Appel a projets de recherche 2003 – 2005

Objectives

We use optimal control theory to identify the physical parameters by fusing the observed data and dynamic model. Traditionally, the measurements form gauge stations are available for model calibration. They’re just bulk values and sometimes unavailable due to inundation. The remote sensing data which is distributed in space can be suitable too for the parameters calibration. Though they are qualitatively applied to flood monitoring because of their low-accuracy until now, it is possible to extract some useful information in some areas and to be expected more with the progresses of modern remote sensing technique. The collaboration with Cemagref (C. Puech, R. Hostache, A. Paquier) who extract pertinent usable information, we manage to assimilate the satellite image into flood prediction model based on DassFlow and to obtain the knowledge of the contributions of satellite image to identify physical parameters.

Work and results

Summary of accomplished work

1. 
   Dassflow model improvement for satisfying the computation of practical application
   

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  Mixed quadrilateral and triangle unstructured grids
  
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  Bottom slope term balance using flat bottom assumption
  
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  Modeling the wetting and drying process
  
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  Semi-implicit scheme for friction term to improve the numerical stability
  

2. 
   Assimilation of water level image into the hydraulic model
   

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  Introduce the new form of cost function to utilize the implicit information of image information for improving the identification of time-dependent parameters
  
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  Examine the contributions of one water level image information to time-dependent and time-independent parameters using a toy test case
  
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  Assimilating an incompletely combined point-wise measure and an image observation which are similar to the Moselle river for achieving the preliminary knowledge of the practical application of assimilation.
  

Numerical experiments and results

Twin experiments using toy test case

The observed water level images were assimilated into the hydraulic model to identify time-independent and time-dependent parameters using the toy test case. The identification experiments of initial condition and Manning roughness coefficient show that they’re helpful to identify the time-independent (or distributed parameters) because they’re spatially distributed. However, they don't offer the evolution information directly. Hence, when it’s applied to identify time-dependent parameters, extra information needs to be considered by introducing extra terms to the cost function (see the results obtained from basic and new proposed cost function in Figure below). If both kinds of parameters are controlled, problems become stiff. To identify them successfully, not only enough observations should be supplied, but also scaling technique should be carefully adopted.

These preliminary twin experiments help to understand the contributions of images to the parameter identification. But, ideal observations are difficult to obtain in practical applications. Considering the availability, the experiments of assimilating the incompletely combined the point-wise (or time series data) and image observations which are similar to the Moselle river are carried out to achieve the knowledge of the practical application of assimilation (see Fig.3). It’s assumed that one image only can be obtained in some parts of the study area during the flood event and the time series data from gauge stations are only available before and after flooding. The inflow discharge is identified successfully with these observations. It indicates that single image observations may help to compensate the unavailable measurements from regular way at the flood period.

Fig.2 Comparison of identification using two forms of cost function

Fig. 3 Identification of inflow discharge with incompletely combined observations

(configuration similar to the real case Moselle)

Work in progress (Moselle real data)

Based on the knowledge of image assimilation from the toy test case, now we have started to carry out the study of practical application, i.e. the Moselle River. The simulation of the Moselle River with the manual adjusted parameters has been examined. Next step, we will center on the practical application of assimilation in the Moselle River. First, we manage to identify lumped and distributed Manning roughness coefficient (n) with available observations in the application of the Moselle River. Then, we make an attempt to identify inflow discharge and time-dependent n if possible. Meanwhile, we will study the possibility to determine the better observed instant of satellite image for a good identification using toy test case. The study of the assimilation application in the Moselle River is expected to be finished in the next two months.
Fig. Gauche. Mesures disponibles

Droite. Cas test reel Moselle. Manning par zone après identification


Publications récentes (relatives à l’objectif 1)
Revues internationales
Ig. Gejadze, J. Monnier. On a 2D zoom for 1D shallow-water model: coupling and data assimilation. Soumis, 2006.
M. Honnorat, J. Monnier and F.-X. Le Dimet. Lagrangian data assimilation for river hydraulics simulations. Computing and Visualization in Science, soumis, 2006.
X. Lai, J. Monnier. Variationnal assimilation of spatial distributed water level

into a 2D hydraulic model. En préparation (résultats obtenus en totalité).
R. Hostache, X. Lai, J. Monnier, C. Puech. Calibration of a 2D flood model using one satellite image. Application to Moselle river. En préparation.

Conférences internationales
W. Castaings, D. Dartus, M. Honnorat, F.-X. Le Dimet, Y. Loukili and J. Monnier. Automatic differentiation : A tool for variational data assimilation and adjoint sensitivity analysis for flood modeling. In H. M. Brücker, G. Corliss, P. Hovland, U. Naumann, and B. Norris, editors, Automatic Differentiation : Applications, Theory, and Implementations, volume 50 of Lectures Notes in Computational Science and Engineering, pages 249-262. Springer, 2005
Ig. Gejadze, J. Monnier. A joint data assimilation coupling algorithm applied to shallow-water flood models.

ECCOMAS CFD, Egmond aan Zee, september 2006.

Ig. Gejadze, J. Monnier. On data assimilation for a 1D-net river model with 2D zoom areas

Computational Methods in Water Resources, XVI International Conference, Copenhaguen, 2006.

M. Honnorat, X. Lai, J. Monnier and F.-X. Le Dimet. Variational data assimialtion for 2D fluvial hydraulics simulations.

Computational Methods in Water Resources, XVI International Conference, Copenhaguen, 2006.

M. Honnorat, J. Monnier and F.-X. Le Dimet. Lagrangian data assimilation for river hydraulics simulations.

European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006.

M. Honnorat, X. Lai, F.-X. Le Dimet, J. Monnier. Assimilation of Images for River Hydraulic Simulations. ICIAM Zurich, 2007.
Rapports techniques
M. Honnorat, F.-X. Le Dimet, Y. Loukili and J. Monnier. Dassflow : a direct and adjoint model for 2D Shallow water flows. Research Report RR-5756, INRIA, 2005.
I. Gejadze, M. Honnorat, X. Lai, J. Marin, J. Monnier. Dassflow v2.0: a variational data assimilation software for river flows. Research Report RR-, INRIA, à paraître 2007.

Rapport relatif à l’objectif 2 « Estimations de l’incertitude sur l’extension d’une zone inondable »
Personnes engagées sur le projet :

JB Faure (25%)

2 post-doctorats à 100% (Otmane Souhar sur financement Cemagref et Célestin Leupi sur BAC Région de 10 mois).

Logiciel : MAGE