting from reference flows (the steady-state uniform ones) corresponding to different shear regimes, the exact expressions of all fields $(\bsigma, \bu, p)$ are calculated formally by a perturbation expansion method. The calculations are such that all field expressions remain valid for any laminar viscous regimes. The calculations are presented either in a mean slope coordinate system with local variations of the topography or in the Prandtl coordinate system, hence valid in presence of any non flat basal topography. Formal error estimates proving the consistency of the derivations are stated. An unified one-equation model (lubrication type in the depth variable $h$) is derived at order $1$. Next, few unified two-equation models in variable $(q,h)$ (shallow water type) are stated and discussed. The classical first order models from the literature are recovered if considering the corresponding particular cases (generally, flat bottom with a particular regime and/or specific basal boundary condition). Two one-dimensional numerical examples illustrate the robustness of these new multi-regime formulations (the change of flow regimes being due either to a sharp change of the mean-slope topography or to a sharp change of basal boundary condition).

Published
2016

23. On the assimilation of altimetric data in 1D Saint-Venant river flow models

Author

Hélène Roux, Jerome Monnier, Pierre Brisset, Pierre-André Garambois, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Matériaux et nanosciences d'Alsace, Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Strasbourg (UNISTRA), Institut de mécanique des fluides de Toulouse (IMFT), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole Nationale du Génie de l'Eau et de l'Environnement de Strasbourg - ENGEES (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE), Institut National des Sciences Appliquées de Strasbourg - INSA (FRANCE), Université de Strasbourg - UNISTRA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), CNES Tosca, Monnier, Jerome, Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées, Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
010504 meteorology & atmospheric sciences, Saint-Venant, Mécanique des fluides, River flow, 0208 environmental biotechnology, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 02 engineering and technology, Inflow, Residual, 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Data assimilation, Strickler, Streamflow, Variational data assimilation, [SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology, Manning, Hydrologie, 0105 earth and related environmental sciences, Water Science and Technology, Elevation, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Inverse problem, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], SWOT, Geodesy, 6. Clean water, 020801 environmental engineering, Ocean surface topography, [SDU.STU.HY] Sciences of the Universe [physics]/Earth Sciences/Hydrology, Identifiability, Discharge, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Altimetry, Geology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; Given altimetry measurements, the identification capability of time varying inflow dischargeQin(t)and13the Strickler coefficientK(defined as a power-law inhthe water depth) of the 1D river Saint-Venant model is investi-14gated. Various altimetry satellite missions provide water level elevation measurements of wide rivers, in particular the15future Surface Water and Ocean Topography (SWOT) mission. An original and synthetic reading of all the available16information (data, wave propagation and the Manning-Strickler’s law residual) are represented on the so-callediden-17tifiability map.The latter provides in the space-time plane a comprehensive overview of the inverse problem features.18Inferences based on Variational Data Assimilation (VDA) are investigated at the limit of the data-model inversion19capability : relatively short river portions, relatively infrequent observations, that is inverse problems presenting a20lowidentifiability index. The inflow dischargeQin(t)is infered simultaneously with the varying coefficientK(h). The21bed level is either given or infered from a lower complexity model. The experiments and analysis are conducted for22different scenarios (SWOT-like or multi-sensors-like). The scenarios differ by the observation frequency and by the23identifiability index. Sensitivity analyses with respect to the observation errors and to the first guess values demon-24strate the robustness of the VDA inferences. Finally this study aiming at fusing relatively sparse altimetric data and25the 1D Saint-Venant river flow model highlights the spatiotemporal resolution lower limit, also the great potential in26terms of discharge inference including for a single river reach.

Published
2018

24. Inference of effective river properties from remotely sensed observations of water surface

Author

Jerome Monnier and Pierre-André Garambois

Subjects
symbols.namesake, Ocean surface topography, Observational error, Temporal resolution, Froude number, symbols, Elevation, Inverse, Bathymetry, Geodesy, Surface water, Water Science and Technology, Remote sensing
Abstract

The future SWOT mission (Surface Water and Ocean Topography) will provide cartographic measurements of inland water surfaces (elevation, widths and slope) at an unprecedented spatial and temporal resolution. Given SWOT like synthetic data, hierarchical-complexity forward flow models are revisited, then few inverse formulations allowing to infer the river low flow bathymetry, roughness and discharge (A_{0},K,Q) are derived and assessed. The concept of an effective low flow bathymetry A_{0} (the real one being never observed), hence an effective river dynamics description, is introduced. The few inverse models elaborated for inferring (A_{0},K,Q) are analyzed in two contexts: 1) remotely sensed observations of the water surface (surface elevation, width and slope) only are available ; 2) one additional water depth measurement (or estimate) is available. The inverse models elaborated are independent of data acquisition dynamics; they are assessed on 91 synthetic test cases sampling a wide range of steady-state river flows (the Froude number varying between 0.05 and 0.5 for 1 km reaches) and in the case of a flood on the Garonne River (France) characterized by large spatio-temporal variabilities. It is demonstrated that the most complete shallow-water like model which allows to separate the roughness and bathymetry terms is the so-called low Froude model. In Case 1), the resulting RMSE on the inferred discharges are on the order of 15\% for first guess errors larger than 50\% . An important feature of the present inverse methods is the fairly good accuracy of the discharge Q obtained, while the identified roughness coefficient K includes the measurement errors and the misfit of physics between the real flow and the inverse models hypothesis; the later neglecting the unobserved temporal variations of the flow and the inertia effects. A compensation phenomena between the identified values of K and the unobserved bathymetry A_{0} is highlighted, while the present inverse models lead to an effective river dynamics model accurate in the range of the discharge variability observed. In Case 2), the effective bathymetry profile for 80 km of the Garonne River is retrieved with 1\% relative error only. Next, accurate effective topography-friction pairs and also discharge can be inferred. Finally, defining river reaches from the observation grid averages the river properties in each reach, hence tends to smooth the hydraulic variability.

Published
2015

25. Inverse algorithms for 2D shallow water equations in presence of wet dry fronts. Application to flood plain dynamics

Author

Jerome Monnier, Denis Dartus, Ronan Madec, Jean-Paul Vila, Frédéric Couderc, Kévin Larnier, Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ), Centre National de la Recherche Scientifique ( CNRS ), Institut National Polytechnique [Toulouse] ( INP ), Institut de mécanique des fluides de Toulouse ( IMFT ), Institut National Polytechnique [Toulouse] ( INP ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Institut de mécanique des fluides de Toulouse (IMFT), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT), and Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP)

Subjects
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], 010504 meteorology & atmospheric sciences, Floodplain, variational data assimilation, Inverse, 010103 numerical & computational mathematics, Inflow, 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Data assimilation, Sensitivity (control systems), 2D shallow water, flood plain, 0101 mathematics, Shallow water equations, Physics::Atmospheric and Oceanic Physics, 0105 earth and related environmental sciences, Water Science and Technology, geography, Finite volume method, geography.geographical_feature_category, wet-dry front, Front (oceanography), [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], sensitivity, [ SPI.MECA.MEFL ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Algorithm, finite volume, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Geology, [ SDE.ES ] Environmental Sciences/Environmental and Society
Abstract

International audience; The 2D shallow water equations adequately model some geophysical flows with wet-dry fronts (e.g. flood plain or tidal flows); nevertheless deriving ac- curate, robust and conservative numerical schemes for dynamic wet-dry fronts over complex topographies remains a challenge. Furthermore for these flows, data are generally complex, multi-scale and uncertain. Robust variational in- verse algorithms, providing sensitivity maps and data assimilation processes may contribute to breakthrough shallow wet-dry front dynamics modelling. The present study aims at deriving an accurate, positive and stable finite vol- ume scheme in presence of dynamic wet-dry fronts, and some corresponding inverse computational algorithms (variational approach). The schemes and algorithms are assessed on classical and original benchmarks plus a real flood plain test case (Lèze river, France). Original sensitivity maps with respect to the (friction, topography) pair are performed and discussed. The iden- tification of inflow discharges (time series) or friction coefficients (spatially distributed parameters) demonstrate the algorithms efficiency.

Published
2016

26. An intercomparison of remote sensing river discharge estimation algorithms from measurements of river height, width, and slope

Author

Brett F. Sanders, Michael Durand, Jerome Monnier, Micah Mukolwe, John W. Fulton, Ernesto Rodriguez, Nicole Goutal, Paul D. Bates, Faisal Hossain, David M. Bjerklie, Tamlin M. Pavelsky, E. Humphries, Guy Schumann, Jochen E. Schubert, Hélène Roux, J. M. Fiset, J. T. Minear, Renato Prata de Moraes Frasson, Laurence C. Smith, Pierre-André Garambois, Jeffrey Neal, Sophie Ricci, Xiao-Ming Chen, G. Di Baldassarre, Colin J. Gleason, Nicolas Flipo, Lauriane Vilmin, Ohio State University [Columbus] (OSU), University of Massachusetts [Amherst] (UMass Amherst), University of Massachusetts System (UMASS), Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Connecticut Water Science Center, United States Geological Survey [Reston] (USGS), University of Southern California (USC), Institut de mécanique des fluides de Toulouse (IMFT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), Jet Propulsion Laboratory (JPL), NASA-California Institute of Technology (CALTECH), School of Geographical Sciences [Bristol], University of Bristol [Bristol], University of North Carolina [Chapel Hill] (UNC), University of North Carolina System (UNC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), NWS Ohio River Forecast Center, NOAA National Weather Service (NWS), Department of Earth Sciences [Uppsala], Uppsala University, Environment Canada, Centre de Géosciences (GEOSCIENCES), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), US Geological Survey [Lakewood], Laboratoire National d’Hydraulique et Environnement (EDF R&D LNHE), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Department of Civil and Environmental Engineering, University of Washington [Seattle], US Geological Survey [Golden], Institute for Water Education (UNESCO–IHE), Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), University of California [Irvine] (UC Irvine), University of California (UC), Milieux Environnementaux, Transferts et Interactions dans les hydrosystèmes et les Sols (METIS), Université Pierre et Marie Curie - Paris 6 (UPMC)-École Pratique des Hautes Études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées, Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique - CERFACS (CERFACS), Université Pierre et Marie Curie - Paris 6 (UPMC)-École pratique des hautes études (EPHE), Nalon, Pascale, Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), MINES ParisTech - École nationale supérieure des mines de Paris, CERFACS, University of California [Irvine] (UCI), University of California, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), non-UU output of UU-AW members, and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Environmental Engineering, 010504 meteorology & atmospheric sciences, Meteorology, Mécanique des fluides, 0208 environmental biotechnology, Bioengineering, 02 engineering and technology, Sciences de l'ingénieur [physics]/Autre, 01 natural sciences, Civil Engineering, Standard deviation, Physical Geography and Environmental Geoscience, Range (statistics), SWOT mission, remote sensing of rivers, Remote sensing discharge, [SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology, 0105 earth and related environmental sciences, Water Science and Technology, Remote sensing, Hydrology, Discharge, [SDE.IE]Environmental Sciences/Environmental Engineering, discharge algorithms, SWOT, 6. Clean water, 020801 environmental engineering, Ancillary data, Water resources, Ocean surface topography, 13. Climate action, [SDU.STU.HY] Sciences of the Universe [physics]/Earth Sciences/Hydrology, Environmental science, Satellite, [SDE.IE] Environmental Sciences/Environmental Engineering, Algorithm, Surface water
Abstract

International audience; The Surface Water and Ocean Topography (SWOT) satellite mission planned for launch in 2020 will map river elevations and inundated area globally for rivers >100 m wide. In advance of this launch, we here evaluated the possibility of estimating discharge in ungauged rivers using synthetic, daily ‘‘remote sensing’’ measurements derived from hydraulic models corrupted with minimal observational errors. Five discharge algorithms were evaluated, as well as the median of the five, for 19 rivers spanning a range of hydraulic and geomorphic conditions. Reliance upon a priori information, and thus applicability to truly ungauged reaches, varied among algorithms: one algorithm employed only global limits on velocity and depth, while the other algorithms relied on globally available prior estimates of discharge. We found at least one algorithm able to estimate instantaneous discharge to within 35% relative root-mean-squared error (RRMSE) on 14/16 nonbraided rivers despite out-of-bank flows, multichannel planforms, and backwater effects. Moreover, we found RRMSE was often dominated by bias; the median standard deviation of relativeresiduals across the 16 nonbraided rivers was only 12.5%. SWOT discharge algorithm progress is therefore encouraging, yet future efforts should consider incorporating ancillary data or multialgorithm synergy to improve results.

Published
2016

27. Assimilation of spatially distributed water levels into a shallow-water flood model. Part I: Mathematical method and test case

Author

Jerome Monnier, Xijun Lai, Nanjing Institute of Geography and Limnology (Niglas), Chinese Academy of Sciences [Beijing] (CAS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Parameter identification, 010504 meteorology & atmospheric sciences, 0207 environmental engineering, 02 engineering and technology, Inflow, 01 natural sciences, Shallow water equations, Data assimilation, Hydrology (agriculture), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Satellite imagery, 020701 environmental engineering, 0105 earth and related environmental sciences, Water Science and Technology, Remote sensing, Satellite image, Flood myth, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDE.ES]Environmental Sciences/Environmental and Society, Water level, Temporal strategy, Waves and shallow water, Variational data assimilation (4D-var), 13. Climate action, Environmental science, Flood model, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Recent applications of remote sensing techniques produce rich spatially distributed observations for flood monitoring. In order to improve numerical flood prediction, we have developed a variational data assimilation method (4D-var) that combines remote sensing data (spatially distributed water levels extracted from spatial images) and a 2D shallow water model. In the present paper (part I), we demon- strate the efficiency of the method with a test case. First, we assimilated a single fully observed water level image to identify time-independent parameters (e.g. Manning coefficients and initial conditions) and time-dependent parameters (e.g. inflow). Second, we combined incomplete observations (a time ser- ies of water elevations at certain points and one partial image). This last configuration was very similar to the real case we analyze in a forthcoming paper (part II). In addition, a temporal strategy with time over- lapping is suggested to decrease the amount of memory required for long-duration simulation.

Published
2009

28. Inference of the bottom properties in shallow ice approximation models

Author

Jerome Monnier and P.-E Des Boscs

Subjects
010504 meteorology & atmospheric sciences, Scale (ratio), Field (physics), Applied Mathematics, Mathematical analysis, Geodesy, Optimal control, 01 natural sciences, Computer Science Applications, Theoretical Computer Science, 010101 applied mathematics, Data assimilation, Generalized Newtonian fluid, Signal Processing, Measured depth, Lubrication, Slip ratio, 0101 mathematics, Mathematical Physics, 0105 earth and related environmental sciences, Mathematics
Abstract

This study proposes a new inverse method to infer the bottom topography and the friction coe cient in the Shallow Ice Approximation (SIA) models (lubrication type models for generalized Newtonian fluid flows). The method is based on the definition of three sub-regimes and an a-priori slip ratio law. Next, explicit calculations 10 provide a first depth estimation for each sub-regime, and this first estimation can be improved by solving an elliptic linear-quadratic optimal control problem (variational assimilation of the surface measurements e.g. by satellite). The friction field is a by-product of the depth inverse method, it can be explicitly deduced. The numerical results performed on multi-regime numerical flows demonstrate the robustness of the method even in presence of uncertain surface measurements and independently of the depth measurement locations (on contrary 15 if inverting the regularized depth-averaged mass equation only). Moreover the few derived depth estimations make possible to determine the adequate slope scale in the SIA models.

Published
2017

29. Inverse rheometry and basal properties inference for pseudoplastic geophysical flows

Author

Nathan Martin, Jerome Monnier, Jet Propulsion Laboratory (JPL), NASA-California Institute of Technology (CALTECH), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)

Subjects
Power-law fluid, Parameter identification, Constitutive equation, General Physics and Astronomy, Inverse, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, Slip (materials science), Non-linear sliding, Physics::Fluid Dynamics, [SDU.STU.VO]Sciences of the Universe [physics]/Earth Sciences/Volcanology, [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Mathematical Physics, Mathematics, Shear thinning, Augmented Lagrangian, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Rheometry, Automatic differentiation, Geophysics, Mechanics, Non-Newtonian fluid, Exponent, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Sensitivity analysis, Power-law fluid, Non-linear sliding, Sensitivity analysis, Parameter identification, Augmented Lagrangian, Automatic differentiation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

The present work addresses the question of performing inverse rheometry and basal properties inference for pseudoplastic gravity-driven free-surface flows at low Reynolds’ number. The modeling of these flows involves several parameters, such as the rheological ones or the state of the basal boundary (modeling an interface between the base and the fluid). The issues of inverse rheometry are addressed in a general laboratory flow context using surface velocity data. The inverse characterization of the basal boundary is proposed in a geophysical flow context where the parameters involved in the empirical effective sliding law are particularly difficult to estimate. Using an accurate direct and inverse model based on the adjoint method combined with an original efficient solver, sensitivity analyses and parameter identification are performed for a wide range of flow regimes, defined by the degree of slip and the non-linearity of the viscous sliding law considered at the bottom. The first result is the numerical assessment of the passive aspect of the viscosity singularity inherent to a power-law pseudoplastic (shear-thinning) description in terms of surface velocities. From this result, identification of the two parameters of the constitutive law, namely the power-law exponent and the con- sistency, are performed. These numerical experiments provide, on the one hand, a very robust identifica- tion of the power-law exponent, even for very noisy surface velocity observations and on the other hand, a strong equifinality problem on the identification of the consistency. This parameter has a minor influence on the flow, in terms of surface velocities. Typically for temperature-dependent geophysical fluids, a law describing a priori its spatial variability is then sufficient (e.g. based on a temperature vertical profile). This study then focuses on the basal properties interacting with the fluid rheology. An accurate joint identification of the scalar valued triple ( n , m ; β) (respectively the rheological exponent, the non linear friction exponent and the friction coefficient) is achieved for any degree of slip, allowing to completely infer the flow regime. Next, in a geophysical flow context, identifications of a spatially varying friction coefficient are performed for various perturbed bedrock topography. The (2D-vertical) results demonstrate a severely ill-posed problem that allows to compute a given set of surface velocity data with different topography/friction pairs.

Published
2014

30. Four-field finite element solver and sensitivities for quasi-Newtonian flows

Author

Jerome Monnier, Nathan Martin, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematical optimization, Discretization, Augmented Lagrangian method, Applied Mathematics, augmented Lagrangian, Mixed finite element method, Solver, Finite element method, variational sensitivities, Computational Mathematics, Nonlinear system, four-field saddle-point, Variational inequality, viscoplastic, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], mixed finite element, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], adjoint method, Mathematics, Extended finite element method
Abstract

International audience; A computationally efficient finite element algorithm for power law fluid is elaborated in view of extensive direct and inverse simulations. We adopt a splitting technique to simplify the nonlinear structure of the fluids equations and derive a four-field saddle point formulation for which we prove the existence of a solution. The resolution of the corresponding variational inequalities is based on an augmented Lagrangian method and a mixed finite element discretization. The resulting iterative solver reveals to be fast and robust with low memory consumption. The time-saving provided by the algorithm compared to the standard algorithms of fixed point and Newton increases with the number of degrees of freedom and the nonlinearity of the problem. It is therefore well-suited for the solution of large problems with a great number of elements and for corresponding adjoint-based computations. Bidimensional numerical experiments are performed on two realistic situations of gravity flows: an experimental viscoplastic steady wave and a continental glacier. In the present study, results emphasize that for both cases, the modeling at bottom plays a strongly dominant role. Using surface velocitiy observations, the sensitivity analysis with respect to a spatially varying power-law exponent highlights the importance of an accurate knowledge of the rheology at high shear rate. The one on the basal sliding allows to detect the presence of a short wavelength (two times the thickness) free-slip area indetectable from surface velocities.

Published
2014

31. FREE CONVECTION WITH RADIATIVE THERMAL TRANSFER OF GREY BODIES: ANALYSIS AND APPROXIMATION BY FINITE ELEMENT METHODS

Author

Jerome Monnier

Subjects
Convection, Physics, Natural convection, Applied Mathematics, Weak solution, Thermodynamics, 010103 numerical & computational mathematics, Mechanics, Thermal transfer, 01 natural sciences, Finite element method, 010101 applied mathematics, Thermal conductivity, Modeling and Simulation, Radiative transfer, Uniqueness, 0101 mathematics
Abstract

We study a steady-state free (or mixed) convection model in two- or three-dimensions of space, taking into account radiative thermal transfer of grey bodies separated by a nonparticipating media. The existence of a weak solution is proved and the uniqueness is obtained when the viscosity and thermal conductivity of the fluid are large enough. Then, we discretize the model using classical finite element schemes and prove in detail the existence, uniqueness and the convergence of the discrete solution (when the viscosity and the thermal conductivity are large enough and the step size is small enough).

Published
2000

32. ASSIMILATION OF ONE SATELLITE SAR IMAGE FOR FLOOD SIMULATIONS: METHOD AND TEST CASE (MOSEL RIVER)

Author

Xijun Lai, Renaud Hostache, Jerome Monnier, and Christian Puech

Subjects
Synthetic aperture radar, Waves and shallow water, Geography, geography.geographical_feature_category, Data assimilation, Flood myth, Floodplain, Calibration, Water level, Communication channel, Remote sensing
Abstract

In view of improving numerical flood prediction, a variational data assimilation method (4D-var) applied to a 2D shallow water model and using distributed water level obtained from one Synthetic Aperture Radar (SAR) image is presented. The RADARSAT-1 image leads to water levels with a ±40cm average vertical uncertainty of a Mosel River flood event (1997, France). Assimilated in the 2D shallow water hydraulic model, these SAR derived spatially distributed water levels prove to be capable of enhancing model calibration. Indeed, the assimilation process can identify some optimal Manning friction coefficients. Moreover, used as a guide for sensitivity analysis, remote sensing water levels allow also in identifying some areas in the floodplain and the channel where Manning friction coefficients are homogeneous. This allows basing the spatial segmentation of roughness coefficient on floodplain hydraulic functioning.

Published
2011

33. Assimilation of spatial distributed water levels into a shallow-water flood model. Part II: using a remote sensing image of Mosel river

Author

Christian Puech, Xijun Lai, Renaud Hostache, Jerome Monnier, Centre de Recherche Public - Gabriel Lippmann (LUXEMBOURG), Nanjing Institute of Geography and Limnology (Niglas), Chinese Academy of Sciences [Beijing] (CAS), Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Territoires, Environnement, Télédétection et Information Spatiale (UMR TETIS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-AgroParisTech-Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF), Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Laboratoire Jean Kuntzmann [2007-2015] (LJK [2007-2015]), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), CHINESE ACADEMY OF SCIENCES NANJING CHN, Partenaires IRSTEA, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019]), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann [2007-2015] (LJK [2007-2015]), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
Synthetic aperture radar, 010504 meteorology & atmospheric sciences, Floodplain, 0207 environmental engineering, Context (language use), Hydrograph, Digital Elevation Model, 02 engineering and technology, 01 natural sciences, Hydraulic modelling, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Satellite SAR images, Data assimilation, Roughness parameters, Variational data assimilation, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 020701 environmental engineering, Hydraulic coherence, 0105 earth and related environmental sciences, Water Science and Technology, Remote sensing, geography, geography.geographical_feature_category, Flood myth, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDE.ES]Environmental Sciences/Environmental and Society, Water level, Waves and shallow water, 13. Climate action, [SDE]Environmental Sciences, Environmental science, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

[Departement_IRSTEA]Territoires [TR1_IRSTEA]SYNERGIE; International audience; With rapid flood extent mapping capabilities, Synthetic Aperture Radar (SAR) images of river inundation prove to be very relevant to operational flood management. In this context, a recently developed method provides distributed water levels from SAR images. Furthermore, in view of improving numerical flood prediction, a variational data assimilation method (4D-var) using such distributed water level has been developed in Part I of this study. This method combines an optimal sense remote sensing data (distrib- uted water levels extracted from spatial images) and a 2D shallow water model. In the present article (Part II of the study), we also derive water levels with a ±40 cm average vertical uncertainty from a RADARSAT-1 image of a Mosel River flood event (1997, France). Assimilated in a 2D shallow water hydraulic model using the 4D-var developed method, these SAR derived spatially distributed water levels prove to be capable of enhancing model calibration. Indeed, the assimilation process can identify optimal Manning friction coefficients, at least in the river channel. Moreover, used as a guide for sensitivity anal- ysis, remote sensing water levels allow also identifying some areas in the floodplain and the channel where Manning friction coefficients are homogeneous. This allows basing the spatial segmentation of roughness coefficient on floodplain hydraulic functioning.

Published
2010

34. Assimilation of one satellite SAR image for flood simulations. Method and test case (Moser river)

Author

Renaud Hostache, Xijun Lai, Jerome Monnier, Christian Puech, Centre de Recherche Public - Gabriel Lippmann (LUXEMBOURG), Nanjing Institute of Geography and Limnology (Niglas), Chinese Academy of Sciences [Beijing] (CAS), Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Territoires, Environnement, Télédétection et Information Spatiale (UMR TETIS), and Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-AgroParisTech-Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF)

Subjects
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDE.ES]Environmental Sciences/Environmental and Society
Abstract

International audience; In view of improving numerical flood prediction, a variational data assimilation method (4D-var) applied to a 2D shallow water model and using distributed water level obtained from one Synthetic Aperture Radar (SAR) image is presented. The RADARSAT-1 image leads to water levels with a ±40cm average vertical uncertainty of a Mosel River flood event (1997, France). Assimilated in the 2D shallow water hydraulic model, these SAR derived spatially distributed water levels prove to be capable of enhancing model calibration. Indeed, the assimilation process can identify some optimal Manning friction coefficients. Moreover, used as a guide for sensitivity analysis, remote sensing water levels allow also in identifying some areas in the floodplain and the channel where Manning friction coefficients are homogeneous. This allows basing the spatial segmentation of roughness coefficient on floodplain hydraulic functioning.

Published
2010

35. Identification of equivalent topography in an open channel flow using Lagrangian data assimilation

Author

Marc Honnorat, Jerome Monnier, Nicolas Riviere, Etienne Huot, François-Xavier Le Dimet, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Coupling environmental data and simulation models for software integration (Clime), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Inria Grenoble - Rhône-Alpes

Subjects
010504 meteorology & atmospheric sciences, Hydraulics, Flow (psychology), 0207 environmental engineering, 02 engineering and technology, 01 natural sciences, Theoretical Computer Science, law.invention, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Data assimilation, Open channel, law, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Equivalent topography, Variational data assimilation, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 020701 environmental engineering, 0105 earth and related environmental sciences, Jet (fluid), Adjoint model, business.industry, Numerical analysis, General Engineering, Mechanics, Manning formula, Open-channel flow, Lagrangian observations, Computational Theory and Mathematics, Modeling and Simulation, Weir, Computer Vision and Pattern Recognition, Telecommunications, business, Software, Geology
Abstract

International audience; We present a Lagrangian data assimilation experiment in an open channel flow above a broad-crested weir. The observations consist of trajectories of particles transported by the flow and extracted from a video film, in addition to classical water level measurements. However, the presence of vertical recirculations on both sides of the weir actually conducts to the identification of an equivalent topography corresponding to the lower limit of a surface jet. In addition, results on the identification of the Manning coefficient may allow to detect the presence of bottom recirculations.

Published
2010

36. Coupling superposed 1D and 2D shallow-water models: Source terms in finite volume schemes

Author

Joël Marin, Enrique D. Fernández-Nieto, Jerome Monnier, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemática Aplicada I (IMUS), IMUS, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)

Subjects
General Computer Science, Computer science, 01 natural sciences, 010305 fluids & plasmas, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Superposition principle, Coupling, Robustness (computer science), 0103 physical sciences, Calculus, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Numerical tests, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Main channel, 76M12 (65M08 76B07 86-08 86A05), Shallow-water equations, ComputingMilieux_MISCELLANEOUS, River, Finite volume method, Superposition, General Engineering, Flood plain, 010101 applied mathematics, Waves and shallow water, Finite volume, River Flood plain, Well-balanced, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We study the superposition of 1D and 2D shallow-water equations with non-flat topographies, in the context of river-flood modeling. Since we superpose both models in the bi-dimensional areas, we focus on the definition of the coupling term required in the 1D equations. Using explicit finite volume schemes, we propose a definition of the discrete coupling term leading to schemes globally well-balanced (the glo- bal scheme preserves water at rest whatever if overflowing or not). For both equations (1D and 2D), we can consider independent finite volume schemes based on well-balanced Roe, HLL, Rusanov or other scheme, then the resulting global scheme remains well-balanced. We perform a few numerical tests showing on the one hand the well-balanced property of the resulting global numerical model, on the other hand the accuracy and robustness of our superposition approach. Therefore, the definition of the coupling term we present allows to superpose a local 2D model over a 1D main channel model, with non-flat topographies and mix incoming-outgoing lateral fluxes, using independent grids and finite vol- ume solvers.

Published
2010

37. Superposition of local zoom model and simultaneous calibration for 1D-2D shallow water flows

Author

Jerome Monnier, Joël Marin, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematical optimization, 010504 meteorology & atmospheric sciences, General Computer Science, 0207 environmental engineering, Context (language use), 02 engineering and technology, 01 natural sciences, Theoretical Computer Science, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Superposition principle, Coupling, Data assimilation, Applied mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Zoom, 020701 environmental engineering, Shallow water equations, Physics::Atmospheric and Oceanic Physics, 0105 earth and related environmental sciences, Mathematics, Numerical Analysis, Applied Mathematics, Shallow water, Optimal control, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SDE.ES]Environmental Sciences/Environmental and Society, Flood plain, Waves and shallow water, Modeling and Simulation, Zoom model, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We address the problem of coupling 2D shallow water equations with 1D shallow water equations (St-Venant equations), as applied to river-floodplain flows. Mathematical coupling conditions are derived classicaly from the 3D Navier-Stokes equations by integrating over the vertical wet section, when overflowing occurs. It leads to extra source terms in the 1D equations. Next we assume to be in a variational data assimilation context, then the optimal control process allows to couple both models and assimilate data simultaneously (Joint Assimilation Coupling algorithms). Two different versions of JAC algorithms are presented and compared. In a numerical test case, we superimpose the local 2D model on the 1D global model. The results show the efficiency of the present simultaneous superposition-assimilation approach.

Published
2009

38. Lagrangian data assimilation for river hydraulics simulations

Author

Jerome Monnier, François-Xavier Le Dimet, Marc Honnorat, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Wesseling P., Oñate E. et Périaux J. editors, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)

Subjects
010504 meteorology & atmospheric sciences, Hydraulics, 0207 environmental engineering, 02 engineering and technology, 01 natural sciences, Theoretical Computer Science, law.invention, Physics::Fluid Dynamics, symbols.namesake, Data assimilation, law, Calculus, Initial value problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 020701 environmental engineering, Shallow water equations, ComputingMilieux_MISCELLANEOUS, Physics::Atmospheric and Oceanic Physics, 0105 earth and related environmental sciences, Numerical analysis, General Engineering, Eulerian path, Mechanics, 6. Clean water, Euler equations, Computational Theory and Mathematics, Flow (mathematics), Modeling and Simulation, symbols, Computer Vision and Pattern Recognition, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Software, Geology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We present a method to use lagrangian data from remote sensing observation in a variational data assimilation process for a river hydraulics model based on the bidimensional shallow water equations. The trajectories of particles advected by the flow can be extracted from video images and are used in addition to classical eulerian observations. This lagrangian data brings information on the surface velocity thanks to an appropriate transport model. Numerical twin data assimilation experiments in an academic flow configuration demonstrate that this method makes it possible to significantly improve the identification of local bed elevation and initial conditions.

Published
2009

39. Numerical modeling of electrowetting by a shape inverse approach

Author

Jerome Monnier, Patrick Chow-Wing-Bom, Patrick Witomski, Claire Scheid, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles (EDP), and Laboratoire Jean Kuntzmann (LJK)

Subjects
Capillary action, energy minimization, Computation, design, Inverse, Geometry, 02 engineering and technology, Curvature, 01 natural sciences, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], MSC: 49Q10, 74M15, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Shape optimization, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, 010306 general physics, Mathematics, shape optimal, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Plane (geometry), Applied Mathematics, Mechanics, electrowetting, 021001 nanoscience & nanotechnology, contact point, curvature, Electrowetting, 0210 nano-technology, Constant (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We model an electrified droplet spreading on a solid surface. The model aims to seek a drop shape that minimizes its total energy (capillary, electrostatic, and gravitational). We derive the equations and the shape gradient; then we detail the shape optimization algorithm and present some numerical results. Up to a critical applied voltage value, the computed angles fit the predictions of Lippman's equation (plane capacitor approximation). Then, when increasing the voltage, we observe an overestimate of the Lippman prediction. Numerical computations of the curvature show that it remains constant everywhere except in the vicinity of the contact point, where it increases sharply.

Published
2009

40. A consistent intermediate wave speed for a well-balanced HLLC solver

Author

Jerome Monnier, Didier Bresch, Enrique D. Fernández-Nieto, Departamento de Matemática Aplicada I (IMUS), IMUS, Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Modelling, Observations, Identification for Environmental Sciences (MOISE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)

Subjects
Wave velocity, Pollutant transport, Geometry, 010103 numerical & computational mathematics, General Medicine, Wave speed, Solver, 01 natural sciences, 010101 applied mathematics, 13. Climate action, Applied mathematics, 0101 mathematics, Physics::Atmospheric and Oceanic Physics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; In this work, we present a HLLC scheme modification for application to nonhomogeneous shallow-water equations with pollutant transport. This new version is related to the definition of a consistent approximation of the intermediate wave speed. Numerical results are presented to illustrate the importance of such approximation to get appropriate pollutant concentration profiles.

Published
2008

41. On a 2D zoom for 1D shallow-water model: coupling and data assimilation

Author

I. Yu. Gejadze, Jerome Monnier, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
010504 meteorology & atmospheric sciences, Hydraulics, Computer science, 0207 environmental engineering, Computational Mechanics, General Physics and Astronomy, Context (language use), 02 engineering and technology, 01 natural sciences, law.invention, Coupling, Shallow water equations, Operator (computer programming), Data assimilation, law, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Variational data assimilation, Zoom, 020701 environmental engineering, Physics::Atmospheric and Oceanic Physics, 0105 earth and related environmental sciences, Flood modeling, Mechanical Engineering, Optimal control, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Waves and shallow water, Mechanics of Materials, Zoom model, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In the context of river hydraulics we elaborate the idea of a 'zoom' model locally superposed on an open-channel network global model. The zoom model (2D shallow water equations) describes additional physical phenomena, which are not represented by the global model (1D shallow water equations with storage areas). Both models are coupled using the optimal control approach when the zoom model is used to assimilate local observations into the global model (variational data assimilation) by playing the part of a mapping operator. The global model benefits from using zooms, while no substantial modification to it is required. Numerical results on a toy test case show the feasibility of the suggested method.

Published
2007

42. Flow patterns in the vicinity of triple line dynamics arising from a local surface tension model

Author

Jerome Monnier, Iulian Cotoi, Adel M. Benselama, Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Triple line, Computer Networks and Communications, 010102 general mathematics, Contact line, Computational Mechanics, Surface tension gradient, Geometry, Mechanics, Slip (materials science), Flow pattern, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Surface tension, Solid substrate, Control and Systems Engineering, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; We model and simulate numerically a droplet impact onto a solid substrate. The triple line dynamics modelling is implicit (as opposed to classical explicit mobility relations), it is based on the Shikhmurzaev equations. These equations include generalized Navier slip type boundary conditions with extra local surface tension gradient terms. Numerical results when spreading are presented. A particular attention is paid to flow patterns near the contact line.

Published
2007

43. On variational data assimilation for 1D and 2D fluvial hydraulics

Author

F. X. Le Dimet, Jerome Monnier, Igor Yu. Gejadze, Marc Honnorat, Modelling, Observations, Identification for Environmental Sciences ( MOISE ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut National Polytechnique de Grenoble ( INPG ) -Centre National de la Recherche Scientifique ( CNRS ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Institut National Polytechnique de Grenoble ( INPG ), Edts Bonilla-Moscovo-Platero-Vega, Modelling, Observations, Identification for Environmental Sciences (MOISE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, 010504 meteorology & atmospheric sciences, Meteorology, Hydraulics, Fluvial, 010103 numerical & computational mathematics, Inflow, 01 natural sciences, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, law.invention, Waves and shallow water, Geography, Data assimilation, law, Boundary value problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Trajectory (fluid mechanics), Shallow water equations, 0105 earth and related environmental sciences
Abstract

International audience; We address two problems related to variational data assimilation (VDA) as applied to river hydraulics (1D and 2D shallow water models). First, we seek to estimate accurately some parameters such as the inflow discharge, manning coefficients, the topography and/or the initial state. We develop a method which allow to assimilate lagrangian data (trajectory particles at the surface e.g. extracted from video images). Second, we develop a joint data assimilation - coupling method. We seek to couple accurately a 1D global net-model (rivers net) and a local 2D shallow water model (zoom into a flooded area), while we assimilate data. Numerical twin experiments are presented.

Published
2006

44. Flow Patterns in the Vicinity of Triple Line Dynamics Arising from a Local Surface Tension Model

Author

I. Cotoi and Jerome Monnier

Subjects
Triple line, Surface tension, Computer science, Drop (liquid), Surface tension gradient, Geometry, Mechanics, Slip (materials science), Boundary value problem, Flow pattern
Abstract

We model and simulate numerically a droplet impact onto a solid substrate. The triple line dynamics modelling is implicit (as opposed to classical explicit mobility relations), it is based on the Shikhmurzaev equations. These equations include generalized Navier slip type boundary conditions with extra local surface tension gradient terms. Numerical results when spreading and recoiling are presented. A particular attention is paid to flow patterns near the contact line.

Published
2006

45. T2DInverse: Towards calibration and sensitivity analysis into Telemac2D using automatic differentiation

Author

YOUSSEF LOUKILI, Marc Honnorat, Jerome Monnier, System identification and optimization in physics and environment (IDOPT), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), and INRIA

Subjects
PARAMETER IDENTIFICATION, AUTOMATIC DIFFERENCIATION, VARIATIONAL DATA ASSIMILATION, TELEMAC2D, RIVER HYDRAULICS, FLOOD MODELLING, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], SENSITIVITY ANALYSIS, TAPENADE V2.0
Abstract

The industrial system Telemac2D, developed by LNHE-EDF and commercialized by Sogreah Co., is an software dedicated to the hydrodynamical and environmental modelling of maritime and river flows. It is based on finite element method and is written in Fortran 90. Our final objective is to include a full variational data assimilation process in the system. This requires the development of an adjoint model. We plan to obtain it using the Automatic Differentiation (AD) tool Tapenade v2.0. In this study, we prepare and validate a reduced version of Telemac2D that is both meant for river flows and suitable to Tapenade v2.0. Then, we establish a strategy of AD according to limitations of the current release of Tapenade (v2.0). Also, the optimization chain is achieved thanks to the unconstrained minimizer N1QN3 based on a quasi-Newton type method. The final objective is to exploit the fluvial measurements and observations in an optimal manner in Telemac2D, in order to identify the partially known or lacking parameters (bathymetry, bed friction, inflow discharge and initial state).

Published
2005

46. A Local Surface Model applied to Contact Line Dynamics

Author

Jerome Monnier, Patrick Witomski, Laboratoire de Modélisation et Calcul (LMC - IMAG), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Capillary wave, Applied Mathematics, Mechanics, Stokes flow, 01 natural sciences, 010305 fluids & plasmas, Surface tension, Physics::Fluid Dynamics, MESH: Local Marangoni effect, Stokes flow, Shikhmurzaev's model, Existence-uniqueness, Slip type boundary condition, Nonlinear system, Classical mechanics, Free surface, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Capillary surface, Boundary value problem, 010306 general physics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], ComputingMilieux_MISCELLANEOUS, Analysis, Mathematics
Abstract

International audience; We consider a set of equations modelling contact line dynamics. The model consists of the Navier-Stokes free surface flow with local slip type boundary conditions and gradient surface tension coupled with a mesoscopic local surface model (nonlinear degenerated equations) describes the surface tension variations. The dynamical contact angle and the local surface tension variations are unknowns of the model. We present some mathematical and numerical results.

Published
2005

47. Analysis of a Local Hydrodynamics Model with Marangoni effect

Author

Jerome Monnier, Patrick Witomski, Laboratoire de Modélisation et Calcul (LMC - IMAG), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Dynamic contact line, numerical computation, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, 010305 fluids & plasmas, Theoretical Computer Science, Surface tension, Singularity, surface tension, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Numerical Analysis, Mesoscopic physics, Marangoni effect, Applied Mathematics, Numerical analysis, 010102 general mathematics, General Engineering, Mechanics, Shikhmurzaev's model, Finite element method, Computational Mathematics, Classical mechanics, Computational Theory and Mathematics, Free surface, non-linear local surface model, Software, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We study a mathematical model treating of the dynamic contact line problem, supposed to describe the main features of the advancing triple line (rolling motion and variable contact angle) and to remove the singularity. The model is composed by a macroscopic hydrodynamic free surface flow model (Navier-Stokes) coupled with a mesoscopic local surface model. Detailed mathematical and numerical analysis of the 1D steady-state local surface model are done: existence and uniqueness of the exact and numerical solutions, extra properties of the derivatives, and convergence of finite element schemes. Some numerical results of the two models treated separately are presented for a 2D plunging tape configuration.

Published
2004

48. Shape sensitivities in a Navier-Stokes flow with convective and gray bodies radiative thermal transfer

Author

Jerome Monnier, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), System identification and optimization in physics and environment (IDOPT), Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Convection, shape optimal design, radiosity, Control and Optimization, Thermal transfer, 01 natural sciences, 010305 fluids & plasmas, grey bodies, 0103 physical sciences, Radiative transfer, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Differentiable function, 0101 mathematics, Mathematics, Navier–Stokes flow model, Applied Mathematics, Mathematical analysis, shape sensitivities, radiative heat transfer, Inverse problem, Forced convection, 010101 applied mathematics, Exact differential, Control and Systems Engineering, Thermal radiation, coupled flow problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Software
Abstract

International audience; We study a shape optimal design problem for a forced convection flow: the steady-state Navier-Stokes equations coupled with an integro-differential thermal model. The thermal transfers are convective, diffusive and radiative with multiple reflections (model of gray bodies, radiosity equation). The inverse problem consists in minimizing a smooth cost function which depends on the solution, with respect to the domain of the equations. We prove the differentiability of the solution with respect to the domain. It follows the cost function differentiability. We introduce the adjoint state equation and obtain the exact differential of the cost function. The computational method of shape sensitivities and the optimization process are presented too.

Published
2003

49. Shape optimal design problem with convective and radiative thermal transfer: Analysis and implementation

Author

Jerome Monnier, Denise Chenais, Jean-Paul Vila, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), System identification and optimization in physics and environment (IDOPT), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematical optimization, shape sensitivity, Control and Optimization, 02 engineering and technology, elliptic partial differential equations, Management Science and Operations Research, 01 natural sciences, 020901 industrial engineering & automation, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, optimal design, Mathematics, Partial differential equation, Applied Mathematics, Numerical analysis, radiative heat transfer, Function (mathematics), Finite element method, 010101 applied mathematics, Exact differential, Nonlinear system, Elliptic partial differential equation, Adjoint equation, finite-element method, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; We present a study of an optimal design problem for a coupled system, consisting of a steady-state potential flow equation and a thermal equation taking into account radiative phenomena with multiple reflections. The state equation is a non-linear integro-differential system. We seek to minimize a cost function which depends on the temperature, with respect to the domain of the equations. First, we consider an optimal design problem in an abstract framework and, with the help of the classical adjoint state method, we give an expression of the cost function differential. Then, we apply this result in two spatial dimensions to the non-linear integro-differential system considered. We prove the differentiability of the cost function, we introduce the adjoint state equation, and we give an expression of its exact differential. Then, we discretize the equations by a finite element method and we use a gradient type algorithm to decrease the cost function. We present numerical results as applied to the automotive industry.

Published
2001

50. Convective and radiative thermal transfer with multiple reflections. Analysis and approximation by a finite element method

Author

Jean-Paul Vila, Jerome Monnier, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), System identification and optimization in physics and environment (IDOPT), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Convection, Applied Mathematics, Numerical analysis, Mathematical analysis, 010103 numerical & computational mathematics, Thermal transfer, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Finite element method, 010101 applied mathematics, Nonlinear system, Classical mechanics, Modeling and Simulation, Thermal, Heat transfer, Radiative transfer, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and twodimensional numerical results of thermal exchanges under a car bonnet are presented.

Published
2001

Catalog

Books, media, physical & digital resources
See catalog results